J. Cent. South Univ. (2017) 24: 2829-2841

DOI: https://doi.org/10.1007/s11771-017-3698-z

Thermodynamic optimization and fluid selection of organic Rankine cycle driven by a latent heat source

XU Peng(徐鹏)¹, LU Jian(吕建)¹, LI Tai-lu(李太禄)¹, ZHU Jia-ling(朱家玲)²

1. School of Energy and Safety Engineering, Tianjin Chengjian University, Tianjin 300384, China;

2. Key Laboratory of Efficient Utilization of Low and Medium Grade Energy, Ministry of Education(Tianjin University), Tianjin 300072, China

Central South University Press and Springer-Verlag GmbH Germany,part of Springer Nature 2017

Abstract: Organic Rankine cycle (ORC) is applicable for the heat-work conversion. Whereas, there also exist a lot issues that influence the efficiency and the cost of the system. In this work, eleven pure working fluids (as categorized into alkanes, and fluorinated alkanes) are investigated based on the first and second law of thermodynamics. The major objective is to obtain the most suitable working fluid for the latent heat source. The results show that the working fluid is an important factor of the system performance. The heat absorption of the working fluid in the evaporator is inversely proportional to the evaporating temperature, but the thermal and exergetic efficiencies are just the opposite. RC318 has the highest net power output and the lowest outlet temperature of the heat source, but its global warming potential (GWP) value is too high. The cyclohexane shows the highest thermal efficiency among the fluids investigated. Moreover, the figure of merit (FOM) of the isobutane is higher than that of other working fluids. Overall, the cyclohexane shows that the optimal comprehensive performance is more feasible for medium grade heat source in engineering applications.

Key words: organic Rankine cycle; working fluids; thermodynamics; low-temperature; evaporating temperature

1 Introduction

Renewable energies have attracted much more attention as a result of the shortage of the global energy, such as solar energy [1], geothermal energy [2], the waste heat [3], ocean thermal energy [4], and wind energy. Among them, the heat-work conversion for low- and medium-temperature heat source is the most frequently studied. Especially, the organic Rankine cycle (ORC) has attracted much attention due to its simple cycle configuration, high reliability and flexibility, and convenient maintenance in the past few decades [5–8]. Whereas, the thermal efficiency is low, only 8%–12% [9], but the economic benefit is poor.

According to the research in recent years, in order to improve the utilization of the heat source, the optimization of the ORC system has been mostly focused on, such as the minimization of the system irreversibility loss and the choice of the working fluids. MAGO et al [10] did an analysis about the exergy destruction and obtained that the exergy destruction in evaporator is about 77%, much higher than other cycle configuration. ZHU et al [11] analyzed the plate heat exchangers (PHE) in evaporator and found that by optimizing its design, the PHEs will effectively be smaller than the real example given, with a consequent reduction in cost. CLEMENTE et al [12] investigated scroll expanders derived from the compressors in the heating, ventilation and air- conditioning (HVAC) field to recover heat from an internal combustion engine. WANG et al [13] proposed a novel system combining a dual loop ORC with a gasoline engine. LI et al [14] investigated the low temperature solar thermal electric generation with ORC. MAVROU et al [15] proposed a systematic sensitivity analysis procedure explicitly considering the impacts of working fluid and ORC design/operating decisions on the ability of the ORC to operate under conditions different from its nominal design settings to select working fluid mixtures in view of operating variability in solar organic ranking cycles (ORC). HE et al [16] proposed a combined ORC system utilizing exhaust waste as its heat source and liquid natural gas (LNG) as its heat sink to provide alternative power for an LNG- fired vehicle and examined five working fluids at various working conditions, and they found that R236fa has the highest thermal efficiency. WU et al [17] presented the performance of ORC using hot air as heat resource using zeotropic mixture fluids R227ea/R245fa, Butane/R245fa and RC318/R245fa as the working fluids. The result indicates that better thermal performance can be achieved when the temperature difference of cooling water is near the temperature glide of zeotropic mixture in the condenser. DESAI et al [18] did a thermo- economic analysis and selection of working fluid for solar ORC.

There are also some scholars focus on the components change of the ORC system for the power output and economy of the system, such as the regenerative organic Rankine cycle (RORC), the parallel double-evaporator organic Rankine cycle (PDORC), the two-stage series organic Rankine cycle (TSORC) and so on. MAGO et al [19], XI et al [20], PEI et al [21], FERNNDEZ et al [22], and ROY et al [23] analyzed RORC and found that the supercritical RORC is preferable for high temperatures heat source. The internal heat exchanger is the main factor to system efficiency. LI et al [24] proposed and compared PDORC with the ORC to show that the irreversible loss of the PDORC is lower than that of the ORC. BORSUKIEWICZ-GOZDUR et al [25] tried to increase the working fluid flow rate as a kind of method to enhance the power output of geothermal power plant. LI et al [26] constructed and experimentally analyzed the RORC and found that the thermal load of the condenser and the irreversible loss reduced at the same time. Moreover, the thermal efficiency of the RORC is higher than that of the ORC by 1.83%.

Besides the cycle parameters and the cycle configuration, the working fluid has an important influence on the system performance. BADR et al [27] investigated thermodynamic and thermophysical properties of organic working fluids. HUNG et al [28] used ammonia, benzene, R11, R12, R134a and R113 as the working fluid, respectively, and compared the efficiencies of ORCs with each working fluid. SALEH et al [29] gave a thermodynamic screening of 31 pure component working fluids for ORCs, the largest amount of heat can be transferred to a supercritical fluid and the least to a high-boiling subcritical fluid. Based on the first and second laws of the thermodynamics, YARI [30, 31] investigated several dry fluids for ORC, and DESAI et al [32] presented that the dry fluids were the better working fluid for ORC utilizing low-grade heat sources. Also, the wet fluids were investigated by HUNG et al [33], showing that the wet fluids with very steep saturated vapor curves in the T–s diagram for the refrigerant-series and benzene-series fluids had a higher overall performance in energy conversion efficiencies than that of dry fluids. LIU et al [34] presented that the thermal efficiency and the total heat recovery efficiency were different for various working fluids.

For the pure working fluids, their thermodynamic properties may be the issues in engineering applications, such as corrosive, toxic, flammable and environmental harmful. So the mixed working fluids are a way to solve the issues. For example, some hydrocarbons have a very good power performance, but flammable is a problem for hydrocarbons working fluids. Therefore, adding a certain proportion of the working fluid which has excellent performance and flame retardant, can realize safe and efficient application of the working fluids. PAPADOPOULOS et al [35] presented that the selection of the working fluids significantly limited the opportunities of identifying highly performing options. CHEN et al [36] indicated that zeotropic mixtures had a higher efficiency. LAKEW et al [37] found that the power output of the R227ea is highest for the heat source temperature range from 80 °C to 160 °C, and the R245fa gave the highest power output when the temperature ranges from 160 °C to 200 °C. PASETTI et al [38] presented an improved survey method for the evaluation of the thermal stability of working fluids for ORCs. LI et al [39] proposed a novel combined cooling, heating and power organic Rankine cycle (CCHP-ORC) system installed with heat pumps to select optimal zeotropic mixtures and determined the component concentration that gives a better performance.The results showed that R141b/R134a, R141b/R152a and R123/152a have a higher COP and exergy efficiency than others. MAVROU et al [40] investigated the performance of working fluid mixtures for use in solar ORC with heat storage employing flat plate collectors (FPC) and assessed the impact of heat source variability on the ORC performance for different working fluid mixtures, and a mixture of neopentane-2-fluoromethoxy-2- methylpropane at 70% neopentane was the most efficient in all the considered criteria simultaneously. Besides the mentioned above, many factors should be considered for the working fluid choice, such as specific volume, low viscosity, global warming potential (GWP), ozone depletion potential (ODP), high latent heat of vaporization, high thermal conductivity and a stable operating pressure. It should be pointed out that a large number of researchers have focused on the heat-work conversion for low- and medium-grade sensible heat, and few literatures have been found to discuss the working fluid selection of ORC driven by low- and medium-grade latent vapor resource resources.

In this work, the saturated vapor was adopted as the heat source, which has the latent and sensible heat at the same time, and eleven kinds of working fluids was chosen for comparison. Based on the first and second laws of thermodynamics, the parameters, such as power output, irreversible loss, total thermal conductance, exergetic efficiency, and thermal efficiency were optimized. The ORC with each working fluid was identified based on the cycle performance.

2 System descriptions

Figure 1 shows the system flow chart of the ORC, which can be categorized in three loop circuits according to the working media: the heat source, the working fluid, and the heat sink. As shown in Fig. 1, it can be got that the ORC is made of an evaporator, a turbine, a generator, a condenser, a pump, a hot water pump, a cooling water pump, and a cooling tower.

Fig. 1 Schematic diagram of an ORC system

The heat source is saturated vapor, which comes from metallurgical plant and steel mills. Compared with geothermal water, there is the latent heat of saturated vapor, which is far greater than the sensible heat under the condition of unit mass. When the saturated vapor releases heat and flows out of evaporator in the form of water, it can be used in other aspects.

The saturated vapor first flows into the evaporator to transfer heat to the working fluid to generate high-pressure vapor (Figs. 1 and 2, state 1), and it is released into the atmosphere. The working fluid absorbs the heat from the saturated vapor to generate high- pressure in the evaporator, then the vapor flows into the turbine and its enthalpy is converted into shaft work to drive the generator. The vapor existed from the turbine (Figs. 1 and 2, state 2) is led to the condenser where it is liquefied by cooling water. The liquid available at the condenser outlet (Figs. 1 and 2, state 3) is pressurized by the pump and flow into the evaporator (Figs. 1 and 2, state 4). The ORC can be identified as 1→2→3→4, shown by black lines. The cooling water goes into the condenser driven by the cooling water pump. Then a new cycle begins. The T–s diagram is shown in Fig. 2.

3 Modeling

Based on the first and second laws of thermodynamics, the energetic and exergetic analysis were carried out for the working fluid researched. For simplicity, the following hypotheses are made:

1) The saturated vapor is supplied in a steady-state condition, at a heat source of 130 °C;

2) Superheated vapor is considered at the evaporator outlet, with a degree of superheat of 5 K. Supercooled liquid is considered at the condenser exit, with a degree of superheat of 5 K;

3) The kinetic and potential energy changes are negligible;

4) Pressure drops throughout the evaporator, the condenser and the pipelines are negligible;

5) The temperature and friction losses are negligible.

Fig. 2 T–s schematic diagram of an ORC system

The mathematical model for ORC is expressed by the following equations:

Turbine:

                      (1)

where η and h denote the efficiency and enthalpy, respectively; the subscripts t and s represent the turbine and isentropic process, respectively.

             (2)

                       (3)

where W and m_wf stand for the power output and the mass flow rate, respectively; the subscript wf means the working fluid.

                           (4)

where I and s represent the irreversible loss and the entropy, respectively; T₀ stands for the environment temperature.

Condenser:

Figure 3 shows the T–q diagram of the heat transfer process in the condenser. Clearly, as presented in Fig. 3, it can be seen that the processes of T₂→T_2′→T_2″→T₃ and T_cw,in→T_cw,1→T_cw,2→T_cw,out represent the temperature variations of the working fluid and the cooling water in the condenser, respectively. There are superheated vapor of the working fluid at the condenser inlet and super-cooled fluid at the condenser outlet. The process in condenser is composed of three parts: super-cooling, condensing and pre-cooling, which separately represented by I, II and III. T_cw,1 and T_cw,2 are the temperature of cooling water leaving and entering the condensing part.

Fig. 3 T–q diagram for heat transfer in condenser

                          (5)

                         (6)

                         (7)

           (8)

where Q denotes the thermal load; the subscripts c and I, II, III stand for the three sections of condenser shown in Fig. 3.

                             (9)

                            (10)

                           (11)

         (12)

where (KA)_c,I, (KA)_c,II and (KA)_c,III are the thermal conductance of sections I, II and III of condenser, respectively; K , A and △T stand for the heat transfer coefficient, the heat transfer area, and the logarithm mean temperature difference, respectively.

(13)

                           (14)

                        (15)

where W_p,cw means the power consumption of the cooling water pump, P_cw is the pressure loss in the cooling water circuit and ρ_cw represents the density for the cooling water; subscripts cw and p stand for the cooling water and the pump, respectively.

                      (16)

                         (17)

                         (18)

where h_4s is specific enthalpy at the pump outlet experiencing an isentropic process.

Figure 4 shows the temperature difference variation between saturated vapor and working fluid in the evaporator versus the heat transfer rate q, T–q diagram. From Fig. 4, it can be evidently seen that the processes of T₄→T_4′→T_4″→T₁ and T_sv,in→T_sv,1→T_sv,2→T_sv,out represent the temperature variations of the working fluid and the saturated vapor in the evaporator, respectively. There are superheated vapor of the working fluid at the condenser inlet and super-cooled fluid at the condenser outlet. With condenser, the evaporator also can be divided into three sections: preheating, evaporating and vapor superheating sections; which are represented by I, II and III. T_sv,1 and T_sv,2 represent the temperatures of saturated vapor leaving and entering the evaporating section.

Fig. 4 T–q diagram for heat transfer in evaporator

                         (19)

                        (20)

                        (21)

          (22)

where the subscripts 1 and 4 stand for the outlet and inlet of the working fluid at evaporator.

                             (23)

                            (24)

                           (25)

         (26)

where (KA)_e,I, (KA)_e,II and (KA)_e,III are the thermal conductance of Sections I, II and III of evaporator, respectively.

  (27)

                           (28)

where W_p,sv, p_sv, η_p,sv and ρ_sv are the power consumption of saturated vapor pump, the pressure provided by the saturated vapor pump, the efficiency of the saturated vapor pump, and the density for the saturated vapor; the subscripts sv, in and out represent the saturated vapor, the inlet and outlet of the evaporator for saturated vapor, respectively.

Total irreversibility:

                    (29)

The total thermal conductance of heat exchangers:

                     (30)

    (31)

Net power output:

             (32)

where η_m and η_g are the mechanical efficiency and the efficiency of the generator.

The heat flow rate released to the environment Q₀ is:

        (33)

where C_sv and C_cw are the heat capacities of the saturated vapor and the cooling water, respectively.

The volumetric flow rate (VFR, R_vf) is given as:

                         (34)

where v₁ and v₂ stand for the volumetric flow rate of the inlet and outlet at the turbine, respectively.

Thermal efficiency:

                           (35)

The exergy for saturated vapor at inlet and outlet of the evaporator can be expressed as

                         (36)

where h_sv,in and h_sv,out denote the enthalpy of the saturated vapor at the evaporator inlet and outlet.

    (37)

Exergetic efficiency:

                            (38)

where EX_sv is the exergy input into the cycle provided by saturated vapor.

4 Results and discussion

In this work, eleven kinds of pure working fluids were used in the subcritical ORC based saturated vapor as an example for low- and medium-grade heat source, and the main physical properties of the working fluids are shown in Table 2. Table 3 shows the system parameters and ambient conditions used in this work, which is obtained from an existed practical ORC system.

From Table 2, it can be seen that the GWP of working fluid RC318 is 10250, much bigger than other working fluids, which means RC318 has a stronger influence on greenhouse effect. Also the ALT of RC318 reaches the maximum value of all working fluid, which represents that it is a long time for RC318 to exist in the natural environment without being damaged or break down. Among the working fluids, the alkanes, including isobutane, isopentane, n-pentane, n-hexane, n-pentane, n-decane and cyclohexane, have the flammable characteristics. It should be known that the type changing of the turbine usually leads to the variation of expansion efficiency. To simplify the calculation, it is assumed that the isentropic efficiency of the turbine is unchanged. And the mass flow rate of saturated vapor is 1 kg/s.

Table 2 Thermodynamic properties of working fluids

Table 3 Data used to simplify calculation in this work

4.1 Mass flow rate of working fluids

Figure 5 shows the variation of the mass flow rate of the different working fluids versus the evaporating temperature. It can be seen that the variation trends of mass flow rate of all working fluids are the same. A rise in evaporating temperature decreases the mass flow rate. Based on the law of energy conservation, the mass flow rate is directly inversely proportional to the enthalpy difference of the working fluid between the inlet and outlet of the evaporator with the heat and cold source remaining steady. And the increase of the evaporating temperature decreases the enthalpy of the evaporate outlet, therefore leading to a drop in the mass flow rate of the working fluids. The mass flow rate of RC318 ranges from 2.607 kg/s to 1.982 kg/s with the evaporating temperature change from 75 °C to 95 °C, and the mass flow rate of cyclohexane ranges from 0.5742 kg/s to 0.3592 kg/s, which are the maximum and minimum values at the same evaporating temperature, respectively. The variation curves of the n-pentane,n-hexane, n-heptane and n-decane are almost the same line. From big to small, the total order is m_RC318, m_R123, m_R245fa, m_R141b, m_isobutane, m_isopentane, m_n-pentane, m_n-hexane, m_n-heptane, m_n-decane and m_cyclohexane in turn.

Fig. 5 Variation of mass flow rate of different working fluids versus evaporating temperature

4.2 Net power output

Figure 6 demonstrates the variation of the net power output of different working fluids versus the evaporating temperature. As shown in Fig. 6, the net power output first increases and reaches its maximum, and then decreases with the increment of the evaporating temperature, which applies to all the working fluids. It also can be seen that the W_net corresponding to T_e,turning is the optimal W_net for each working fluid, so T_e,turning can be regarded as the T_e,opt. In essence, the two parameters can be deemed as one. From Eq. (32), the net power output, W_net, is proportional to W_t, which is due to that the values of the power consumptions, W_p, W_hp and W_cp, are relatively much smaller compared with W_t. The maximum net power output is 20.67 kW for RC318 when the evaporating temperature comes to 38℃, while the cyclohexane keeps the minimum net power output at the same evaporating temperature. For net power output,the performance of the working fluids decreases in the order: RC318, R245fa, isobutane, R123, isopentane, n-pentane, R141b, n-hexane, n-heptane, n-decane and cyclohexane. From the cost of turbine, it can be obtained that a larger m_wf will increase the thickness of the wall of turbine, so the cost of turbine will increase.

Fig. 6 Variation of net power output of different working fluids versus evaporating temperature

The saturated vapor outlet temperature versus the evaporating temperature for various working fluids is presented in Fig. 7. As shown, the rise of T_sv,out is proportional with T_e, and the change rate of T_sv,out to T_e is almost the same for all working fluids. The T_sv,out of the RC318 is always lesser than other working fluids at the same evaporating temperature, and it ranges from 42.98 °C for T_e=75 °C to 59.31 °C for T_e=95 °C, whereas the T_sv,out of the cyclohexane is greater than the left working fluids in the same situation, and the range of variation is from 65.93 °C for T_e=75 °C to 87.38 °C for T_e=95 °C. The differences between the T_sv,out of alkanes, like n-pentane, n-heptane, n-hexane and n-decane, are in a small range. In this work, the heat source is saturated vapor, which means that there are latent heat and sensible heat existing in the process of heat transfer. From Eq. (22), it can be obtained that with the inlet temperature of the evaporate fixed, the increase of the t_sv,out decreases the quantity of heat transferred from the heat source.

Fig. 7 Saturated vapor outlet temperature versus evaporating temperature for various working fluids

4.3 Irreversible loss

Figure 8 demonstrates the influence of the evaporating temperature on the irreversibility of the system for various working fluids. The irreversible loss of the system contains the irreversible loss caused by condenser, evaporator, pump and turbine, respectively. It can be seen from Fig. 8 that the irreversible loss of the system decreases with the increment of evaporating temperature. The irreversible loss of the system of RC318 is the largest in the 11 kinds of working fluids, which ranges from 35.23 kW to 29.39 kW. Whereas, the value I_cyclohexane is the least value and its change range is from 28.53 kW to 18.16 kW. At the same time, the changing curve of I_n-hexane, I_n-pentane, I_n-heptane and I_n-decane is almost coincident. Combined with Fig. 7, it can be obtained that with the heat that working fluids absorbed from heat source reducing, the irreversible loss of the system decreases together.

Fig. 8 Influence of evaporating temperature on irreversibility of system for various working fluids

Figure 9 illustrates the entropy generation of the system with the evaporating temperature for various working fluids. The entropy generation S_g is composed of the system S_g,c, S_g,e, S_g,p and S_g,t, in which subscripts c, e, p and t represent condenser, evaporator, pump and turbine, respectively. Among them, the entropy generation caused by evaporate is greater than other system components for each working fluid. As shown in Fig. 9, the entropy generation of RC318 is the biggest of all working fluids, whereas S_{g,cyclohexane} is minimum under the same t_e, from 0.1048 kJ/K to 0.08785 kJ/K and 0.08599 kJ/K to 0.05431 kJ/K, respectively. From Eq. (31), it can be obtained that S_g is related with the mass flow rate of saturated vapor and cooling water and the entropy difference of saturated vapor and cooling water in the inlet and outlet of evaporator and condenser, respectively. Whereas m_sv, S_gw,in, S_cw,out and S_cw,in are unchanged, so the variation of S_g depends on m_cw and S_gw,out. Combined Fig. 6, it can be obtained that the value of m_cw is much greater than m_sv (m_sv=1 kg/s), and the mass flow rate of cooling water plays a decisive role. So the variation trend of S_g is consistent with that of m_cw.

Fig. 9 Entropy generation of system with evaporating temperature for various working fluids

4.4 Mass flow rate of cooling water

The variation of the mass flow rate of the cooling water versus the evaporating temperature for various fluids is shown in Fig. 10. Evidently, as shown in Fig. 10, the mass flow rate of the cooling water is gradually reduced with the increase of evaporating temperature. The value of m_cw,RC318 is greater than other medium, and its variation range is from 16.2 kg/s to 12.93 kg/s with T_e rises from 75 °C to 95 °C, while m_cyclohexane varying from 11.71 kg/s to 7.562 kg /s, which is less than other working fluids. From Eq. (15), it can be obtained that m_cw is proportional to m_wf and the difference between h₂ and h₃, and it is inversely proportional to c and T_cw. On account of the value of h₅, c and T_cw are fixed, so just m_wf and h₂ are taken in account. Combined with Fig. 5, as T_e increases, the mass flow rate of working fluids, m_wf, decreases. Whereas the enthalpy of condenser inlet, h₂, increases with T_e. But the absolute value of m_wf to T_e is greater than the value of h₂ to T_e, so the rising in T_e leads to the decreasing of m_cw.

Fig. 10 Variation of mass flow rate of cooling water versus evaporating temperature for various fluids

4.5 Thermal conductance

Figure 11 illustrates the thermal conductance of condenser versus the evaporating temperature for different working fluids. Clearly, as presented in Fig. 11, the thermal conductance of condenser decreases with the rising of evaporating temperature for each working fluid. In all the working fluids, KA_c,RC318 is the biggest, which ranges from 178 kW/°C to 128.8 kW/°C; whereas KA_c,n-decane is the smallest, the variation range of which is 136.9 kW/°C to 77.92 kW/°C. By calculating, the change rate of the gap between the working fluids, which is adjacent to each other in Fig. 7, is not very big. The value of KA_c to T_e can be approximately regarded as constant and is different from each other for all working fluids. From Eq. (12), it can be obtained that KA_c is proportional to the thermal load in condenser, and is inversely proportional to the log mean temperature difference in condenser. From Fig. 3, the rising of T_sv,out decreases the thermal load in evaporator, so Q_c will also diminish as Q_e, moreover, △T_c is proportional to T_e.

Fig. 11 Thermal conductance of condenser versus evaporating temperature for different working fluids

Figure 12 illustrates the thermal conductance of evaporator versus the evaporating temperature for different working fluids. Apparently, it can be got from Fig. 12 that the maximum value of KA_e appeared when the working fluid is RC318; the minimum value of KA_e occurred when cyclohexane was used as working fluid, whereas the shape of the curve is different for different working fluids. The change trend of RC318 first increases when KA_e,RC318 reaches the maximum value 22.44 kW/°C for T_e=80 °C, and then decreases with the increment of T_e like a straight line; each change rate of the rest curves in Fig. 8 can be approximately regarded as constant. From Eq. (26), it can be obtained that KA_e is determined by the thermal load in evaporator and the log mean temperature difference in the evaporator. The rising of the T_e results in the decrease of the log mean temperature difference in the evaporator and the thermal load of the evaporator. For RC318, when T_e<80 °C, the change rate of △T to T_e is greater than that when T_e>80 °C. The variation range of KA_e,RC318 is from 22.17 kW/°C to 20.72 kW/°C, and the variation range of KA_{e,cyclohexane} is from 13.08 kW/°C to 10.28 kW/°C.

Fig. 12 Thermal conductance of evaporator versus evaporating temperature for different working fluids

Figure 13 illustrates the total thermal conductance of system versus the evaporating temperature for different working fluids. Clearly, as presented in Fig. 13, KA decreases with the increase of T_e, and the change trend of KA is semblable with KA_c for all working fluids. From Eq. (30), KA is got by KA_c and KA_e. It can be clearly obtained from Figs. 11 and 12 that KA_c is much greater than KA_e because of the smaller temperature difference in the condenser. So KA_c is the key factor which determines the variation trend of KA, and that is the reason why KA and KA_c show the similar change rules for every working fluid. Put Figs. 7–9 together, it can be seen that Q_c and Q_e are both reduced as the T_sv,out increases, and the total KA also decreases with the change of Q_c and Q_e. The maximum value, KA_RC318, ranges from 200.2 kW/°C to 149.5 kW/°C, whereas the minimum value, KA_n-decane, ranges from 151 kW/°C to 88.78 kW/°C.

Fig. 13 Total thermal conductance of system versus evaporating temperature for different working fluids

4.6 Volumetric flow rate

Figure 14 shows the variation of the volumetric flow rate versus the evaporating temperature for different working fluids. Obviously, as presented in Fig. 14, it can be obtained that the VFR of the n-decane is higher than that of other working fluids, and the VFR of the isobutene is lower than that of the rest working fluids. It also can be known that the system condensing pressure can be regarded as a constant due to the environment condition is unchanged. So T_e is the only factor affecting the size of VFR: VFR is proportional to T_e. From MACCHI et al [46], there exists an inversely proportional relationship between VFR and turbine efficiency: lower values of VFR deliver higher turbine efficiency. From the point of economic, INVERNIZZI et al [47] presented that in order to achieve a turbine efficiency higher than 80%, the VFR should be lower than 50. So the maximum and minimum of the turbine efficiency are isobutane and n-decane, respectively. But, for all working fluids, the turbine efficiency is higher than 80%. Moreover, it can be got that the length of the turbine will increase with the increase of the VFR, then the cost of turbine will also increase. The variation range of VFR_n-decane is from 12.02 for T_e=75 °C to 28.66 for T_e=95 °C, meanwhile the variation range of VFR_isobutene is from 3.198 for T_e=75 °C to 5.121 T_e=95 °C.

Fig. 14 Variation of volumetric flow rate versus evaporating temperature for different working fluids

4.7 Figure of merit

Figure 15 shows the variation of the figure of merit (FOM, F_om) versus the evaporating temperature for different working fluids. The concept of FOM is put forward by MIKIELEWICZ [48], FOM is treated as an important index to evaluate the merits of the working fluids, which is expressed as follows:

                          (39)

where J_a is the ratio of c_p,e and r_e, c_p,e and r_e are the sensible heat and the latent heat of vaporization of working fluids, respectively.

Fig. 15 Variation of figure of merit versus evaporating temperature for different working fluids

As shown in Fig. 15, the FOMs of all working fluids have the consistent trends which decrease with the increases of t_e. Among them, FOM_isobutane is obviously higher than that for other working fluids, and FOM_R141b is evidently lower than that for the left working fluids. So the performance of the isobutane is excellent than that of others. FOM_isobutane ranges from 0.5641 to 0.4811 and FOM_R141b ranges from 0.5305 to 0.4433, when T_e increases from 75 °C to 95 °C. From Eq. (39), it can be seen that FOM is directly proportional to the sensible heat of the working fluid (c_p,e), and is inversely proportional to the evaporating temperature (T_e) and the latent heat of the working fluid (r_e). Combined Figs. 11, 13 and 14, there is a rule that FOM is inversely proportional to thermal efficiency and exergy efficiency.

4.8 Size parameter

As the analysis of working fluids is described from the point of thermodynamics, the size parameter (SP, P_s) is brought up to measure the turbine efficiency for the different working fluids. The parameter SP is defined by MACCHI et al [46] as follows:

                               (40)

where V_out stands for volume flow rate of the working fluids at the outlet of the turbine, and h_2s is specific enthalpy at the turbine outlet experiencing an isentropic process.

Figure 16 shows the variation of the size parameters versus the evaporating temperature for different working fluids. As presented in Fig. 16, it can be clearly seen that SP_n-decane is significantly higher than the values of other working fluids, and SP_isobutane is lower than that of other working fluids. The value of n-decane changes from 2.899 for T_e=75 °C to 2.408 for T_e=95 °C, and the SP of isobutane ranges from 0.5641 for T_e=75 °C to 0.4811 for T_e=95 °C. The change trend of FOM decreases with the increase of T_e. According to Ref. [20], a higher value of SP results in higher turbine efficiency. Then combined Fig. 12 and Eq. (40), it can be obtained that the enthalpy difference of inlet and outlet increases with increasing T_e; at the same time, the mass flow rate of working fluids increases also. That is the reason why SP becomes smaller with the increase of T_e. From the point view of economic, a higher SP will increase the size of turbine, so the cost of turbine will also increase.

Fig. 16 Variation of size parameters versus evaporating temperature for different working fluids

4.9 System efficiency

Figures 17 and 18 show the exergetic efficiency and thermal efficiency of system versus the evaporating temperature for different working fluids. Evidently, it can be seen from Figs. 17 and 18 that η_ex and η_th are proportional to T_e for all working fluids. Whereas the ratio of η_ex to T_e is not consistent and it becomes smaller and smaller, but the variation trend is almost unchanged. From Eq. (38), it can be seen that η_ex is determined by W_net and the exergy at the inlet and outlet of the evaporator for saturated vapor. From Fig. 7, increasing T_e will result in increasing T_sv,out, and the difference between EX_sv,in and EX_sv,out will reduce with the increase of T_sv,out. From Fig. 6, it can be known that W_net first increases and then decreases. That is the reason why the variation trends do not keep consistent. For all working fluids, the maximal value of the η_ex is η_{ex,cyclohexane}, which ranges from 32.37% for T_e=75 °C to 39.51% for T_e=95 °C. On the contrary, the η_ex,RC318 is the minimum value and its range is from 28.75% for T_e=75 °C to 33.37% for T_e=95 °C.

Fig. 17 Exergetic efficiency of system versus evaporating temperature for different working fluids

Fig. 18 Thermal efficiency of system versus evaporating temperature for different working fluids

Table 1 Validation of numerical model with previous published data [29] for various fluids-based ORC

From Eq. (37), it can be got that η_th relies on W_net, m_wf and the enthalpy at the inlet and outlet of the evaporator for saturated vapor. For all working fluids, the maximal value of η_th is η_{th,cyclohexane}, which ranges from 6.914% for T_e=75 °C to 9.451% for T_e=95 °C; on the contrary, η_th,RC318 is the minimum value and its range is from 5.317% at T_e=75 °C to 6.856% at T_e=95 °C.

From the above analysis, it can be obtained that the evaporating temperature is the most key parameter for the system performance of the ORC and should be optimized in engineering applications. Furthermore, the optimal working fluid differs with one evaluation index to another. Overall, the cyclohexane has excellent comprehensive performance.

5 Validation

Numerical solution is validated with the results of SALEH et al [29] for various working fluids-based ORC without regenerator under the same operating conditions. The results of present solutions show a very good agreement with the results in the reference, as shown in Table 1. The discrepancies mainly derive from the selection of equation of state (EOS) that the BACKONE EOS is adopted in reference while the fundamental EOS is selected in this work.

6 Conclusions

Eleven pure working fluids (as categorized into alkanes and fluorinated alkanes) are screened for organic Rankine cycle driven by the latent heat. The main conclusions are summarized as follows.

1) The evaporating temperature is the most important parameter of the ORC, and the optimal evaporating temperature will minimize the irreversible loss and the entropy generation and is different with the working fluid, so it should be optimized to obtain the optimal system performance, especially for the low- and medium-grade heat sources.

2) RC318 shows the highest net power output as a result of the lowest outlet temperature of the heat source, so the corresponding system efficiency is the lowest. Moreover, the high GWP value also limits the utilization of RC318.

3) The n-decane has the lowest total thermal conductance, but its volumetric flow ratio and size parameter are too high to restrict its application.

4) The cyclohexane suggests the highest thermal and exergetic efficiencies, and it shows outstanding overall performances and can be used in engineering applications.

The cycle parameters and the working fluid selection are the two main aspects that should be considered for the actual ORC plants, and the system performance must be optimized based on the temperature level of the heat source and heat sink.

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(Edited by FANG Jing-hua)

Cite this article as: XU Peng, LU Jian, LI Tai-lu, ZHU Jia-ling. Thermodynamic optimization and fluid selection of organic Rankine cycle driven by a latent heat source [J]. Journal of Central South University, 2017, 24(12): 2829–2841. DOI:https://doi.org/10.1007/s11771-017-3698-z.

Foundation item: Project(51406130) supported by the National Natural Science Foundation of China

Received date: 2016-02-29; Accepted date: 2016-05-17

Corresponding author: LI Tai-lu, Lecturer, PhD; Tel: +86–22–28305107; E-mail: litl@tcu.edu.cn