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 Copyright © 2017 ASME Downloaded From: http://proceedings.asmedigitalcollection.asme.org/ on 10/25/2017 Terms of Use: http://www.asme.org/about-asme/terms-of-use 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 Copyright © 2017 ASME Downloaded From: http://proceedings.asmedigitalcollection.asme.org/ on 10/25/2017 Terms of Use: http://www.asme.org/about-asme/terms-of-use 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 Copyright © 2017 ASME Downloaded From: http://proceedings.asmedigitalcollection.asme.org/ on 10/25/2017 Terms of Use: http://www.asme.org/about-asme/terms-of-use 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 Copyright © 2017 ASME Downloaded From: http://proceedings.asmedigitalcollection.asme.org/ on 10/25/2017 Terms of Use: http://www.asme.org/about-asme/terms-of-use 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 Copyright © 2017 ASME Downloaded From: http://proceedings.asmedigitalcollection.asme.org/ on 10/25/2017 Terms of Use: http://www.asme.org/about-asme/terms-of-use (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 Copyright © 2017 ASME Downloaded From: http://proceedings.asmedigitalcollection.asme.org/ on 10/25/2017 Terms of Use: http://www.asme.org/about-asme/terms-of-use Table 1 – DP Performance for SCR and ICR $ ! %#!# %"-071 0!# (%%"10:1 8> 8> 3 ?;6-6 ?;6-6 3 !# %%"091 =>< <== 3 %#$$(#071 9-87 >-87 7-;? 8-9; / $$!*#%% %071 .$ :89-> :79->= !"#$$!# +0$ %#!"1 >; >8 B (# +0$ %#!"1 >7 >8 B 22("#%!#&) $$ ?< ?< B #$$(#!$$0#!!#1 8-; 8-; B #$$(#!$$0 %#!!#! +1 / 8-; B #$$(#!$$0%!#1 8 8 B < ! < ! B (# !! !*0B!$$!*#%1 / / B %!#!! !*0B!$$!*#%1 / / B !"#$$!#!# 7;>-; 8?7-9 (# !# 8?=-; ;99-? % "(% 9<6-; ;>;-? "!#0"%+1 6-99 6-;? . $.$ $(!# 79?-7 8:8-< % + 9>-< :7-: B #$$(#!$$0("-$1 #$$(#!$$0("-$1 power conditions when the component matching has been successful. %$ 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 Copyright © 2017 ASME Downloaded From: http://proceedings.asmedigitalcollection.asme.org/ on 10/25/2017 Terms of Use: http://www.asme.org/about-asme/terms-of-use !''7 " #%&&"% #& ! • • • • • • • • • • • • • • !'' *%! #& "!' &! &! &!2, '"%%&&*%"&&56&, %""%567*#%'"%56%, ,>"%%'&#! ,>"%%'&#!&592?4:2:;6 "%%'&#!&% "%%'&#!&%#%&!'3<='"=9 3<!% !'6 "%&#!+% % 6 "%&#!+%-5*%!1B:9 ! &'"'% ! &'"'% !" #%&&"%/ *'' #%'*%%& #%'*% '",'%2'"!' • • • • • • • • • • • • '%&(& !'*%!*%+%'%&(& '*&!*%! "%+%-#"!'0*'*&!*%!" 1B:93<!% !'6 &'"!"%%&#"!!*%!/ !! !*%! *%! / "# *'' #%'*%%"# ' *';! '!' '",'%2'"!' • !'%2'"!' !'%2'"!' "%!5B:9 "%! 5 93<6 6 • "%!5B:9 *''&A!' +&*%! +&*%! "!("!""#*&! " #('-A"!("!""#*&!'&+&2"%!& @ *&'$* *&'$* "%" #('-A@ %!'!'"!(" " #'*("!7%!'!'"!("!&(& 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) ' # /+& /+& /+& /+& /+& /+& # (. +& / ( !/ !)+ '+/ '*+ '-) '-/ '.- ('' *(). '+.*,(/-+*')/&. &)) )./,.'()-+(&)-+ -/// &(' **.'/'/+-. ).& '.*(' &*' *,&--(&-'/*('(,('*&- &*, *-+'/()'/+ *,-. ()+.+ &+& +'''-(),(+,&+/+ ),/- &-( "" ' 2 ),&*. ).+. (,)+' )&), ***,' *'*) *.,.- *)/- +)**, **') ,-,.* +*,( 2 .+ .* .( .) .& /) 2 +. ')( '+* '-& (,, # /+& /+& /+& /+& /+& /+& # (. +& / ( !/ !)+ ()+ ('* (*. (+( (,+ (. 2 .( .( .) .) .) .) Table 2b – COT (TET) as Handle (SCR) & " .*% ,*% -%% -*% .%% &%%% " '- '- '- '- '- '- &*. &*) &** &*. &*. &+& 1 1 )'(- &*-)+'.,*)&(.%- %(( (+%)- (-*- -' )')+*&)-)-''(%& ,)*( %&- ',&-* ',)' -& )')), &*%, ')%*& -.-& %'& '.'.) (%++ -' )'(--&*,*,'+-&&&&%*) %'+ ('(), ()&, -' )'(-( &*-& '-(')&'*&) %(% ()'(, (+** -' )'(*&&+&+'(&-,(&*,&& %(, (-*%) )%- -( *'))+(/')'+))/' (*(, &+/ )-& (+-//*)&+-'-(+. &*- **(&+)-*)/+/,.*(((*+ &+& *++&,)+**/+/.,.(**'/ &+* *-(,+*'*/+,.)+, (,., &+- +'&'.)'&/'-&(.-)/'/, &-- " " 2 +.+/' *'*' *--)- ),'+ ,+'/) )*'( ,+-(- )-'+ -*(&, ),( --(/' +&-' 2 .( -/ ,/ -* ,- /) 2 .' .( -/ -, -/ -( 2 -' /( '&' ''' ',( Table 3b – COT (TET) as Handle (ICR) !! & 1 -* -) -) -* -* -+ " .*% ,*% -%% -*% .%% &%%% " '- '- '- '- '- '- '(* ''* '', ''- '(( ')' 1 *) +* ,. .% &&( 8 )&((*'.&(&*((.& ')'+ )&))' ',(' )()'*&+&%* )&)')',+'))*--) &-'+ )&)%-',-.()-%,.'%&-+ )&(*+'--&(*&)&,''+%( )&'),(%,%'*-'(.',*(, %*. %(. %)) %). %** %+, ! ! 1 *-*.& )&)& ),(*- ()%& *%&) (+)' *'+, (-(( *+',+ )%&, +(+'* )('- 1 -' -) -( -( -( -& 1 ++ ,* -( .( &&) 1 -& -( -' -' -' -' Copyright © 2017 ASME Downloaded From: http://proceedings.asmedigitalcollection.asme.org/ on 10/25/2017 Terms of Use: http://www.asme.org/about-asme/terms-of-use 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 2 "'# ()+ *'))+(/')'+))/' (*(, &+/ +.+/' *'*' .' .( "'# '2 ()- *')&*(/,-/+*/.*(+)&+ &,' ,&'&) *(' .( .( '&* "'# (2 ()+ *'))+(/')'+))/' (*(, &+/ +.+/' *'*' .' .( '&& " '#)2 (- *&/(*)-)&' +/+ (('// &+* ,*(') )*+- .& -+ /( "'# *2 (** *'((/)'&*++*,&(()++- &+- +/,/* )/*, .( .' /- " '#+2 (*' *'(+/ )&*/ +()-,('.., &+) +-+-+ ).&' .' .' /& Note: For the last 2 columns, divide numbers by 100 to get the actual % or decrease. 2 2 ! ! ! 2 2 2 2 "'# '+/ *(). '+.*,(/-+*')/&. &)) ),&*. ).+. .( .+ "'# '2 '+. *()/ '+-)/(/*/'')-+( &)( )+.&' ).*' .( .+ // // '&& "'# (2 '+/ *(). '+.*,(/-+*')/&. &)) ),&*. ).+. .( .+ '&& '&& '&& " '#)2 ',) *()((',*-+(/.)*'))+. &)( ),&.. )-&( .( ., /, '&& /, "'# *2 ',) *()'(',+-/(/)+/ '(-. &)& )+,(- )+.- .& ./ /( // /) " '#+2 ',) *()&.',,')(.,/''(&-. &(/ )*/.* )*+( .( ., .- /- ./ Note: For the last 2 columns, divide numbers by 100 to get the actual % increase or decrease. Table 4b – ODPs for ICR (Reactor Pressure Loss) 2 2 ! ! ! 2 2 '&) '&( '&& '&& ''& .) '&( /+ /. /( increase 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 Copyright © 2017 ASME Downloaded From: http://proceedings.asmedigitalcollection.asme.org/ on 10/25/2017 Terms of Use: http://www.asme.org/about-asme/terms-of-use 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. &% &$ &" & & %% %$ %" % % #% #& $ $ $ $! $" $# 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 '& '$ '" ' ' && &$ &" & & ! !% " "% # #% $ Figure 8 – Recuperator Map (Hot Side) Effectiveness "(% "($ "(# "( "'+ "'* "') "'( " # $ % & ' 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 Downloaded From: http://proceedings.asmedigitalcollection.asme.org/ on 10/25/2017 Terms of Use: http://www.asme.org/about-asme/terms-of-use % • $' $& $$ $" $ #' #& #$ #" ! " # $ % • * Figure 10 – Recuperator Map (Hot Side) - High Pressure Losses "%!! "#!! "!!! • (!! '!! %!! #!! ! !!! "!! #!! $!! %!! • &!! '!! 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 Downloaded From: http://proceedings.asmedigitalcollection.asme.org/ on 10/25/2017 Terms of Use: http://www.asme.org/about-asme/terms-of-use 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] REFERENCES [1] F. Carre, P. Yvon, P. Anzieu, N. Chauvin, and J.-Y. Malo, “Update of the French R&D strategy on gascooled reactors,” Nucl. Eng. Des., vol. 240, no. 10, pp. 2401–2408, Oct. 2010. [2] G. Locatelli, M. Mancini, and N. Todeschini, “Generation IV nuclear reactors: Current status and future prospects,” Energy Policy, vol. 61, pp. 1503– 1520, Oct. 2013. [3] A. Gad-Briggs and P. Pilidis, “Analyses of Simple and Intercooled Recuperated Direct Brayton Helium Gas Turbine Cycles for Generation IV Reactor Power Plants,” J. Nucl. Eng. Radiat. Sci., pp. 1–11, 2016. [4] A. Gad-Briggs, P. Pilidis, and T. Nikolaidis, “A Review of The Turbine Cooling Fraction for Very High Turbine Entry Temperature Helium Gas Turbine Cycles For Generation IV Reactor Power Plants,” ASME J. Nucl. Eng. Radiat. Sci., 2017. [5] K. N. Pradeepkumar, A. Tourlidakis, and P. Pilidis, “Analysis of 115MW, 3-Shaft, Helium Brayton Cycle using Nuclear Heat Source,” in Proceedings of ASME Turbo Expo 2001 Land, Sea & Air. June 4-7, 2001., 2001. [6] K. N. Pradeepkumar, A. Tourlidakis, and P. Pilidis, “Design and Performance review of PBMR Closed Cycle Gas Turbine Plant in South Africa.,” in International Joint Power Generation Conference. June 4-7 2001., 2001. [7] K. N. Pradeepkumar, A. Tourlidakis, and P. Pilidis, “Performance Review: PBMR Closed Cycle Gas Turbine Power Plant.,” in Proceedings of Technical Committee Meeting on HTGR - Power Conversion Systems. International Atomic Energy Agency. 14-16 November 2000, 2001, pp. 99–112. [8] M. Kulhanek and V. Dostal, “Supercritical carbon dioxide cycles. Thermodynamic analysis and comparison.” Czech Technical University Prague, Prague, Czech Republic, 2007. [9] C. B. Baxi, a. Shenoy, V. I. Kostin, N. G. Kodochigov, a. V. Vasyaev, S. E. Belov, and V. F. Golovko, “Evaluation of alternate power conversion unit designs for the GT-MHR,” Nucl. Eng. Des., vol. 238, no. 11, pp. 2995–3001, Nov. 2008. [10] K. G. Kyprianidis, “Multi-disciplinary conceptual design of future jet engine systems. (Ph.D Thesis),” Cranfield University, 2010. D. R. Pitts and L. E. Sissom, Theory and Problems of Heat Transfer, 2nd Editio. New York: McGraw-Hill, 1997. H. A. Navarro and L. C. Cabezas-Gomez, “Effectiveness-NTU Computation With a Mathematical Model for Cross-Flow Heat Exchangers,” Brazilian J. Chem. Eng., vol. 24, no. 4, pp. 509–521, 2007. H. Sato, X. L. Yan, Y. Tachibana, and K. Kunitomi, “GTHTR300—A nuclear power plant design with 50% generating efficiency,” Nucl. Eng. Des., vol. 275, pp. 190–196, Aug. 2014 12 Copyright © 2017 ASME Downloaded From: http://proceedings.asmedigitalcollection.asme.org/ on 10/25/2017 Terms of Use: http://www.asme.org/about-asme/terms-of-use

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