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Progress in the Modelling of Air Flow Patterns in Softwood Timber Kilns.

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Dev. Chem. Eng. Mineral Process. 12(3/4),pp. 249-261, 2004.
Progress in the Modelling of Air Flow
Patterns in Softwood Timber Kilns
T.A.G. Langrish"' and R.B. Keey2
Department of Chemical Engineering, University of Sydney,
New South Wales 2006, Australia
Wood Technology Research Centre, University of Canterbury,
Private Bag 4800, Christchurch, 8004, New Zealand
'
Progress in modelling air flow patterns in timber kilns using computational fluid
dynamics (CFD) is reviewed in this work. These simulations are intended to predict
the distribution of the flow in the fillet spaces between boards in a hydraulic model of
a timber kiln. Here, the flow regime between the boards is transitional between
laminar and turbulent flaw, with Reynolds numbers of the order of 5000. Running the
simulation as a transient calculation has shown few problems with convergence
issues, reaching a mass residual of 0.2% of the total inflow afler 40 to 100 iterations
per time step for time steps of 0.OI s. Grid sensitivity studies have shown that nonuniform grids are necessary because of the sudden changes in flow cross section, and
the flow simulations are insensitive to grid refinement for non-uniform grids with
more than 300,000 cells. The best agreement between the experimentally-measured
flow distributions between fillet spaces and those predicted by the simulation have
been achieved for (effective) bulk viscosities between the laminar viscosity for water
and ten times that value. This change in viscosity is not vely large (less than an order
of magnitude), given that effective turbulent viscosities are typically several orders of
magnitude greater than laminar ones. This result is consistent with the transitional
flows here. The effect of weights above the stack can reduce the degree of nonuniformity in air velocities through the stack, especially when thick weights are used,
because the stack may then be separated from the eddy at the top of the plenum
chamber.
* Author for correspondence (timl@chem.eng.usyd.edu.au).
249
T.A. G. Langrish and R.R.Keey
Introduction
Plantation-grown softwood timber (mainly Pinus rudiuta) is processed in Australia
and New Zealand in considerable quantities. Annual production of softwood timber in
Australia [ l ] is in the region of 1 million m3, while in New Zealand 3.3 million m3 is
processed as board timber, of which one-thud was exported in 1998. This processing
involves a drylng step that is significant in terms of both its energy usage and its
importance in determining the final quality of the product. Softwood sawnboards are
often seasoned in kilns at temperatures above 100°C. Reduction of the drytng time is
the principal benefit of this technique, known as high-temperature drying of timber.
Under these conditions, external convection is relatively more important in
determining the drying time than at the lower temperatures traditionally used in kiln
seasoning. In addition, appearance-grade timbers are kiln-dried under so-called
"accelerated" conventional schedules with relatively long drying times (although short
compared with hardwoods). It is desired to improve kiln techniques so that more
timber can be dried at higher temperatures without loss of quality.
High-temperature drying of timber is normally carried out with air velocities of the
order of 7 m s" (or more) between the boards. A typical kiln layout involves rows of
boards separated by spacer sticks or stickers. The separation between these rows is
the board-row spacing (typically between 15 and 25 mm). There are also gaps
between board edges, referred to here as board-edge gaps, which are an inevitable
result of both imperfect sawing and shrinkage, and are usually of the order of 1 mm.
These gaps lead to enhancements in the mass-transfer coefficients, both at the leading
edges of the boards and over the entire board. These enhancements have been
measured experimentally by Kho et al. [2], and have been numerically simulated most
recently by Sun [3] and Hua et al. [4] using the k-E turbulence model whch assumes
well-developed turbulence in the free stream. There is general agreement amongst all
this previous work that the temperature variations in the kiln do not have a dominant
influence on the air flow patterns in such highly forced-convection flows. The amount
of water vapour lost in drying is negligible compared with the air flow rate through the
stack, so the influence of drying on the air flow patterns is normally neglected in this
type of study. The flow patterns influence both heat and mass transfer rates.
250
Progress in the Modelling of Air Flow Patterns in S o fio o d Timber Kilns
The distribution of the flow in the fillet spaces between boards in a hydraulic
model of a timber kiln has been measured by Nijdam and Keey [ 5 ] , with more details
being given in Nijdam and Keey [ 6 ] . The simulations reported in this work are
intended to predict these measurements, in which the flow regime between the boards
is transitional between laminar and turbulent flow, with Reynolds numbers of the
order of 5000.
The purpose of low Reynolds number turbulence models is to allow direct
integration through the boundary layer towards the wall, allowing fine detail to be
resolved in these regions. However, they do not affect the assumption of welldeveloped turbulence in the bulk flow [7]. As such, they are not valid approaches for
simulating flow situations that are transitional throughout the flow domain. In other
words, at present there are no true developed models for transitional flows. The low
Reynolds number turbulence models available are actually h g h Reynolds number
models that allow integration of the turbulence equations to the wall. The constants in
the hgh Reynolds number turbulence models have been fitted to data where the
Reynolds numbers are generally above 20,000.
The approach here is to simulate the flows assuming, firstly laminar flow only,
then to implement a wall damping fimction to interpolate between the laminar
viscosity at the wall and the effective (bulk) viscosity. The effective viscosity is fitted
to experimental data.
Theoretical Methods, Geometry and Operating Conditions
CFX4 [S] is a general purpose CFD code that solves the conservation equations
governing fluid flow via a fmite volume method. In this work, equations are solved
for the conservation of mass and momentum for the isothermal, incompressible flow
of water in a hydraulic model of a hgh-temperature kiln. Details of the kiln geometry
and operating conditions are given in Nijdam and Keey [ 5 ] . For example, the
temperature of the water was 2OoC, and the hydraulic model was scaled to retain both
geometrical and dynamic similarity (same Reynolds number) as a full-scale kiln with
air flowing though it.
251
T.A.G. Langrish and R.B. Keey
The treatment of turbulence in transitional flows remains problematic, and welldeveloped turbulence cannot be assumed in the bulk of the flow for these cases.
Hence, turbulence models, such as the k-e turbulence model, that make this
assumption of well-developed turbulence are questionable under these conditions.
Regardless of what the turbulence is in the main flow, it is necessary to account for the
damping of turbulence near the wall. Here, a van Driest wall damping fbnction, as
described in Wilcox [7], has been used to interpolate between the laminar viscosity at
the wall (p,)and a fitted effective (bulk) viscosity (p,) in the main body of the flow:
Here y+ is the dimensionless distance from the wall ( y G / p i ), p is the gas density,
‘I is
the local shear stress and y is the actual distance fiom the nearest wall.
Results and Discussion
(i) Convergence
Running the simulation as a transient calculation has shown few problems with
convergence issues, reaching a mass residual of 0.2% of the total inflow after 40-100
iterations per time step for time steps of 0.01 s. Such low mass residuals at each time
step are accepted as being evidence of reasonable convergence [9], so time steps of
0.01 s have been used in all the simulations reported here.
(ii) Grid Sensitivity
When starting the simulation, the maximum time derivatives are initially hgh, as
would be expected when starting a real piece of experimental equipment.
The
maximum time derivatives do not disappear entirely, as they would be expected to do
if the situation was eventually completely steady, and the time derivatives continue to
oscillate indefinitely after an induction period.
However, the impact of the
unsteadiness on the flow distribution between fillet spaces appears to be minimal,
252
Progress in the Modelling of Air Flow Patterns in Softwood Timber Kilns
7
Figure 1. The effect of grid density on the predicted flow distribution (average and
maximum predicted velocities in the hydraulic kiln) for the non-uniformgrids.
Grids have been produced with grid lines concentrated in the regions of highest
pressure gradients ("non-uniform" grids), as described earlier. In the case of the
coarsest non-uniform grid, there are between 10 and 22 grid lines in the fillet spaces
(with a total of 323,608 cells), with the highest number being concentrated at the top
of the plenum chamber where the pressure gradients are greatest. In a second nonuniform grid, there are between 12 and 30 grid lines in the fillet spaces and a total of
475,872 cells. The predicted flow distributions at long times from the start are shown
in Figure 1 for both grids, showing no significant grid density effect. This absence of
grid sensitivity suggests that the coarse, non-uniform grid with 323,608 cells is
adequate for hrther studies. This grid is shown in Figure 2 for the area in the top fillet
spaces.
253
T.A. G. Langrish and R.B. Keey
(iii) Flow Distributions
The previous (laminar flow) estimates shown in Figure 1 have used the dynamic
viscosity of water in the hydraulic model of the kiln used here, 9 x
kg m-’ s-’
throughout the flow field. By definition, the hydraulic model is a water model of a real
kiln that is scaled to have the same Reynolds number as a full-scale kiln with air
flowing through it. Figure 3 shows the impact on the flow distribution between boards
of effective viscosities of 9 x
kg m-’ s-’ (the base case), 9 x l o 3 kg m‘’ s-I, and
9 x lo-’ kg m-l s-’. The flow fields for effective viscosities of 9 x
9x
kg m-’ s-’ and
kg m-’ s-’ near the top of the stack are shown in Figures 4 and 5 . Higher
effective viscosities smooth out the flow distribution more and reduce the size of the
recirculation zone near the top of the stack. Compared with the experimental
distribution, an effective viscosity of 9 x
kg m-’ s” shows too much variation in
velocity with changing board number, while an effective viscosity of 9 x 1O 3 kg m-’ s-’
shows closer agreement. T h s change in viscosity is not very large (less than an order
of magnitude), given that effective turbulent viscosities are typically several orders of
magnitude greater than laminar ones. This result is consistent with the transitional
flows here.
A finer variation of effective viscosity has been carried out for the results shown in
Figure 6 , which shows the impact on the flow distribution between boards of effective
viscosities of 2 x
kg m-‘ s-I, 4 x l o 3 kg m-’ s-I, and 6 x 10” kg m-’ s-I. The flow
field near the top of the stack, for viscosity of 6 x 10” kg rn-’s-I, is shown in Figure 7.
The changes in the flow field in this region are not large for the small variation in
viscosity over the range from 2 to 6 x 10” kg m-’s-’. While the variation of velocity
with board number is reasonable in terms of the range between maximum and
minimum velocities, the predicted position of the peak velocity (board 3) is different
to that observed (board 4). It is important to note that these are predicted water
velocities for the hydraulic kiln. The difference may reflect the variation in the
effective turbulent viscosity throughout the flow field, although this variation cannot
be accurately modelled given the transitional flow regime for these experiments.
254
Progress in the Modelling of Air Flow Patterns in Sofmood Timber Kilns
Figure 2. Fine non-uniform grid in the vicinity of the top fillet spacings of the
hydraulic kiln.
~
~~
~~
..
~~~~
~~~~
- - 0 -
9 00E-03
9.00E-02
1
2
3
4
5
6
7
8
9
1
0
1
1
1
2
1
3
Board Number
Figure 3. The effect of total viscosity on the predictedflow distribution (maximum
predicted velocities in the hydraulic kiln) for a viscosity range of 9 x I
kg m-’ s-’ to
9 x I 0-2kg m-’ s-’.
255
T.A.G. Langrish and R.B. Keey
Figure 4. The predictedflow pattern in the upper part of the plenum chamber for the
hydraulic kiln (predicted velocity magnitudes shown in legend) for a total viscosity of
9 x l o 4 kg m-' s-'.
Figure 5. The predictedflow pattern in the upper part of the plenum chamber f o r the
hydraulic kiln (predicted velocity magnitudes shown in legend) for a total viscosity of
9 x 10.' kg rn-' s-'.
2.56
Progress in the Modelling of Air Flow Patterns in Softwood Timber Kilns
The agreement between prediction and experiment for the flow distribution with an
effective viscosity of 6 x
kg m-’ s-’ is reasonable, in the sense that the maximum
velocity is predicted to be in the third fillet space, whereas the actual maximum
velocity is in the fourth fillet space. Ths slight disagreement in the prediction of the
point of maximum velocity also corresponds to a predicted vortex zone in Figure 7
that is more elongated than the actual vortex, which was more circular. Nevertheless,
the predicted visualization in Figure 7 is quite close in appearance to the experimental
one [ 5 ] . The observed vortex zone is about three boards high and just under half the
plenum chamber wide, while the predicted one is also three boards high although
slightly narrower.
Nevertheless, the best fitted effective viscosity of 6 x 10” kg my’s-’ is not very far
above the molecular viscosity of water (1 x 10” kg m-’ s-I) (less than an order of
magnitude), given that effective turbulent viscosities are typically several orders of
magnitude greater than laminar ones. This result is consistent with the transitional
flows here. This fitted effective viscosity is meaningful for assessing the effects of
different stack geometries for this system.
0.80
.......................
0 10
-~
.
.._.._.,.I
..
.......
.... ........
~
- * 6 00E-03
-+experiment
t
Figure 6. The effect of total viscosity on the predicted jlow distribution (maximum
predicted velocities in the hydraulic kiln) for a viscosity range of 2 x
kg m-’ s-’to
6 x IO” kg rr-’ s-’.
25 7
lhc significance ul‘ the predicted vortex and eddying at the top nf the chanihelr IS
that this region currcsponds to rclatively tow velociries (even back fIo\.t) in the iilIet
spaces at the top ufthe stack Eflecrlve contouring ofthe Fin region in the roof and ul‘
the plenum chamber is likely to be rrecessary to reduce tht:, prt3blem which i s linked
to
the mornenturn of the flow ernergrng from the roof region and tile sharp change
flow direction that is required at the ctirmnce to the plenum chamhcr
in
area [6].
Figure 8 shows the efkct of blocking the gaps at the top af the stack, simulating
the situatrair where there are weights hetween the top of the stack and below the faris
(iivcn that a large eddy is predicted (see Figure 9) in the plenum chamber, covertrig
the first thrce brads, the reduced range of alltximurn velocities caused by blocking
these iirst three board gaps is possibly not roo surprising. For no blockage (the hast:
case, see Iiigurc !it, thc range of velocities is from 0,31 to 0.52 m s
progressively more gaps reduces the amount of varrstwn
bloiked. 0.39 to 0.54 m s
in
’
Blocking
tile velocitj (one gap
’.two paps k1oclt.d. 0 40 to 0.5X rn s
I:
ttixre gaps blockcd:
0 . 5 8 to 0.64 ni s ’ 1 Even w i t h thrtc: gaps covered, the eddy is not prcdrcted to move
significantly, so the cfkct o f weights tvlth suf’ficienr thickness above the stack 1s llkely
to
reduce ttte degree of rrcln-untf~~rrmty
f ~ 31r
i velocities thmttgh the stack.
Progress in the Modelling of Air Flow Patterns in Softwood Timber Kilns
i
0.70
0
f 0.30 1
0.20
0.10- 0.00
-+-onegap
blocked
--*-.twogaps
blocked
three gaps
blocked
-
~
Figure 8. The effect of blocking the gaps at the top of the stack, simulating the
situation where there are weights between the top of the stack and below the fans.
Figure 9. The predictedflow distribution where three gaps are blocked at the top of
the stack, where the blockage covers the size of the main eddy.
259
Conclusions
i'ur 11mtransitional f10w ctmulatrrco, c o I w q w c e ha$ reached catasfactory tdcrances
1% ttcn
tlic
c t ~ l i ~ i B ~ ~Etas
i i t r ihecn rim
in trart5tcnr la&,
ftlecfirng J n
of the total inthiu 'xtter 30 to 100 iteriitictns per ttnie stcp firr t m e steps o f 0 0 1 s. tirid
scnsiaiviry studies have showi tl-rat ~ion-umiformgrid\ are rreccs,siq hccause of tile
w&ic.n clianges
1n
flow cross
~ ~ t i o r and
i .
the flow
'rirniildfiotis drc'
imensitwe to grid
refnrmcnt fur non-unifonri grids with rnore than 300,000 c e k The hest agrcrment
bstw*ceii the cxpcrinienlally-m~rtsurcd Row distributions betwen fillet spaces and
tfiusc
predicttd by the sintilation haw been achieved fur total I rffectiw) tiux>sitics
betwecn thc imiinat tiscostty fctr water and ten tines that ralue T h i s ctwnge
LII
v~m)siry1s nut very large (less than an order of mgnttude), given that effcctsve
rurbuicnt viscosities
ones. This rcsult
15
ilIC
typically wvcral orders of mgnitudc greeter than laminar
consistent w t t i thc transitional flows here '1 he effect of weights
with sufficient thickness above the stack i s likely to rc*ducc the degree of ntrn-
uniformity in air vctocitics through the stack, hecauw the stack may then be \eparatcd
from the eddy at the top of rhe plenum chamber
Acknowledgements
l'hanks are dtie to the Kcw Zcaland Fuunciatton for Research Science and "I'echiiolog)
t Publrc Gooti Scicucc f:untl) under sub-contract PXOO for financial support.
assistance of. Dr J J h'iltfsm and Associate Professor D.F, Fletcher
in
ilhc
tlic Department
of Chemical Engineering ar the 1 3uversity of Sydney. Austrrtfta, is also acknoalrdged
fir helphtl cnmmcnts, iriiiial wntk. advice regarding turbulence modelling in C'FL3 and
fcecibacli.
Progress in the Modelling of Air Flow Patterns in Softwood Timber Kilns
4.
5.
6.
7.
8.
9.
Hua, L., Bibeau, E., He, P., Gartshore, I., Salcudean, M., Bian, Z., and Chow, S. 2001. Modelling of
Airflow in Wood Kilns, Forest Products Journal, 5 1(6), 74-8 1.
Nijdam, J.J., and Keey, R.B. 1999. Airflow Behaviour in Timber (Lumber) Kilns, Drying Technology
- An International Journal, 17(7&8), 15 11-1 522.
Nijdam, J.J., and Keey, R.B. 2002. An Experimental Study of Airflow in Lumber Kilns, Wood
Science and Technology, 36, 19-26.
Wilcox, D.C. 1996. Turbulence Modelling for CFD, DCW Industries, Inc., California.
CFDS-CFX4.2: User Manual. 1999. Computational Fluid Dynamics Service, AEA Technology PLC,
Hanvell Laboratory, Didcot, Oxfordshire, UK.
Fletcher, D.F., Haynes, B.S.,Chen, J., and Joseph, S.D. 1998. Computational Fluid Dynamics
Modelling of an Entrained Flow Gasifier, Appl. Math. Modelling, 22(10), 747-757.
261
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