Optimized performances comparison of organic Rankine cycles for low grade waste heat recovery

Journal of Mechanical Science and Technology 26 (8) (2012) 2301~2312

www.springerlink.com/content/1738-494x DOI 10.1007/s12206-012-0603-4

Optimized performances comparison of organic Rankine cycles

for low grade waste heat recovery† Enhua Wang, Hongguang Zhang*, Boyuan Fan and Yuting Wu

College of Environmental and Energy Engineering, Beijing University of Technology, Beijing, 100124, China

(Manuscript Received December 17, 2011; Revised March 21, 2012; Accepted March 27, 2012)

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Abstract An organic Rankine cycle (ORC) can be applied to recover the low-grade waste heat. In this paper, the performances of five different

types of ORC are evaluated. These configurations include a simple ORC, an ORC with an internal heat exchanger (IHE), an ORC with an open feed organic fluid heater (OFOH), an ORC with a closed feed organic fluid heater (CFOH), and an ORC with a reheater. First, the feasible working region is defined for an ORC operating together with an internal combustion engine. Subsequently, the thermal efficiency of each ORC is maximized using a genetic algorithm. Finally, the characteristics of each ORC are analyzed and compared using a combination of the first law and second law method. Our analysis indicates that the ORC with an IHE showed the best thermody-namic performance. The ORC with an OFOH and the ORC with a CFOH are sub-optimal while the simple ORC and the ORC with a reheater are the last choice. The effects of the expander inlet pressure, the condenser outlet temperature and the expander isentropic effi-ciency on system performance of each ORC were also analyzed.

Keywords: Genetic algorithm; Internal combustion engine; Organic Rankine cycle; Performance optimization; Waste heat recovery ---------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------- 1. Introduction

Energy conservation and environmental protection have be-come much more important with the rapid development of industrialization and urbanization in China. In 2010, 80% of the diesel fuel and 40% of the gasoline fuel were consumed by vehicles in China. As the number of vehicles continues to increase, more energy will be required to run these vehicles. However, the combustion products from internal combustion engines, which are exhausted to the ambient air, cause serious environmental issues. Investigations into Beijing air pollution show that 60% of CO discharge, 86.8% of HC discharge, and 54.7% of NOx discharge are produced by vehicle engines. From a thermal equilibrium viewpoint, the useful power out-put propelling a vehicle accounts for only 26% to 34% of the total energy generated by fuel combustion. The resulting wasted heat transferred to the environment takes up 60% to 70% of the total combustion energy. Therefore, engine waste heat recovery is a potentially significant technique that could be used to improve fuel thermal efficiency, reduce fuel con-sumption, and decrease engine emissions. The thermal effi-ciency of an organic Rankine cycle (ORC) is the highest among all the currently available technical solutions used to

recover low-grade waste heat, and is the technique nearest to potential mass production.

Many factors influence the performance of an ORC, such as system structure design, working fluid selection, and configu-ration of the operating conditions. Various investigations have been conducted by researchers regarding system structure design of ORC systems for engine waste heat applications. Aly studied a method for improving the output power and fuel economy of a diesel engine via a bottom Rankine cycle, which could recover waste heat from the coolant and the exhaust gas [1]. Arias et al. presented a theoretical study of waste heat recovery for an internal combustion engine operating in a hybrid vehicle (spark ignition engine and electric motor). Three Rankine cycle configurations were considered: a cycle running with the exhaust gas, a cycle running with the engine coolant system, and a combined system [2]. Mago et al. stud-ied two types of ORCs using different dry organic fluids, for converting waste heat to power from low-grade heat sources. Results showed that the thermal efficiency of the ORC with an IHE was better than that of a basic ORC [3]. Vaja and Gam-barotta performed a thermodynamic analysis of a vapor cycle matched with a stationary internal combustion engine. Three different cycle setups were considered: a simple cycle with the use of only engine exhaust gas as a thermal source, a simple cycle with the use of exhaust gas and engine cooling water, and a regenerated cycle. The analysis demonstrated that a 12%

*Corresponding author. Tel.: +86 10 6739 2469, Fax.: +86 10 6739 2774 E-mail address: [email protected]

† Recommended by Associate Editor Tong Seop Kim © KSME & Springer 2012

2302 E. Wang et al. / Journal of Mechanical Science and Technology 26 (8) (2012) 2301~2312

increase in overall efficiency could be achieved with respect to an engine with no bottoming [4]. Generally, these investiga-tions only considered two types of ORCs: a simple ORC and an ORC with an IHE.

In fact, other kinds of ORC structures, like OFOH, CFOH, or an ORC with a reheater, are also often used in power plants. Yari presented an analysis for ORCs using dry organic fluids as the working fluids based on the first and second laws of thermodynamics. The considered ORCs were a simple ORC, an ORC with an IHE, a regenerative ORC, and a regenerative ORC with an IHE. The results showed that the regenerative ORC with an IHE has the best thermodynamic performance [5]. For the sake of exploitation of low-temperature, liquid-dominated geothermal sources, Desideri and Bidini examined a simple Rankine cycle, a regenerated Rankine cycle with an open type regenerator, and a regenerated Rankine cycle with an IHE. These three cycle configurations were compared to conventional single and dual flash steam power plants and the Kalina cycle. Results showed that the regenerated Rankine cycle with an IHE was the most promising cycle and that there was a potential for performance optimization by modifying the main working parameters [6]. These investigations only considered the performances of the ORCs when the working parameters were fixed, but the ORC’s thermal efficiencies did not achieve their maximum values for most of these scenarios.

ORC performance varies with a number of operating pa-rameters including expander inlet pressure and condenser outlet temperature. Tendencies in performance variation for different types of ORC cannot be kept consistent when the working parameters themselves vary synchronously. There-fore, each ORC’s performance must be based on a single common working region, not merely on some identical work-ing points. Instead, different ORCs can be compared by using maximum performance values. However, these extreme val-ues are not possible to be achieved for different ORC struc-tures when using the same working parameters. One option is to use an optimization search method to find these extreme points. Meanwhile, confirming optimized performance for each type of ORC provides a good reference for the design of an entire ORC and engine system.

In this study, a feasible working region for five different types of ORC was set up according to the working conditions of a vehicle engine to develop clear and unique operational characteristics. With a better understanding of these character-istics, a more efficient ORC structure could be designed and a more efficient multi-stage ORC could be developed according to these different operational strategies. First, we defined a working region based on the expander inlet pressure, the con-denser outlet temperature, and the maximum temperature of the working fluid. Subsequently, five types of ORC were tak-en into account: a simple ORC, an ORC with an IHE, an ORC with an OFOH, an ORC with a CFOH, and an ORC with a reheater. All these ORCs possess a simple single-stage struc-ture and have unique distinct working principles. Next, we adopted an optimization search method, based on a genetic

algorithm, to find the working parameters of each ORC that maximize thermal efficiency. Finally, the distinct working characteristics of these five ORCs were analyzed and com-pared according to the optimization results.

2. Systems description

In order to improve the Rankine cycle performance, ORCs can be implemented with a superheater, internal heat ex-changer, reheater, open feed heater, or a closed feed heater. The organic Rankine cycle is similar to a normal Rankine cycle that operates with steam, except the ORC uses an or-ganic fluid as the working fluid. The schematics and corre-sponding T-s diagrams of the five ORCs are displayed in Fig. 1-5 to illustrate the working characteristics of each of the dif-ferent ORC configurations.

The system structure of a simple ORC is shown in Fig. 1. The system consists of a Freon pump, an evaporator, an ex-pander, and a condenser. The low-pressure, saturated liquid is first pressurized by the pump then evaporated in the evapora-tor. The thermodynamic state of the working fluid at the eva-porator outlet could be a saturated gas or a superheated gas. In this research, R245fa was adopted as the working fluid. The physical properties of R245fa are listed in Table 1. R245fa is a nonflammable liquid, which has a high critical temperature and pressure, and a boiling point slightly below room tem-perature. Meanwhile, R245fa is a slightly dry organic working fluid with low latent heat and specific volume, whose thermo-physical properties are well suited for energy recovery appli-cations operating under a not so high evaporating pressure. The environmental properties of R245fa include a zero ozone depletion potential (ODP) and a low global warming potential (GWP) [7, 8]. These environment-friendly properties are also very important advantages of R245fa. Because R245fa is a dry organic working fluid, it becomes superheated at the expander outlet. A single screw expander developed by Beijing Univer-sity of Technology was used as the expanders [9].

The system layout of an ORC with an IHE is displayed in Fig. 2. The IHE transfers heat from the superheated gas at the expander outlet to the sub-cooled liquid at the pump outlet. Both the ORC with an OFOH and the ORC with a CFOH can effectively decrease cycle exergy destruction rates; therefore, these two configurations were also studied in this paper. The schematic and T-s diagram for the ORC with an OFOH is shown in Fig. 3. The saturated liquid 1 is pumped to an inter-mediate-pressure sub-cooled state 2. The liquid is then mixed in the OFOH with stream 6 extracted from the expander. The working fluid at the OFOH outlet is in the saturated liquid

Table 1. Properties of R245fa.

Organic fluid

Molecular weight

[kg/kmol]

crT [K]

crP [MPa]

bpT

[K]

R245fa 134.05 427.2 3.639 288.05

E. Wang et al. / Journal of Mechanical Science and Technology 26 (8) (2012) 2301~2312 2303

state. Subsequently, it is pressurized by pump 2 and vaporized in the evaporator. The schematic and T-s diagram of the ORC with a CFOH is given in Fig. 4. The heat exchanging process

of a CFOH can be accomplished without requiring the pres-sure of stream 6 equaling that of stream 2. At the CFOH outlet, stream 8 is at a saturated liquid state, and is pressurized by

Fig. 1. Schematic and T-s diagram of a simple ORC.

Fig. 2. Schematic and T-s diagram of an ORC with an IHE.

Fig. 3. Schematic and T-s diagram of an ORC with an OFOH.

Fig. 4. Schematic and T-s diagram of an ORC with a CFOH.


pump 2. Subsequently, stream 9 mixes with stream 3 in the mixer.

When water is used as the working fluid in a Rankine cycle, a reheater can improve the dryness of the steam and avoid damage to the turbine. In order to study the effect of a reheater on ORC performance, this paper also studied an ORC with a reheater. The schematic and T-s diagram of an ORC with a reheater is given in Fig. 5. The superheated gas expanded in high-pressure expander 1 is delivered to the reheater. There, the working fluid is again reheated to a certain high tempera-ture before it is transmitted to low-pressure expander 2.

3. Thermodynamic modeling and optimization

Based on the operating conditions for the ORCs assembled on a vehicle, along with the requirements of the expanders, the thermodynamic model assumptions were as follows:

(1) All the cycles operated in steady states. (2) The expander inlet pressure ranged from 2 to 3 MPa. (3) The condenser outlet temperature ranged from 300 to

360 K. (4) The maximum temperature of the working fluid was set

to 460 K. (5) The maximum temperature difference between the su-

perheated gas and saturated gas at the same pressure, defined as the superheated temperature, was set to 100 K.

(6) The pressure loss and heat rejection of the pipes were

ignored. Constraints (2) through (5) define a parameter space for

when the ORC is operating together with the engine, called the feasible working region. The performance of the various ORCs were analyzed and compared based on this feasible working region. Table 2 lists the configuration parameters for the optimization calculation. Table 3 describes the mathemati-cal model for each of the ORCs. The detailed introductions of these models are found in Refs. [10-14].

The temperature of the engine exhaust gas is higher than that of the ORC working fluid when the engine is running. An ORC with a higher thermal efficiency can be considered more suitable for waste-heat recovery applications when the heat addition quantity from the exhaust gas is identical. Therefore, one evaluation index for comparing ORC performance is the thermal efficiency of each ORC. The thermal efficiency calcu-lation process indicates that the thermal efficiency value does not relate to the mass flow rate of the working fluid. For this reason, the mathematical models listed in Table 3 calculate the thermal efficiency using a unit mass flow rate (1 kg/s). The third column shows the energy equations for each ORC sub-system using the first law analysis. The fourth column lists the exergy equations according to the second law analysis. More-over, the last column displays the optimization models for the genetic algorithm. In these models, the thermal efficiency was selected as the optimization object. The constraint conditions for each ORC were fabricated according to their unique opera-tion principles.

The optimization process is presented below. First, the ex-pander inlet pressure and condenser outlet temperature are set to certain values in the feasible working region. At the same time, the superheated temperature at the evaporator outlet and the intermediate pressure of the expander for the OFOH or the CFOH are configured as input variables for the optimization calculation program. Subsequently, the optimized thermal efficiencies of each ORC are calculated using a genetic algo-rithm (GA) toolbox programmed in Matlab. Second, accord-ing to system sensitivity analysis, the expander inlet pressure and condenser outlet temperature are configured to different values. The optimization routines are performed again to ob-tain another set of optimization values. Various values of these two parameters are selected in the feasible working region and

Fig. 5. Schematic and T-s diagram of an ORC with a reheater.

Table 2. Configuration parameters for the optimization calculation.

Parameters Values

Pump isentropic efficiency ηp 0.7

Expander isentropic efficiency ηs 0.75, 0.6, 0.45

Effectiveness of IHE εIHE 0.9

Reference temperature T0 [K] 273

Heat source temperature TH [K] 600

Cold source temperature TL [K] 293

Maximum working fluid temperature Tmax [K] 460

Maximum superheated temperature Tsup,max [K] 100

Condensation temperature Tcond [K] 300 ~ 360

Evaporation pressure Pevap [MPa] 2 ~ 3


the optimization calculation is repeated for each parameter pair. Third, the exergy destruction rates are calculated at each optimized working point. Finally, the results are analyzed for each ORC and their operation characteristics determined in the feasible working region.

The last column of Table 3 provides the mathematic model for each of the ORCs used in the genetic algorithm. The ther-mal efficiency of each type of ORC is the optimization object

of the fitness function. The superheated temperature is defined as the temperature difference between the superheated gas and the saturated gas at identical pressures, and is the input vari-able for the simple ORC and the ORC with an IHE. With re-gard to the ORC with an OFOH and the ORC with a CFOH, the input variables are the superheated temperature and the intermediated pressure where the working fluid is extracted. Considering the ORC with a CFOH, if the intermediated pres-

Table 3. Mathematical models of the ORCs.

Cycles Subsystems Energy equations Exergy destruction rate equations GA models

Pump 2 1 2 1( ) ( )p s pW m h h m h h η= − = −& & & 0 2 1( )pI T m s s= −& &

Evaporator 3 2( )eQ m h h= −& & 0 3 2 3 2[( ) ( ) ]e HI T m s s h h T= − − −& &

Expander 3 4 3 4( ) ( )s s sW m h h m h h η= − = −& & & 0 4 3( )sI T m s s= −& & Simple ORC

Condenser 4 1( )cQ m h h= −& & 0 1 4 1 4[( ) ( ) ]c LI T m s s h h T= − − −& &

sup3max ( )

( )th

s p e

f T

W W Q

η =

= − && &

3 max

1 3

sup3 sup,max

:

00

0

St

T TP P

T T

⎧ − ≤⎪

− ≤⎨⎪ ≤ ≤⎩


IHE 3 2 5 6( ) ( )m h h m h h− = −& &

( )5 6 5 2( )T T T Tε = − − 0 3 2 6 5( )IHEI T m s s s s= − + −& &


Expander 4 5 4 5( ) ( )s s sW m h h m h h η= − = −& & & 0 5 4( )pI T m s s= −& &

ORC with IHE


sup 4max ( )

( )th

s p e

f T

W W Q

η =

= − && &

4 max

1 4

sup 4 sup,max

:

00

0

St

T TP P

T T

⎧ − ≤⎪

− ≤⎨⎪ ≤ ≤⎩

Pump1 1 2 1 2 1(1 )( ) (1 ) ( )p s pW m x h h m x h h η= − − = − −& & & 1 0 2 1(1 )( )pI T m x s s= − −& &

OFOH 3 6 2(1 )mh mxh m x h= + −& & & 0 3 6 2[ (1 ) ]OFOHI T m s xs x s= − − −& &

Pump2 2 4 3 4 3( ) ( )p s pW m h h m h h η= − = −& & & 2 0 4 3( )pI T m s s= −& &


Expander 5 6 6 7( ) (1 )( )s s s s sW m h h m x h hη η= − + − −& & & 0 6 5 7 6[( ) (1 )( )]sI T m s s x s s= − + − −& &

Regenerative ORC with

OFOH

Condenser 7 1(1 )( )cQ m x h h= − −& & 0 1 6 1 6(1 )[( ) ( ) ]c LI T m x s s h h T= − − − −& &

sup5 6

1 2

max ( , )

( )th

s p p e

f T P

W W W Q

η =

= − − && & &

6 5

1 6

5 max

sup5 sup,max

:

00

00

St

P PP PT TT T

⎧ − ≤⎪

− ≤⎪⎨ − ≤⎪⎪ ≤ ≤⎩

Pump1 1 2 1 2 1(1 )( ) (1 ) ( )p s pW m y h h m y h h η= − − = − −& & & 1 0 2 1(1 )( )pI T m y s s= − −& &

CFOH 3 8T T= ; 6 8 3 2( ) (1 )( )my h h m y h h− = − −& & 0 8 6 3 2[ ( ) (1 )( )]CFOHI T m y s s y s s= − + − −& &

Pump2 2 9 8 9 8( ) ( )p s pW y h h y h h η= − = −& 2 0 9 8( )pI T my s s= −& &

Mixer 4 9 3(1 )h yh y h= + − 0 4 9 3[ (1 ) ]mI T m s ys y s= − − −& &

Evaporator 5 4eQ h h= −& 0 5 4 5 4[( ) ( ) ]e HI T m s s h h T= − − −& &

Expander 5 6 6 7( ) (1 )( )s s s s sW m h h m y h hη η= − + − −& & & 0 6 5 7 6[( ) (1 )( )]sI T m s s y s s= − + − −& &

Regenerative ORC with

CFOH

Condenser 7 1(1 )( )cQ m y h h= − −& & 0 1 7 1 7(1 )[( ) ( ) ]c LI T m y s s h h T= − − − −& &

sup5 6

1 2

max ( , )

( )th

s p p e

f T P

W W W Q

η =

= − − && & &

6 5

1 6

5 max

sup5 sup,max

:

00

00

St

P PP PT TT T

⎧ − ≤⎪

− ≤⎪⎨ − ≤⎪⎪ ≤ ≤⎩



Expander1 1 3 4 3 4( ) ( )s s sW m h h m h h η= − = −& & & 1 0 4 3( )sI T m s s= −& &

Reheater 5 4( )rhQ m h h= −& & 0 5 4 5 4[( ) ( ) ]rh HI T m s s h h T= − − −& &

Expander2 2 5 6 5 6( ) ( )s s sW m h h m h h η= − = −& & & 0 6 5( )sI T m s s= −& & ORC with Reheater


sup3 4 sup5

1 2

max ( , , )

( ) ( )

th

s s p e rh

f T P T

W W W Q Q

η =

= + − +& && & &

4 3

1 4

3 max

5 max

sup3 sup,max

sup5 sup,max

:00

00

0

0

StP PP PT TT TT T

T T

− ≤⎧⎪ − ≤⎪⎪ − ≤⎪⎪ − ≤⎨⎪ ≤ ≤⎪⎪ ≤ ≤⎪⎪⎩


sure is known, the temperature and enthalpy values of point 8 with a saturated liquid state can be calculated. The pressure at point 3 equals to the expander inlet pressure. At the same time, the temperature at point 3 is the same with point 8. Therefore, the enthalpy of point 3 can be calculated. If the superheated temperature at point 5 and the intermediated pressure at point 6 are known, the enthalpy at point 6 can be calculated accord-ing to the expander energy equation. As a result, the mass ratio of ORC with CFOH can be calculated according to the CFOH energy equation. For the ORC with a reheater, the input variables are the superheated temperature at the inlet of expander 1, the pressure at the outlet of expander 1, and the superheated temperature at the inlet of expander 2.

A genetic algorithm is a stochastic global search method that simulates natural biological evolution [15, 16]. The GA operates on a population of potential solutions, applying the principle of survival of the fittest to iterate closer approxima-tions to a solution. At each generation, a new set of approxi-mations is created by the process of selecting individuals ac-cording to their level of fitness in the problem domain and breeding them together using operators borrowed from natural genetics. A GA uses three main types of rules at each step to create the next generation from the current population. Selec-tion rules select the individuals, called parents, which contrib-ute to the population at the next generation. Crossover rules combine two parents to form children for the next generation. Mutation rules apply random changes to individual parents to form children. Our optimization program is performed using the GA Toolbox of Matlab [17]. The parameters are config-ured under the graphical user interface (GUI). The selection function is selected as the tournament method, the adaptive feasible item is the mutation function for the nonlinear con-strained genetic algorithm, the crossover function is the arith-metic method, and the migration option is the forward method.

The optimization routines were programmed according to the optimization model of each ORC. At the beginning of the optimization calculation, the population of the input variables is generated and the routine calculates the thermal efficiency of each individual. The thermodynamic properties of the working fluid under various conditions were computed by REFPROP, which was developed by the National Institute of Standards and Technology of the United States [18]. Then according to the thermal efficiencies of all individuals, the routine sequentially executes the scaling function, the selec-tion function, the crossover function, and the mutation func-tion to generate the next population generation. The GA runs 20 generations of evolution before obtaining the optimized values of the input variables. Subsequently, the thermody-namic values of every state point are calculated as well as the energy load and the exergy destruction rate of each subsystem of ORCs. Exergy is the maximum amount of work done by a subsystem as it approaches thermodynamic equilibrium with its surroundings by a sequence of reversible processes. The exergy destruction rate labels the loss of exergy during the process and is obtained from the exergy balance equations

using the second law analysis method [19].

4. Performances analysis and comparison

Optimization results were calculated for all five types of ORCs using an expander inlet pressure of 3 MPa, a condenser outlet temperature of 300 K, and an expander isentropic effi-ciency of 0.75. The expander inlet pressure and condenser outlet temperature were set to the limit values specified by the constraints (2) and (3) because thermal efficiency increases with the augmentation of expander inlet pressure and de-creases with condenser outlet temperature [20]. Table 4 gives the calculated thermodynamic properties of the working fluid in the ORCs. The expansion pressure ratio, calculated as the ratio of the inlet to outlet pressure of the expander, achieved

Table 4. Thermodynamic properties of the working fluid in the ORCs.

Cycles State no. Pressure (MPa)

Temperature (K)

Enthalpy (kJ/kg)

Entropy (kJ/kg K)

1 0.1599 300 235.36 1.1232

2 3 301.64 238.39 1.1262

3 3 449.64 548.57 1.9339 Simple ORC

4 0.1599 377.93 500.13 1.9775

1 0.1599 300 235.36 1.1232

2 3 301.64 238.39 1.1262

3 3 357.05 316.15 1.3625

4 3 459.98 563.03 1.9657

5 0.1599 389.99 512.51 2.0098

ORC with IHE

6 0.1599 310.48 434.76 1.7873

1 0.1599 300 235.36 1.1232

2 0.8901 300.43 236.14 1.1239

3 0.8901 358.07 317.93 1.3725

4 3 359.98 320.53 1.3747

5 3 429.51 518.01 1.8643

6 0.8901 387.77 500.69 1.8793

ORC with

OFOH

7 0.1599 352.02 474.26 1.9066

1 0.1599 300 235.36 1.1232

2 3 301.64 238.39 1.1262

3 3 360.20 320.85 1.3756

4 3 360.80 321.75 1.3781

5 3 429.42 517.87 1.8639

6 0.9367 388.96 501.33 1.8782

7 0.1599 351.89 474.14 1.9063

8 0.9367 360.20 321.16 1.3814

ORC withCFOH

9 3 362.11 323.72 1.3836

1 0.1599 300 235.36 1.1232

2 3 301.64 238.39 1.1262

3 3 447.87 546.05 1.9282

4 0.6756 404.40 521.96 1.9483

5 0.6756 404.46 522.03 1.9485

ORC with

Reheater

6 0.1599 375.33 497.49 1.9705


18.762 for both the simple ORC and the ORC with an IHE. The maximum expansion pressure ratio is 6 for the single screw expander; therefore, both ORCs needed two-stage ex-panders. For the ORC with an OFOH, the ORC with a CFOH, and the ORC with a reheater, the expansion pressure ratio of the high-pressure expanders were 3.370, 3.203, and 4.441, respectively, and the expansion pressure ratio of the low-pressure expanders were 5.567, 5.858, and 4.225, respectively. Thus, only one-stage expanders were required for these last three types of ORCs.

The maximum working temperature must be limited when using an organic fluid or the fluid will be pyrolysed. An ORC with a relatively low maximum temperature is considered advantageous. From the results of Table 4, the maximum tem-perature of R245fa for a simple ORC is 449 K. Since the eva-poration pressure is 3 MPa, the corresponding superheated temperature is 33 K. The heat addition quantity and output power both increase if the superheated temperature exceeds 33 K. However, the output power augmentation is less than the change in the heat addition quantity. If the superheated tem-perature is less than 33 K, the heat addition quantity and out-put power both decrease. Nevertheless, the drop in output power is greater than of drop in the heat addition quantity. Therefore, there exists an optimal superheated temperature.

The maximum temperature for an ORC with an IHE is 460 K, which is the constraint value for the feasible working re-gion. The calculated superheated temperature is 44 K. This superheated temperature comes from the fact that R245fa is a dry organic working fluid, which transforms to the super-heated gas state at the expander outlet. Therefore, the IHE can transfer lots of heat from the superheated gas to the sub-cooled liquid at the pump outlet. Thus, the heat addition quantity during the evaporation process for an ORC with an IHE is less than the heat addition quantity of a simple ORC. Meanwhile, the power output by the expander is almost the same as for that of the simple ORC. For that reason, the thermal efficiency increases with an increase in the superheated temperature for an ORC with an IHE.

The maximum temperature of the ORC with an OFOH and the ORC with a CFOH are the lowest (429 K). The relevant superheated temperature is 13 K. If the superheated tempera-ture continues to increase, the thermal efficiencies of these two ORCs will decrease. Taking the ORC with an OFOH as an example, the output work of the expander, the heat addition quantity of the evaporator and the input work of pump 1 all increase when the overheat temperature continues to rise from 13 K. However, the increased proportion of the heat addition quantity is greater than the increase seen in the other quantities. For this reason, the thermal efficiency drops. Considering the optimized performance for an ORC with a reheater, the aug-mentation of the working fluid temperature in the reheater is close to zero. This means that only reheating R245fa without the help of other approach cannot contribute to the ORC’s thermal efficiency.

Table 5 lists the energy load and the exergy destruction rate

results for the ORCs when the mass flow rate of the working fluid is set to 1 kg/s. The power consumed by the pump for each ORC is about 3 kW and the heat addition quantity of the simple ORC is 310 kW. However, the heat addition quantity of the ORC with an IHE is 246 kW, 20% lower than the sim-ple ORC. The heat addition quantities of the ORC with an OFOH and the ORC with a CFOH are around 197 kW, which are the smallest values, 36% lower than when compared to the simple ORC. The reason for this low value is that nearly 30% of the working fluid is extracted in the expander and the inter-nal energy of the working fluid at the evaporator inlet is sig-nificantly enhanced. The heat addition quantity of the ORC with a reheater is very close to that of the simple ORC because the amount of heat addition in the reheater approached zero.

The output power of the simple ORC is 48 kW, while the output power of the ORC with an IHE is slightly higher at 50 kW. The reason for this higher value is that, although the su-perheated temperature of the ORC with an IHE was the high-est, and the working fluid enthalpy was increased at the ex-pander inlet, the increase of enthalpy change during the ex-

Table 5. Results of energy load and exergy destruction rate.

Cycles Subsystems E (kW) I (kW)

Pump 3.0348 0.8249

Evaporator 310.18 79.3622

Expander 48.442 11.9183 Simple ORC

Condenser 264.77 13.4611

Pump 3.0348 0.8249

IHE 77.757 3.7726


Expander 50.519 12.0429

ORC with IHE

Condenser 199.4 4.4849

Pump1 0.54 0.1473

OFOH - 4.1169

Pump2 2.60 0.5925


Expander 35.581 9.2503

ORC with OFOH

Condenser 165.04 6.0185

Pump1 2.082 0.5659

CFOH 56.57 4.1328

Pump2 0.804 0.1821

Mixer - 0.0012


Expander 35.19 9.1500

ORC with CFOH

Condenser 163.81 5.9634

Pump 3.035 0.8249


Expander1 24.096 5.4717

Reheater 0.0729 0.0160

Expander2 24.542 6.0154

ORC with Reheater

Condenser 262.13 12.9151


pansion process was very limited. Therefore, the output work of the expander only increased slightly. The output power of the ORC with an OFOH and the ORC with a CFOH are the small-est at about 35kW. The output power for these ORCs is 27% lower than the output power of simple ORC. When these two ORCs operate at their optimized working points, where the relevant thermal efficiencies are maximized, the working fluid enthalpy at the expander inlet is greater than that of the simple ORC by just 5.47%. The enthalpy decrement in the expanders of these two ORCs is very close to the simple ORC if there is no extraction of working fluids. However, there is a considerable amount of working fluid that is extracted and not thoroughly expanded. Therefore, both output powers drop significantly.

A comparison of the thermal efficiencies is shown in Fig. 6, where Pe = 3 MPa, Tc = 300 K, and ηs = 0.75. In Fig. 6, the simple ORC, the ORC with an IHE, the ORC with an OFOH, the ORC with a CFOH, and the ORC with a reheater are rep-resented as ‘a’, ‘b’, ‘c’, ‘d’, and ‘e’, respectively. These repre-sentations are also used in the following figures. Fig. 6 shows that the thermal efficiency of the simple ORC is the smallest at 14.64% while the thermal efficiency of the ORC with an IHE is the largest at 19.23%. The optimized thermal efficiency of the ORC with an IHE is nearly 31% larger than the opti-mized thermal efficiency of the simple ORC. The thermal efficiency of the ORC with a CFOH is slightly higher than that of the ORC with an OFOH. Compared to the simple ORC, the thermal efficiencies of these two ORCs are higher by about 12.6%.

The thermal efficiency of the ORC with a reheater is slightly greater than that of the simple ORC by 1.23%. The mechanisms that cause these discrepancies among the ORCs can be explained as follows. Because an IHE can transfer lots

of heat from the superheated gas to the sub-cooled liquid at the opposite side, the heat addition quantity during the evapo-ration process is less than for that of the simple ORC. Mean-while, the output power of the ORC with an IHE is a little bit larger than that of the simple ORC. Therefore, the thermal efficiency of the ORC with an IHE is significantly better when compared to the simple ORC. The heat addition quantities of the ORC with an OFOH and the ORC with a CFOH are sig-nificantly lower than that of the simple ORC (113 kW). How-ever, the output powers of these two ORCs decrease even further because nearly 30% of the working fluid is extracted in the middle of the expansion process. Hence, the thermal effi-ciencies are slightly higher than for that of the simple ORC but less than the thermal efficiency of the ORC with an IHE. Considering the ORC with a reheater, the optimized thermal efficiency is slightly higher than for that of the simple ORC. The overall heat addition quantity and output power of the low-pressure expander increase when the working fluid tem-perature rises in the reheater. However, the increased amount of heat addition quantity is greater than that of the output power. As a result, the overall thermal efficiency cannot im-prove with increasing heat addition quantity for the reheater.

A comparison of exergy destruction rates is given in Fig. 7, which shows that the exergy destruction rate is the highest for the simple ORC at 105 kW. The exergy destruction rates of the ORC with an OFOH and the ORC with a CFOH are the smallest, 40% less than the exergy destruction rate of the sim-ple ORC. This lower value is mainly because nearly 30% of the working fluid does not reject heat in the condenser, which means that the heat addition quantity obviously decreases. The exergy destruction rate of the ORC with an IHE is 30% small-er than for that of the simple ORC due to lower exergy de-struction rates at the evaporator and the condenser.

5. Working parameters sensitivity analysis

So far, the optimized performance of various ORCs has been analyzed and compared under conditions where the ex-pander inlet pressure was 3 MPa and the condenser outlet temperature was 300 K. A sensitivity analysis with regard to these two parameters, and the isentropic efficiency of the ex-pander, was then conducted using a custom calculation pro-gram.

For the analysis, the expander inlet pressure was first se-lected as the analyzed parameter and the optimized perform-ances based on the different pressures were calculated. The thermal efficiency results are given in Fig. 8(a). All of the thermal efficiencies decrease linearly as the expander inlet pressure is reduced from 3 MPa to 2 MPa. The thermal effi-ciency of the simple ORC decreases from 14.64% to 13.31%, while the thermal efficiency of the ORC with an IHE de-creases from 19.23% to 18.06%. The other ORCs saw similar drops in thermal efficiency: the ORC with an OFOH saw a decrease from 16.43% to 14.86%; the ORC with a CFOH decreases from 16.47% to 14.89%; and the ORC with a rehea-

Fig. 6. Thermal efficiency comparison of various ORCs.

Fig. 7. Exergy destruction rate comparison of various ORCs.


ter decreases from 14.82% to 13.46%. The decreases are due to the heat addition quantities of the various ORCs that de-crease nearly proportionally to the expander inlet pressure. Meanwhile, the output power of the ORCs decreases even further. Therefore, all the thermal efficiencies diminish. How-ever, the ORC with an IHE maintains the highest thermal efficiency as the pressure varied. The thermal efficiencies of the ORC with an OFOH and the ORC with a CFOH are also higher than for that of the simple ORC. The thermal efficiency of the ORC with a reheater is very close to the similar simple

ORC value. The results indicate that just reheating the work-ing fluid cannot improve performance. The calculation results for the ORC with an OFOH are also very close to that of the ORC with a CFOH because the outlet temperatures of the CFOH are constrained to an identical value in the thermody-namic models.

The superheated temperature results are shown in Fig. 8(b). It can be seen that the optimized superheated temperature of the ORC with an IHE rises gradually as the expander inlet pressure drops, while the others are all reduced. Considering the other types of ORCs except for the ORC with an IHE, the output power of the expander reduces rapidly as the expander inlet pressure decreases. To prevent the thermal efficiency from falling down, the heat addition quantity should be de-creased accordingly. Thus, the superheated temperature re-quires to be reduced gradually. The maximum temperature profiles are displayed in Fig. 8(c). The maximum working temperature of the ORC with an IHE is maintained at the lim-ited value, while the others are reduced with the expander inlet pressure. Enhancing the superheated temperature of the ORC with an IHE can improve the system performance. However, for other types of ORC, the optimized superheated temperature should be regulated according to the expander inlet pressure.

The calculated total exergy destruction rates are displayed in Fig. 8(d). The figure shows that the exergy destruction rates for the simple ORC and the ORC with a reheater decrease linearly from 105 kW to 98 kW as the pressure drops from 3 MPa to 2 MPa. This drop is due to the exergy destruction rate of every subsystem of these two ORCs decreasing linearly with decreasing pressure. The overall exergy destruction rate for the ORC with an IHE increases slightly from 73 kW to 75 kW. The reason for this increase is that the exergy destruction rates of the pump and expander decrease with decreasing pres-sure. Because the heat addition quantity is virtually unchang-ing with changing pressure, the heat exchanged in the IHE significantly increases while the heat rejection quantity in the condenser only increases slightly. Therefore, the exergy de-struction rates of the IHE, evaporator and condenser all in-crease. As a result, the total exergy destruction rate rises as the pressure drops. The exergy destruction rates for the ORC with an OFOH and the ORC with a CFOH decrease slightly from 64 kW to 63 kW because the exergy destruction rates of all subsystems, except the evaporator, decrease slightly with de-creasing pressure.

Next, the condenser outlet temperature was selected as the analyzed parameter and the optimized performances based on different temperatures were calculated. The thermal efficiency results are provided in Fig. 9(a). All of the thermal efficiencies decrease as the temperature increases from 300 K to 360 K: the thermal efficiency of the simple ORC decreases from 14.64% to 7.25%; the ORC with an IHE decreases from 19.23% to 9.90%; the ORC with an OFOH decreases from 16.43% to 7.88%; the ORC with a CFOH decreases from 16.47% to 7.98%; and the ORC with a reheater decreases from 14.82% to 7.25%. The decrease experienced by all the

121314151617181920

1.8 2 2.2 2.4 2.6 2.8 3Expander inlet pressure (MPa)

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effi

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) z

a b c d e

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Exer

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Fig. 8. Performance variation with expander inlet pressure.


ORCs is because the decrease of output power is much greater than the decrease in heat addition quantity. The superheated temperature results are shown in Fig. 9(b). It can be seen that the optimized superheated temperature of the ORC with an IHE is maintained at the limited value as the condenser outlet temperature rises. The optimized superheated temperatures of the simple ORC and the ORC with a reheater are decreased. On the contrary, those of the ORC with an OFOH and ORC with a CFOH are increased slightly.

The calculated overall exergy destruction rates are dis-played in Fig. 9(c), showing that the exergy destruction rates of the simple ORC and the ORC with a reheater decrease line-arly from 105 kW to 87 kW as the temperature increases from 300 K to 360 K. The reason for the decrease is that, although the exergy destruction rate of the condenser significantly in-creases as the temperature rises, the exergy destruction rate of the evaporator decreases even faster. Meanwhile, the exergy destruction rates of all the other subsystems increase slightly. As a result, the overall exergy destruction rates of these two ORCs decrease as the temperature rises. The overall exergy destruction rate of the ORC with an IHE decreases from 73 kW to 67 kW because the exergy destruction rates of all the subsystems, except for the condenser, decrease. The exergy destruction rates of the ORC with an OFOH and the ORC

with a CFOH decrease from 64 kW to 59 kW because the exergy destruction rates of the condenser and pump 1 increase as the temperature increases. However, the exergy destruction rates for the evaporator and the expander decrease even fur-ther while the other subsystems’ exergy destruction rates all only decrease slightly. Hence, the overall exergy destruction rates of these two ORCs decrease.

The last analyzed parameter was the isentropic efficiency of the expander. Optimized performances were calculated based on three different values of the isentropic efficiency: 0.75, 0.60, and 0.45, respectively. The resulting thermal efficiencies are given in Fig. 10(a). All of the thermal efficiencies decrease linearly as the isentropic efficiency diminishes from 0.75 to 0.45: the thermal efficiency of the simple ORC decreases from 14.64% to 8.40%; the ORC with an IHE decreases from 19.23% to 11.94%; the ORC with an OFOH decreases from 16.43% to 9.31%; the ORC with a CFOH decreases from 16.47% to 9.38%; and the ORC with a reheater decreases from 14.82% to 8.63%. The decrease in thermal efficiency is primarily due to the expander output power decreasing sig-nificantly as the isentropic efficiency drops. The superheated temperature results are shown in Fig. 10(b). It can be seen that the optimized superheated temperature of the ORC with an

6

8

10

12

14

16

18

290 300 310 320 330 340 350 360 370Condenser outlet temperature (K)

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effi

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61116212631364146

290 300 310 320 330 340 350 360 370Condenser outlet temperature (K)

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290 300 310 320 330 340 350 360Condenser outlet temperature (K)

Exer

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Fig. 9. Performance variation with condenser outlet temperature.

7

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0.4 0.45 0.5 0.55 0.6 0.65 0.7 0.75 0.8Expander isentropic efficiency

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Exer

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Fig. 10. Performance variation with expander isentropic efficiency.


IHE is maintained at the limited value as the expander isen-tropic efficiency drops, while the others are all increased.

The calculated overall exergy destruction rates of the ORCs are displayed in Fig. 10(c). The exergy destruction rates of the simple ORC and the ORC with a reheater increase linearly from 105 kW to 130 kW as the isentropic efficiency decreases from 0.75 to 0.45. When the isentropic efficiency decreases, the exergy destruction rates of the pump and the evaporator remain virtually unchanged. However, the exergy destruction rates of the expander and the condenser significantly increase. For this reason, the overall exergy destruction rates of these two ORCs increase as the isentropic efficiency falls. The overall exergy destruction rate of the ORC with an IHE in-creases from 73 kW to 83 kW because the exergy destruction rates of all the subsystems, except for the evaporator, increase with decreasing isentropic efficiency. The exergy destruction rates of the ORC with an OFOH and the ORC with a CFOH increase from 64 kW to 84 kW due to all of the exergy destruc-tion rates of the subsystems increasing, particularly those of the expander and condenser, as the isentropic efficiency drops.

6. Conclusions

In this study, the optimized performances of five different ORCs were evaluated by using an optimization search method to determine the optimal thermal efficiency and corresponding exergy destruction rate for each ORC. Based on the results of this analysis, we conclude the following:

(1) The optimized thermal efficiency of a simple ORC is the smallest. On the contrary, the optimized thermal efficiency of an ORC with an IHE is the largest. The thermal efficiencies of an ORC with an OFOH and an ORC with a CFOH are in the middle. With working parameters of Pe = 3 MPa, Tc = 300 K, and ηs = 0.75, the calculated thermal efficiency of the sim-ple ORC was 14.64%. The thermal efficiency of the ORC with an IHE was 31% larger than the thermal efficiency of the simple ORC. The thermal efficiency of the ORC with an OFOH was very close to that of the ORC with a CFOH, both 12% larger than the thermal efficiency of the simple ORC.

(2) The exergy destruction rate of a simple ORC at the op-timized working condition is the largest among the analyzed ORCs. On the contrary, the exergy destruction rates of an ORC with an OFOH and an ORC with a CFOH are the lowest while the exergy destruction rate of an ORC with an IHE is in the middle. Using working parameters of Pe = 3 MPa, Tc = 300 K, and ηs = 0.75, the exergy destruction rate of the simple ORC was 105 kW. The exergy destruction rate of the ORC with an IHE was 30% smaller than the simple ORC’s exergy destruction rate. The exergy destruction rate of the ORC with an OFOH was very close to that of the ORC with a CFOH with both exergy destruction rates 39% smaller than the rate of the simple ORC.

(3) All of the optimized thermal efficiencies of the ORCs obviously decreased as the expander inlet pressure dropped from 3 MPa to 2 MPa. The exergy destruction rates of the

simple ORC and the ORC with a reheater exhibited the largest decreases. However, the exergy destruction rate of the ORC with an IHE increased slightly with decreasing pressure while the exergy destruction rates of the ORC with an OFOH and the ORC with a CFOH decreased slightly. All the optimized ther-mal efficiencies of the ORCs decreased significantly when the condenser outlet temperature rose from 300 K to 360 K. The exergy destruction rates of the simple ORC and the ORC with a reheater decreased sensibly when the temperature rose. How-ever, the exergy destruction rates of the other ORCs decreased slightly. The thermal efficiencies of the ORCs decreased con-siderably when the expander isentropic efficiency dropped while the exergy destruction rates of the ORCs increased.

(4) All the optimized superheated temperatures of the ORCs are decreased almost linearly with the expander inlet pressure, except for the ORC with an IHE. However, they are increased when the expander isentropic efficiency reduces. When the condenser outlet temperature is increased gradually, the opti-mized superheated temperatures of the simple ORC and ORC with a reheater are decreased, but those of the ORC with an OFOH and ORC with a CFOH are increased slightly. No mat-ter how these three parameters vary, the optimized super-heated temperature of the ORC with an IHE is maintained at the maximum value.

(5) After comprehensively evaluating the optimized ther-modynamic performance of these five ORCs, the ORC with an IHE shows the best overall performance. The ORC with an OFOH and the ORC with a CFOH are sub-optimal while the simple ORC and the ORC with a reheater are the last choice.

Acknowledgment

This work was sponsored by the National Basic Research (973) Program of China (Grant #2011CB707202, Grant #2011CB710704), the National High-Tech Research and De-velopment Program of China (863 Program) (Grant No. 2009AA05Z206), and the Funding Project for Academic Hu-man Resources Development in Institutions of Higher Learn-ing Under the Jurisdiction of Beijing Municipality (Grant No. PHR201008019).

Nomenclature------------------------------------------------------------------------

h : Enthalpy (kJ/kg) s : Entropy (kJ/kg·K) I& : Exergy destruction rate (kW) w& : Power at unit mass flow rate (kW) T : Temperature (K) P : Pressure (MPa) q& : Heat transmission rate at unit mass flow rate (kW) m& : Mass flow rate of working fluid (kg/s) x : Mass ratio of ORC with OFOH (%) y : Mass ratio of ORC with CFOH (%) η : Efficiency ε : Effectiveness of heat exchanger (%)


Subscript

0 : Reference state 1,2,2s,3,4,4s,5,6,6s,7,7s,8,9,9s : State points in cycle p : Pump e : Evaporator s : Single screw expander c : Condenser n : Net th : Thermal tot : Total H : Heat source L : Cold source bp : Boiling point cr : Critical max : Maximum min : Minimum sup : Superheated evap : Evaporation cond : Condensation

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Hongguang Zhang got his bachelor’s degree, the master degree and doctorate from Beijing Institute of Technology, China, in 1992, 1995, and 1998. From 1998 to 2000, he worked in the Institute of Engineering Thermophysics, Chinese Academcy of Sciences as a post doctor. Later he taught at Beijing University of

Technology. Now he is a professor of the College of Envi-ronmental and Energy Engineering. His research interests include combustion control and energy conservation of inter-nal combustion engine.

Enhua Wang got his bachelor’s degree and master’s degree from Tsinghua University, China, in 2000 and 2003. Later he worked at the Beijing Automo-tive Technology Center Co. Ltd. as an engineer. Now he is a post-graduate student at Beijing University of Tech-nology. His research interests include

organic Rankine cycle for waste heat recovery.

Documents

Optimized performances comparison of organic Rankine cycles for low grade waste heat recovery