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ICONE25-67714

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Proceedings of the 2017 25th International Conference on Nuclear Engineering
ICONE25
July 2-6, 2017, Shanghai, China
ICONE25-67714
ANALYSES OF OFF-DESIGN POINT PERFORMANCES OF SIMPLE AND
INTERCOOLED BRAYTON HELIUM RECUPERATED GAS TURBINE CYCLES FOR
GENERATION IV NUCLEAR POWER PLANTS
Arnold Gad-Briggs
Cranfield University
Cranfield, Bedfordshire, U.K.
Email: a.a.gadbriggs@cranfield.ac.uk
Pericles Pilidis
Cranfield University
Cranfield, Bedfordshire, U.K.
ABSTRACT
The Design Point (DP) performance of a Nuclear Power
Plant (NPP) is fairly straightforward to establish for a given
mass flow rate, turbomachinery compressor Pressure Ratio
(PR) and reactor Core Outlet Temperature (COT). The plant
components are optimum for that point but this is no longer the
case if the plant's operating conditions are changed for part-load
performance. Data from tests or previous operating experiences
are useful in determining typical part load performance of
components based on characteristic maps. However, when
individual components are linked in a plant, the range of
operating points for part load performances are severely
reduced. The main objective of this study is to derive OffDesign Points (ODPs) for the Simple Cycle Recuperated (SCR)
and Intercooled Cycle Recuperated (ICR) when considering a
temperature range of -35 to 50°C and COTs between 750 to
1000°C, using a modelling & performance simulation tool
designed specifically for this study, which calculates the best
operational equilibrium ODPs that are critical to the economics
of the NPP. Results show that the recuperator High-Pressure
(HP) side and reactor pressure losses alter the actual operating
parameters (mass flow rate and compressor PR). The SCR
yielded a drop in plant cycle efficiency of 1% for a 4% pressure
loss in comparison to the ICR (5%) for the same amount of
recuperator HP losses. Other parameters such as the precooler
and recuperator Low-Pressure (LP) losses still retain the same
operating inlet PRs and mass flow rates regardless of the
magnitude of the losses. In the absence of characteristic maps
in the public domain, the ODPs have been used to produce
characteristic trend maps for first order ODP calculations. The
analyses intend to aid the development of cycles for Generation
IV NPPs specifically Gas Cooled Fast Reactors (GFRs) and
Very High Temperature Reactors (VHTRs), where helium is
the coolant.
INTRODUCTION
Generation IV (GEN IV) reactors design intent is to
advance the designs of Nuclear Power Plants (NPPs), with one
of the main focus being on part power cycle efficiency. The
criticality of the economics of the cycle lies in demonstrating
improvements when compared to the incumbent designs.
Furthermore, beyond deriving better plant efficiencies at
Design Point (DP), the Off-Design Point (ODP) is equally
important to ensure the plant runs at its most efficient when
changes are necessary. However, this is challenging because
the coupled individual components limit the amount of ODPs
for the plant to run at optimum. Furthermore, finding these
ODPs require complex iterative calculations. The objective is to
use DPs to derive a set of ODPs for the Simple Cycle
Recuperated (SCR) and Intercooled Cycle Recuperated (ICR)
configurations when a temperature range of -35°C to 50°C, and
a reactor Core Outlet Temperature (COT) range of 750°C to
1000°C are considered in addition to analyses of the component
effects on the ODPs. The cycles are analysed in a closed
Brayton direct configuration using helium as the working fluid.
NOMENCLATURE
Notations
Area (m2)
Spec. Heat of Gas at Constant Pressure (J/kg K)
Compressor Work (W)
Mass Flow Rate (kg/s)
Non-Dimensional Mass Flow
Q
Reactor Thermal Heat Input
Heat Flux (W/m2)
Pressure (Pa)
Pressure Ratio
Specific Work/Power Output (W/Kg/s)
Temperature (K or )
Temperature Ratio (T4 / T1; expressed in Kelvin)
1
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CH
Precooler
CIT
Core Inlet Temperature
CN
Corrected Speed
COT
Core Outlet Temperature
DP
Design Point
GEN IV Generation Four
GFR
Gas-Cooled Fast Reactor
GIF
Generation IV International Forum
HP
High-Pressure
HE
Recuperator
HPC
High Pressure Compressor
ICR
Intercooled Cycle Recuperated
ISA
International Standard Atmosphere
LP
Low-Pressure
LPC
Low Pressure Compressor
M
Mixer (Fig. 5)
NPP
Nuclear Power Plant
NTU
Number of Transfer Units
ODP
Off-Design Point
OPR
Overall Pressure Ratio
R
Reactor
RPV
Reactor Pressure Vessel
S
Splitter (Fig. 5)
SCR
Simple Cycle Recuperated
TET
Turbine Entry Temperature
Generation IV (Gen IV) Systems
The Generation IV (Gen IV) systems of interest are the
Gas-Cooled Fast Reactor Systems (GFRs) and Very-HighTemperature Reactor Systems (VHTRs). The GFR is cooled by
helium. It encompasses a reactor with high temperature
capability and a nuclear core with fast spectrum. The Core
Outlet Temperature (COT) is between 850-950°C and is based
on an efficient Brayton cycle. The benefits of using helium as a
working fluid include single phase cooling in all circumstances,
chemical inertness and neutronic transparency [1]. The VHTR
is also a helium cooled (in gaseous phase) high temperature
thermal reactor including graphite moderation in solid state.
Graphite also has the advantage of retaining good mechanical
properties at high temperature. Helium as a stable coolant is
required in this reactor configuration in order not to cause a
chemical reaction with the graphite moderator. There are
planned and on-going development projects for the GFR and
VHTR. These projects relate to testing of basic concepts and
performance phase validation. These demonstrators are
discussed in [2].
Turbine Work (W)
Work (W)
Useful Work (W)
Greek Symbols
Ratio of Specific Heats
Delta, Difference
Effectiveness (Heat Exchanger; cooling)
Efficiency
Referred Temperature Parameter
Referred Pressure Parameter
Subscripts
Turbine Temperature (also known as Blade Temp.)
Compressor
Compressor Inlet
Compressor Map
Compressor Outlet
Cooling
Compressor Exit Coolant
e
Power for Electrical Conversion
Turbine Entry Temperature
Helium
Helium with minimum gas conditions
Intercooled Cycle; intercooled coefficient
Isentropic (Compressor)
Isentropic (Turbine)
Reactor (Heat Source)
Reactor (Heat Source) Inlet
Reactor (Heat Source) Pressure Losses
Reactor (Heat Source) Outlet
Plant Non-Dimensional Flow Conditions
Precooler Inlet (also applicable to intercooler)
Precooler Pressure Losses (same as above)
Precooler Outlet (same as above)
Recuperator
Recuperator cold side
Recuperator hot side
Recuperator High Pressure Losses
Recuperator Low Pressure Losses
Recuperator Real (specific heat transfer)
Recuperator Max (specific heat transfer)
Station number
Station Inlet
Thermal Power
Turbine
Turbine Map
Turbine Outlet
Turbine Inlet
Simple and Intercooled Recuperated Brayton Cycles
The Simple Cycle Recuperated (SCR) and Intercooled
Cycle Recuperated (ICR) Nuclear Power Plant (NPP)
configurations have been documented extensively in [3]. The
SCR and the ICR both have the compressor and turbine as part
of the turbomachinery, the precooler, reactor and recuperator.
One of the main differences is the ICR employs an intercooler
aft of the compressor in addition to a second compressor.
Superscripts
’
Recuperator inlet conditions
Abbreviations
C
Compressor
2
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Another notable difference is their respective plant
performances. The ICR improves the specific and useful work
by reducing the compressor work. The working fluid
downstream of the first compressor undergoes a reduction in
temperature in the intercooler. The temperature is reduced to
the same inlet temperature as the first compressor, prior to entry
into the second compressor [4]. This effect on the overall plant
cycle efficiency of the ICR translates into an increase of 3%
and upwards in comparison to the SCR when optimised turbine
cooling methods are utilised [4]. One of the main drawbacks
with the ICR is the complexity of the plant configuration with
an intercooler. The benefits of changing from air to helium in a
nuclear gas turbine, including the thermodynamic
consequences, have been extensively covered in [5], [6] and
[7]. The papers focus on off-design operation, control and
transient operational modes of a helium nuclear gas turbine
plant. The papers do not analyse conditions as proposed in this
study but provide good theoretical bases for application.
curves in the turbine map relate to a turbine configuration
where the choking is dependent on speed i.e. happens in the
rotor. However for this study, the model uses a single curve per
NPP configuration indicating that choking happens in the
stators and is not dependent on speed. The turbomachinery
maps are generic maps using relative values. They are based on
open source experimental data. Although the maps do not relate
to any NPP tests, the turbomachinery components behave in the
same way. As a necessity, the maps were corrected to reflect
helium as the working fluid and scaled using scaling factors
within the model to the size of the turbomachinery components.
This approach was considered satisfactory for the study.
The model calculation method did not adopt a
conventional approach for matching of the components. Rather
a comprehensive method was used in the absence of
characteristic maps for the intercooler, the recuperator at the
high and low-pressure sides and the reactor. This method varies
the compressor PR and the enthalpy drop ratio (the enthalpy
drop is also used to gauge the degree of heat rise by the reactor)
amongst the array of input data to calculate the ODPs. The
calculation method is explained further in the section ODP
Component Matching Process. Figure 5 depicts the model
structure for SCR but it is interchangeable for ICR. The
equations implemented within the code environment are
described in the proceeding sections for steady state DP and
ODP calculations against each component and cycle.
When focusing on Off-Design Point (ODP) performance,
the model encompasses the turbomachinery component maps,
which are represented as polynomials within the model. The
compressor map is first characterised by corrected nondimensional speed curves, which are plots of the compressor
Pressure Ratio (PR) as a function of the non-dimensional mass
flow (NDMF). Secondly, isentropic efficiency lines are plotted
with the compressor efficiency as a function of the compressor
PR. The turbine can be characterised by a single curve plotted
for a specific NPP configuration, with the NDMF as a function
of the enthalpy drop ratio (also an indicator of the heat rise in
the reactor). Similarly, to the compressor, the turbine isentropic
efficiency curves can be presented by the component efficiency
as a function of the turbine PR or the enthalpy drop ratio. The
compressor and turbine maps are illustrated in Figs. 3 and 4
respectively. With reference to the turbine map NDMF, it can
be observed that the NDMF for any constant speed line rises to
a certain level of enthalpy drop ratio or turbine PR and remains
constant in the choking region. In other words, the maximum
value of mass flow rate is reached at an enthalpy drop ratio or
turbine PR that produces choking conditions in the turbine. The
Modelling of Nuclear Power Plants and Performance
Simulation Tool
Figures 1 and 2 illustrate typical schematics of the SCR
and the ICR NPPs respectively. Table 1 provides the key
Design Point (DP) values for modelling, using the FORTRAN
based modelling and performance simulation tool designed
specifically for this study. With regard to DP performance, the
tool has been designed to calculate the mass flow rate,
temperature and pressures for each component based on known
cycle inlet conditions and COTs, with consideration of
component efficiencies, pressure losses and cooling
requirements in order to derive the NPP output and efficiency.
The tool can also analyse the effects on cycle output, capacity
and efficiency by investigating changes to any of the above
parameters.
Figure 1 – Typical Simple Cycle with Recuperator
(SCR) [8]
Compressor
Prerequisite parameters for DP considerations of the
compressor include the compressor PR, compressor inlet
conditions (temperature, pressure and mass flow rate),
component efficiency and the working fluid gas properties (
and ).
The compressor outlet pressure (in Pa) is:
(1)
The isentropic efficiency of the compressor is and is also
indicative of the specific work input or total temperature
increase.
3
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Thus, the temperature (°C) at the exit can be derived
from the inlet temperature, PR, isentropic efficiency and ratio
of specific heats:
(2)
The mass flow rate (kg/s) at inlet is equal to the mass flow
rate at outlet as there are no compositional changes:
(3)
Figure 3 – Compressor Map Showing Corrected
Speed Lines and Contours of Efficiency [10].
Figure 2 – Typical Intercooled Cycle with Recuperator
(ICR) [9]
(4)
whereby (5)
The compressor work (W) is the product of the mass flow
rate, specific heat at constant pressure and the temperature
delta:
Figure 4 – Turbine Map Compressor Map Showing
Corrected Speed Lines and Contours of Efficiency
[10].
Bypass splitters (S in Fig. 5) are incorporated within the
performance simulation tool to allow for compressed coolant to
be bled for reactor and turbine cooling.
Turbine
Prerequisite parameters of the turbine include the turbine
inlet conditions (temperature, pressure and mass flow rate), the
pressure at outlet, component efficiency and the working fluid
gas properties ( and ).
4
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Figure 5 – Performance Simulation Tool Structure for
SCR [4]
The temperature (°C) at the outlet is derived from the
following expression:
(6)
(9)
(10)
(11)
With , the energy balance is:
(7)
(12)
Thus, the hot outlet (°C) is:
(13)
With regard to pressures, the exit conditions can be
calculated if the pressure drops (%) across the hot and cold
sides are known:
Recuperator
The calculation method for the rate of heat transfer is based
on the Number of Transfer Units (NTU) method, which has
been documented by [11] and applied for complex cross flow
heat exchangers by [12]. The algorithm in the code ensures
satisfactory results and numerical stability.
Prerequisite
parameters
include
the
recuperator
effectiveness, hot and cold inlet conditions (pressure and
temperature) and the delta pressures due to losses at the high
and low pressure sides.
Effectiveness of the recuperator is given as:
A mixer (M in Fig. 5) is incorporated within the
performance simulation tool to allow for the coolant to mix
with the hot gas to simulate turbine cooling.
The temperature for the cold end (°C) is then expressed as:
As with the compressor, Eqs. (3) and (4) also apply to the
turbine for mass flow rate (kg/s) conditions and turbine work
(W) but:
With helium as the working fluid, is considered to be
constant, thus in the energy
balance equation. The temperatures at the hot and cold ends can
be obtained when considering Eq. (10) (either hot or cold sides)
and considering an arbitrary effectiveness.
and the real heat flux (W/m2) is:
(14)
(15)
Due to no compositional changes, mass flow rate (kg/s)
conditions are:
(8)
(16)
(17)
Precooler and Intercooler
Prerequisite parameters for the precooler and intercooler
(ICR and IC only), take into account that the components are
upstream of the first and second compressors respectively, thus
compressor inlet temperature and pressure are of importance
including the pressure losses. The conditions for the precooler
are as follows:
The maximum amount of heat flux (W/m2) of the
recuperator , must consider the hot and the cold inlet
conditions. It must also consider the minimum specific heat
because it is the fluid with the lowest heat capacity to
experience the maximum change in temperature. This is
expressed as:
5
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(18)
(19)
(20)
the debited cooling flows will have to be added to the total flow
for ODP matching. Thus, the COT and the TET are the same
temperature.
Cycle Calculations
The useful work, specific work and thermal efficiency
output values are of interests after executing each set of
thermodynamic station parametric calculations. The useful
work (We), that is the work available for driving the load is:
With regard to the intercooler, Eqs. (18), (19) and (20) also
apply, but are differentiated for the intercooler. An addition of a
second compressor for ICR only, means that the PR for both
compressors is determined as:
(21)
whereby Eq. (27) is also applicable to the ICR and IC cycles
but the is the summation of the LPC and HPC work
requirements to be delivered by the turbine. The specific work
or capacity of the plant (W/kg/s) is:
whereby the coefficient denotes the number of intercoolers
in the cycle +1, leading to a reduction in the PR per compressor
(ICR only).
Modular Helium Reactor
The helium reactor is a heat source with pressure losses.
The prerequisite are the thermal heat input from burning the
fuel and the known reactor design pressure losses.
The heat source does not introduce any compositional
changes, thus mass flow rate (kg/s) is:
(27)
(28)
and the thermal efficiency (%) of the cycle is:
(29)
The DP performance values for the SCR and ICR are provided
in Table 1. They were derived based on modest turbomachinery
efficiencies for the purpose of having comparable efficiencies
with the experimental maps used for this study.
(22)
Pressure taking into account losses (%):
Expressions for ODP Performance Calculations
When calculating the ODP performance, the maps become
part of the process. Furthermore, they are scaled for capacity
purposes to suit the particular plant cycle configuration, thereby
avoiding the use of multiple maps. For constant speed steady
state ODP performance, the temperature inlet conditions into
the compressor for station 1 (ignoring compressor geometry
measurements) is expressed as a referred parameter for
standard ISA conditions of temperature for the purpose of
determining the reference speed curve. This is corrected into a
dimensionless parameter for the purpose of adapting the map
for helium and is expressed as:
(23)
and the thermal heat input (Wt) is:
(24)
whereby (25)
A mixer (see Fig. 5) is incorporated within the code to
allow for coolant to be mixed with the heated fluid upstream of
the reactor to simulate reactor vessel cooling.
Cooling Calculations
Prerequisites to calculate the cooling flow from the
compressor exit, which is required for the cycle (cooling flow is
taken as a percentage of mass flow rate) are the turbine metal
temperature (simply known as blade metal temperature),
compressor exit coolant temperature, COT/TET (simply known
as gas) and cooling effectiveness. The cooling effectiveness
(<1) is expressed as:
(30)
Equation 30 defines the speed as the handle and
determines the corresponding polynomial speed curve for the
inlet temperature (as shown in Fig. 3).
Once the inlet conditions are defined, the model proceeds
to calculate each component station condition. For the benefit
of establishing the NDMF across all components, firstly the
compressor incorporates the below referred parameter for
temperature and pressure, which is also corrected from the map
to a dimensionless expression to get the true NDMF for helium.
(26)
In the case of this study, Eq. 26 is ignored because no
turbine or reactor core cooling is considered for the purpose of
simplifying the ODP performance calculations. This is because
6
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Table 1 – DP Performance for SCR and ICR
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ODP Component Matching Process
It is important for compatibility purposes that the NDMF,
plant output (useful work ignoring losses in the electric
generator) and turbomachinery rotational speed are satisfied for
matching to be successful. When calculating the ODP
performance, it is necessary to select a variable or ‘handle’,
which is used to determine the matching conditions of the plant.
A direct method of obtaining the ODP performance is not
possible. The calculation process is iterative. The shaft
coupling of the turbomachinery components and the generator
determines the method required for effective matching. For this
study, a single shaft direct coupling between the
turbomachinery and the electric generator running at a constant
rotational speed (independent of load variation of the plant) is
utilised, therefore compatibility of rotational speed is satisfied
by default. For NDMF compatibility, the plant NDMF, which is
based on the conditions between station 1 to station 4 must
equal the respective NDMF on the turbine map, which
corresponds to the actual enthalpy drop ratio. With
consideration of a given matching tolerance, the NDMF
compatibility is expressed as:
Ignoring component geometry, the NDMF considers the mass
flow rate, temperature and pressure at inlet and the gas
properties:
(32)
whereby Eq. (32) is for the SCR and also applicable to the
ICR. For the ICR, the sequence in Eq. (32) begins from station
2a. Figure 6 describes the process of matching and calculating
the ODP performance.
* Recuperator effectiveness is based on technological improvements in [13]
Results and Discussion
Variation of Inlet Temperature (T1)
Tables 2a and 3a provide the ODP performance results for the
handle variation of T1 (-35°C to 50°C) for the SCR and the ICR
respectively. The SCR and ICR both show increases in PR from
DP (28°C) as T1 moves to the right i.e. the temperature is
reduced (see Fig. 3). The ODP with T1 at 50°C shows a
reduction in PR as expected. With regards to Tables 2a and 3a,
an increase in PR is proportional to increase in mass flow rate
and correlates to an increase to the right of the compressor map.
Equation (31) denotes that the changing parameter in the
expression is the mass flow rate, which has to change in line
with the PR in accordance with the typical characteristics of the
map. The resultant effect is different for both cycles. The SCR
indicates that the ODP equilibriums whereby T1 is less than the
DP value of 28°C, showed increases in cycle efficiency and
power output. This was not the case for the ICR; more
specifically with the cycle efficiency. The ODPs in very low
temperature inlet conditions (between 9°C to -9°C) yielded
cycle efficiencies that are 10% to 18% lower than the DP cycle
efficiency for the ICR.
(31)
Equation 31 also fully applies to the turbine map,
whereby it is corrected to give the true NDMF values for
helium. With regards to other stations of the NPP, the
dimensionless part of Eq. 31 is calculated in the absence of
component maps for the intercooler, recuperator HP & LP side
and the reactor. This is made possible because the compressor
has established the flow conditions upstream. For the actual
ODP calculation process, the sequence of calculations
commences by scaling the map using scaling factors, then Eq.
30 to define the inlet temperature by selecting the specific
speed curve polynomial. Subsequently, Eqs. 1 to 25 are used to
calculate the component and station ODP performance values,
with the dimensionless part of Eq. 31 utilised to calculate the
NDMF for each component of interest. Equation 26 is ignored
for ODP performance purposes for reasons previously
explained. Equations 27 to 29 are then used to calculate the part
7
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Figure 6 – Plant Matching Process
Table 3 – ODP Performance for ICR
Table 3a – T1 (Corrected Speed Line) as Handle (ICR)
Table 2 – ODP Performance for SCR
Table 2a – T1 (Corrected Speed Line) as Handle (SCR)
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Table 2b – COT (TET) as Handle (SCR)
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Table 3b – COT (TET) as Handle (ICR)
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Copyright © 2017 ASME
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The intercooler is the additional component and suggests
that the temperature variation and off-design operation using
the intercooler may have an adverse effect on the efficiency of
the ICR at modest temperatures below the DP. The reason is
because, the ICR aims to reduce the compressor work of the
cycle but there is a notable increase in compressor work, which
is not beneficial for the ICR. This reduces the useful work and
subsequently the cycle efficiency. On the other hand, a T1
higher than the DP value has less of an effect on the efficiency
of the ICR, in comparison to the SCR for their given DP
efficiency values. This also correlates with the power output of
the cycles, whereby the ICR achieves a 71% part power output
at 50°C, in comparison to 58% for the SCR.
Table 4a – ODPs for SCR (Reactor Pressure Loss)
Variation of COT/TET (T4)
Tables 2b and 3b provide the ODP performance results
for the handle variation of the COT (750°C to 1000°C). The
trends for power output, mass flow rate and efficiency are as
per expectation on the single corrected speed curve (no
variation in T1). The ODP performance is slightly better for
ICR; 12% more power output at 750°C COT than the SCR
although this is significantly reduced to 3% at 900°C. This
indicates that the ODP performance at lower COT is better
suited to the ICR. The efficiency is also slightly improved for
the ICR. There is a noticeable difference between both cycles,
which is less favourable for the ICR. This is to do with the
change in mass flow rate. The change at 750°C equates to an
increase of 0.26% for the ICR in comparison to 0.20% for SCR.
The reduction in mass flow rate at 1000°C equates to 0.07% for
the SCR in comparison to 0.21% for ICR. At 1000°C, the
reduction in mass flow rate is greater for the ICR by a factor 3.
This will impact control methods for the power plant and may
mean a sizeable inventory may be required for the ICR in
comparison to the SCR.
Variation of Recuperator HP Pressure Loss
There is no operational restriction to be observed as it is the
case for the reactor. As such, there is no obvious trend in the
derived ODPs. However, the ICR ODP performance for a pressure
loss up to 5% yielded ~8% drop in cycle efficiency.
With regard to the SCR, there are negligible adverse effects in
operating the ODP up to 4% pressure loss for the recuperator (1%
cycle efficiency drop in ODP for up to 4% pressure loss). At 5%
pressure loss, the ODP gives a 5% efficiency drop for the SCR. The
difference in the SCR and ICR with regards to the effects on
efficiency suggests that the matching process is less complex for the
SCR due to less components. In both cycles, the recuperator high
pressure losses can be considered as a handle when calculating the
ODP performance because the inlet conditions with regards to mass
flow rate and cycle inlet PR are altered to give the optimum
conditions in off-design settings.
Variation of Reactor Pressure Loss
Tables 4a and 4b provide the ODP performance results
for the variation of the reactor pressure loss (1 to 5%). The
reactor pressure losses are comparable for both cycles with no
real trends, with the exception of mass flow rate reduction. This
is because the scenario for matching considerations ensures that
the heat input for DP is not exceeded or is as close as possible
to the DP due to safety operational reasons. When the ODP
efficiency values in Tables 4a and 4b are considered, a pressure
loss of 5% can amount to an efficiency drop of 8% and 11% for
the ICR and SCR respectively. However, if there are no
concerns with operational safety, ODP conditions at lesser
matching tolerances could be derived, that would minimise the
drop in efficiency so long as there are no limitations on heat
input in the reactor. In such a scenario where there are no
limitations, the reactor pressure loss could be considered as a
handle, which could be varied. Another consideration is the
load following capabilities of each cycle to maintain the reactor
thermal power. The plant will have to operate at the calculated
ODPs; more so, the control system times to achieve the reactor
thermal power will be of importance to the choice of cycle.
2
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Note: For the last 2 columns, divide numbers by 100 to get the actual %
or decrease.
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or decrease.
Table 4b – ODPs for ICR (Reactor Pressure Loss)
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Variation of Precooler and Recuperator LP Pressure Losses
The DP conditions at inlet with regards to mass flow
rate and PR were unchanged during ODP performance
calculations for the precooler and the recuperator low pressure
losses. This also means that there is no change in the
compressor work, but the turbine work is reduced and will
result in lower useful work. For both losses, the recuperator hot
gas temperature at inlet is slightly higher and will yield to a
slightly hotter gas going into the precooler, due to the reduced
heat flux of the recuperator, which is affected by the pressure
9
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drops. This translates to a reduction in cycle efficiency. Given
there are no changes in inlet conditions, there is no benefit in
performing complex ODP matching calculations using these
losses as handles, thus no need for maps. The first order DP
performance calculations are also applicable. The losses can
then be varied to understand the effect, thus the ODP iterative
calculation and lengthy process is not necessary. The precooler
effects are more pronounced for the cycle efficiency; overall,
both pressure loss effects are higher in the SCR (11%
recuperator LP loss; 14% precooler) in comparison to ICR (6%
recuperator LP loss; 6% precooler) but more importantly the
losses are the same, whether in design or off-design.
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Deriving Characteristic Maps of ODP Performance
Figures 7 to 11 illustrate characteristic maps for the
recuperator (effectiveness, HP losses for the cold and hot side)
and the reactor for first order ODP calculations. With regards to
Figs. 7 and 8, these maps apply to the recuperator cold side (HP
side) and hot side (LP side). They are based on the
effectiveness of the recuperator and linearly plot the
effectiveness as a function of a dimensionless parameter.
Figures 9 and 10 apply to the HP side (cold) and LP side (hot)
respectively for the SCR and ICR, based on variation of the HP
side pressure loss. The curves plot a dimensionless value as a
function of the pressure losses and it is accurate to within +1%
(error margin). Figures 9 and 10 are only utilised after the
recuperator has been matched based on a known effectiveness
and HP pressure loss. The dimensionless parameter in Figs. 7 to
10 considers in all cases the NDMF divided by the mass flow
rate at inlet into the recuperator and then that expression is
divided by the same expression but for the outlet, which will
vary based on the station temperature and pressures. Figure 11
is the reactor map, which covers the SCR and ICR and
characterises the temperature delta between Core Inlet
Temperature (CIT) and COT as a function of the reactor heat
input divided by the mass flow. An increase in heat input is also
based on an increase in mass flow. Thus it is expected that the
degree of heat input divided by mass flow, will directly be
dependent on the amount of temperature rise required by the
reactor to deliver the ODP COT.
It is recommended that a major part of the development
activity for Gen IV should be dedicated to validating the results
and characteristics maps against all operating design and off
design conditions. This will enable the optimisation of the tools
such as the one utilised in this study. Ideally, it should be based
on operational data to improve the applicability and accuracy of
such tools, which will encourage its use thereby reduce costs
associated with extensive test activities.
Figure 7 – Recuperator Map (Cold Side) Effectiveness
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Figure 9 – Recuperator Map (Cold Side) - High
Pressure Losses
Conclusion
In summary, the objective of this study was to use the
DPs of a SCR (140MW rating) and ICR (250MW rating) to
derive the ODP performance for a temperature range between 35 to 50°C and COT between 750 to 1000°C using a modeling
and performance simulation tool designed for this study.
10
(
.
Copyright © 2017 ASME
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% •
$'
$&
$$
$"
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"
#
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%
•
*
Figure 10 – Recuperator Map (Hot Side) - High
Pressure Losses
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•
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Figure 11 – Reactor Map
The results provide good bases to support preliminary cycle
part power performance design, testing, validation and
verification activities of Gas Cooled Fast Reactors (GFR) and
Very High Temperature Reactors (VHTR) for Generation IV
NPPs. The main conclusions are:
•
•
•
The ODP in very low temperature inlet conditions
(between 9°C to -9°C) yielded cycle efficiencies that
are 10% to 18% lower than the DP cycle efficiency of
the ICR. This was not the case for the SCR. It requires
investigating with the focus being on the intercooler. It
is proposed to look at this in another study whereby
the ICR can be compared to the Intercooled Cycle (IC)
without recuperation.
The ODP performance, when COT is varied is slightly
better for ICR; 12% more power output at 750°C COT
than the SCR although this is significantly reduced to
•
•
11
3% at 900°C.
This indicates that the ODP
performance at lower COT is better suited to the ICR.
There is a noticeable difference between the SCR and
ICR with regard to changes in mass flow rate, when
the COT is varied. The reduction in mass flow rate at
1000°C equates to 0.07% for the SCR in comparison
to 0.21% for ICR. At 1000°C, the reduction in mass
flow rate is greater for the ICR by a factor 3. This will
impact control methods for the power plant and may
mean a sizeable inventory may be required for the ICR
in comparison to the SCR.
Another consideration is the load following
capabilities of each cycle to maintain the reactor
thermal power. The plant will have to operate at the
calculated ODPs; more so, the control system times to
achieve the reactor thermal power will be of
importance to the choice of cycle to avoid high
thermal flux for longer than necessary periods in the
reactor.
It is proposed to considering the recuperator HP loss
as a handle, which can be varied when calculating
ODP performance for SCR and ICR. As noted for the
SCR, up to 4% pressure loss for the recuperator results
in 1% cycle efficiency drop in ODP. The recuperator
HP loss has an adverse effect on the ICR for ODP
performance (5% drop in cycle efficiency for a
pressure loss of 4%).
There is no benefit of ODP performance when
considering the precooler and recuperator LP side
pressure losses and their effects on the part power
performance. This is because the DP conditions at
inlet with regards to mass flow rate and PR are
unchanged.
Control methods, which can be utilised for both cycle
configurations need to be investigated to understand
requirements for achieving efficient part power
performances.
For NPP economics, the cost of operating the plants at
part power for the various scenarios analysed herein, is
not
understood.
Thus
a
Techno-economic
Environmental and Risk Analysis study needs to be
conducted to aid better financial decisions on choice of
plant configuration for optimum part power cycle
efficiencies.
Validation is recommended for the tools such as the
one developed for this study. This will enable
optimisation to improve the applicability and accuracy
Copyright © 2017 ASME
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and will encourage its use thereby reducing costs
associated with extensive test activities.
[11]
ACKNOWLEDGMENTS
The authors wish to thank the Gas Turbine Engineering
Group at Cranfield University for providing the necessary
support in progressing this research study in particular Dr.
Theoklis Nikolaidis for his valuable input in assessing the
model and this technical recommendations during the paper
review.
[12]
[13]
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12
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