Journal of Thermal Science Vol.27, No.* (2018) ****

https://doi.org/10.1007/s11630-018-1023-2

Article ID: 1003-2169(2018)00-0000-00

A Review of Modeling Approaches and Tools for the Off-design Simulation of Organic Rankine Cycle LIU Liuchen1, ZHU Tong 1*, GAO Naiping1, GAN Zhongxue2 1. School of Mechanical Engineering, Tongji University, Shanghai 201803, China 2. ENN Science & Technology Ltd., Hebei 065001, China © Science Press, Institute of Engineering Thermophysics, CAS and Springer-Verlag GmbH Germany, part of Springer Nature 2018

Abstract: Organic Rankine Cycles (ORCs) are an effective way to produce electricity from low-grade heat sources, which cannot be effectively obtained using conventional high-temperature Rankine cycles. Due to the lack of available information regarding the real Organic Rankine Cycle units on industrial level, off-design simulation under diversified operating conditions plays a significant role for both the system performance prediction and control strategy design. This paper summarizes the theoretical basis, modeling approaches and tools for ORC off-design simulations. Firstly, a review was conducted on the individual state-of-the-art convective heat transfer correlations and void fraction models. Secondly, different kinds of modeling approaches and simulation tools were proposed, highlighting their relevant characteristics, and were categorized for their specific applications. Moreover, an in-depth analysis of technical challenges related to various applications and focusing on the model accuracy and complexity, computational efficiency, as well as the model compatibility were extensively described and discussed. Finally, the current research trends in this field and the development for further investigations were presented.

Keywords: Organic Rankine Cycle (ORC), low-grade heat, modeling approach, off-design

1. Introduction Among the fields of theoretical and commercial investigations, conventional gas- and steam-based systems still play a dominant role in large-scale power generation. The open-cycle gas turbines (Brayton cycle) are widely used wherever natural gas reserves are in abundance. However, the closed-cycle steam power plants (Rankine cycle) are the preferred solution if coal or nuclear are used as the main energy source. There are certain occasions when the open-cycle or closed-cycle turbines are neither techni-

cally nor economically beneficial [1, 2]. As shown in Fig. 1, for low temperature (below 250°C) or low-capacity (especially, when the system scale is smaller than 2 MWe) waste heat recovery applications, it is proposed to effectively convert the low-grade heat into useful mechanical power by substituting water with an organic compound as the working fluid in the conventional closed-loop Rankine cycle. Such a technology is marked with a universally known acronym of ORC (Organic Rankine Cycle) [3]. Fig. 2 illustrates the general construction of a simple

Type of Contribution: Invited review Received: April 4, 2018 Corresponding author: ZHU Tong, Professor E-mail: [email protected] This study is financially supported by the National Key Basic Research Program of China 973 Program (Grant No. 2014CB249201). www.springerlink.com

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J. Therm m. Sci., Vol.27, No.*, 2018

OR RC system, w which consistts of an evap porator, an exxpander, a conddenser, and a working flu uid pump. Thhe pu ump feeds thee liquid organnic fluid into the t evaporatoor, wh here the fluid is heated by low-grade heeat source. Thhe evaporating orgganic fluid is afterwards ex xpanded in thhe pander to yieeld mechanicaal work for producing p eleccexp triccal power ussing a coaxiaal generator. Then, the low w preessure organicc fluid is coolled down to liquid state in a condenser and iis then pumpeed back to thee evaporator tto d the rellevant T-S diaacontinue the cyycle. Fig. 3 depicts t ic graam of such a cycle. The four main thermodynami pro ocesses includde the isobaric heat absorp ption process iin thee evaporator (6-1), the exxpansion proccess in the exxpander (1-2), thee isobaric conndensation pro ocess (2-5), annd T processess 1-2s and 5-66s thee pumping prrocess (5-6). The aree the ideal isenntropic processses. Over the last two decadees, ORC systeems have beeen wiidely demonsttrated to be a favorable sollution to geneeratee power from low-grade heeat sources in many differennt engineering appplications. More M conventiional ones innude electricityy production from f geotherm mal or biomasss clu [1,, 4], and cogenneration for CHP C (Combined Heating annd Po ower) system [5, 6]. Meannwhile, many innovative apppliications, such as solar therm mal power geeneration [7-99], waaste heat recovery from IC CE (Internal Combustion C Enngin ne) on cars and trucks [10-13], [ and thermoelectriic conversion from m waste heatt in various industrial proocessses are also ggaining maturiity [14].

Fig g. 1

ORC appplication fields in the heat source temperaature-pow wer output planee.

Fig. 2

Simplified schheme of the ORC C cycle

Fig. 3 T-S T diagram of tthe ORC cycle

2. Sco ope and topiccs Onee of the main topics of OR RC investigations is the work reliability r and d flexibility uunder variouss operating conditiions. This is due d to the reasson that a sized and built ORC system s often operates undder various conditions, c which differ from itss nominal desiign point. In this t regard, o most ORC C units can be identified. two rellevant levels of For so ome applicatio ons, in particcular the morre conventional ones, o the systeems are inhereently either staationary or quasi-sstationary. Thiis means that the heat inpu ut from the temperrature of low--grade heat ssources has a relatively fixed value v or chan nges very sloowly in equaal periods. Meanw while, such a system is ofteen directly co onnected to an AC C power grid and the geneerated power is mainly used fo or the local ellectrical consuumption. In th hese cases, the exp pander’s rotatiing speed is uusually stabilizzed using a frequen ncy converterr and needs nno stringent reequirement for thee control straategies. Thereefore, the sysstem’s dynamic behavior has no particularr importance under u such mstances, and the t design of control system m is usualcircum ly not critical. On th he other hand, d, the effectivee operation ovative applicaations of ORC C systems ofteen depends of inno heavily y on the dynaamic behaviorr and control strategies. In casee of the recoveery of waste hheat from steeel stamping water in i industrial processes, p thee handling of highly infrequen nt and large variations in heat input iss the main challen nge for operatiing ORC in auutomotive app plications. Instead of the operational o coonditions, thee system’s nce can also bbe influenced by several off-dessign performan inheren nt aspects. On ne aspect is thee cycle config guration [4]. Two most m commonly used configgurations are the t simplified cy ycle, and the regenerative cyycle, where th he expander’s ou utlet exhaust is used to ppreheat the ev vaporator’s inlet fluid using a reecuperator. M More complex configurations, such as tran ns-critical cyccle and cascaade cycle, d for specificc applicationss. Another might be employed nce in perform mances of varrious cycle aspect is the differen onents. For example, e the working flu uid’s mass compo flow raate through th he volumetric expander varries almost

LIU U Liuchen et all.

A review off modeling apprroaches and toools for the off-design simulatio on of Organic R Rankine Cycle

pro oportionally w with the rotattional speed as well as thhe inllet vapor denssity, while thee working flu uid’s mass flow w ratte will be inddependent of the rotationaal speed and is rou ughly proportional to the innlet vapor presssure. Similarlly, thee mass flow rate throughh a volumetrric feed pum mp maainly dependss on its rotatiional speed, whereas if thhe speeed pump is uused, then it also a depends on o the pressurre diffference. Meaanwhile, whenn dynamic beh havior and conntro ol strategy are taken into acccount, the ressponse speed oof thee two main heeat exchangerss (evaporator and condenseer), determined usinng the mass and a heat capaacitance of diifp the key role r in analyssis ferrent equipmennt types, will play [13 3, 15]. Usuallly, compact devices, such h as plate heaat exchangers, exhhibit a dynamiic response qu uicker than thhe sheell-and-tube hheat exchangeers. Moreover, it should bbe furrther noted thaat the descripttion of dynam mic behavior foor meechanical devvices (pump and a expander)) is commonlly avoided due to their negligibble heat transffer irreversibiily compared too their relativve faster mech hanical interaccity tio on. Last but nnot least, the effect of diffferent workinng flu uid charge levvels should also a be precisely predictedd. Ind deed, the overcharging off working flu uid would deecreease the effecctive phase change c heat trransfer area iin heat exchangerrs, while an insufficient working fluiid charge would leead to cavitatiion at the inleet of a pump aas a expander [16, 17]. weell as at the suuction port of an In summary,, the problem ms described above can bbe sollved by resorrting to model-based simu ulations to deescrribe the transient behavioor of an OR RC system annd evaluate the sysstem performaance where criitical situationns n occur. Speecifically, a trrue off-design n ORC modeel can mu ust implemennt both the energy e and mass m balancees, wh hich are dictatted by (i) the heat h source an nd the heat sinnk, (ii)) the cycle coonfiguration and a the geom metries of com mpo onents, and (iiii) the total am mount of work king fluid in thhe sysstem as well as its reparttition through h main compoonents during thee off-design operation. o Fig g. 4 depicts thhe

Fig g. 4

Number oof published arrticles on organic Rankine cyccle (ORC) reesearch using the t three keyw words of “ORC C”, “ORC sim mulation” and “ORC off-desiign” (updated tto January 22018).

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number of published d articles deaaling with sim milar topics [18]. Itt can be found that, by seaarching the keeywords of ‘simulaation’ and ‘offf-design’, thee related num mber of papers haas grown moree than four tim mes in the last decade.

3. Theeoretical bassis The off-design siimulation moodel of an OR RC system synthessizes the basicc theory of theermodynamics, heat and mass trransfer, fluid mechanics, m fluuid machinery y as well as data prrocessing tech hnologies. Ass mentioned above, the detailed off-design modeling m of O ORC systems is preferably carrried out using a modular aapproach, in which, the overalll system modeel is obtained using the con nnection of sub-mo odels represen nting the inddividual comp ponents of the cy ycle. They in nclude heat eexchangers, expanders, pumps, fluid reserv voir, and pipeeline. One off the most sophistticated points is how to eestablish the multi-zone heat ex xchanger mod dels. Since thee heat transferr characteristics of o two-phase flow f are quitee different from m those of single-phase flow, models m for bboth the evaporator and nser are propo osed to dividee it into three parts, corconden responding to the liq quid-phase zoone, the two-p phase zone, z [13]. It iis well known n that heat and thee gas-phase zone transfer in two-phasse zone invollves phase ch hange heat transfer, including the t evaporatioon and condeensation of workin ng fluid. Therrefore, enoughh attention needs to be paid to o properly iden ntify the convvective heat trransfer coefficien nts in multi-zo one heat exchhangers. It is a common practice to use "state-of-the-art" ccorrelations from fr previudies as initiaal guesses to predict the convective ous stu heat transfer coefficcients of two--phase zone. The ORCd literature su urvey revealedd several avaailable emrelated pirical boiling flow correlations,, which were published ngor et al. [19 9], Chen et al. [20], Wetterm mann et al. by Gun [21], Zou Z et al. [22]], Cooper et aal. [23], Han et al. [24], and Am malfi et al. [25]. Correlatioons from [19-22] can be used iff the evaporato or is a fin-tubbe heat exchan nger, while correlaations from [2 23-25] are suiitable for platte heat exchangeers. Tables 1 and 2 list th the general in nformation about these t correlations. Morreover, the available a conndensation co orrelations, which are commonlly used for O ORC simulatio on, can be nvestigations of Cavallini et al. [26], obtaineed from the in Akers et al. [27], Sh hah et al. [288], Qian [29], Han et al. nd Longo et al. a [31]. Correllations from [26-29] can [30], an be useed if the con ndenser is a sshell-and-tubee heat exchangeer, while another correlatioon from [28] as well as from [3 30] and [31] are a suitable foor plate heat exchangers. Generaal information n about these correlations is summarized in n Tables 3 and d 4. The same single--phase correlaation can be applied to both th he hot and colld fluids in thhe same heat exchanger. Correlaations from [2 29] can be ussed to calculaate the sin-

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J. Therm. Sci., Vol.27, No.*, 2018

gle-phase convective heat transfer coefficient in fin-tube heat exchangers, while the Gnielinski correlations [32] are recommended for shell-and-tube heat exchangers. Furthermore, Chisholm et al. [33], Wanniarachchi et al. [34], Thonon [35], and Martin [36] have proposed three correlations for single phase flows in plate heat exchangers. Table 5 summarizes the general information about these five correlations. It is worth pointing out that there are more than fifty correlations that could be considered practical, and the ones listed in this paper are just a non-exhaustive summary of the most commonly used correlations obtained from the ORC-related literatures. From the practical point of view, the readers are recommended to select the heat transfer correlations on a case-by-case basis to fully consider the type of working fluid, the geometry of heat exchangers, the operating conditions of the system, and the effect of lubricant oil. Extensive experimental work is also required for certain applications. The discussion about this topic is much less common in ORC-related researches. A thorough search of literature yielded only two papers dedicated to the identification of heat transfer correlations. Pan et al. [37] investigated the impact of Table 1

various heat transfer correlations to calculate the mass of working fluid based upon a 3 kWe system using a fin-tube heat exchanger as an evaporator, and a shell-andtube heat exchanger as a condenser. Four cases using different working fluids were discussed. Unfortunately, the study was just theoretical and no experimental data was reported. Dickes et al. [38] used a 2 kWe unit as the case study and the simulations of various correlations for plate and fan coil heat exchangers were compared with the experimental values. In addition, all previously existing heat transfer correlations are obtained from steadystate experimental measurements. If the system’s dynamic behavior has been considered, accurate calculation of the heat transfer coefficient in real time will arouse more interest for further investigations. After precise calculations of convective heat transfer coefficients, a proper prediction of the variation in fluid density along the heat exchanger becomes essential for high-precision estimation of the theoretical working fluid charge. In single-phase zones, the fluid density is nearly invariable and can be determined in a rather straight forward way from the fluid’s thermodynamic state. However, in the case of a two-phase flowing mixture, the density

Evaporating flow correlations for fin-tube heat exchangers

Authors and fluids

Equations

K=K fc F+K nbS

Gungor et al. [19] water/ pentane

K nb =55Pr 0.12 (  log Pr) 0.55 M 0.5q 0.67 , S  K nb  0.9 K 0.85 fc , 0.41 0.75   1 l  x  F  x   1  3000Bo 0.86  1.12     , F  0 F  x  dx, 1 x   g  1 S , 1.17 1  2.53  10 6 Re l F 1.25 2000  Re  10000



K f ,2  K fc F+K nbS,

Chen et al. [20] water/methanol/ cyclohexane/pentane



K fc  0.023

l d

X tt  10

1 ,  0.736 F  1   0.213  ,  2.35   X tt   K nb  0.00122

Re l 0.8 Prl 0.4

X tt  10

k l 0.79C p ,l 0.45  l 0.49 Tsat 0.24 p sat 0.75

 0.5  l 0.29  v 0.24 h fg

ΔTsat =Tw  Tsat ,

1

,S 



1  2.53  10 6 Re l F 1.25



1.17

ΔPsat =Psat (Tw )  p sat (Tsat ),

10 4  Re  10 6 Wettermann et al. [21] R116/R134a/SF6

0.37 -2.2 0.67 -2        0.01 0.7   l   0.4   l  0.01 K vo    K  x   K fc =K lo 1  x  1  8 1  x      x 1  x   1.2 x    K       v   v      lo   1 K f ,2   K  x  dx,570  Re  87000



0

K

Zou et al. [22] R170/R290

 K fc F 

2

 P  K nb =55    Pcr 

  K nb S  , K fc  0.023

0.12

2

  P    lg    Pcr   

l d

Re l 0.8 Prl 0.4

0.55

M 0.55q 0.67

 x  F  x   1  3000Bo 0.86  1.12   1 x 

0.75

   l   g 

0.41 1

, F   F  x  dx,2000  Re  5000 0



-0.5

LIU Liuchen et al.

A review of modeling approaches and tools for the off-design simulation of Organic Rankine Cycle

is not only function of the fluid temperature, pressure, and quality, but also depends on the void fraction characterizing the flow. Therefore, the charge estimation in heat Table 2

exchangers is directly impacted by the void fraction model used to characterize the evaporation or condensation.

Evaporating flow correlations for plate heat exchangers

Authors and fluids

Equations

H Cooper et al. [23] R123

 q / A

0.67c 2

 0.12  0.2log Rp   c1  55Pred   log Pred 

0.55c2

MM 0.5 , 1000  Re  40000

f  2.5Re 0.3 Nu  c1  C  Rec2 m Bo0.3 Pr 0.4 ,

Han et al. [24] R410a

C  2.81(Pco/Dh ) 0.041 2.83, m  0.746(Pco/Dh ) 0.082 0.61, 2500  Re  9000, P  f

Amalfi et al. [25] R410a/R134a

Table 3

2    L  N Geq  , Geq  Gc 1 x  x( f )1/2 .   Dh  f  g  

1.101 -0.224       c1  982  We 0.315c 2  Bo 0.32  l  ,     max   v  Nu   0.248 -0.223       Re v 0.315c2  Re lo 0.315c2  Bd 0.235  Bo 0.198  l  ,  c1  18.495    max   v  

Bd  4 Bd  4

Condensing flow correlations for shell-and-tube heat exchangers

Authors and fluids

Cavallini et al. [26] R410a/R134a

Equations

Re l,eq 

ud 0

l g

1

l

2

, Nu c  0.05Re l,eq 0.8 Prl 0.33 , K f ,2  Nu c

l d0

,

3000  Re  55000 Akers et al. [27] R410a/R22

Re l,eq 

ud 0

l g

1

l

2

1

1

,Nu c  5.03Re l,eq 3 Prl 3 , K f ,2  Nu c

l d0

, Re  50000

Shah et al. [28] R134a

0.38 5  P   Nu c  0.023Re l 0.8 Prl 0.4   2.2542  cr   , K f ,2  Nu c l ,2100  Re  42000 d0  P    9

Qian [29] water

 m l 3 l 2 g  K f ,2  0.752    N td 0 l t b  t w  

Table 4

0.25

, Re  35000

Condensing flow correlations for plate heat exchangers

Authors and fluids Shah et al. [28] R134a

Equations

 3.8 x 0.76 (1  x ) 0.04  Nu  Nu l (1  x ) 0.8  , 0.38 Prred  

Nu l  c1  0.023Re 0.5c2 Pr 0.4 ,2100  Re  42000,

Nu  c1  C  Re c 2 m Bo 0.3 Pr 1/ 3 , C  11.22( Pco /D h ) 2.83 4.5 ,

Han et al. [30] R410a/R22

m  0.35( Pco /D h ) 0.23 1.48 , 2500  Re  9000, f  Ge1  Re Ge 2 , P  Ge1  3521.1 co   Dh 

Longo et al.[31] HFC134a/410a/236fa HC600a/290a/1270 HFO1234yf/1234ze

4.17

    2 

7.75

P  , Ge 2  1.024  co   Dh 

0.25  L  k l 3 l 2 g h lat  ,  c1  0.943   Nu   k   l TL   c 0.445 Pr 1/3 ,  c1  1.875 Re 2

5

Re  1600 Re  1600

0.0925

    2 

1.3

.

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J. Therm. Sci., Vol.27, No.*, 2018

Table 5

Single-phase correlations for fin-tube [30], shell-tube [32], and plate heat exchangers [33-36]

Authors and fluids

Equations

Qian [30] water

Re  3000 64 / Re, f  h  St    u m  C p , St  Pr 2 / 3  , f  0.316Re  0.25, 3000  Re  5000 8 0.184Re  0.2, Re  5000 

Gnielinski [32] R410a

h  Nu , Nu  d

Chisholm et al.[33] water

Nu  0.72 0.41 Re 0.59 [(90   ) / 30] 0.66 , f  0.8Re 0.25  1.25 [(90   ) / 30] 3.6 ,30     80  , 1000  Re  40000

Wanniarachchi et al.[34] water



f  Re  1000  Pr   d  23  -2 6 8 1     , f  1.82log Re  1.64  ,2000  Re  10 0.5 2  f   3   l    1  12.7    Pr  1    8   

Nu=(Nu l3 +Nu 3t ) 1/3Pr 1/3 (μ/μ w ) 0.17 , Nu l =3.65(π/2-θ) -0.455Re -0.339? c 2 , Nu t =

12.6 Re c 2 (0.646+0.00111(π/2-θ)) , (π/2-θ) 1.142

f  [ f l3  f t3 ]1/ 3 , f l  1774( / 2   ) 1.026 Re 1 , f t  46.6( / 2   ) 1.08 Re  p , p  0.00423( / 2   )  0.0000223( / 2   ) 2 , 1  Re  10000

Nu  C1  Re m  Pr 1/ 3 Thnon [35] R410a/R134a

f  C 2  Re  p

  75  , C1  0.1000, C 2  28.21, m  0.687, p  0.900   60  , C1  0.2267, C 2  26.34, m  0.631, p  0.830   45 , C1  0.2998, C 2  18.19, m  0.645, p  0.682   30  , C1  0.2946, C 2  45.57, m  0.700, p  0.670 50  Re  15000 Nu  c1  0.205  Pr 1/ 3 ( f  Re 2  sin(2 )) c2 0.374

Martin [36] R410a/R22

1 cos 1  cos   f 0.045tan   0.009sin   f 0 / cos 3.8 f 1 16 / Re, f0   2 (1.56ln Re  3) ,

Re  2000 Re  2000

149.25/ Re  0.9625, Re  2000 f1   0.289 Re  2000 , 9.75/ Re

The void fraction is defined as the fraction of vapor area on the local fluid interface, which can be considered as a function of vapor quality. In order to accurately calculate it, assumptions of various void fraction models are introduced in several previous literatures. The homogeneous model, proposed by James et al. [39], considered a uniform mixture and similar flow velocities for liquid and gas phases. However, the accuracy of model was limited due to its simplicity. Therefore, corrections are needed to modify the homogeneous model. The main modifications include slip ratio, Xtt (Lockhart-Martinelli number), and mass flow rate corrections. The slip ratio correction is a correlation aimed at the ratio of gas phase velocity to that of the liquid phase. Typical models are proposed by Zivi [40] and Smith [41]. The Xtt correction considers the difference in velocity and dynamic viscosity between the liquid and gas phases in the two-phase zone. Relevant models include the L-M [42] and Baroczy [43] models. Moreover, the mass flow rate correction considers the comprehensive impact of fluid velocity, dynamic viscosity, and surface tension, whereas such models have been reported by Hughmark [44], Premoli [45], T-B [46], and Yashar [47]. Table 6 summarizes the detailed mathematical equations obtained from some typical models. The applicability of different void fraction models in refrigerant systems has been well studied by comparing the calculation results with the experi-

mental measurements. However, the investigations related to ORC systems have rarely been reported in literature [37, 38].

4. Modeling approaches Numerical simulations play an essential role in the investigation of ORC systems. The model-based simulation methodology must rely on the availability of each suitable sub-model, capable of precisely interpreting the system behavior in both the steady state and transient conditions. This section describes different simulation approaches and each independent component’s sub-models in detail. 4.1 Steady-state heat exchanger models Generally speaking, the main components in an ORC system can be divided into two types, namely the heat exchangers and the mechanical devices. For the heat exchangers, both the steady-state and dynamic models have been employed to represent their thermodynamic behavior. Regarding the steady-state models, the most common approach for ORC systems is to use a simplified thermodynamic analysis. In particular, assumptions are made regarding the degrees of sub-cooling at the outlet of a condenser (or pump inlet) and superheating at the evaporator outlet (or expander inlet), as well as the evaporating

LIU Liuchen et al. Table 6

A review of modeling approaches and tools for the off-design simulation of Organic Rankine Cycle

7

Equations of different void fraction models Authors

Equations 

1 3

Zivi [40]

ug   g  =  ul   l 

Smith [41]

     0.4   l  0.4  x   ug   g   =0.4+0.6   ul 0.4  0.6 x      

L-M [42]

 l    g    g    l     1+X 0.8 -0.378 , tt   x  =f  X tt  =  0.823-0.157ln X tt ,  1 x  X tt =    x 

0.1

0.9



0.5

0.5



X tt  10 X tt  10

 y   1  F1   yF2  1  yF 2   0.22 0.08     F1  1.578Re l 0.19  l  , F2 =0.0273We l Re l 0.51  l   g   g      1  1 G 2 d in ,  ,We l  y   l l  1  x   g  1     x   l  ug ul

Premoli [44]

1

Hughmark [47]

and condensing temperatures (or pressures). It is a common choice to assume a constant value for the isentropic efficiency of a pump and expander and to assume the compression and the expansion to be adiabatic. The cycle is solved by calculating the relevant thermodynamic states of the cycle and the performance of the system in terms of the power produced at the expander and the overall cycle efficiency. Gurgenci [48] developed a semi-analytical model for both the heat exchangers and the mechanical devices, which describes the system’s off-design performance based on design point. The empirical black-box parameters must be calibrated using data obtained from an ORC system operated following a predefined control strategy. However, the model was not explicit enough. Ibarra et al. [49] developed a partial off-design model of an ORC unit. The influence of evaporating pressure, condensing pressure, expander’s rotational speed, and expander’s inlet temperature on the system performance has been investigated. However, only the off-design behaviors of turbo-machine and recuperator are considered, and no model has been used for heat exchangers. Moreover, the influence of heat source, heat sink, and ambient conditions is not taken into account. Lecompte et al. [50] developed an off-design model by interconnecting sub-models of each component. The optimal rotational speed of a pump, which maximizes the system’s net power output, has been investigated. Comparing superheated and partially evaporating operations, the net power output can

  x   f ( Z ) , Z 

1

Re  6 Fr 8 1

1    4

be improved by 2% - 12%. Song et al. [51] established an off-design model to predict the influence of heat source and cooling water supply temperatures on the performance of a 530 kWe system. Möller and Gullapalli [52, 53] developed the “SSP ORC simulation” tool based on SWEP SPP software for both the design and the off-design performance modeling. The software can perform a detailed modeling of brazed plate heat exchangers. Two case studies have been used to validate the model. This type of simplified thermodynamic modeling is useful as a preliminary investigation of the effect of working fluid and operating conditions on the cycle performance of the ORC system. In fact, this methodology represents a typical working fluid screening method or an objective function to be optimized, given a set of desired working conditions. However, the physical characteristics and behavior of real system components are not taken into account. Therefore, it is not possible to accurately predict the off-design performance of a particular system. High accuracy steady-state models are usually discretized in order to include the spatial changes. The more common ones are the three-zone models. A counter flow heat exchanger model can be established using the effectiveness-NTU method or LMTD (logarithmic mean temperature difference) method. In order to precisely predict the heat transfer coefficient, both the phase-change heat exchangers were divided into three zones, namely the liquid zone, the two-phase zone and the vapor zone. Each

8

J. Therm. Sci., Vol.27, No.*, 2018

of them was characterized using proper heat transfer correlations, which can be calibrated based upon experimental data. Quoilin [54] built a semi-empirical model of an ORC unit by interconnecting sub-models of each component. The pump and expander’s rotational speeds have been optimized to maximize the system’s net thermal efficiency under off-design conditions. Wang et al. [55] built a semi-empirical off-design model by interconnecting the components’ sub-models. The ORC unit was operated under a sliding pressure control to keep a constant degree of superheating and a varying mass flow rate of the working fluid. However, no experimental validation was provided. Hu et al. [56] discussed three control schemes to operate a geothermal ORC unit, namely the constant pressure strategy, the sliding-pressure strategy and the optimal-pressure strategy. Both the mass flow rate of the working fluid and the variable inlet guide vanes were used to adapt the system’s off-design behavior as a function of the heat input. Li et al. [57] analyzed the performance of a geo-thermal ORC system in response to the heat source and heat sink variations. Sliding pressure control strategy was applied. Ziviani et al. [58] developed a chargesensitive or subcooling-sensitive ORC off-design model. Both the entire ORC model and the sub-models have been Table 7

intensively validated using experimental measurements. Liu et al. [59] developed a charge-oriented off-design model to assess the behavior of heat exchangers under part-load conditions and the impact of different charge under part-load conditions. Again, no experimental validation was reported in the work. Dickes et al. [60] compared the accuracy and quickness of three different modeling approaches, namely the constant efficiency, the polynomial-based, as well as the semi-empirical model for ORC off-design simulation. Their investigations were performed at both the component- and the cycle-level. Later on, they [38] developed a steady-state charge-sensitive model, which used the system’s boundary conditions rather than any pre-set constraint to predict the off-design performance of a 2kWe recuperative ORC system. 4.2 Dynamic heat exchanger models With regards to dynamic models, they can be used to explore a system’s dynamic behavior, understand its main features, such as response speed, presence of performance oscillation, inverse response dynamics and delays, more or less pronounced nonlinear behavior, coupling between various control inputs and controlled outputs. To

Non-exhaust literature survey of ORC off-design studies (steady-state simulations) Authors

System descriptions

HEX

model

EP&PP model

Gurgenci [48]

150 kWe ORC unit supplied by a solar pond, R114, dynamic turbine, HEX: shell-and-tube

Semi-empirical model

Semi-empirical model

Ibarra et al. [49]

Theoretical 5 kWe ORC system, R245fa/SES36, scroll expander, HEX info not specified Experimental 11 kWe ORC prototype, R245fa, BPHEXs, twin screw expander

Thermodynamic model

Constant-efficiency model

Thermodynamic model

Semi-empirical model

Song et al. [51]

WHR 530 kWe ORC system, R123, radial inflow turbine, HEX info not specified

Thermodynamic model

Constant-efficiency model

Möller and Gullapalli. [52,53]

Two Craft Engine CE10, R245fa/R134a, scroll expander, BPHEXs

Thermodynamic model

Constant-efficiency model

Quoilin [54]

Experimental 2 kWe ORC prototype, R123, scroll expander, BPHEXs

[24] [30] [34]

Semi-empirical model

Wang et al. [55]

CPC solar collectors supplying a 250 kWe ORC unit R245fa, multi-stage turbine, BPHEXs, thermal storage

[24] [33]

Semi-empirical model

Hu et al. [56]

70 kWe geothermal ORC system, R245fa, radial-inflow turbine, BPHEXs

[24] [30] [33]

Semi-empirical model

Li et al. [57]

1.5 MWe geothermal Kalina (KCS34) unit (H2O+NH3, multi-stage axial turbine, 4 BPHEXs Two experimental systems: (i) 11 kWe ORC unit (R245fa, BPHEXs, screw expander); (ii) 5 kWe ORC unit (R134a, BPHEXs, scroll expander)

[24] [33]

Lecompte et al. [50]

Ziviani et al. [58]

Liu et al. [59]

Dickes et al. [60]

Dickes et al. [38]

Constant-efficiency model

[33] [30] [35]

Semi-empirical model

Theoretical 3 kWe ORC system, R123, scroll expander, shell-and-tube condenser, fin-tube evaporator, no recuperator Two experimental units: (i) 3 kWe ORC system (R245fa, BPHEXs, scroll expander, diaphragm pump); (ii) 10 kWe ORC unit (R245fa, BPHEXs, scroll expander)

[19] [29] [32]

Semi-empirical model

[33] [30] [35]

Constant-efficiency/ Semiempirical/ Polynominal regression model

2 kWe ORC system for solar thermal application, R245fa, scroll expander, 2 BPHEXs + 1 fan coil , with recuperator

[23-25][28-31] [34-36]

Semi-empirical model

BPHEX: Brazed Plate Heat Exchanger.

LIU Liuchen et al.

A review of modeling approaches and tools for the off-design simulation of Organic Rankine Cycle

this end, a proper dynamic model can precisely depict a system’s response in small step changes according to the control input around different operating points. Moreover, if the modeling tools allow, the simulation can also obtain a linearized approximation of system dynamics around on-design and off-design setting points [3]. Dynamic models in existing literatures mainly rely on dynamic heat exchanger models and compared to heat exchangers, consider expander and pump with static models due to their fast response. The governing equations for mass, momentum and energy balances can be solved using either the FV (finite volume or discretized method) or the MB (moving boundary or lumped parameter model) method. In FV based methods, heat exchanger length is typically divided into a number of control volumes, in which, mass and energy balance equations are solved to find the state of working fluid [15]. In MB based methods, heat exchanger is divided into three zones based on working fluid's phase (liquid zone, two-phase zone, and gas zone). The observation of physical behavior, which differs a lot between the single-phase zone and the two-phase zone, remains as a fundamental challenge for these methods [14]. Additional numerical issues, including stability and flow reversal, exist in both methods. There are limited number of dynamic ORC models, which are able to handle generalized conditions. Vaja [15] proposed theoretical methods and a full library of dynamic models, which can represent the components that usually appear in energy conversion systems based on Matlab. The results of this investigation represent the main phenomenon that occurs in the real systems to get a full and deep understanding of the way they operate and respond to transient and off-design operating condition. Wei et al. [61] compared the moving boundary model and discretization techniques in terms of accuracy, complexity and simulation speed. They concluded that both the models have good accuracy, while the moving boundary model is faster, and therefore, is more suitable for control design applications. Quoilin et al. [62] developed a dynamic model of ORC, which focused specifically on the time-varying performance of heat exchangers, while three different control strategies were proposed and compared based on the evaluation of system performance under part-load conditions. Bamgbopa et al. [63] established a simplified transient model for an ORC operating under variable heat input. This approach considers that the response of the system to heat input variations is mainly dictated by the evaporator. Overall, the system is assembled using dynamic models for heat exchangers and static models for the pump and the expander. Manente et al. [64] established a hybrid dynamic/static off-design model to determine the optimal operating parameters (pump speed, turbine capacity factor, and air

9

flow rate through condenser) to maximize the system output power in response to ambient temperature and geo-fluid temperature variations. Xie et al. [65] built a dynamic model based on four basic operating modes, namely the start-up mode, the turbine turning mode, the power mode, and the protection mode, to reveal the dynamic behavior of ORC combined with the heavy-duty diesel engines. The authors proposed that it would be better to take full consideration of reducing the operating mode switching to pursuing the maximum cycle efficiency. Hou et al. [66] included MB based condenser and evaporator models, which consisted of sub-cooled liquid and two-phase region for the evaporator, and superheated vapor and two-phase region for the condenser. They also included a liquid receiver tank, which was considered independently from the condenser. Zhang et al. [67] developed a complete dynamic model of an ORC system with an evaporator, a condenser and a liquid receiver tank. Their tank model assumed that the inlet and outlet mass flow rates were equal at all times, while the model did not consider their contributions to pressure evolution of the complete system. Ziviani et al. [68] analyzed the advances and challenges of the most recent ORC technologies. The development and validation of a micro-ORC system simulation model have also been reported. At the end of the paper, the authors proposed a comprehensive guideline for developing a powerful simulation tool for ORC systems. Yousefzadeh et al. [69] presented a massconserving dynamic model to capture dynamic response of an ORC system. Both the evaporator and the condenser are modeled using FV method. The system dynamic response is tracked specifically considering the evaporator pressure, condenser pressure, degree of superheating at the evaporator’s outlet, degree of sub-cooling at the condenser’s outlet, and especially, the mass distribution along the evaporator, condenser and liquid receiver tank. This model is novel due to the integration methodology of its sub-models. Mazzi et al. [70] considered the real physical and operating characteristics of all main ORC components, with particular focus on the geometries of commercial heat exchangers, to properly simulate the mass and thermal inertias. Moreover, a suitable control system is chosen to govern the off-design operation, which takes into account all real operating constraints. A list of general information about these eleven investigations is presented in Table 8. 4.3 Models for mechanical devices As another core component of the ORC system, mechanical devices have a vital role to play in the overall performance of a system. In this section, three different kinds of modeling approaches are summarized for mechanical devices, namely the constant-efficiency method, the polynomial regression method, and the semi-empirical method.

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J. Therm. Sci., Vol.27, No.*, 2018

Table 8

Non-exhaust literature survey of ORC off-design studies (dynamic simulations) System descriptions

HEX model

Vaja [15]

Authors

270 kWe scale ORC system, saturated non-regenerative, R123, HEX: Pipe-in-pipe, Turbo-expander

MB

Wei et al. [61]

Theoretical 100 kWe ORC system, superheated non-regenerative R245fa, HEX: Pipe-in-pipe, Turbo-expander

FV/MB

Quoilin et al. [62]

kWe scale ORC system, Superheated non-regenerative, R245fa, HEX: Pipe-in-pipe, scroll-expander

FV

Constant-efficiency model

Bamgbopa et al. [63]

15 kWe ORC system, superheated non-regenerative, R152A/ R1234YF/R245FA, HEX: Pipe-in-pipe, Twin screw expander

FV

Semi-empirical model

Manente et al. [64]

6 MWe geothermal ORC system, superheated regenerative, isobutane or R134a, HEX: Not specified, Turbo-expander

Not specified

Constant-efficiency model

Xie et al. [65]

20 kWe ORC, superheated non-regenerative, R245fa/R123/water, HEX: Pipe-in-pipe, Turbo-expander

Not specified

Constant-efficiency model

Hou et al. [66]

100 kWe ORC system, superheated non-regenerative, R245fa, HEX: Fin-tube, Turbo-expander 100 kWe ORC system, superheated non-regenerative, R245fa, HEX: Finned coils, Scroll-expander

MB

Constant-efficiency model

MB

Constant-efficiency model

Ziviani et al. [68]

1.5 kWe ORC system, superheated non-regenerative, R245fa, HEX: Plate, Scroll-expander

FV

Semi-empirical model

Yousefzadeh et al. [69]

Scale info not specified, superheated non-regenerative , R134a, HEX: Plate, Scroll-expander

FV

Constant-efficiency model/ Semi-empirical model

Mazzi et al. [70]

4500 kWe ORC system, Superheated regenerative, Cyclopentane, HEX: Shell-and-tube, Turbo-expander

FV

Semi-empirical model/ Polynomial regression model

Zhang et al. [67]

The constant-efficiency method imposes constant performance parameters without considering individual operating conditions. Specifically, for pumps and expanders, the typical performance indicators, such as isentropic efficiency and volumetric efficiency, are usually incorporated as constant values. Due to its mathematical simplicity, this kind of model requires little computational efforts. Meanwhile, the constant-efficiency method possesses very poor precision for predicting the performance at both the component- and the cycle-level, and therefore, leads to the highest simulation residuals. Therefore, this kind of model could only be considered for off-design simulation, provided the ORC system operates very close to the nominal operating point. The polynomial-regression models use polynomial regressions to depict the effect of different operating conditions on system’s performance. Usually, second-order multivariate polynomial is applied for developing the component’s sub-model to keep the methodology systematic. Second-order polynomials (quadratic functions) are recommended to limit the Runge phenomenon and over-fitting. As shown in Eq. (1), the constant a is the polynomial coefficient, while X, Y, and Z are the most representative independent input variables that influence the component’s efficiency. These variables should be carefully identified for each type of component. 2

2

2

 =  a ijk X iY j Z k

(1)

i 0 j 0 k 0

Although the polynomial-based models consider components individually and in more detail than the con-

EP&PP model Constant-efficiency model Semi-empirical model

stant-efficiency method, they are also quicker to calibrate and evaluate. Runge phenomenon and over-fitting can also be very good limitations. Nevertheless, the reliability of this kind of models can drop when coupled together. Therefore, they could only be successful for characterizing the individual components’ performance and within their calibration ranges for interpolation. The third way for describing the components’ performance is to access the semi-empirical models, which implement modified physics-based equations. This kind of models usually relies on a limited number of physically meaningful equations, whose individual parameters can be tuned to fit a reference dataset from real operating processes. Therefore, they can actually represent the physics of processes, which the two previous types of model cannot. Considering the volumetric expanders as an example, Lemort et al. [71] identified a semi-empirical model for eight parameters of a scroll expander and their simulation results have been validated with the experimental measurements. Their analysis pointed out that the internal leakages, the supply pressure drops, and the mechanical losses are the main losses affecting the performance of expander. Meanwhile, the pumps are simulated in a similar manner. The effective mass flow of the working fluid delivered by the pump is calculated as an ideal mass flow rate, to which, an internal recirculation leakage is deduced. The mass flow rate characterizing these leakages is modeled using an incompressible flow through an equivalent orifice. Finally, the mechanical consumption of the pump is obtained by modifying the isentropic power with mechanical losses. In short,

LIU U Liuchen et all.

A review off modeling apprroaches and toools for the off-design simulatio on of Organic R Rankine Cycle

sem mi-empirical m models are acccurate enoug gh to reflect thhe component’s phhysical behavior. Furthermo ore, this kind oof odels show goood, robust performance fo or both the fiitmo tin ng and extrappolations at componentc and a cycle-leveel analyses, thoughh they requiree higher calibrration and sim mn between thesse ulaation times. A more detaileed comparison thrree modeling approachess in off-design conditions caan be found in a pprevious workk [60], in which, the authorrs perimentally validated the model for bo oth the compooexp nents and the ooverall ORC system. s Furth her informatioon about relevant liiteratures is prresented in Taables 7 and 8. 4 Charge-sen nsitive modelss for ORC sysstem 4.4 In the past ttwo years or so, a relativ vely new topiic about the chargge-sensitive models m for OR RC systems haas merged amongg the scientifiic community y. Such modeels em have been extennsively used inn vapor comprression coolinng forr both the desiign and perforrmance predicctions. A pioneer chharge-sensitivee model was established bby Ro ossi [72] in orrder to detect the automateed fault and ddiagnostics in vaapor compresssion equipmeent. Simulatioon ol, called ACM MODEL was used u to interconnect the fouur too maain sub-modells comprisingg of compressor model, conndenser model, evaporator model m and exp pansion devicce odel. The soluution algorithm m was based on three residdmo uals, namely thhe total refriggerant charge in the system m, ween the inlet of distributioon thee enthalpy diffference betw tub bes and the exxpansion deviice’s outlet, an nd the pressurre diffference betweeen the liquidd line’s outlet and the expannsio on device’s innlet. This simuulation tool haas been successsiv vely updated bby Shen [73, 74] for more precise predicctio ons of the imppact of different charge leveels over a widde ran nge of operatting conditionns. Moreover, the effects oof sm mall percentagges of lubricannt, contained in the refrigeerant flow, on thee performancee of system were w also invessgated. Unfortuunately, their application a to o ORC system ms tig is much less coommon. Actually, many off the issues innvestigated abouut vapor comppression cycles can also bbe plied to ORC C systems. Ass shown in Fig. 5, the totaal app wo orking fluid chharge of a sim mple system is calculated bby sum mming the chharge estimatiions from eveery componennt. If the initial chaarge is an inpuut, the charge residual can bbe ven by Eq. (2)). giv

11

ORC charge-sensitiv c ve modeling. The first pap per was reported by Ziviani ett al. [58], whho developed their ORC l Thee model could d either use modelss in Python® language. a speciified sub-cooling or accounnt for the totall charge of workin ng fluid as an input. A simp mplified metho od to simulate thee liquid receiv ver was introdduced. Furtheermore, the heat trransfer coefficients in varrious compon nents were calculaated using state-of-the-art coorrelations (seee Table 7) and Ziv vi’s void fracttion model [400] was used to calculate the two-phase flow's density. Thhe overall cy ycle model ntal setups. was vaalidated against two differeent experimen They concluded c thaat the overall cycle efficien ncy can be estimatted within the maximum rrelative error of ±20%, while the accuracy of the degrree of sub-co ooling was d by Liu et within ±1.5 K. The second paper was proposed 9], who developed anotheer mass-orien nted model al. [59 ® using Matlab M langu uage to simullate a 3 kWe ORC unit. Their model impleemented statee-of-the-art correlations valuate heat trransfer coeffiicients and (see Taable 7) to ev used Lockhard-Mar L rtinelli void ffraction mod del [42] to calculaate the two-phase flow's ddensity. The off-design model was used to estimate the ccharge of worrking fluid requireed under nomiinal conditionss and was useed to depict the heaat exchanger’ss behavior undder part-load conditions. c In addiition, the mod del was used to assess the impact of differen nt initial charrges levels. H However, the model has not yett been validateed using experrimental data.. The latest charge-sensitive mod deling has beeen introduced by Dickes 38]. Their work emphasizess the complex xity of heat et al. [3 exchan nger’s modeliing and demoonstrates how w state-ofthe-art correlations may be used to identify th he convecoefficients and nd how the modeling m of tive heeat transfer co charge helps in asseessing their reeliability. Thee modeling nment used to conduct their study was also environ Matlab b® and an opeen-access libraary ORCmKiit [75] was built to o explore the models m develooped in the fraame of this work.

Ncomponents

Charge ressid =Charge initiial -



Charge C i

(22)

i

Furthermore,, the total chaarge calculatiion model is a comprehensive integration of o continuity equation, annd m conservation ns. Meanwhil e, maass, energy, annd momentum thee degree of suuperheat of exppander’s inlet vapors and thhe sub b-cooling of ffluid at the coondenser’s ou utlet closely deepend on initial ccharge level off the working fluid. The literaturee contains onlly three articles dedicated tto

Fig. 5

Relationship among variouus parameters in i a simple ORC system

5. Sim mulation toolls There are severall simulation toools, which can process

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J. Therm. Sci., Vol.27, No.*, 2018

a system model (both commercial and open-source) written in executable simulation code. The choice of software for the ORC simulation mainly depends on the type of analysis (steady state or dynamic), and the coding level necessary to implement each components’ characteristics. Accordingly, the existed simulation tools can be divided into two categories [68], namely the coding-based software, (such as, EES® [76], Matlab® [77], Phyton™ [78]), and libraries-orientated softwares (such as, Simulink® [77], Modelica® [79], Dymola® [80], Cycle-Tempo® [81], and Aspen Plus® [82]). The difference between these two categories is the possibility of setting a proper type of model equation. Using the coding-based software, the user has more freedom to set the equation instead of using the already implemented equations available in the object-oriented libraries. However, the Table 9

user can also connect them properly and set the parameters. Among the libraries-orientated softwares, Vankeirsbilck et al. [83] used Cycle-Tempo® platform and integrated the Fluidprop library [84] to compare the performance of a steam cycle and ORC for small scale power generation. Manente et al. [85] used Aspen Plus® to simulate a subcritical geo-thermal power plant. The model was validated and adjusted by comparing its real operational data. The model was then run to determine the best strategy for distributing the available geothermal fluid to optimize its performance under off-design conditions. Table 9 summarizes the main features of useful simulation tools as well as their ability to access different fluid property libraries. A more detailed review of available tools for thermodynamic system simulation was presented by Connolly et al. [86].

Summary of the existed simulation tools for ORC modeling

Software

Type

Summary

References

Modelica

Library -based Code-based Library -based

EES®

Code-based

Support non-linear algebraic systems, REFPROP®√, COOLProp®√

Phyton™

Code-based

High level coding, comparable to Perl, Java, REFPROP®√, COOLProp®√

AMESim®

Library -based

Ready-to-use components, Steady–Unsteady analyses, REFPROP®×, COOLProp®×

Library -based Library -based Code-based

Thermodynamic analysis, Optimization of energy systems, Fluidprop®

[83]

Support non-linear algebraic systems, Complete fluids and solids Libraries

[85]

®

Matlab /Simulink ®

Cycle-Tempo

®

®

Aspen Plus

®

®

®

S-Functions, Steady-Unsteady analyses , REFPROP √, COOLProp √ Object-orientated language, Unsteady analyses, REFPROP®√, COOLProp®√

6. Discussion System modeling plays a key role in simulating and optimizing a process. Due to the various application areas of ORC systems, the selected model should firstly be accurate enough as required by the application. System-level models are required to carry out reproduction of overall system performance, which results from the interaction of its main components and the surrounding (operating conditions), rather than focusing on their detailed individual behavior. Nevertheless, when taking a new system into account, a fairly detailed system model is usually fundamental in nature, and is built in a modular construction by interconnecting system-level components’ sub-models. These components are often described or calibrated using the results of sophisticated component sub-models appearing in process design. For instance, a simplified one-dimensional model can be derived for heat exchangers with complex geometry by selecting suitable correction factors to obtain similar design performance, and by using simplified correlations to describe the off-design behavior. The level of detail should

[15][49][55][57][60] [64][65][67][70] [61][62] [54][71] [58][72-74] [59][68]

be appropriate for simulation purposes to capture the static performance with sufficient accuracy, and the dynamic behaviors on the time scales relevant for the control design object. Meanwhile, the component models used for such a model should also be validated using experimental data, or any other source of trusted reference data. Furthermore, it is important to mention that this summary of modeling approaches is not exhaustive, while some other types of models can be found in literature. For instance, the more complex simulation tools, such as CFD [85,88], more complex regression models [89], and advanced deterministic models [90] (models, which involve physical and chemical phenomena in the processes) exist to simulate different components. These models are often computationally rigorous and can hardly be coupled together for performing system-level simulations. In short, a proper simulation for a particular application can be obtained through the trade-off between model accuracy and computational efficiency. Fig. 6 depicts different modeling approaches and their applications, which have been summarized according to the current literature review.

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Fig.. 6

A review off modeling apprroaches and toools for the off-design simulatio on of Organic R Rankine Cycle

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Summary of the modeling g approaches annd their applicaations according g to current literrature review

7. Conclusion ns Organic Rannkine Cycle (ORC) ( system m is a reliablle waay to convert low-grade heeat into electriicity, either foor ind dustrial wastee heat recoverry or renewable energy apppliications, incluuding geotherm mal, biomass, and solar ennerg gy. Due to a vvast spectrum of application ns of ORC sysstem ms, the numbber of design methodologies, technicaal app proaches, andd modeling toools are also mushrooming m aas evidenced by thhe large numbber of publisheed articles oveer thee last two deccades. Amongg these ORC-related investtigations, the off--design modeling plays a significant s rol e. here are manyy models, whicch vary in acccuracy, compuuTh tattional compleexity, data reqquirement, ph hysical robusstness, and appliicability. Thiss paper provides a compreehensive literaturre review of thheoretical bassis, approachees, RC systems, foor and tools for offf-design simuulation of OR bo oth steady statee and transiennt conditions. Comprehensiive backgrounnd for differen nt kinds of offfdesign simulatioons has been provided p in th he current worrk. heoretical basiis has also beeen summarized. Furthermorre, Th various simulattion approachhes for heat exchangers e annd meechanical devvices have been categorizzed, and maiin advantages and disadvantages of each are discussed. Thhe focusing on the t charge-sen nsitive modeels lattest studies fo have been repoorted. Finally, a concise su ummary of thhe ost common toools in this fieeld have been provided. mo The aim of thhis review is to t provide useers in academiia and in industry with the infoormation, whiich would hellp ociated tools tto theem in selectinng suitable moodels and asso address particuular engineerring and dessign problem ms. oreover, the ddeterminationn of azeotropic properties oof Mo wo orking fluids (azeotropes),, charge-sensitive modelinng forr different kinnds of system m, control strrategy orienteed dy ynamic simulaations, online identification n and modelinng du uring real-timee operations based b on optiimization algoorith hm need furthher research work. w

[2]

[3]

[4]

[5]

[6]

[7]

[8]

[9]

Reeferences [10] [1 1] Quoilin, S., Broek, M., Declaye, D S., Dewallef, D P., annd

Lemort, L V. Tech hno-economic ssurvey of orgaanic rankine cy ycle (ORC) sysstems. Renewabble and Sustainable Energy Reviews, R 2013, 22(22): 2 168‒1886. Morisaki, M T., Ik kegami, Y. Influ luence of temp perature diffeerence calculatiion method on the evaluation of Rankine cy ycle performan nce. Journal off Thermal Science, 2014, 23(1): 68‒76. Macchi, M E. and Astolfi, A M. Orgganic Rankine Cycle C (ORC) power systems – technologies and applications. Elsevier ed d. Woodhead Publishing P Seriees in Energy, United U Kingdom, 2016. Lecompte, L S., Huisseune, H H., van den Broek. B M., Vanslambrouck. V B., and De Paeepe. M. Review w of organic Rankine R cycle (O ORC) architecttures for waste heat recoverry. Renewable and Sustainablle Energy Rev views, 2015, 22: 448‒461. Morita, M I., Tanimura, K., Haayamizu, Y., Yamada, Y T., Horibe H A., Haru uki, N., and Set etoguchi, T. Stu udy of cycle ou utput improveement by wor ork-fluid includ ding phase ch hange material. Journal of Theermal Science, 2016, 2 25(6): 558‒563. Tan, T Y., Chen Y., Wang, L. Theermodynamic Analysis A of a mixed m refrigerant ejector refrrigeration cycle operating with w two vaporr-liquid separaators. Journal of Thermal Science, 2018, 27(3): 2 230‒240.. maanaoui, Y., aand Faik, A. A study of orSaifaoui, D., Elm ganic working fluids f of an orgaanic Rankine cycle c for song power plannt. Applied So olar Energy, laar concentratin 2014, 50(3): 158 8‒167. An, A W., Wu, J., Zhu, T., and Zhhu, Q. Experim mental investiigation of a co oncentrating PV V/T collector with Cu9S5 nanofluid spectrral splitting filtter. Applied En nergy, 2016, 184: 197‒206. An, A W., Li, J., Ni, N J., and A. Taaylor, R., and Zh hu, T. Analysis of a temp perature depenndent optical window w for nanofluid-based spectral splittin ing in PV/T pow wer generatiion applications. Energy conv nversion and management, m 2017, 151: 23‒31. Fu, J., Liu, J., Xu, X Z., Deng, B.., and Liu, Q. An A approach fo or IC engine coolant c energyy recovery based on low-

14

[11]

[12]

[13]

[14]

[15]

[16]

[17]

[18]

[19]

[20]

[21]

[22]

[23]

J. Therm. Sci., Vol.27, No.*, 2018 temperature organic Rankine cycle. Journal of Central South University, 2015, 22(2): 727‒734. Zhang, T., Zhu, T., An, W., Song, X., Liu, L., and Liu, H. Unsteady analysis of a bottoming Organic Rankine Cycle for exhaust heat recovery from an Internal Combustion Engine using Monte Carlo simulation. Energy conversion and management, 2016, 124: 357‒368. Ma, J., Liu, L., Zhu, T., and Zhang, T. Cascade utilization of exhaust gas and jacket water waste heat from an Internal Combustion Engine by a single loop Organic Rankine Cycle system. Applied Thermal Engineering, 2017, 107: 218‒226. Jensen, J. Dynamic modeling of thermo-fluid systems with focus on evaporators for refrigeration. PhD Thesis, Technical University of Denmark, Copenhagen, Denmark, 2003. Tartiere, T., and Astolfi, M. A World Overview of the Organic Rankine Cycle Market. Energy Procedia, 2017, 129: 2‒9. Vaja, I. Definition of an object oriented library for the dynamic simulation of advanced energy systems: methodologies, tools and application to combine ICE-ORC power plants. PhD Thesis, University of Parma, Parma, Italy, 2009. Lee, Y., Kuo, C., Liu, C., Fu, B., Hsieh, J., and Wang, C. Dynamic response of a 50kW organic Rankine cycle system in association with evaporators. Energies, 2014, 7(4): 2436‒2448. Yang, X., Xu, J., Miao, Z., Zou, J., and Yu, C. Operation of an organic Rankine cycle dependent on pumping flow rates and expander torques. Energy, 2015, 90: 864‒878. Elsevier ScienceDirect. Available online: http://www.sciencedirect.com/, 2018, (accessed 01 Janurary 2018). Gungor, K., and Winterton, R. Simplified general correlation for saturated flow boiling and comparisons of correlations with data. Chemical Engineering Research and Design, 1987, 65(2): 148‒156. Chen, J. A correlation for boiling heat transfer to saturated fluids in convective flow. Industrial and Engineering Chemistry Process Design and Development, 1996, 5(3): 322‒329. Wettermann, M., and Steiner, D. Flow boiling heat transfer characteristics of wide-boiling mixtures. International Journal of Thermal Sciences, 2000, 39(2): 225‒235. Zou, X., Gong, M, Chen, G., Sun, Z., Zhang, Y., and Wu, J. Experimental study on saturated flow boiling heat transfer of R170/R290 mixtures in a horizontal tube. International Journal of Refrigeration, 2010, 33(2): 371‒ 380. Cooper, M. Saturation nucleate pool boiling - a simple correlation. Institution of Chemical Engineers Symposium Series, 1984, 86: 785‒793.

[24] Han, D., Lee, K., and Kim, Y. Experiments on the characteristics of evaporation of R410A in brazed plate heat exchangers with different geometric configurations. Applied Thermal Engineering, 2003, 23(10): 1209‒1225. [25] Amalfi, R., Vakili-Farahani, F., and Thome, J. Flow boiling and frictional pressure gradients in plate heat exchangers. Part 2: comparison of literature methods to database and new prediction methods. International Journal of Refrigeration, 2016, 61: 185‒203. [26] Cavallini, A., and Zecchin, R. High velocity condensation of organic refrigerants inside tubes. Proceedings 8th International Congress of Refrigeration. Washington, DC, vol. 2, 1974, 193‒200. [27] Akers, W., Deans, H., and Crosser, O. Condensation heat transfer within horizontal tubes. Chemical Engineering Progress Symposium Series, 1959, 55: 171‒176. [28] Shah, M. A general correlation for heat transfer during film condensation inside pipes. International Journal of Heat Mass Transfer, 1979, 22(4): 547‒556. [29] Qian, S. Heat Exchanger Design Manual. 1rd ed. Chemical Industry Press of China, Peking, China, 2006, pp. 365‒370. [30] Han, D., Lee, K., and Kim, Y. The characteristics of condensation in brazed plate heat exchangers with different chevron angles. Journal of the Korean Physical Society, 2003, 43(1): 66‒73. [31] Longo, G., Righetti, G. and Zilio, C. A new computational procedure for refrigerant condensation inside herringbone-type Brazed Plate Heat Exchangers. International Journal of Heat and Mass Transfer, 2015, 82: 530‒536. [32] Gnielinski, V. New equations for heat and mass transfer in turbulent pipe and channel flows. International Chemical Engineering, 1976, 16(2): 359‒368. [33] Chisholm, D., and Wanniarachchi, A. Layout of plate heat exchangers. ASME/JSME Thermal Engineering Proceeding. ASME New York, 1991, 4: 433‒438. [34] Wanniarachchi, S., Ratnam, U., Tilton, B., and Dutta-Roy, K. Approximate correlations for chevron-type plate heat exchangers. Proceedings of the 30th national heat transfer conference, New York, 1995: 145‒151. [35] Thonon, B. Design Method for Plate Evaporators and Condensers. 1st International Conference on Process Intensification for the Chemical Industry. BHR Group Conference Series Publication, 1995(18): 37‒47. [36] Martin, H. A theoretical approach to predict the performance of chevron-type plate heat exchangers. Chemical Engineering and Processing, 1996, 35(4): 301‒310. [37] Pan, Y., Liu, L., and Zhu, T. Simulation of working fluid mass distribution in small-scale Organic Rankine Cycle system under sub-critical conditions. Energy conversion and management, 2018, 131: 884‒896. [38] Dickes, R., Dumont, O., Guillaume, L., Quoilin, S., and Lemort, V. Charge-sensitive modelling of organic Ran-

LIU Liuchen et al.

[39]

[40]

[41]

[42]

[43]

[44] [45]

[46] [47]

[48]

[49]

[50]

[51]

[52]

[53] [54]

[55]

A review of modeling approaches and tools for the off-design simulation of Organic Rankine Cycle

kine cycle power systems for off-design performance simulation. Applied Energy, 2018, 212: 1262‒1281. James, R., and Marshall, S. Dynamic analysis of a refrigeration system. Proceedings of the Institute of Refrigeration, 1973, 70: 13‒24. Zivi, S. Estimation of steady-state team void-fraction by means of the principle of minimum entropy production. Journal of Heat Transfer, 1964, 86(2): 247‒252. Smith, S. Void fraction in two-phase flow: a correlation based upon an equal velocity headmodel. Proceedings of the Institution of Mechanical Engineers, 1969, 184: 647‒ 664. Lockhart, R. and Martinelli, R. Proposed correlation data for isothermal two-phase two-component flow in pipes. Chemical Engineering Progress, 1949, 45: 39‒48. Baroczym, C. Correlation of liquid fraction in two-phase flow with application to liquid metals. Fertility and Sterility, 1963, 95(8): 2707‒2710. Hughmark, G. Holdup in gas-liquid flow. Chemical Engineering Progress, 1962, 58: 62‒65. Premoli, A., Francesco, D., and Prina, A. A dimensional correlation for evaluating two-phase mixture density. La Termotecnica, 1971, 25: 17‒26. Taitel, Y., and Barnea, D. Two-phase slug flow. Advances in Heat Transfer, 1990, 20: 83‒132. Yashar, D., Wilson, M., and Kopke, H. An investigation of refrigerant void fraction in horizontal microfin tubes. HVAC & R Research, 2001, 7(1): 67‒82. Gurgenci, H. Performance of power plants with organic Rankine cycles under part-load and off-design conditions. Solar & Wind Technology, 1986, 36(1): 45‒51. Ibarra, M., Rovira, A., Alarcón-Padilla, D., and Blanco, J. Performance of a 5kWe Organic Rankine Cycle at partload operation. Applied Energy, 2014, 120(3): 147‒158. Lecompte, S., Martin, V., and Paepe, M. Optimal part-load operation of an 11kWe organic Rankine cycle for waste heat recovery. Proceedings of ECOS 2016. Portoroz, Slovenia, 2016, Paper #295. Song, J., Gu, C., and Ren, X. Parametric design and off-design analysis of organic Rankine cycle (ORC) system. Energy Conversion and Management, 2016, 112: 157‒165. Möller, A., and Gullapalli, V. System cost and efficiency optimization by heat exchanger performance simulations. Energy Procedia, 2017, 119: 459‒465. Gullapalli, V. Modeling of brazed plate heat exchangers for ORC systems. Energy Procedia, 2017, 129: 443‒450. Quoilin, S. Sustainable energy conversion through the use of Organic Rankine cycles for waste heat recovery and solar applications. PhD Thesis, University of Liège, Liège, Belgium, 2011. Wang, J., Yan, Z., Zhao, P., and Dai, Y. Off-design performance analysis of a solar-powered organic Rankine

[56]

[57]

[58]

[59]

[60]

[61]

[62]

[63]

[64]

[65]

[66]

[67]

[68]

15

cycle. Energy Conversion and Management, 2014, 80(4): 150‒157. Hu, D., Zheng, Y., Wu, Y., Li, S., and Dai, Y. Off-design performance comparison of an organic Rankine cycle under different control strategies. Applied Energy, 2015, 156: 268‒279. Li, H., Hu, D., Wang, M., and Dai, Y. Off-design performance analysis of Kalina cycle for low temperature geothermal source. Applied Thermal Engineering, 2016, 107: 728‒737. Ziviani, D., Woodland, B., Georges, E., Groll, E., Braun, J. and Horton, W. Development and a validation of a charge sensitive organic Rankine cycle (ORC) simulation tool. Energies, 2016, 9(1): 389. Liu, L., Zhu, T., and Ma, J. Working fluid charge oriented off-design modeling of a small scale organic Rankine cycle system. Energy Conversion and Management, 2017, 148: 944‒953. Dickes, R., Dumont, O., Daccord, R., Quoilin, S., and Lemort, V. Modelling of organic Rankine cycle power systems in off-design conditions: an experimentallyvalidated comparative study. Energy, 2017, 123: 710‒ 727. Wei, D., Lu, X., Lu, Z., and Gu, J. Dynamic modeling and simulation of an Organic Rankine Cycle (ORC) system for waste heat recovery. Applied Thermal Engineering, 2008, 28(10): 1216‒1224. Quoilin, S., Aumann, R., Grill, A., Schuster, A., Lemort, V., and Spliethoff, H. Dynamic modeling and optimal control strategy of waste heat recovery Organic Rankine Cycles. Applied Energy, 2011, 88(6): 2183‒2190. Bamgbopa, M., and Uzgoren, E. Quasi-dynamic model for an organic Rankine cycle. Energy Conversion and Management, 2013, 72: 117‒124. Manente, G., Toffolo, A., Lazzaretto, A., and Paci, M. An Organic Rankine Cycle off-design model for the search of the optimal control strategy. Energy, 2013, 58(9): 97‒ 106. Xie, H., and Yang, C. Dynamic behavior of Rankine cycle system for waste heat recovery of heavy duty diesel engines under driving cycle. Applied Energy, 2013, 112(4): 130‒141. Hou, G., Bi, S., Lin, M., Zhang, J., and Xu, J. Minimum variance control of organic Rankine cycle based waste heat recovery. Energy Conversion and Management, 2014, 86: 576‒586. Zhang, J., Zhou, Y., Wang, R., Xu, J., and Fang, F. Modeling and constrained multivariable predictive control for ORC (Organic Rankine Cycle) based waste heat energy conversion systems. Energy, 2014, 66(4): 128‒138. Ziviani, D, Beyene, A., and Venturini, M. Advances and challenges in ORC systems modeling for low grade thermal energy recovery. Applied Energy, 2014, 121(121):

16 79‒95. [69] Yousefzadeh, M., and Uzgoren, E. Mass-conserving dynamic organic Rankine cycle model to investigate the link between mass distribution and system state. Energy, 2015, 93(1): 1128‒1139. [70] Mazzi, N., Rech, S., and Lazzaretto, A. Off-design dynamic model of a real Organic Rankine Cycle system fueled by exhaust gases from industrial processes. Energy, 2015 90(1): 537‒551. [71] Lemort, V., Quoilin, S., Cuevas, C., and Lebrun, J. Testing and modeling a scroll expander integrated into an Organic Rankine Cycle. Applied Thermal Engineering, 2009, 29(14): 3094‒3102. [72] Rossi, T. Detection, Diagnosis, and evaluation of faults in vapor compression equipment. Ph.D. Thesis, Purdue University, West Lafayette, IN, USA, 1995. [73] Shen, B. Improvement and validation of unitary air conditioner and heat Pump Simulation Models at off-design conditions. Ph.D Thesis, Purdue University, West Lafayette, IN, USA, 2006. [74] Shen, B., Braun, J., and Groll, E. Improved method for simulating unitary air conditioners at off-design conditions. International Journal of Refrigeration, 2009, 32(7): 1837‒1849. [75] Dickes, R., Ziviani, D., de Paepe, M., van den Broek, M., and Quoilin, S. ORCmKit: an open-source library for organic Rankine cycle modelling and analysis. Proceedings of ECOS 2016, Portoroz, Slovenia, 2016. [76] EES – Klein SA. Engineering equation solver. Middleton, WI: F-Chart Software, 2008. [77] MathWorks – Mathlab and simulink for technical computing. http:// www.mathworks.com/, 2018, (accessed 01 March 2018). [78] Phyton™. Phyton programming language. http://www. python.org/, 2018, (accessed 01 March 2018). [79] Modelica Association. Specification, Tutorials. http://www. modelica.org/, 2018, (accessed 01 March 2018). [80] Dynasim AB. Dynamic modeling laboratory. http://www. dymola.com/, 2018, (accessed 01 March 2018). [81] Cycle-Tempo simulation software – Developed by TU Delft and TNO. http:// www.cycle-tempo.nl/, 2018, (ac-

J. Therm. Sci., Vol.27, No.*, 2018 cessed 01 March 2018). [82] Aspen Plus®. https://www.aspentech.com/en/products/ engineering/aspen-plus/, 2018, (accessed 01 March 2018). [83] Vankeirsbilck, I., Vanslambrouck, B., Gusev, S., and De Paepe, M. Efficiency comparison between the steam cycle and the organic Rankine cycle for small scale power generation. 2nd European conference on polygeneration, Tarragona, Spain, 2012. [84] Colonna, P., and van der Stelt, T.P. FluidProp: a program for the estimation of thermo physical properties of fluids. Energy technology section. Delft University of Technology, Delft, The Netherlands. www.FluidProp.com/, 2018, (accessed 01 March 2018). [85] Manente, G., Field, R., Di Pippo, R., Tester, J.W., Paci, M., and Rossi, N. Hybrid solar-geothermal power generation to increase the energy production from a binary geothermal plant. Proceedings of IMECE 2011, Denver, USA, 2011. [86] Connolly, D., Lund, H., Mathiesen, B., and Leahy, M. A review of computer tools for analyzing the integration of renewable energy into various energy systems. Applied Energy, 2010, 87: 1059‒1082. [87] Bhutta, M., Hayat, N., Bashir, M., Khan, A., Ahmad, K., and Khan, S. CFD applications in various heat exchangers design: a review. Applied Thermal Engineering, 2012, 32(1): 1‒12. [88] Zheng, Y., Hu D., Cao, Y., and Dai, Y. Preliminary design and off-design performance analysis of an Organic Rankine Cycle radial-inflow turbine based on mathematic method and CFD method. Applied Thermal Engineering, 2017, 112: 25‒37. [89] Declaye, S., Quoilin, S., Guillaume, L., and Lemort, V. Experimental study on an open drive scroll expander integrated into an ORC (Organic Rankine Cycle) system with R245fa as working fluid. Energy, 2013, 55(1): 173‒ 183. [90] Dickes, R. Design and fabrication of a variable wall thickness two-stage scroll expander to be integrated in a micro-solar power plant. Master Thesis. University of Liege, Liege, Belgium, 2013.