Thermodynamic Performance Analyses and Optimization of Dual-Loop Organic Rankine Cycles for Internal Combustion Engine Waste Heat Recovery

Featured Application

This work examined the effects of an internal combustion engine (ICE) exhaust gas temperature on dual-loop organic Rankine cycles (DORC) for ICE waste heat recovery. High-temperature loop evaporation, condensation temperatures, and superheat degrees were optimized. Results could provide theoretical and data support for determining suitable operating parameters and working fluid for DORC with various engine exhaust gas temperatures.

Abstract

Waste heats of an internal combustion engine (ICE) are recovered by a dual-loop organic Rankine cycle (DORC). Thermodynamic performance analyses and optimizations are conducted with 523.15–623.15 K exhaust gas temperature (T_g1). Cyclopentane, cyclohexane, benzene, and toluene are selected as working fluids for high-temperature loop (HTL), whereas R1234ze(E), R600a, R245fa, and R601a are selected as working fluids for low-temperature loop (LTL). The HTL evaporation temperature, condensation temperature, and superheat degree are optimized through a genetic algorithm, and net power output is selected as the objective function. Influences of T_g1 on system net power output, thermal efficiency, exergy efficiency, HTL evaporation temperature, HTL condensation temperature, HTL superheat degree, exhaust gas temperature at the exit of the HTL evaporator, heat utilization ratio, and exergy destruction rate of the components are analyzed. Results are presented as follows: the net power output is mainly influenced by HTL working fluid. The optimal LTL working fluid is R1234ze(E). The optimal HTL evaporator temperature increases with T_g1 until it reaches the upper limit. The optimal HTL condensation temperature increases initially and later remains unchanged for a cyclopentane system, thus keeping constant for other systems. Saturated cycle is suitable for cyclohexane, benzene, and toluene systems. Superheat cycle improves the net power output for a cyclopentane system when T_g1 is 568.15–623.15 K.

1. Introduction

Increased fossil fuel consumption causes environmental pollution, global warming, and energy crisis; waste heat recovery is considered a promising technology for solving these problems [1,2,3]. The waste heat utilization of internal combustion engine (ICE) can effectively reduce the use of fossil fuels and is crucial for saving energy and reducing emission because oils consumed by ICE account for approximately 60% of the total oil consumption, and more than 55% of fuel energy is emitted through waste heat [4,5,6,7].

Among all of the existing solutions for the waste heat utilization of ICE, organic Rankine cycle (ORC) is a promising technology. ORC uses organic working fluids; this technology has advantages of simple structure, favorable applicability, and user-friendliness over conventional steam Rankine cycle and is ideal for utilizing medium-to-low temperature heat sources (<350 °C) [8,9,10,11]. Many researchers have conducted studies on ICE waste heat recovery using ORC and have discovered the favorable potential of this technology [12,13,14,15,16,17,18]. Shu et al. [12] used ORC to recover waste heat of diesel engine using alkanes as working fluids. Their results showed that cyclohexane and cyclopentane are the most suitable working fluids through comprehensive consideration. Vaja et al. [13] performed a thermodynamic analysis of ICE waste heat recovery using ORC, benzene, R11, and R134a as working fluids and considered different cycle configurations. Their results indicated that the overall efficiency of ORC is better by 12% than when ORC is not applied. Song et al. [17] designed an optimized ORC for marine diesel engine waste heat recovery and conducted economic and off-design analyses. Their results demonstrated that an optimized ORC is technically feasible and economically attractive.

ICE waste heat resources mainly consist of engine exhaust and jacket cooling water; given the high temperature of engine exhaust gas when a single-stage ORC is applied for waste heat recovery, the match between an engine exhaust gas and a high-temperature loop (HTL) may exacerbate, and the utilization of engine jacket cooling water is low [19,20]. Therefore, many researchers have adopted a dual-loop organic Rankine cycle (DORC) for ICE waste heat recovery and conducted system analysis, parametric analysis, and configuration comparison. Shu et al. [21,22,23] designed several systems for utilizing the ICE waste heat. Their results showed that R143a and R1234yf are favorable working fluids for low-temperature loop (LTL), and low condensation temperature can improve system performance. Tian et al. [19] investigated a regenerative transcritical system for ICE waste heat recovery. Their results showed the toluene is a favorable option for HTLs. Zhang et al. [24] developed a novel DORC to recover waste heat from exhaust gas, intake air, and coolant. Their results indicated that DORC can relatively improve output power by 14–16% in the peak of the effective thermal efficiency region. Yang et al. [25] studied a DORC for diesel engine waste heat recovery under various operating conditions; these authors selected R245fa as the working fluid and discussed performance on the basis of the first and second laws of thermodynamics. Their conclusion revealed that DORC can enhance the system thermal efficiency by 13% in comparison with the original system. Wang et al. [26,27] used DORC to harness the wasted heat from ICE and calculated the performance of a combined engine–ORC system under the entire operating region of an engine. Their results indicated that the relative increment rate of net power output can reach 22% in the peak thermal efficiency region. Choi and Kim [28] investigated a DORC waste heat recovery system, used water and R1234yf for HTLs and LTLs, and analyzed the thermodynamic properties of a waste heat recovery power generation system. Their results showed that the DORC can enhance 2.824% propulsion efficiency in comparison with the original engine. Song et al. [29,30] conducted a parametric analysis of the DORC system; these authors selected cyclohexane, toluene, and water as working fluids for HTLs, and used R245fa, R236fa, and R123 for LTLs. Their conclusion showed that the DORC can increase the net power output by 11.6% in comparison with an original diesel engine. A few researchers have conducted parameter optimization for DORCs. Yang et al. [31] explored DORC parameter optimization using R245fa for maximizing net power output and minimizing heat transfer area and used optimization parameters, such as evaporation pressure, superheat degree, and condensation temperature. Their results indicated that the maximum net power output can reach 23.62 kW.

Considering that exhaust gas is the main heat source of ICE waste heat, the exhaust gas temperature will considerably affect the working fluid selection for the two loops, the system thermal performance, and the operating parameters. Many works on the DORC have been based on fixed exhaust gas temperature, and a few studies have discussed the influence of exhaust gas temperature on the working fluid selection for two loops. In addition, HTL evaporation temperature, condensation temperature and superheat degree are important operation parameters. Many studies have been conducted using a saturated cycle or fixed HTL condensation temperature, but a few studies have considered these operational parameters together for different working fluid systems. The change in engine exhaust gas temperature will affect the exergy destruction rate, and thus this change must be analyzed.

The engine exhaust gas temperatures of 523.15–623.15 K are considered in the present work because these temperatures are common and suitable for ORC application [6,29,30]. Cyclopentane, cyclohexane, benzene, and toluene [12,18,29,32,33,34,35,36] are selected as the HTL working fluids because they possess efficient thermal performance with high temperature and favorable environmental and high decomposition temperature. Furthermore, R1234ze(E), R600a, R245fa, and R601a are selected as working fluids for LTLs [8,37,38,39,40,41] given the efficient environmental and thermal performances with low temperature. The working fluid properties are listed in

Table 1. Working fluids properties. ODP: ozone depletion potential; GWP: global warming potential.

	Molecular Mass/(g·mol−1)	Critical Temperature/K	Critical Pressure/kPa	Normal Boiling Point/K	ODP	GWP
cyclopentane	70.13	511.7	4515	322.4	0	low
cyclohexane	84.16	553.6	4075	353.9	0	low
benzene	78.11	562.1	4894	353.2	0	low
boluene	92.14	591.8	4126	383.8	0	low
R1234ze(E)	114.04	382.5	3636	254.2	0	6
R600a	58.12	407.8	3629	261.4	0	low
R245fa	134.05	427.2	3651	288.3	0	950
R601a	72.15	460.4	3378	301.0	0	low

[8,12,29,38], ODP is the ozone depletion potential; GWP is the global warming potential.

By considering the exhaust gas acid dew point temperature limit, the present work optimizes HTL evaporation temperature, condensation temperature and superheat degree for maximizing net power output with 523.15–623.15 K engine exhaust gas through a genetic algorithm. Moreover, the effects of ICE exhaust gas temperature on net power output, thermal efficiency, exergy efficiency, HTL evaporation temperature, HTL condensation temperature, HTL superheat degree, exhaust gas temperature at the exit of an HTL evaporator, heat utilization ratio and exergy destruction rate of the components are studied.

2. System Model

A schematic of the DORC is illustrated in Figure 1. The DORC consists of an HTL and an LTL. The HTL is used to recover the waste heat of engine exhaust gas, and the LTL absorbs the heat of the jacket cooling water and released by HTL.

For HTL: An HTL working fluid pump pressurizes saturated liquid from a condenser/evaporator to an HTL evaporation pressure (1–2). The high-pressure liquid absorbs heat from an engine exhaust gas in the HTL evaporator and is heated to a saturated or superheat vapor (2–5). The saturated or superheated vapor from the HTL evaporator enters the HTL turbine and expands to perform work (5–6). The exhaust vapor exits from the HTL turbine and then enters the condenser/evaporator to release heat to the LTL (6–1).

For LTL: An LTL working fluid pump pressurizes saturated liquid from an LTL condenser to an LTL evaporation pressure (1′–2′). The liquid from the LTL working fluid pump enters an LTL preheater and absorbs heat to preheating (2′–7′), and then working fluid enters the condenser/evaporator and absorbs heat for evaporating (7′–4′). Working fluid with a saturated state enters the LTL turbine and generates power (4′–5′). The exhaust vapor enters the LTL condenser and condenses to a liquid (5′–1′).

2.1. High-Temperature Loop

The T-s diagram of an HTL is depicted in Figure 2. Two cases for a pinch point temperature difference (PPTD) position of the HTL evaporator are observed. When the PPTD of the HTL evaporator is at an HTL working fluid evaporation bubble point (State point 3, VPP) [8], the HTL mass flow rate is calculated as follows:

$$m_{\mathrm{H}}=\frac{m_{\mathrm{g}}{c}_{\mathrm{pg}}\left(T_{g1}-T_{g2}\right)}{\left(h_5-h_3\right)}$$

(1)

$$h_5=f\left(p_{\mathrm{He}},T_5\right)$$

(2)

where h is the specific enthalpy; m_g is the mass flow rate of the engine exhaust gas; c_pg is the specific heat capacity of the engine exhaust gas at constant pressure, which is set to 1.1 kJ/(kg·K) [42]; T_g is the engine exhaust gas temperature; and p_He is the HTL evaporation pressure.

When the PPTD is at the working fluid inlet (State point 2, PPP), the HTL mass flow rate is calculated as follows:

$$m_{\mathrm{H}}=\frac{m_{\mathrm{g}}{c}_{\mathrm{pg}}\left(T_{g1}-T_{\mathrm{g}3}\right)}{\left(h_5-h_2\right)}$$

(3)

$$T_{\mathrm{g}3}=T_2+\Delta T_{\mathrm{pp}1}$$

(4)

The power produced by the HTL turbine can be expressed as follows:

$$P_{\mathrm{H}}=m_{\mathrm{H}}\left(h_5-h_{6\mathrm{s}}\right){\eta }_{\mathrm{t}}=m_{\mathrm{H}}\left(h_5-h_6\right)$$

(5)

where η_t is the turbine isentropic efficiency.

The power consumed by the HTL working fluid pump can be calculated as follows:

$$P_{\mathrm{Hp}}=\frac{m_{\mathrm{H}}\left(h_{2\mathrm{s}}-h_1\right)}{{\eta }_{\mathrm{p}}}=m_{\mathrm{H}}\left(h_2-h_1\right)$$

(6)

where η_p is the working fluid pump efficiency.

The HTL net power output is equal to the power produced by the HTL turbine minus the power consumed by the HTL working fluid pump.

$$P_{\mathrm{Hnet}}=P_{\mathrm{H}}-P_{\mathrm{Hp}}$$

(7)

2.2. Low-Temperature Loop

In Figure 3, two cases are identified for the LTL. If T_3′ + T_pp2 ≤ T_jw1, then Case 1 occurs. In Figure 3a, the LTL working fluid is preheated by the jacket cooling water to a two-phase state.

When the PPTD of an LTL preheater is at State point 3′, the LTL working fluid mass flow rate can be expressed as follows:

$$m_{\mathrm{L}}=\frac{m_{\mathrm{H}}\left(h_6-h_1\right)+m_{\mathrm{jw}}{c}_{\mathrm{pw}}\left(T_{\mathrm{jw}1}-T_{\mathrm{jw}2}\right)}{\left(h_{4^{\prime }}-h_{3^{\prime }}\right)}$$

(8)

$$T_{\mathrm{jw}2}=T_{3^{\prime }}+\Delta T_{\mathrm{pp}2}$$

(9)

When the PPTD of the preheater occurs at State point 2′, the mass flow rate is expressed as follows:

$$m_{\mathrm{L}}=\frac{m_{\mathrm{H}}\left(h_6-h_1\right)+m_{\mathrm{jw}}{c}_{\mathrm{pw}}\left(T_{\mathrm{jw}1}-T_{\mathrm{jw}3}\right)}{\left(h_{4^{\prime }}-h_{2^{\prime }}\right)}$$

(10)

$$T_{\mathrm{jw}3}=T_{2^{\prime }}+\Delta T_{\mathrm{pp}2}$$

(11)

where c_pw is the specific heat capacity of the jacket cooling water at constant pressure, which is set to 4.18 kJ/(kg·K); m_jw is the jacket cooling water mass flow rate; T_jw is the jacket cooling water temperature; and ∆T_pp2 is the LTL preheater PPTD.

If T_3′ + T_pp2 > T_jw1, then Case 2 occurs (Figure 3b). The LTL working fluid is only preheated to State point 7′. When the PPTD of the preheater is at State point 7′, m_L is calculated as follows:

$$m_{\mathrm{L}}=\frac{m_{\mathrm{H}}\left(h_6-h_1\right)}{\left(h_{4^{\prime }}-h_{7^{\prime }}\right)}$$

(12)

$$h_{7^{\prime }}=f\left(p_{\mathrm{Le}},T_{7^{\prime }}\right)$$

(13)

$$T_{7^{\prime }}=T_{\mathrm{jw}1}-\Delta T_{\mathrm{pp}2}$$

(14)

where p_Le is the LTL evaporation pressure.

When the PPTD of the preheater occurs at State point 2′, m_L is obtained using Equations (10) and (11).

The cooling water mass flow rate is calculated as follows:

$$m_{\mathrm{w}}=\frac{m_{\mathrm{L}}\left(h_{6^{\prime }}-h_{1^{\prime }}\right)}{c_{\mathrm{pw}}\left(T_{\mathrm{w}2}-T_{\mathrm{w}1}\right)}$$

(15)

where T_w is the cooling water temperature.

The power consumed by a cooling water pump is

$$P_{\mathrm{pw}}=\frac{m_{\mathrm{w}}gH}{{\eta }_{\mathrm{pw}}}$$

(16)

where H is the cooling water pump head, and g is the gravitational acceleration, which is set to 9.8 m/s².

The power produced by the LTL turbine is calculated as

$$P_{\mathrm{L}}=m_{\mathrm{L}}\left(h_{4^{\prime }}-h_{5\prime \mathrm{s}}\right){\eta }_{\mathrm{t}}=m_{\mathrm{L}}\left(h_{4^{\prime }}-h_{5^{\prime }}\right)$$

(17)

The power consumed by the LTL working fluid pump can be expressed as

$$P_{\mathrm{Lp}}=\frac{m_{\mathrm{L}}\left(h_{2\prime \mathrm{s}}-h_{1^{\prime }}\right)}{{\eta }_{\mathrm{p}}}=m_{\mathrm{L}}\left(h_{2^{\prime }}-h_{1^{\prime }}\right)$$

(18)

The LTL net power output is

$$P_{\mathrm{Lnet}}=P_{\mathrm{L}}-P_{\mathrm{Lp}}-P_{\mathrm{pw}}$$

(19)

2.3. System

The system net power output is equal to the HTL net power output plus the LTL net power output

$$P_{\mathrm{net}}=P_{\mathrm{Hnet}}+P_{\mathrm{Lnet}}$$

(20)

The engine exhaust gas waste heat and jacket cooling water heat utilization ratios correspond to the following equations:

$${\eta }_{\mathrm{g}}=\frac{T_{\mathrm{g}1}-T_{\mathrm{g}3}}{T_{\mathrm{g}1}-T_0}$$

(21)

$${\eta }_{\mathrm{jw}}=\frac{T_{\mathrm{jw}1}-T_{\mathrm{jw}3}}{T_{\mathrm{jw}1}-T_0}$$

(22)

where T₀ is the ambient temperature set to 288.15 K [42].

The thermal efficiency is expressed as follows:

$${\eta }_{\mathrm{th}}=\frac{P_{\mathrm{net}}}{m_{\mathrm{g}}{c}_{\mathrm{pg}}(T_{\mathrm{g}1}-T_{\mathrm{g}3})+m_{\mathrm{jw}}{c}_{{}_{\mathrm{pw}}}(T_{\mathrm{jw}1}-T_{\mathrm{jw}3})}$$

(23)

2.4. Exergy

The system exergy efficiency can be obtained using the following equation:

$${\eta }_{\mathrm{ex}}=\frac{P_{net}}{E_{\mathrm{tot}}}$$

(24)

where E_tot is the total exergy [29,30]:

$$E_{\mathrm{tot}}=m_{\mathrm{g}}{c}_{\mathrm{p}\mathrm{g}}\left[\left(T_{\mathrm{g}1}-T_0\right)-T_0\ln \left(\frac{T_{\mathrm{g}1}}{T_0}\right)\right]+m_{\mathrm{jw}}{c}_{\mathrm{pw}}\left[\left(T_{\mathrm{jw}1}-T_{\mathrm{jw}3}\right)-T_0\ln \left(\frac{T_{\mathrm{jw}1}}{T_{\mathrm{jw}3}}\right)\right]$$

(25)

The exergy destruction rate of each component can be calculated as follows:

$$I=\frac{E_{\mathrm{d}}}{E_{\mathrm{tot}}}$$

(26)

where E_d is the exergy destruction of each component. The calculation formulations are summarized in

Table 2. Calculation formulation of exergy destruction.

Components	Exergy Destruction
HTL evaporator	$E_{\mathrm{dHe}}=m_{\mathrm{g}}{c}_{\mathrm{pg}}\left[\left(T_{\mathrm{g}}{}_1-T_{\mathrm{g}3}\right)-T_0\ln \left(T_{\mathrm{g}}{}_1/T_{\mathrm{g}3}\right)\right]-m_{\mathrm{H}}\left[\left(h_5-h_2\right)-T_0\left(s_5-s_2\right)\right]$
condenser/evaporator	$E_{\mathrm{dce}}=m_{\mathrm{H}}\left[\left(h_6-h_1\right)-T_0\left(s_6-s_1\right)\right]-m_{\mathrm{L}}\left[\left(h_{4^{\prime }}-h_{7^{\prime }}\right)-T_0\left(s_{4^{\prime }}-s_{7^{\prime }}\right)\right]$
HTL turbine	$E_{\mathrm{dHt}}=m_{\mathrm{H}}{T}_0\left(s_6-s_5\right)$
HTL working fluid pump	$E_{\mathrm{dHp}}=m_{\mathrm{H}}{T}_0\left(s_2-s_1\right)$
exhaust gas from HTL evaporator	$E_{\mathrm{dHeout}}=m_{\mathrm{g}}{c}_{\mathrm{pg}}\left[\left(T_{\mathrm{g}}{}_3-T_0\right)-T_0\ln \left(T_{\mathrm{g}}{}_3/T_0\right)\right]$
LTL preheater	$E_{\mathrm{dLpre}}=m_{\mathrm{jw}}{c}_{\mathrm{pw}}\left[\left(T_{\mathrm{jw}1}-T_{\mathrm{jw}3}\right)-T_0\ln \left(T_{\mathrm{jw}1}/T_{\mathrm{jw}3}\right)\right]-m_{\mathrm{L}}\left[\left(h_{7^{\prime }}-h_{2^{\prime }}\right)-T_0\left(s_{7^{\prime }}-s_{2^{\prime }}\right)\right]$
LTL condenser	$E_{\mathrm{dLc}}=m_{\mathrm{L}}\left[\left(h_{5^{\prime }}-h_{1^{\prime }}\right)-T_0\left(s_{5^{\prime }}-s_{1^{\prime }}\right)\right]$
LTL turbine	$E_{\mathrm{dLt}}=m_{\mathrm{L}}{T}_0\left(s_{5^{\prime }}-s_{4^{\prime }}\right)$
LTL working fluid pump	$E_{\mathrm{dLp}}=m_{\mathrm{L}}{T}_0\left(s_{2^{\prime }}-s_{1^{\prime }}\right)$

.

2.5. Assumptions

The following assumptions are created to simplify the analysis:

(1) The DORC system is in a steady state.

(2) The pump and turbine efficiencies are constant.

(3) The heat losses and pressure drops are neglected.

3. Model Validation

The model in the present work is consistent with the author’s previous article [43] and is compared with DORC data of Literature [29,30];

Table 3. Data comparison between the present work and the literature.

	HTL	LTL		HTL	LTL
	Cyclohexane	R245fa		Toluene	R236fa
evaporation temperature/K	480.3	349.0		440.3	378.9
net power output/kW (literature [29])	64.0	47.2		32.6	64.6
net power output/kW (present work)	64.01	46.58		32.61	63.59
relative error/%	0.0	1.3		0.0	1.6
	HTL		LTL
	Water		R123	R236fa	R245fa
evaporation temperature/K	480.0		347.5	369.0	352.3
net power output/kW (literature [30])	54.5		46.0	60.6	49.4
net power output/kW (present work)	54.52		45.21	59.32	48.53
relative error/%	0.0		1.7	2.1	1.8

Relative error = |data of present work–data of literatures|/data of literatures × 100%

displays the comparison results. The HTL net power outputs in the present work are consistent with the literature, and the maximal relative error is 2.1%. Moreover, the calculation accuracy is reliable.

4. Optimization Method

The net power output is the objective function. Optimization variables include HTL evaporation temperature (T₃), HTL condensation temperature (T₁), and HTL superheat degree (T₅–T₄). The optimization ranges are listed in

Table 4. Optimization ranges of the operating parameters.

Optimization Parameters	Lower Limit	Upper Limit
HTL evaporation temperature	HTL condensation temperature + 5 K	HTL working fluid critical temperature − 15K
HTL condensation temperature	HTL working fluid normal boiling point	LTL working fluid critical temperature − 15K + ∆Tpp2
HTL superheat degree	0 K	Tg1 − ∆Tpp1 − T4

. The lower limit of T₃ is T₁ plus 5 K. The difference between working fluid critical temperature and the upper limit of T₃ must be 15 K to prevent the HTL working fluid from approaching the critical point. The lower limit of T₁ is HTL working fluid saturated temperature at the pressure of 101 kPa to avoid the contamination of non-condensable gases [29,30,43]; the upper limit is the LTL working fluid critical temperature minus 15 K and then plus ∆T_pp2 to avoid the LTL working fluid from approaching the critical point. The lower limit of HTL superheat degree is 0 K, and the upper limit is T_g1 minus ∆T_pp1 and T₄ to avoid the heat transfer temperature of the HTL evaporator from being lower than ∆T_pp1. In addition, the exhaust gas temperature at the exit of the HTL evaporator must be higher than the acid dew point temperature, which is 373.15 K [42]. By contrast, the LTL evaporation temperature must be lower than the LTL working fluid critical temperature minus 15 K.

The genetic algorithm is a random search method based on the evolution rule of organisms; this algorithm was invented by Prof. Holland in 1975 on the basis of the ideas of natural selection. The genetic algorithm mainly includes selection, crossover, and mutation calculations. Selection calculation selects good individuals from the generation. Crossover calculation is used for individuals to generate new individuals. Mutation calculation is adopted to avoid a local optimal solution. In the genetic algorithm, a population of candidate solutions to an optimization problem is evolved toward improved solutions. When the genetic algorithm is used, a population of randomly generated individuals is selected as the initial population, and iterative calculation begins. The population in each iteration is called a generation. The fitness of every individual in the population is calculated in each generation. If it does not satisfy the stopping criteria, then the more fit individuals are randomly selected from the population, and each individual is modified by crossover and mutation operators for creating a new generation. The new generation of candidate solutions is used for net iteration. When an appropriate fitness level is reached or the maximal generations are formed, the calculation is terminated, and the results are shown [6,44]. A flowchart of the genetic algorithm is demonstrated in Figure 4.

The genetic algorithm has been extensively used for optimization [6,37,45,46,47,48,49,50,51]. Yang et al. [6] selected a net power output per unit heat transfer area and exergy destruction rate as the objective functions and optimized evaporation pressure, superheat degree, and condensation temperature for ORC using the genetic algorithm. Xi et al. [46] set exergy efficiency as the objective function and performed turbine inlet pressure, turbine inlet temperature, and the fractions of the flow rate of the regenerative optimization for an ORC through the genetic algorithm. Wang et al. [47] selected a ratio of the net power output to the total heat transfer area as the performance evaluation criterion and optimized key thermodynamic design parameters for the ORC through the genetic algorithm. Thus, the present work used the genetic algorithm in MATLAB for optimization, and the parameter setting of the genetic algorithm is presented in

Table 5. Parameter setting of the genetic algorithm.

Parameters	Value
population size	50
crossover fraction	0.8
maximal generations	500
function tolerance	10−6

. The fluid properties are calculated using Refprop 9.0.

5. Result and Discussion

The data of ICE are from an inline six-cylinder turbocharged engine. The exhaust gas mass flow rate is 7139 kg/h; the jacket cooling water mass flow rate and temperature are 6876 kg/h and 363.15 K, correspondingly [18]. The PPTD of the HTL evaporator is the largest [5,19] because the heat transfer performance of engine exhaust gas is low; the PPTD of the HTL evaporator is set to 20 K on the basis of Literature [18,43]; the PPTDs of the LTL preheater and condenser/evaporator are set to 10 K on the basis of Literature [40,43]; and PPTD of 5 K is common for an LTL condenser [5,19,40,43]. The DORC parameters are listed in

Table 6. DORC parameters.

Parameters	Symbol	Value
PPTD of HTL/K	∆Tpp1	20
PPTD of LTL preheater and condenser/evaporator/K	∆Tpp2	10
PPTD of LTL condenser/K	∆Tpp3	5
cooling water inlet temperature/K	Tw1	298.15
cooling water outlet temperature/K	Tw3	303.15
turbine efficiency/%	ηt	80
working fluid pump efficiency/%	ηp	75
cooling water pump efficiency/%	ηpw	85
cooling water pump head/m	H	20
ambient temperature/K	T0	288.15

[43].

5.1. Thermal Performance

In Figure 5, the net power output increases with T_g1. The DORC net power output is mainly affected by HTL working fluids, and LTL working fluids have minimal influence on the net power output. When HTL working fluids are the same, the relative deviation (|maximal net power output−minimal net power output|/minimal net power output × 100%) of the net output power affected by different LTL working fluids is less than 3%. Thus, selecting a suitable HTL working fluid is important. When T_g1 is 523.15–598.15 K, cyclopentane and R1234ze(E) are used, and the maximal net power output is 56.9–117.3 kW. When T_g1 is 603.15–618.15 K, cyclohexane and R1234ze(E) are used, and the maximal net power output is 125.6–133.4 kW. When T_g1 is raised to 623.15 K, the HTL and LTL optimal working fluids are benzene and R1234ze(E), respectively, and the maximal net power output is 142.4 kW.

Table 7. Optimal working fluids and net power output with T_g1 of 523.15–623.15 K.

Tg1/K	HTL Working Fluid	LTL Working Fluid	Maximal Net Power Output/kW
523.15–598.15	cyclopentane	R1234ze(E)	56.9–117.3
603.15–618.15	cyclohexane	R1234ze(E)	125.6–133.4
623.15	benzene	R1234ze(E)	142.4

presents the optimal working fluids and the corresponding net power outputs. R1234ze(E) is optimal for LTLs when the HTL working fluids are cyclopentane, cyclohexane, and benzene. T_g1 will not affect the optimal LTL working fluid. When the HTL working fluid is toluene, the PPTD of the condenser/evaporator will be higher than ∆T_pp2 when R1234ze(E) is used for the LTL considering the lower limits of the HTL condensation and the LTL evaporation temperatures. Therefore, R245fa is used for maximizing the net power output.

In Figure 5a, when cyclopentane is used for HTL, the net power output increases with T_g1. The optimal HTL evaporation temperature does not reach the upper limit when T_g1 is 523.15–553.15 K, and the increasing trend of the net power output remains unchanged. The optimal HTL evaporation temperature reaches the upper limit, and the optimal HTL superheat degree is 0 K when T_g1 increases to 558.15 K. The HTL evaporation temperature is suitable for T_g1, and the increment rate of the net power output increases. The evaporation temperature becomes unsuitable for increasing T_g1, and the optimal HTL superheat degree is not 0 K when T_g1 increases to 568.15 K. The increment rate of the net power output decreases. When cyclohexane is used for the HTL, T_g1 is 523.15–598.15 K, the optimal HTL evaporation temperature does not reach the upper limit, and the PPTD of the HTL evaporator is at VPP. The net power output increases with the T_g1. When T_g1 increases to 603.15 K, the PPTD of the HTL evaporator occurs at PPP, T_g3 cannot decrease, and the increment rate of net power output decreases.

Figure 5b exhibits that, when benzene is used for HTL and T_g1 is 523.15–613.15 K, the optimal HTL evaporation temperature does not reach the upper limit, and the net power output increases with T_g1. The optimal HTL evaporation temperature reaches the upper limit, and the PPTD of the HTL evaporator is at VPP when T_g1 rises to 618.15 K. Furthermore, T_g3 rapidly decreases with the increase in T_g1, thereby increasing the increment rate of the net power output. The optimal HTL evaporation temperature does not reach the upper limit, and the PPTD of the HTL evaporator occurs at VPP when toluene is used for the HTL, and T_g1 is 523.15–623.15 K. Therefore, the net power output increases with T_g1.

Figure 6 illustrates that thermal efficiency increases with T_g1 because the increment rate is larger in the net power output than in heat absorption. The maximal thermal efficiency is 14.6–19.6% with the T_g1 of 523.15–623.15 K when toluene and R601a are used for HTL and LTL, correspondingly. The thermal efficiencies of cyclopentane, cyclohexane, and benzene system are also maximal when R601a is used for LTL. The R1234ze(E) used for the LTL will cause minimal thermal efficiency.

Figure 6a shows that the optimal HTL evaporation temperature does not reach the upper limit when cyclopentane is used for HTL, and T_g1 is 523.15–553.15 K. The thermal efficiency increases with T_g1. The net power output increases rapidly when T_g1 is 558.15–563.15 K, thus also rapidly increasing thermal efficiency. The HTL evaporation temperature is unsuitable for the increase in T_g1, the increment rates of the net power output and thermal efficiency decrease when T_g1 increases to 568.15 K. When cyclohexane is used and T_g1 is 523.15–593.15 K, the optimal HTL evaporation temperature does not reach the upper limit, and the thermal efficiency increases with T_g1. When T_g1 increases to 598.15 K, the optimal HTL evaporation temperatures of the R600a, R245fa, and R601a systems reach the upper limit; moreover, the irreversibilities between exhaust gas and HTL increase, and the increment rate of thermal efficiency decreases. For the R1234ze(E) system, the optimal HTL evaporation temperature reaches the upper limit with the T_g1 of 603.15 K.

Figure 6b demonstrates that, when benzene is used for HTL, and T_g1 is 523.15–613.15 K, the optimal HTL evaporation temperature does not reach the upper limit, and the thermal efficiency increases with T_g1. When T_g1 increases to 618.15 K, the optimal HTL evaporation temperature reaches the upper limit, and the increment rate of thermal efficiency decreases. When toluene is used for HTL, and T_g1 is 523.15–623.15 K, the optimal HTL evaporation temperature does not reach the upper limit, and the increment rate of thermal efficiency remains unchanged.

Figure 7 displays that the variations in exergy efficiency with T_g1 are different with various HTL working fluids. Furthermore, Figure 7a illustrates that, when cyclopentane is used for HTL, and T_g1 is 523.15–553.15 K, the optimal HTL evaporation temperature does not reach the upper limit, the increasing T_g1 improves net power output, and the exergy efficiency increases with increasing T_g1. When T_g1 is 558.15–563.15 K, the optimal HTL evaporation temperature reaches the upper limit, and the optimal HTL superheat degree is 0 K; furthermore, the HTL evaporation temperature is suitable for T_g1, and the exergy efficiency increases rapidly with T_g1. When T_g1 increases to 568.15 K, the HTL evaporation temperature is unsuitable for increasing T_g1, and the optimal HTL superheat degree is not 0 K; with the increase in T_g1, the irreversibilities between exhaust gas and HTL increase, and the exergy efficiency decreases slowly. When cyclohexane is used for HTL, and T_g1 is 523.15–598.15 K, the optimal HTL evaporation temperature does not reach the upper limit, and the PPTD of the HTL evaporator occurs at VPP; in addition, the exergy efficiency increases with T_g1. When T_g1 increases to 603.15 K, the PPTD of the HTL evaporator occurs at PPP, and the optimal HTL evaporation temperature reaches the upper limit; moreover, T_g3 cannot decrease, although the increase in T_g1 will improve the net power output and will increase the irreversibilities between exhaust gas and the HTL given the HTL evaporation temperature upper limit, and the exergy efficiency begins to decrease slowly.

Figure 7b depicts that, when benzene is used for HTL, and T_g1 is 523.15–613.15 K, the optimal HTL evaporation temperature does not reach the upper limit, and the exergy efficiency increases with T_g1. When T_g1 increases to 618.15 K, the optimal HTL evaporation temperature reaches the upper limit, and the PPTD of the HTL evaporator occurs at VPP. The HTL evaporation temperature is suitable for T_g1 at the moment; with the increase in T_g1, T_g3 rapidly decreases, the increment rate of net power output increases, and then increment rate of exergy efficiency increases. When toluene is used for the HTL, and T_g1 is 523.15–623.15 K, the optimal HTL evaporation temperature does not reach the upper limit, and the PPTD of the HTL evaporator occurs at VPP; furthermore, with the increase in T_g1, the exergy efficiency increases, but the increasing trend is unchanged; when R1234ze(E) is used for LTL, the exergy efficiency is much smaller than that of other systems because the PPTD is higher in the condenser/evaporator than in ∆T_pp2. When R601a is used for LTL, the exergy efficiency is maximal; when R1234ze(E) is used for LTL, the exergy efficiency is minimal.

5.2. Operating Parameter

When the HTL working fluid is given, the variation in optimized HTL evaporation temperature, HTL condensation temperature, HTL superheat degree, exhaust gas temperature at the exit of the HTL evaporator and heat utilization ratio, exergy destruction rate with an increase in T_g1 for the four LTL working fluids are similar, and the systems with maximal net power output for four HTL working fluids are investigated. The four systems identified are cyclopentane + R1234ze(E), cyclohexane + R1234ze(E), benzene + R1234ze(E), and toluene + R245fa.

Figure 8 depicts the effects of T_g1 on the optimal HTL evaporation temperature. With the increase in T_g1, the increasing HTL evaporation temperature can improve temperature match with exhaust gas. The optimal HTL evaporation temperature increases initially for the cyclopentane system. When T_g1 rises to 558.15 K, the optimal HTL evaporation temperature reaches the upper limit. When cyclohexane is used for HTL, the optimal HTL evaporation temperature increases initially with T_g1. When T_g1 rises to 603.15 K, the optimal HTL evaporation temperature reaches the upper limit. When benzene is used for HTL, the optimal HTL evaporation temperature initially increases with T_g1. When T_g1 rises to 618.15 K, the optimal HTL evaporation temperature reaches the upper limit. Given the high upper limit of the HTL evaporation temperature, for the toluene system, the optimal HTL evaporation temperature increases with T_g1.

Figure 9 demonstrates the effects of the T_g1 on the optimal HTL condensation temperature. The optimal HTL condensation temperature remains unchanged for cyclohexane, benzene, and toluene systems, and the optimal HTL condensation temperature is the lower limit (the saturated temperature at the pressure of 101 kPa); moreover, the low HTL condensation temperature will enhance the DORC performance, and similar results are obtained by several parameter analysis studies [5,21,23,43]. The optimal HTL condensation temperature increases with 523.15–563.15 K T_g1 when cyclopentane is used for HTL, and the saturated cycle is used. The superheated cycle is used when T_g1 is raised to 568.15 K, and the optimal HTL condensation temperature remains unchanged. It is higher than the lower limit (322.3 K) because the decrease in HTL condensation temperature will decrease T_g3, and T_g3 must be higher than or equal to the exhaust gas acid dew point temperature to avoid low-temperature acid corrosion. Moreover, when the HTL condensation temperature increases to 351.0 K, T_g3 is equal to the exhaust gas acid dew point temperature and maintains at 351.0 K.

The HTL evaporation temperature upper limits are high, given the high critical temperatures of cyclohexane, benzene, and toluene. When T_g1 increases, the increasing HTL evaporation temperature can improve the temperature match with the heat source, the superheated cycle is unnecessary, and the optimal HTL superheat degree is 0 K for cyclohexane, benzene, and toluene systems. In particular, the saturated cycle will generate more power output than the superheated cycle for these systems. However, the HTL evaporation temperature upper limit for the cyclopentane system is lower than other working fluids. When T_g1 increases to 568.15 K, the HTL evaporation temperature is unsuitable for increasing T_g1, and the superheated cycle is used to improve temperature match between the engine exhaust gas and HTL given the limit of the HTL evaporation temperature. In Figure 10, when T_g1 is 523.15–563.15 K, the saturated cycle is improved; when T_g1 is 568.15–623.15 K, superheated cycle will increase the net power output, the optimal HTL superheat degree increases initially with the increase in T_g1 and then remains unchanged upon reaching 16.3 K (16.3 K is not the upper limit of optimization setting), and the maximum optimal superheat degree is independent of T_g1.

5.3. Exhaust Gas Temperature at the Exit of the HTL Evaporator and Heat Utilization Ratio

In Figure 11, the variation trend in T_g3 with T_g1 is different with varying HTL working fluid systems. T_g3 of the cyclopentane system decreases with T_g1 of 523.15–553.15 K, and the optimal HTL evaporation temperature is not the upper limit. T_g3 decreases with the increase in T_g1, When T_g1 rises to 558.15 K, the optimal HTL evaporation temperature reaches the upper limit, and T_g3 increases and then decreases. When T_g1 rises to 568.15 K, the superheated cycle is used, and T_g3 reaches the lower limit. Initially, when cyclohexane is used, T_g3 decreases with the increase in T_g1. When T_g1 increases to 603.15 K, the PPTD of the HTL evaporator occurs at PPP, T_g3 increases, and then remains at 375.5 K. T_g3 of the benzene system increases initially and then decreases with the T_g1 of 523.15–613.15 K. When the T_g1 increases to 618.15 K, the optimal HTL evaporation temperature reaches the upper limit, and T_g3 increases and then decreases rapidly with the increase in T_g1. Considering that the lower limit of the HTL condensation temperature for the toluene system is the highest, the optimal HTL condensation temperature of this system is higher than the other systems, and T_g3 of the toluene system is higher than the other systems. With the increase in T_g1, T_g3 increases initially and later decreases. When the net power output is maximal, T_g3 is not constantly at the lower limit and will be affected by a cycle type (saturated or superheated cycle), the HTL evaporator temperature value, and the PPTD of an HTL evaporator.

Figure 12 illustrates the variation trend of η_g with T_g1. When cyclopentane is used for HTL, and T_g1 is 523.15 –553.15 K, the optimal HTL evaporation temperature does not reach the upper limit, and the increase in T_g1 decreases T_g3. With the increase in T_g1, η_g increases. When T_g1 is 558.15–563.15 K, the optimal HTL evaporation temperature reaches the upper limit, and the optimal HTL superheat degree is 0 K. With the increase in T_g1, T_g3 initially increases and later rapidly decreases; although T_g3 initially increases with small degrees, T_g1 increases. With the increase in T_g1, η_g increases slowly and later rapidly increases. When T_g1 increases to 568.15 K, the superheated cycle is used, and T_g3 remains unchanged. In Equation (21), η_g increases. When cyclohexane is used for HTL, and T_g1 is 523.15–598.15 K, the optimal HTL evaporation temperature does not reach the upper limit, and the PPTD of HTL evaporator occurs at VPP. η_g increases with the increase in T_g1. When T_g1 increases to 603.15 K, the PPTD of HTL evaporator occurs at PPP, and the optimal HTL evaporation temperature reaches the upper limit, T_g3 cannot decrease, and the increment rate of η_g decreases. When benzene is used for HTL, and T_g1 is 523.15–613.15 K, the optimal HTL evaporation temperature does not reach the upper limit. η_g increases with the increase in T_g1. When T_g1 is 618.15–623.15 K, the optimal HTL evaporation temperature reaches the upper limit, and the PPTD of the HTL evaporator remains at State point three. T_g3 increases initially and then decreases rapidly, and η_g decreases initially and then increases rapidly. When toluene is used for HTL, and T_g1 is 523.15–623.15 K, the optimal HTL evaporation temperature does not reach the upper limit. With the increase in T_g1, η_g is mainly affected by the increase in T_g1, although T_g3 increases initially and later decreases, while η_g increases. When cyclopentane is used for HTL, and T_g1 is 623.15 K, the maximal η_g is 74.6%.

In Figure 13, with the increase in T_g1, η_jw of the cyclopentane system increases initially, then decreases, and finally increases. When T_g1 increases from 563.15 K to 568.15 K, the cycle type changes from saturated to superheated. η_jw decreases with the increase in T_g1. With the increase in T_g1, η_jw increases for the cyclohexane and toluene systems. η_jw of the benzene system increases initially with the increase in T_g1. When T_g1 increases to 618.15 K, the optimal HTL evaporation temperature reaches the upper limit and the PPTD of the HTL evaporator still occurs at VPP, and η_jw decreases initially and later increases. Considering that the optimal HTL condensation temperatures of the cyclopentane, cyclohexane, and toluene systems are lower than T_jw1, Case 1 occurs, and η_jw is higher than 35%. When toluene is used, Case 2 occurs, η_jw is lower than 26%, and Case 2 must be avoided. The cyclopentane system has a higher η_jw than the other systems. When T_g1 is 623.15 K, the maximal η_jw is 51.8%. An increase in T_g1 can improve η_jw.

5.4. Exergy Destruction Rate

The reduction in system exergy destruction is an effective means of improving the system net output power. The investigation of exergy destruction can identify the component with the most potential for reducing exergy destruction. The present work focuses on the exergy destruction rates of exhaust gas from HTL evaporator (I_Hout), LTL condenser (I_Lc), HTL evaporator (I_He), condenser/evaporator (I_ce), LTL preheater (I_Lpre), HTL turbine (I_Ht), LTL turbine (I_Lt), and working fluid pumps (I_p) with T_g1 for different HTL working fluids.

Figure 14 illustrates that, when cyclopentane is used for HTL, I_Hout and I_Lpre decrease with the increase of T_g1, because η_g and η_jw are improved by increasing T_g1. Because the superheat degree is 0 K and the optimal HTL evaporation temperature initially fails to reach the upper limit, then reaches the upper limit, and superheat degree is finally not 0 K. I_Lc initially declines and then increases with T_g1. I_He decreases initially with the increase in T_g1 because the HTL evaporation temperature can increase with the increase in T_g1 to improve temperature match. Afterward, the superheated cycle is used given the upper limit of the HTL evaporation temperature, which is unsuitable for increasing T_g1, thereby increasing I_He. I_He decreases initially and then increases with T_g1. Moreover, I_ce, I_Ht, and I_p increase initially and then decrease eventually. The variation in I_Lt is also affected by the HTL evaporation temperature and superheat degree. I_Lt remains unchanged initially, later increases, and finally decreases slowly with the increase in T_g1. When T_g1 is 523.15–538.15 K, I_out is maximal at higher than 17% because η_g is low. Furthermore, I_Lc is the second largest exergy destruction rate. When T_g1 is 543.15–623.15 K, the η_g is improved by increasing T_g1, and I_Lc is maximal at higher than 15.5%. When T_g1 is 543.15–608.15 K, I_Hout is the second largest exergy destruction rate at less than 10%; when T_g1 is 613.15–623.15 K, I_He increases and becomes the second largest given the upper limit of the HTL evaporation temperature. The condenser/evaporator is also a component, which has a large exergy destruction rate. When T_g1 is 578.15–593.15 K, I_ce exceeds I_He and becomes the third largest exergy destruction rate. When T_g1 is 523.15–553.15 K, I_Lpre is the fourth largest exergy destruction rate at higher than 5%; when T_g1 is 573.15–623.15 K, the heat absorption ratio of the jacket cooling water accounting for the total heat absorption decreases, and I_Lpre decreases and becomes the second smallest exergy destruction rate considering the increase in exhaust gas heat absorption. When T_g1 is 568.15 K, the variation in I_Ht is larger than I_Lt because the HTL cycle type changes from a saturated to a superheated cycle. I_p is minimal at less than 1%.

Figure 15 presents that, when cyclohexane is used for HTL, I_Hout and I_Lpre decrease with the increase in T_g1 because η_g and η_jw are improved by increasing T_g1. When T_g1 is 523.15–598.15 K, the optimal HTL evaporation temperature does not reach the upper limit and is suitable for T_g1. I_He decreases initially; when T_g1 increases to 603.15 K, the optimal HTL evaporation temperature reaches the upper limit and is unsuitable for T_g1. I_He then increases. Given that the optimal HTL evaporation temperature does not reach the upper limit initially, the variation in I_Lc is small. With the increase in T_g1, I_Lc initially decreases and later increases; given the increase in I_He, I_Lc decreases with the increase in T_g1 when the optimal HTL evaporation temperature reaches the upper limit. An unchanged HTL condensation temperature corresponds to a small variation in I_Lt. I_Lt initially decreases, then increases, and finally decreases with the increase in T_g1. Considering that I_He decreases initially and then increases, I_ce, I_Ht, and I_p increase initially and later decrease with the increase in T_g1. When T_g1 is 523.15–553.15 K, I_out is maximal at higher than 16%, and I_Lc is the second largest exergy destruction rate. When T_g1 is 558.15–623.15 K, I_out decreases from 15.3% to 8.2% and becomes the second largest exergy destruction rate given the improvement of η_g by increasing T_g1; I_Lc is maximal at higher than 15%. When T_g1 is 523.15–598.15 K, I_He is the third largest exergy destruction rate. However, when T_g1 increases to 603.15 K, I_He rapidly decreases to 4.1% and becomes the sixth largest exergy destruction rate. When T_g1 is 603.15–623.15 K, I_ce is the third largest exergy destruction rate at higher than 7.5%. When T_g1 is 523.15–553.15 K, I_Lpre is the fourth largest exergy destruction rate at higher than 5%; when T_g1 is 573.15–623.15 K, I_Lpre becomes the second smallest exergy destruction rate. Given the increasing heat absorption from exhaust gas with increasing T_g1, I_Ht is higher than I_Lt when T_g1 is 583.15–623.15 K. Considering that the optimal HTL condensation temperature is constant, a minimal change in I_Lt is observed. I_p is the smallest exergy destruction rates of the system.

Figure 16 exhibits that the optimal HTL evaporation temperature does not reach the upper limit when T_g1 is 523.15–613.15 K because benzene is used for HTL. Thus, η_g is improved by increasing T_g1, and I_Hout decreases with the increase in T_g1. When T_g1 increases to 618.15 K, the optimal HTL evaporation temperature reaches the upper limit, and η_g decreases and then I_Hout increases; when T_g1 increases to 623.15 K, I_Hout later decreases considering the increase in η_g. Given the increase in η_jw, I_Lpre decreases with the increase in T_g1. Considering that the optimal HTL evaporation temperature does not reach the upper limit, I_He increases initially and later decreases with the increase in T_g1. The variation is small; when T_g1 increases to 618.15 K, the optimal HTL evaporation temperature reaches the upper limit, and I_He decreases rapidly. The sudden changes in 618.15–623.15 K for other components are also affected by the value of the HTL evaporation temperature. With the increase in T_g1, I_Lc and I_Lt decrease initially and later increase. I_ce, I_Ht, and I_p increase with T_g1. When T_g1 is 523.15–588.15 K, I_Hout is the largest exergy destruction rate at higher than 15%. When T_g1 is 593.15–623.15 K, I_Hout decreases considerably and then I_Lc becomes the largest given the improvement of η_g. When T_g1 is 523.15–613.15 K, I_He is the third largest. When T_g1 is 618.15–623.15 K, I_He decreases rapidly to 4.8%, and I_Ht becomes the third largest because the optimal HTL evaporation temperature reaches the upper limit. When T_g1 is 588.15–623.15 K, I_Lpre is the second smallest; the I_p is the smallest.

In Figure 17, when toluene is used for HTL no sudden changes are observed because the optimal HTL evaporation temperature does not reach the upper limit. Given the improvement of η_g, I_Hout decreases with the increase in T_g1. Considering that the optimal HTL evaporation temperature increases with T_g1, I_He decreases with the increase in T_g1. Furthermore, I_Lc, I_ce, and I_Ht increase with T_g1 due to the decrease in I_Hout and I_He. Given that the HTL condensation temperature is unchanged and the power consumed by the pump is small, the relative variations in I_Lpre, I_Lt, and I_p are less than 0.5% between the maximal and minimal values. Considering the low η_g, I_Hout is the largest exergy destruction rate, and it is followed by I_Lc and I_He. I_p, I_Lpre, and I_Ht are less than the other components with T_g1 of 523.15–623.15 K.

The variations in the exergy destruction rate with T_g1 are different for various HTL working fluids. I_Hout and I_Lc are the top two in most cases, but I_He and I_ce are also important. Given the limit of acid dew point temperature, I_Hout is inevitable for the cyclopentane system; an increase in T_g1 will improve η_g for the cyclohexane, benzene, and toluene systems. Moreover, when cyclopentane is used, and T_g1 is 623.15 K, I_Hout is decreased to 7.8%. Considering the isothermal phase characteristic of pure fluids (When pure working fluid evaporates or condenses at constant pressure, the evaporation or condensation temperature is also constant), significant irreversibilities are observed in the HTL evaporator and LTL condenser [3,52,53], thus leading to large I_Lc and I_He. The use of zeotropic mixtures with non-isothermal phase change characteristics will cause improved temperature matches between the ICE exhaust gas and HTL, LTL, and cooling water [3,43] and then decrease I_Lc and I_He. When T_g1 is high (higher than or equal to 537.15 K for the cyclopentane and cyclohexane systems, 593.15 K for the benzene system, and 598.15 K for the toluene system), I_Lpre is the second smallest exergy destruction rate. I_p is the minimal exergy destruction rate.

6. Conclusions

DORC is used for ICE waste heat recovery. The HTL evaporation temperature, condensation temperature and superheat degree are optimized by genetic algorithm, and the net power output is the objective function. The effects of T_g1 on net power output, thermal efficiency, exergy efficiency, HTL evaporation temperature, HTL condensation temperature, HTL superheat degree, exhaust gas temperature at the exit of the HTL evaporator, heat utilization ratio, and exergy destruction rate are analyzed.

The main conclusions are obtained as follows:

1. The net power output of the DORC is primarily influenced by the HTL working fluid, and the relative deviation between the maximal and minimal net power outputs affected by the LTL working fluid is less than 3%. When T_g1 is 523.15–598.15 K, cyclopentane is the optimal HTL working fluid for maximizing the net power output; when T_g1 is 603.15–618.15 K, cyclohexane is the optimal HTL working fluid; when T_g1 increases to 623.15 K, benzene is the optimal HTL working fluid. R1234ze(E) is the optimal working fluid of LTL.

2. The optimal HTL evaporator temperature increases with T_g1 until reaching the upper limit. The optimal HTL condensation temperature initially increases and then remains unchanged for the cyclopentane system; in addition, it is maintained at a lower limit of the HTL condensation temperature for the cyclohexane, benzene, and toluene systems. Saturated cycle is suitable for these systems. Superheat cycle can improve the net power output for the cyclopentane system with T_g1 of 568.15–623.15 K.

3. The optimal exhaust gas temperature at the exit of the HTL evaporator is not constantly at the lower limit, but is at the lower limit for the cyclopentane system at 568.15–623.15 K; the exhaust gas temperature at the exit of the HTL evaporator is higher than the lower limit for the cyclohexane, benzene and toluene systems. The increase in exhaust gas temperature can improve the heat utilization ratio.

4. Variations in the exergy destruction rates with T_g1 are distinct for the different HTL working fluid systems. I_Hout and I_Lc are the top two in most cases. When cyclopentane is used and exhaust gas temperature is 623.15 K, and the minimal I_Hout is 7.8%. I_p is the minimal exergy destruction rate.