The organic Rankine cycle (ORC) is one of the promising waste heat recovery (WHR) technologies used to improve the thermal efficiency, reduce the emissions and save the fuel costs of internal combustion engines. In the ORCWHR system, the evaporator is considered to be the most critical component as the heat transfer of this device influences the efficiency of the system. Although the conventional Finite Volume (FV) model can successfully capture the complex heat transfer process in the evaporator, the computation time for this model is high as it consists of many iterative loops. To reduce the computation time, a new evaporator model using the fuzzy inference technique is developed in this research. The developed fuzzy based model can predict the evaporator outputs with an accuracy of over 90% while it reduces the simulation time significantly. This model is then integrated with other components of the ORC to simulate a completed ORC-WHR system for internal combustion engines. The influence of operating parameters on the performance of the WHR system is investigated in this paper

Chowdhury, J I

Nguyen, B K

Soulatiantork, P

The organic Rankine cycle (ORC) is one of the promising waste heat recovery (WHR) technologies used to improve the thermal efficiency, reduce the emissions and save the fuel costs of internal combustion engines. In the ORC-WHR system, the evaporator is considered to be the most critical component as the heat transfer of this device influences the efficiency of the system. Although the conventional Finite Volume (FV) model can successfully capture the complex heat transfer process in the evaporator, the computation time for this model is high as it consists of many iterative loops. To reduce the computation time, a new evaporator model using the fuzzy inference technique is developed in this research. The developed fuzzy based model can predict the evaporator outputs with an accuracy of over 90% while it reduces the simulation time significantly. This model is then integrated with other components of the ORC to simulate a completed ORC-WHR system for internal combustion engines. The influence of operating parameters on the performance of the WHR system is investigated in this paper

Chowdhury, J.I.

Soulatiantork, P.

Nguyen, B.K.

White Rose Research Online

This is a repository copy of Simulation of Waste Heat Recovery System with Fuzzy Based Evaporator Model.White Rose Research Online URL for this paper:http://eprints.whiterose.ac.uk/134144/Version: Accepted VersionProceedings Paper:Chowdhury, J.I., Soulatiantork, P. orcid.org/0000-0003-3212-8220 and Nguyen, B.K. (2018) Simulation of Waste Heat Recovery System with Fuzzy Based Evaporator Model. In: 2017 11th Asian Control Conference (ASCC). 2017 11th Asian Control Conference (ASCC), 17-12-2017-20-12-2017, Gold Coast, Australia. IEEE , pp. 2143-2147. ISBN 978-1-5090-1573-3 https://doi.org/10.1109/ASCC.2017.8287506eprints@whiterose.ac.ukhttps://eprints.whiterose.ac.uk/Reuse Items deposited in White Rose Research Online are protected by copyright, with all rights reserved unless indicated otherwise. They may be downloaded and/or printed for private study, or other acts as permitted by national copyright laws. The publisher or other rights holders may allow further reproduction and re-use of the full text version. This is indicated by the licence information on the White Rose Research Online record for the item. Takedown If you consider content in White Rose Research Online to be in breach of UK law, please notify us by emailing eprints@whiterose.ac.uk including the URL of the record and the reason for the withdrawal request. © © 2017 IEEE. Personal use of this material is permitted. Permission from IEEE must be obtained for all other uses, in any current or future media, including reprinting/republishing this material for advertising or promotional purposes, creating new collective works, for resale or redistribution to servers or lists, or reuse of any copyrighted component of this work in other works  Simulation of Waste Heat Recovery System with Fuzzy Based Evaporator Model J. I. Chowdhury, P. Soulatiantork, B. K. Nguyen, Member, IEEE   Abstract— The organic Rankine cycle (ORC) is one of the promising waste heat recovery (WHR) technologies used to improve the thermal efficiency, reduce the emissions and save the fuel costs of internal combustion engines. In the ORC- WHR system, the evaporator is considered to be the most critical component as the heat transfer of this device influences the efficiency of the system. Although the conventional Finite Volume (FV) model can successfully capture the complex heat transfer process in the evaporator, the computation time for this model is high as it consists of many iterative loops. To reduce the computation time, a new evaporator model using the fuzzy inference technique is developed in this research. The developed fuzzy based model can predict the evaporator outputs with an accuracy of over 90% while it reduces the simulation time significantly. This model is then integrated with other components of the ORC to simulate a completed ORC-WHR system for internal combustion engines. The influence of operating parameters on the performance of the WHR system is investigated in this paper. I. INTRODUCTION Most of the energy produced by internal combustion engines is expelled to the environment via the exhaust and coolant systems. The expelled energy makes the engine running cost high and is one of the major causes of global warming and environmental pollution. In order to reduce fuel consumption, waste heat recovery (WHR) has been used to collect the heat from the exhaust or coolant and convert it into either mechanical or electrical power, which increases the thermal efficiency of the engine (1). The ORC WHR system consists of four major components: pump, evaporator, expander and condenser, as shown in Figure 1. Liquid refrigerant is pumped to the evaporator where it is heated and vaporized by the heat sources. This vaporized fluid is then expanded and produces mechanical energy output through the shaft of the expander.    Figure 1. Components of a typical Organic Rankine Cycle (ORC) WHR system technique is a highly time consuming method since it consists of many iterative loops (5, 6), therefore, it has a limitation in real time control applications. In order to reduce the computation time of the evaporator model, a new evaporator model using the fuzzy inference technique is introduced and described in this paper. The developed fuzzy based evaporator model is then integrated and simulated with models of other components in the WHR system to investigate the effect of operating parameters on the performance of the WHR system. II.  FUZZY BASED EVAPORATOR MODEL Among the conventional heat exchangers available in the market, a plate heat exchanger has a large heat transfer area along with high compactness which is suitable to recover a maximum amount of heat from the heat sources (5). This type of heat exchanger is therefore used as the evaporator for the simulation in this research. The geometrical dimensions and parameters of the selected evaporator are listed in Table 1.  TABLE I SPECIFICATIONS OF THE EVAPORATOR (7) A generator is normally coupled with the expander shaft to    convert mechanical energy into electrical power. Exhaust products from the expander pass through the condenser where secondary cooling fluid removes extra heat and converts the exhaust back to a liquid. The operating conditions of the ORC have a significant influence on the thermal efficiency and heat utilization f the WHR system. Two classified operating conditions of the ORC waste heat recovery system can be observed: subcritical and supercritical. The operating pressure of the subcritical ORC is below the critical pressure of the working fluid; while the supercritical ORC is run at a pressure higher than the critical pressure. Modelling of the evaporator in the ORC WHR system has been addressed in several reports (2, 3). Despite high accuracy and robustness (4), the  finite  volume  odelling  J. I. Chowdhury is now with the Cranfield University, Cranfield, MK43 0AL, UK (email: j.chowdhury@cranfield.ac.uk). P. Soulatiantork is with the Queen’s University Belfast, Belfast BT9 5AH, UK (email: p.soulatiantork@qub.ac.uk).     Symbol Parameter Value  A Heat transfer area of the evaporator 5.78 m2 L Length of the plate 0.478 m W Width of the plate 0.124 m Np Number of plates 100   K Thermal conductivity 15 W/m K   The fuzzy technique introduced by Mamdani & Assilian (8) is used to develop the evaporator model in this research. The proposed fuzzy-based evaporator model consists of three inputs and two outputs and is shown in Fig. 2. The mass flow rate of refrigerant m r , the mass flow rate of hot fluid m h  and the temperature of hot fluid Th are considered as the inputs of the model; whereas the evaporator heat input Qev  and the  B. K. Nguyen is with the University of Sussex, Brighton, BN1 9QT, UK (phone: +44 (0)12-7387-2869; email: b.k.nguyen@sussex.ac.uk).   Figure 2. Fuzzy inference system for evaporator  evaporator outlet temperature Tev are considered to be the outputs of the model. The fuzzy-based evaporator model represents the nonlinearity of the system by a logical mapping of its input variables to the output variables. The fuzzy logic is used to predict an unknown output of a system by establishing the degree of matching among the known inputs and outputs relationships. The development steps of the fuzzy-based evaporator model canbe described as follows: Step 1: Variables identification The  minimum  and  maximum  values  of  the  inputs  and  (a) (b) Figure 5. Fuzzy surface of the evaporator outlet temperature with respect to  m r  and  m h (a), and with respect to  m r   and  Th (b)  outputs   variables  of   the   fuzzy  model  are  as  follows: [m r min , m r max ]  [28.6 (gm/s), 255 (gm/s)], (a) (b) Figure 6. Fuzzy surface for the evaporator power with respect to  m rand [m h min , m h max ]  [50 (gm/s), 300  (gm/s)], [Th min ,Th max ] [403 (K), 525 (K)], [Qev min ,Qev max ] = [-11 (kW), 80 (kW)] and [Tev min ,Tev max ]  [336 (K), 517 (K)], respectively. These ranges were identified from the inputs and outputs of the WHR system and adjusted from the knowledge and experience of the system and were normalized over the m h  (a), and with respect to  m r   and  Th  (b)  interval [0, 1], as shown in Figs. 3-4. The actual crisp values of the model parameters are calculated from the normalised values         as         follows: m r   28.6  226.4 m r ; m h   50  250 m h ;  Th   403  122Th ;  Tev   336 181Tev ;  Qev   11  91Qev  where m r  , m h , Th  , Tev  and Qev are the normalised values of their corresponding variables. Step 2: Fuzzification The variables ranges identified in step 1 are divided into several linguistic levels. The linguistic levels assigned to the input and output variables of the model are as follows: VL: Very Low; L: Low; LM: Low to Medium; M: Medium; MH: Medium to High; H: High and VH: Very High. The input and output membership functions are shown in Figs. 3 and 4. Step 3: Fuzzy rules and fuzzy reasoning The fuzzy rules of the evaporator model are created using the above fuzzy sets of the input and output variables and can be presented as follows:  Figure 3. Membership functions of input variables. Rule  i : IF m r  is   i AND m h is i AND  Th is   i THEN Tev is i AND Qev is i (1) where  i  1, 2, 3.....n ,  n is the number of fuzzy rules,   i , i ,  i , i , i are the i th fuzzy sets of the input and output         Figure 4. Membership functions of output variables variables of the fuzzy system. The fuzzy rules used in this model are shown in Figs. 5-6. Step 4: Defuzzification The centroid defuzzification method (9) is used in this paper to convert the aggregated fuzzy set to a crisp output value Y from the fuzzy set  in V  R . The crisp output from the aggregated fuzzy set is computed as follows: 0 Finite volume model Fuzzy based model Ramp profile Mass flow rate (gm/s) Evaporator outlet temperature (K) Evaporator power (kW) Temperature (k) 300    200    100    0 550    500    450    400 0 500 1000 1500 Time (s) Figure 7. Heat source mass flow rate and temperature   70 60 50 40 30 20 10 0 500 1000 1500 Time (s) Figure 8. Prediction of the evaporator power with respect to ramp profile.  440 430     Figure 10.   Overall model of the ORC-WHR system.  a) The mass flow rates of the pump and through all other components are assumed to be equal, m p   m r ,i   m exp   m c . b) Pressure at the pump outlet is equal to the pressure of the  evaporator  and  at  the  expander  inlet,  such that 420 410 Pp,o  Pev,i  Pev,o  Pexp,i . 400 390 380 c) Pressure at the expander outlet and in the condenser is equal  to  the  pressure  at  the  pump  inlet,  such  that  370 0 500   Time (s)  1000 1500 Pexp,o    Pc     Pp,i . Figure 9. Prediction of the evaporator outlet temperature with respect to ramp profile.  V   ( y). ydy   d) The enthalpy at the pump outlet and at the evaporator inlet are equal, H p,o  Hr,i . e) Enthalpy and specific volume of the refrigerant at the pump inlet is a function of inlet pressure, Y V   ( y)dy (2) H p,i , p  f (Pp,i ) and the temperature of the refrigerant at the inlet of the evaporator is a function of The crisp value of Qev above expression. and Tev were calculated using the the   enthalpy   and   pressure   at   the   pump   outlet, Tr,i  f (Pp,o , H p,o ) . To predict the fuzzy model outputs, the evaporator is simulated with the heat source shown in Fig. 7 and a random ramp profile of refrigerant flow rates. The fuzzy model outputs, Qev and Tev , are compared with the conventional FV method (7) and presented in Figs. 8-9. The RMSE and congruency of fit between the fuzzy model and the FV model for the  Qev  are 0.95 kW and 93.68%, and for Tev are 1.48 K and 89.16%, respectively. Results show that the developed fuzzy model canbe used to estimate the evaporator outputs accurately. The time used for the simulation of the random heat source in the fuzzy- based model is 5.19 s, compared to 3820.6 s of the FV model.  III.  OVERALL MODEL OF WHR SYSTEM The overall model of the cycle shown in Fig. 10 is built by interconnecting all subcomponents in the WHR system. The inputs and outputs of the adjacent components are as follows:  TABLE 2 OVERALL MODEL PARAMETERS  Input variables Output variables N p , Pp,i , Pp,o, m h ,Th Qev ,Tev ,Wp ,Wexp,Qc  By interconnecting the individual inputs and outputs of each component, a set of overall model inputs-outputs can be defined and listed in Table 2. IV.  SIMULATION RESULTS A generic heat source in terms of variable mass flow rate and temperature (Fig. 7)defined by Quoilin et al. (10) is used for the investigation of the waste heat recovery system at supercritical condition. The working fluid of the ORC used in this simulation is R134a, which is widely used for commercial purposes, readily available and has a high auto- ignition temperature. To investigate the effect of operating parameters on the system output, a random pump speed profile ranging from 200RPM to 1750RPM, and its corresponding mass flow rate (Fig. 11) is used in the simulation. The range of the mass flow rate profile of the selected pump is from 28.8 gm/s to 249.5 gm/s. The pump outlet pressure is set to 6 MPa. This value is well above the critical pressure of the R134a refrigerant which is 4.06 MPa. The outputs of the fuzzy based evaporator are shown in Figs. 12-13. In Fig. 12, it shows that the minimum and maximum heat absorbed by the evaporator is 4.17 kW and 61.8 kW, respectively. Fig. 13 shows the evaporator outlet temperature under the variable heat source and random refrigerant flow rates at the evaporator. The evaporator temperatures in this simulation are varied from 379 K to 448 K.       Mass flow rate Temperature Finite volume model Fuzzy based model Ramp Profile Mass flow rate of refrigerant (gm/s) Evaporator power (kW) Evaporator outlet temperature (K) Cycle efficiency (%) Heat recovery efficiency (%)  250  200  150  100  50  0 0 500 1000 1500 Time (s) Figure 11.   Mass flow rate of refrigerant 18  16  14  12  10  8  6 0 500 1000 1500 Time (s)  Figure 15.     ORC ycle efficiency 70  60  50  40  30  20  10  0 0 500               Time (s)              1000 1500   45 40 35 30 25 20 15 10 0 500 1000 1500      450 440 430 420 Figure 12.    Evaporator heat input Time (s)   Figure 16.     Heat recovery efficiency  410 400 The  heat power  Qh  in Eq. 6 is the  total available heat  390 380 370 0 500 1000 1500 Time (s) capacity of the heat source which is calculated by Qh   m h (Hh,i   Hh,ref  )  (6) Figure 13.   Evaporator outlet temperature where  H h,i  and H h,ref are the heat source enthalpies at  10 9 8 7 6 5 4 3 2 1 0 0 500               Time (s)              1000 1500 the inlet of the evaporator and at the reference temperature of 303 K, respectively. The cycle efficiency of the ORC depends on several factors including the temperature of the evaporator, heat of vaporisation, pressure ratio at the expander, etc. Fig. 15 shows the cycle efficiency of the ORC-WHR model for the selected  heat  source.  The  cycle  efficiency  varies   from Figure 14.   Expander power output.   The expander power output is shown in Fig. 14 In this simulation, the maximum power output of around 9 kW is observed. The performance of the ORC-WHR system is calculated by two basic parameters: cycle efficiency and heat recovery efficiency as follows: around 6.6% to around 17%, depending on the combination of the mass flow rate and temperature of the hot fluid and refrigerant. The WHR system in this simulation is able to recover up to 44% (Fig. 16) of the heat from the specified heat source as shown in Fig. 8. It can be seen from Figs. 15 and 16 that the trends of the cycle and heat recovery efficiency are opposite to each other. V. CONCLUSIONS In  this research,  the  development  of  the fuzzy based WNet cy ev  Qev hr h (3)   (4) evaporator model and its integration with other components in the ORC-WHR system have been presented. The performance of the fuzzy base evaporator model and the WHR system including cycle and heat recovery efficiency has also been investigated. The fuzzy-based model proposed in this paper does not where cy is the cycle efficiency, which is the ratio of net work output o the heat recovered at the evaporator, hr is the heat recovery efficiency which is defined as the amount of heat recovered from the given heat source. Qev is the evaporator power which is one of the outputs of the fuzzy based evaporator model. require complex mathematical formula and iteration loops; therefore, it can reduce the simulation time significantly. The investigation of the ORC based WHR model in this paper can provide an overall mapping and characterization of the output ranges of the waste heat recovery system with respect to different input ranges. The developed model is suitable to predict the effect of mass flow rate of the refrigerant on the evaporator outlet temperature, which is t e The  net  work output Wnet in  Eq.  5  is  calculated by critical parameter for the control of the WHR system in real subtracting the pump work work as follows. W p from  the  expander gross time.   ACKNOWLEDGMENT Wnet   (Wexp  Wp ) (5) The authors gratefully acknowledge the Queen’s University   Belfast   and   the Engineering   and   Physical Q Expander power output (kW) Q                 Sciences Research Council (EPSRC) for their support in this research.   REFERENCES [1] Glover, S.; Douglas, R.; Glover, L.; McCullough, G. Preliminary analysis of Organic Rankine Cycles to improve vehicle effici ncy. Proc. IMechE D J. Automob. Eng. 2014, 228, pp.1142–1153. [2] Quoilin, S.; Aumann, R.; Grill, A.; Schuster, A.; Lemort, V.; Spliethoff, H. Dynamic modeling and optimal control strategy of waste heat recovery Organic Rankine Cycles. Appl. Energy 2011, 88, pp. 2183–2190. [3] Feru, E.; Willems, F.; Jager, B.D.; Steinbuch, M. Modeling and control of a parallel waste heat recovery system for Euro-VI heavy- duty diesel engines. Energies 2014, 7, pp. 6571–6592. [4] Karellasa, S.; Schuster, A.; Leontaritis, A.-D. Influenc  of supercritical ORC parameters on plate heat exchanger design. Appl. Therm. Eng. 2012, 33, pp. 70–76. [5] Sun, J.; Li, W. Operation optimization of an Organic Rankine Cycle (ORC) heat recovery power plant. Appl. Therm. Eng. 2011, 31, pp. 2032–2041. [6] Patiño, J.; Llopis, R.; Sánchez, D.; Sanz-Kock, C.; Cabello, R.; Torrella, E. A comparative analysis of a CO2 evaporator model using experimental heat transfer correlations and a flow pattern map.  Int. J. Heat Mass Transfer 2014, 71, pp. 361–375. [7] Chowdhury, J.I., Nguyen, B.K., Thornhill, D.: Modelling of Evaporator in Waste Heat Recovery System using Finite Volume Method and Fuzzy Technique, Energies, 2015, 8, (12), pp. 14078- 14097. [8] Mamdani, E.H., Assilian, S.: An experiment in linguistic synthesis with a fuzzy logic controller, International Journal of Man-Machine Studies, 1975, 7, (1), pp. 1-13. [9] Ross, T.J.: Fuzzy logic with engineering applications (John Wiley, Chichester, U.K., 3 2010). [10] Quoilin, S., Aumann, R., Grill, A., Schuster, A., Lemort V., Spliethoff H.: Dynamic modeling and optimal control strategy of waste heat recovery Organic Rankine Cycles, Applied Energy, 2011, 88, pp. 2183-2190. 

Simulation of Waste Heat Recovery System with Fuzzy Based Evaporator Model

Chowdhury, Jahedul

Soulatiantork, Payam

Nguyen, Bao

Queen's University Belfast Research Portal

Simulation of Waste Heat Recovery System with Fuzzy BasedEvaporator ModelChowdhury, J., Soulatiantork, P., & Nguyen, B. (2017). Simulation of Waste Heat Recovery System with FuzzyBased Evaporator Model. In The 2017 Asian Control Conference: Proceedings  IEEE .Published in:The 2017 Asian Control Conference: ProceedingsDocument Version:Peer reviewed versionQueen's University Belfast - Research Portal:Link to publication record in Queen's University Belfast Research PortalPublisher rights © IEEE Explore. This work is made available online in accordance with the publisher’s policies. Please refer to any applicable terms of useof the publisher.General rightsCopyright for the publications made accessible via the Queen's University Belfast Research Portal is retained by the author(s) and / or othercopyright owners and it is a condition of accessing these publications that users recognise and abide by the legal requirements associatedwith these rights.Take down policyThe Research Portal is Queen's institutional repository that provides access to Queen's research output. Every effort has been made toensure that content in the Research Portal does not infringe any person's rights, or applicable UK laws. If you discover content in theResearch Portal that you believe breaches copyright or violates any law, please contact openaccess@qub.ac.uk.Download date:06. Nov. 2017   Abstract— The organic Rankine cycle (ORC) is one of the promising waste heat recovery (WHR) technologies used to improve the thermal efficiency, reduce the emissions and save the fuel costs of internal combustion engines. In the ORC-WHR system, the evaporator is considered to be the most critical component as the heat transfer of this device influences the efficiency of the system. Although the conventional Finite Volume (FV) model can successfully capture the complex heat transfer process in the evaporator, the computation time for this model is high as it consists of many iterative loops. To reduce the computation time, a new evaporator model using the fuzzy inference technique is developed in this research. The developed fuzzy based model can predict the evaporator outputs with an accuracy of over 90% while it reduces the simulation time significantly. This model is then integrated with other components of the ORC to simulate a completed ORC-WHR system for internal combustion engines. The influence of operating parameters on the performance of the WHR system is investigated in this paper. I. INTRODUCTION Most of the energy produced by internal combustion engines is expelled to the environment via the exhaust and coolant systems. The expelled energy makes the engine running cost high and is one of the major causes of global warming and environmental pollution. In order to reduce fuel consumption, waste heat recovery (WHR) has been used to collect the heat from the exhaust or coolant and convert it into either mechanical or electrical power, which increases the thermal efficiency of the engine (1). The ORC WHR system consists of four major components: pump, evaporator, expander and condenser, as shown in Figure 1. Liquid refrigerant is pumped to the evaporator where it is heated and vaporized by the heat sources. This vaporized fluid is then expanded and produces mechanical energy output through the shaft of the expander. A generator is normally coupled with the expander shaft to convert mechanical energy into electrical power. Exhaust products from the expander pass through the condenser where secondary cooling fluid removes extra heat and converts the exhaust back to a liquid.  The operating conditions of the ORC have a significant influence on the thermal efficiency and heat utilization of the WHR system. Two classified operating conditions of the ORC waste heat recovery system can be observed: subcritical and supercritical. The operating pressure of the subcritical ORC is below the critical pressure of the working fluid; while the  J. I. Chowdhury is now with the Cranfield University, Cranfield, MK43 0AL, UK (email: j.chowdhury@cranfield.ac.uk).   P. Soulatiantork is with the Queen’s University Belfast, Belfast BT9 5AH, UK (email: p.soulatiantork@qub.ac.uk).  supercritical ORC is run at a pressure higher than the critical pressure. Modelling of the evaporator in the ORC WHR system has been addressed in several reports (2, 3). Despite high accuracy and robustness (4), the finite volume modelling technique is a highly time consuming method since it consists of many iterative loops (5, 6), therefore, it has a limitation in real time control applications. In order to reduce the computation time of the evaporator model, a new evaporator model using the fuzzy inference technique is introduced and described in this paper. The developed fuzzy based evaporator model is then integrated and simulated with models of other components in the WHR system to investigate the effect of operating parameters on the performance of the WHR system.  II. FUZZY BASED EVAPORATOR MODEL Among the conventional heat exchangers available in the market, a plate heat exchanger has a large heat transfer area along with high compactness which is suitable to recover a maximum amount of heat from the heat sources (5). This type of heat exchanger is therefore used as the evaporator for the simulation in this research. The geometrical dimensions and parameters of the selected evaporator are listed in Table 1. B. K. Nguyen is with the University of Sussex, Brighton, BN1 9QT, UK (phone: +44 (0)12-7387-2869; email: b.k.nguyen@sussex.ac.uk).  Simulation of Waste Heat Recovery System with Fuzzy Based Evaporator Model J. I. Chowdhury, P. Soulatiantork, B. K. Nguyen, Member, IEEE  Figure 1. Components of a typical Organic Rankine Cycle (ORC) WHR system   TABLE I SPECIFICATIONS OF THE EVAPORATOR (7)   Symbol Parameter Value A Heat transfer area of the evaporator 5.78 m2 L Length of the plate 0.478 m W Width of the plate 0.124 m Np Number of plates 100 K Thermal conductivity 15 W/m K    The fuzzy technique introduced by Mamdani & Assilian  (8) is used to develop the evaporator model in this research. The proposed fuzzy-based evaporator model consists of three inputs and two outputs and is shown in Fig. 2. The mass flow rate of refrigerant rm , the mass flow rate of hot fluid hm  and the temperature of hot fluid hT  are considered as the inputs of the model; whereas the evaporator heat input evQ  and the evaporator outlet temperature evT  are considered to be the outputs of the model. The fuzzy-based evaporator model represents the nonlinearity of the system by a logical mapping of its input variables to the output variables. The fuzzy logic is used to predict an unknown output of a system by establishing the degree of matching among the known inputs and outputs relationships. The development steps of the fuzzy-based evaporator model can be described as follows:  Step 1: Variables identification The minimum and maximum values of the inputs and outputs variables of the fuzzy model are as follows: ],[ maxmin rr mm [28.6 (gm/s), 255 (gm/s)], ],[ maxmin hh mm  [50 (gm/s), 300  (gm/s)], ],[ maxmin hh TT [403 (K), 525 (K)], ],[ maxmin evev QQ= [-11 (kW), 80 (kW)] and ],[ maxmin evev TT [336 (K), 517 (K)], respectively. These ranges were identified from the inputs and outputs of the WHR system and adjusted from the knowledge and experience of the system and were normalized over the interval [0, 1], as shown in Figs. 3-4. The actual crisp values of the model parameters are calculated from the normalised values as follows:  rr mm   4.2266.28 ; hh mm   25050 ;  hh TT 122403 ;  evev TT 181336 ;  evev QQ  9111 where rm ,hm ,hT ,evT and evQ  are the normalised values of their corresponding variables.  Step 2: Fuzzification The variables ranges identified in step 1 are divided into several linguistic levels. The linguistic levels assigned to the input and output variables of the model are as follows: VL: Very Low; L: Low; LM: Low to Medium; M: Medium; MH: Medium to High; H: High and VH: Very High. The input and output membership functions are shown in Figs. 3 and 4.  Step 3: Fuzzy rules and fuzzy reasoning The fuzzy rules of the evaporator model are created using the above fuzzy sets of the input and output variables and can be presented as follows: Rule i : IF rm is i AND hm is i AND hT is i THEN evT is i AND evQ is i                                                       (1)  Figure 2. Fuzzy inference system for evaporator     Figure 3. Membership functions of input variables.  Figure 4. Membership functions of output variables   (a)                                                  (b)  Figure 5. Fuzzy surface of the evaporator outlet temperature with respect to rm  and hm (a), and with respect to rm  and hT  (b)    (a)                            (b) Figure 6. Fuzzy surface for the evaporator power with respect to rm  and hm (a), and with respect to rm  and hT   (b)      where ni .....3 ,2 ,1 , n is the number of fuzzy rules, i , i ,i , i , i  are the i th fuzzy sets of the input and output variables of the fuzzy system.  The fuzzy rules used in this model are shown in Figs. 5-6.  Step 4: Defuzzification  The centroid defuzzification method (9) is used in this paper to convert the aggregated fuzzy set to a crisp output value Y  from the fuzzy set   in RV  . The crisp output from the aggregated fuzzy set is computed as follows:  VVdyyydyyY)().(                                         (2) The crisp value of evQ  and evT  were calculated using the above expression. To predict the fuzzy model outputs, the evaporator is simulated with the heat source shown in Fig. 7 and a random ramp profile of refrigerant flow rates. The fuzzy model outputs, evQ  and evT , are compared with the conventional FV method (7) and presented in Figs. 8-9. The RMSE and congruency of fit between the fuzzy model and the FV model for the evQ  are 0.95 kW and 93.68%, and for evT  are 1.48 K and 89.16%, respectively. Results show that the developed fuzzy model can be used to estimate the evaporator outputs accurately.  The time used for the simulation of the random heat source in the fuzzy-based model is 5.19 s, compared to 3820.6 s of the FV model.   III. OVERALL MODEL OF WHR SYSTEM The overall model of the cycle shown in Fig. 10 is built by interconnecting all subcomponents in the WHR system. The inputs and outputs of the adjacent components are as follows:   a) The mass flow rates of the pump and through all other components are assumed to be equal, cirp mmmm   exp, . b) Pressure at the pump outlet is equal to the pressure of the evaporator and at the expander inlet, such that ioevievop PPPP exp,,,,  . c) Pressure at the expander outlet and in the condenser is equal to the pressure at the pump inlet, such that ipco PPP ,exp,  . d) The enthalpy at the pump outlet and at the evaporator inlet are equal, irop HH ,,  . e) Enthalpy and specific volume of the refrigerant at the pump inlet is a function of inlet pressure, )(, ,, ippip PfH  and the temperature of the refrigerant at the inlet of the evaporator is a function of the enthalpy and pressure at the pump outlet, ),( ,,, opopir HPfT  .  By interconnecting the individual inputs and outputs of each component, a set of overall model inputs-outputs can be defined and listed in Table 2. IV. SIMULATION RESULTS A generic heat source in terms of variable mass flow rate and temperature (Fig. 7) defined by Quoilin et al. (10) is used for the investigation of the waste heat recovery system at supercritical condition. The working fluid of the ORC used in  Figure 7. Heat source mass flow rate and temperature  Figure 8. Prediction of the evaporator power with respect to ramp profile.  Figure 9. Prediction of the evaporator outlet temperature with respect to ramp profile.     0 500 1000 15000100200300Mass flow rate (gm/s)  400450500550Temperature (k)Time (s)Mass flow rate Temperature 0 500 1000 1500010203040506070Time (s)Evaporator power (kW)  Finite volume modelFuzzy based modelRamp profile0 500 1000 1500370380390400410420430440Time (s)Evaporator outlet temperature (K)  Finite volume modelFuzzy based modelRamp Profile  Figure 10. Overall model of the ORC-WHR system.  TABLE 2 OVERALL MODEL PARAMETERS  Input variables Output variables hhopipp TmPPN ,,,, ,,   cpevev QWWTQ ,,,, exp     this simulation is R134a, which is widely used for commercial purposes, readily available and has a high auto-ignition temperature. To investigate the effect of operating parameters on the system output, a random pump speed profile ranging from 200RPM to 1750RPM, and its corresponding mass flow rate (Fig. 11) is used in the simulation. The range of the mass flow rate profile of the selected pump is from 28.8 gm/s to 249.5 gm/s. The pump outlet pressure is set to 6 MPa. This value is well above the critical pressure of the R134a refrigerant which is 4.06 MPa.  The outputs of the fuzzy based evaporator are shown in Figs. 12-13. In Fig. 12, it shows that the minimum and maximum heat absorbed by the evaporator is 4.17 kW and 61.8 kW, respectively. Fig. 13 shows the evaporator outlet temperature under the variable heat source and random refrigerant flow rates at the evaporator. The evaporator temperatures in this simulation are varied from 379 K to 448 K.  The expander power output is shown in Fig. 14 In this simulation, the maximum power output of around 9 kW is observed.  The performance of the ORC-WHR system is calculated by two basic parameters: cycle efficiency and heat recovery efficiency as follows:          evNetcyQW                                                       (3)          hevhrQQ                                                 (4) where cy is the cycle efficiency, which is the ratio of net work output to the heat recovered at the evaporator, hr is the heat recovery efficiency which is defined as the amount of heat recovered from the given heat source. evQ  is the evaporator power which is one of the outputs of the fuzzy based evaporator model. The net work output netW  in Eq. 5 is calculated by subtracting the pump work pW from the expander gross work as follows. )( exp pnet WWW                                                  (5) The heat power hQ in Eq. 6 is the total available heat capacity of the heat source which is calculated by )( ,, refhihhh HHmQ                                       (6) where ihH ,  and refhH ,  are the heat source enthalpies at the inlet of the evaporator and at the reference temperature of 303 K, respectively. The cycle efficiency of the ORC depends on several factors including the temperature of the evaporator, heat of vaporisation, pressure ratio at the expander, etc. Fig. 15 shows the cycle efficiency of the ORC-WHR model for the selected heat source. The cycle efficiency varies from around 6.6% to around 17%, depending on the combination of the mass flow rate and temperature of the hot fluid and refrigerant. The WHR system in this simulation is able to recover up to 44% (Fig. 16) of the heat from the specified heat source as shown in Fig. 8.  Figure 11. Mass flow rate of refrigerant  Figure 12. Evaporator heat input  Figure 13. Evaporator outlet temperature  Figure 14. Expander power output.     0 500 1000 1500050100150200250Time (s)Mass flow rate of refrigerant (gm/s)0 500 1000 1500010203040506070Time (s)Evaporator power (kW)0 500 1000 1500370380390400410420430440450Time (s)Evaporator outlet temperature (K)0 500 1000 1500012345678910Time (s)Expander power output (kW)  0 500 1000 1500681012141618Time (s)Cycle efficiency (%)0 500 1000 15001015202530354045Time (s)Heat recovery efficiency (%)  It can be seen from Figs. 15 and 16 that the trends of the cycle and heat recovery efficiency are opposite to each other.  V. CONCLUSIONS In this research, the development of the fuzzy based evaporator model and its integration with other components in the ORC-WHR system have been presented. The performance of the fuzzy base evaporator model and the WHR system including cycle and heat recovery efficiency has also been investigated. The fuzzy-based model proposed in this paper does not require complex mathematical formula and iteration loops; therefore, it can reduce the simulation time significantly. The investigation of the ORC based WHR model in this paper can provide an overall mapping and characterization of the output ranges of the waste heat recovery system with respect to different input ranges. The developed model is suitable to predict the effect of mass flow rate of the refrigerant on the evaporator outlet temperature, which is the critical parameter for the control of the WHR system in real time.   ACKNOWLEDGMENT The authors gratefully acknowledge the Queen’s University Belfast and the Engineering and Physical Sciences Research Council (EPSRC) for their support in this research.   REFERENCES [1] Glover, S.; Douglas, R.; Glover, L.; McCullough, G. Preliminary analysis of Organic Rankine Cycles to improve vehicle efficiency. Proc. IMechE D J. Automob. Eng. 2014, 228, pp.1142–1153. [2] Quoilin, S.; Aumann, R.; Grill, A.; Schuster, A.; Lemort, V.; Spliethoff, H. Dynamic modeling and optimal control strategy of waste heat recovery Organic Rankine Cycles. Appl. Energy 2011, 88, pp. 2183–2190. [3] Feru, E.; Willems, F.; Jager, B.D.; Steinbuch, M. Modeling and control of a parallel waste heat recovery system for Euro-VI heavy-duty diesel engines. Energies 2014, 7, pp. 6571–6592. [4] Karellasa, S.; Schuster, A.; Leontaritis, A.-D. Influence of supercritical ORC parameters on plate heat exchanger design. Appl. Therm. Eng. 2012, 33, pp. 70–76. [5] Sun, J.; Li, W. Operation optimization of an Organic Rankine Cycle (ORC) heat recovery power plant. Appl. Therm. Eng. 2011, 31, pp. 2032–2041. [6] Patiño, J.; Llopis, R.; Sánchez, D.; Sanz-Kock, C.; Cabello, R.; Torrella, E. A comparative analysis of a CO2 evaporator model using experimental heat transfer correlations and a flow pattern map. Int. J. Heat Mass Transfer 2014, 71, pp. 361–375. [7] Chowdhury, J.I., Nguyen, B.K., Thornhill, D.: Modelling of Evaporator in Waste Heat Recovery System using Finite Volume Method and Fuzzy Technique, Energies, 2015, 8, (12), pp. 14078-14097. [8] Mamdani, E.H., Assilian, S.: An experiment in linguistic synthesis with a fuzzy logic controller, International Journal of Man-Machine Studies, 1975, 7, (1), pp. 1-13. [9] Ross, T.J.: Fuzzy logic with engineering applications (John Wiley, Chichester, U.K., 3 2010). [10] Quoilin, S., Aumann, R., Grill, A., Schuster, A., Lemort V., Spliethoff H.: Dynamic modeling and optimal control strategy of waste heat recovery Organic Rankine Cycles, Applied Energy, 2011, 88, pp. 2183-2190.       

J. I. Chowdhury

P. Soulatiantork

B. K. Nguyen

Crossref

Simulation of waste heat recovery system with fuzzy based evaporator model

Chowdhury, Jahedul I.

Nguyen, Bao Kha

Cranfield CERES

   Abstract— The organic Rankine cycle (ORC) is one of the promising waste heat recovery (WHR) technologies used to improve the thermal efficiency, reduce the emissions and save the fuel costs of internal combustion engines. In the ORC-WHR system, the evaporator is considered to be the most critical component as the heat transfer of this device influences the efficiency of the system. Although the conventional Finite Volume (FV) model can successfully capture the complex heat transfer process in the evaporator, the computation time for this model is high as it consists of many iterative loops. To reduce the computation time, a new evaporator model using the fuzzy inference technique is developed in this research. The developed fuzzy based model can predict the evaporator outputs with an accuracy of over 90% while it reduces the simulation time significantly. This model is then integrated with other components of the ORC to simulate a completed ORC-WHR system for internal combustion engines. The influence of operating parameters on the performance of the WHR system is investigated in this paper. I. INTRODUCTION Most of the energy produced by internal combustion engines is expelled to the environment via the exhaust and coolant systems. The expelled energy makes the engine running cost high and is one of the major causes of global warming and environmental pollution. In order to reduce fuel consumption, waste heat recovery (WHR) has been used to collect the heat from the exhaust or coolant and convert it into either mechanical or electrical power, which increases the thermal efficiency of the engine (1). The ORC WHR system consists of four major components: pump, evaporator, expander and condenser, as shown in Figure 1. Liquid refrigerant is pumped to the evaporator where it is heated and vaporized by the heat sources. This vaporized fluid is then expanded and produces mechanical energy output through the shaft of the expander. A generator is normally coupled with the expander shaft to convert mechanical energy into electrical power. Exhaust products from the expander pass through the condenser where secondary cooling fluid removes extra heat and converts the exhaust back to a liquid.  The operating conditions of the ORC have a significant influence on the thermal efficiency and heat utilization of the WHR system. Two classified operating conditions of the ORC waste heat recovery system can be observed: subcritical and supercritical. The operating pressure of the subcritical ORC is below the critical pressure of the working fluid; while the  J. I. Chowdhury is now with the Cranfield University, Cranfield, MK43 0AL, UK (email: j.chowdhury@cranfield.ac.uk).   P. Soulatiantork is with the Queen’s University Belfast, Belfast BT9 5AH, UK (email: p.soulatiantork@qub.ac.uk).  supercritical ORC is run at a pressure higher than the critical pressure. Modelling of the evaporator in the ORC WHR system has been addressed in several reports (2, 3). Despite high accuracy and robustness (4), the finite volume modelling technique is a highly time consuming method since it consists of many iterative loops (5, 6), therefore, it has a limitation in real time control applications. In order to reduce the computation time of the evaporator model, a new evaporator model using the fuzzy inference technique is introduced and described in this paper. The developed fuzzy based evaporator model is then integrated and simulated with models of other components in the WHR system to investigate the effect of operating parameters on the performance of the WHR system.  II. FUZZY BASED EVAPORATOR MODEL Among the conventional heat exchangers available in the market, a plate heat exchanger has a large heat transfer area along with high compactness which is suitable to recover a maximum amount of heat from the heat sources (5). This type of heat exchanger is therefore used as the evaporator for the simulation in this research. The geometrical dimensions and parameters of the selected evaporator are listed in Table 1. B. K. Nguyen is with the University of Sussex, Brighton, BN1 9QT, UK (phone: +44 (0)12-7387-2869; email: b.k.nguyen@sussex.ac.uk).  Simulation of Waste Heat Recovery System with Fuzzy Based Evaporator Model J. I. Chowdhury, P. Soulatiantork, B. K. Nguyen, Member, IEEE  Figure 1. Components of a typical Organic Rankine Cycle (ORC) WHR system   TABLE I SPECIFICATIONS OF THE EVAPORATOR (7)   Symbol Parameter Value A Heat transfer area of the evaporator 5.78 m2 L Length of the plate 0.478 m W Width of the plate 0.124 m Np Number of plates 100 K Thermal conductivity 15 W/m K    The fuzzy technique introduced by Mamdani & Assilian  (8) is used to develop the evaporator model in this research. The proposed fuzzy-based evaporator model consists of three inputs and two outputs and is shown in Fig. 2. The mass flow rate of refrigerant rm , the mass flow rate of hot fluid hm  and the temperature of hot fluid hT  are considered as the inputs of the model; whereas the evaporator heat input evQ  and the evaporator outlet temperature evT  are considered to be the outputs of the model. The fuzzy-based evaporator model represents the nonlinearity of the system by a logical mapping of its input variables to the output variables. The fuzzy logic is used to predict an unknown output of a system by establishing the degree of matching among the known inputs and outputs relationships. The development steps of the fuzzy-based evaporator model can be described as follows:  Step 1: Variables identification The minimum and maximum values of the inputs and outputs variables of the fuzzy model are as follows: ],[ maxmin rr mm [28.6 (gm/s), 255 (gm/s)], ],[ maxmin hh mm  [50 (gm/s), 300  (gm/s)], ],[ maxmin hh TT [403 (K), 525 (K)], ],[ maxmin evev QQ= [-11 (kW), 80 (kW)] and ],[ maxmin evev TT [336 (K), 517 (K)], respectively. These ranges were identified from the inputs and outputs of the WHR system and adjusted from the knowledge and experience of the system and were normalized over the interval [0, 1], as shown in Figs. 3-4. The actual crisp values of the model parameters are calculated from the normalised values as follows:  rr mm   4.2266.28 ; hh mm   25050 ;  hh TT 122403 ;  evev TT 181336 ;  evev QQ  9111 where rm ,hm ,hT ,evT and evQ  are the normalised values of their corresponding variables.  Step 2: Fuzzification The variables ranges identified in step 1 are divided into several linguistic levels. The linguistic levels assigned to the input and output variables of the model are as follows: VL: Very Low; L: Low; LM: Low to Medium; M: Medium; MH: Medium to High; H: High and VH: Very High. The input and output membership functions are shown in Figs. 3 and 4.  Step 3: Fuzzy rules and fuzzy reasoning The fuzzy rules of the evaporator model are created using the above fuzzy sets of the input and output variables and can be presented as follows: Rule i : IF rm is i AND hm is i AND hT is i THEN evT is i AND evQ is i                                                       (1)  Figure 2. Fuzzy inference system for evaporator     Figure 3. Membership functions of input variables.  Figure 4. Membership functions of output variables   (a)                                                  (b)  Figure 5. Fuzzy surface of the evaporator outlet temperature with respect to rm  and hm (a), and with respect to rm  and hT  (b)    (a)                            (b) Figure 6. Fuzzy surface for the evaporator power with respect to rm  and hm (a), and with respect to rm  and hT   (b)      where ni .....3 ,2 ,1 , n is the number of fuzzy rules, i , i ,i , i , i  are the i th fuzzy sets of the input and output variables of the fuzzy system.  The fuzzy rules used in this model are shown in Figs. 5-6.  Step 4: Defuzzification  The centroid defuzzification method (9) is used in this paper to convert the aggregated fuzzy set to a crisp output value Y  from the fuzzy set   in RV  . The crisp output from the aggregated fuzzy set is computed as follows:  VVdyyydyyY)().(                                         (2) The crisp value of evQ  and evT  were calculated using the above expression. To predict the fuzzy model outputs, the evaporator is simulated with the heat source shown in Fig. 7 and a random ramp profile of refrigerant flow rates. The fuzzy model outputs, evQ  and evT , are compared with the conventional FV method (7) and presented in Figs. 8-9. The RMSE and congruency of fit between the fuzzy model and the FV model for the evQ  are 0.95 kW and 93.68%, and for evT  are 1.48 K and 89.16%, respectively. Results show that the developed fuzzy model can be used to estimate the evaporator outputs accurately.  The time used for the simulation of the random heat source in the fuzzy-based model is 5.19 s, compared to 3820.6 s of the FV model.   III. OVERALL MODEL OF WHR SYSTEM The overall model of the cycle shown in Fig. 10 is built by interconnecting all subcomponents in the WHR system. The inputs and outputs of the adjacent components are as follows:   a) The mass flow rates of the pump and through all other components are assumed to be equal, cirp mmmm   exp, . b) Pressure at the pump outlet is equal to the pressure of the evaporator and at the expander inlet, such that ioevievop PPPP exp,,,,  . c) Pressure at the expander outlet and in the condenser is equal to the pressure at the pump inlet, such that ipco PPP ,exp,  . d) The enthalpy at the pump outlet and at the evaporator inlet are equal, irop HH ,,  . e) Enthalpy and specific volume of the refrigerant at the pump inlet is a function of inlet pressure, )(, ,, ippip PfH  and the temperature of the refrigerant at the inlet of the evaporator is a function of the enthalpy and pressure at the pump outlet, ),( ,,, opopir HPfT  .  By interconnecting the individual inputs and outputs of each component, a set of overall model inputs-outputs can be defined and listed in Table 2. IV. SIMULATION RESULTS A generic heat source in terms of variable mass flow rate and temperature (Fig. 7) defined by Quoilin et al. (10) is used for the investigation of the waste heat recovery system at supercritical condition. The working fluid of the ORC used in  Figure 7. Heat source mass flow rate and temperature  Figure 8. Prediction of the evaporator power with respect to ramp profile.  Figure 9. Prediction of the evaporator outlet temperature with respect to ramp profile.     0 500 1000 15000100200300Mass flow rate (gm/s)  400450500550Temperature (k)Time (s)Mass flow rate Temperature 0 500 1000 1500010203040506070Time (s)Evaporator power (kW)  Finite volume modelFuzzy based modelRamp profile0 500 1000 1500370380390400410420430440Time (s)Evaporator outlet temperature (K)  Finite volume modelFuzzy based modelRamp Profile  Figure 10. Overall model of the ORC-WHR system.  TABLE 2 OVERALL MODEL PARAMETERS  Input variables Output variables hhopipp TmPPN ,,,, ,,   cpevev QWWTQ ,,,, exp     this simulation is R134a, which is widely used for commercial purposes, readily available and has a high auto-ignition temperature. To investigate the effect of operating parameters on the system output, a random pump speed profile ranging from 200RPM to 1750RPM, and its corresponding mass flow rate (Fig. 11) is used in the simulation. The range of the mass flow rate profile of the selected pump is from 28.8 gm/s to 249.5 gm/s. The pump outlet pressure is set to 6 MPa. This value is well above the critical pressure of the R134a refrigerant which is 4.06 MPa.  The outputs of the fuzzy based evaporator are shown in Figs. 12-13. In Fig. 12, it shows that the minimum and maximum heat absorbed by the evaporator is 4.17 kW and 61.8 kW, respectively. Fig. 13 shows the evaporator outlet temperature under the variable heat source and random refrigerant flow rates at the evaporator. The evaporator temperatures in this simulation are varied from 379 K to 448 K.  The expander power output is shown in Fig. 14 In this simulation, the maximum power output of around 9 kW is observed.  The performance of the ORC-WHR system is calculated by two basic parameters: cycle efficiency and heat recovery efficiency as follows:          evNetcyQW                                                       (3)          hevhrQQ                                                 (4) where cy is the cycle efficiency, which is the ratio of net work output to the heat recovered at the evaporator, hr is the heat recovery efficiency which is defined as the amount of heat recovered from the given heat source. evQ  is the evaporator power which is one of the outputs of the fuzzy based evaporator model. The net work output netW  in Eq. 5 is calculated by subtracting the pump work pW from the expander gross work as follows. )( exp pnet WWW                                                  (5) The heat power hQ in Eq. 6 is the total available heat capacity of the heat source which is calculated by )( ,, refhihhh HHmQ                                       (6) where ihH ,  and refhH ,  are the heat source enthalpies at the inlet of the evaporator and at the reference temperature of 303 K, respectively. The cycle efficiency of the ORC depends on several factors including the temperature of the evaporator, heat of vaporisation, pressure ratio at the expander, etc. Fig. 15 shows the cycle efficiency of the ORC-WHR model for the selected heat source. The cycle efficiency varies from around 6.6% to around 17%, depending on the combination of the mass flow rate and temperature of the hot fluid and refrigerant. The WHR system in this simulation is able to recover up to 44% (Fig. 16) of the heat from the specified heat source as shown in Fig. 8.  Figure 11. Mass flow rate of refrigerant  Figure 12. Evaporator heat input  Figure 13. Evaporator outlet temperature  Figure 14. Expander power output.     0 500 1000 1500050100150200250Time (s)Mass flow rate of refrigerant (gm/s)0 500 1000 1500010203040506070Time (s)Evaporator power (kW)0 500 1000 1500370380390400410420430440450Time (s)Evaporator outlet temperature (K)0 500 1000 1500012345678910Time (s)Expander power output (kW)  0 500 1000 1500681012141618Time (s)Cycle efficiency (%)0 500 1000 15001015202530354045Time (s)Heat recovery efficiency (%)  It can be seen from Figs. 15 and 16 that the trends of the cycle and heat recovery efficiency are opposite to each other.  V. CONCLUSIONS In this research, the development of the fuzzy based evaporator model and its integration with other components in the ORC-WHR system have been presented. The performance of the fuzzy base evaporator model and the WHR system including cycle and heat recovery efficiency has also been investigated. The fuzzy-based model proposed in this paper does not require complex mathematical formula and iteration loops; therefore, it can reduce the simulation time significantly. The investigation of the ORC based WHR model in this paper can provide an overall mapping and characterization of the output ranges of the waste heat recovery system with respect to different input ranges. The developed model is suitable to predict the effect of mass flow rate of the refrigerant on the evaporator outlet temperature, which is the critical parameter for the control of the WHR system in real time.   ACKNOWLEDGMENT The authors gratefully acknowledge the Queen’s University Belfast and the Engineering and Physical Sciences Research Council (EPSRC) for their support in this research.   REFERENCES [1] Glover, S.; Douglas, R.; Glover, L.; McCullough, G. Preliminary analysis of Organic Rankine Cycles to improve vehicle efficiency. Proc. IMechE D J. Automob. Eng. 2014, 228, pp.1142–1153. [2] Quoilin, S.; Aumann, R.; Grill, A.; Schuster, A.; Lemort, V.; Spliethoff, H. Dynamic modeling and optimal control strategy of waste heat recovery Organic Rankine Cycles. Appl. Energy 2011, 88, pp. 2183–2190. [3] Feru, E.; Willems, F.; Jager, B.D.; Steinbuch, M. Modeling and control of a parallel waste heat recovery system for Euro-VI heavy-duty diesel engines. Energies 2014, 7, pp. 6571–6592. [4] Karellasa, S.; Schuster, A.; Leontaritis, A.-D. Influence of supercritical ORC parameters on plate heat exchanger design. Appl. Therm. Eng. 2012, 33, pp. 70–76. [5] Sun, J.; Li, W. Operation optimization of an Organic Rankine Cycle (ORC) heat recovery power plant. Appl. Therm. Eng. 2011, 31, pp. 2032–2041. [6] Patiño, J.; Llopis, R.; Sánchez, D.; Sanz-Kock, C.; Cabello, R.; Torrella, E. A comparative analysis of a CO2 evaporator model using experimental heat transfer correlations and a flow pattern map. Int. J. Heat Mass Transfer 2014, 71, pp. 361–375. [7] Chowdhury, J.I., Nguyen, B.K., Thornhill, D.: Modelling of Evaporator in Waste Heat Recovery System using Finite Volume Method and Fuzzy Technique, Energies, 2015, 8, (12), pp. 14078-14097. [8] Mamdani, E.H., Assilian, S.: An experiment in linguistic synthesis with a fuzzy logic controller, International Journal of Man-Machine Studies, 1975, 7, (1), pp. 1-13. [9] Ross, T.J.: Fuzzy logic with engineering applications (John Wiley, Chichester, U.K., 3 2010). [10] Quoilin, S., Aumann, R., Grill, A., Schuster, A., Lemort V., Spliethoff H.: Dynamic modeling and optimal control strategy of waste heat recovery Organic Rankine Cycles, Applied Energy, 2011, 88, pp. 2183-2190.       

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Simulation of waste heat recovery system with fuzzy based evaporator model

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