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239.Журнал Сибирского федерального университета. Сер. Техника и технологии №1 2014

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Copyright ??? «??? «??????» & ??? «A???????? K????-C?????»
Журнал Сибирского федерального университета
2014
Journal of Siberian Federal University
7 (1)
Техника и технологии
Engineering & Technologies
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Editorial Advisory Board
Chairman:
Eugene A. Vaganov
Members:
Josef J. Gitelzon
Vasily F. Shabanov
Andrey G. Degermendzhy
Valery L. Mironov
Gennady L. Pashkov
Vladimir V. Shaidurov
Vladimir V. Zuev
Editorial Board:
Editor-in-Chief:
Mikhail I. Gladyshev
Founding Editor:
Vladimir I. Kolmakov
Managing Editor:
Olga F. Alexandrova
Executive Editor for Engineering &
Technologies:
Vladimir A. Kulagin
CONTENTS / СОДЕРЖАНИЕ
Liudmila V. Kashkina,
Olesya P. Stebeleva, Tatiana Y. Emelyanova,
Eleonora A. Petrakovskaya and Oleg A. Bayukov
Hydrodynamic Dispersion of Calcium Aluminosilicate from
Technogenic and Nonmetallic Materials
?3?
Anna A. Lyamkina, Sergey P. Moshchenko,
Yuri G. Galitsyn and Alexey I. Lyamkin
Plasmonic Antenna for Bright NV Centers in Ultradispersed
Detonation Diamonds
? 13 ?
Sergey P. Sahanskiy
Control of the Shape of Semiconductor Crystals when Growing
in Czochralski Method
? 20 ?
А.В. Минаков, Д.В. Гузей,
А.С. Лобасов, Д.А. Дектерев, М.И. Пряжников
p=???2?%-.*?C?!,???2=???%? ,?????%"=?,? "/?3?????%L
*%?"?*?,, ?=?%?,?*%?2, ?= %??%"? %*?,?= =???,?, "
C! ?%2%??%? 2?C?%%K????,*?
? 32 ?
А.Ю. Радзюк, Е.Б. Истягина
}*?C?!,???2=???%? %C!??????,?
!=?,=???%? ?",???,, ?,?*%?2,
!??,?=
2????,
C!,
? 48 ?
Н.Д. Демиденко, Л.В. Кулагина
),?????/L ??2%? ,?????%"=?, ?2=?,%?=!?/. !??,?%" "
2?.?%?%?,???*,. C??=.
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??.-???. ?. 9,6. ?????? ???. ?????? ????????. ????? 1000 ???. ????? 841.
?????????? ? ?? ??? ???. 660041, ??????????, ??. ?????????, 82a.
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Editorial board for Engineering & Technologies:
Vladimir Kulagin ? Series Editor, Siberian Federal
University, Russia
Yury Alashkevich ? Siberian State Technological
University, Russia
Sereeter Batmцnkh ? Institute of Heat Engineering
and Industrial Ecology Mongolian Academy of
Sciences, Mongolia
Yuri Biba ? Dresser-Rand Company, USA
Carsten Drebenstedt ? Technische University
Bergakademie Freiberg, Germany
Yury Galerkin ? Saint Petersburg State Polytechnic
University, Russia
Gennady Gritsko ? Institute of Petroleum Geology and
Geophysics Russian Academy of Sciences, Siberian
Branch, Russia
Georg Guggenberger ? Institute of Soil Science Leibniz
University Hannover, Germany
Lev Endzhievsky ? Siberian Federal University, Russia
Feng-Chen Li ? School of Energy Science and
Engineering Harbin Institute of Technology, China
Vladimir Makarov ? Siberian Federal University, Russia
Aleksandr Mineev ? Siberian Federal University, Russia
Vladimir Moskvichev ? Special Designing and
Technological Bureau ?Nauka? Krasnoyarsk
Scientific Center of the Russian Academy of
Sciences, Siberian Branch, Russia
Bernard Nacke ? Institute of Electrotechnology Leibniz
University of Hannover, Germany
Oleksandr Nemchin ? CEO of the State Research
Institute of Innovative Technologies in Power
Energy and Energy Efficiency of the Fuel and
Energy Ministry of Ukraine, Ukraine
Valeriy Nikulin ? Kamsk Institute of Humanitarian and
Engineering Technologies, Russia
Oleg Ostrovski ? University of New South Wales,
Australia
Harald Oye ? Norwegian University of Science and
Technology, Norway
Vasili Panteleev ? Siberian Federal University, Russia
Petr Polyakov ? Siberian Federal University, Russia
Victor Timofeev ? Siberian Federal University, Russia
Ibragim Khisameev ? Kazan State Technological
University, Russia
Anatoly Shvidenko ? International Institute for Applied
Systems Analysis, Austria
Galina Chiganova ? Siberian Federal University, Russia
????????????? ? ??????????? ???
?? ? ??77-28-722 ?? 29.06.2007 ?.
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???????? ??????? ?????????? ??????????? ??
????????? ?????? ??????? ??????? ? ?????????
????» (???????? 2010 ?.)
Alex Y. Lipovka and Yuri L. Lipovka
Determining Hydraulic Friction Factor for Pipeline
Systems
? 62 ?
Nelya S. Chernetskaya,
Mikhail Yu. Chernetskiy
and Alexander A. Dekterev
Numerical Investigation of Influence Thermal
Preparation Coal on Nitric Oxides Formation in
Combustion Process
? 83 ?
А.П. Скуратов,
Д.И. Махов, Е.А. Павлов
j%?C??2?!?%? ?%???,!%"=?,? , %C2,?,?=?,
C!%????= ?,2? ??,2*%" C?=2,?/
? 96 ?
Alexander V. Vasilenko
and Valentin B. Kashkin
Satellite Microvibration and Atmospheric Turbulence
Effect on Satellite-to-Ground Optical Communication
Link
? 103 ?
Maxim A. Spikin,
Vladimir A. Pozdnyakov
and Sergey S. Hudyakov
Construction of Geographic Information System of
Corporate Level in Geological Prospecting
? 109 ?
В.И. Гнатюк,
В.И. Пантелеев, А.А. Заименко
o%2???,!%"=?,?
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Journal of Siberian Federal University. Engineering & Technologies 1 (2014 7) 3-12
~~~
??? 504.5: 620.193.16
Hydrodynamic Dispersion
of Calcium Aluminosilicate from Technogenic
and Nonmetallic Materials
Liudmila V. Kashkinaa,
Olesya P. Stebeleva *, Tatiana Y. Emelyanovaa,
Eleonora A. Petrakovskayab and Oleg A. Bayukovb
a
Siberian Federal University,
79 Svobodny, Krasnoyarsk, 660041, Russia
b
L.V. Kirensky Institute of Physics SB RAS
50/38 Akademgorodok, Krasnoyarsk, 660036, Russia
a
Received 05.12.2013, received in revised form 18.12.2013, accepted 24.01.2014
Physicochemical properties of two calcium aluminosilicate materials after reducing in the
hydrodynamic rotary generator in supercavitation mode were studied. The samples are the crystal
ceramic foam based on Kansko-Achinsk lignite-ash and the porous glass material obtained from
low-manganese nonmetallic feed. X-ray phase analysis, EPR-method, NPR-method (the Mossbauer
Effect) and optical microscopy were used. It was found that the material is changing its stucrure in
a hydrodynamic dispersion process caused by high-cavitation. The nature of the changes depends
on its initial state.
Keywords: hydrodynamic dispersion, cavitation, crystal ceramic foam, porous glass material.
Introduction
Currently, treatment processes of technogenic materials allowing not only to extract the most
valuable components of the waste, but also to obtain new materials with desired properties are
developed and implemented. However, these technologies are energy intensive, since more than
50 % of the energy consumed for cominution of the basic substance. Recent studies have shown that
energetically low-cost technology of hydrodynamic dispersion (crushing in a liquid medium) can
be successfully used for fi ne powdering [1-8]. In [8] it was shown that used rotary hydrodynamic
generator of low productivity under specified modes for 1 minute of dispersion at the initial average
ash size of 175 microns produces an particle with average size of 25 microns, i.e. ash particles
are ?grind down? by almost 7 times ( the concentrations less than 3 wt %). If dispersed ash with
an average initial size of 25 microns under the same conditions, then the output can be obtained
particles having an average particle size of 3,5 ? 4 mkm. Thus, in two phases (2 min. dispersion)
particle size can be reduced from 175 microns to 4 microns, i.e. by more than 40 times. At higher
*
© Siberian Federal University. All rights reserved
Corresponding author E-mail address: olessteb@rambler.ru
#3#
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Liudmila V. Kashkina, Olesya P. Stebeleva? Hydrodynamic Dispersion of Calcium Aluminosilicate from Technogenic?
Fig. 1. The density function of particle size distribution: 1 ? initial ash, 2 ? ash after dispersion (concentration
3 %), 3 ? ash after dispersion with increased (25 %) concentration
concentrations (25 %) dispersion effect is considerably less. Ash can grind from 175 microns to 60
mkm (Fig. 1).
One of the main factors determining the efficiency of the technology is the cavitation effect
(from Lat. Cavitas ? emptiness), which occurs due to sudden sharp pressure reducing in the flow
of a moving fluid (hydrodynamic cavitation). Cavities filled with gas, vapor or a mixture thereof
(cavitation bubbles, cavities) are formed in a liquid. As a result, the concentration of mechanical
energy of the fluid in very small volumes of cavitation bubbles, a high density of energy, according
to some estimates up to 1015 J/m 3 [9]. Crushing occurs at high energy exposing of cumulative
fluid microjets and shock waves generated by the collapse of cavitation bubbles on the solid
particles. The temperature and pressure near the collapsing bubbles can be above 2000 K and
100 MPa [9, 10].
Experimental technicues
Physical basis of cavitational effects are studied well, but the consequences to which they lead,
are not always known. In view of the complexity of high-energy cavitation processes in the dispersion,
theoretical and experimental research in this area is relevant for the development of efficient treatment
processes for technogenic materials. A study was made of hydrodynamic dispersion of materials
from industrial waste produced by the method of pyrometallurgical melting in a reducing medium
[11]. Two kinds of calcium aluminosilicate powder of average dispersion (100 to 200 microns) were
investigated:
1. The crystalline material was ? ceramic foam. It is produced by a self-propagating crystallization
during remelting of silica foam from Kansko-Achinsk lignite-ash. Ash composition (wt %): SiO2 ?
45-54; CaO ? 15-33; Al2O3 ? 5-12; C ? 1-2; Fe[?]O[y] ? 7-11; MgO ? 3-6; Na2O ? 0,1-1; SO3 ? 0,1-0,6;
TiO2 ? 0,1-0,3; K 2O ? 0,8-1,5; it also contains impurities of transition metals such as Ti, Mn, Cr, etc.
The ceramic foam consist of anorthite crystal structure, gehlenite, wollastonite, iron oxides, transition
metals Ti, Mn, Cr, etc. in small quantities.
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Liudmila V. Kashkina, Olesya P. Stebeleva? Hydrodynamic Dispersion of Calcium Aluminosilicate from Technogenic?
2. The porous glass material derived from the melt of nonmetallic materials low in of manganese
by the thermal shock method. The composition is (wt %): SiO2 ? 44,41; CaO ? 32,46; Al2O3 ? 7,82;
Fe2O3 ? 1,14; MnO ? 4,88; MgO ? 0,71; Na2O ? 0,16; SO3 ? 0,1-0,6; TiO2 ? 0,186; K 2O ? 1,82.
The dispersion was carried out in the hydrodynamic rotary generator with two-bladed wedge
impeller in mode supercavitation. Engine power ? 1 kW, volume of the working chamber ? 3?10 -4 m3.
At supercavitation mode, the bubbles are located in the tail of nonstationary supercavities, generated
behind the rotor and the stable cavitation effect on the dispersing phase without destroying the impeller
is implemented [10]. Three-percent water suspension of the glass and the ceramic foam powders is
processed for 2 minutes at the rotor speed 10 000 r/min.
That said the part of the dispersed phase precipitated, and another part remained in a state of
stable suspension. The precipitate and the suspension was dried in a Petri dish at temperature of 250
°C for 72 hours. The study was carried out by method of optical microscopy, XRD (diffractometer
SMART APEX II), NGR ? Mossbauer Effect (MS1104Em spectrometer), EMR (X-band spectrometer
SE/X-2544).
Intrpritation and discussion of research results
According to the data of optical microscopy particle size of the ceramic foam and glass ceramics
decreased by an average almost an order ? to a fineness state after dispersion [12]. XRD spectra of
the initial sample ceramic foam (diffractometer SMART APEX II), are characteristic of crystalline
material (Fig. 2). The spectra are well manifested phase lines of anorthite CaAl2SO8 (d = 3,20; 2,95;
2,14 Е), gehlenite 2CaO SiO2 Al2O3 (d = 2,30; 2,04 Е), wollastonite Ca SiO3 (d = 2, 97; 2,80; 1,83 Е),
hematite Fe2O3 (d = 2,69; 2,53; 2,20 Е).
We obtained sediment and suspension after the dispersion of the sample. The XRF spectrum
profile of sediment is similar to spectrum of the initial sample, but changes were also observed. Along
with the decrease in intensity of some lines until their disappearance there are new well resolved
lines of such phases as Al (OH)3 (d = 4,34; 2,23; 2,03; 1,67 Е), Al2O3 * H2O (d = 3,99; 3,214; 2,558 Е),
Al2 (OH)4Si2 (d = 7,17; 3,847; 3,37 Е), which wasn?t in the initial sample. In other words both partial
destruction of the crystal structures of the material and synthesis of new compounds with the active
participation of water is obtained.
The initial glass material is preferably an amorphous medium containing an amount of crystalline
phase is not recorded by an X-ray method. Fig. 3 shows the XRD spectrum of the tested glass, whose
form is characteristic of the X-ray amorphous material.
Under dispersing the porous structure of the sample is actively destroyed, it increases the degree of
sample?s amorphousness. Degree of amorphous suspension (Fig. 4, line a) is greater than the sediment
(Fig. 4, line b). Synthesis of new crystalline phases in this sample isn?t detected.
EMR spectra (electronic magnetic resonance) registered on EPR ? spectrometer X-band SE/X2544. EMR spectrum of initial ceramic foam sample is represented by line of complex shape which
is formed by magnetic centers in the sample, which lines are overlapped with each other. Spectra
simulation has allowed to allocate the three centers (Fig. 5). Paramagnetic (phase I), paramagnetic
phase is formed apparently by iron salts. Parameters: g-factor = 1,8; linewidth ?H = 46 mT. Phase
II ? magnetite (spinel) with parameters g = 2,13; ?H = 108 mT. Hematite (phase III)) ? g = 3,3;
?H = 128 mT.
#5#
Copyright ??? «??? «??????» & ??? «A???????? K????-C?????»
Fig. 2. XRD spectrum of the initial powder of ceramic foam
Fig. 3. XRD spectrum of the initial glass material powder
Fig. 4. XRD spectrum of glass material after dispersion (a ? suspension, b ? sediment)
Copyright ??? «??? «??????» & ??? «A???????? K????-C?????»
Liudmila V. Kashkina, Olesya P. Stebeleva? Hydrodynamic Dispersion of Calcium Aluminosilicate from Technogenic?
Difference in g-factors values of considered phases from listed in [13] caused by complex
structure of the ceramic foam that is also observed in other studies [14]. Obtained from EMR data
on the magnetization in arbitrary units (given in brackets) allow determining the contribution to the
magnetism of these phases (for the degree of increase): III (5177) ? I (8567) ? II (9472).
After dispersing the restructuring of the paramagnetic component ceramic foam associated
possibly with change of iron valence is fixed by EMR spectra of sediment. Spectra simulation (Fig. 6b)
allows to select the line with the parameters g = 2,02; ?H = 79 mT, which value the same with the
values of g and ?H ?for magnetite particles [14] and the line g = 2,6; ?H = 100 mT (hematite).
The temperature behavior of sediment magnetization is typical for samples superparamagnetic
nanoparticles (Fig. 6a). With decreasing temperature, the lines displaced in lower field, the width
Fig. 5. Spectrum simulation of the initial sample EMR ceramic foam
?
b
Fig. 6. a ? EMR spectrum of ceramic foam sediment after dispersion, b ? simulation of the EMR spectrum
#7#
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Liudmila V. Kashkina, Olesya P. Stebeleva? Hydrodynamic Dispersion of Calcium Aluminosilicate from Technogenic?
decreases. This can be related to increasing exchange interaction, narrowing line (Lorentz line shape)
or structural changes. So for magnetite (phase II) at 293 K the magnetization value per unit is equal
to 41112, at 77-10475, respectively. Hematite (phase III) at 293 K ? 33800, at 77-15377, respectively. A
sharp drop in the magnetization of hematite shows greater magnetic permeability for these particles
compared with magnetite particles. The line broadening after dispersion can be related to an increase
in the contribution of surface heterogeneity with decreasing particle size, or increasing the dimensional
dispersion. The values of g-factors also a bit changed for these reasons.
Analysis of the EPR spectra of the initial sample glass material showed that it has a structure with
a developed surface, contains manganese oxides (line 1, Fig. 7) and iron (low-field part of the spectrum,
line 2, Fig. 7). The fraction containing manganese quantitatively dominates. Line parameters 1 at 293
?: g = 2,0075; ?H = 49,2 mT. Temperature reduction to 77 K leads to a line shift in the lower field g =
2,015 and the broadening of the line to 62 mT. State of iron complexes is paramagnetic ? signal increased
with decreasing temperature, g-factor equal to 4,54, typical for low-symmetric state of iron.
After grinding the sample (sediment) contains manganese oxide (line 1, Fig. 8). Line parameters
have changed slightly: g = 2,013, ?H = 50,4 mT. Iron component in the EPR spectrum is almost
unnoticeable. The component containing iron, it is shifted to lower field: g = 4,54 (line 2, Fig. 8)
prevails in suspension EPR spectrum.
The manganese oxide is in much smaller amount than in the initial sample (line 1a, Fig. 8).
Line parameters have changed: g = 2,038, ?H = 53 mT, it can be associated with increasing in
particle fineness and surface changing. Thus, as a result of glass material grinding accompanied by
cavitation enrichment effect is observed: phase manganese prevails in the sediment, and iron phase in
suspensions.
Mossbauer spectra were measured with a source Co57 (Cr) on the ceramic foam before and after
the dispersion are shown in Fig. 9. Spectra represent the sum of several Zeeman sextets and quadrupole
doublets caused by different states and positions of iron.
Probability of the hyperfine fields in the experimental spectrum, defined for different valence
states of iron, show a wide the field distribution near the 510 and 470 kOe for Fe3 + with a characteristic
chemical shift value of ~ 0.3 mm/s and near 440 kOe Fe2,5 + with a characteristic chemical shift value
Fig. 7. EPR spectra of the glass material initial sample
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Copyright ??? «??? «??????» & ??? «A???????? K????-C?????»
Liudmila V. Kashkina, Olesya P. Stebeleva? Hydrodynamic Dispersion of Calcium Aluminosilicate from Technogenic?
Fig. 8. EPR spectrum of sediment and glass material suspensions after dispersion
Fig. 9. Mossbauer spectra of the initial ceramic foam and sediment samples
of ~ 0,7 mm/s. The appearance of mixed valence iron indicates that the sample contains magnetite.
Deviation of the values of the hyperfine fields of 490 and 460 kOe inherent to stoichiometric magnetite
indicates magnetite defects. Fitting model spectrum consisting of four sextets and two doublets to the
experimental spectrum leads to Mossbauer parameters shown in Table 1.
Mossbauer spectroscopy results have shown that the samples contain three iron phases: hematite,
magnetite and paramagnetic phase. Hematite phase has hyperfine field of ~ 510 kOe, which is less
than 517 kOe in stoichiometric hematite. This decrease of the field probably related to the dilution of
hematite by aluminum contained in the initial ceramic foam.
In the magnetite phase (spinel) identified tetrahedral positions Fe3 + (A) and octahedral positions
Fe3 + (B) and Fe2,5 + (B), in contrast to the stoichiometric magnetite, which are observed only two
sextet: Fe3 + (A + B) with a typical field H = 490 kOe and Fe2,5 + (B) with a typical field 460 kOe. Initial
ceramic foam contains appreciable amounts of CaO and Al2O3. Calcium and aluminum cations are
capable of entering into the spinel lattice, thus Ca2 + prefers tetrahedral and Al3 + ? octahedral spinel.
#9#
Copyright ??? «??? «??????» & ??? «A???????? K????-C?????»
Liudmila V. Kashkina, Olesya P. Stebeleva? Hydrodynamic Dispersion of Calcium Aluminosilicate from Technogenic?
Table 1. Mossbauer parameters of iron cations in the samples of the initial ceramic foam and after dispersion
(sediment)
Initial
ceramic foam
Ceramic foam
after
dispersion
(sediment)
IS, mm/s
±0,01
H, kOe
±3
QS, mm/s
±0,02
W, mm/s
±0,02
S, ±0,03
Phase
0,35
510
-0,44
0,26
0,03
?-Fe2O3
0,28
476
-0,10
0,45
0,13
Fe3+(A)
0,36
443
-0,37
0,93
0,18
Fe3+(B)
0,69
437
0
1,08
0,38
Fe2.5+(B)
0,28
0
1,33
0,78
0,16
Fe3+
0,97
0
1,98
0,95
0,12
Fe2+
0,36
511
-0,49
0,30
0,05
?-Fe2O3
0,30
475
-0,04
0,54
0,17
Fe3+(A)
0,56
447
-0,22
0,66
0,19
Fe3+(B)
0,58
415
0
1,36
0,33
Fe2,5+(B)
0,29
0
1,31
0,77
0,15
Fe3+
1,03
0
2,01
0,89
0,10
Fe2+
IS ? isomer chemical shift relative to ?-Fe, N ? hyperfi ne field at the iron nucleus, QS ? quadrupole splitting, W ? width of the
absorption line, S ? lobar population position.
This diamagnetic dilution of magnetite decreases the values of the hyperfine fields at the positions of
the spinel and wide distribution of the fields due to the occurrence of non-equivalent positions of iron
on the number of magnetic neighbors.
Cations Fe3 + and Fe2 + are found in the paramagnetic phase ceramic foam. Probably the
paramagnetic phase formation is an aluminosilicate containing iron in two valence states.
Spinel formation by dispersing doesn?t experience any changes. There is only a decrease in
mixed-valence cations, Fe2,5 + and change Mossbauer parameters. This is probably due to the oxidation
of magnetitethat can be the result of oxidation of the surface cations at reducing the size of spinel
formation and the conversion of magnetite part to hematite.
Conclusion
Thus, studies have shown that the profound structural changes in the material occur in the process of hydrodynamic dispersion due to high energy cavitational influence. The character of changes
depends on the initial state of matter. The structure of dispersible particles in the crystalline material
is not similar to initial. There is not only the destruction of the initial structure, but also the formation
of new crystallographic phases.
Manganese and iron in sediment and suspension of porous silica foam redistribute by grinding.
The sediment contains manganese more than suspension. Potential application field of this effect is the
foam exemption of transition metal impurities down to low concentrations (mass fraction %).
Copyright ??? «??? «??????» & ??? «A???????? K????-C?????»
Liudmila V. Kashkina, Olesya P. Stebeleva? Hydrodynamic Dispersion of Calcium Aluminosilicate from Technogenic?
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[13] Noginova N., Chen F., Weaver T. and all. // J.Phys.: Condens Matter. 2007. ? 19.
P. 208-246.
[14] ???????????? ?.?., ??????? ?.?., ?????? ?.?., ????????? ?.?. // ???. 2005. ?. 75.
?. 117-120.
Copyright ??? «??? «??????» & ??? «A???????? K????-C?????»
Liudmila V. Kashkina, Olesya P. Stebeleva? Hydrodynamic Dispersion of Calcium Aluminosilicate from Technogenic?
????????????????? ???????????????
???????-??????????????? ??????????
?? ???????????? ? ????????? ?????
?.?. ????????,
?.?. ????????? , ?.?. ???????????,
?.?. ?????????????, ?.?. ???????
?
????????? ??????????? ???????????
??????, 660041, ??????????, ??. ?????????, 79
?
???????? ?????? ??.?.?. ?????????? ?? ???
??????, 660036, ??????????, ?????????????, 50/38
?
??????? ??????-?????????? ???????? ???? ???????-??????????????? ?????????? ?????
??????????? ? ????????????????? ?????????? ????????? ???? ? ?????? ??????????????.
??????????? ??????? ? ??????????????? ???????????? ?? ?????? ??? ????? ??????-????????
????? ? ???????? ??????????????, ?????????? ?? ????????? ????? ? ?????? ???????????
????????. ??? ??????? ???? ???????????? ?????? ???, ???, ??? (?????? ??????????),
?????????? ???????????. ????????, ??? ? ???????? ?????????????????? ??????????????? ??
???? ????????????????????? ?????????????? ??????????? ? ?????????? ?????????? ????????
??????????? ?????????. ????????, ??? ???????? ????????? ??????? ?? ????????? ?????????
???????????? ?????????.
???????? ?????: ????????????????? ???????????????, ?????????, ????, ????????????,
???????? ??????????????.
Copyright ??? «??? «??????» & ??? «A???????? K????-C?????»
Journal of Siberian Federal University. Engineering & Technologies 1 (2014 7) 13-19
~~~
??? 538.975
Plasmonic Antenna
for Bright NV Centers
in Ultradispersed Detonation Diamonds
Anna A. Lyamkinaa*, Sergey P. Moshchenkoa,
Yuri G. Galitsyna and Alexey I. Lyamkinb,c
a
Rzhanov Institute of Semiconductor Physics,
13 Lavrent?eva, Novosibirsk, 630090, Russia
b
Siberian Federal University,
79 Svobodny, Krasnoyarsk, 660041 Russia
c
Molecular Electronic Department, KSC SB RAS,
50 Akademgorodok, Krasnoyarsk, 660036, Russia
Received 14.11.2013, received in revised form 08.12.2013, accepted 21.01.2014
In this work we present a theoretical analysis of plasmon nanoantennas for a diamond cluster
containing a bright NV center. The results are obtained by the numerical simulations using the discrete
dipole approximation. A gold shell around the diamond core is considered as antenna. It is shown
that by varying the size of the nanodiamond core and the thickness of the gold shell the position of the
plasmon resonance can be tuned to the emission of a NV center. A resonator shaped as a droplet-like
metal cluster is proposed. It provides the selectivity of the radiation polarization that is required for
applications in quantum informatics.
Keywords: plasmon nanoantenna, NV center, detonation nanodiamond.
Introduction
Nitrogen vacancies in diamond are among the most promising solid-state quantum emitters for
quantum cryptography applications [1, 2]. One of the main advantages of these bright centers is the
stability of the quantum states of impurity spins during a long time (order of ms) even at the room
temperature. Therefore, these isolated vacancies with weak surrounding sensitivities are perfect
candidates for single photon sources.
For effective applications individual NV centers should be selectively addressed and excited
and then the optical signal needs to be efficiently collected for following post-processing. Due to the
wide bandgap of diamond (5.45 eV) the use of inter-band absorption to excite centers is complicated.
Currently for experimental studies of optical processes in NV centers laser emission with a wavelength
of 532 nm is mainly used for pumping. However, the efficiency of such an excitation while being
sufficient for fundamental research appears to be too low for any device prototype, so improving
*
© Siberian Federal University. All rights reserved
Corresponding author E-mail address: lyamkina@isp.nsc.ru
# 13 #
Copyright ??? «??? «??????» & ??? «A???????? K????-C?????»
Anna A. Lyamkina, Sergey P. Moshchenko? Plasmonic Antenna for Bright NV Centers in Ultradispersed Detonation?
the efficiency of pumping is of great practical importance. At the same time, for the single photons
treatment the radiation of nitrogen vacancy should be directed by placing nearby an antenna that is
tuned to its emission wavelength. A plasmon resonator presents an attractive option for such a selective
antenna [3]. Effective interaction of the localized plasmon with the external electric field provides the
necessary pumping, and significantly enhances the incident field and thus provides a spatial selectivity
of excitation. The rate of spontaneous irradiation can be increased through the Purcell effect [4] by
adjusting the plasmon resonance frequency of the antenna to the characteristic NV center emission
and thus the information transfer rate can be significantly enhanced. Finally, the design of plasmonic
modes of the system consisting of a bright center with an antenna and a nanowaveguide shaped as a
plasmonic strip allows for transmission of the signal in the form of the plasmon excitation. That leads
to reducing the size of the device to subwavelength dimensions.
In this work a theoretical analysis of plasmon nanoantennas for a diamond cluster containing an
NV center is presented. Nanoantennas have the form of a gold shell around the diamond core. It is
shown that by varying the size of the nanodiamond core and the thickness of the gold shell the position
of the plasmon resonance can be adjusted to the emission of a NV center. When a contact in the form of
a disk is included to the consideration the symmetry degeneracy is removed. That leads to the arising
of an additional resonant wavelength which can be used to pump the vacancy. Also, a resonator shaped
as a droplet-like metal cluster is proposed providing the selectivity of the radiation polarization that is
required for applications in the quantum information.
Methods
In this work numerical simulations using the discrete dipole approximation (DDA) were used to
study the plasmonic antennas [5]. In DDA a target is replaced by an array of point dipoles and then
the electromagnetic scattering problem for an incident periodic wave interacting with this array can
be solved quite precisely. Thus any shape can be modeled provided the interdipole distance is small
enough to perform shape features. The polarizabilities of the dipoles are determined by the material
dielectric constants. The output of the DDA simulations used in this work is the efficiency of the
nanostructure absorption Qabs defined as the absorption cross section normalized to the geometrical
2
cross section: Qabs C abs S � a eff
, where Cabs denotes the absorption cross section and aeff is the effective
radius, i.e. the radius of a sphere with an equivalent volume: V
4 3
Saeff .
3
Results and discussion
The easiest way to create a hybrid plasmon resonator is the deposition of a metal (e.g. gold)
directly onto the surface of the nanodiamond to form a core-shell type structure. It is well known
that in such a structure the position of the plasmon resonance depends strongly both on the materials
and in the ratio of the dielectric core size and the metal shell thickness [6]. We performed simulations
for spherical diamond particles having sizes that are typical for a detonation synthesis method [7]
with a gold shell of varying thickness. Fig. 1 shows the absorption spectra of the diamond spheres
with the diameter in a range of d = 4 ч 10 nm coated with a gold layer thickness of 2 nm. It is seen
that with the increase in the core size the plasmon resonance is shifted to longer wavelengths due to
the corresponding increase of the gold shell size. The resonance wavelength for d = 10 nm is 620 nm
# 14 #
Copyright ??? «??? «??????» & ??? «A???????? K????-C?????»
Anna A. Lyamkina, Sergey P. Moshchenko? Plasmonic Antenna for Bright NV Centers in Ultradispersed Detonation?
Fig.1. Absorption spectra for spherical diamond particles with the diameter d = 4-10 nm covered by a gold shell
with the thickness l = 2 nm
Fig. 2. Absorption spectra for spherical diamond particles with the diameter d = 8 nm covered by a gold shell with
the thickness of l = 1-6 nm
which is close to the zero-phonon line of the nitrogen vacancy (637 nm). Fig. 2 presents absorption
spectra for particles with the constant diameter d = 8 nm and a gold shell thickness of 1 ? 6 nm. Here
the inverse relationship is observed, the thicker the gold film the larger the spectral shift to shorter
wavelengths. Apparently, this is due to the interaction of the plasmon modes on the inner and outer
surfaces of the metal sphere.
Therefore, by varying available geometrical parameters such as the size of the nanodiamond core
and the thickness of the gold shell one can tune the plasmon resonance to the NV center emission.
To study the system including both the radiative center with the antenna and a plasmonic waveguide
we examined a model consisting of a diamond particle with a shell placed on top of a metal disk. The
model is schematically shown in the inset in Fig. 3. In this configuration the symmetry of the object is
reduced, that leads to the removal of the polarization degeneracy when the light incidence is angular
# 15 #
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Anna A. Lyamkina, Sergey P. Moshchenko? Plasmonic Antenna for Bright NV Centers in Ultradispersed Detonation?
Fig. 3. Absorption spectra for spherical diamond particles with the diameter d = 10 nm covered by the gold
shell with the thickness of l = 2 nm placed on the gold disk with a diameter of 14 nm and the height of 4
nm for different polarizations of the incident light. The spectrum for a particle without disk is shown for
comparison
towards the symmetry axis. In our numerical simulations this angle was set to be 45є. The simulation
results for the diamond core with d = 10 nm coated by 2 nm of gold and placed on a gold disk having a
diameter of 14 nm and a height of 4 nm are shown in Fig. 3.
The removal of degeneracy leads to the splitting of plasmon modes and, together with the
already presented resonance peak at 620 nm a new short-wave peak appears at 550 nm. Thus it is
possible to achieve the presence of several plasmon modes and to drive resonances by controlling the
system geometry. When a long-wavelength plasmon mode is tuned to the resonance with the radiative
center, the pumping and the signal collection can be carried out via different channels using the same
resonator. Furthermore, as demonstrated in Fig. 3 different polarizations of the incident light can
correspond to different resonant wavelengths. This sensitivity to the emitted photon polarization can
be used to implement the qubit states 0 and 1 which are the orthogonal polarizations of emitted photons
respectively detected by the same plasmon antenna. However, for the described system the absorption
ratio for TE and TM polarizations is small, so the plasmon resonator geometry needs to be optimized
to exploit this effect.
Another viable option of a metal resonator is a droplet of metal located on the substrate near
the nanodiamond. The arrays of such droplets can be formed with the deposition of group III
metals during MBE growth [8]. First, the diamond particles can be placed near the droplets fi rst
with an atomic force microscope to detect the effect of individual pairs. Then the deposition of
diamonds can be carried out e.g. by the laser evaporation of a suspension [9]. Such structures with
a density of complexes of 107-1010 cm-2 perform a new metamaterial, namely an active medium
with high optical efficiency. In our previous research we examined the metal droplets produced by
this method [8] and showed that they can be effectively used for the design of plasmonic modes
[10]. A droplet, being a segment of the sphere is schematically shown with the incident light in
the inset in Fig. 4, while Fig. 4 itself presents the absorption spectra for the indium droplet with
a height of 40 nm and a base diameter of 350 nm for the TE polarization and different angles of
# 16 #
Copyright ??? «??? «??????» & ??? «A???????? K????-C?????»
Anna A. Lyamkina, Sergey P. Moshchenko? Plasmonic Antenna for Bright NV Centers in Ultradispersed Detonation?
Fig. 4. Absorption spectra for an indium droplet with a height of 40 nm and a base diameter of 350 nm for TE
polarization and different angles of incidence
Fig. 5. Angle dependence of absorption for resonance wavelengths obtained in Fig. 4 for TE and TM polarizations
incidence ?. The presence of diamond particles i.e. a dielectric sphere near a massive metal cluster
has only a small effect on its plasmon resonances, so at this stage the presence of the particles was
not taken into account.
Fig. 4 confirms that there is a set of resonant wavelengths and the resonance intensity depends
significantly on the incidence angle of light. The wavelength of 620 nm is close to the emission of
nitrogen vacancy as was mentioned above, and the peak at 480 nm can be used for pumping, for
example, by an argon laser. Fig. 5 demonstrates the angular dependence of the absorption at the
resonance wavelengths obtained from Fig. 4 for the TE and TM polarizations.
When the angle of incidence increases the absorption of TM wave decreases significantly, while
the absorption of the TE wave increases. For instance, for the angle of 75є the ratio of absorption
# 17 #
Copyright ??? «??? «??????» & ??? «A???????? K????-C?????»
Anna A. Lyamkina, Sergey P. Moshchenko? Plasmonic Antenna for Bright NV Centers in Ultradispersed Detonation?
amplitudes for TE and TM light is a factor of 4/0.4 = 16. Such a significant difference in the intensity
provides a high selectivity of the droplet nanoantenna to the polarization.
Conclusion
In this study we investigated the plasmonic nanoantenna for diamond particles possessing a
bright NV center. Resonators in a form of a gold shell around the diamond core and a metal droplet
were considered. It was shown that by changing the size of the diamond core and the golden shell
thickness the plasmon resonance can be tuned to the emission of a NV center. When a contact modeled
as a gold disk was considered the polarization degeneracy was removed and an additional resonant
wavelength appeared in the spectrum. The short-wavelength line can be used to pump the NV center
while the emitted signal is enhanced and collected by the long-wavelength plasmon mode within the
same antenna. A resonator shaped as a metal droplet was demonstrated to provide a high polarization
selectivity that is required for applications in quantum information.
The work was supported by the RFBR (12-07-31133, 13-02-00959). AAL acknowledges the
financial support via RF president scholarship (SP-805.2013.3).
References
[1] Beveratos A. et al. // Phys. Rev. Lett. 2002. Vol. 89. P. 187?901.
[2] Aharonovich I. , Greentree A.D., Prawer S. // Nature Photonics. 2011. Vol. 5. P. 397.
[3] Choy J.T., Hausmann B.J.M., Babinec T.M. et al. // Nature Photonics. 2011. Vol. 5. P. 739.
[4] Purcell E.M. // Phys. Rev. 1946. Vol. 69. P. 681.
[5] Draine B.T., Flatau P.J. // J. Opt. Soc. Am. A. 1994. Vol. 11. P. 1491.
[6] Jain P.K., El-Sayed M.A. // Nano Lett. 2007. Vol. 7. ? 9. P. 28?54.
[7] ?????? ?.?., ???????? ?.?., ?????? ?.?., ?????? ?.?. // ?????? ??????? ? ??????.
1984. Vol. 20. ? 5. ?. 100.
[8] Lyamkina A.A., Dmitriev D.V., Galitsyn Yu.G. et al. // Nanoscale Res Let. 2011. Vol. 6. P. 42.
[9] Karmenyan A., Perevedentseva E., Chiou A., Cheng C.?L. // Journal of Physics: Conference
Series. 2007. Vol. 61. P. 513.
[10] Lyamkina A.A., Moshchenko S.P. // J. Phys. Chem. 2013. Vol. 117 (32). P. 16564.
Copyright ??? «??? «??????» & ??? «A???????? K????-C?????»
Anna A. Lyamkina, Sergey P. Moshchenko? Plasmonic Antenna for Bright NV Centers in Ultradispersed Detonation?
?????????? ???????
??? NV-????????????? ???????
? ???????????????? ????????????? ???????
?.?. ????????, ?.?. ????????,
?.?. ????????, A.?. ???????,?
?
???????? ?????? ???????????????
??. ?.?. ??????? ?? ???
??????, 630090, ???????????, ??. ???????????, 13?
?
????????? ??????????? ???????????
??????, 660041, ??????????, ??. ?????????, 79
?
????? ???????????? ??????????? ??? ?? ???
??????, 660036, ??????????, ?????????????, 50
? ?????? ?????? ???????? ????????????? ?????? ?????????? ?????????? ??? ????????
??????, ?????????? NV-?????. ??????????? ?????????? ???????? ??????? ??????????
????????????? ? ?????????????? ?????????? ????????????? ????????. ???????????
??????? ? ???? ??????? ???????? ?????? ????????? ???? ? ????????????? ?????. ????????,
??? ? ??????? ????????? ??????? ???? ? ??????? ???????? ????? ???????? ??????????
??????????? ????????? ?? ????????? NV-??????. ????? ? ???????? ?????????? ????
?????????? ????????????? ?????, ??????? ???????????? ????????????? ?? ???????????,
??????????? ??? ?????????? ? ????????? ???????????.
???????? ?????: ?????????? ???????????, NV-?????, ????????????? ?????????.
Copyright ??? «??? «??????» & ??? «A???????? K????-C?????»
Journal of Siberian Federal University. Engineering & Technologies 1 (2014 7) 20-31
~~~
??? 004.7
Control of the Shape of Semiconductor Crystals
when Growing in Czochralski Method
Sergey P. Sahanskiy*
Siberian Federal University
79 Svobodny, Krasnoyarsk, 660041, Russia
Received 16.10.2013, received in revised form 14.12.2013, accepted 12.01.2014
A model of the formation temperature and the rate of withdrawal of semiconductor crystals when
grown by the method of ?Czochralski?, which allows you to control the shape of the crystals,
providing a fl at solidifi cation front and getting a quality fi nished product.
Keywords: model, growing, semiconductor chips.
Introduction
Base extraction methods monocrystals from a melt process ?Czochralski? is that the small
single-crystal seed is introduced into the melt shallow and is then slowly pulled from the melt, the
melt temperature and controlling the pulling speed of the single crystal. In the process of pulling
the right cone shape of the crystal, its cylindrical part and reverse cone, the control system is
programmed by the software changes the drawing speed and temperature of the crystal. The process
of pulling crystals from the melt requires compliance with a number of conditions that deliver quality
material specified geometry. Changes in single crystal pulling rate, and degree of cooling of the melt
temperature to a predetermined geometry affect crystal and largely determine the number of defects
in the crystal lattice [1-3]. Therefore, for the growth of perfect single crystals brands use automated
systems management, control and direction in the growth temperature, current speed and diameter
of the single crystal.
Basis by pulling single crystals from the melt by the method of ?Czochralski? consists in the fact
that a small single-crystal seed shallow injected into the melt and then slowly pull it out of the melt
by controlling the melt temperature and the rate of extraction of a single crystal. In the process of
pulling the right cone shape of the crystal, its cylindrical part and reverse cone, the control system is
programmed by software changes the pulling rate and the temperature of the crystal.
The control system in growing single crystals of germanium-based optical method for determining
the current diameter of the crystal is shown in Fig. 1. Under source control the camera in the single
crystal growth of diameter d, with a pulling speed V? and the rotating crystal (seed) W?, and the molten
metal in the crucible with an inner diameter D rotates with angular velocity W?. Computer-controlled
crystal pulling speed V?, crystal rotation W?, crucible rotation W? through the appropriate drive. Control
*
© Siberian Federal University. All rights reserved
Corresponding author E-mail address: Sahanskiy@yandex.ru
# 20 #
Copyright ??? «??? «??????» & ??? «A???????? K????-C?????»
Sergey P. Sahanskiy. Control of the Shape of Semiconductor Crystals when Growing in Czochralski Method
W?
V?
W?
7
1
V?
2
X?; '?
11
3
13
12
4
17
d
18
14
DD
6
T?
15
5
16
W?
19
W?
8
V?
V? 9
10
X?; '?
Fig. 1. The control system in growing single crystals of germanium: 1 ? rotational drive seed; 2 ? move the seed
drive; 3 ? optical system; 4 ? image converter meniscus; 5 ? Temperature sensor; 6 ? temperature control; 7 ?
computers; 8 ? drive crucible rotation; 9 ? stepper motor; 10 ? stepper motor control unit; 11 ? encoder seed;
12 ? camera; 13 ? bar; 14 ? molten metal; 15 ? crucible; 16 ? heater; 17 ? pyrometer to measure the axial gradient
in the solid crystal; 18 ? a digital computer axial gradient; 19 ? crystal solidification front
of the temperature of the melt is based on the issuance of the job temperature ?? of the computer on the
temperature control.
As the feedback sensor is used for temperature radiation pyrometer aimed at the lateral surface
of the graphite heater. Information about the grown crystal diameter optical system comes with the
transmitter, based on what the system is determined by the current position of the brightness of the halo
of the meniscus of the crystal and the calculation of the control signal is proportional to the deviation
of the diameter of the crystal grown from the set of the program. Linear axial gradient in the solid part
of the growing crystal is calculated by the continuous measurement of the grown crystals additional
pyrometer, a distance of 1 ? 2 cm from the crystallization front of the crystal.
If the system control growing crystal from the melt by a method ? Czochralski ? in accordance
with a predetermined shape ( geometry ) growing a single crystal pulling form rate control and the
# 21 #
Copyright ??? «??? «??????» & ??? «A???????? K????-C?????»
Sergey P. Sahanskiy. Control of the Shape of Semiconductor Crystals when Growing in Czochralski Method
temperature of the crystal, while ensuring crystal solidification front is close to the flat, during
the whole process, it gives the ability to provide high quality of the single crystals. The closer the
speed and temperature control are obtained close to the shape of the crystal for a given thermal
conditions, the smaller the correction with the influence on the rate and temperature at the current
deviation from the predetermined diameter to the cylindrical portion of the crystal.
To maintain a stable single-crystal crystal growth requires further smooth transition
from the initial stage of pulling the seed crystal to the crystal growing direct cone, as well as
to complete the transition from the direct cultivation of a cone on the cylindrical portion of
the crystal. These conditions must be observed during the formation of inverted cone of the
crystal.
Condition of smooth changes in the shape of crystals grown in these areas is necessary to
ensure the continued growth of single-crystal germanium single crystals of large diameter (150
mm), with the provision in the fi nal crystal minimum dislocation and lack of low-angle boundaries.
Violation of a smooth transition when pulling single crystals of germanium can lead to failures of
single crystal growth and the inability to obtain this type of fi nished product.
The shape of the grown single crystal germanium (90 mm diameter), and management of key
growth parameters on the installation drawing for temperature and speed, with the mapping of the
control signal, a variation of the current diameter of the set, in relative numerical units shown in
Fig. 2-4.
In general, the management of the main parameters of growing single crystal of germanium is
shown in Fig. 5
The form of the forward and reverse cone crystal grown in Fig. 5 has the form kosinousoidalnyh
continuous lines in the areas of direct and inverted cone, with zero initial and fi nal coupling angle
to the surface of the crystal grown. This ensures a smooth transition and stability of single-crystal
growth of a crystal in the transition area.
The following are the mathematical expressions for the formation of the program goals of the
temperature T(x), and the rate of withdrawal V??(x), which allow you to automate the data entry
process parameters in the control system.
Management model temperature and velocity (Fig. 6) during crystal growth can be represented
by the expression (1):
T(x) = F(Z, Y, V?? (x), L(x), x),
(1)
where T(x) ? the average temperature of the melt in the zone of the crystallization front, V??(x) ? the
software the speed crystal pulling; x ? coordinate movement along the axis of the crystal; L(x)- a
linear axial gradient in the solid crystal; Z ? vector geometry grown crystal; Y ? vector thermo
physical material parameters.
When growing all major semiconductor crystals (germanium, silicon, and gallium arsenide)
their crystallization front of the crystal, which separates the liquid from the solid part of the melt is
raised above the surface of the melt on the value of 1 ? 5 cm.
If we equate the weight of the lifted weight of the column of liquid melt (to the front of
crystallization), the surface tension forces acting on the circumference and height of the bar to take
into account the expression of the melt through the heat balance at the interface, it is possible to obtain
# 22 #
Copyright ??? «??? «??????» & ??? «A???????? K????-C?????»
Fig. 2. Bar d = 90 mm
Fig. 3. Graph of the temperature of the heater ?? sites: 1 ? growing area right cone; 2 ? growing area of the cylinder; 3 ? land cultivation inverted cone; 4 ? section ingot annealing
Fig. 4. Plot of the rate of withdrawal and seed V? control signal ?y at sites: 1 ? growing area right cone; 2 ? growing
area of the cylinder; 3 ? growing area inverted cone; 4 ? section ingot annealing
Copyright ??? «??? «??????» & ??? «A???????? K????-C?????»
Sergey P. Sahanskiy. Control of the Shape of Semiconductor Crystals when Growing in Czochralski Method
d?(x), ?, V??, L
0
L
d?
?
V??
x1
x2
x3
x
Fig. 5. Building process parameters of growing single crystals of germanium: d? ? job diameter grown single
crystal; ? ? software job law of temperature change; L ? job axial gradient, x -moving crystal; x1 ? coordinate
completion of the formation of the crystal right cone; x2 ? coordinate completion of the formation of the cylindrical part of the crystal; x3 ? coordinate the completion of the formation of inverted cone crystal; V?? ? software job
law change the rate of withdrawal
Y
U?
U?
?
O?
O??
E
7?
d0
d1
Z
MANAGEMENT MODEL
DURING CRYSTAL GROWTH
x1
x2
T(x) = F( Z, Y, V??(x), L(x), x)
x3
T(x)
V??(x)
L(x)
Fig. 6. Management model for crystal
the dependence [2] crystal diameter d of withdrawal speed Vs and temperature T melt in the form of
an expression (2):
d
Ct �
>L CV � V? @ ,
>T T? @
(2)
# 24 #
Copyright ??? «??? «??????» & ??? «A???????? K????-C?????»
Sergey P. Sahanskiy. Control of the Shape of Semiconductor Crystals when Growing in Czochralski Method
where CV
U? �
E
O??
; Ct
4�
V � O??
;
U ? � O? � g
V? ? crystal pulling speed; ?? ? the crystallization temperature of the material; ? ? the average
temperature of the melt in the zone of the crystallization front; L ? linear axial gradient in the solid
crystal; E ? latent heat of fusion of the material; ?? ? thermal conductivity of the melt; ??? ? factor
thermal conductivity of the crystal; g ? acceleration of gravity; ? ? the surface tension of the melt; ?? ?
u. the density of the liquid material; d ? diameter of the crystal grown.
To set the average temperature of the melt expression (2) can be written as (3):
T ( x) T? Ct
>L CV � V?? ( x)@ ,
d ? ( x)
(3)
where d?(x) ? the program goals of the grown crystal diameter; V??(x) ? the software the speed crystal
pulling; x ? coordinate movement of the crystal.
In B. M. Turowski, B. A. Sakharov [4] that the curvature of the crystallization front is defined by
the ratio of the axial and radial gradients in the grown crystal, which in turn depend on the crystal for
a given diameter of the thermal fields in the crystal and the melt and the rate of withdrawal. With the
increase in the rate of withdrawal of the axial gradient in the crystal increases (increasing heat flux
caused by the release of latent heat of crystallization) and the crystallization front bends upward.
Speed control drawing of germanium crystals in a closed heat snap allows you to create a flat
crystallization front during the growth of the crystal right cone and a cylindrical part that is needed for
many brands of the germanium crystal and minimizes dislocation grown crystal.
Equation (2) can be seen as (4) to determine the appropriate rate of withdrawal of the crystal:
?
Ct
>L CV � V? @ ,
(4)
d
where ? = [T ? T?] ? the value of the average heat melt relative to the temperature of crystallization of
the material ??.
In general, according to the equations overheating ? is a function of the axial gradient in the crystal
L and given the rate of withdrawal V? crystal. The overheating ? can be determined by measuring
thermocouples area adjacent to the front of the crystallization of the material when developing specific
technology of crystal growth.
Overheating of the melt value of the average ? for the material, germanium (Ge) is in the range
of 0.1-2 ??.
Using a linear approximation of the pulling rate on the key areas of crystal growth (straight cone, the
cylindrical part and reverse cone) can obtain expressions for the determination of the speed command
to pull cone, the cylindrical part of the crystal and the formation of inverted cone, respectively:
V?? ( x) V0 x>V0 V1 @
;
x1
V?? ( x) V1 x x1 >V1 V2 @
;
x2 x1 # 25 #
Copyright ??? «??? «??????» & ??? «A???????? K????-C?????»
Sergey P. Sahanskiy. Control of the Shape of Semiconductor Crystals when Growing in Czochralski Method
V?? ( x) V2 x x2 >V3 V2 @
,
x3 x 2 where V?(x) = V??(x) ? software job pulling speed drills; V0 - initial crystal pulling speed when
switched on automatic; V1 ? pulling speed of the crystal at the end of the formation of inverted cone;
V2 ? pulling speed formation of the crystal at the end of the cylinder; V3 ? pulling speed of the crystal
at the end of the formation of inverted cone; x1 ? coordinate completion of the formation of the
crystal right cone; x2 ? coordinate completion of the formation of the cylindrical part of the crystal;
x3 ? coordinate the completion of the formation of inverted cone crystal; x ? coordinate-axis of the
crystal.
In order to determine the coordinates of the rate of withdrawal at the nodal points (V0, V1, V2, V3)
transform (4) to (5):
V? (d )
Є
O � d є Ei
,
«L »
Ct ј CV
¬
(5)
where V?(d) ? crystal pulling speed; d ? crystal diameter; ?i ? technological droop rate (0,95-0,25).
From (5) for the rate of withdrawal of nodes obtain expressions:
V0
Є
O � d0 є E0
;
« L0 »
Ct ј CV
¬
V1
Є
O � d1 є E 1
;
« L0 »
Ct ј CV
¬
V2
Є
O � d1 є E 2
;
« L1 »
Ct ј CV
¬
V3
Є
O � d0 є E3
,
« L1 »
Ct ј CV
¬
where L0 ? axial gradient at the beginning of the cylindrical part of the crystal; L1 -axial gradient at the
end of the cylindrical part of the crystal; V0, V1, V2, V3 ? nodes pulling rate; d0 ? craned neck diameter
of the crystal when the automatic mode; d1 ? diameter of the cylindrical part crystal.
Technological adjustment coefficients ?i are introduced to the possibility of adjusting the rate of
withdrawal on the basis of technical requirements (eg, uniform doping of the crystal along its length,
assuming a certain amount of deflection of the crystallization front in the direction of the melt on the
cylindrical part of the growing crystal.)
Cosine law for the continuous calculation of main controller in the plant growth is controlled by
the cones in a continued fraction Jacobi [5] standard accuracy of the expression:
cos( x)
є
Є
»
«
K2
»,
S / 2 x � « K1 K4
2
»
«
S / 2 x K 3 «¬
S / 2 x 2 K 5 »ј
where K1 = 6,63550098; K2 = ? 729,384055; K3 = 52,9056381; K4 = 1212.885446; K5 = 15,8503569
# 26 #
Copyright ??? «??? «??????» & ??? «A???????? K????-C?????»
Sergey P. Sahanskiy. Control of the Shape of Semiconductor Crystals when Growing in Czochralski Method
Using a linear approximation of the parameters on the remaining sections of the crystal growth, it
is possible to obtain an expression for calculating the rate of the control program and the temperature
at all sites, with the linear law of the job of the axial gradient, based on the installation of measuring
the results of the previous drawing of the crystal.
Expression on orders diameter d?(x) and temperature ?(x) on the right cone crystals take the form:
d ? ( x)
d0 d1 d 0 § d1 d 0 · � cos§Ё S
2
T?? ( x) T? Ct �
Є
«d 0
¬
Ё
©
2
·
Ё x � x ёё ;
© 1 №
ё
№
>L0 CV � V?? ( x)@
d d0 § d1 d0 · � cos§Ё S
1
Ё
©
2
2
ё
№
·є
Ё x � x ёё»
© 1 №ј
,
where x1 ? coordinate completion of the formation of the crystal right cone; L0 ? the axial gradient in the
crystal into the conical part; d0 ? craned neck diameter of the crystal; d1 ? diameter of the cylindrical
part of the crystal.
Expression on orders diameter d?(x) of the crystal and the temperature ?(x) on the cylindrical part
of the crystal are as follows:
d ? ( x)
d1 ;
Є
є
L1 L0 « L0 >x x1 @ � x x CV � V?? ( x)»
2
1
ј,
T ( x) T? Ct � ¬
d1
where x2 ? coordinate completion of the formation of the cylindrical part of the crystal; L1 ? axial
gradient in the crystal at the end of the cylindrical part.
Expression specifying diameter d?(x) of the crystal and the temperature ?(x) on the opposite cone
takes the following form:
d ? ( x)
d0 d1 d 0 § d1 d 0 · � cosЄ S
2
T?? ( x) T? Ct �
Ё
©
2
ё
№
є
� x x2 » ;
«
x
x
¬ 3 2
ј
>L1 CV � V?? ( x)@
Є
d1 d0 § d1 d0 · � cosЄ S � x x є є
Ё
ё
«d 0 2 »»
«
2
© 2 №
¬ x3 x2
јј
¬
,
where x3 ? coordinate the completion of the formation of inverted cone crystal.
In turn, the expression for the linear plots of growing jobs right cone crystal and its cylindrical
part and reverse cone will look like:
d ? ( x)
d0 d ? ( x)
d1 ;
x>d1 d 0 @
;
x1
# 27 #
Copyright ??? «??? «??????» & ??? «A???????? K????-C?????»
Sergey P. Sahanskiy. Control of the Shape of Semiconductor Crystals when Growing in Czochralski Method
d ? ( x)
d1 x x2 >d1 d 0 @
.
x3 x 2 Simulation speed and temperature grown single crystals of germanium-based model and the
reduced thermal constant of the material [6] is shown in Fig. 7-10 for the linear and for the reference
cosine inverse cone type crystal (cosine law isolated solid line).
Modeling the velocity and temperature of the single crystal silicon grown for the same crystal
form as germanium, but using permanent thermal silicon material, shown in Fig. 11-12 (with a separate
cosine law of formation and reverse cones crystal solid line).
d?(x), cm
12
10
8
6
4
2
0
0
50
100
150
200
250
x, mm
Fig. 7. Setting the diameter of the crystal germanium: x1 = 50 mm; x2 = 210 mm; x3 = 260 mm; d0 = 0,5 cm;
d1 = 11 cm
V?, mm / min
1.2
1
0.8
0.6
0.4
0
50
100
150
200
250
x, mm
Fig. 8. Setting the rate of withdrawal of germanium at: d0 = 0,5 cm; x1 = 50 mm; x2 = 210 mm; x3 = 260 mm;
d1 = 11 cm; ? = 0,4 ° C; ?1 = 0,8; ?2 = 0,8; ?3 = 0,4; ?4 = 0,6; L0 = 20 ° C / cm; L1 = 40 ° C / cm
# 28 #
Copyright ??? «??? «??????» & ??? «A???????? K????-C?????»
T, ??
955
950
945
940
935
0
50
100
150
200
250
x, mm
Fig. 9. Temperature setting pulling germanium: d0 = 0,5 cm; x1 = 50 mm; x2 = 210 mm; x3 = 260 mm; d1 = 11 cm;
? = 0,4 ° C; ?1 = 0,8; ?2 = 0,8; ?3 = 0,4; ?4 = 0,6; L0 = 20 °C / cm; L1 = 40 ° C/cm
d?(x), cm
12
10
8
6
4
2
0
0
10
20
30
40
50
x, mm
Fig. 10. Setting the diameter of the germanium crystal with a straight cone: d0 = 0,5 cm; x1 = 50 mm; x2 = 210 mm;
x3 = 260 mm; d1 = 11 cm
Copyright ??? «??? «??????» & ??? «A???????? K????-C?????»
Sergey P. Sahanskiy. Control of the Shape of Semiconductor Crystals when Growing in Czochralski Method
V?, mm / min
9
8
7
6
5
4
0
50
100
150
200
250
x, mm
Fig. 11. Setting the drawing speed of silicon: d0 = 0,5 cm; x1 = 50 mm; x2 = 210 mm; x3 = 260 mm; d1 = 11 cm;
? = 0,4 °; ?1 = 0,8; ?2 = 0,8; ?3 = 0,4; ?4 = 0,6; L0 = 20 ° C / cm; L1 = 40 °C/cm
?
T, ??
?
?
?
1470
1460
1450
1440
1430
1420
1410
0
50
100
150
200
250
Fig. 12. Setting the draw temperature of silicon at: d0 = 0,5 cm; x1 = 50 mm; x2 = 210 mm; x3 = 260 mm;
d1 = 11 cm; ? = 0,4 °; ?1 = 0,8; ?2 = 0,8; ?3 = 0,4; ?4 = 0,6; L0 = 20 °C/cm; L1 = 40 °C/cm
Findings
A model of formation temperature and the rate of withdrawal of semiconductor crystals with a
cosine law, the formation of cones in the crystal growth process of the ? Czochralski ?, which allows
you to enter this control in managing the installation drawing, providing a flat crystallization front of
the crystal and obtaining high-quality finished products.
The proposed mathematical model of the process control growing semiconductor crystals can
be successfully applied to the extraction plants such as semiconductor crystal silicon, germanium,
# 30 #
Copyright ??? «??? «??????» & ??? «A???????? K????-C?????»
Sergey P. Sahanskiy. Control of the Shape of Semiconductor Crystals when Growing in Czochralski Method
gallium arsenide, and the algorithm can easily programmable and operates in real time under the
current master controllers with floating-point operations per system commands.
References
[1] ????????? ?.?. // ???????????. ?????????????. ??????????. 2008. ? 1. C. 42?46.
[2] ????????? ?.?. ?????????? ????????? ??????????? ?????????????? ????????:
??????????. ??????????: ???. ???. ??????????. ??-?, 2008. 104 ?.
[3] ????????? ?.?. // ????- ? ?????????????? ???????. 2012. ? 6. C. 2?5.
[4] ????????? ?.?., ??????? ?.?. // ??????? ????? ?????????. ?.: ????? ??????-???????????
?????????? ??????????, 1969. ?. 25. ?. 94?103.
[5] ?????????????? ?.?., ?????? ?.?. ?????????? ???????????? ??????? ?? ???. ????:
???????, 1977. 207 ?.
[6] ??????? ?.?., ????????? ?.?., ??????????? ?.?. ?????????? ????????: ?????????? /
???. ?.?. ?????????, ?.?. ???????. ?.: ???????????????, 1991. 1232 c.
?????????? ?????? ????????????????? ??????????
??? ??????????? ?? ??????? ????????????
?.?. ?????????
????????? ??????????? ???????????
??????, 660041, ??????????, ??. ?????????, 79
?????????? ?????? ???????????? ??????????? ? ???????? ??????????? ?????????????????
?????????? ??? ??????????? ?? ??????? ????????????, ??????? ????????? ????????? ??????
??????????, ??????????? ??????? ????? ?????????????? ? ????????? ???????????? ???????
?????????.
???????? ?????: ??????, ???????????, ????????????????? ?????????.
Copyright ??? «??? «??????» & ??? «A???????? K????-C?????»
Journal of Siberian Federal University. Engineering & Technologies 1 (2014 7) 32-47
~~~
??? 532.5
????????-????????????????? ????????????
??????????? ????????? ????????????
?? ?????? ?????? ????????
? ??????????? ??????????????
?.?. ????????,?*, ?.?. ??????, ?.?. ????????,?,
?.?. ?????????,?, ?.?. ??????????
?
????????? ??????????? ???????????,
??????, 660041, ??????????, ??. ?????????, 79
?
???????? ??????????? ??. ?.?. ??????????? ?? ???,
??????, 630090, ???????????, ??. ????????? ???????????, 1
Received 19.09.2013, received in revised form 14.12.2013, accepted 25.02.2014
???????????? ?????????? ????????-?????????????????? ???????????? ???????????
? ???????? ??????????? ????????? ???????????? ? ?????????????? ??????????????.
???????????? ???? ????????? ??? ???????????????? ???? ? ?????????????? ????????????
?? ?????? ?????? Al2O3. ????? ?????????? ? ????????????? ????????????? ?? 800 ?? 6500.
???????? 20-?????????? ?????????????? ??????????? ? ?????????? ??????. ??? ????????
???? ???????????? ????????? ?????? ???????? ?????????????????? ?????????, ??????????
?? ????????????????? ???????, ??????? ????????????? ??????? ????????? ???????????? ?
?????????? ???????. ?????? ????????????? ??????? ????????? ? ?????????????? ??????????
??????????????????? ?????? ??????? SST. ???????? ?????????????????? ???????? ?
?????????????.
???????? ?????: ??????????, ????????????, ??????????????, ?????????????.
1. ????????
?????????????? ????????????? ??????????? ? ????????? ? ??? ?????? ?????????????????? ? ?????????????? ???????????? ??????????? ? ????????? ????? ???????? ???????????????,
?????? ? ??????????????????? ??????? ?????? ? ???????????. ???????????? ???? ????????
???????????? ??????????? ? ????????? ????????????? ?????? ????????????? ????????? ?
????????? ? ???????? ????????? ??????? ??????? ? ???????? ???????????? ???????????? ???
??????????? ????????????????. ???????????? ? ??????????????? ????????????? ? ?????? ?????????????? ????????? ? ????????? ??????????? ?????? ??????????? ? ????????????,
????????? ? ????????????? ?????????????? ? ????? ??????????? ????????? ? ???????? ????????? ? ???????????? ?????? ?????????? ???????. ????????????, ??????????? ? ?????????
??????????? ? ???, ??????, ????? ?????, ?????, ????????? ? ????????? ?????? ???????,
*
© Siberian Federal University. All rights reserved
Corresponding author E-mail address: tov-andrey@yandex.ru
# 32 #
Copyright ??? «??? «??????» & ??? «A???????? K????-C?????»
?.?. ???????, ?.?. ?????? ????????-????????????????? ???????????? ??????????? ????????? ?????????????
????????, ??? ????????????? ???????? ????????? ????????????? ? ????????????, ??? ???????????? ??????? ?????????????. ?????? ?????????? ???????? ? ?????????????? ??????????? ??? ????? ?????????????? ??????????? ???????? ? ???????? 70-? ????? (Ahuja, 1975 [1]).
???????? ?????? ?????????? ? ?????????? ????????? ? ?????????? ?? ????????? ? ???????
????????? ????????????? ????????????????. ? 1993 ???? ??????? ????????????? ???????
(Al2O3, 13 ??) ??????? ???? ???????????? ??? ????????? ???????? ? ???????????????? ???????
???????? (Masuda, 1993 [2]), ? ????? ??????? ???????????? ?????????? ????????? ??? ?????????? ? ??????? ? ???????????. ?????? ???????????? ????????, ??? ???? ????? ????? ???????
?????????? ? ???????? (???? ???????? ?? ??????) ???????? ? ????? ???????????????? ????????????? ?? 60 %, ??????????? ? ?? 60 %, ???????????? ????????? ?????? ? ?? 300 %.
???????? ?? ???????? ?????????? ?????, ? ??????? ??????????? ????????????? ?????????? ???????? ????????? ???????? (??., ????????, ???? ????? ?????? [3] ? ????????
[4]). ????????????????? ?????? ????? ????????????? ? ???? ??????????????? ???? ?????.
?????? ???????? ???????????????? ? ????????????, ???????? ?? ?? ???????????? ??? ???????????? ????????? ?????????. ????? ????, ?????????? ????????? ??????? ??? ???????? ?????????????.
??????????? ????? ?????????? ?????????? ??????????? ??? ????????????? ??????????
[5]. ?????????? ???? ????????????? ??????????????? ? ???, ??? ?????????????? ???????
??? ????? ?????????, ???????????? ??? ?????? ?????????, ?? ?????????, ????? ????????
???????? ???????????? ?????????? ?????????? ?????? ??? 0,5 % [4]. ????? ????, ???????
??????????, ??? ??????????????? ?????????? ??????????? ??? ?????????? ?????????? [6].
?????????? ?? ???? ????????, ???????????? ??? ?????????-???????????? ????????. ? ?????
? ???? ???????? ??????????? ????????????? ?? ?????? ????? ?????? ???????????? ????????,
?? ? ???????????? ??????? ??????? ? ??????????????? ????? ??????.
????? ????????? ?????? ???????? ????????-????????????????? ???????? ???????????
????????? ???????????? ?? ?????? ?????? ???????? ? ??????????? ?????????????? ? ?????? ???????????? ?????????????? ?????? ??? ???????? ???????????.
2. ???????? ???????????????? ?????????
???????????? ?? ???????? ??????????? ????????? ???????????? ????????? ?? ???????????? ?????? ??????? ??????????? ???. ????????? ???????????? ????? ???????????
????????????? ???????, ? ??????? ????????????? ????????? ? ?????????? ????????? ? ??
???????????? ???? ? ?????? ???????????????. ?? ???. 1 ???????? ?????????? ????????????????? ?????????. ? ??????? ?????? ??????? ???????? ??????????? ??????? ?? ????????
?????????? ???????? ? ?????????????, ????? ??????????? ???????? ????????? ? ?????????????, ??? ?????? ????? ????????, ????????????? ?? ???????? ???????. ?????? ??????? ????????? ? ????? ???????? ???????????? ? ??????? ???????? ????????. ???????? ????????????? ???????? ?? ?????????? ??????? ???????????? ??????. ? ??????????? ??????????
???????? ??????????? ???? ???????? ? ?????? 1000 ??. ????????? ????????, ?????????? ?
???????????, ???????????? ??? ?????? ?????????? Omix. ?????? ???????? ? ????? ???????? ????????????? ??? ?????? ?????????????, ??????? ???? ?????????????? ?????????????? ? ????????? 3 %.
# 33 #
Copyright ??? «??? «??????» & ??? «A???????? K????-C?????»
?.?. ???????, ?.?. ?????? ????????-????????????????? ???????????? ??????????? ????????? ?????????????
???. 1. ????????????????? ?????????
G2
t4
t3
G1
t2
t1
???. 2. ????? ???????????? ??????????????
????? ???????????? ??????????????, ??????????? ?????? ?????????, ????????? ??
???. 2. ????????????? ???????????? ????? ????????? ?????. ?????????? ????? ????? ???????:
?????????? ??????? ????? d1 = 0,013 ?, ??????? ??????? d2 = 0,015 ?, ????? l = 1 ?. ???????
????? ?????????????? ????? ???????: ?????????? ??????? d3 = 0,025 ?, ??????? ???????
d4 = 0,027 ?, ????? l = 1 ?. ?? ?????????? ????? ??????????? ???????? ????????????, ?? ??????? ? ??????????? ????. ??????? ?????? ?????????????? ????????? ? ??????? ?????????
?????????????, ??????? ??????????? ???? ?? ????? ?? ??????? ????????????? ???????????
????????? ? ????? 6 °?. ? ???????????? ?????? ?? ??????? ??????? ??? ?????????? ? ?????
G2 = 13,788 ?/???. ?????? ?? ?????????? ??????? G1 ???????????? ??? ?????? ??????? ?
????????? ?? 0,4 ?? 3,3 ?/???. ??? ????????? ?????????? ?????????????? ?? ?????? ? ??????? ????? ???????? ???? ??????????? ????????? (t1, t2, t3, t4), ???????????? ? ???????????
???-200.
??????????? ?????????????? ?????????? ??? ????????? ????????????? ?? ?????? ? ???????, ? ????? ? ?????????? ?????. ????????????? ?? ?????????? ????? ?????? ???????? ?????,
?????? ???????? ??????? ????????? ?? ????? ? ?????? ?? ?????:
.
Q??? GC
1 p1 t1 t2 # 34 #
Copyright ??? «??? «??????» & ??? «A???????? K????-C?????»
?.?. ???????, ?.?. ?????? ????????-????????????????? ???????????? ??????????? ????????? ?????????????
??????????????, ?? ??????? ????? ????????????? ???????????? ?????
Q????? G2Cp2 t4 t3 .
????? Cp1 ? Cp2 ? ????????? ???????????? ??????????????; G1 ? G2 ? ???????? ???????
??????????????. ???????? ????????? ? ???????????? ????????? ?????? ???????? ?????? ????? ?
?????????? ????????????. ????????? ????????????? ??? ?????? ???????????????, ????????? ????????, ??? ?????? ????? ?? ????????? 5 %.
????????? ????????????? ????? ???????, ???????????? ?????????????? ???????, ???????? ????????? ???????:
Q??? Slk't ,
??? l ? ????? ??????????? ??????????? (?????????? ?? ???? ?????????? ? ??????? ?????);
?t ? ????????????????????? ????????????? ?????.
??????????? ????????????? ??? ??????????? ??????????? ??????? ?? ?????????
k
1
d
1
1
1
(
ln( 2 ) )
D 1 d1 2O d1 D 2 d 2
,
??? d1, d2 ? ?????????? ? ??????? ???????? ?????????? ?????; ?1, ?2 ? ???????????? ??????????? ?? ?????????? ? ??????? ??????? ?????????? ?????; ? ? ??????????? ????????????????
?????.
??????????? ????????????? ????? ??? ????????, ?????? ???????? ??? ??????????????
???????. ??????? ? ?????? ?????? ??????????????? ????????? ???????? ???????????? ??????????? ?? ?????????? ???????. ???? ??????????? ?????????? ????????? ???????:
D
G1C p (t2 t1 )
(tw ts ) S
.
(1)
????? t w ? ??????? ?????????????? ??????????? ?????? ??????, ?????????? ??????????? tw = (t1 + t2 + t3 + t4 ) / 4 ?? ?????? ?????????? ?? ?????? ? ??????? ?? ??????????????;
t s = (t1 + t2 ) / 2 ? ??????? ??????????? ???????? ?? ?????????? ???????, G1 ? ???????? ??????
????????????? ?? ?????????? ???????; S ? ??????? ?????????? ??????? ??????????? ?????????? ?????.
???????????? ?? ???????????? ??????????? ????????? ???? ????????? ??? ???????????????? ???? ? ???????????? ?? ?????? ?????? Al 2O3. ?????? ?? ??????? ??????????,
???????????? ??????????? ??? ??? ???????? ???????????? ?????????? Al 2O3 ? ????, ?????? 1 %. ????? ???????? ???????????? ??????? ????????????? ??? ???????????, ?????????
??????? ???????? ???????????? ??????????? ???????? ???????? ????????????, ? ???????
?? ????? ????????????? ???????. ??????????? ?????? ???????? ??? ?????????? ? ???
«????????? ?????????? ??????????» (?. ?????). ???????? ??????? ???????? ?? ?????
95 % ???. ?-Al 2O3; ????? 3 % ? ?????? ?????? ??????? ??????????????????? ????????;
2 % ? ????????????? ???? (????, ????????????), ????. ???????? ????????? ?? 0,6 ?? 1,7 ?/
??3. ??????? ????? ??????????? ?????. ???????? ???????????, ?????????? ??????? ???,
# 35 #
Copyright ??? «??? «??????» & ??? «A???????? K????-C?????»
?.?. ???????, ?.?. ?????? ????????-????????????????? ???????????? ??????????? ????????? ?????????????
?)
?)
???. 3. ??????????? ??????????????? ?????????? Al2O3 (?); ??????????? ????????????? ?????????? ??
???????? (?). ?? ??? ??????? ? ?????? ?????????? (? ??), ? ?? ??? ??????? ? ?????????? N ??????????
??????? ???????
35-40 ? 2/?. ??????????? ??????????? ?????? ??????? ????????? ?? ???. 3?. ???????????
??????? ????????? ?????? ??????? ? ????????? ???????? ?????????? ?? ???. 3?. ????????????? (??????? ??????????????) ?????? ? 36 ??; ?????? ??????? ?? ??????????? ? 45 ??;
??????? ???????? ?????? ? 54 ??.
??? ????????????? ???????????? ???????????? ??????????? ??????????? ???????. ????? ?????????? ? ???? ???????????? ?????????? ??????????? ?????? ???????? ??????? ? ????????????? ??? ?????????? ????????????? ?????????? ???????? ? ?????????????? ??????????? ????-?. ??? ??? ???????????? ???????????? ?? ????????????.
?????????? ????? ??????? ???????????? ????????? ? ???????? ????????????? ?? ?????????? ???????. ? ???? ???????????? ????????? ???????????? ??????? ????????????? ? ?????????? ???????? ???????? ???????????? ??????????? ?? ??????? (1).
3. ?????????????? ??????
? ????????? ????????
??? ????????????? ??????? ? ??????????? ????????????? ???????????? ?????????????
????? ????????, ?????????? ?? ?????? ????????? ?????? ??? ??????????????????? ?????
[7-10]. ??????????? ??? ????????????? ??? ????????????? ????- ? ?????????????? ???????
???????? ? ??????? [8, 9]. ???????????? ??????? ????????? ??? ????????????? ???????????
????????????? ???? ???????? ? ?????? [10]. ? ?????? ?????? ???????????? ???????????????
??? ?????????? ??????????? ???????????? ?????, ??????? ??????? ??????????? ???????????
????????????:
’ � (U v ) 0 ,
wU v
’ � (U vv)
wt
(2)
’p ’ � T Ug ,
??? ? ? ????????? ????????????, p ? ????????, v ? ?????? ????????, ? T ? ?????? ?????? ??????????.
????????? ?????????? ??????? ??????????????? ? ????????? ????:
# 36 #
Copyright ??? «??? «??????» & ??? «A???????? K????-C?????»
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і C P dT ,
T0
??? CP ? ???????? ????????????:
CP
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M � U p C P, f
U
,
??? ? ? ???????? ???? ??????????, ?f ? ????????? ???????????? ????????, ?p ? ????????? ????????? ???????????, C P , f ? ???????????? ???????????? ????????, C P , p ? ???????????? ????????? ??????.
????????? ????????????, ? ???? ???????, ??????????? ???
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???????? ????????? ???????:
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??? ?f ? ?p ? ???????????? ???????????? ?????????? ???????????? ???????? ? ??????.
????????? ???? ??????? ??????? ??????? ???????????? ???????? ?? ?????? ?????????,
????????? ??? ?????? ?????????????? ????????????? [11, 12] ? ?? ???????? ????????. ?????????? ????????? ? ??????????????? ???????? ??????? ????????????? ????????????????
? ???????? ?????????????. ????????? ???????? ?????????? ????????????????? ? ????????????? ???????????? ???????? ? ???????????????? ?????????????. ?????? ????? ???????????
????? ????????? ?????????????? ??????????, ??? ? ????????? ????? ?????????? ? ????? ?????? ????? ??????????? ????????? ????????????? ???????? ???? ????. ????????????? ?????? ??
????? ? ????? ?????? ??????? ????????? ???????????? ?????????????, ????????? ?? ???????? ????????? ?????? ??????????? ?? ???????? ????????????, ? ?? ????? ??? ????????????
?????????? ??????? ??????????? ?? ???????? ??????. ????????? ???????????? ??????????
?????? ????????????? ??? ?????????????, ???? ??? ? ????????????? ????????? ????????????????? ??????, ????????? ??? ?? ???? ????? ???????? ?????????????? ?????????????? ????????? ????????????? ? ????? ? ????? ?????? ?? ???????? ??????? ????????? ?????????????
???????? ? ???????????????? ?? ???? ???????????? ????????? ??????????.
??? ?? ?????, ??????? ?????? ??????????, ??? ??????????? ???????????? ???????????????? ???????????? ? ?????? ?????? ?????? ???? ???????????? ?? ????????? ???????????????? ?????????? [13]:
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O p 2O f O p O f � 1 E 3 � M
(4)
??? ?f ? ???????????????? ???????????? ????????; ? p ? ???????????????? ????????? ???????????; ? ? ????????? ??????? ???????? ? ????????? ??????? ???????, ? ?????? ??????
? = 0,1.
????????? ???????????, ?????????? ??? ?????? ?????????? (4), ? ??????????????????
??????? [14-17] ????????? ?? ???. 4. ?????, ??? ?????????????? ???? ?????????? ??????????? ????? ????????? ???????????, ??? ???????????? ?????????? ?????????.
???????? ?????????????? ?????????????? ???????????? ???? ???????? ???????????????
? ???? ????????????. ????????? ???????? ???? ????????? ??? ??????????? 20 °? ??? ??????
???????????? ???????????? ???-4. ?????????? ???????? ???????? ???????????? ???? ?????
1,31 ???Ч?, ??? ???????? ?? 30 % ????, ??? ??? ?????? ????. ????? ???????, ? ???????? ???????? ???????????? ???????????? ???
? = 1,31? f,
(5)
??? ? f ? ???????? ????, ????????? ?? ???????????.
????????????? ?????????????? ???? ????????? ??? ?????? ??????????? ?????? ??????? SST [18]. ??? ???? ???????????? ???????? ???????? ?????? ?? ??????????? (4)-(5). ??????????? ????????????? ???????? ?? ??????????? ?????????? ?????? ?? ????????????? ??????????? ???? ??????? ??? ????.
??????? ?????????????? ????????? ? ????????? ??????????????? ??????????. ?????????
??????? ???????????? ????? ????????? ?????, ??????? ???????? ????????? ???????????????
????????? ??????????????. ????????? ??????? ???????? ?? ???. 7. ??? ??????? ??????????????
????????????????? ????????? ????? ?? ????????? ? ??????? ??????. ????? ?????????? ????????? ????? ????????? 56 000 (80 ?? ??????? ? 700 ?? ????? ??????). ?? ??????? ????? ????????
???????, ??? ? ? ????????????, ????????? ?????????? ?????? G2 = 0,2298 ??/?. ???????????
???????? ?? ?????? ? ????????????? ? ?????? ?? ?????????? ??????? ?????????? ?????? ??
???. 4. ????????? ????????? ? ????????????????? ???????????????? ???????????? Al2O3
# 38 #
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?????????????? ??????? ??? ???????? ? ?????????? ??????? ??? ???????????. ?? ?????? ??
????????? ??????? ?????????? ??????? ????? ??? ???? ???????. ? ?????????? ???????? ?????????? ??????? ???????? ??????????? ?? ??????? ?? ?????????????? ?, ??? ? ????????????, ??
??????? (1) ???????? ??????? ???????? ???????????? ???????????.
4. ?????????? ????????????
??? ??????????? ????????? ????????????????? ????????? ? ????????????? ?????????????? ?????? ??????? ???? ????????? ????? ????????? ?? ?????? ????. ?????? ???? ?? ???????
??????? ??? ????? G2 = 0,2298 ??/?, ??????????? ???? ?? ????? ?? ??????? ?????? ???? ?????????? 6 °?. ?????? ?? ?????????? ??????? G1 ???????????? ??? ?????? ??????? ? ?????????
?? 0,4 ?? 3,3 ?/???. ??????????? ???? ?? ????? ?? ?????????? ??????, ?????????? ? ????????????, ????????? ?? ???. 5. ????? ????????????? ??????????? ???? ?? ?????????? ???????
??????????????? ????????? ????????? ??????? ? ??????? ???????? ? ?????????? ??????.
?????? ???????? ??????????? ?? ????? ?? ?????????? ?????? ?????????? ? ??????? ? ????????
????????? ???????.
?? ???. 6?7 ????????? ?????????????? ??????????? ? ???????? ? ??????? ??????? ?????????????? ??? ???? ???????? ????? ??????????, ??????????????? ??????????? ? ????????????? ??????? ???????.
?? ???. 8 ???????????? ????????????????? ? ????????? ??????????? ????? ????????? ??
????? ??????????. ????? ????????? ?????????? ??????????? ???????? Nu = (ad)/?, ??? d ? ??????? ?????????? ?????? ??????????????; ? ? ??????????? ???????????????? ????, ??????????? ?? ??????? ??????????? ????????; ? ? ??????? ???????? ???????????? ???????????,
??????????? ?? ??????? (1). ????? ?????????? ????? ????????????? ????? ??????????? ???????: Re = ?Ud/?, ??? U ? ??????????????? ????????, ? ? ????????? ????, ? ? ???????? ????. ???
????????? ? ????????????? ? ???????? ?? ???. 8 ????????? ???????????? ??????????? ?????
???. 5. ??????????? ???? ?? ????? ?? ?????????? ??????
# 39 #
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?)
???. 6. ???? ??????????? ? ?????????????? (?) ? ?????? ???????? (?) ? ??????? ?????????? ???????
?????????????? ??? Re = 868
?
?)
???. 7. ???? ??????????? ? ?????????????? (?) ? ?????? ???????? (?) ? ??????? ?????????? ???????
?????????????? ??? Re = 5485
????????? ?? ????? ??????????. ??? ??????????? ?????? ??????? ? ???????? ????????? ????§ Re Pr d ·
???????? ???????? [19] ????? ????????? ????? ??????? ??? Nu = 1,55Ё
ё
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0.33
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ёё
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????????); ? ??, ? ? ? ???????? ???????? ???? ??? ??????? ??????????? ?????? ? ????????. ???
????????????? ?????? ????? ????????? ????? ??????? ?? ?????????? ??????? [19]:
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§P ·
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© P? №
0.14
.
??? ????? ?? ??????? ?? ???. 8, ? ??????? ????? ?????????? ?? 2600 ?? 3000 ??????????? ?????????-???????????? ???????, ???????????????? ?????? ??????????? ????????????
???????????. ????????????????? ?????? ????????? ? ??????? ???????????? ? ????????????
???????? ? ????????????? ???????????? ??? ? ??????????, ??? ? ? ???????????? ??????.
???????????? ?????????? ??????????? ??????? ?? ?????????? ????????????????? ??????
?? ????????? 5 %. ?????????????, ???????????? ????????????????? ???????? ???????????
???????????? ??????????? ? ????????? ?????? ????? ??????? ???????????.
? ????????? ????? ?????? ? ???????? ????????????? ?? ?????????? ??????? ?????????????? ????????????, ??????? ???? ???????????? ?? ??????????? ?????? ????????. ???????????? ??????????? ? ????, ??? ??? ???? ???????, ?????????? 1 % ?? ??????.
??????????? ???????? ???????????? ??????????? ?? ??????? ????????????? ?? ?????????? ??????? ????????? ?? ???. 9. ?????, ??? ??-?? ????, ??? ???????? ???????????? ????????
?? 30 % ????, ??? ? ????, ?????????-???????????? ??????? ? ???????????? ????????? ???
??????? ????? ??????? ????????? ???????. ??? ????????????? ???????? ??????? ? ?????? ??????????? ?????? ??????? ?????????? ???????????? ????????? ???????? ?? 17 % ????????
???????? ???????????? ???????????. ? ?????? ?? ????????????? ?????? ??????? ??? ???????????? ??????????? 25%-??? ????????? ???????????. ??? ??????? ? ???????? ??????????
?? ?????? ?? ????????????????, ?? ? ?? ???????? ????????????. ? ?????? ??????????????? ??-
???. 8. ????????? ????????????, ??????? ? ???????????? ?????????? ??? ?????? ????
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?????????????? ??????????? ??? ??????????? ?? ????, ????????? ??????????? ??? ????????.
??? ???????? ???????????? ??????? ??????????? ???????????, ???????? ??????? ???????,
?????????????? ????????? ?-2/5?3/5. ? ???? ??????, ???? ???? ???????????????? ?????????????
?? ???? ?????????? ??????????? ?????? ????? ??? ????????, ????? ????? ????? ????????? ???????????. ??? ? ???? ?????????? ? ?????? ????????????. ????? ???????, ???? ????????, ???
?????????????? ??????????? ?? ???? ?????????? ????????????? ???????? ????????????? ???????. ????????????? ?????? ?????????????? ??????????? ??????? ?? ??????????? ?????
????????? ? ????????????????? ????????????, ? ??????, ?? ????????? ?????? ? ?? ????????????. ??? ???? ??????????? ?????????? ????????? ??????????? ??? ?????? ?????? ??????
???????????? ?????? ? ?? ?????????.
? ???? ???? ??? ???????? ??????????? ???????????? ??????????? ?????????? ?? ????????
????, ??????? ??????? ???????? ? ???????????? ??? ???????? ??????? ????? ???????????????
?????? ?????? ??????????, ? ??????, ? ????? ?????? ? ?????? ??????? ???????. ?? ???? ??????? ??????? ???????????????? ??????????? ???????????? ??????????? ?? ????? ??????????.
??????????????? ??????????? ????????? ?? ???. 10. ?????????????? ??????????? ??? ????????????? ???????????? ? ????????????? ????? ?????????? ? ?????????? ?????? ???????
??????????? ????, ??? ??? ????????????? ???????, ? ?????????? ???????? ???????? 20 %. ?
????????? ????????????? ?? ????? ?????????? ???????????? ???? ??? ???????? ????? ?????????? ????? 2800 ??? ???????????? ????? ??????????? ?????????-???????????? ???????.
? ??????? ????????????? ??????? ???????? ???????????? ??????????? ??? ???????????? ??
????????? ???? ???????? ???????? ?? 10 % ????, ??? ??? ?????? ????.
?? ???. 11-12 ????????? ????????? ????????? ???????? ??????????? ? ??????????? ??????? ?????????????? ??? ?????? ???? ? ????????????. ????? ????????, ??? ? ??????????
?????? ??????? ??????? ?????????????? ???????????? ???? ? ???????????? ??????, ??? ???
???. 9. ??????????? ???????????? ??????????? ??? ???? ? ???????????? ?? ???????
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???. 11. ???????? ??????????? ? ??????????? ??????? ?????????????? ??? ?????? ???? (?) ?
???????????? (?) ??? ??????? 0,016 ??/?
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????????? ?????????? ? ?????????????????? ???????? ???????? ???????????? ??????????? ??? ???????????? ???????? ?? ???. 13. ??????????? ??????? ? ???????????? ? ??????????
?????? ?????????? 3 %, ??? ????? ??????? ?????????? ??????? ???????????. ? ????????????
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???????????? (?) ??? ??????? 0,05 ??/?
???. 13. ????????? ?????????? ? ?????????????????? ???????? ???????????? ??????????? ???
????????????
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?????????? ??? ????????? ????????? ??????????? ?????? ????????? ???????? ??????????
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???????? ??? ????????? ??? ???????????? ???????. ????????? ??????? ???????????? ???? ?
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????????? ??????????????? ??????? ???????????? ? ?????????? ???????. ?????????????? ?
???????? ?????? ??? ????????? ????? ?? ?????????.
??????????
????????? ????????-????????????????? ???????????? ??????????? ????????? ?????????????? ???????????? ?? ?????? ?????????? Al2O3 ? ??????????? ?????????????? ?
?????????? ? ???????????? ???????. ???????????? ????????, ??? ?????????? ? ????????
????????????? ???????????? ??????????? ??????????? ?? ???????? ???????????? ???????????. ??? ???? ????? ??????????? ??? ?????????????? ???????????, ??? ? ??? ?????????. ??? ????????????? ???????? ????? ?????????? ? ?????? ??????????? ?????? ???????
?????????? ???????????? ????????? ?? 20 % ????????????????? ??????????. ? ?????? ??
????????????? ?????? ??????????? ???????? 10%-??? ????????? ???????????? ???????????. ??? ??????? ? ???????????? ???????? ?????????? ?? ?????? ?? ????????????????,
?? ? ?? ???????? ????????????. ??? ?????????????? ?????????? ?????? ??????? ??????????? ??????????? ?????????????? ???????????????? ????? ? ?? ??????? ?? ????????.
????????? ???????????????? ????????????? ??-?? ??????? ? ??? ?????? ?????? ????????
????????, ? ?????????? ?????? ?? ????? ?????????????? ??????????? ??? ???????????
?? ????, ????????? ??????????? ????????. ? ???????????? ?????? ???????? ??????? ???????, ????????? ??????????? ??????????? ????????? ??????? ?? ?????? ?? ???????????????? ?????????????, ?? ? ?? ??? ????????. ????? ???? ???? ???????????????? ?????????????
?? ???? ?????????? ??????????? ?????? ????? ??? ????????, ????? ????? ????? ?????????
???????????, ??? ? ???? ???????? ? ?????? ????????????. ????? ???????, ?????????????
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?? ????????? ?????? ? ?? ????????????. ??? ???? ??????????? ?????????? ????????? ??????????? ????? ?????? ??????????? ???????????? ? ????????? ??????????. ??? ???????????? ????? ??????????.
??? ????????????? ??????????? ? ?????? ???????????? ????????????????? ???????? ?
?????? ?????????? ????????????. ?????????? ?????? ?????? ????????, ??? ????? ?????? ????????????????? ????????? ?????? ???????????? ?? ??????????? ????????? ????????????
??? ? ??????????, ??? ? ???????????? ?????? ???????. ?????? ????????? ??????????? ??????? ? ???????????? ??????? ? ???, ??? ????? ?????????? ?????? ?????????? ????????????
???????? ?????? ?? ?????? ? ??????? ?????? ???? ????????? ???????????, ??????????? ?
????????????? ?????????????? ???????????? ?????????? ? ??????.
?????? ????????? ??? ????????? ????????? ???? (??????12-08-33061 ? 13-0100052) ? ??? «??????? ? ??????-?????????????? ????? ????????????? ??????» ?? 20092013 ??.» (?????????? ? 16.740.11.0642, 14.A18.21.0344, 8756, 14.132.21.1750), ????? ?????????? ?? ??-6296.2013.8.
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?.?. ???????, ?.?. ?????? ????????-????????????????? ???????????? ??????????? ????????? ?????????????
?????? ??????????
[1] Ahuja A.S. // J. Appl. Phys. 1975. V. 46.
[2] Masuda H., Ebata A., Teramae K. and Hishinuma N. // Netsu Bussei (Japan). 1993. V. 4.
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[3] ????? ?.?., ?????? ?.?. // ???????????: ??????, ?????, ??????????. 2010. ?. 1 (1).
?. 156?177.
[4] ??????? ?.?., ???????? ?.?., ??????? ?.?. // ??????????? ? ????????????. 2010. ? 2.
?. 173?188.
[5] Godson L., Raja B., Mohan Lal D., Wongwises S. // Renewable and sustainable energy reviews.
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[9] ??????? ?.?., ????? ?.?., ???????? ?.?., ???????? ?.?. // ??????????? ? ????????????.
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[10] ??????? ?.?., ??????? ?.?., ????? ?.?., ????????? ?.?. ???????? ???????? ? ???????.
?.: ??? «????? ? ??????????». 2013. ?. 5. ? 5. ?. 194?200.
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[19] ???????? ?.?., ??????? ?.?. ???????????? ?????????? ? ?????????? ?????: ?????????????????? ??????? [??????????? ??????]. ??????????: ???, 2012. 79 ?.
Copyright ??? «??? «??????» & ??? «A???????? K????-C?????»
?.?. ???????, ?.?. ?????? ????????-????????????????? ???????????? ??????????? ????????? ?????????????
Experiment-Calculated Investigation
of Forced Convection of Alumina Nanofluid
in Direct Flow Heat Exchanger
Andrey V. Minakova,b,
Dmitriy V. Guzey , Alexander S. Lobasova,b,
Dmitriy A. Dektereva,b and Maxim I. Pryazhnikova
a
Siberian Federal University,
79 Svobodny, Krasnoyarsk, 660041, Russia
b
Institute of Thermophysics named after S.S. Kutateladze SB RAS,
1 Lavrentev, Novosibirsk, 630090, Russia
a
The results of the experiment-calculated study of heat transfer of nanofluids forced convection in the
recuperative heat exchanger were set out. The experiments for distilled water and one per cent Al2O3based nanofluid were carried out. The Reynolds number in the experiments varied from 800 to 6500.
20 per cent intensification of heat transfer in laminar flow were shown. Numerical model describing
heat and mass transfer processes, based on the hydrodynamic approach, which implies a solution
of the Navier-Stokes and energy conservation equations was used for the calculation. Zonal twoequation model of Menter SST was used for calculation of turbulent flow. Satisfactory agreement with
experiment was obtained.
Keywords :heat transfer, nanofluids, turbulence, hydrodynamics.
Copyright ??? «??? «??????» & ??? «A???????? K????-C?????»
Journal of Siberian Federal University. Engineering & Technologies 1 (2014 7) 48-54
~~~
??? 532.528
????????????????? ??????????? ?????? ???????
??? ?????????? ???????? ????????
?.?. ??????*, ?.?. ????????
????????? ??????????? ???????????,
??????, 660041, ??????????, ??. ?????????, 79
Received 20.11.2013, received in revised form 24.12.2013, accepted 04.02.2014
???????????? ?????????? ?????????????????? ???????????? ??????? ??????? ???
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?????????? ? ??????? ????????, ?????? ??????????, ???????????, ???????????????, ???????????? ???????. ?????????????? ???????? ????????? ????? ? ?????? ???????????? ?????????? ????????? ? ????? ?????????, ?????? ????? ??????? ??? ???????????? ????????
????? ???? ?? ?????? ?????????? ??? ????????????, ?? ? ? ???????? ?????????? ??????,
?????????????. ???????????? ??????????? ?????? ??????? ??????? ? ??? ???????? ?? ??????????????, ?????????????? ? ???????????????? ?????????????? ????????? ????????? ?
??????.
??? ?????????????? ????????????? ??????? ??????? ?????? ?????????? ??????????
????????????? ???????????, ???????? ?????? ?? ??????? ???????? ????? ?????????, ?????????? ????????? ??? ???????? ? ????? ???????:
F
2 p p? ,
UV 2
(1)
??? p ? ???????? ??????????? ??????, ??; p? ? ???????? ?????????? ????? ???????? ??? ??????????? ???????, ??; ? ? ????????? ?????, ??/?і; V ? ???????? ?????? ?? ????? ? ???????, ?/?.
?????????? ????????? ????????? ? ????????? ? ?????????? ????????? ???????? ? ?????? ????????? ???????? ??? ??????????, ?????????, ? ?????????, ? ???????????? ????? ?????????, ???????? ? ????????? ?????????? ????????.
*
© Siberian Federal University. All rights reserved
Corresponding author E-mail address: d327@mail.ru
# 48 #
Copyright ??? «??? «??????» & ??? «A???????? K????-C?????»
?.?. ??????, ?.?. ????????. ????????????????? ??????????? ?????? ??????? ??? ?????????? ???????? ????????
??? ????????????????? ???????? ????????????? ? ???????? ????????? ?????????? ????????? ?????? [1]:
?) ?????????? ? ???????? ?????? ??????????;
?) ???????????????? ? ???????????????? ??????;
?) ?????????????? ??????, ?????????? ?? ????????? ?????????? ?????? (???????, ????????, ???????? ???????? ? ?.?.);
?) ???????????? ??????;
?) ????????????? (?????????, ????????????????);
?) ?????????????.
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???? ???????? ?? ??? ??? ???? ????????.
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?????? ? ????????. ??????????? ????? ????????????? ????????????? ???????? ??? ???????
?????????? ???? ? ??????????? ??????????? ????????????? [2]. ?? ????, ????? ?????? ???????? ????????????????? ????????? ? ?????????? ????????? ????????. ????????? ?????????
??????? [3] ??????????? ??????????? ?????????? ?, ??, ? ???????? ?????? Dr, ?-1, ??? ??????
???????? ????? ????????
W
Dr
z?
,
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(2)
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,
R 2 rx2
(3)
??? z ? ????????? ?????????? ????????????? ?????????????????? ??????????; ? ? ?????? ??
???? ??????? ????????, ?·?; l ? ?????? ????????? ??????????? ???????, ?; R ? ?????? ???????, ?; rx ? ??????? ?????? ???????, ?; ? ? ??????? ????????, ?-1.
??? ?????? ? ???????, ?? ???????????????? ?????????? ?????????? ??????, ?????????
??????????? ?????????? ? ???????? ?????? ?????? ???? ????? ?????????? ??? ???????????
???????? ???????? ???????????? ???????? K
W
, ??·?. ? ????????????? ?????? ???????
Dr
??-?? ????????? ?????????? ?????? ?????????? ???????? ????????? ?, ??? ?????????, ?????????? ??????? ?? ???? ??????? ????????, ??? ????? ??????????????? ???????? ???????? ? ?
????????? ??????? ?????? ?????????.
??? ???????????? ????????????? ????????????? ????????? ? ?????????????? ??????
???? ??????????? ????????????????? ?????????. ????????? ??????? ?? ???? ?????????????
???????? ? ?????????? ??????????? ???? ? ??????????? ??????? ????????, ??????????? ?????? ? ?????????? ?????? (???. 1).
? ???????????? ?????????????? ??????? ??????????? ???????, ?????????????? ????? ????????????? ??????????? ??????????. ??? ?????????????? ??????????? ??????? ?
# 49 #
Copyright ??? «??? «??????» & ??? «A???????? K????-C?????»
?.?. ??????, ?.?. ????????. ????????????????? ??????????? ?????? ??????? ??? ?????????? ???????? ????????
8
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???. 1. ????? ????????????????? ?????????: 1 ? ??????? ???????; 2 ? ???????? ???????; 3 ? ?????????????
???????????; 4 ? ????????????? ??????????? ??????????; 5 ? ?????? ????????????? ????????; 6 ?
??????????? ??????; 7 ? ????????? ?????; 8 ? ??????????; 9 ? ?????????; 10 ? ?????????
???. 2. ??????????? ????????????? ???????? ?? ????? ???????? ? ???????? ? ?????????
??????? ???? ???????? ???????? ??????? ? ??? ???????????? ????????????? ???????????,
????????????? ??????????????? ???????? ??????. ? ???????? ??????? ???????? ????? ?????????? ????????????? ????, ??????? ???????? ? ??????? ??????????????? ????????. ?? ????
???????????? ? ????????? ??????????? ??????????? ??????????, ????? ?????????? ???????
????? ???????? ???????? ?? ????????? ????? ????????. ????? ??????????? ? ????????? ????????? ??????????? ???????? ?? 0,1 ?? 0,01 ??? ??? ??????? ???????? ?? 3000 ?? 9000 ??/???.
? ???????? ????????? ????????? ??????? ???????? ???? ???? ?? ??????? ?????????. ??????
????????????????? ????? ????????? ????????? ??? ?? ?????? ?????? ????. ?????????? ???????????? ???????????? ?????????? ?? ???. 2.
# 50 #
Copyright ??? «??? «??????» & ??? «A???????? K????-C?????»
?.?. ??????, ?.?. ????????. ????????????????? ??????????? ?????? ??????? ??? ?????????? ???????? ????????
?????? ?????????? ??????
?????????? ???????, ????????? ? ????????????????? ?????????, ????????????? ???????
??????? ???????, ????????????????? ?????????? ?????????? ??????. ??? ??????????? ???????? ???????? ??? ??????, ????? ???????? ? ????????? ?????? ??????????? ?????????? ??
????????????. ??? ??????????? ??????? ?? ??????? ?????????? ?????? ???? ??????? ????????, ??????????????? ???????????? ???????? (???. 3, ??????? ??????) ? ?????????????
?????????? p = 0,01 ??? (???. 3, ?????? ??????).
?????????? ????????? ??????? ??????? ???????????? ????????????? ????????? ??????????? ???? ???????? (2) ? (3), ????? ??????? ???????? ???????????? ????????????? ????????
? ?????????????? ????????????????. ?????? ?? ???? ???????????????? ?????????????? ????????????? ????, ?????????????, ????? ????????:
Wk
2� I
SlR 2
(4)
??? I ? ???????????? ???; ?, k ? ??????????? ??????????????, ????????? ?? ?????????????
???????????????? ?????????, ???????????? ?????????? ??????? ???????? ? ????????? ????????????????? ????? ?????????. ? ???????? ???????????? ??????? ??? ??????????? ? (3) ????
??????? ???????? ??????????? ??????? ( rx
1
R), ??? ??? ?????? ??? ?????????? ??????????
2
????????????? ????????, ??? ?????????????? ???????????? ?????????????. ????? ??????????? ????????? ?????? ????????? ?? ?????????? ??????? ???????????? ?? ???. 4.
??????????? ????????????????? ??????????? ? ?????? ??????????, ???????? ?????? ????????? (???. 5).
?????????? ??????????? ??????????, ??? ??? ??????? ? ??????? ????????? ?????? ???????? ?????? ?????? ? ????????? ??????, ??? ????????????? ????????????? ?????????? ????-
???. 3. ??????????? ???????? ???? ?? ????? ????????: ? ? p = 0,1 ???; ? ? p = 0,01 ???
# 51 #
Copyright ??? «??? «??????» & ??? «A???????? K????-C?????»
?.?. ??????, ?.?. ????????. ????????????????? ??????????? ?????? ??????? ??? ?????????? ???????? ????????
????????????????????
???. 4. ????? ??????????? ????????? ?????? ????????? ?? ?????????? ???????
???. 5. ??????????? ???????? ?????? ?? ??????????? ??????????: ? ? p = 0,01 ???; ? ? p = 0,1 ???;
? ? ? ? ?????? ????????? ???????????? ????????
??? ???????????? ???????? (???. 5, ?????? ??????). ??????, ??????? ????, ????????? ?????????????? ???????? ???????, ??? ??????????????? ?? ????????? ??????? ??????.
????? ???????, ????????? ?????? ??????? ????? ???? ???????????????? ?? ?????????
????????????? ??????????, ? ?????? ???????? ?? ???????? ??????????? ???????? ?????? ??
?????????? ?????????? D = f(?) ? ?????????? ?????.
??? ??????????? ??????????, ??? ??????? ????????? ????? ???????, ???? ?????????? ???????? ???????? ???? ???????? ??????, ?????????? ????? ?????? ????????? D-? ? ??????
?????, ?????????? ?? ??????????? ????????? ????????????????? ??????. ?? ???????????
??????? ??????? ?????, ?????? ??????? ???? ?????????? ?? ?????????? ???????? ???????? ???
??????????? ???????? (???. 6).
?? ???. 6 ???????? ??????, ??????????????? ??????????? ?? (1) ?????? ?????????.
??????? ???????? ?????? ??????? ?? ????????? ? ?????????????? ????????? ? ?????????
0,8 < ?< 1,6. ???????????? ????? ???????????????? ????????????????? ????? ?????? ? ???# 52 #
Copyright ??? «??? «??????» & ??? «A???????? K????-C?????»
?.?. ??????, ?.?. ????????. ????????????????? ??????????? ?????? ??????? ??? ?????????? ???????? ????????
???. 6. ??????????? ?????? ??????? ?? ????? ???????? ? ???????? ? ?????????
???? ?????????? ????? ????????? ????? ????????? ?????????? ?????????? ??????? (1)
??? ??????????? ???????? ???????? ? ???????????? ????????????.
?????????? ?????????? ????????? ?????????? ????? ??????? ? ????????????????? ???????? ? ??????? ????????? ????????? ???????? ? ????????? ? ??????????? ??? ???????????????? ????????????? ?????????. ???????????, ???????? ??????????? ?? (???. 6), ????? ????
???????? ??? ?????? ????????????? ????????????? ?????????????, ? ?????? ?? ????????? ???????? ???? ??????? ? ??????????? I-n (???. 2).
??????
?????????? ??????????? ????????????????? ?????????, ??????????? ????????? ???????????? ??????????? ???????? ????????? ? ????????????? ? ??????????????? ???????
? ??????? ????????? ????????? ? ???????? ?????????? ?????. ?????????? ? ???????????
?????, ??????????? ?? ????????? ??????????? ?????????? ? ???????? ?????? ??????????
????? ??????? ??? ?????????? ???????? ????????.
?????? ??????????
[1] ????????? ?.?. ????????? ? ??????? ?????????????? ??????????????. ?.: ???????,
1978. 308 ?.
[2] ????????? ?.?., ?????? ?.?., ??????? ?.?. // ????????????? ?????????. 2008. ? 6.
?. 70-74.
[3] ?????? ?.?., ????? ?.?. ????????: ?????????, ??????, ??????????. ???.: ?????????,
2007. 560 ?.
Copyright ??? «??? «??????» & ??? «A???????? K????-C?????»
?.?. ??????, ?.?. ????????. ????????????????? ??????????? ?????? ??????? ??? ?????????? ???????? ????????
Experimental Determination of the Flow Regime
in the Radial Motion of the Fluid
Alexander U. Radzyuk and Elena B. Istyagina
Siberian Federal University,
79 Svobodny, Krasnoyarsk, 660041, Russia
Presents the results of investigation of flow regimes radial motion of liquid. Proposed to use a change
of the dependence of speed of the shift from of the rate of the shift from shifting stresses as the criterion,
allowing to define a transition moment from a continuous stream to the stream cavitation. Described
the design the experimental setup, an algorithm of constructing nomograms to determine the mode of
movement in the continuous stream and gas-liquid stream by water.
Keywords: radial motion of the fluid, cavitation, rheology.
Copyright ??? «??? «??????» & ??? «A???????? K????-C?????»
Journal of Siberian Federal University. Engineering & Technologies 1 (2014 7) 55-61
~~~
??? [665.63+662.764]:62.50
????????? ????? ????????????
???????????? ???????
? ??????????????? ?????
?.?. ??????????, ?.?. ?????????*
?
???? «?????» ??? ?? ???
??????, 660049, ??????????, ??. ????, 53
?
????????? ??????????? ???????????,
??????, 660041, ??????????, ??. ?????????, 79
Received 18.11.2013, received in revised form 14.12.2013, accepted 12.01.2014
? ?????? ???????????? ?????????????? ?????? ??? ???????????? ? ????????????
????????? ??????????????? ????? ??? ???????? ? ??????????????? ???????????.
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? ???????? ? ???????? ? ???? ???????????????? ????????? ? ??????? ???????????.
????????? ????????? ???????????? ???????????? ??????? ????????? ?????. ???
????? ?????????????? ??????? ?????? ??? ??????? ???????????? ???????? ????????,
?????????, ????????, ??????????? ??????? ????? ? ??????????? ????????????
?????, ??????? ?? ?????????? ? ???????????????? ???????. ???????????? ??????????
??????? ??????????????? ??????????. ???????????? ????? ????? ???? ???????????
??? ????????????? ???????????????? ????????? ? ????????????????????? ?
??????????????? ??????????????.
???????? ?????: ?????????????? ?????????????, ??????? ? ??????????????? ???????????,
???????????????, ????????? ?????.
??? ???????????????????? ??????? ????? ? ?????????????? ? ???????? ?? ??????????? ? ???????????????? ?????????? ????????? ????????? ????. ???? ???????? ????????? ??????? [1]: ????? ? ??? ??????? ? ????????, ????????????? ? ?????? ????????.
???????? ???????? ?? ?????? ???????? ????????? ? ?????? ?????????, ????? ???????????? ? ??????????? ? ?? ??????? ????? ?????? ? ?????????. ? ?????? ????????? ??????????? ????????????? ?????, ?????????????? ????? ??? ??????????????? ???????
????? ? ???????????? ??????? ????? ?????????. ??????????? ??????? ? ???? ??????????????? ???????? ????? ????????????? ? ?????????? ?????, ???????? ?????. ?????????? ??????????? ???????????? ??????? ????? ?????, ??????????? ??? ???????? ???????
(???. 1).
??????? ??????? ??????? ?????? ????????? ? ??????? ????, ?????? ????????? ?????????????? ???????? ????? ?? ???? ??????? ?????. ??????? ?????? ????????? ? ??????????? ????.
*
© Siberian Federal University. All rights reserved
Corresponding author E-mail address: klvation@gmail.com
# 55 #
Copyright ??? «??? «??????» & ??? «A???????? K????-C?????»
?.?. ?????????, ?.?. ????????. ????????? ????? ???????????? ???????????? ??????? ? ??????????????? ?????
??????? ??????? ??????? ?????? ???????? ???????????? ???????, ????? ???????? ???????? ?????
????? ?????? ?? ????????? ? ???????? ????????
????? ? ?????????? ? ???? ???????, ??????? ??????? ?????????? ????????? ?????. ? ?????? ??????
????? ???????????? ??????? ???????????? ???????
??????. ???????????? ?????? ??????? ??????? ?.?.
?????????? [2].
? ?????????????? ??????? ??????? ????????
??????? ??????? ????????? ??????????? ? ?????? ???????, ?? ??? ????????????? ????????????
??????? ???????????? ?????? ??????. ??? ????????? ?????? ?????????? ??? ????????? ??????????????:
1. ?????? ????? ????? ??????????? ?????.
2. ???????? ????????? ????????????, ?????
????????????? ??? ??????????? ???????????, ??????????????? ? ??????.
3. ????? ??????? ?????????????? ????????????? ???????, ??????? ?????????? ? ?????????? ??????? ????? ?????? ???????? ? ????????, ???????????. 1. ????? ????????? ????: 1 ? ???????;
???? ? ????????????????? ???????????.
2 ? ?????????? ??????; 3 ? ?????? ????????
4. ????????????? ???????????? ????????? ???
(???????? ??????); 4 ? ?????? ?????????; 5 ?
?????????? ???????? ?????, ???? ??????? ???????
??????? ?????; 6 ? ??????? ?????????????
????; 7 ? ??????? ?????????? ????; 8 ?
?????? ????? ??????????? ?? ???? ???????, ??????
?????????. ??????: I ? ???? ?????; II ?
??? ????????? ?????????? ???????? ?? ?????????
????? ?????; III ? ??????? ? ??????; IV ?
? ?????????? ???????? ???????? ? ??????? ???????????? ????
????.
5. ??????????? ????? ????????? ?? ????? ??????.
6. ???????? ? ??????? ????? ???????? ??????? ????????? ??????????.
7. ??????? ????????? ????????????? ????????.
?????? ?? ??????? ???????? ???????? ????, ????? ???????? ????????? ????????? ??????????????? ???????:
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# 56 #
(1)
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?.?. ?????????, ?.?. ????????. ????????? ????? ???????????? ???????????? ??????? ? ??????????????? ?????
????? x(l,t) ? ???????????? ???????? ????????, ?(l,t), u (l,t), T?(l,t) ? ?????????, ????????
? ??????????? ??????? ?????; T1c(l,t), T2c(l,t) ? ??????????? ??????????? ? ???????????
??????? ???????????? ?????; t, l ? ????????? ? ???????????????? ??????????.
????????? ???????
?
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D 3 , T? ( 0 , t )
D 4 , Tc1 ( L , t )
D 5 , Tc2 ( 0 , t )
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(12)
?? ???. 2?5 ?????????? ?????????? ???????? ???????????? ??????? ??? ????????? ????????? ???????? ??? ????????? ?(l), ???????????? x(l), ???????? u(l) ? ??????????? ??????? ????? T?(l). ??? ???? ?? ????????? ??????? ??????? ?(0)=720 ??/?3, x(0)=0,47, u(0)=5 ?/?,
T?(0)=450 °C, T1c(L)=270 °C. ????? ????????? ?????? ?????????? ? ????? ±5 % ??? ??????????
????????? ????????? ??????????.
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?????????? ????????????????? ?????? ? ???????????????? ? ??????????.
Copyright ??? «??? «??????» & ??? «A???????? K????-C?????»
???. 2. ??????? ????????????? ????????? ??????? ????? ?? ????? ???????
???. 3. ??????? ????????? ???????????? ?? ????? ???????
???. 4. ??????? ????????? ???????? ??????? ????? ?? ????? ???????
Copyright ??? «??? «??????» & ??? «A???????? K????-C?????»
?.?. ?????????, ?.?. ????????. ????????? ????? ???????????? ???????????? ??????? ? ??????????????? ?????
???. 5. ??????? ????????? ??????????? ??????? ????? ?? ????? ???????
?????? ??????????
[1] ?????? ?.?., ????????? ?.?., ?????????? ?.?., ???????? ?.?. ???????? ? ????????
???????????????????? ? ??????????. ?.: ??? «?????-???????????», 2000. 677 ?.
[2] ?????????? ?.?. // ???? ????? ??????? ????. ?.: ???????????, 1945. ? 6. ?. 87?106.
[3] ????????? ?.?. // ??????? ???????? ???????????????? ????????????. ?????????? ?????????????? ??????? ? ???????????. 2012. ? 3 (20). ?. 13?21.
[4] ????????? ?.?., ??????? ?.?., ????? ?.?. ????????????? ? ?????????????? ?????????? ?????????????? ??????. ???????????: ?????, 2012. 424 ?.
[5] ????????? ?.?., ???????? ?.?. ????????????? ? ??????????? ??????????? ?????? ?
??????????????? ???????????: ????. ??????? ??? ?????. ??????????: ??? ????, 2006. 210 ?.
Copyright ??? «??? «??????» & ??? «A???????? K????-C?????»
?.?. ?????????, ?.?. ????????. ????????? ????? ???????????? ???????????? ??????? ? ??????????????? ?????
Numerical Research Method
of Stationary Modes in Technological Furnaces
Nikolay D. Demidenkoa and Ludmila V. Kulaginab
a
SDTB «Nauka» KSC SB RAS
53 Mira, Krasnoyarsk, 660049, Russia
b
Siberian Federal University,
79 Svobodny, Krasnoyarsk, 660041, Russia
In article we propose mathematical models for stationary and dynamic processes of technological
furnaces as object with distributed parameters. This mathematical model is based on the laws of
conservation of energy, mass and impulse and includes differential equations in private derivatives.
Computational investigation of stationary modes of tubular furnaces is conducted. Formulated
boundary-value problem for calculation concentration of combustible substance, density, speed,
temperature of the flue gas and temperature of the heated raw materials going on division in rectificative
column. Results of calculation technological parameters are presented. The proposed method can be
used at automation rectificative plant in petroleum-refining and petrochemical industry.
Keywords: mathematical modeling, distributed parameter systems, heat mass exchange, numerical
method.
Copyright ??? «??? «??????» & ??? «A???????? K????-C?????»
Journal of Siberian Federal University. Engineering & Technologies 1 (2014 7) 62-82
~~~
??? 697.34 : 532.551: 62408.8
Determining Hydraulic Friction Factor
for Pipeline Systems
Alex Y. Lipovka* and Yuri L. Lipovka
Siberian Federal University,
79 Svobodny, Krasnoyarsk, 660041, Russia
Received 21.11.2013, received in revised form 23.12.2013, accepted 04.02.2014
A comparative analysis of many well-known formulas for Darcy friction factor was carried out to
determine accuracy and computational costs. To ensure a smooth transition from laminar fl ow to
turbulent a cubic interpolation algorithm proposed to cover critical zone.
Keywords: hydraulic friction factor, critical zone, Darcy friction factor, pipeline systems,
interpolation.
Introduction
The core of all known methods of analyzing the hydrodynamic state in regulated pipeline
systems are methods of calculating flow distribution [1], [2], and all of them require calculation
of hydraulic friction factor ?, which depends on the surface of the pipe wall, and the flow mode of
the liquid. Determination of ? in the critical zone between laminar and transitional flows (Fig. 1)
is related to certain difficulties. The goal of this article is to systematize the known methods of
calculating ? and offer readers a general approach to the defi nition of ? on the whole range of
Reynolds numbers.
Models and algorithms used
Head loss in a steady flow of liquid in round pressure pipes is calculated using Darcy-Weisbach
equation
?? ??? ??
?
????
? ? ??
????
??
?
(1)
where l,dint ? length and inner pipe diameter, m; ?? ? sum of minor loss coefficients; v ? velocity of
fluid, m/s; ? ? gravitational acceleration, m/s2.
Equation (1) obviously shows importance of valid definition of friction factor, which has at least
the same impact weight as length of a pipe. When ?? = 0 deviations of both ? and l have linear impact
on total headloss.
*
© Siberian Federal University. All rights reserved
Corresponding author E-mail address: alex.lipovka@gmail.com
# 62 #
Copyright ??? «??? «??????» & ??? «A???????? K????-C?????»
Alex Y. Lipovka and Yuri L. Lipovka. Determining Hydraulic Friction Factor for Pipeline Systems
Fig. 1. Classical Moody chart for friction factor as function of k_e/d_int and Re reproduced with proposed model
for critical zone
For laminar flow, with small Reynolds number Re < 2300, headloss depends on physical properties
of fluid (viscosity and density) and its velocity, and does not depend on pipe inner walls roughness
height, hydraulic friction factor is given by Poiseuille equation (1840)
? ? ???‡?
(2)
For turbulent flow in smooth pipes (the roughness of inner tube surface covered with laminar
sublayer) Blasius (1913) equation can be used, which is valid for 4000 ? Re ? 100000
? ? ???????‡???? ?
(3)
For hydraulically smooth pipes Prandtl (1932) proposed formula
?
??
(4)
? ? ???‡ ??? ? ????
For hydraulically smooth pipes also known Altshul equation (Re ? 104)
? ? ??????? Ћ‰‡ ? ??????
(5)
and Nikuradse equation (Re ? 105)
? ? ?????? ? ??????‡????? ?
(6)
Colebrook-White (1939) equation describes behaviour of hydraulic friction factor with Re > 4000
in conduits that are flowing completely full of fluid for smooth and rough pipes.
# 63 #
Copyright ??? «??? «??????» & ??? «A???????? K????-C?????»
Alex Y. Lipovka and Yuri L. Lipovka. Determining Hydraulic Friction Factor for Pipeline Systems
?
??
? ?? Ћ‘‰?? ?
??
????
?
??
??? ???? ‡ ??
(7)
where k? ? roughness height of inner tube surface, m.
Because of implicit nature of Colebrook equation (7) ? is obtained either numerically, or by
composing approximation formulas. Recently, the Lambert W function was used to get explicit form
of (7).
For transition zone of turbulent flow between smooth and rough pipes Altshul equation can be
used in hydraulic calculations of thermal pipeline networks
? ? ???? ?
??
???? ????
?
? ?
????
‡
(8)
For turbulent zone in the area of quadratic law of flow Prandtl-Nikuradse formula can be used
?
??
????? ? ?Ћ‰
(9)
???? ?
?
??
and Shifrinson formula
? ? ???? ?
?? ????
? ?
????
(10)
Some of the other most known equations for friction factor are:
? Moody equation (1947)
106
??
? ? ?????? ?? ? ?? ? 10
?
?
???? ‡
4
??
?
??
(11)
? Wood equation (1966)
? ? ????? ?
where
\ ? ???? ?
?? ?????
??
?? ???? ?\
? ???? ?
‡ ?
?
? ? ?? ?
?
????
????
????
?? ?????
?
?
????
(12)
(13)
? Eck equation (1973)
?
??
? ??Ћ‰ ?
??
??
? ??
????????? ‡
(14)
? Churchill equation (1973)
?
??
? ??Ћ‰ ?
??
? ???
? ? ? ??
????????
‡
(15)
? Jain and Swamee equation (1976)
?
??
? ??Ћ‰ ?
??
????
?
??
??????? ‡???
# 64 #
(16)
Copyright ??? «??? «??????» & ??? «A???????? K????-C?????»
Alex Y. Lipovka and Yuri L. Lipovka. Determining Hydraulic Friction Factor for Pipeline Systems
? Jain equation (1976)
?
??
? ??Ћ‰ ?
??
????? ???
??
? ??
?????????
‡
(17)
? another Churchill equation (1977)
?
??
? ??
?
? ? ? ?? ? ?
? ?
???
?4? ? 4? ?
‡
where
(18)
??
? ???
??
4? ? ??????? Ћђ ?? ? ? ????
?? ?
‡
????
4? ? ?
????? ??
? ?
‡
(19)
(20)
? Chen equation (1979)
?
??
? ??Ћ‰ ?
?? 1?1098 5?8506
??
5?0452
1
?
lg ?
? 0?8981 ?? ?
?
?
??????????
‡
2?8257 ????
‡
(21)
? Round equation (1980)
?
??
? ???Ћ‰ ?
‡
??
?
0?135 ‡ ? ? ? ? ???
????
(22)
? Barr equation (1981)
???
???
‡
????? Ћ‰ ?
?? ???
???
? ??Ћ‰ ???
?
?
??? ???
???? ?
???????
‡
??
?
???
???
‡ ?? ?
?
? ?
?? ????
???
???
?
(23)
? Zigrang and Sylvester equation (1982)
?
??
? ??Ћ‰ ?
??
????
??
????
??
??
?
Ћ‰ ?
?
Ћ‰ ?
? ??? ?
???????
??? ????
??? ???? ‡
‡
‡
(24)
? ??Ћ‰ ?
??
????
??
??
?
Ћ‰ ?
? ?? ?
‡
???????
??? ???? ‡
(25)
or
?
??
? Haaland equation (1983)
?
??
? ???? Ћ‰ ??
????
??
??
? ??
?
??? ????
‡
(26)
? Serghides equation (1984)
?
?\? ? \? ?
? ? ?\? ?
?
\? ? ?\? ? \?
??
(27)
# 65 #
Copyright ??? «??? «??????» & ??? «A???????? K????-C?????»
Alex Y. Lipovka and Yuri L. Lipovka. Determining Hydraulic Friction Factor for Pipeline Systems
or
??
?
?\? ? ??????
? ? ?????? ?
? ?
\? ? ?\? ? ?????
(28)
where
\? ? ?? Ћ‰ ?
??
??
? ??
??? ???? ‡
(29)
????\?
??
?
??
??? ????
‡
(30)
????\?
??
?
??
??? ????
‡
(31)
??
??
?????
?
?
??
??? ???? ‡?????
‡
(32)
\? ? ??Ћ‰ ?
\? ? ??Ћ‰ ?
? Manadilli equation (1997)
?
??
? ??Ћ‰ ?
? Monzon, Romeo and Royo equation (2002)
??
?
? ?? Ћ‰ ?
?????? ????
??
??????
??????
??
?????
??
?
Ћ‰ ?
Ћ‰ ??
?
‡
????????? ‡
??????????
??????
??????
??? ?
??
?
??????? ? ‡
(33)
? Dobromyslov equation (2004) [7]
?? ? ???
?
?
?
??? ????
??
??
Ћ‰???? ? ?
?
??? ????
Ћ‰ ?
?
??
?????? ?? ? ?? Ћ‰ ?
(34)
where
? ???
Ћ‰????
?
Ћ‰????? ?
(35)
????
?
??
(36)
??? b > 2, b = 2
???? ? ??? ?
? Goudar and Sonnad equation (2006)
?
??
? ?????? Ћђ ?
?????? ‡
?
??
(37)
?? ? ??????????
where
? ? ?????‡
??
? Ћђ??????? ‡??
????
? Rao and Kumar equation (2006) [6]
# 66 #
(38)
Copyright ??? «??? «??????» & ??? «A???????? K????-C?????»
Alex Y. Lipovka and Yuri L. Lipovka. Determining Hydraulic Friction Factor for Pipeline Systems
?
??
? ? Ћ‰ ?
????
??
? ? ?? ? ???
(39)
where
?????
? ? ? ? ??
? ? ??????
??
????? ? ? ? ?????
(40)
?????????
?? ?
??
??? ?
(41)
? ? ??????
(42)
? ? ??????
(43)
? Vatankhah and Kouchakzadeh equation (2008)
?
??
?????? ‡
? ?????? Ћђ ?
?
??
(44)
?? ? ???????????????
where
? ? ?????‡
??
? Ћђ??????? ‡??
????
(45)
? Buzzelli equation (2008)
?
‡
????
??
????
??
??
? ? ? Ћ‰ ?
?
(46)
where
??
?????? Ћђ?‡?? ? ????
??
?
????
(47)
?
?? ? ?????
?
??
‡ ? ???? ??
??? ????
(48)
? Goudar and Sonnad approximation (2008) [4]
?
where
?
? ? ?Ћђ ? ? ? ?????? ??
???
??
?????? ? ????? ?? ?
????? ? ? ???
(49)
???
?
??
???
?? ? ??? ? ? ? ??? ? ??
?
?
?
???
(50)
(51)
???
? ??? Ћђ ? ??
?
(52)
?
? ? ?? ? Ћђ ? ??
???
(53)
?
? ??? ? ????? ?
(54)
# 67 #
Copyright ??? «??? «??????» & ??? «A???????? K????-C?????»
Alex Y. Lipovka and Yuri L. Lipovka. Determining Hydraulic Friction Factor for Pipeline Systems
? ??? ?? ? Ћђ????
(55)
Ћђ???? ??
?
????
(56)
??
??
??
?
??? ? ????
(57)
??
?
?
Ћђ????
(58)
? Avci and Kargoz equation (2009)
??
???
?
?
?Ћђ?‡? ? Ћђ ?? ? ???? ‡ ? ?? ? ??? ? ???
????
????
??? ?
(59)
? Evangleids, Papaevangelou and Tzimopoulos equation (2010)
??
?????? ? ????????? ?? ? Ћ‰ ‡??
?Ћ‰ ?
??
????? ?
?
??
????? ???? ‡??????
?
(60)
? Brki? solution based on Lambert W-function (2011) [5]
?
where
??
? ?? Ћ‰ ?
? ? Ћђ ?
??
???? ?
?
??
???? ????
??
??
??
??? ??
????? Ћђ ?
?
Ћђ?? ? ??? ???
(61)
(62)
Didier Clamond [3] proposed (2009) a special algorithm of iterative calculation of ?, which
gives accuracy close to limits of computer type double after two iterations. It requires calculation of
logarithm once for initial estimation and one time per iteration.
? ? ?????
(63)
where
????
??
?
????
(64)
?? ? ??????????????????????????
(65)
?? ? Ћђ???? ? ?????????????????????
(66)
? ??? ?? ? ????
(67)
Ћђ??? ? ???? ? ? ??? ??
? ? ?? ? ???
? ??????????????
?? ? ?? ? ? ??? ??? ???? ? ????? ? ???? ?
????????
???
? ? ?? ? ? ??? ? ???? ? ?
?
????
# 68 #
(68)
(69)
Copyright ??? «??? «??????» & ??? «A???????? K????-C?????»
Alex Y. Lipovka and Yuri L. Lipovka. Determining Hydraulic Friction Factor for Pipeline Systems
? ??? ???????????????????? ????
(70)
Hydraulic regime in critical zone is neither laminar, nor turbulent. It is complex and unstable,
and thus, there are no formulas to describe friction factor for this zone. It is often suggested to
exclude calculations in this area. However, sustainable mathematical model requires smooth and
continuous functions. To solve this problem we can construct interpolation curve between two
regimes ? laminar and turbulent. Dunlop cubic interpolation for 2000 ? Re ? 4000 is widely adopted,
with its coefficients set to match boundary equations of Poiseiulle for laminar flow and Swameeand-Jain for turbulent.
? ? ?? ? ?? ? ?? ? ?? ? ??
(71)
where
? ? ???????? Ћђ ?
? ?
Ќ?
????
?
??
??? †??? ???????
Ќ?
????
? ??? ?
??? †??? ‡
(73)
? ??? ?
? ?? ?
(72)
(74)
??????????
??
? ?
(75)
‡
?
????
(76)
? ? ? ? ?
(77)
? ? ????? ? ?? ? ??? ?
(78)
? ? ?????? ? ?? ? ? ?
(79)
? ? ?????? ? ? ? ??? ??
(80)
?
Goal setting
Instability of hydraulic regime in critical zone does not allow analytical definition of friction
factor, which is why it is often suggested to exclude this regime from calculations. But, if we build
mathematical software to calculate flow distribution in complex pipeline networks, we prefer smooth
and continuous functions.
Main goal of mathematical modeling of ? in critical zone is building interpolation curve between
laminar flow and transition zone of turbulent flow.
Technique of calculation of hydraulic friction factor
A comparative analysis of existing formulas for Darcy friction factor for turbulent regime was
carried out. Value of hydraulic friction factor, calculated by known formulas was substituted to original
Colebrook-White equation (7), and absolute mean square deviation is shown on series of plots in fig.
2-6. Results show that lowest deviation (highest accuracy) gives Clamond method.
# 69 #
DidierClamond
Blasius(smooth)
Altshul(smooth)
Altshul
Nikuradse(smooth)
Prandtl,Nikuradse?
Shifrinson
Moody
Wood
Eck
Churchill
Jain,Swamee
Jain
Churchill,1977
Chen
Round
Barr
Zigrang,Sylvester
Haaland
Serghides
Manadilli
Monzon,Romeo,Royo
Goudar,Sonnad
Vatankhah,?
Buzelli
Avci,Kargoz
Evangleidsandother
Dobromyslov
Rao,Kumar
Goudar,Sonnad,2008
Brki?
8,84E?16
3,21E+00
1,82E+00
1,34E?02
1,73E+00
6,92E?01
6,92E?01
4,76E?02
5,62E?02
3,39E?02
1,33E?02
1,21E?02
1,11E?02
1,32E?02
3,77E?03
6,25E?02
3,92E?02
3,87E?04
1,39E?02
4,89E?06
1,30E?02
4,07E?04
2,35E?03
3,77E?04
5,21E?04
1,47E?02
5,53E?03
6,68E?02
6,92E?01
4,56E?13
1,60E?02
DidierClamond
Blasius(smooth)
Altshul(smooth)
Altshul
Nikuradse(smooth)
Prandtl,Nikuradse?
Shifrinson
Moody
Wood
Eck
Churchill
Jain,Swamee
Jain
Churchill,1977
Chen
Round
Barr
Zigrang,Sylvester
Haaland
Serghides
Manadilli
Monzon,Romeo,Royo
Goudar,Sonnad
Vatankhah,?
Buzelli
Avci,Kargoz
Evangleidsandother
Dobromyslov
Rao,Kumar
Goudar,Sonnad,2008
Brki?
7,49E?16
3,55E+00
2,20E+00
3,15E?03
2,11E+00
1,54E?01
1,59E?01
1,37E?02
1,75E?02
3,03E?02
2,05E?02
2,07E?02
1,91E?02
2,08E?02
9,83E?04
5,42E?03
1,73E?02
9,92E?05
1,45E?03
3,80E?08
1,84E?02
4,76E?04
1,46E?03
2,84E?04
7,29E?05
1,21E?02
1,92E?03
5,00E?02
1,54E?01
1,53E?14
1,96E?02
DidierClamond
Blasius(smooth)
Altshul(smooth)
Altshul
Nikuradse(smooth)
Prandtl,Nikuradse?
Shifrinson
Moody
Wood
Eck
Churchill
Jain,Swamee
Jain
Churchill,1977
Chen
Round
Barr
Zigrang,Sylvester
Haaland
Serghides
Manadilli
Monzon,Romeo,Royo
Goudar,Sonnad
Vatankhah,?
Buzelli
Avci,Kargoz
Evangleidsandother
Dobromyslov
Rao,Kumar
Goudar,Sonnad,2008
Brki?
6,57E?16
3,63E+00
2,29E+00
1,03E?03
2,20E+00
2,90E?02
3,36E?02
2,03E?03
1,41E?02
1,53E?02
1,24E?02
1,33E?02
1,15E?02
1,17E?02
1,78E?04
6,09E?03
5,01E?03
9,06E?06
2,31E?03
4,28E?09
1,24E?02
2,28E?04
8,19E?04
4,18E?05
1,12E?05
7,53E?03
3,86E?03
1,38E?02
2,88E?02
3,84E?16
1,19E?02
Copyright ??? «??? «??????» & ??? «A???????? K????-C?????»
Fig. 2. Absolute mean square deviation for k_e / d_int = 0,05
Fig. 3. Absolute mean square deviation for k_e / d_int = 0,01
Fig. 4. Absolute mean square deviation for k_e / d_int = 0,001
Copyright ??? «??? «??????» & ??? «A???????? K????-C?????»
DidierClamond
Blasius(smooth)
Altshul(smooth)
Altshul
Nikuradse(smooth)
Prandtl,Nikuradse?
Shifrinson
Moody
Wood
Eck
Churchill
Jain,Swamee
Jain
Churchill,1977
Chen
Round
Barr
Zigrang,Sylvester
Haaland
Serghides
Manadilli
Monzon,Romeo,?
Goudar,Sonnad
Vatankhah,?
Buzelli
Avci,Kargoz
Evangleidsand?
Dobromyslov
Rao,Kumar
Goudar,Sonnad,?
Brki?
9,47E?16
2,57E+00
1,16E+00
1,52E?01
1,11E+00
1,46E+00
1,47E+00
5,30E?02
8,00E?02
6,57E?02
9,98E?03
9,05E?03
8,33E?03
9,77E?03
4,33E?03
1,37E?01
4,86E?02
1,29E?03
2,03E?02
2,73E?05
9,99E?03
4,96E?04
2,42E?03
4,01E?04
5,02E?04
6,51E?03
5,56E?03
4,64E?02
1,46E+00
7,09E?13
9,25E?03
Alex Y. Lipovka and Yuri L. Lipovka. Determining Hydraulic Friction Factor for Pipeline Systems
DidierClamond
Blasius(smooth)
Altshul(smooth)
Altshul
Nikuradse(smooth)
Prandtl,Nikuradse?
Shifrinson
Moody
Wood
Eck
Churchill
Jain,Swamee
Jain
Churchill,1977
Chen
Round
Barr
Zigrang,Sylvester
Haaland
Serghides
Manadilli
Monzon,Romeo,?
Goudar,Sonnad
Vatankhah,?
Buzelli
Avci,Kargoz
Evangleidsandother
Dobromyslov
Rao,Kumar
Goudar,Sonnad,2008
Brki?
8,93E?16
1,55E+00
9,74E?02
1,17E+00
1,21E?01
2,47E+00
2,49E+00
1,62E?01
1,86E?01
1,61E?01
2,04E?02
1,93E?02
1,79E?02
1,99E?02
2,05E?03
8,79E?02
1,70E?02
1,43E?03
1,30E?02
4,62E?05
8,54E?03
4,94E?04
1,28E?03
3,28E?04
2,44E?04
1,50E?02
4,95E?03
1,07E?01
2,47E+00
7,33E?13
2,87E?03
Fig. 5. Absolute mean square deviation for k_e / d_int = 0,0001
Fig. 6. Absolute mean square deviation for k_e / d_int = 0,000001
It is clear that Clamond method gives highest accuracy for all ranges of k_e / d_int . Second
place goes to method of Goudar and Sonnad (2008), in the smooth pipes zone it gives almost identical
accuracy, and for the rest of turbulent flow its absolute mean square deviation is 3 degrees higher. It
should be noted that both methods provide much better accuracy than rest of researched functions.
Relative CPU time was also compared. Code for SciLab was written for all functions and the
required computational time was measured using timer() function. Figure 7 shows bar-plot with results
expressed in percents.
Results, obtained from Clamond method, were treated as the most accurate, and other results
? ??
were compared to them afterwards. Relative deviation ??? ??? ?? ???????? ? ???? is shown on series of
???????
plots on figures 8-22. Five series of calculation were made for different k? / dint: 0,000001; 0,0001; 0,001;
0,01; 0,05. To provide a better overview and innerview of results each of the plots is introduced in three
scales ? fullscale and zoomed (with relative deviation axis upper limit set to 10% and to 1%).
These plots (figures 8-22) provide an interesting insight on behavior of different equations for
hydraulic friction factor, but still does not give a clear criteria to consider accuracy. That criteria would
be mean square deviation of given results from ideal (which is Clamond solution in our case). Futher
calculations were carried out and results are shown on bar-plots in figures 23-27.
# 71 #
Copyright ??? «??? «??????» & ??? «A???????? K????-C?????»
Alex Y. Lipovka and Yuri L. Lipovka. Determining Hydraulic Friction Factor for Pipeline Systems
100
100
90
82
75
80
70
62
57
60
50
40
32
25
30
20
16
56
56
40
31
35
39 40 41 40 38
73
53
50
39
39
57
45
40
32 33
54
28
18
Dobromyslov
Rao,Kumar
Goudar,Sonnad,2008
Brki?
0
DidierClamond
Blasius(smooth)
Altshul(smooth)
Altshul
Nikuradse(smooth)
Prandtl,Nikuradse(turbulent?
Shifrinson
Moody
Wood
Eck
Churchill
Jain,Swamee
Jain
Churchill,1977
Chen
Round
Barr
Zigrang,Sylvester
Haaland
Serghides
Manadilli
Monzon,Romeo,Royo
Goudar,Sonnad
Vatankhah,Kouchakzadeh
Buzelli
Avci,Kargoz
10
Fig. 7. Relative CPU time to compute friction factor
One way to describe ? in critical zone (fig. 1) is to build cubic interpolation function. There is
widely adopted cubic interpolation developed by Dunlop. He took Poiseuille equation for laminar flow
and Swamee-and-Jain equation for turbulent flow as boundary conditions.
In order to provide smooth transition from laminar regime to turbulent using more accurate
solution of Colebrook-White equation given by Clamond we propose use of general cubic interpolation
polynomial, which allows setting any functions as boundary conditions..
General cubic interpolation polynomial is given as
???? ????? ? ??? ??? ???? ?? ? ??? ??? ???? ?? ? ??? ??? ???? ? ? ? ? ?
(81)
We need to solve the following system of equations to find coefficients a, b, c, d.
???? ????? ? ? ?? ????? ? ?
???? ????? ? ? ?? ????? ? ?
? ? ??? ????? ? ? ??? ????? ??
?
????? ????? ? ? ??? ????? ??
(82)
Solving system of equations (82) for a, b, c, d gives:
???
??
????? ????? ? ? ?? ????? ?? ? ???? ????? ? ? ??? ????? ??????? ? ???? ??
(83)
(84)
????? ? ???? ??
????? ????? ? ? ?? ????? ?? ? ???? ????? ? ? ???? ????? ??????? ? ???? ??
????? ? ???? ??
(85)
? ? ??? ????? ?
# 72 #
Copyright ??? «??? «??????» & ??? «A???????? K????-C?????»
%
100
90
80
70
60
50
40
30
20
10
0
1,00E+03
1,00E+04
1,00E+05
1,00E+06
1,00E+07
1,00E+08
Re
Altshul(smooth)
Nikuradse(smooth)
Altshul
Blasius(smooth)
Prandtl,Nikuradse(turbulentflow)
Shifrinson
Moody
Wood
Eck
Churchill
Jain,Swamee
Jain
Churchill,1977
Chen
Round
Barr
Zigrang,Sylvester
Haaland
Serghides
Manadilli
Monzon,Romeo,Royo
Goudar,Sonnad
Vatankhah,Kouchakzadeh
Buzelli
Avci,Kargoz
Evangleids,Papaevangelou,Tzimopoulos
Dobromyslov
Rao,Kumar
Goudar,Sonnad,2008
Brki?
Fig. 8. Relative deviation for k_e / d_int = 0,05
Copyright ??? «??? «??????» & ??? «A???????? K????-C?????»
%
10
9
8
7
6
5
4
3
2
1
0
1,00E+03
1,00E+04
1,00E+05
1,00E+06
1,00E+07
1,00E+08
Re
Fig. 9. Relative deviation for k_e / d_int = 0,05 (upper limit set to 10 %)
1
0,9
0,8
0,7
0,6
0,5
0,4
0,3
0,2
0,1
0
1,00E+03
1,00E+04
1,00E+05
1,00E+06
Fig. 10. Relative deviation for k_e / d_int = 0,05 (upper limit set to 1 %)
1,00E+07
1,00E+08
Re
Copyright ??? «??? «??????» & ??? «A???????? K????-C?????»
%
100
90
80
70
60
50
40
30
20
10
0
1,00E+03
1,00E+04
1,00E+05
1,00E+06
1,00E+07
1,00E
Re
1,00E+06
1,00E+07
1,00E+
Re
Fig. 11. Relative deviation for k_e / d_int = 0,01
%
10
9
8
7
6
5
4
3
2
1
0
1,00E+03
1,00E+04
1,00E+05
Fig. 12. Relative deviation for k_e / d_int = 0,01 (upper limit set to 10 %)
%
1
0,9
0,8
0,7
0,6
0,5
0,4
0,3
0,2
0,1
0
1,00E+03
1,00E+04
1,00E+05
1,00E+06
Fig. 13. Relative deviation for k_e / d_int = 0,01 (upper limit set to 1 %)
1,00E+07
1,00E+
Re
Copyright ??? «??? «??????» & ??? «A???????? K????-C?????»
%
100
90
80
70
60
50
40
30
20
10
0
1,00E+03
1,00E+04
1,00E+05
1,00E+06
1,00E+07
1,00E+08
Re
1,00E+06
1,00E+07
1,00E+08
Re
1,00E+07
1,00E+08
Re
Fig. 14. Relative deviation for k_e / d_int = 0,001
%
10
9
8
7
6
5
4
3
2
1
0
1,00E+03
1,00E+04
1,00E+05
Fig. 15. Relative deviation for k_e / d_int = 0,001 (upper limit set to 10 %)
%
1
0,9
0,8
0,7
0,6
0,5
0,4
0,3
0,2
0,1
0
1,00E+03
1,00E+04
1,00E+05
1,00E+06
Fig. 16. Relative deviation for k_e / d_int = 0,001 (upper limit set to 1 %)
Copyright ??? «??? «??????» & ??? «A???????? K????-C?????»
%
100
90
80
70
60
50
40
30
20
10
0
1,00E+03
1,00E+04
1,00E+05
1,00E+06
1,00E+07
1,00E+08
Re
1,00E+07
1,00E+08
Re
Fig. 17. Relative deviation for k_e / d_int = 0,0001
%
10
9
8
7
6
5
4
3
2
1
0
1,00E+03
1,00E+04
1,00E+05
1,00E+06
Fig. 18. Relative deviation for k_e / d_int = 0,0001 (upper limit set to 10 %)
%
1
0,9
0,8
0,7
0,6
0,5
0,4
0,3
0,2
0,1
0
1,00E+03
1,00E+04
1,00E+05
1,00E+06
Fig. 19. Relative deviation for k_e / d_int = 0,0001 (upper limit set to 1 %)
1,00E+07
1,00E+08
Re
Copyright ??? «??? «??????» & ??? «A???????? K????-C?????»
%
100
90
80
70
60
50
40
30
20
10
0
1,00E+03
1,00E+04
1,00E+05
1,00E+06
1,00E+07
1,00E+08
Re
1,00E+06
1,00E+07
1,00E+08
Re
1,00E+07
1,00E+08
Re
Fig. 20. Relative deviation for k_e / d_int = 0,000001
%
10
9
8
7
6
5
4
3
2
1
0
1,00E+03
1,00E+04
1,00E+05
Fig. 21. Relative deviation for k_e / d_int = 0,000001 (upper limit set to 10 %)
%
1
0,9
0,8
0,7
0,6
0,5
0,4
0,3
0,2
0,1
0
1,00E+03
1,00E+04
1,00E+05
1,00E+06
Fig. 22. Relative deviation for k_e / d_int = 0,000001 (upper limit set to 1 %)
100,0
90,0
80,0
70,0
60,0
50,0
40,0
30,0
20,0
10,0
0,0
Fig. 24. Mean square deviation for k_e / d_int = 0,01
Dobromyslov
Rao,Kumar
Goudar,Sonnad,2008
Brki?
3,7
1,0
0,8
0,8
0,8
0,8
0,1
8,3
0,3
5,04E-04
0,3
2,35E-07
0,8
0,1
0,1
7,13E-03
7,09E-04
2,7
0,4
0,8
1,7
5,44E-14
0,8
15,5
20,0
Dobromyslov
Rao,Kumar
Goudar,Sonnad,2008
Brki?
10,0
1,8
27,9
27,3
30,0
65,0
40,0
6,2
12,0
1,1
2,0
1,4
1,0
1,0
1,0
1,0
0,1
1,3
0,8
4,14E-03
0,2
1,55E-06
0,9
0,0
0,1
0,0
3,21E-03
1,6
0,1
2,4
6,1
6,31E-13
1,0
8,2
0,0
Blasius(smooth)
Altshul(smooth)
Altshul
Nikuradse(smooth)
Prandtl,Nikuradse(turbulent?
Shifrinson
Moody
Wood
Eck
Churchill
Jain,Swamee
Jain
Churchill,1977
Chen
Round
Barr
Zigrang,Sylvester
Haaland
Serghides
Manadilli
Monzon,Romeo,Royo
Goudar,Sonnad
Vatankhah,Kouchakzadeh
Buzelli
Avci,Kargoz
80,1
81,2
79,3
90,0
68,0
64,0
100,0
Blasius(smooth)
Altshul(smooth)
Altshul
Nikuradse(smooth)
Prandtl,Nikuradse?
Shifrinson
Moody
Wood
Eck
Churchill
Jain,Swamee
Jain
Churchill,1977
Chen
Round
Barr
Zigrang,Sylvester
Haaland
Serghides
Manadilli
Monzon,Romeo,Royo
Goudar,Sonnad
Vatankhah,Kouchakzadeh
Buzelli
Avci,Kargoz
Copyright ??? «??? «??????» & ??? «A???????? K????-C?????»
80,0
70,0
60,0
50,0
Fig. 23. Mean square deviation for k_e / d_int = 0,05
10,0
Fig. 26. Mean square deviation for k_e / d_int = 0,0001
2,57E-11
0,5
32,9
3,1
4,0
1,4
0,6
0,6
0,5
0,6
0,2
3,7
1,6
1,41E-02
0,6
1,75E-04
0,6
3,51E-02
0,1
1,51E-02
1,94E-02
1,7
0,3
3,0
18,8
1,64E-11
0,8
18,8
18,9
20,0
Dobromyslov
Rao,Kumar
Goudar,Sonnad,2008
Brki?
10,0
0,6
30,0
2,2
3,5
2,7
0,5
0,5
0,4
0,5
0,2
5,2
2,3
4,62E-02
0,8
9,45E-04
0,4
3,45E-02
0,1
1,60E-02
1,95E-02
0,4
0,2
1,7
0,0
43,1
50,9
42,4
50,0
24,4
33,0
36,5
0,0
Blasius(smooth)
Altshul(smooth)
Altshul
Nikuradse(smooth)
Prandtl,Nikuradse(turbulent?
Shifrinson
Moody
Wood
Eck
Churchill
Jain,Swamee
Jain
Churchill,1977
Chen
Round
Barr
Zigrang,Sylvester
Haaland
Serghides
Manadilli
Monzon,Romeo,Royo
Goudar,Sonnad
Vatankhah,Kouchakzadeh
Buzelli
Avci,Kargoz
60,0
Dobromyslov
Rao,Kumar
Goudar,Sonnad,2008
Brki?
20,0
5,8
30,0
37,3
40,0
23,7
50,0
Blasius(smooth)
Altshul(smooth)
Altshul
Nikuradse(smooth)
Prandtl,Nikuradse(turbulent?
Shifrinson
Moody
Wood
Eck
Churchill
Jain,Swamee
Jain
Churchill,1977
Chen
Round
Barr
Zigrang,Sylvester
Haaland
Serghides
Manadilli
Monzon,Romeo,Royo
Goudar,Sonnad
Vatankhah,Kouchakzadeh
Buzelli
Avci,Kargoz
Copyright ??? «??? «??????» & ??? «A???????? K????-C?????»
100,0
90,0
80,0
70,0
40,0
Fig. 25. Mean square deviation for k_e / d_int = 0,001
100,0
90,0
80,0
70,0
60,0
Copyright ??? «??? «??????» & ??? «A???????? K????-C?????»
Alex Y. Lipovka and Yuri L. Lipovka. Determining Hydraulic Friction Factor for Pipeline Systems
100,0
72,2
90,0
80,0
60,0
56,4
56,4
70,0
4,5
4,8
2,75E-11
0,3
Dobromyslov
Rao,Kumar
Goudar,Sonnad,2008
Brki?
0,0
Blasius(smooth)
Altshul(smooth)
Altshul
Nikuradse(smooth)
Prandtl,Nikuradse(turbulent?
Shifrinson
Moody
Wood
Eck
Churchill
Jain,Swamee
Jain
Churchill,1977
Chen
Round
Barr
Zigrang,Sylvester
Haaland
Serghides
Manadilli
Monzon,Romeo,Royo
Goudar,Sonnad
Vatankhah,Kouchakzadeh
Buzelli
Avci,Kargoz
10,0
2,1
20,0
15,4
6,2
0,7
0,7
0,7
0,7
9,21E-02
2,4
2,9
7,98E-02
0,6
0,0
0,2
0,0
0,1
1,82E-02
1,85E-02
0,6
0,2
4,3
30,0
20,1
40,0
23,1
50,0
Fig. 27. Mean square deviation for k_e / d_int = 0,000001
(86)
? ? ?? ????? ?
It is widely accepted in hydraulic calculations that critical zone lays in 2000 < Re < 4000, which
is why x1 = 2000, x2 = 4000.
Differential can be computed numerically
? ? ????? ?
??? ??? ????? ? ??????
?
????
(87)
Conclusion
Results of comparative analysis provide engineers and software developers a clear choice of
method to choose based on accuracy (figures 23-27) and computational time (fig. 7)
Method of Clamond to solve Colebrook-White equations clearly sets aside from other methods
because of its constant highly accurate results for all ranges of Reynolds number and k_e / d_int.
We propose easy to use algorithm of cubic interpolation for critical zone, which provides smooth
transition and allows using any chosen functions as boundary.
References
[1] Todini E., Pilati S. // Computer applications in water supply, B. Coulbeck and C. H. Orr, eds.,
Wiley, London, 1988. P. 1?20.
[2] Lipovka A., Lipovka Y. // Journal of Siberian Federal University. Engineering & Technologies
1 (2013 6) 28?35.
[3] Clamond D. // Ind. Eng. Chem. Res., 2009. Vol. 48. No. 7. P. 3665?3671.
[4] Goudar C.T., Sonnad J.R. // Hydrocarbon Processing Fluid Flow and Rotating Equipment
Special Report, 2008. P. 79?83.
# 81 #
Copyright ??? «??? «??????» & ??? «A???????? K????-C?????»
Alex Y. Lipovka and Yuri L. Lipovka. Determining Hydraulic Friction Factor for Pipeline Systems
[5] Brki?, Dejan. // Petroleum Science and Technology 29 (15), 2011. P. 1596?1602.
[6] Rao A.R., Kumar B. // Journal of Indian Water Works Association, Oct-Dec, 2006. P. 29?36.
[7] ??????????? ?.?. ??????? ??? ?????????????? ???????? ???????? ???? ?? ??????????
??????????. ?. 1. ?.: ??? «???????????? ??????», 2004.
??????????? ????????????
??????????????? ??????
? ?????????????? ????????
?.?. ???????, ?.?. ???????
????????? ??????????? ???????????,
??????, 660041, ??????????, ??. ?????????, 79
???????? ????????????? ?????? ?????? ????????? ?????? ??? ??????????? ????????????
??????????????? ?????? ? ?????? ? ????? ?????? ???????? ? ???????? ???????. ???
??????????? ???????? ???????? ?? ??????????? ?????? ? ??????????? ? ??????????? ????
????????? ???????? ?????????? ???????????? ?????? ????.
???????? ?????: ??????????? ??????????????? ??????, ??????????? ????, ??????????????
???????, ????????????.
Copyright ??? «??? «??????» & ??? «A???????? K????-C?????»
Journal of Siberian Federal University. Engineering & Technologies 1 (2014 7) 83-95
~~~
??? 662.612: 662.613: 66.088
Numerical Investigation
of Influence Thermal Preparation Coal
on Nitric Oxides Formation
in Combustion Process
Nelya S. Chernetskayaa,
Mikhail Yu. Chernetskiya,b* and Alexander A. Dektereva,b
a
Siberian Federal University
79 Svobodny, Krasnoyarsk, 660041, Russia
b
Kutateladze Institute of Thermophysics, SB RAS,
1 Lavrentev, Novosibirsk, 630090, Russia
Received 05.12.2013, received in revised form 21.01.2013, accepted 02.02.2014
Emissions of nitrogen oxides from coal combustion are a major environmental problem because
they have been shown to contribute to the formation of acid rain and photochemical smog.
Coal thermalpreparation before furnace delivery is effective method to reduce NOx emissions,
shown by experiments in small-scale facilities [1]. This paper presents the mathematical model
of burning thermal preparation coal. Validation of the model was carried out on laboratoryscale plant of All-Russia thermal engineering institute. Modeling of low-emissive burner with
preliminary heating coal dust is made for the purpose of search of burner optimal constructions
which provides low concentration of nitric oxides in the boiler. For modeling are used in-house
CFD code «SigmaFlow» [2].
Keywords: NOx, boiler, thermalpreparation coal, CFD.
Introduction
Existing problems of using coal in the boiler units to a large extent can be overcome by the
burning of coal dust to expose to heat treatment directly at the plant. Heat treatment of coal samples
leads to significant changes in the composition and properties of solid residue, which is to reduce the
yield of volatile substances and oxygen, to increase the caloric content of residual volatile matter and
calorific solid residues. Good flammability of products of heat treatment, high caloric content and their
reactivity, environmental cleanliness provide ample opportunities for use in thermal power plants the
pre-thermal preparation of coal before burning.
In 1980-1983 at the experimental facility of the institute, detailed studies of the influence of
preliminary heat of fuel preparation on the nitrogen oxides formation were carried out. Coal dust, with
varying degrees of metamorphism: berezovskiy lignite coal (Vdaf = 44.7 %, Ndaf = 0.8 %), ekibustuzskiy
*
© Siberian Federal University. All rights reserved
Corresponding author E-mail address: micch@yandex.ru
# 83 #
Copyright ??? «??? «??????» & ??? «A???????? K????-C?????»
Nelya S. Chernetskaya, Mikhail Y. Chernetskiy? Numerical Investigation of Influence Thermal Preparation Coal?
bituminous coal (Vdaf = 31.2 %, Ndaf = 1.5 %) and kuznetskiy lean coal (Vdaf = 13.5 %, Ndaf = 2.2 %)
were used. The studies were conducted in a wide range of temperature (until 820 єC) and heating
rate of air into the burner (? = 0.92?1.25). It was found that preheating of highly concentrated dust
suspension in a gaseous medium by a factor of the oxygen ? ? 0.05 until 600?820 єC outlet of fuel
nitrogen oxides can be reduced by 2-5 times. These studies were confirmed on the demonstration
plant of heat power 1.12 MW at combustion kuznetskiy low-caking coal. When heated dust to 585 єC
decrease emissions of nitrogen oxides is almost 2.5 times compared with conventional regime without
heating the dust reached. It is established that the heating of pulverized coal considerably improves
conditions: temperature increase in the axial zone of reverse flow at the initial part of a torch and in
the core burning is reduced almost by half the distance from the mouth of the burner to the zone of
maximum temperatures.
The data obtained were used to develop a full-scale pulverized-coal burner design with prethermal treatment of fuel. In 1983-1984 this burner heat output of 60 MW has been implemented and
tested on an industrial boiler TPP-210A. Further tests were carried out on other boiler units using the
system for heating fuel in burners. All tests confirmed the feasibility of using these burners. In all
cases it was possible to reduce nitrogen oxide emissions from 1200 and 1800 to 500 and 700 mg/m3
respectively at combustion of kuznetskiy lean and low-caking coals [3].
To further implement this technology on the boilers of various designs at burning coals of various
grades is necessary to conduct additional studies, including by means of numerical simulations. In this
paper the mathematical model and some results of thermal preparation coal combustion calculation are
examined.
Mathematical model
The model of non-isothermal incompressible multi-component gas was assumed as a model of
flow in combustion chamber. The gas flow in the studied problem is considered as established, thus all
equations are written in the steady-state form. It is assumed that combustion gases consist of N2, O2,
CO2, H2O and complex of volatiles VOL. The model includes the following equations:
equation of continuity
wU
’ Uv
wt
0;
(1)
equation of momentum balance
wU v
’ U v � v ’p ’( ? m ?t )
wt
( U U f )g
where the viscous stress tensor is
W ijm
W
W W
Є wui wu j 2 wuk є
) G ij
»,
3 wxk »ј
¬« wx j wxi
P «(
?t is the Reynolds stress tensor;
equation of i-th component concentration (mass fraction) transfer
# 84 #
(2)
Copyright ??? «??? «??????» & ??? «A???????? K????-C?????»
Nelya S. Chernetskaya, Mikhail Y. Chernetskiy? Numerical Investigation of Influence Thermal Preparation Coal?
§
·
P
wU fi
’ U v � f i ’ Ё ( Di t ) �’fi ё Si ,
Sci
wt
©
№
(3)
where D is the molecular diffusion constant, Sc ? turbulent Schmidt number, S ? source term describing reactions;
equation of energy transfer
§
·
c P
wU h
’ U v � h ’ Ё (O P t ) �’T ё
wt
Pr
t
©
№
Sch S R ,
(4)
Sch, SR are source terms describing, correspondingly, energy effect of reactions and radiation heat
transfer.
The modified high-Reynolds k-? model of turbulence (Chen k-? model) is used to describe the
turbulent characteristics of flow. The equations determining the kinetic energy of turbulence and its
dissipation rate have a form (Chen and Kim, 1987):
§
·
P
wU k
’ U v � k ’ Ё ( P t ) �’k ё G UH
wt
V
k
©
№
(5)
§
·
P
wUH
’ U v � H ’ Ё ( P t ) �’H ё
V
wt
H
©
№
2
2
H
H
G
C1 G C2 U C3
Uk
k
k
where G is the rate of turbulence generation:
G W t ij
w ui
,
w xj
turbulent viscosity is determined as
Pt
CP U
k2
H
.
Reynolds stress tensor has a form
W ijt
Є wui wu j 2
є
) G ij U k » .
3
¬« wx j wxi
ј»
Pt « (
The empirical constants C? = 0.09, ?k = 0.8, ?? = 1.15, ?1 = 1.15, C2 = 1.9, C3 = 0.25 are given in
the work (Chen and Kim, 1987). These constants are approved for a wide class of isothermal flows. The
form of k-? model is adapted for fully developed turbulent flows. In the near-wall region wall function
are used to save computational resources.
Temperature of mixture T in each point of flow field is found using the known local values of
enthalpy and mixture components content:
N
h = ? hm (T ) f m ,
m =1
# 85 #
Copyright ??? «??? «??????» & ??? «A???????? K????-C?????»
Nelya S. Chernetskaya, Mikhail Y. Chernetskiy? Numerical Investigation of Influence Thermal Preparation Coal?
where the dependencies of component enthalpy on temperature hm(T) is described by polynomials of
5th degree.
The radiation is the dominant heat transfer mechanism. The modeling of radiant energy transfer
is conducted basing on the P1 approximation of spherical harmonics for a grey medium (Siegel and
Howell, 1992). The advantage of this method is easiness of its matching with methods of aerodynamics
and heat transfer calculation realized in curvilinear meshes. The absorption coefficients were calculated
using the weighted-sum-of-gray-gases model.
Calculation of volatile fuel components combustion is based on the use of global irreversible
reactions between fuel and oxidant. To describe the reaction in turbulent flows with large mixing time
used a hybrid model using the kinetic model and the eddy break up model to determine the reaction
rate. According to this model as the resultant velocity is chosen the lowest from rates:
MIN ( Ri , KIN , Ri , EBU )
Ri
(6)
Coal Dust Combustion. The Lagrange method was used in the present work to model of coal dust
motion. During the modeling, the main forces acting on a particle were the force of phases interaction
(aerodynamic resistance force) and gravity force. As the coal particles moves, it is heated up and it
undergoes a number of process: extraction of residual moisture and volatile components, combustion
of volatile components and char. When the coal particle advances in the furnace, the reaction processes
of vaporization, coal pyrolysis and char combustion are considered. The coal particle consists of
four components: water, volatiles, carbon and ash. Vaporization of moisture from the coal particle is
described by the diffusion-limited model. Coal pyrolysis is modelled by a simple, one-step mechanism
and the volatile composition is assumed to be constant. The reaction rate of coal pyrolysis is taken from
experimental data.
Char combustion is controlled by the chemical surface reaction and the oxygen diffusion to the
particle. This model includes the factor ? which describes the transition between the char combustion
regime limited by the rate of oxygen diffusion and the regime is sufficiently limited by the chemical
reaction rate. Char particles are considered to burn at constant density and variable size.
The diameter change of a particle follows:
dG
dW
KC
S
2
U?
EC
O2
D
1
k .diff
D
D
k.kin.
(8)
(273/ Tg )*D K
k.kin
DK D
Nu
(7)
1
DK
D
* K sc
D
1
if D
k .kin
KD
k .diff
k.diff
if D
k .diff
k .kin
! KD
k.diff
NuD D
G
2 0.22 Pe0.66
K? e
E? / RT
# 86 #
(9)
Copyright ??? «??? «??????» & ??? «A???????? K????-C?????»
Nelya S. Chernetskaya, Mikhail Y. Chernetskiy? Numerical Investigation of Influence Thermal Preparation Coal?
?k is the density of the char particle (kg m-3); KSC is the char combustion rate (kg m-2*s-1); NuD is the
diffusion Nusselt number; D is the bulk molecular diffusion coefficient (m2/s); ?k, kin is the reaction-rate
coefficient for a chemical reaction (ms-1), ?k,diff is the reaction-rate coefficient for diffusion (ms-1).
The instantaneous burning rate of an individual particle is determined from temperature, velocity,
and size information by solving the energy balance for the particle, assuming a spherical, homogeneous,
reacting particle surrounded by a chemically frozen boundary layer (i.e., single-film model). Heat
losses from convection and radiation are considered, as well as the effects Stefan flow:
mpCp dTp
4Sr dt
2
p
4
HV (Trad
Tp4 ) Dconv (T Tp ) QH
4Srp2
(10)
?conv is the convection heat transfer coefficient:
Dconv
NuO
2rp
The correction to the heat-transfer equation due to Stefan flow is provided modification of Nusselt
number:
Pe 37
Pe Pe Pe
Nu 2 Pe2 2 960
4
2
where Pe is a Peclet number, Pe is a modified version of the Peclet number (i.e., the ratio of the
convective velocity of the net mass leaving the particle surface to the diffusive velocity of heat leaving
the surface).
When char burn, heat losses from convection is much larger than that is predicted for not burning
particles. In the model is used correlation coefficient Kcomb:
comb
Dconv
Dconv ?comb
K comb
145e
(11)
5000
Tg
comb
, ?conv ? are convective heat transfer coefficients for burning and not burning coal particle
respectively. Present model of coal particle combustion was validated in [4].
The influence of particles on the averaged gas motion, the gas components concentration and
enthalpy was taken into account on the base of PSI-cell method proposed by Crow (Crow et al.,
1977).
NOx Formation. In the process of NOx formation simulation three mechanisms are taken into
account: formation of thermal NOx according Zeldovich?s model (Zeldovich, 1946), formation of
prompt NOx according the Fenimore?s model (Fenimore, 1979) and formation of fuel NOx (Magel et al.,
1996). Additional equations for NO and intermediate hydrogen cyanide HCN transfer are introduced:
? conv
wU f NO
’ U vf NO ’ D’f NO S NO
wt
wU f HCN
’ U vf HCN ’ D’f HCN S HCN
wt
# 87 #
(12)
Copyright ??? «??? «??????» & ??? «A???????? K????-C?????»
Nelya S. Chernetskaya, Mikhail Y. Chernetskiy? Numerical Investigation of Influence Thermal Preparation Coal?
The source term in the equation of NO transfer describing thermal mechanism (Zeldovich, 1946)
may be written as
d > NO @
Sthermal-NOx = M NO
dt
where d[NO]/dt is calculated as following:
2 >O @ k1k2 >O2 @> N 2 @ - k-1k-2 > NO @
d > NO @
dt
2
k2 >O2 @ k-1 > NO @
(13)
Assuming the partial equilibrium for oxygen atom density [O], we obtain
>O @
36.64T 1/ 2 >O2 @
1/ 2
exp -27123 / T Reaction rate constants (m3/(mol?s)) are equal
k1 1.8 �108 exp -38370 / T k-1
3.8 �107 exp -425 / T k2
1.8 �10 4 � T � exp -4680 / T k-2
3.8 �103 � T � exp -20820 / T The prompt NOx forms in the presence of hydrocarbon radicals which prevail in fuels with high
molecular H:C rate. The mechanism of prompt NOx formation was described by Fenimore (1979).
Source term in the equation of NO transfer may be written
S prompt - NOx
M NO
d > NO @
dt
,
d[NO]/dt is calculated according the expression:
d > NO @
dt
a
§ E ·
k pr >O2 @ > N 2 @>VOL @ exp Ё - a ё ,
© RT №
(14)
where
k pr
1.2 �107 RT / p a 1
Ea
60 kcal � mol 1
Oxygen reaction order a depends on flame conditions (de Soete, 1975).
The fuel NOx is a result of reaction between oxygen and fuel nitrogen. In the process of coal fuel
gasification and char burn there takes place the transformation of nitrogen containing compounds to
NH3 (ammonia) and HCN (hydrogen cyanide). Depending on scheme of chemical reactions between
these compounds and combustion gases, formation of NO or N2 takes place.
Modified de Soete model (Magel et al., 1996), consisting of three global reactions, is realized to
calculate the fuel NOx :
# 88 #
Copyright ??? «??? «??????» & ??? «A???????? K????-C?????»
Nelya S. Chernetskaya, Mikhail Y. Chernetskiy? Numerical Investigation of Influence Thermal Preparation Coal?
dxHCN
3.5 �1010 exp(3370 / T ) xHCN xOa 2
dt
dxHCN
3 �1012 exp(30200 / T ) xHCN xNO
dt
dxNO
2.7 �106 exp(9466 / T ) xNO xCn H m
dt
(15)
Numerical algorithms. Conservation equations for gas phase are written down in a generalized
conservation law in a control volume. For the volume finite-difference analog of equation is written
down. For calculation of diffusion flow on the face of control volume centrally-difference scheme with
second order precision is employed.
At the approximation of convective terms Leonard?s scheme is employed that is substantially
minimizes the circuit viscosity. For connection velocity and pressure fields SIMPLE-C procedure is
employed.
Results
Validation of the model was carried out on laboratory-scale plant of All-Russia thermal
engineering institute. This plant consists of dust preheater in which coal is heated until specific
temperature, burner consisting of two coaxial cylinder and combustor. Coal-gas mixture from a
preheater moves on the internal flow path, air- on to the external. Original fuel compound is shown in
Table 1. Coal and gas compound after preheater are shown in Table 1, 2. Experiments and numerical
calculations are carried out with two coal sorts used: brown and black lean coals. The stationary
plant is shown in Fig. 1.
The calculation results for black coal are shown in Fig.2, 3. Fig. 3 shows concentration NOx along
the furnace. One can see satisfactory agreement with experimental data at volatile nitrogen to total
nitrogen ratio equal to one. In Fig. 4, 5 the comparison of calculated and experiment results for brown
Table 1. Coal composition
Black lean Coal
W
A
C
H
Until
1.8
After
0.3
O
22.7
67.8
2.79
25.1
70.77
1.12
S
N
V
2.72
0.45
1.66
13
0.67
0.45
1.49
4.4
Brown coal
Until
10.4
4.84
59.5
3.81
20.34
0.34
0.76
45.7
After
0.2
7.78
77.57
2.94
10.21
0.37
0.83
18
Table 2: Gas composition, %
CO2
CO
H2
15.8
10.6
6.6
26.9
18.7
5.1
CH4
N2
O2
NOx
0.9
61.2
0.5
0,005
Black lean Coal
1.52
44.7
0.3
0.016
Brown coal
# 89 #
Copyright ??? «??? «??????» & ??? «A???????? K????-C?????»
Fig. 1. The stationary plant
Fig. 2. Temperature (°C) Along the combustor (Black lean coal, ?tp=790 є?)
Fig. 3. NOx concentration,(mg/m3). Along the combustor
Copyright ??? «??? «??????» & ??? «A???????? K????-C?????»
Nelya S. Chernetskaya, Mikhail Y. Chernetskiy? Numerical Investigation of Influence Thermal Preparation Coal?
Fig. 4. Temperature (°C) along the combustor (Brown coal, ?tp=612 є?)
Fig. 5. NOx concentration,(mg/m3). Along the combustor
coal. The profiles of the temperature and NOx concentration are generally in good agreement with the
measurements.
For research heating, combustion coal and also influence of application of thermo-preparation
concentration for decrease of nitric oxides the geometrical model of a burner consisting from muffle
and furnace extension has been constructed. For research of initial development of a flame, and also,
for the purpose of approach to real working conditions of a burner the limited area of combustion space
was considered. The sizes of a burner are shown in Fig. 6. Computational grid of burner is presented
in Fig. 7.
For calculation there was used black coal the structure of which is represented in Table 3. The
analysis of the used coal is given in Table 4.
Fuel with grinding 30 micrometer and a part of primary air at the temperature 25 є? is tangentially
supplyed in to the an input 1 (Fig.6). In the cannel 2 supply of fuel (d=90 micrometer) and air at the
temperature 120 °C. Secondary air at the temperature 300 °C is supplied into the cannel 3. Results of
modeling in the form of distribution of temperature and concentration are resulted in Fig.8.
Then, with the aim to study the influence of use of burner with thermo-preparation on decrease of
nitric oxides concentration on an exit furnace chamber, modeling of boiler PK-39-IIM (see Fig.10) was
carried out. As the initial data for a boiler results of modeling of burner were employed presents above.
Comparison was made with a basic variant of boiler without thermo-preparation. The temperature on
# 91 #
Copyright ??? «??? «??????» & ??? «A???????? K????-C?????»
Fig. 6. Geometrical model, m
Fig. 7. Computational grid of burner
Table 4. Operating conditions of the pulverized-coal
combustion burner
Table 3. Coal composition
Characteristic, %
Cr
Hr
O
r
Nr
S
r
A
r
Wr
V
daf
Q r i,
kcal/kg
43
Fuel rate, kg/s
2,08
2,7
Total air flow, m /h
3
7
Temperature secondary air, °C
0,8
Temperature dust air mixture
0,6
Excess air coefficient
39,6
6,3
31,4
3917
467640
300
120
0,812
Copyright ??? «??? «??????» & ??? «A???????? K????-C?????»
Fig. 8. Module of velocity, m/s
Fig. 9. Temperature distribution, °C
Fig. 10. PK-39-IIM scheme
Copyright ??? «??? «??????» & ??? «A???????? K????-C?????»
Nelya S. Chernetskaya, Mikhail Y. Chernetskiy? Numerical Investigation of Influence Thermal Preparation Coal?
Fig. 11. The nitric oxides concentration upheight of furnace chamber
an exit of furnace was 1167 °C. Unburned carbon 0.17 %. NOx concentration on an exit from furnace
was 275 mg/nm3 (see Fig.11).
Conclusion
1. Applicability of the burning thermal preparation coal mathematical model has been validated by
comparing its predictions with the experimental data of a laboratory-scale pulverized-coal combustion
burner. The results of the calculation show good agreement with the measurements.
2. Numerical research of low emissive burner with step supply of air and preliminary heating
coal dust was executed. As a results of calculation optimal sizes of a burner providing heating air-andcoal mixture have been found. The given warming up provides an intensive exit of flying that give the
chance to lower nitric oxides concentration on an initial site of a flame.
3. On the basis of the data received at the modeling of low emissive burner modeling of boiler PK39-IIM with thermally prepared fuel was carried out. Application of the given technology of preliminary
heating coal dust provides to reduction of nitric oxides concentration in combustion products to level
of 275 mg/nm3.
Acknowledgement
This work was supported by the Ministry of Education and Science of the Russian Federation.
government contract ? 14.A18.21.1962 and Russian Foundation for Basic Research (Grant ? 14-0801079).
References
[1] Babiy V.I., Alaverdov P.I., Barbarash V.M. et. al. // Thermal Engineering. 1983. ? 9.
P. 10-13.
[2] Chernetskii, M. Yu. and Dekterev A.A. // Flame Combustion, Explosion, and Shock Waves.
2011. Vol. 47(3). P. 280?288.
# 94 #
Copyright ??? «??? «??????» & ??? «A???????? K????-C?????»
Nelya S. Chernetskaya, Mikhail Y. Chernetskiy? Numerical Investigation of Influence Thermal Preparation Coal?
[3] Babiy V.I., Verboveckiy E. Kh., Artem?ev Iu. P. // Thermal Engineering 2000. ? 10. P. 21-28.
[4] Chernetskiy M., Dekterev A., Gavrilov A. // Proc. of ICCHMT09. 2009. P. 409-412.
[5] Crow C.T., Sharma M.P., Stock D.E. // J. Fluids Engg., Trans. of the ASME. 1977. Vol. 99.
P. 25?332.
[6] Zeldovich Y.B., Sadovnikov P.Y., Frank-Kamenetckiy D.A. // 1947 AS USSR. P. 317.
[7] Fenimore C.P. // 17th Symp. (Int.) Comb., The Combustion Institute, Pittsburgh, 1979. P. 661.
[8] De Soete G.G. // In 15th Symp. (Int?l.) on Combustion, The Combustion Institute, 1975.
P. 1093.
[9] Magel H.C., Greul U., Schnell U. et. al. // In Proc. Joint Meeting of the Portuguese, British,
Spanish and Swedish Section of the Combustion Institute, Madeira, 1996. Vol 1. P. 123-130.
????????? ????????????
??????? ??????????????? ????
?? ??????????? ?????? ?????
? ???????? ???????
?.?. ??????????,
?.?. ??????????,?, ?.?. ?????????,?
?
????????? ??????????? ???????????,
??????, 660041, ??????????, ??. ?????????, 79
?
???????? ??????????? ??. ?.?. ??????????? ?? ???,
??????, 630090, ???????????, ??. ????????? ???????????, 1
??????? ??????? ????? ??? ???????? ????? ???????? ????? ?? ???????? ?????????????
???????, ??? ??? ??? ?????? ???????? ????????????? ????????? ?????? ? ?????.
??????????????? ???? ????? ??? ????????? ? ???????? ?????? ????????? ???????????
??????? ??????????? ??????? ?????. ? ?????? ?????? ???????????? ?????????????? ??????
??????? ???????? ????, ????????? ??????????????? ???????????????. ????????????
?????????????? ?????? ???? ????????? ? ?????????????? ?????????????????
??????, ?????????? ?? ??????? ?????? ???. ????????? ??????? ? ????? ???????????
????????????????? ??????????? ?????????? ? ?????????????? ??????????????? ??????
???????? ?????????????? ????????????? SigmaFlow.
???????? ?????: ?????? ?????, ???????? ??????, ??????????????? ????, ??????????????
?????????????.
Copyright ??? «??? «??????» & ??? «A???????? K????-C?????»
Journal of Siberian Federal University. Engineering & Technologies 1 (2014 7) 96-102
~~~
??? 621.74:669.23: 536. 42
???????????? ?????????????
? ??????????? ???????? ????? ??????? ???????
?.?. ?????????*,
?.?. ??????, ?.?. ???????
?
????????? ??????????? ???????????,
??????, 660041, ??????????, ??. ?????????, 79
?
??? «???????????»,
??????, 660027, ??????????, ???????????? ??????, 1
Received 10.10.2013, received in revised form 04.12.2013, accepted 12.14.2014
?? ?????? ??????????? ?????????? ANSYS ? ProCAST ??????????? ???????????? ??????
????? ??????? ? ??????????????? ????????? ? ????????? ????. ??????? ??????? ????????
?????????? ?????? ???????? ????????? ?? ??????? ?????????????? ???????. ???????????
?????????????? ???????????, ??????????? ??????? ???????? ????????? ????????, ? ?????
????????? ????????????? ? ?????????? ??????? ? ??????? ??????? ???????.
???????? ?????: ???????????? ?????? ?????, ??????????? ????????? ANSYS ? ProCAST,
?????? ???????, ?????????, ????????? ???, ???????? ?????????, ????????? ????????.
????????
? ???????????? ????????? ? ??????? ?? ??????????? ???????? ?????????? ??? ???????,
????????? ? ????????? ?????????, ??????????? ? ???????? ??????, ??????? ?? ???? ?? ?????????????? ???????????? ?????????, ? ????????? ????????????? ??-?? ????????? ???????. ???, ??? ????? ??????? ??????? ????? ????????? ??????? ?? ??????????? ? ? ??????
??????, ???? ? ???????????? ???????? ??????, ??????????? 15?20 %. ????????????? ?????
???????? ???????, ??? ???????, ? ??????????????? ???????? ?????????? ????????? ????????
??????????? ?????????, ?????????? ??????? ? ???????????? ???????? ?? ?????? ?????????????? ?????????. ??????? ???????? ????????????? ????? ??????? ??????? ?????????????
???????? ??????????????? ?????????????, ???????????? ???????? ????????? ? ???????????
?????????? ????????????? ? ??????????? ????????? ???????????????? ???????. ? ?????????, ????????????? ??????? ????????????? ????????????? ???????? ????????? ???????????
???????? ???????????? ???????? ????? ? ???????? ?? ????????? ??????????, ????????? ?????? ?? ????????? ????? ??????????, ??????? ??????????, ? ????? ????????? ?????????? ?????????????? ??????? ??????? ??????? ???????.
? ?????? ???????????? ?????????? ??????????????? ????????????? ????? ??????? ??????? ? ???????????? ????????? ? ?????????????? ??????????? ?????????? ANSYS ? ProCAST.
*
© Siberian Federal University. All rights reserved
Corresponding author E-mail address: a.skuratov@mail.ru
# 96 #
Copyright ??? «??? «??????» & ??? «A???????? K????-C?????»
?.?. ????????, ?.?. ?????? ???????????? ????????????? ? ??????????? ???????? ????? ??????? ???????
?? ???? ???? ???????? ??????????? ??? ???????????? ?????? ????????, ? ??????? ???????? ???????????????? ????????? (? ?????????, ????????????????? ? ????????) ???????? ??
?????? ???????? ????????? (???). ????????? ?????? ??????? ??????????????? ???? ???????
?? ??????????? ???????? ???????? ???????? ?????. ???????? ???? ???????????? ???????????
? ??????????? ???????????? ????????? ???????? ?????????? ???????? ???????, ???????????? ?????????????? ???????? ????????? ????????, ?????????? ??????? ? ?????????? ???????? ? ??????? ???????.
????????????? ?????
?? ???. 1 ???????? ????? ????????????? ???????? ???????????????? ????? ???????
? ???????????? ??????????????? [1]. ??????????????? ??????? ????????? ?????? ???????
??????????? ? ?????????: ? ???????????? ???? ?????????? ????????? ??????? ? ????????? ??? ??????????, ????? ???? ?????? ??????????? ? ??????? ????????? ????? ??????? ?
?????? ????????? ? ???????????? ????? ????????. ?? ?????????? ????? ????? ?????????????? ??????? ??? ????????? ?????????? ? ???????? ?????????. ????? ? ????????????
? ??????????????? ??????????? ??????? ?????? ??????? ????????? ????? ?????????????
? ?????????.
?????? ????????? ????????? ??????? ? ???????? ????? ????????? ? ?????????????? ???????????? ????????? ANSYS. ??????????? ???????? ProCAST ???????? ?????? ? ????????
?????????????? ???? ??? ?????????????? ??????? ????????????? ?????????? ?????????
?????, ????????????? ? ?????????? ??????? ???????. ???????, ??? ? ??????????? ??????? ProCAST ??? ??????? ??????? ? ????????? ??????????????? ???????????? ????? ????????
?????????, ??? ??????? ???????? ?????????? ? ????? ???????? ????????? ? ??? ? ?????????
????????.
?? ???. 2, ? ???????? ???????? ????????????? ?????? ???????, ????????? ? ???????????
????????? ANSYS ? ??????????????? ? ?????? ProCAST. ??????? ?????????????? ???????
???????? 0,300 ? 0,104 ? 0,074 ?. ????? ?????? ???????? ?? 131510 ????????? ? ???? ??????????.
? ?????? ??? ?????????? ????????????? ???????????? ?????????? ? ??????? ??????? ZOX (?????????????? ??????? ?? ???. 2, ?).
???. 1. ????? ???????? ????? ???????? ???????
# 97 #
Copyright ??? «??? «??????» & ??? «A???????? K????-C?????»
?.?. ????????, ?.?. ?????? ???????????? ????????????? ? ??????????? ???????? ????? ??????? ???????
???. 2. ???????? ?????? ??????? (?) ? ????????? ??????? ZOX (?)
???????? ????????????? ??????????? ? ??????? ?????????? ?????????? ??????????
????????????????, ??? ?????? ??????????? ??????????? ?? ??????? ????????? ???????? ???????? ? ????????? ?? ??? ????????? OZ:
??
?
?
??
?
??
?
??
?
? ????? ? ?
????? ? ? ????? ? ? ???? ??
??
????
????
????
????
????
????? ? ?? ???? ????
??
??
(1)
??
?????
? ? ???? ??? ;; qv (x,y,z,?) ? ???????, ??????????????? ???????? ???????? ????
??
??
????? ???????? ????????, ??; v? ? ???????? ???????? ??? ????????? (???????? ?????), ?/?.
???????, ??? ???????? qv ????? ??????????????? ????????? ???????? ????????????? ??????
[2]. ??????? ????????? (1) ??? ???????? ??????? ? ????????? ??????????? ??????????, ???
??? ???????? v? ? qv ????? ????.
?? ??????? ????????? ?????? ? ??????? XOY ??????????? ????????? ??????? ??????? ???? (??????????? ??????????? ??????? ?????? ??????????? ????????? ????????), ?? ????
????????? ???????????? ?????? ? ???????? ????.
? ????? ?????? ??????????? ????????????? ?? ??????????? ?????? ? ??????????? ????
??? ???????????? ?? ?????????
????? ?
?
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? ?? ??? ??? ?
?
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(2)
??? ?1 ? ?2 ? ?????????????? ??????????? ??????????? ?? ?????? ? ?????????? ?????? ????????? ? ?? ?? ???????? ?????? ? ??????????? ????, ??/(?2·?); ?u ? ?? ?????????????? ???????
?????? ????????? ? ??????? ??????????? ???????? ?????????? ?????? ????? ??????? ????????? ? ????????????????? ???????, ?; ? u ? ? ? ?????????????? ???????????? ???????????????? ?????? ????????? ? ???????, ??/(?·?).
??? ????? ?? ????????? (2), ??? ??????? ???????? ??? ????????? ??????????? ????????
?????? ????? ???????? ????????? ? ???????? ????????????? ????????????????? ???????.
? ??????? ?????? ??? ??????? ???????? ?1 ????????? ?????????? ?????? ??????????. ?????
# 98 #
Copyright ??? «??? «??????» & ??? «A???????? K????-C?????»
?.?. ????????, ?.?. ?????? ???????????? ????????????? ? ??????????? ???????? ????? ??????? ???????
????, ????????? ?? ??????????????, ??? ???????????? ????? ?????????? ?? ?????? ?????? ? ?
???????? ????? ??????? ?????????? ?? ?????????? ?????? [4]:
?
? ???
??? ??? ? ? ???? ????? ?
E? ?????
???????
??
?? ??? ???
(3)
??? ? ? ????? ?????????????, ?; ? ? ??????????, ???????????? ?? ??????? ? ??????????? ??????;
?? = ??(?) ? ??????? ???????? ?????? ?? ??????????? ???????, ?; t(x,?) ? ????????????? ????
????????; ?l = ?l(t) ? ????????????? ??????????? ????????? ?????????? ??????? ???????,
1/?.
??? ?????????? ?????????????? ??????? ???????, ??? ??????? ?????????? ???????????????? ?????????? ????????? ?????????? ?????????? ?? ????? ??????????? ??????? ????????? ??? ??????????????? ????? ????? ? ??????????? ?????? ????.
?????????? ? ?? ??????????
????????? ?????????????? ?????? ??????????? ???? ???????? ???????? ??????????
?? ?????????????? ??????: ???????? ????? v? (???????? ???????? ??? ?????????), ??????????? ???????????? ??????? T? ? ????????????? ?????????? ????????? q?. ? ????????
???????? ???????????? ?????????? ????????? ??????? ??????? ??????????? ????????
????????? ????????. ???????? ????????? ?????????? ?????????????? ??????????? ??????????????? ???????????? ?????????: v? ?? 0,02 ?? 0,012 ?/? (????? ????? ?? ?? 15 ?? 25 ?),
?? ? ?? 2042 ?? 2192 ?, q? ? ?? 100 ?? 600 ???/? 2. ???????? q? ??????????? ???????????????? ?????????? ? ??????? ???????? ???????????? ???, ??????? ????????? ? ????????? ??
200 ?? 3500 ??/(? 2 ·?). ???????, ???, ??????? ?????? ???? ? ?????????, ????? ?????????
?????????? ????????? ?????? q? ?? ??????????? ??????? ??????????? ????????? ?, ??????????????, ????????? ??????????????. ??????????????? ???????? ??????? ???????????
?? ?????? [5].
?? ???. 3,? ???????? ????????????? ???? ???????, ?????????? ? ??????? ???????? ???????,
??????????????? ???????????? ????????: v? = 0,02 ?/? (?? = 15 ?); T? = 2092 K; q? = 100 ???/?2.
?????, ??? ????? ?????????????? ??????????? ?????? ???? ?? ??? ?????????, ??? ????????
???????? ????????? ????????????? ????????? ????????.
????????? ?????? ??????? ??????? ?? ??????????? ???????? ?????????? (??? ???????????? ???? ??????) ?? ???????? ????????? ???????? ?????. ??????????? ???????????? ???????
????????? ???? ???? ?????????? ?, ??? ?????????, ????????????-????????? ??????? ?? ???????????? ?????? ?????????????? ? ????????????? ????????????? ? ?????????? ????????
? ?????? ???????. ???, ????????, ?????? ????????????? ????? ??? ?????????? T? ? v? ??????????????? ? ??????????? ??????????? ?????? ??????? ? ????????????? ??????? ??????. ???
???? ?????????? ???????? ?????? ??????? ? ??????? ????? ????????? ?? ???? ?????????????? ???????? q? ??????????? ???????? ?????????????? ?? ?????? ?????????? ??????? ??????
? ?????????????? ????????? ???????? ????????? ????????. ???????, ??? ???????? ???????
??????????? ???????? ?????????? ?????? ??????????? ? ?????????? ?????????????? ??????????? ? ?????? ????? ??????? ???????? [6].
?????? ???????? ??????????? ????????????-????????? ??????? ????????? ????????,
????????? ??????????? ??????????? ????? ? ???? ???????????? ????????? ??????? ???????
# 99 #
Copyright ??? «??? «??????» & ??? «A???????? K????-C?????»
?.?. ????????, ?.?. ?????? ???????????? ????????????? ? ??????????? ???????? ????? ??????? ???????
???. 3. ????????????? ???? ? ????????? ??????? ??????? ??? ??????? ????? 15 ? (?) ? 20 ? (?)
???. 4. ????????????? ???? ? ????????? ??????? ??????? ?? ????????? ????? ????????
(???. 3,?). ??? ???? ?????????? ????????? ??????????? ????????? ???????? ?????????? ????? ???????: v? = 0,016 ?/? (?? = 20 ?); T? = 2112 K; q? = 600 ???/?2.
????????? ?????? ??????? ???????????? ??????????? ???????? ????????, ?????????? ?
??????? ANSYS ? ProCAST. ???????????, ??? ???????? ? ????????? ???????? ?????????????
????? ? ????? ??????? ????????? ?????????? ?????? (???. 4). ???, ????????, ? ??????? ???????
# 100 #
Copyright ??? «??? «??????» & ??? «A???????? K????-C?????»
?.?. ????????, ?.?. ?????? ???????????? ????????????? ? ??????????? ???????? ????? ??????? ???????
???. 5. ????????????? ???? ? ????????? ??????? ??????? ? ???????? ????????? ???????? ????? ????????
?????? ? ???????????????
???? ?????????? ?????????????? ???????? ????????????? ?????????????? ???? ? ??????? ??????? ZOX ?? ????????? ?????. ??? ???? ?????????? ????? «?» ?? ??? OZ, ??????? ?? ???????? ??????? ??????? 2003 ?, ???????????? ???????? ????? ?????? ?????????? ? ??????? ??
0,005 ? (??. ???. 4).
?????????? ?????? ????????? ???????? ????????? ? ?????????????? ???????????? ??????
ProCAST, ??? ?????? ? ???????? ???????? ???????????? ??????? ????????? ???????? ? ??????????? ????????????? ??? ? ?????? ??????. ???????????, ??? ??? ????????? ???????? ?????????? ????? ????????????? ? ?????????? ???????? ??????? ??????? ?? ??????????. ????????
????????? ???????? ?? ????????? 3 % ?? ?????? ??????. ?? ???. 5 ????? ?????????? ??????
?????????? ???? ????????????? ????????? ????????, ??????? ????? ??????? ????? 8 ??.
??????????
?? ?????? ??????????? ?????????? ANSYS ? ProCAST ??????????? ???????????? ?????? ????? ??????? ? ???????????? ?????????. ????????????? ?????? ?????????? ????????????? ????? ? ???????? ??????? ??????? ?????????? ? ??????? ??????????? ??????? ???????? ??????.
??????? ??????? ???????? ?????????? ?????? ???????? ????????? ?? ??????? ????????? ???????: ???????? ????? ??? ???????? ??? ?????????, ??????????? ????????? ???????? ?
????????????? ?????????? ?????????. ? ?????????? ???????????? ????????????-?????????
???????????? ??????????? ??????????? ????????? ??????????????? ??????? ?????, ??????????? ????????? ????????????? ? ?????????? ???????, ? ????? ??????? ???????? ?????????
???????? ? ??????? ??????? ???????.
# 101 #
Copyright ??? «??? «??????» & ??? «A???????? K????-C?????»
?.?. ????????, ?.?. ?????? ???????????? ????????????? ? ??????????? ???????? ????? ??????? ???????
?????? ??????????
[1] ???????? ?.?. ?????????-???????? ???????????? ??????????? ???????? ? ???????. ?.:
???????????, 1974. 320 ?.
[2] ?????????? ?.?. ???????????? ??????. ?: ???????????, 1977. 160 ?.
[3] ???????? ?.?., ?????????? ?.?. ???????????????? ?????? ?????????? ? ??????????????? ????? ???????????? ????? ?????????: ??????? ???????. ??????????: ???-?? ???, 1986.
120 ?.
[4] ???????? ?.?. // ???????. ???. ? ????. ????. ????. ???????, 2011. 17 ?.
[5] ???????? ?.?. ??????????????? ???????? ???????? ??? ??????? ????????????: ?????????? ???. ?.: ???????????, 1989. 384 ?.
[6] ???????? ?. ?. ?????? ???????????? ???????. ?????? ???????? ??????. ?????????????
? ?????????? ???????: ??????? ??? ?????. ?.: ???-?? ???? ??. ?. ?. ???????, 1998. 360 ?.
Computer Simulation
and Optimization Casting Process
Ingot Platinum
Alexander P. Skuratova,
Dmitry I. Makhova and Yevgeny A. Pavlovb
a
Siberian Federal University,
79 Svobodny Str., Krasnoyarsk, 660041, Russia
b
Krastsvetmet
1 Transportny Proezd, Krasnoyarsk, 660027, Russia
On the basis of ANSYS software complexes and ProCAST developed computer model casting platinum
in a water cooled mold with movable bottom. We studied the influence of operating parameters of work
of the foundry installation on the crystallization of ingots. Installed quantitative dependences allowing
to reduce the magnitude of the shrink shell, and also exclude the surface and internal defects in the
ready ingot platinum.
Keywords: computer model casting, software packages ANSYS and ProCAST, platinum ingots, a water
cooled mold, mobile bottom, the regime parameters, shrink shell.
Copyright ??? «??? «??????» & ??? «A???????? K????-C?????»
Journal of Siberian Federal University. Engineering & Technologies 1 (2014 7) 103-108
~~~
??? 621.396:629.056.8
Satellite Microvibration
and Atmospheric Turbulence Effect
on Satellite-to-Ground Optical Communication Link
Alexander V. Vasilenko* and Valentin B. Kashkin
Siberian Federal University
79 Svobodny, Krasnoyarsk, 660041, Russia
Received 18.11.2013, received in revised form 10.01.2014, accepted 12.02.2014
Satellite-to-ground optical communication link bit error rate (BER) depending on atmospheric
propagation, pointing errors is considered. The theoretical and numerical estimations of BER for
GEO to Earth link under various conditions are proposed.
Keywords: satellite communication, lasercom, turbulence, tracking error, bit error rate.
Introduction
The most capacious communication links are needed to deliver data from low Earth orbit satellites
to ground data-processing centers. To provide near-realtime data transmission geostationary relay
satellites are used. Due to point-to-point link architecture it is advantageous to use free space optical
data transmission technics which provide more capacious communication links in comparison with
radio-frequency systems with same onboard equipment mass and energy consumption.
This paper is devoted to some aspects of developing GEO-Earth optical link, namely simultaneous
effect of satellite?s microvibration and atmospheric turbulence.
Theory
Assuming low atmospheric attenuation (i.e. ?clear sky? conditions) there are two major factors
on link performance ? microvibrations of telescope base and effect of atmospheric turbulence on
propagating laser beam. Both effects lead to statistical variance of received radiation intensity.
We assume that transmitter pitch and roll angle tracking errors due to microvibrations obey
normal distribution. Total tracking error may be described as:
x = x 2p + xr2 ,
(1)
where xp and xr are pitch angle and roll angle tracking errors respectively. Assuming that RMS errors
for each angle are equal and that errors are independent, probability density function of the error x,
measured from line of sight is described by Rayleigh distribution:
*
© Siberian Federal University. All rights reserved
Corresponding author E-mail address: a.v.vasilenko@mail.ru
# 103 #
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Alexander V. Vasilenko and Valentin B. Kashkin. Satellite Microvibration and Atmospheric Turbulence Effect?
f ( x) =
? x2 ?
x
exp ? ? 2 ? .
2
?
? 2? ?
(2)
Since in the beam intensity is distributed by normal distribution, received intensity at distance
z is [1]:
I ( z, ? ) =
? ?2 ?
p 2
exp ? ?2 2 ? ,
2
2
z ?w
? w ?
(3)
where p is transmitted power, ? is tracking error (line of sight misalignment), w is beam
divergence.
At the receiver plane, random transmitter?s tracking error leads to additional amplitude modulation
of the signal. Assuming that unmodulated signal is transmitted, probability distribution function of
received signal power is given by [2]:
g ( I ) = f ( I ( z , ? ) ?1 ) ?
d
(I ( z, ? )?1 ).
d?
(4)
As it seen from (3) that beam divergence w decrease leads to higher powers at receiver however
beam divergence w decrease to values comparable with tracking error will lead to unwanted signal
modulation.?
Besides modulation due to tracking error, atmospheric effects on laser beam must be considered.
Major atmospheric effects are:
? atomic and molecular absorption
? Rayleigh scattering
? aerosol absorption and scattering
? the effect of atmospheric turbulence
? astronomical aberration
We assume negligible probability of rescattering then photon which been removed from beam
reaches the receiver. Thus atomic and molecular absorption, Rayleigh scattering, aerosol absorption
and scattering lead only to signal attenuation. The effect of atmospheric turbulence results in random
amplitude modulation and obeys statements (5-9) [3]:
? ? ? I ? 1 2 ?2 ?
? ? ln ?
?+ ?I ? ?
1
?< I >? 2 ? ?
exp ? ? ?
f ? (I ) =
?
?
2? I2
2?? I2 I
?
?
??
??
(5)
? I2 = A(exp 2? ?2 ? 1)
(6)
?
? ?2 = 0.56k 7/6 sec(? )11/6 ? Cn2 (h)h5/6 dh
(7)
0
7/6
?
? Drx 2
? ?
A = ?1 + 1.1?
? ?
??
? ? hs cos(? ) ? ??
?1
# 104 #
(8)
Copyright ??? «??? «??????» & ??? «A???????? K????-C?????»
Alexander V. Vasilenko and Valentin B. Kashkin. Satellite Microvibration and Atmospheric Turbulence Effect?
? ? 2
?
2
? ? Cn (h)h dh ?
?
hs = ? ?0
?
?
2
5/6
? ? Cn (h)h dh ?
?0
?
6/7
(9)
Where f?(I) is modulation probability distribution function, <I> is received signal power assuming
no turbulence, ? is zenith angle, k is wavenumber, Drx is receiver aperture diameter, Cn2 is refractivity
structure parameter.
To describe Cn2 numerically we used model:
2
10
h ?
? 21 ?
?
Cn2 (h) = 0.00594 ? ? (10?5 h ) exp ? ?
?+
27
1000
? ?
?
?
h
h
?
?
?
?
+2.7 Ч10?16 exp ? ?
? + A0 exp ? ?
?
? 1500 ?
? 100 ?
(10)
Accounting atmospheric turbulence and tracking error effects signal probability distribution
function at the receiver may be described as conjunction:
?
fg ( I ) = ? g ( I ) f ? ( I ? x)dx .
(11)
0
To define an optimal divergence angle, we consider bit error rate ? an erroneous bit to total bit
received quantity ratio. In case of using on-off keying modulation, bit error rate may be estimated as
[2]:
1
? Q ?
BER(Q) = erfc ?
?,
2
? 2?
where erfc( x) =
1
?
?
? exp(?t
2
)dt and Q =
x
(12)
i1 ? i0
? 02 + ? 12
. In Q-factor definition there are:
i0,1 ? is electrical current, generated by photodetector when 0 and 1 bits are received respectively.
Since signal at the receiver is random we should consider mean BER given as:
?
3 I0
0
0
< BER >= ? BER(Q) g ( I )dI =
where I 0 =
? BER(Q) g ( I )dI
(13)
p 2
is intensity on a beam axis. The replacement of limit of integral in (13) is valid
z 2 ? w2
because g(I) is negligible for I > 3I0.<BER> depends on beam divergence as well and it?s minimum
corresponds to optimal divergence for given conditions.
Atmospheric conditions
The link model built allows calculating BER for given link parameters and environmental
conditions. Atmospheric parameters used in numerical calculations are shown at
Fig 1-3.
Solid line corresponds to measured Cn2 [4], dotted ? model approximation used in this
paper.
# 105 #
Copyright ??? «??? «??????» & ??? «A???????? K????-C?????»
Alexander V. Vasilenko and Valentin B. Kashkin. Satellite Microvibration and Atmospheric Turbulence Effect?
Fig. 1. Model aerosol particle size distribution [6]
Fig. 2. Model aerosol particle height distribution [6]
Solid line corresponds to meteorological range of visibility at the surface of 23 km, dotted line ? 5 km
Fig. 3. Cn vertical profile
Numerical results
Fig. 4, 5 provides calculated BER versus beam divergence for given parameters and conditions for
GEO-Earth downlink scenario (shown at Table 1).
It was assumed what there is continental aerosol mix with average refractive index 1.4+0.016i.
Vertical aerosol distribution was calculated using model [3] basing on meteorological range of visibility
at the surface.
Solid line corresponds to meteorological range of visibility at the surface of 23 km, dotted line ?
5 km
As is seen from Fig. 4, 5 there is BER minimum due to simultaneous effect of satellite microvibration
and atmospheric turbulence. The minimum of BER-curve corresponds to ?optimal? transmitter?s
divergence and strongly depends on meorological conditions. There is also slight relationship between
?optimal? transmitter?s and receiver design.
# 106 #
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Alexander V. Vasilenko and Valentin B. Kashkin. Satellite Microvibration and Atmospheric Turbulence Effect?
Table 1. Link parameters
Parameter
Value
Receiver?s latitude
56° N
RMS tracking error due to satellite microvibration
(roll)
RMS tracking error due to satellite microvibration
(pitch)
Carrier wavelength
1??
1??
1590 nm
Transmitter power
5W
Transmitting and receiving optics transmittance
0.75
Receiver optical filter bandpass
10 nm
Receiver detector type
APD
Modulation
On-off keying, 500 Mbps
Receiver effective aperture
350mm/750 mm
Fig. 4. Average BER versus transmitter beam divergence for receiver effective aperture 350 mm. Solid
line corresponds to meteorological range of visibility
at the surface of 23 km, dotted line ? 5 km
Fig. 5. Average BER versus transmitter beam divergence for receiver effective aperture750 mm
Thus worse expected meteorological conditions as well as receiver design must be taken into
account at early stages of onboard optical communication hardware development to reach the best
possible BER.
References
[1] Hecht E. Optics. Addison Wesley, 2002. 704 p.
[2] Papoulis. A., Pillai S.U. Probability, random variables, and stochastic processes. McGrawHill, 2002. 852 p.
[3] Hemmati H. Near-Earth Laser Communications. CRC Press, 2008. 374 p.
[4] Smith F. The Infrared & Electro-Optical Systems Handbook. V. 2. Atmospheric propagation
of radiation 1993. 322 p.
[5] Toyoshima M. // Proceedings of SPIE. 2007. Vol. 6551. P. 1-11.
# 107 #
Copyright ??? «??? «??????» & ??? «A???????? K????-C?????»
Alexander V. Vasilenko and Valentin B. Kashkin. Satellite Microvibration and Atmospheric Turbulence Effect?
[6] ???? ?.?. ??????????? ???????? ??????????? ??????. ?. 2. ?????????? ??????
?????????. ?., 1986. 253 ?.
??????????? ????????????? ?????????
???????????? ????????
? ??????????? ??????????????
?? ????? ????? ??????????? ?????????
«??????? ? ?????»
?.?. ?????????, ?.?. ??????
????????? ??????????? ???????????
??????, 660041, ??????????, ??. ?????????, 79
??????????? ?????? ????????? ?? ??????????? ??????? ?????? ??????????? ?????? ?????
«??????? ? ?????» ??????????? ???????????? ??????. ???????????? ?????????? ?????????
?????? ??????????? ??????? ?????? ??? ????????? ???????.
???????? ?????: ??????????? ?????, ???????? ?????, ??????????? ??????????????, ??????
????????, ??????????? ??????? ??????.
Copyright ??? «??? «??????» & ??? «A???????? K????-C?????»
Journal of Siberian Federal University. Engineering & Technologies 1 (2014 7) 109-115
~~~
??? 550.8:681.518
Construction of Geographic Information System
of Corporate Level in Geological Prospecting
Maxim A. Spikin*,
Vladimir A. Pozdnyakov and Sergey S. Hudyakov
Siberian Federal University
79 Svobodny, Krasnoyarsk, 660041, Russia
Received 02.12.2013, received in revised form 15.01.2014, accepted 21.02.2014
The paper describes the experience of application of geographic information technologies and
methods of processing of the Earth remote sensing data for solving practical tasks in the search
for hydrocarbon deposits. The most important feature of technological processes in this sphere is
the necessity to analyze large fl ows of spatially distributed data of different nature in real time.
We propose a service-oriented approach to organize a geographic information system (GIS) in
order to optimize the solution of tasks in nature management and exploration for oil and gas
studies.
Keywords: GIS, geoinformation technology, geographic information system, earth remote sensing
data, geodatabase.
Introduction
Currently, there is a tendency in exploration work that volumes of diverse data are constantly
increasing, the range of current tasks is expanding, the number of applied methods and technologies
of prospecting and exploration of mineral resources, particularly oil and gas, is growing. As a result,
there are difficulties in operational management and analysis of large flows of heterogeneous data
that leads to a slowdown in the speed of decision-making. Topological nature of information makes
it possible to create a single information-analytical system and integrate data of different production
services and departments. The integration of different data types and structures into a single
information space substantially increases the information content and the effectiveness of researches.
Exploration for hydrocarbon reserves in geographical and geological conditions of Eastern Siberia
is a very complex and fi nancially costly task. The necessity to optimize the processes of handling of
large amounts of heterogeneous data appeared because of the given factors. One of the solutions for
this task is the application of geographic information systems based on object-oriented technologies
and the Earth remote sensing data (RSE) [1-3]. The geographic information system that we offer
makes it possible to carry out a sophisticated spatial analysis of data, provides a wide range of tools
and supports operations with objects of industrial and fi nancial activities of oil companies, namely:
wells, pipelines, roads, hydrography objects and human settlements, infrastructure, geophysical
*
© Siberian Federal University. All rights reserved
Corresponding author E-mail address: spikin@mail.ru
# 109 #
Copyright ??? «??? «??????» & ??? «A???????? K????-C?????»
Maxim A. Spikin, Vladimir A. Pozdnyakov? Construction of Geographic Information System of Corporate Level?
profiles and seismic sounding points, the elements of oil fields infrastructure and natural ecosystems,
various documents and other data.
Problem statement
In exploration for oil and gas the effectiveness of managerial decision-making on basis of the
results of heterogeneous data interpretation depends directly on the quality and possibility of prompt
and complex use of retrospective and current data of geological, geophysical and environmental
studies. Such data typically have geospatial nature. Fig. 1 shows a general scheme of spatial data use
in processing of geological and geophysical information. However, even at the contemporary stage of
development of geographic information technologies a lot of organizations often allow inefficient use of
spatial and archival data in processing and interpretation of geological and geophysical information.
The analysis of this scheme can distinguish interrelated problems, namely: the inefficient use of
spatial data and the use of spatial data of bad quality, which significantly reduces the effectiveness of
processing and interpretation of geological data.
The problem of inefficient use of spatial data and geographic information technologies is primarily
related to the absence or lack of understanding of the processes of creation and processing of spatially
distributed information, lack of specialists in the field of digital cartography with a clear understanding
of the processes. One of the solutions for this problem can be engaging specialists into analytical
groups who have necessary skills and practical experience in the field of cartography and geographic
information technologies.
The problem of quality of spatial data also takes place. It implies the use of redundant, irrelevant
and sometimes false information and also reduces the effectiveness and accuracy of data processing.
Some departments of different oil and gas companies often use «raw» and unverified information
obtained from dubious sources while processing and interpreting geological and geophysical data.
[2] A typical example of this is a significant difference between coordinates and altitudes of points of
geophysical observations (pickets of geophysical profiles and boreholes) and their actual horizontal
and vertical positions. This kind of discrepancy may be due to both objective and subjective
reasons.
Fig. 1. A general scheme of spatial data use
# 110 #
Copyright ??? «??? «??????» & ??? «A???????? K????-C?????»
Maxim A. Spikin, Vladimir A. Pozdnyakov? Construction of Geographic Information System of Corporate Level?
j
Fig. 2. The example of discrepancy between spatial positions of seismic profiles and wells and their actual positions
Fig. 2 clearly shows the discrepancy between a spatial position of seismic profiles and wells and
their actual position. The true position of the objects was found by using the results of high-precision
satellite imagery. The analysis of spatial data revealed that more significant errors took place several
times, and it can be connected with improper determination of positions under severe conditions of
Eastern Siberia. It should be mentioned that this type of errors can be revealed and corrected by
verification on basis of modern high-precision remote sensing techniques [3].
Considering the problem of data quality it is also necessary to consider the question of openness of
spatial data and copyright to them. The data should be presented in an open form of digital cartographic
information and at the same time should keep enough information about the investigated objects.
GIS application as the way to improve
the effectiveness of exploration work
The present-day specialized geographic information systems are quite complex, functionally
redundant and costly software. This makes users work with software that is relatively easy to
understand and use, including, for example, vector and raster editors. It again leads to an inefficient
use of information resources. We think that the development of a specialized GIS and its application
in production departments will help to create a united geo-information resource on basis of which the
# 111 #
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Maxim A. Spikin, Vladimir A. Pozdnyakov? Construction of Geographic Information System of Corporate Level?
Fig. 3. The diagram of a service-oriented GIS of corporate level
results of field geological and geophysical research of the studied Earth interior objects, topographic
surveying, remote sensing data and other subject information will be fully integrated. This integration
will help to improve the quality of interaction between elements, get rid of redundancy and use function
of storage and data management most effectively.
The solution of the problem that is considered in the given article should be found in the area of
already known or developed specialized GIS and technologies of processing geological and geophysical
information. Typically, during the development of such GIS, structured data are stored in specialized
databases of corporate level, where the main integration component is a spatial component. In this case
the functions of management, storage and database access are assigned to the GIS.
Currently, web-mapping technologies that let a broad range of people use geological and
geophysical data without experience of work with complex specialized software and necessary
qualifications became widely used. Data services are used for implementation of this technology, and a
regular Internet browser serves as a tool for access to them. In this case, technical functioning of GIS
is hidden from the end user that facilitates not only using but servicing the system.
A GIS based on the service-oriented architecture (SOA) is a very convenient technological
solution to implement distributed systems of access to spatial data. When designing an SOA GIS
geographic data and functions are implemented as separate web services, which are then combined in
a layered data structure and rendered in a user interface, for example, in a Web browser using a «thin»
client technology. A functional diagram of such a service-oriented GIS of corporate level is shown in
Fig. 3.
It is necessary to point out the main advantages of using the concept of service-oriented architecture
(SOA) in GIS: all the logic of the system functioning and data storage are implemented on the server;
a clear structure of the information system: data providers, infrastructure and users; saving on the
cost of client software and system maintenance; high fault-tolerance and distribution of the elements
of the system; the ability to integrate with existing enterprise information systems. Without going into
technical details, the algorithm of actions of the service-oriented GIS user is as follows: the user opens
a web browser; logs into the system; gets his/her own set of data and functions in accordance with his/
# 112 #
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Maxim A. Spikin, Vladimir A. Pozdnyakov? Construction of Geographic Information System of Corporate Level?
Fig. 4. The example of a user interface for the access to GIS data
her roles (rights) in the system. The example of the developed on basis of SOA software interface for
the access to GIS data is presented in Fig. 4.
Thus, the use of service-oriented architecture for GIS development makes it possible to form
a new group of users of spatially distributed information that is a group of «special experts» in the
effective use of heterogeneous spatial data without specific knowledge about GIS. In other words, the
end user, using spatially distributed mapping and analysis services as layers and web applications, gets
a full-fledged GIS without using complex multi-specialized software.
Discussing results
The use of the proposed approach to the implementation of the tasks of processing geological
and geophysical information affects the quality of managerial decision-making. Practice shows that
in performing work the optimal basis for integration process is a spatial component, as most of the
studied objects have a clear position in three-dimensional coordinate space. In this case it is easy to
compare and interrelate objects of ground infrastructure and objects of geological environment (Fig. 5,
6). The integration framework in oil and gas exploration is normally the results of digital cartography
that include digital topographic base (including digital terrain and relief models), orthophotoplans on
basis of satellite imagery of high spatial resolution as (Fig. 5). This makes it possible to position different geological objects of study in the real three-dimensional coordinate space with maximum accuracy (Fig. 6), in particular, create reliable geostatistical and hydrodynamic models of hydrocarbon
deposits.
Fig. 6 is the example of using a superposition of some materials stored in specialized databases
for situational analysis of geological and geophysical information. Data and results of geological and
geophysical research are displayed in real three-dimensional coordinate space. In addition, all current
and retrospective attribute information about geological and geophysical objects under study (results
of well logging, materials of core hole research, the results of processing and interpreting seismic data,
etc.) is in full access.
# 113 #
Copyright ??? «??? «??????» & ??? «A???????? K????-C?????»
Fig. 5. The example of integrating orthotransformed results of high-precision satellite imagery (orthophotoplans)
and digital terrain models (DTM)
Fig. 6. The example of integration geological and geophysical data into a single project
Copyright ??? «??? «??????» & ??? «A???????? K????-C?????»
Maxim A. Spikin, Vladimir A. Pozdnyakov? Construction of Geographic Information System of Corporate Level?
Conclusion
It is shown that the use of service-oriented architecture of building GIS will optimize the process
of solving environmental problems in exploration for oil and gas. A scheme for implementing a serviceoriented enterprise GIS is offered. Completed testing of the system with respect to spatially distributed
data of geological and geophysical studies is made.
References
[1] Hudyakov S.S., Pozdnyakov V.A., Efimov A.S. // Geophysics (Seismic technologies-I). 2002.
P. 80?82.
[2] Hudyakov S.S., Pozdnyakov V.A. Efimov A.S. // Seismic technologies. 2004. ? 2. P. 35?37.
[3] Pozdnyakov V.A., Hudyakov S.S. // Seismic technologies. 2009. ? 3. P.83?86.
[4] Pozdnyakov V.A., Hudyakov S.S. // Journal of Siberian Federal University. Technique and
technologies 4 (2011 4) 419?428.
?????????? ????????????????? ???????
?????????????? ??????
??? ?????????? ?????????????????? ?????
?.?. ??????,
?.?. ?????????, ?.?. ???????
????????? ??????????? ???????????,
??????, 660041, ??????????, ??. ?????????, 79
? ?????? ??????? ???? ?????????? ????????????????? ?????????? ? ??????? ?????????
?????? ?????????????? ???????????? ????? ??? ??????? ???????????? ????? ??? ???????
????????????? ?????????????. ????????? ???????????? ??????????????? ????????? ?
???? ??????? ???????? ????????????? ????????????? ? ?????? ????????? ??????? ???????
?????? ???????????????-?????????????? ?????? ????????? ???????. ????????? ????????????????????? ?????? ? ??????????? ????????????????? ??????? (???) ??? ???????????
??????? ????? ?????????????????? ? ??? ?????????????????? ?????????????.
???????? ?????: ????????????????? ??????????,
????????????? ???????????? ?????, ???? ?????????.
?????????????????
???????,
Copyright ??? «??? «??????» & ??? «A???????? K????-C?????»
Journal of Siberian Federal University. Engineering & Technologies 1 (2014 7) 116-124
~~~
??? 130.2:62;141.2+62:1+620.9:001.891.57
?????????????? ? ???????? ??????????
??????????????????? ???????????
?.?. ???????,
?.?. ????????? *, ?.?. ?????????
a
??????????????? ???????????????
??????????? ???????????,
??????, 236022, ???????????, ??., ?????????, 1
?
????????? ??????????? ???????????
??????, 660041, ??????????, ??. ?????????, 79
?
Received 21.10.2013, received in revised form 09.11.2013, accepted 15.01.2014
???????????? ???????? ???????????? ?????????? ??????????????????? ???????????
(???????????? ??????????, ??????????????? ? ????????????) ????????? ??????????
??????????????, ?????????? ZP-??????, ZP-???????????? ? ZP-????????????.
???????? ?????: ?????????? ???????????????????, ??????????????, ?????????
????????????????, Z-?????????, ZP-??????, ZP-????????????, ZP-????????????.
??? ???????? ?? [1-10], ????????? ??????????? ???????? ???????????? ?????????? ??????????????????? ???????? ??????????? ????????: ???????????? ???? ?????? [1-3], ???????????? ?????????? [1-3], ??????????????? [4, 5] ? ???????????? [8]. ???????????? ?????????
?? ??? ????? ?????????? ? ??????????????? [7, 10] (?? ??????????? «potential») (???. 1). ???
???? ??? ???????????? ?????????? ???????????? ? ???????????? ? ??????? ???????????????
???????????? ????? ????????? ??????????? ???????-??????, ???????????? ??????? ???????
(??????, ?????, ?????????????, ???????????, ???????????, ?????, ???????? ??????????????,
????? ?????- ? ??????????, ???????? ????, ??????????? ????? ? ?.?.). ????? ? ??????????? ?????
?????? ????????, ???????????? ??????????????, ? ???????? ? ??????????????? ?????????????? ????????? ??????????? ??????? ? ????????????? ???????? ?????. ?????????????????
??????????? ???????????? ????????? ???????? ????, ??????????? ? ??????? ????? ??????
??????????, ? ????? ????????????? ??????????? [1].
??? ??????????????? ?????? ???????????? ??????? ????????? ???????????? ?????????? ????????? ???????????, ????????????? ? ??????????? ????????????? ?????????? ???????, ?? ???????? ???????? ?? ?????? ????????? ????????? ?????? ???? ????????? ?????????????????? ??????????? ??? ?????? ??? ??????????? ???????????????? [7,10]. ????????,
??? ????????????? ? ?????????????? ????????? ?????????????? ???????? ? ??????????? ?
*
© Siberian Federal University. All rights reserved
Corresponding author E-mail address: pvi.05@mail.ru
# 116 #
Copyright ??? «??? «??????» & ??? «A???????? K????-C?????»
?.?. ??????, ?.?. ?????????? ?????????????? ? ???????? ?????????? ??????????????????? ???????????
???. 1. ???????? ???????????? ?????????? ??????????????????? ? ????? ? ??? ?????????
??????????????
???????????? ????????????? ? ???????? ?????????? ?????????? ????????????????. ?????
??????? ???????? ????????????????? ???????????, ????????????? ? ???, ???, ?????? ????????, ??????? ???????????????? ?? ????? ???????? ???? ? ??????????????, ??? ????????
???????? ??????? «?????????????????», ??????? ????? ?? ??????? ?????????? ? ???????????
??????? ?????????? ? ??????????? ??????????. ?? ????? ?? ????????? ? ????????? «???????? ??????????????», ??????? ?? ?????? «?????????» ?????????? ?????????? ??????????
????? ? ? ??????????? ?????????? ??????????? ?? ???????????.
????? ???????, ? ???????? ???????????? ?????????? ??????????????????? ??? ??????????????? ????? ???????? ?????????, ????????????? ? ??????????? ?????????? ????????????????, ?? ???????? ???????? ?? ?????? ????????? ????????? ?????? ???? ?????????
?????????????????? ??????????? ??? ?????? ??????????? ???????????????? ???????? [7, 9].
?????????? ???????? ? ????????? ?????????????? ??????? ?????????? ????????????????
(???. 2).
????????? ???????????????? (????????? ????????? ????????????????) ? ?????????? ??
????????? ??????? ??????? ?????????? ??????? ????? ??????????????????? ??????????? (?
?????) ??? ?????????? ????????????????? ????????, ? ????? ???????, ? ???????????????????,
??????????????? ?????? ??????? ??????????? ?????????????? ?????????, ? ? ??????. ?????????????????? ??????????? ???????????? ??? ???????? ? ???????? ?? ???? ?? ?????????????
??? ??????????????? ?????? ????????? ???????????????? ?????????????. ??? ???? ? ????????
????????? ??????? ???? ??????, ?????????? ??? ???????????? ???????? ??????????????????
????????, ???? ?????? ??????? ??????????? ?????????????? ?????????. ????????? ?????????? ??????? ????????????, ? ????? ???????, ???????? ???? ?????? ?? ?????????????????? ?
???????, ?? ?????? ??????? ???????? ?????????? ????????????? ????????, ? ? ?????? ? ????????? ?????????? ????????????? ?????????? ? ??????? [7, 10].
# 117 #
Copyright ??? «??? «??????» & ??? «A???????? K????-C?????»
?.?. ??????, ?.?. ?????????? ?????????????? ? ???????? ?????????? ??????????????????? ???????????
???. 2. ? ??????? ?????????? ?????????? ???????????????? ???????????
??????? ???????? ?????????????? ??????? ?????? ??????? ?? ?????????????, ?????
??? ??????????? ???????????????? ??????????, ?? ????, ????? ?????????? ?? ???????????
??? ?????? ???????????????? ????????? ????? ??????? ???????????? ??????????????????? ? ????????? ?????????????? ????????? ?????????????????? ?????? ?????????, ???????
????? ?? ????, ???? ?? ? ??? ???? ??????????? ????? ?????? ?????????? ???????????????????. ??? ???? ????? ? ????????? ??? ?????????? ?? ???????????? ????????? ??????
???????: ??-??????, ?? ????? ????????? ??????? ??????????, ??? ????????? ???????????????? ??????????? ???????? ????????? ????????????, ?.?. ??? ????? ?????????? ??? ?????
??????????? ???????????????? ????????? ?????????????????; ??-??????, ?????? ?????????????? ????? ? ??? ???????????????? ??? ????? «?????? ?????????? ???????????????????»; ?-???????, ??? ??????????? ??????? ??????????? ?????? ??????????? ??????????????????? ?? ?????? ?????????? ???????????? ??????? ??????????? ???????????; ?-?????????,
??? ????????? ?????? ?????? ??????????????????, ???? ???????? ? ??????????? ??? ????????? ??????????? ???????????????? ???????? ?????????? ?????? ??????; ?-?????, ???
???????????? ????? ???????????? ??????????? ????????? ????????????????? ?????????
???????????????? ????? ???? ??????????? ? ???????????? ???????? ?????????? ???????????????????; ?-??????, ????? ??????? ????? ? ????????? ???????? ????????????? ?????
???? ?? ????????????? ??????????? ?????????????????? ????? ????? (??? ???? ?????????)
????????? ????????????????? (?? ????????? ?????????? ???????? ??? ??????? ?? ?????????? ??? ???????? ????), ??????? ? ???? ?? ?? 99 % ?? ????? ??????? ???????????????
????? ??????????????????.
??? ???? ????? ??????????? ??????????? ???? ?????????????? ???????, ????????????
???????? ???? ????????? ?????????, ?????????????? ? ??????? ????????? ?? ?????????
??????? ???????? ????????????? [1-3, 9, 10], ?????????? ??? Z-????????? (?? ?????? ?????
??????? ?????????? ??????? George Kingsley Zipf) ? ???????????? ????????? ??????? [7]:
'W1
f
f
і W (r )dr і W1 (r )dr ,
0
0
# 118 #
(1)
Copyright ??? «??? «??????» & ??? «A???????? K????-C?????»
?.?. ??????, ?.?. ?????????? ?????????????? ? ???????? ?????????? ??????????????????? ???????????
??? ?W1 ? ????????? ???????????????? ??????????? (???. 2);
W(r) ? ????????????????? ??????, ?????????? ??? ???????????? ???????? ?????????????????? ???????? (r ? ????);
W1(r) ? ?????? ??????? ??????????? ?????????????? ?????????, ?????????? ?? ??????
????????? ???? ?????? [3, 7, 8].
??? ????????? ???????? ???????? ??????????? ????????? ???????????? ??????????
??????????????????? (???????????? ???? ??????, ???????????? ??????????, ???????????????, ???????????? ? ?????????????? ?????????????????? ? ???. 1) ??????????? ???????????????? ??????? ???????????: ???????????? ???? ?????? [3, 10], ? ????? ???????-????????
[9, 10], GZ-???????? [4, 5, 10], ASR-???????? [8, 10] ? ZP-???????? [7, 10] (???. 3).
????? ???????, ?????? ??????????? ? ??????????? ????????? ?????????????? ??????
??????? ???????????? ZP-??????, ??? ??????? ?????????? ?????? ????????? ????????????
?????????? ???????????????????, ?????????????? ?? ????? ?????????????? ??? ??????????
ZP-????? ???????????????? ??????????? [7]. ??? ?????? «ZP-??????» («???-??-??????») ???????? ????? ???????????? ??????????? ?? ????? «?????? ? ??????? Z-??????????». ? ???????????? ? ???????? ? ???????? ??????? ????????? ???????? ? ???? ???????????? «ZP» ???????? ?? ??????????? «Z-Potential». ? ?????? ZP-??????? ????? ???????? ?????? Z-??????????,
???????????? ????????????? ????????. ?????? ??????? ? Z1-?????????: ? ???????? ?????????
??????????????? ???????? ??????????????? ?????????????, ??????????????? ?????? ???????
??????????? ?????????????? ?????????, ??????????? ? ????????? ????????????? ??????????.
?????? ??????? ? Z2-????????? ? ????? ? ???????? ????????? ??????????????? ???????? ??????????????? ?????????????, ??????????????? ?????? ??????? ??????????? ?????????????? ?????????, ??????????? ? ????????? ????????????? ?????????? ????? ZP-???????????? [7, 9, 10].
???. 3. ?????? ????????? ???????????? ?????????? ??????????????????? ???????????
# 119 #
Copyright ??? «??? «??????» & ??? «A???????? K????-C?????»
?.?. ??????, ?.?. ?????????? ?????????????? ? ???????? ?????????? ??????????????????? ???????????
???. 4. ????????? ? ???????? ???????? ZP-?????? ?????????????? ???????????: ??? ? ??????????
????????????? ????????; ?? ? ??????????????????
ZP-???? ??????????????? ????????????? ??? ??????? ??????? ??????????? ?? ?????????
?????????? ???????. ?? ????????????, ??? ?????????????????? ??????????? ? ????? ?????? ? ??????? ???? ?????? ?????????? ?? ????????, ??????????????? ??????? Z1-??????????,
? ????? ? Z2-??????????. ??? ???? ZP-???????????? ??????????????? ??? ??????? ???????
?? ?????? ????????? ????????? ?????????????? ??????????? ???????????, ???????????? ?
??????????? ?? ???????-?????????? [7]. ZP-????????????? ?????????? ????????? ?????????
?????????????????? ???????? ?????? ?????????????? ????? ?? ?????? ??????? ???????????? ???????? ????????????? ???????? ? ?????? ??????????????? ??????????? ?????????????????? [7, 10].
?? ???. 4 ???????? ????????? ZP-?????? ?????????????? ???????????. ?????????? ?????? ? ?????? ????????? ???? ?????? ??????????? ?? ??????????????????, ?????????? ? ????
???? ? ????? ?????? (????????? ??????????? ?????????? ?? ?????????? ????????? ???????????, ?????????????, ???????? ? ?????????????? ??????? ? ?????????? ??????????, ???# 120 #
Copyright ??? «??? «??????» & ??? «A???????? K????-C?????»
?.?. ??????, ?.?. ?????????? ?????????????? ? ???????? ?????????? ??????????????????? ???????????
?????? ? ????????????? ???????? ?????????????????? ????????, ?????????????? ?????????
? ????????? ???????? ??????????????? ?????????????, ??????? ???????????? ????????, ???????? ?????? ?????????? ????????????? ??????????, ZP-?????, Z-??????????, ??????????
ZP-???????????? ? ??.) [7].
?????? ??????? ZP-?????? ?????????? ??????????? ????????? ???????????? ??????????
??????????????????? ? ?????????????? (???. 4), ??????? ???????? ????????? ?????????:
????????? ????????? ? ???????? ?????? ?? ??????????????????, ?????????? ???????? ?????????????, ???????????? ??????????, ?????????? ?????????? ????????????? ??????????
? ?????? ?? ???? ?????? Z1-?????????? ????????????????. ?????? ??????? ZP-?????? ?????????????? ??????????????? ?????? ????????????? ???????? ???????????? ??????????
??????????????????? ???????????, ??????? ?????????????? ?? ?????? ?????????? ????????,
??????????? ?? ???????????? ?????????? ?????????????, ???????????????? ???????????
???????????? ??????????? ???????? ? ?????? [7].
?????? ??????????? ? ??????????? ????????? ?????????????? ?????? ZP-??????
(???. 3), ?????????? ZP-???????????? ? ZP-????????????, ??????? ????????? ?????????
?????????? ZP-??????. ZP-???????????? ????? ????? ??????????? Z2-?????????? ??????????? ? ? ???? ?????? ???????? ???????????????? ?????????? ? ZP-????????????. ??????
???????????? ??????????? ???????? ?????????? ????????? ???????????, ?????????? ? ???
??????????????? ????? ? ???????????? ????????? ?????????? ??????????. ????? ??????????? ???????? ?????????????????? ? ???????, ???????????? ZP-????? ? ?? ?? ?????? ??????????????? ?????????????????? ????????. ??? ????????? ????????? ????? ???????? ????????????? ?? ?????????????????? ? ?????????? ????????????? ?????????, ? ????? ??????????
Z2-????????? ????????????????.
?????????? Z1- ? Z2-?????????? ????????? ??????? ? ??????????????? ? ???????? ???????? ZP-?????? ? ZP-????????????. ????? ? ?????? ??????? ?? ?????? ?????????
????????? ?????????????? ??????????? ?????? ???????? ?????????????????? ???????????, ? ????? ????? ???????? ? ????? ???????? ??????????????????. ??????????? ?????? ???????-?????????? ????????? ???????? ??????? ????????????, ?? ?????? ???????
????????????? ????? ???????? ?????????????????? ????????. ???????????? ?????????? ??????????? ??????????? ?????? ????? ???????????????? ???????????, ??? ?????????
?????????? ?????? ????????? ?? ?????? ? ???????? ??????????????, ? ????? ???????????
?????????? ? ?????????????? ? ???????????? ??????????????????? ????????. ???????
????????, ??? ???????? ??????????? ???????? ?? ?????? ????? ???????? ?????????? ZP????, ?????????? ????? ???????? ?????????????????? ? ?????? ?????? ??? ??????? ??
???????? ???????????.
?????????? ?????????? ????????? ZP-?????? ?????????????? ?? ???????????? ?????????, ??????????? ?? ???. 5. ??? ??? ??????????, ?????????? ?????? ?????? ????, ? ??????? ????? ??????? ???????? ?????????? ? ?????????? ????????????????. ? ?????? ???????
?????????? ???????????? ?????? ???????? ????????? ? ???????????? ?????????? ????? ??
????????? ??????????. ? ?????? ??????? ????????? ????? ?????? ???????????? ???????????
???????? ? ??????, ??? ??????? ??? ?? ?????? ???????? ???????? ?????????? ZP-?????? ???????????? ????????? ??????? ??????. ?????????????? ??? ???????? ???????? ??????????# 121 #
Copyright ??? «??? «??????» & ??? «A???????? K????-C?????»
?.?. ??????, ?.?. ?????????? ?????????????? ? ???????? ?????????? ??????????????????? ???????????
???. 5. ???????? ?????????? ???????? ZP-??????
????? (??? ????? ??????????? ????????? ????????) ? ????????????? (??? ??????????? ?????????) ? ?????? ???????? ???????? ???????????? ?????????? ???????????????????. ??????
??????? ????????? ??? ?? ?????? ?????????? ???????? ZP-?????? ???????, ?????? ?????, ?????????????? ??????????? ? ?????????????? ??????????? ???????????.
? ????? ?????? ??? ????????? ????????? ????? ???????? ?? ??????? ????????????? ?
?????? ?????????? ????????? ??????? ? ???????, ?????????? ?? ???????? ??????? ??????.
? ????? ??????????????? ??????????? ???????? ????????? ZP-??????: ??????????????, ZP???????????? ? ZP-???????????? (?????? ? ????? ????????????? ????????), ? ????? ?????????? ?????????, ????????????, ????????? ????????? ????????, ???????????? ?? ???????????? ???????? ?? ?????????? ????????? ?????????, ?????????????? ? ??????? ????????
?????????????????? ?? ??????????? ????????? [7, 10].
? ????? ???????????????? ??????? ???????? ?????????????? ?????? ???????????, ???????? ????? ???????? ???????? ???????? ??????? ?? ????????? ?????. ?????? ??????? ???????
?? ????????? ????????? ???????????????? ? ??????????? ??? ?????????? ?????? ?? ????????? ???????? ???????: ??????? ????????? ???????? ????????? ? ????????? ????????;
??????? ????????? ???????????????? ?????? ????????? ??????; ?????????? ????????? ????????? ???? ?????????? ??????????? ?????????? ???????? (???. 5). ???? ??????? ??????? ?
??????????? ????????, ?? ??????????, ?????????? ?? ?????????? ????????, ??????????? ?
???? ?????? ? ???????? ?????????? ??????? ?????????????????? ?? ????????? ????????? ?????????. ?? ????????? ????? ?????????????? ?????? ????????????? ?????????? ZP-?????? ?
???????????? ????? ???????????. ?? ?????? ?????? ????????????? ????? ???? ??????? ??????? ? ?????????? ??? ????????? ????????? ????????????????. ???? ????? ??????????????? ?
?? ???????????? ????, ????? ???????????? ZP-????????????, ? ? ???????? ?????????????? ?????????? ???????????????? ??????????? ?? Z2-, ? Z1-????????? (?? ???. 5 ???????? ?????????
??????). ???????? ??????????? ????????, ????? ???? ??????????? ?? ???????????? ???? ??
# 122 #
Copyright ??? «??? «??????» & ??? «A???????? K????-C?????»
?.?. ??????, ?.?. ?????????? ?????????????? ? ???????? ?????????? ??????????????????? ???????????
??????? ?????????? Z1-??????????, ? ????? ?????????? ????????? ZP-????????????, ? ????
ZP-?????? ??????????? ?????? ?? ?????????? Z2-??????????.
????? ???????, ? ?????? ZP-??????? ????? ??????? Z-??????????, ? ??? ????????? ??????????? ???????? ZP-???????????? ? ZP-????????????, ????????????????? ??? ???????
??????? ?? ?????? ????????? ????????? ??????????? ???????????, ???????????? ? ??????????? ?? ???????-??????????. ZP-?????? ????????? ??????????? ??? ??????????? ZP-????,
??????????? ????????? ????????????????, ? ????? ?????????? ?????? ????????????? ??????????????????. ?????? ????????? ZP-??????? ????????? ?????????? ????????????????
????????????????, ??????? ?????????????? ? ??????? ?????????? ?????????.
?????? ??????????
[1] ?????? ?.?. ????? ???????????? ?????????? ????????????: ??????????. ???. 29. ?????????????? ????????????. ?.: ???-?? ??? ????? ????????? ????????????, 2005. 384 ?.
[2] ?????? ?.?. ??????????? ?????????? ??????????????????? ????????????? ??????????????????? ????????? (???????????): ??????????. ?.: ???-?? ??? ???, 2006. 147 ?.
[3] ?????? ?.?., ??????? ?.?. ? ??. ????????????? ??????: ???????. ???????????: ???-??
???, 2009. 650 ?.
[4] ?????? ?.?., ??????? ?.?. ??????????????? ?????????????????? ????????????? ??????????????????? ????????? ?? ??????????? ????? ????????: ??????????. ?.: ???-?? ???
???, 2009. 92 ?.
[5] ?????? ?.?., ??????? ?.?. ??????????????? ?????????????????? ?? ?????? GZ-???????:
??????????. ???????????: ???, 2010. 144 ?.
[6] ?????? ?.?. ????? ???????????? ?????????? ????????????: ??????: ????????-??????.
???????????: ??? «??????????», 2012. 19 ?. ????? ???????: http://gnatukvi.ru/index.files/zakon.
pdf.
[7] ?????? ?.?. ????????? ???????????????? ???????????: ???????: ????????-??????. ???????????: ??? «??????????», 2012. 56 ?. ????? ???????: http://gnatukvi.ru/index.files/potential.
pdf.
[8] ?????? ?.?. ? ??. ???????????? ?????????????????? ???????? ????????????? ??????????????????? ????????? ? ?????????????? ??????????? ?????????: ??????????. ???????????:
???-?? ???, 2012. 289 ?.
[9] ?????? ?.?. ???????, ??????????, ????????????????: ????????-????. ?., 2000?2013.
????? ???????: http://www.gnatukvi.ru.
[10] ?????? ?.?. ????? ???????????? ?????????? ????????????. ???????????? ??????,
???????. ? ???. ?.: ???-?? ??? ? ????? ????????? ????????????, 2005?2013. ????? ???????:
http://gnatukvi.ru/ind.html.
Copyright ??? «??? «??????» & ??? «A???????? K????-C?????»
?.?. ??????, ?.?. ?????????? ?????????????? ? ???????? ?????????? ??????????????????? ???????????
Potentialization in Methodology
of Power Consumption Technocenosis
Victor I. Gnatyuka,
Vasily I. Panteleevb and Alexander A. Zaimenkoa
a
Kaliningrad State Technical University,
1 Sovetsky, Kaliningrad, 236022, Russia
b
Siberian Federal University,
79 Svobodny, Krasnoyarsk, 660041, Russia
The proposed methodology of optimal control of a power consumption technocenosis (interval
estimation, forecasting and normalization) to add one more procedure potentialization includes the
steps of ZP-analysis, ZP-regulation and ZP-planning.
Keywords: control of a power consumption, potentialization, potential for energy savings, Z-potential,
ZP-analysis, ZP-regulation, ZP-planning.
?????????? ????????? ????????, ??????? ????? ??????? ????? 8 ??.
??????????
?? ?????? ??????????? ?????????? ANSYS ? ProCAST ??????????? ???????????? ?????? ????? ??????? ? ???????????? ?????????. ????????????? ?????? ?????????? ????????????? ????? ? ???????? ??????? ??????? ?????????? ? ??????? ??????????? ??????? ???????? ??????.
??????? ??????? ???????? ?????????? ?????? ???????? ????????? ?? ??????? ????????? ???????: ???????? ????? ??? ???????? ??? ?????????, ??????????? ????????? ???????? ?
????????????? ?????????? ?????????. ? ?????????? ???????????? ????????????-?????????
???????????? ??????????? ??????????? ????????? ??????????????? ??????? ?????, ??????????? ????????? ????????????? ? ?????????? ???????, ? ????? ??????? ???????? ?????????
???????? ? ??????? ??????? ???????.
# 101 #
Copyright ??? «??? «??????» & ??? «A???????? K????-C?????»
?.?. ????????, ?.?. ?????? ???????????? ????????????? ? ??????????? ???????? ????? ??????? ???????
?????? ??????????
[1] ???????? ?.?. ?????????-???????? ???????????? ??????????? ???????? ? ???????. ?.:
???????????, 1974. 320 ?.
[2] ?????????? ?.?. ???????????? ??????. ?: ???????????, 1977. 160 ?.
[3] ???????? ?.?., ?????????? ?.?. ???????????????? ?????? ?????????? ? ??????????????? ????? ???????????? ????? ?????????: ??????? ???????. ??????????: ???-?? ???, 1986.
120 ?.
[4] ???????? ?.?. // ???????. ???. ? ????. ????. ????. ???????, 2011. 17 ?.
[5] ???????? ?.?. ??????????????? ???????? ???????? ??? ??????? ????????????: ?????????? ???. ?.: ???????????, 1989. 384 ?.
[6] ???????? ?. ?. ?????? ???????????? ???????. ?????? ???????? ??????. ?????????????
? ?????????? ???????: ??????? ??? ?????. ?.: ???-?? ???? ??. ?. ?. ???????, 1998. 360 ?.
Computer Simulation
and Optimization Casting Process
Ingot Platinum
Alexander P. Skuratova,
Dmitry I. Makhova and Yevgeny A. Pavlovb
a
Siberian Federal University,
79 Svobodny Str., Krasnoyarsk, 660041, Russia
b
Krastsvetmet
1 Transportny Proezd, Krasnoyarsk, 660027, Russia
On the basis of ANSYS software complexes and ProCAST developed computer model casting platinum
in a water cooled mold with movable bottom. We studied the influence of operating parameters of work
of the foundry installation on the crystallization of ingots. Installed quantitative dependences allowing
to reduce the magnitude of the shrink shell, and also exclude the surface and internal defects in the
ready ingot platinum.
Keywords: computer model casting, software packages ANSYS and ProCAST, platinum ingots, a water
cooled mold, mobile bottom, the regime parameters, shrink shell.
Copyright ??? «??? «??????» & ??? «A???????? K????-C?????»
Journal of Siberian Federal University. Engineering & Technologies 1 (2014 7) 103-108
~~~
??? 621.396:629.056.8
Satellite Microvibration
and Atmospheric Turbulence Effect
on Satellite-to-Ground Optical Communication Link
Alexander V. Vasilenko* and Valentin B. Kashkin
Siberian Federal University
79 Svobodny, Krasnoyarsk, 660041, Russia
Received 18.11.2013, received in revised form 10.01.2014, accepted 12.02.2014
Satellite-to-ground optical communication link bit error rate (BER) depending on atmospheric
propagation, pointing errors is considered. The theoretical and numerical estimations of BER for
GEO to Earth link under various conditions are proposed.
Keywords: satellite communication, lasercom, turbulence, tracking error, bit error rate.
Introduction
The most capacious communication links are needed to deliver data from low Earth orbit satellites
to ground data-processing centers. To provide near-realtime data transmission geostationary relay
satellites are used. Due to point-to-point link architecture it is advantageous to use free space optical
data transmission technics which provide more capacious communication links in comparison with
radio-frequency systems with same onboard equipment mass and energy consumption.
This paper is devoted to some aspects of developing GEO-Earth optical link, namely simultaneous
effect of satellite?s microvibration and atmospheric turbulence.
Theory
Assuming low atmospheric attenuation (i.e. ?clear sky? conditions) there are two major factors
on link performance ? microvibrations of telescope base and effect of atmospheric turbulence on
propagating laser beam. Both effects lead to statistical variance of received radiation intensity.
We assume that transmitter pitch and roll angle tracking errors due to microvibrations obey
normal distribution. Total tracking error may be described as:
x = x 2p + xr2 ,
(1)
where xp and xr are pitch angle and roll angle tracking errors respectively. Assuming that RMS errors
for each angle are equal and that errors are independent, probability density function of the error x,
measured from line of sight is described by Rayleigh distribution:
*
© Siberian Federal University. All rights reserved
Corresponding author E-mail address: a.v.vasilenko@mail.ru
# 103 #
Copyright ??? «??? «??????» & ??? «A???????? K????-C?????»
Alexander V. Vasilenko and Valentin B. Kashkin. Satellite Microvibration and Atmospheric Turbulence Effect?
f ( x) =
? x2 ?
x
exp ? ? 2 ? .
2
?
? 2? ?
(2)
Since in the beam intensity is distributed by normal distribution, received intensity at distance
z is [1]:
I ( z, ? ) =
? ?2 ?
p 2
exp ? ?2 2 ? ,
2
2
z ?w
? w ?
(3)
where p is transmitted power, ? is tracking error (line of sight misalignment), w is beam
divergence.
At the receiver plane, random transmitter?s tracking error leads to additional amplitude modulation
of the signal. Assuming that unmodulated signal is transmitted, probability distribution function of
received signal power is given by [2]:
g ( I ) = f ( I ( z , ? ) ?1 ) ?
d
(I ( z, ? )?1 ).
d?
(4)
As it seen from (3) that beam divergence w decrease leads to higher powers at receiver however
beam divergence w decrease to values comparable with tracking error will lead to unwanted signal
modulation.?
Besides modulation due to tracking error, atmospheric effects on laser beam must be considered.
Major atmospheric effects are:
? atomic and molecular absorption
? Rayleigh scattering
? aerosol absorption and scattering
? the effect of atmospheric turbulence
? astronomical aberration
We assume negligible probability of rescattering then photon which been removed from beam
reaches the receiver. Thus atomic and molecular absorption, Rayleigh scattering, aerosol absorption
and scattering lead only to signal attenuation. The effect of atmospheric turbulence results in random
amplitude modulation and obeys statements (5-9) [3]:
? ? ? I ? 1 2 ?2 ?
? ? ln ?
?+ ?I ? ?
1
?< I >? 2 ? ?
exp ? ? ?
f ? (I ) =
?
?
2? I2
2?? I2 I
?
?
??
??
(5)
? I2 = A(exp 2? ?2 ? 1)
(6)
?
? ?2 = 0.56k 7/6 sec(? )11/6 ? Cn2 (h)h5/6 dh
(7)
0
7/6
?
? Drx 2
? ?
A = ?1 + 1.1?
? ?
??
? ? hs cos(? ) ? ??
?1
# 104 #
(8)
Copyright ??? «??? «??????» & ??? «A???????? K????-C?????»
Alexander V. Vasilenko and Valentin B. Kashkin. Satellite Microvibration and Atmospheric Turbulence Effect?
? ? 2
?
2
? ? Cn (h)h dh ?
?
hs = ? ?0
?
?
2
5/6
? ? Cn (h)h dh ?
?0
?
6/7
(9)
Where f?(I) is modulation probability distribution function, <I> is received signal power assuming
no turbulence, ? is zenith angle, k is wavenumber, Drx is receiver aperture diameter, Cn2 is refractivity
structure parameter.
To describe Cn2 numerically we used model:
2
10
h ?
? 21 ?
?
Cn2 (h) = 0.00594 ? ? (10?5 h ) exp ? ?
?+
27
1000
? ?
?
?
h
h
?
?
?
?
+2.7 Ч10?16 exp ? ?
? + A0 exp ? ?
?
? 1500 ?
? 100 ?
(10)
Accounting atmospheric turbulence and tracking error effects signal probability distribution
function at the receiver may be described as conjunction:
?
fg ( I ) = ? g ( I ) f ? ( I ? x)dx .
(11)
0
To define an optimal divergence angle, we consider bit error rate ? an erroneous bit to total bit
received quantity ratio. In case of using on-off keying modulation, bit error rate may be estimated as
[2]:
1
? Q ?
BER(Q) = erfc ?
?,
2
? 2?
where erfc( x) =
1
?
?
? exp(?t
2
)dt and Q =
x
(12)
i1 ? i0
? 02 + ? 12
. In Q-factor definition there are:
i0,1 ? is electrical current, generated by photodetector when 0 and 1 bits are received respectively.
Since signal at the receiver is random we should consider mean BER given as:
?
3 I0
0
0
< BER >= ? BER(Q) g ( I )dI =
where I 0 =
? BER(Q) g ( I )dI
(13)
p 2
is intensity on a beam axis. The replacement of limit of integral in (13) is valid
z 2 ? w2
because g(I) is negligible for I > 3I0.<BER> depends on beam divergence as well and it?s minimum
corresponds to optimal divergence for given conditions.
Atmospheric conditions
The link model built allows calculating BER for given link parameters and environmental
conditions. Atmospheric parameters used in numerical calculations are shown at
Fig 1-3.
Solid line corresponds to measured Cn2 [4], dotted ? model approximation used in this
paper.
# 105 #
Copyright ??? «??? «??????» & ??? «A???????? K????-C?????»
Alexander V. Vasilenko and Valentin B. Kashkin. Satellite Microvibration and Atmospheric Turbulence Effect?
Fig. 1. Model aerosol particle size distribution [6]
Fig. 2. Model aerosol particle height distribution [6]
Solid line corresponds to meteorological range of visibility at the surface of 23 km, dotted line ? 5 km
Fig. 3. Cn vertical profile
Numerical results
Fig. 4, 5 provides calculated BER versus beam divergence for given parameters and conditions for
GEO-Earth downlink scenario (shown at Table 1).
It was assumed what there is continental aerosol mix with average refractive index 1.4+0.016i.
Vertical aerosol distribution was calculated using model [3] basing on meteorological range of visibility
at the surface.
Solid line corresponds to meteorological range of visibility at the surface of 23 km, dotted line ?
5 km
As is seen from Fig. 4, 5 there is BER minimum due to simultaneous effect of satellite microvibration
and atmospheric turbulence. The minimum of BER-curve corresponds to ?optimal? transmitter?s
divergence and strongly depends on meorological conditions. There is also slight relationship between
?optimal? transmitter?s and receiver design.
# 106 #
Copyright ??? «??? «??????» & ??? «A???????? K????-C?????»
Alexander V. Vasilenko and Valentin B. Kashkin. Satellite Microvibration and Atmospheric Turbulence Effect?
Table 1. Link parameters
Parameter
Value
Receiver?s latitude
56° N
RMS tracking error due to satellite microvibration
(roll)
RMS tracking error due to satellite microvibration
(pitch)
Carrier wavelength
1??
1??
1590 nm
Transmitter power
5W
Transmitting and receiving optics transmittance
0.75
Receiver optical filter bandpass
10 nm
Receiver detector type
APD
Modulation
On-off keying, 500 Mbps
Receiver effective aperture
350mm/750 mm
Fig. 4. Average BER versus transmitter beam divergence for receiver effective aperture 350 mm. Solid
line corresponds to meteorological range of visibility
at the surface of 23 km, dotted line ? 5 km
Fig. 5. Average BER versus transmitter beam divergence for receiver effective aperture750 mm
Thus worse expected meteorological conditions as well as receiver design must be taken into
account at early stages of onboard optical communication hardware development to reach the best
possible BER.
References
[1] Hecht E. Optics. Addison Wesley, 2002. 704 p.
[2] Papoulis. A., Pillai S.U. Probability, random variables, and stochastic processes. McGrawHill, 2002. 852 p.
[3] Hemmati H. Near-Earth Laser Communications. CRC Press, 2008. 374 p.
[4] Smith F. The Infrared & Electro-Optical Systems Handbook. V. 2. Atmospheric propagation
of radiation 1993. 322 p.
[5] Toyoshima M. // Proceedings of SPIE. 2007. Vol. 6551. P. 1-11.
# 107 #
Copyright ??? «??? «??????» & ??? «A???????? K????-C?????»
Alexander V. Vasilenko and Valentin B. Kashkin. Satellite Microvibration and Atmospheric Turbulence Effect?
[6] ???? ?.?. ??????????? ???????? ??????????? ??????. ?. 2. ?????????? ??????
?????????. ?., 1986. 253 ?.
??????????? ????????????? ?????????
???????????? ????????
? ??????????? ??????????????
?? ????? ????? ??????????? ?????????
«??????? ? ?????»
?.?. ?????????, ?.?. ??????
????????? ??????????? ???????????
??????, 660041, ??????????, ??. ?????????, 79
??????????? ?????? ????????? ?? ??????????? ??????? ?????? ??????????? ?????? ?????
«??????? ? ?????» ??????????? ???????????? ??????. ???????????? ?????????? ?????????
?????? ??????????? ??????? ?????? ??? ????????? ???????.
???????? ?????: ??????????? ?????, ???????? ?????, ??????????? ??????????????, ??????
????????, ??????????? ??????? ??????.
Copyright ??? «??? «??????» & ??? «A???????? K????-C?????»
Journal of Siberian Federal University. Engineering & Technologies 1 (2014 7) 109-115
~~~
??? 550.8:681.518
Construction of Geographic Information System
of Corporate Level in Geological Prospecting
Maxim A. Spikin*,
Vladimir A. Pozdnyakov and Sergey S. Hudyakov
Siberian Federal University
79 Svobodny, Krasnoyarsk, 660041, Russia
Received 02.12.2013, received in revised form 15.01.2014, accepted 21.02.2014
The paper describes the experience of application of geographic information technologies and
methods of processing of the Earth remote sensing data for solving practical tasks in the search
for hydrocarbon deposits. The most important feature of technological processes in this sphere is
the necessity to analyze large fl ows of spatially distributed data of different nature in real time.
We propose a service-oriented approach to organize a geographic information system (GIS) in
order to optimize the solution of tasks in nature management and exploration for oil and gas
studies.
Keywords: GIS, geoinformation technology, geographic information system, earth remote sensing
data, geodatabase.
Introduction
Currently, there is a tendency in exploration work that volumes of diverse data are constantly
increasing, the range of current tasks is expanding, the number of applied methods and technologies
of prospecting and exploration of mineral resources, particularly oil and gas, is growing. As a result,
there are difficulties in operational management and analysis of large flows of heterogeneous data
that leads to a slowdown in the speed of decision-making. Topological nature of information makes
it possible to create a single information-analytical system and integrate data of different production
services and departments. The integration of different data types and structures into 
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