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IV International Seminar on ORC Power Systems, ORC2017 IV International Seminar on ORC Power Systems, ORC2017 13-15 September 2017, Milano, Italy 13-15 September 2017, Milano, Italy

A Modeling Approach for Exchangers TheBoundary 15th International Symposium on District Heating and Cooling A Moving Moving Boundary Modeling Approach for Heat Heat Exchangers with Binary Mixtures with Binary Mixtures Assessing the feasibility of using the heat demand-outdoor

Donghun Kima,*, Davide Ziviania, James E. Brauna, Eckhard A. Grolla Donghunfunction Kim , Davide , James E. Braun ,heat Eckhard A. Grollforecast temperature for Ziviani a long-term district demand a,*

a

a

a,b,c

I. Andrić

a

a

a

Ray W. Herrick Laboratories, Purdue University, USA Ray Purdue University, USA a W. Herrick Laboratories, a b

*, A. Pina , P. Ferrão , J. Fournier ., B. Lacarrièrec, O. Le Correc

Abstract a IN+ Center for Innovation, Technology and Policy Research - Instituto Superior Técnico, Av. Rovisco Pais 1, 1049-001 Lisbon, Portugal Abstract b Veolia Recherche & Innovation, 291 Avenue Dreyfous Daniel, 78520 Limay, France

In this paper, caDépartement modeling approach for a heat exchanger that uses- IMT a binary mixture is presented. A moving boundary method Systèmes Énergétiques et Environnement Atlantique, 4 rue Alfred Kastler, 44300 Nantes, France In this paper, a modeling approach forofa enthalpy heat exchanger that uses binary mixture is presented. A moving method assuming a linear spatial distribution could result in a aconsiderable steady state prediction error,boundary due to the assuming a linear distribution enthalpy could resulta more in a considerable steadyboundary state prediction due to the analytic temperature glide spatial of a binary mixture.ofMotivated from this, accurate moving method error, that incorporates temperature glide of a is binary mixture. from this, more accurate moving boundary that analytic enthalpy distributions presented. TheMotivated enthalpy profiles area derived by defining a specific heatmethod capacity at incorporates each thermodynamic enthalpy distributions is presented. The enthalpy profiles are derived by defining a specificapproach heat capacity atin each thermodynamic phase of a binary mixture and by solving crossflow heat transfer equations. The proposed results accurate predictions Abstract phase of a with binary mixture and by solving crossflow heat transfer The proposed approach results in accurate predictions compared those of a detailed model using the Finite Volumeequations. Method (FVM). The corresponding computation time is two to compared with those of a detailed model using the Finite Volume Method (FVM). The corresponding computation time is two to three times slower than that of a conventional moving boundary approach, but the approach is still computationally advantageous District heating networks are addressed in the literature as one of approach the most is effective solutions for advantageous decreasing the three times slower of a commonly conventional moving boundary approach, but the still computationally compared with the than FVMthat model. greenhouse gasthe emissions from the building sector. These systems require high investments which are returned through the heat compared with FVM model. sales. Due to the changed climate conditions and building renovation policies, heat demand in the future could decrease, © 2017 The Authors. Published by Elsevier Ltd. © 2017 Published by Elsevier Ltd. prolonging the investment return period. © 2017 The The Authors. Authors. Published by Ltd. committee of the IV International Seminar on ORC Power Systems. Peer-review under responsibility of Elsevier the scientific Peer-review under the committee of IV International ORC Systems. The main scope this paper is of to the feasibility of using demand –Seminar outdooron temperature function for heat demand Peer-review underofresponsibility responsibility of assess the scientific scientific committee of the thethe IVheat International Seminar on ORC Power Power Systems. forecast. The district of Alvalade, located in Lisbon (Portugal), was used as a case study. The district is consisted of 665 Keywords: ORC; Moving boundary method; Water-Ethylene Glycol mixture; buildingsORC; that Moving vary in boundary both construction period and Glycol typology. Three weather scenarios (low, medium, high) and three district Keywords: method; Water-Ethylene mixture; renovation scenarios were developed (shallow, intermediate, deep). To estimate the error, obtained heat demand values were compared with results from a dynamic heat demand model, previously developed and validated by the authors. 1. Introduction results showed that when only weather change is considered, the margin of error could be acceptable for some applications 1.The Introduction (the error in annual demand was lower than 20% for all weather scenarios considered). However, after introducing renovation Waste Heat Recovery (WHR) up by means Organic on Rankine Cycleand (ORC) has been identified by Heavy Duty scenarios, the error value increased 59.5%of (depending the weather renovation scenarios combination considered). Waste Heat Recovery (WHR) bytomeans of Organic Rankine Cycle (ORC) has been identified by Heavy Duty Diesel Engine (HDDE) manufacturers in the U.S. as one of the key enabling technologies to accomplish the U.S. The value of slope coefficient increased on average within the range of 3.8% up to 8% per decade, that corresponds to the Diesel Engine (HDDE) manufacturers in the U.S. as one of the key enabling technologies to accomplish the U.S. Department of number Energy of(DOE) efficiency (BTE) goal. A traditional systemof for vehicle decrease in the heatingbrake hoursthermal of 22-139h during the heating season (depending ORC on the WHR combination weather and Department of (DOE) brake efficiency goal. traditional ORC WHR system for vehicle renovation scenarios On thethermal other hand, intercept increased for 7.8-12.7% per decade (depending on the applications thatEnergy hasconsidered). a separate working fluid loopfunction faces (BTE) challenges ofAhigh cost and complexity for working fluid applications that has a separate working fluid loop faces challenges of high cost and complexity for working fluid coupled scenarios). The values suggested could be used to modify the function parameters for the scenarios considered, and improve the accuracy of heat demand estimations. © 2017 The Authors. Published by Elsevier Ltd. * Corresponding author. Tel.: +1-765-494-2132. Peer-review under responsibility of the Scientific Committee of The 15th International Symposium on District Heating and * Corresponding Tel.: +1-765-494-2132. E-mail address:author. [email protected] Cooling. E-mail address: [email protected]

1876-6102 2017demand; The Authors. Published Elsevier Ltd. Keywords:©Heat Forecast; Climatebychange 1876-6102 2017responsibility The Authors. of Published by Elsevier Ltd. of the IV International Seminar on ORC Power Systems. Peer-review©under the scientific committee Peer-review under responsibility of the scientific committee of the IV International Seminar on ORC Power Systems.

1876-6102 © 2017 The Authors. Published by Elsevier Ltd. Peer-review under responsibility of the Scientific Committee of The 15th International Symposium on District Heating and Cooling.

1876-6102 © 2017 The Authors. Published by Elsevier Ltd. Peer-review under responsibility of the scientific committee of the IV International Seminar on ORC Power Systems. 10.1016/j.egypro.2017.09.161

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integration, and safety and environmental issues. A novel idea utilizing the engine coolant, i.e. water and ethylene glycol mixture, as the ORC working fluid, and engine radiator as the condenser for ORC heat rejection is proposed, and its feasibly study is performed and reported in a companion paper. This paper describes an initial modeling effort for the ORC system, especially a heat exchanger, using the mixture. Since heat exchangers influence transient behavior of ORC systems significantly, developing an accurate but computationally efficient heat exchanger model is a key step. The finite volume method (FVM) and moving boundary method (MB) are popular approaches for dynamic heat exchanger modeling [1]. While the FVM divides heat exchangers into a number of fixed control volumes, the MB segments heat exchanges depending on thermodynamic phase of refrigerant, i.e. sub-cooled liquid, two-phase and super-heated vapor and moves control volumes as the length of each phase changes. Consequently, the MB solves fewer equations due to fewer control volumes. Because of the low state dimension, the MB has been the preferred approach for transient modeling and design of controllers. Furthermore, the accuracy of the MB has been validated numerically and experimentally in the literature for vapor compression cycles [2-5] and ORC systems [7-9]. However, in the MB formulation, it is essential to assume a spatial enthalpy profile in lumping a number of control volumes, and hence when the approximation fails the MB can possibly result in a poor prediction. This paper starts from a motivating example for this case (Section 2) and introduces a more reliable MB formulation (Section 3). The results proposed in this paper are limited to the static moving boundary formulation and they will be extended to transients. Nomenclature EG FVM HX MB NTU SC TP WEG

ethylene glycol Finite Volume Method heat exchanger Moving Boundary number of thermal unit subcooled zone two-phase zone water and ethylene glycol mixture

A

heat transfer area [m2] specific heat capacity at a thermodynamic phase j [J/kg-K]

 h

effectiveness [-] enthalpy [J/kg]

c

j p

hj

L

m m i m e

P Q j

mean enthalpy at the jth zone [J/kg] total length of a HX [m] mass flow rate [kg/s] refrigerant mass flow rate at the inlet of a HX [kg/s] refrigerant mass flow rate at the exit of a HX [kg/s] pressure [Pa] heat transfer rate from HX surface to refrigerant for the jth zone [W]

j

mean density at the jth zone [kg/m3]

 zj

temperature [K] mass concentration of a component [kg/kg] length portion for the jth zone [-]

T

subscript

468

e f g h i p s 1 2 12

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exit saturated liquid saturated vapor hot stream inlet primary secondary subcooled zone two phase zone interface between 1st and 2nd zone

2. Motivating example of a moving boundary approach with a two-component mixture As a first step of modeling an integrated ORC system using water and ethylene glycol mixture as a working fluid, a detailed heat exchanger model was developed using FVM. It models an existing counter flow heat exchanger for an ORC test-rig at the Ray W. Herrick Laboratories at Purdue University. The ORC works with R245fa having a scroll expander with nominal capacity of 5 kW, a reciprocating pump and counter flow heat exchangers for the evaporator and condenser. The evaporator transfers heat from steam (secondary fluid) to R245fa (primary fluid). The FVM formulation [1] which divides the evaporator into a number of fixed control volumes and applies mass and energy balances for each control volume and heat transfer correlations for the heat exchanger [10] were used. A static FVM model can be easily obtained by letting the time derivate terms be zeros. The static HX model was validated with available measurements for more than 70 operating conditions [11]. After the validation, the working fluid has been replaced to water/ethylene glycol (50/50) on the static FVM model to investigate heat transfer characteristics using the binary mixture. Although there are questions on the validity of the heat transfer coefficient correlations [10] applied to the mixture, the correlations were used in this paper because our overall discussion is independent of specific correlations and there is a lack of available literature for heat transfer coefficient correlations with this binary mixture. An example temperature profiles (steady state) inside of the evaporator are shown in Fig 2, where TWEG and Ts represent temperatures of the mixture and secondary fluid respectively. The boundary conditions for this test are summarized in Table 1. 100 nodes were used for the FVM and REFPROP [12] was used to retrieve the thermodynamic properties of the water/EG mixture. Note that, unlike a single component fluid, the temperature of the working fluid increases in the two-phase zone (> 0.25 in the x-axis).

Fig. 1: Temperature profiles at evaporator with water/ethylene glycol mixture (FVM)

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Table 1. Boundary conditions for an evaporator Boundary condition

ܲ [atm]

Values

11.35

݉ሶ [kg/s] 0.10

݄௜ [kJ/kg] -23

݉ሶ௦ [kg/s] 0.62

ܶ௦ǡ௜ [oC] 280

Fig. 2: Evaporator Schematic

A moving boundary model under the same boundary conditions was implemented. A static MB model was retrieved by eliminating time-derivative terms of a transient MB model [1], and the set of equations of the static MB models is:

 0 m s c p , s (Ts ,i  Ts ,2 )  U 2 Az2 (Ts ,2  T2 )  0 m i ( h12  he )  U 2 Az2 (Ts ,2  T2 )

(1)

 0 m s c p , s (Ts ,2  Ts ,1 )  U1 Az1 (Ts ,1  T1 ) 0  m i ( hi  h12 )  U1 Az1 (Ts ,1  T1 ) See Fig. 2 for the schematic. For each zone, the mean temperatures of the mixture, T2 for example, was calculated by

T2  T ( P,

h12  he ,  EG ) . 2

(2)

Since a thermodynamic equilibrium point for a binary mixture is specified by three coordinates, the mass concentration of ethylene glycol is included. It is important to mention for later discussion that Eq. (1) is solved with

(he , z1 , Ts ,1 , Ts ,2 ) as unknown variables.

This is because those are the dynamic states of a transient MB model. The MB results are shown in Table 2. The exit enthalpy (or heat transfer rate) is underestimated about 200 kJ/kg (or 20 kW) compared with that of FVM, and it corresponds to 12.54% difference in heat transfer rate. The 10% error may be acceptable for practical cases, however note the significant difference in the length for the subcooled liquid zone: MB predicts 4% while FVM predicts 25% (see Fig. 1). The poor estimation on the length could significantly influence on behaviors of a dynamic MB cycle model, because it means a poor charge estimation of the working fluid and the estimated total charge used as an initial condition for a dynamic cycle model must remain during entire simulation periods. Table 2. Result comparisons between FVM and MB under boundary conditions in Table 1. FVM

݄௘ [kJ/kg] 1649.2

‫ݖ‬ଵ [-] 0.25

ܶത௦ǡଵ [oC] 194.23

ܶത௦ǡଶ [oC] 209.74

ܳሶ [kW]

MB

1439.5

0.04

183.97

212.78

146.25

167.22

470

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3. Analysis and approach Two assumptions were made in the static MB formulation: 1) the exit temperature of the secondary fluid for each control volume is approximately the mean temperature. 2) spatial enthalpy distribution of the working fluid is linear. These are standard assumptions in dynamic MB modeling approaches [1-9]. Note that the linear spatial distribution of enthalpy for each zone implies a linear spatial distribution of temperature for the zone, because temperature changes linearly with a change of enthalpy1. Therefore, the assumptions are weak in a strict sense and there is no guarantee that the MB to be accurate. If the two assumptions hold, (1) becomes the exact energy balances and hence steady MB results should match to that of FVM. Therefore, there is no doubt that the mismatch of the MB comes from the temperature approximations in the MB formulation. Despite the weak assumptions, the MB generally shows good agreements with measurements. This is because most of results are for a pure substance where most of the heat transfer occurs in the two-phase region. Due to the fact that the saturation temperature is fixed with the pressure, the linear distribution assumption automatically holds. Therefore, once the mean temperature of the secondary fluid is properly identified, e.g. using ε-NTU method, the results will be good2. However, for a mixture, once the liquid is saturated and starts to evaporate, i.e. in the twophase region, the water concentration increases in vapor while the concentration of ethylene glycol in liquid increases. Because of the variations of the concentrations, the temperature in the two-phase zone must change according to the Gibbs phase rule (we assumed that pressure loss is negligible in heat exchangers). In this case, there is no reason that the temperature spatial distribution of the working fluid in the two-phase zone follows a linear profile (See Fig. 1). Our approach to handle this problem is to include appropriate temperature profiles for both streams for each zone. Our major assumption is that a linear relationship between changes of temperature and enthalpy, i.e. dT  a  dh for a constant a , is hold for each phase zone even in the two-phase region. The assumption is from the following observation. Fig. 3 shows the T-h diagram for the water/ethylene glycol mixture (50/50 by mass) under various pressures. Inside the saturation dome, T is roughly proportional to h. It is important to clarify that we do not assume enthalpy is linearly distributed in space. It is only assumed that the temperature is linear affine in enthalpy not in space.

Fig. 3: T-h diagram for water/ethylene glycol mixture (50/50)

Due to the enthalpy dependency of temperature in the two-phase zone, it is natural to define (isobaric) specific heat capacity under a fixed mixture concentration which is approximated by

1 Note that temperature change for a pure substance in two-phase is also linear in enthalpy change, since ߲ܶȀ߲݄=0. In addition, we will show this linearity holds for not only a pure substance but also for the mixture at least roughly. 2 Another example where the linear assumption valid is when thermal capacities for two streams are similar under a counter flow heat exchanger.

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c p ,2 :

471

h hg ( P,  EG )  h f ( P,  EG )  . T Tg ( P,  EG )  T f ( P,  EG )

(3)

With this assumption, the heat transfer problem for a binary mixture can be converted to a standard heat exchanger problem [13], and hence the ε-NTU approach can be applied. However, the direct use of the ε-NTU is not adequate for the use of a transient MB model, since states available at each computation step are mean temperatures in the secondary fluid (if dynamics of the stream is not negligible) and the exit enthalpy in the primary fluid. Since the ε-NTU method only relates inlet and outlet temperatures, it is not clear how to use the mean temperatures. In order to relate inlet and outlet temperatures with mean temperatures, an analytic solution was derived for the following crossflow heat transfer equations [13] (the zonal description, i.e. 1 or 2, is dropped in the equation for simplicity).

dTs NTU s  (Ts  Tp ) dx L , dTp NTU p  (Ts  Tp ) L dx where  NTU s

(4)

UA UA , NTU p  , Cs m s c m c p , p . p,s , C p Cs Cp

After integration and algebraic manipulation of the analytic solution of (4), the following equations are derived. Ts = Tp

exp( NTU s - NTU p )(1  ( NTU s - NTU p ))  1 ( NTU s - NTU p )(1- exp( NTU s - NTU p )

exp( NTU s - NTU p )(1  ( NTU s - NTU p ))  1 ( NTU s - NTU p )(1- exp( NTU s - NTU p )

Ts ,e 

T p ,i 

( NTU s - NTU p )  (1- exp( NTU s - NTU p )) ( NTU s - NTU p )(1- exp( NTU s - NTU p )

( NTU s - NTU p )  (1- exp( NTU s - NTU p )) ( NTU s - NTU p )(1- exp( NTU s - NTU p )

Ts ,i

(5)

Tp , e

Note that (5) relates inlet, outlet and the mean temperature for each stream. Using the results, the integral form energy balance becomes

0 m s c p , s (Ts ,i  Ts ,12 (·))  U 2 Az2 (Ts ,2  T2 (·))  0 m i (h12  he )  U 2 Az2 (Ts ,2  T2 (·))  0 m s c p , s (Ts ,12 (·)  Ts ,e (·))  U1 Az1 (Ts ,1  T1 (·))

(6)

0  m i (hi  h12 )  U1 Az1 (Ts ,1  T1 (·)) where (·) emphasizes functional dependency and the corresponding quantities are calculated by (5). 4. Result and discussion The same problem mentioned in Section 2 was solved with (6) and (5) rather than (1). REFPROP [12] is used to calculate specific heat capacity in (3) and that of liquid phase. Table 3 summarizes results comparisons between FVM, the conventional MB and proposed MB that incorporates analytic temperature profiles. The presented MB makes substantially better agreements on the exit enthalpy, subcooling length and mean temperatures of secondary flow compared with the conventional MB. Besides the accuracy, the real benefit using the proposed method is in the capability to retrieve spatial distributions of temperature, enthalpy and density from the calculated mean and inlet temperatures. This is possible because the analytic temperature profiles are enforced in (5) and (6). Comparisons of

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temperature profiles for the primary and secondary fluids are shown in Fig. 4. Although there are some discrepancies due to the approximation in (3), the proposed MB captures nonlinear temperature distributions very reasonably. Because of the capability, it will show accurate charge prediction which is important for simulation of a dynamic MB cycle model. Because the FVM model was implemented with a large number of nodes, i.e. 100, to provide an accurate result, the computation time comparison between the proposed MB and the FVM could exaggerate the speed of the proposed MB. Therefore the FVM was re-simulated with 20 nodes, which provided a reasonably accurate result for the speed comparison. The proposed MB is 2.74 times slower than that of the conventional MB, but is 4.95 times faster than the 20-node FVM. There are several papers that include ε-NTU or LMTD (log mean temperature difference) methods which are conceptually equivalent to our approach. However, those are not applicable to a dynamic MB model if dynamics of secondary flow are not negligible, because available states at each computation time in a dynamic model include mean temperatures rather than interfacial temperatures. Table 3. Result comparisons between each approach FVM

݄௘ [kJ/kg] 1649.2

‫ݖ‬ଵ [-] 0.25

ܶത௦ǡଵ [oC] 194.23

ܶത௦ǡଶ [oC] 209.74

ܳሶ [kW]

Conventional MB

1439.5

0.04

183.97

212.78

146.25

Proposed MB

1648.9

0.28

196.33

212.73

167.19

167.22

Fig. 4: Comparison of temperature profiles between FVM and proposed MB

5. Conclusion and future work A more reliable moving boundary approach that incorporates analytic steady temperature profiles for a heat exchanger is presented and a method to treat temperature glide for a binary mixture is also introduced. The proposed method is tested for a counter flow heat exchanger working with water/ethylene glycol mixture and steam as a primary and secondary fluids. Result comparisons with a detailed model (FVM) and a conventional MB are provided, and the proposed method shows substantially better agreements with FVM. In addition, it is shown that spatial distributions of thermodynamic states can be retrieved using available states, and hence it will significantly improve charge estimation within the MB framework. In future, the approach will be applied to a dynamic MB model and its performance will be tested with transient data for an ORC test-rig.

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Acknowledgements This material is based upon work supported by the Department of Energy Vehicle Technologies Program under Award Number DE-EE0007286. The authors greatly appreciated the support of Dr. Eric Lemmon and Dr. Ian H. Bell from NIST addressing calculation of the thermophysical properties of water /EG mixtures. Finally, the authors would like to acknowledge Mr. Swami Nathan Subramanian and Dr. Abhinav Krishna for their leadership and contributions during the project. Disclaimer This report was prepared as an account of work sponsored by an agency of the United States Government. Neither the United States Government nor any agency thereof, nor any of their employees, makes any warranty, express or implied, or assumes any legal liability or responsibility for the accuracy, completeness, or usefulness of any information, apparatus, product, or process disclosed, or represents that its use would not infringe privately owned rights. Reference herein to any specific commercial product, process, or service by trade name, trademark, manufacturer, or otherwise does not necessarily constitute or imply its endorsement, recommendation, or favouring by the United States Government or any agency thereof. The views and opinions of authors expressed herein do not necessarily state or reflect those of the United States Government or any agency thereof. References [1] Bendapudi, S., Braun, J. E., & Groll, E. A. (2008). A comparison of moving-boundary and finite-volume formulations for transients in centrifugal chillers. International journal of refrigeration, 31(8), 1437-1452. [2] Willatzen, M., Pettit, N. B. O. L., & Ploug-Sørensen, L. (1998). A general dynamic simulation model for evaporators and condensers in refrigeration. Part I: moving-boundary formulation of two-phase flows with heat exchanger. International Journal of refrigeration, 21(5), 398403 [3] Rasmussen, B. P., & Alleyne, A. G. (2004). Control-oriented modeling of transcritical vapor compression systems. Journal of Dynamic Systems, Measurement, and Control, 126(1), 54-64. [4] McKinley, T. L., & Alleyne, A. G. (2008). An advanced nonlinear switched heat exchanger model for vapor compression cycles using the moving-boundary method. International Journal of Refrigeration, 31(7), 1253-1264. [5] Li, B., & Alleyne, A. G. (2010). A dynamic model of a vapor compression cycle with shut-down and start-up operations. International Journal of refrigeration, 33(3), 538-552. [6] Wei, D., Lu, X., Lu, Z., & Gu, J. (2008). Dynamic modeling and simulation of an Organic Rankine Cycle (ORC) system for waste heat recovery. Applied Thermal Engineering, 28(10), 1216-1224. [7] Shi, R., He, T., Peng, J., Zhang, Y., & Zhuge, W. (2016). System design and control for waste heat recovery of automotive engines based on Organic Rankine Cycle. Energy, 102, 276-286. [8] Galindo, J., Dolz, V., Royo-Pascual, L., Haller, R., & Melis, J. (2016). Modeling and Experimental Validation of a Volumetric Expander Suitable for Waste Heat Recovery from an Automotive Internal Combustion Engine Using an Organic Rankine Cycle with Ethanol. Energies, 9(4), 279. [9] Wei, D., Lu, X., Lu, Z., & Gu, J. (2008). Dynamic modeling and simulation of an Organic Rankine Cycle (ORC) system for waste heat recovery. Applied Thermal Engineering, 28(10), 1216-1224. [10] Woodland, B. J. (2015). Methods of increasing net work output of organic Rankine cycles for low-grade waste heat recovery with a detailed analysis using a zeotropic working fluid mixture and scroll expander, Ph.D. Thesis, Purdue University. [11] Accorsi, F. A. (2016). Experimental characterization of scroll expander for small-scale power generation in an Organic Rankine Cycle, M.S. Thesis, Purdue University. [12] Lemmon, E. W., Nell, I.H., Huber, M.L., McLinden, M.O.. NIST Stabdard Reference Database 23: Reference Fluid Thermodynamic and Transport Properties-REFPROP, Version 9.1.1, National Institute of Standards and Technology. 2016. [13] Incropera, F.P., & De Witt, D.P. (1985). Fundamentals of heat and mass transfer, 2nd edition. United States: John Wiley and Sons Inc.