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Exergy-based optimization of an organic Rankine cycle (ORC) for waste heat recovery from an internal combustion engine (ICE)
Accepted Manuscript Exergy-based Optimization of an Organic Rankine Cycle (ORC) for Waste Heat Recovery from an Internal Combustion Engine (ICE) Seyedali Seyedkavoosi, Saeed Javan, Krishna Kota PII: DOI: Reference:
S1359-4311(17)30271-5 http://dx.doi.org/10.1016/j.applthermaleng.2017.07.124 ATE 10792
To appear in:
Applied Thermal Engineering
Received Date: Revised Date: Accepted Date:
13 January 2017 16 June 2017 17 July 2017
Please cite this article as: S. Seyedkavoosi, S. Javan, K. Kota, Exergy-based Optimization of an Organic Rankine Cycle (ORC) for Waste Heat Recovery from an Internal Combustion Engine (ICE), Applied Thermal Engineering (2017), doi: http://dx.doi.org/10.1016/j.applthermaleng.2017.07.124
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Exergy-based Optimization of an Organic Rankine Cycle (ORC) for Waste Heat Recovery from an Internal Combustion Engine (ICE) Seyedali Seyedkavoosi1*, Saeed Javan2, Krishna Kota1 1
Department of Mechanical and Aerospace Engineering, New Mexico State University, NM, USA;
2
Department of Propulsion, KN Toosi University of Technology, Tehran, Iran;
*Author for correspondence: email: [email protected]; Fax (+1-575) 646-6111; Tel (+1-575) 646-6533
Abstract: In this study, exergy analysis of a two-parallel-step organic Rankine cycle (ORC) for waste heat recovery from an internal combustion engine (ICE) is performed. A novel two-step configuration to recover waste heat from the engine coolant fluid and the exhaust gas simultaneously is first introduced. The working fluids considered for this heat recovery system are R-123, R-134a, and water. A comprehensive thermodynamic modeling of the cycle was performed and optimization of the system was carried out to observe the simultaneous effect of key design parameters on the system performance. The net output power and the exergy efficiency were used as the objective functions with a goal of maximizing them. The design variables for this study are the first and second step pressures of the cycle, the pump and the expander isentropic efficiencies, and the exhaust gas temperature after waste heat recovery. The results show R-123 as the best working fluid under the considered conditions, which generates 468 kW of net output power with an exergy efficiency of 21%. A sensitivity study was also performed on the optimized design to identify the component that impacts the ORC performance the most. Keywords: exergy; organic Rankine cycle; internal combustion engine; efficiency; working fluids; waste heat recovery
1. Introduction Considering the strategic importance of hydrocarbon resources, accurate management of them, all the way from the production to consumption process, has attracted a lot of attention during the past decades [1]. For this purpose, several studies were performed on engine thermodynamic cycles. In addition, applied electronic control unit for required decision making resulted in notable improvement in fuel injection time, injected fuel mass flow rate etc. In spite of the fact that many attempts were made in this field to optimize combustion process and cycle operation, there is still a great deal of thermal energy released around the environment as a result of ICE operation limitations. In practice, only one-third of the thermal energy from the fuel changes into efficient mechanical work and there is a considerable proportion of energy wastage through exhaust gases and engine cooling system [2]. Consequently, waste heat recovery techniques for this type of energy system have gained a lot of attention in recent years. Several methods have already been introduced for waste heat recovery from ICEs including thermoelectric, absorption cooling, and Rankine cycle [2]. Waste heat recovery using organic Rankine cycle is recognized as a highly efficient technique compared to other methods [3]. Numerous studies on the application of Rankine cycle in ICEs were conducted. Maizza et al. [7] investigated some thermodynamic and physical properties of several unconventional fluids used in organic Rankine cycles supplied by different waste energy sources. Wipplinger et al. [8] attempted to design a high-pressure, cross flow, stainless steel finned tube heat exchanger recovering applied to recover the waste heat of exhaust gases from ICEs that water side pressure was considered 2 MPa. Drescher et al. [9] developed a software in order to select suitable organic working fluid for waste heat recovery from biomass heat and power plants. All these studies found that the family of alkyl benzenes yielded the highest efficiencies. Endo et al. [10] conducted the exergy analysis of an internal combustion engine and used Rankine cycle to generate hybrid power. They observed that the thermal efficiency of the engine at the speed of 100 km/h increased to 13.2% and using the Rankine cycle was concluded as an efficient way to improve the exergy efficiency of ICEs. Saleh et al. Mehrpooya conducted an exergy analyses of a power plant optimizing solar energy and cold of liquefied natural gas [11]. [12] examined the effect of various working fluids for low-grade temperature Rankine cycle. Wei et al. [13] analyzed two methods for the dynamic modeling of an organic Rankine cycle (ORC) for waste heat recovery. The methods included moving boundary and discretization techniques compared for accuracy, rate and complexity and finally both of them were found to be appropriate, however, the former one was faster to model the system so that it can be more efficient for applications as system control. Mago et al. [14] examined the regenerative organic Rankine cycles using dry working fluids. They concluded that the mentioned configuration results in a higher efficiency compared to simple Rankine cycle configuration. Also, it reduced the amount of waste heat required to produce the same power with a lower irreversibility. Vaja and Gambarotta [15] assessed various configurations for waste heat recovery model based on the ORC from the exhaust gas. They considered three configurations including simple cycle, reheat and regeneration and the results indicated that maximum power generation and efficiency was observed for reheat configuration. Tahir et al. [16] studied the effect of vaned expander for a waste heat recovery Rankine cycle. Srinivasan et al. [17] examined the waste heat recovery potential from exhaust gases of a low-
temperature ICE using an ORC. Tahani et al [18] attempted to introduce two-stage organic Rankine cycles for waste heat recovery from ICEs; this configuration has the ability to recover waste heat from the cooling system and exhaust gases simultaneously. Farzane Gard et al. [19] studied waste heat recovery from a 1.7 liter engine by super critical Rankine cycle. Zhang et al [20] considered a twostage Rankine cycle to recover the waste heat of exhaust gases, coolant fluid, and engine intake air. One stage used to recover heat from exhaust gases and another stage applied to recover remained heat of exhaust gases as well as the heat of two other mentioned resources. They found out that the system has the possibility of enhancing the power 14% to 16% when operates at its highest efficiency. Quoilin et al. [21] proposed criteria to select suitable working fluid and expander type and determined that appropriate selection of these two mentioned items play an important role in waste heat recovery organic Rankine cycle technology. As discussed, most of the previous studies considered configurations such as basic, and basic with preheat and regeneration for maximizing the cycle thermal efficiency. However, Dai et al. [22] stated that in the field of waste heat recovery, the main objective should be the maximization of produced power rather than the thermal efficiency. In this regard, Tahani et al. [23] demonstrated that in simultaneous heat recovery from exhaust gases and coolant, two-stage configuration generates more net output power compared to preheating. Therefore, in this study, a two-parallel-step configuration is investigated for application in the simultaneous recovery of waste heat from the exhaust gases and the coolant. The study focuses on the design of a waste heat recovery system using an ORC to generate electricity and use it in other applications. In order to enhance understanding of the system performance, exergy analysis was used as a tool and the source of irreversibility in each component of the ORC was determined. In addition, a multi-objective optimization with two objective functions (exergy destruction rate and power output) was carried out and a sensitivity analysis was performed to understand the effect of major design parameters on the system performance and identify the potential avenues for improving the system performance. The thermodynamic properties of each state of the system were determined using Engineering Equation Solver (EES) and it was coupled with the MATLAB code to exploit its inbuilt optimization package [24]. The main objectives of the present study are as follows: • Development of a computational code for optimal design of a two-parallel-step Rankine cycle for waste heat recovery simultaneously from the exhaust gases and the engine coolant. • To conduct exergy analysis and use it as a potential tool to design and optimize the system by combining the minimum exergy destruction rate and the maximum output power. • To perform a parametric/sensitivity analysis of the key design variables on the two objective functions to determine the crucial variable that positively impacts the system performance the most.
2. System Description 2.1. Considered ICE
The present study is conducted on a 12 cylinder gas-fired internal combustion engine equipped with a supercharger. The operational data of the engine is summarized in Table 1. According to this information, by recovering exhaust gas heat from 470 oC to 120 oC, about 1700 kW energy recovery will be achieved. Also, engine coolant system releases 1000 kW energy to the environment. Combustion product analysis has shown the mass fraction of each species as follows: 9.1% carbon dioxide, 7.4% water vapor, 74.2% nitrogen, and 9.3% oxygen [15]. Table 1. Operating conditions of the considered ICE [15] Parameter
Value
Output electric power (kW)
2928
Consumed fuel power (kW)
7002
Thermal efficiency (%)
41.8
Engine rotational speed (RPM)
1000
Exhaust gas temperature
470
C)
Exhaust gas mass flow rate (kg/h) 15673 oolant temperature
C)
Coolant volume flow rate (m3/h)
79.9 90
2.2. Two-parallel-step organic Rankine cycle configuration The two-parallel-step organic Rankine cycle configuration is shown in Figure 1. This arrangement for utilizing the energy of exhaust gases from the engine has not been previously studied to the best of authors’ knowledge. The system is comprised of two centrifugal pumps and one expander with two inputs and one output, i.e., a dual expander. The working fluid leaves the condenser at state point 1 and flows in two separate parallel paths. First Step: In this step, the working fluid from the condenser exit is directed into Pump 1 and then enters the heat recovery steam generator (HRG) 1. The rejected heat from the engine coolant system changes the phase of the working fluid to steam which leaves HRG 1 at point 4 and enters the expander as a low-pressure steam. Second Step: In this step, the working fluid flows in parallel with the first step and enters Pump 2 where the pressure increases. This high-pressure liquid enters HRG 2 which utilizes the energy of the exhaust gas and then turns into high-temperature vapor that expands in the dual expander to generate electricity. Since the temperature of the exhaust gas (even at speeds as low as 1000 rpm) is usually higher than the engine coolant, the working fluid is hotter at point 5 than 4. Since it is the same working fluid, with a reasonable matching of the inlet pressures of the two streams with the local pressure of the expander or turbine, it is advantageous and energy-efficient to expand both the streams in a single expander or
turbine with multiple stages by injecting the hot stream at the first stage and the cold stream at a later stage. Such dual expander or turbine designs have been proposed previously where the fuel and the oxidizer were designed to be introduced through two input ports. The dual expander is proposed in this paper as an option to save space (one multi-stage expander vs. two expanders) and detailed design of this expander or other components such as the pumps is not focused upon.
Figure 1: Schematic of the pursued two-parallel-step organic Rankine cycle for waste heat recovery from ICE
2.3 Assumptions Key assumptions used in this work are discussed here. Exergy is the potential tool to assess the energy systems. Exergy has different forms similar to energy. Magnetic and nuclear forms of exergy were neglected in this analysis. The other four major exergies are kinetic, potential, physical, and chemical exergy. It was assumed that the variation in velocity and elevation is not considerable in the ORC and hence the kinetic and potential exergies were considered negligible especially compared to the physical and chemical exergies as the. This assumption is reasonable since the considered ORC design does not include components such as nozzles and/or diffusers that cause large changes in velocity. Furthermore, it is assumed that the exhaust gases do not react and only transfer heat in the HRG. Accordingly, chemical exergy is neglected as well. The isentropic efficiencies of the dual expander and the two pumps were assumed constant. In addition, the exhaust gas temperature after waste heat recovery and the condenser temperature were also assumed constant as their variation is usually very small due to constant engine speed assumed (Table 1) and the phase change processes
respectively. The pursued analysis can be considered reasonable as these assumptions are not expected to particularly alter the qualitative findings. 2.4. Cycle working fluid Working fluids play a significant role in low-grade heat recovery systems. These fluids can be classified into three categories according to the slope of the saturation vapor line in a T-s diagram. They are: a dry fluid with a positive slope; a wet fluid with a negative slope, and an isentropic fluid with infinitely large slope. Liu et al. [25] derived an expression to compute the slope of the saturation vapor curve on a T-s diagram (dT/ds). Defining , the type of the working fluid can be classified among the three aforementioned types. As : a wet fluid.
: a dry fluid,
: an isentropic fluid, and
(1)
Where n was suggested to be 0.375 or 0.38 [25],
represents
, and
denotes enthalpy of
evaporation. Some criteria for working fluid selection for heat recovery ORC were presented in Ref. [23]. In this study, R-123, water, and R-134a were considered. From the T-s diagram (Figure 2) showing the saturated liquid and vapor curves for these fluids, they can be categorized as dry (R-123), wet (water), and isentropic (R-134a) according to the equation 1 in the operating temperature range of a typical heat recovery ORC. Table 2 shows the considered thermodynamic and practical criteria for these fluids. It must be noted that these three fluids also have different values of latent phase change enthalpies with water having the highest value of the three. Thus, their selection also provides scope to consider the impact of the phase change enthalpy on the two chosen objective functions. Table 2. Physical and Thermodynamic properties of the considered working fluids [26] Parameter Working fluid Chemical formula Type ritical temperature C) Critical pressure (MPa) Ozone depletion potential (-) Global warming potential (-) Flammability
R-123
Amount Water
R-134a
C2HCl2F3
H2O
C3H3F5
Dry
Wet
Isentropic
183.7
373.9
101.1
3.66
22.06
4.06
0.01
0.00
0.00
120
0.00
1430
Non-flammable
Non-flammable
Non-flammable
Figure 2. Temperature-entropy diagram of the considered working fluids
3. Exergy Analysis Exergy analysis is a combination of the first and second law of thermodynamics. Many researchers and practicing engineers refer to exergy methods as powerful tools for analyzing, assessing, designing, improving, and optimizing systems and processes. For a control volume in the steady state flow condition, the conservation of mass and energy equations as well as the exergy balance equation are provided below[11, 27, 28]: =
(2) (3) (4)
Net transferred exergy through heat and work can be calculated as follows:
(5)
(6) where ex is specific exergy and is expressed as: (7) Subscript 0 represents the reference condition, which is considered as the ambient condition in this study (i.e. and . Exhaust gas and cooling fluid are the exergy sources of the considered system (8) Exergy destruction in this system occurs in the various components of the heat recovery part including expander, condenser, and pump. The exergy destruction rate for each component of the ORC cycle is defined in Table 3. Table 3. Expression for exergy destruction rate for components of the system Component
Exergy destruction rate
Heat recovery steam generator (hrg) Expander (expd) Condenser (cond) Pump (pmp) Exergy efficiency is another significant indicator which provides a finer understanding of the performance than energy efficiency for system level analysis. Exergy efficiency shows the performance of a system relative to an ideal system. It is defined as the maximum reversible thermal efficiency under equal conditions and is estimated as follows: (8) 4. Results and discussion 4.1. Exergy-based analysis and optimization In this section, the model was used to identify the optimal operating conditions of the system for the three different working fluids through a statistical optimization. The exergy efficiency and the net output power were considered as the objective functions. The first and second step pressures of the cycle i.e., p2 and p3 respectively after the pumps, were considered as the decision variables; the operating ranges of which are tabulated in Table 4. The pinch point limitation and the critical point of the working fluid were the two main considerations that imposed limits on the operating ranges of these decision variables. The critical point limit was imposed as the working fluid does not show distinct liquid and vapor phases above this pressure. This point is the peak of each of the liquid-
vapor saturation curves shown in figure 2. The pinch point is the minimum temperature difference between the available heat source (e.g., exhaust gas) and sink (e.g., ambient air) for the system (or ORC) and the working fluid temperatures in HRGs and the condenser (figure 1) respectively. Imposing this limitation is important as heat exchange between the system and the surroundings is not possible with a lower temperature difference than the pinch point limitation. In other words, if a system (with a constant size) operates very close to the pinch point limit, its performance decreases. Table 4. Confine of decision variables
Operating Range
Decision variable Working fluid R123
(kPa)
Water R134a R123
(kPa)
Water R134a
(200,360) (10,28) (1200,2100) (400, 3600) (100,2500) (2100,3400)
Reason for Limits on the Operating Range
Pinch point limitation
Pinch point & critical point limitation
The values of the expander and pump efficiencies, the exhaust gas and the condenser temperatures are provided in Table 5. Table 5. The value of constant parameters assumed in the optimization Parameter
Value
(%)
80
(%)
80
(°C)
100
(°C)
40
Figure 3 shows the effect of low pressure, p2, on both output power and exergy efficiency of the first step of the cycle for R-123. It can be observed that an increase in this pressure results in an increase in both the output power and the exergy efficiency. Hence, the value of 360 kPa, which is the maximum possible value (Table 4), was selected for p2. Figure 4 demonstrates the effect of the high pressure, p3, on exergy efficiency and net output power of the second stage of the cycle for R-123. With an increase in this pressure, both these quantities exhibited a change of slope and their corresponding maximum values were found to be attained at a pressure of ~2760 kPa. The change of slope in figure 4 can be attributed to the decreasing power and exergy efficiency as the system operates closer to the pinch point limit for R-123. Such decrease was not observed in figure 3 because p2 was much lower than p3.
Figure 3. Net output power and exergy efficiency of low-pressure step for R-123 as the working fluid
Figure 4. Net output power and exergy efficiency of high-pressure step for R-123 as the working fluid Figures 5 and 6 are provided for the first and second stage pressures considering water as the working fluid. Similar trends were observed in this case with water as for the previous case with R123. The optimized pressure for the first and second stages was found to be 28 kPa and 2500 kPa respectively. As thermosphysical properties of water differ from R-123 especially with regards to its very high liquid-vapor phase change enthalpy, a change of slope was not observed in this case even when p3 approaches the pinch point limit. Nevertheless, a decreasing slope was still observed. Figure 7 and 8 show the variation of p2 and p3 on the exergy efficiency and the net output power for R-134a. The trend for p2 was the same as before. However, for increasing p3, the system showed a decreased performance as p3 approached the limiting pressure value (it must be noted that among the three fluids, R-134a has the lowest enthalpy of liquid-vapor phase change). The optimal values for p2 and p3 in this case were found to be 2100 kPa and 2246 kPa, respectively.
Table 6 provides the thermodynamic properties of the considered working fluids at different state points of the cycle for the optimum operating conditions identified for each of these fluids. A particularly interesting observation is the low values of pressures at state points 1, 2, and 4 of the cycle for water and high values of the pressures at the same state points for R-134a. State point 1 corresponds to the condenser exit and state points 2 and 4 correspond to the pressures in the first step. For water, these low pressures might lead to leakage of outside air into the system. For R-134a, the very high operating pressures might cause component damage unless bulky components that could withstand the resulting stresses are employed, which will increase the system weight in the automobile.
Figure 5. Net output power and exergy efficiency of low-pressure step for water as the working fluid
Figure 6. Net output power and exergy efficiency of high-pressure step for water as the working fluid
Table 7 lists the expander power output, pump power input, and exergy efficiency of the cycle for each of the three working fluids. The highest values of the net output power and the exergy efficiency were observed for R-123. Therefore, the ensuing exergy analysis results are presented with R-123 as the working fluid.
Of particular note in this table is the lowest pump power consumption for water. This could be attributed to the following reasons: the mass flow rate of water is much lower than the other two fluids and the density of water in the saturated liquid state is much higher than the other two fluids. Therefore, high density of the liquid phase accompanied with a low density of the vapor phase for working fluid of the ORC can be considered as an advantage. However, because a very small portion of net power output is consumed by the pumping process, the low density of vapor phase can be considered a more important parameter.
Figure 7. Net output power and exergy efficiency of low-pressure step for R-134a as the working fluid
Figure 8. Net output power and exergy efficiency of high-pressure step for R-134a as the working fluid.
Table 6. Thermodynamic property data at different state points of the two-parallel-step ORC for the three working fluids Working Fluid
R-123
Water
R-134a
Property/ Parameter
1
2
3
4
5
6
181.9 45 247.2
360 45.1 247.3
2760 360 2760 46.47 68.22 166 249 424.1 468.6
181.9 56.24 412.5
1.16
1.16
1.16
1.68
1.71
1.75
19.96 9.59 45 188.4 0
11.88 28 45
8.08 2500 45.2
11.88 28 67.51
8.08 2500 224
19.96 9.59 44.97
188.40 190.8
2622
2802
2464
0.64
0.64
0.64
7.79
6.26
7.94
1.50 1161
0.86 2100
0.64 2245
0.86 2100
0.64 2245
1.50 1161
45 115.8
45.85 116.6
45.98 69.61 72.61 116.8 280.4 280.7
45 269.1
0.42
0.42
0.42
0.91
23.06
12.84
10.22 12.84 10.22
0.9
0.9
23.06
Table 7. Expander and pump power and system exergy efficiency for different working fluids. Working Fluid
Parameter
Amount 448.1 20.32
R-123 (%)
21.01 282.6 2.035
Water (%)
13.16 211.2
R-134a
25.65 8.703
Figures 12 and 13 show the exergy destruction rate or anergy rate in different components of the cycle as a function of the pressures in the two steps of the ORC with R-123 as the working fluid. The highest exergy destruction rate can be observed to occur in the HRGs followed by the condenser. Also, the anergy rates for the dual expander and pumps are considerably lower than the components that transfer heat between the system and the sources/sinks to the ORC (i.e., HRGs and the condenser). In general, the total anergy rate was found to decrease with increasing pressure in either step (in accordance with the increase in the exergy efficiency with increasing pressure in figures 3 and 4 for the same working fluid). In both the figures, it can also be observed that with an increasing operating pressure, the anergy rate in the HRGs and the condenser decreased while it showed an increase in the pumps and the dual expander. This is because of the fact that increasing the working fluid pressure increases its temperature and allows for a more isothermal operation in the heat exchange components while it results in increasing the operating temperature range for the pumps and the dual expander. The effect of increasing either p2 or p3 was found to be more pronounced on the dual expander than on the pump, which also affected the total anergy rate causing a change in its slope This could be attributed to the additional entropy generation in the dual expander due to the mixing of the two working fluid streams at different pressures.
Figure 9. Exergy destruction rate vs. pressure for low-pressure stage with R-123 as the working fluid
Figure 10. Exergy destruction rate vs. pressure for high-pressure stage with R-123 as the working fluid.
4.2. Sensitivity analysis In this section, R-123 was assumed as the working fluid with the optimum values of p2, p3, and the state points. The effect of parameters that are not specific to the proposed two-parallel-step ORC such as the expander and pumps’ isentropic efficiencies on the net output power and exergy efficiency are investigated. The aim of this analysis is to understand the importance of these parameters on the two objective functions (i.e., the considered performance metrics) by varying their values since they were kept constant for the optimization study. Figures 14 shows the effect of expander isentropic efficiency on both the net output power and exergy efficiency. As expected, an increase in the expander isentropic efficiency from 60% to 90% (a 30% increase) showed an increase in both these quantities; more specifically, the net output power and the exergy efficiency of the system improved from 331 kW to 506.6 kW (a ~53% increase) and from 15.52% to 23.76% respectively (a ~8% increase).
Exergy efficiency
Net output power
600 Net output power (kW) & Exergy efficiency (%)
506.6 500
448.1 389.5
400
331
300 200 100
15.52
18.27
21.01
23.76
0 60
70
80
90
Expander isentropic efficiency (%)
Figure 11. Effect of expander isentropic efficiency on the net output power and the exergy efficiency of the cycle
Figure 15 illustrates the effect of pump isentropic efficiency on the net output power and the exergy efficiency of the cycle. Again, as expected, with increasing pump isentropic efficiency by 30%, both the quantities showed an increase; however, there is no considerable improvement in these quantities especially when compared to the improvements in figure 14.
Net output power (kW) & Exergy efiiciency (%)
Exergy efficiency 500 450 400 350 300 250 200 150 100 50 0
60
21.01
20.9 70
449.9
448.1
445.7
442.5
20.75
Net output power
80
21.1 90
Pump isentropic efficiency (%)
Figure 12. Effect of pumps isentropic efficiency on net output power and exergy efficiency of the system Comparatively, it is observed that the benefit of improving the expander isentropic efficiency is more conspicuous than increasing the pump isentropic efficiency.
4. Conclusions In this paper, thermodynamic modeling and optimization of a novel two-parallel-step ORC configuration for heat recovery from an ICE heat recovery is presented. The decision variables for the optimization were chosen as the first and second step pressures in the system, which are specific to this new ORC configuration and hence were not studied before. Three different working fluids were studied (a dry, a wet, and an isothermal fluid on the T-s diagram) and the optimal values for these two chosen decision variables were obtained. Using the optimal values, the net output power and the exergy efficiency for each of the three fluids were obtained. Some of the major concluding remarks based on this work are as follows: • Under the chosen conditions, R-123 was found to have the best performance among the three working fluids even though water has the highest value of the liquid-vapor phase change enthalpy. In general, from a thermodynamic perspective, it can be concluded that using a dry fluid on the T-s diagram (here, R-123 whose saturated vapor entropy increases with increasing temperature) as the working fluid for this application could have the potential to realize maximum useful power and exergy efficiencies. From a practical perspective, R-123 has acceptable physical properties to prevent the formation of liquid drops in expander outlet, and environmental properties like low ozone depletion potential, global warming, non-flammability, and non-toxicity. • The pressure of the second step (i.e., the exhaust gas heat recovery step) was found to impact the ORC performance more than the pressure of the first step (i.e., the engine coolant heat recovery step).
The highest exergy destruction rate was found to occur in the heat recovery generators of the ORC. • A sensitivity analysis was also performed to understand the impact of improving the expander and pump efficiencies on the performance. This analysis showed that pursuing improvements to the pump isentropic efficiency is not worthwhile. However, it was observed from the results that a 30% improvement in the isentropic efficiency of the dual expander could result in a 53% increase in the net output power and ~8% increase in the cycle exergy efficiency. This implies that future designs of ORC for this application should consider using high efficiency expanders.
Funding: This research did not receive any specific grant or award from funding agencies in the public, commercial, or not-for-profit sectors.
Nomenclature
CP ex
h P T s
specific heat at constant pressure, [kJ.kg–1·K–1] specific exergy [kJ.kg–1] exergy flow rate [kW] exergy destruction rate [kW] specific enthalpy [kJ.kg–1] mass flow rate [kg·s–1] pressure [kPa] heat transfer rate [kW] temperature [°C] specific entropy [kJ/kg·K–1] work rate [kW]
Greek symbols efficiency [%]
Subscripts C cond e exh expd H HP hrg i LP o pmp Q W 0
cold condenser exit condition exhaust gas expander hot high pressure Heat recovery steam generator inlet condition low pressure output pump heat transfer work reference environment condition
Acronyms HRG ICE RPM ORC
heat recovery steam generator internal combustion engine round per minute (engine speed) organic Rankine cycle
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Highlights 1. A novel two-parallel-step organic Rankine cycle (ORC) is proposed for waste heat recovery from internal combustion engines, where step 1 recovers heat from the engine coolant while step 2 simultaneously recovers heat from the engine exhaust gas 2. Three different working fluids were analyzed and it was observed from the results that the fluid with the highest enthalpy of liquid-vapor phase change may not always be the optimum choice. 3. It was found that increasing the isentropic efficiency of the proposed dual expander offers a great benefit to the ORC performance.
S1359-4311(17)30271-5 http://dx.doi.org/10.1016/j.applthermaleng.2017.07.124 ATE 10792
To appear in:
Applied Thermal Engineering
Received Date: Revised Date: Accepted Date:
13 January 2017 16 June 2017 17 July 2017
Please cite this article as: S. Seyedkavoosi, S. Javan, K. Kota, Exergy-based Optimization of an Organic Rankine Cycle (ORC) for Waste Heat Recovery from an Internal Combustion Engine (ICE), Applied Thermal Engineering (2017), doi: http://dx.doi.org/10.1016/j.applthermaleng.2017.07.124
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Exergy-based Optimization of an Organic Rankine Cycle (ORC) for Waste Heat Recovery from an Internal Combustion Engine (ICE) Seyedali Seyedkavoosi1*, Saeed Javan2, Krishna Kota1 1
Department of Mechanical and Aerospace Engineering, New Mexico State University, NM, USA;
2
Department of Propulsion, KN Toosi University of Technology, Tehran, Iran;
*Author for correspondence: email: [email protected]; Fax (+1-575) 646-6111; Tel (+1-575) 646-6533
Abstract: In this study, exergy analysis of a two-parallel-step organic Rankine cycle (ORC) for waste heat recovery from an internal combustion engine (ICE) is performed. A novel two-step configuration to recover waste heat from the engine coolant fluid and the exhaust gas simultaneously is first introduced. The working fluids considered for this heat recovery system are R-123, R-134a, and water. A comprehensive thermodynamic modeling of the cycle was performed and optimization of the system was carried out to observe the simultaneous effect of key design parameters on the system performance. The net output power and the exergy efficiency were used as the objective functions with a goal of maximizing them. The design variables for this study are the first and second step pressures of the cycle, the pump and the expander isentropic efficiencies, and the exhaust gas temperature after waste heat recovery. The results show R-123 as the best working fluid under the considered conditions, which generates 468 kW of net output power with an exergy efficiency of 21%. A sensitivity study was also performed on the optimized design to identify the component that impacts the ORC performance the most. Keywords: exergy; organic Rankine cycle; internal combustion engine; efficiency; working fluids; waste heat recovery
1. Introduction Considering the strategic importance of hydrocarbon resources, accurate management of them, all the way from the production to consumption process, has attracted a lot of attention during the past decades [1]. For this purpose, several studies were performed on engine thermodynamic cycles. In addition, applied electronic control unit for required decision making resulted in notable improvement in fuel injection time, injected fuel mass flow rate etc. In spite of the fact that many attempts were made in this field to optimize combustion process and cycle operation, there is still a great deal of thermal energy released around the environment as a result of ICE operation limitations. In practice, only one-third of the thermal energy from the fuel changes into efficient mechanical work and there is a considerable proportion of energy wastage through exhaust gases and engine cooling system [2]. Consequently, waste heat recovery techniques for this type of energy system have gained a lot of attention in recent years. Several methods have already been introduced for waste heat recovery from ICEs including thermoelectric, absorption cooling, and Rankine cycle [2]. Waste heat recovery using organic Rankine cycle is recognized as a highly efficient technique compared to other methods [3]. Numerous studies on the application of Rankine cycle in ICEs were conducted. Maizza et al. [7] investigated some thermodynamic and physical properties of several unconventional fluids used in organic Rankine cycles supplied by different waste energy sources. Wipplinger et al. [8] attempted to design a high-pressure, cross flow, stainless steel finned tube heat exchanger recovering applied to recover the waste heat of exhaust gases from ICEs that water side pressure was considered 2 MPa. Drescher et al. [9] developed a software in order to select suitable organic working fluid for waste heat recovery from biomass heat and power plants. All these studies found that the family of alkyl benzenes yielded the highest efficiencies. Endo et al. [10] conducted the exergy analysis of an internal combustion engine and used Rankine cycle to generate hybrid power. They observed that the thermal efficiency of the engine at the speed of 100 km/h increased to 13.2% and using the Rankine cycle was concluded as an efficient way to improve the exergy efficiency of ICEs. Saleh et al. Mehrpooya conducted an exergy analyses of a power plant optimizing solar energy and cold of liquefied natural gas [11]. [12] examined the effect of various working fluids for low-grade temperature Rankine cycle. Wei et al. [13] analyzed two methods for the dynamic modeling of an organic Rankine cycle (ORC) for waste heat recovery. The methods included moving boundary and discretization techniques compared for accuracy, rate and complexity and finally both of them were found to be appropriate, however, the former one was faster to model the system so that it can be more efficient for applications as system control. Mago et al. [14] examined the regenerative organic Rankine cycles using dry working fluids. They concluded that the mentioned configuration results in a higher efficiency compared to simple Rankine cycle configuration. Also, it reduced the amount of waste heat required to produce the same power with a lower irreversibility. Vaja and Gambarotta [15] assessed various configurations for waste heat recovery model based on the ORC from the exhaust gas. They considered three configurations including simple cycle, reheat and regeneration and the results indicated that maximum power generation and efficiency was observed for reheat configuration. Tahir et al. [16] studied the effect of vaned expander for a waste heat recovery Rankine cycle. Srinivasan et al. [17] examined the waste heat recovery potential from exhaust gases of a low-
temperature ICE using an ORC. Tahani et al [18] attempted to introduce two-stage organic Rankine cycles for waste heat recovery from ICEs; this configuration has the ability to recover waste heat from the cooling system and exhaust gases simultaneously. Farzane Gard et al. [19] studied waste heat recovery from a 1.7 liter engine by super critical Rankine cycle. Zhang et al [20] considered a twostage Rankine cycle to recover the waste heat of exhaust gases, coolant fluid, and engine intake air. One stage used to recover heat from exhaust gases and another stage applied to recover remained heat of exhaust gases as well as the heat of two other mentioned resources. They found out that the system has the possibility of enhancing the power 14% to 16% when operates at its highest efficiency. Quoilin et al. [21] proposed criteria to select suitable working fluid and expander type and determined that appropriate selection of these two mentioned items play an important role in waste heat recovery organic Rankine cycle technology. As discussed, most of the previous studies considered configurations such as basic, and basic with preheat and regeneration for maximizing the cycle thermal efficiency. However, Dai et al. [22] stated that in the field of waste heat recovery, the main objective should be the maximization of produced power rather than the thermal efficiency. In this regard, Tahani et al. [23] demonstrated that in simultaneous heat recovery from exhaust gases and coolant, two-stage configuration generates more net output power compared to preheating. Therefore, in this study, a two-parallel-step configuration is investigated for application in the simultaneous recovery of waste heat from the exhaust gases and the coolant. The study focuses on the design of a waste heat recovery system using an ORC to generate electricity and use it in other applications. In order to enhance understanding of the system performance, exergy analysis was used as a tool and the source of irreversibility in each component of the ORC was determined. In addition, a multi-objective optimization with two objective functions (exergy destruction rate and power output) was carried out and a sensitivity analysis was performed to understand the effect of major design parameters on the system performance and identify the potential avenues for improving the system performance. The thermodynamic properties of each state of the system were determined using Engineering Equation Solver (EES) and it was coupled with the MATLAB code to exploit its inbuilt optimization package [24]. The main objectives of the present study are as follows: • Development of a computational code for optimal design of a two-parallel-step Rankine cycle for waste heat recovery simultaneously from the exhaust gases and the engine coolant. • To conduct exergy analysis and use it as a potential tool to design and optimize the system by combining the minimum exergy destruction rate and the maximum output power. • To perform a parametric/sensitivity analysis of the key design variables on the two objective functions to determine the crucial variable that positively impacts the system performance the most.
2. System Description 2.1. Considered ICE
The present study is conducted on a 12 cylinder gas-fired internal combustion engine equipped with a supercharger. The operational data of the engine is summarized in Table 1. According to this information, by recovering exhaust gas heat from 470 oC to 120 oC, about 1700 kW energy recovery will be achieved. Also, engine coolant system releases 1000 kW energy to the environment. Combustion product analysis has shown the mass fraction of each species as follows: 9.1% carbon dioxide, 7.4% water vapor, 74.2% nitrogen, and 9.3% oxygen [15]. Table 1. Operating conditions of the considered ICE [15] Parameter
Value
Output electric power (kW)
2928
Consumed fuel power (kW)
7002
Thermal efficiency (%)
41.8
Engine rotational speed (RPM)
1000
Exhaust gas temperature
470
C)
Exhaust gas mass flow rate (kg/h) 15673 oolant temperature
C)
Coolant volume flow rate (m3/h)
79.9 90
2.2. Two-parallel-step organic Rankine cycle configuration The two-parallel-step organic Rankine cycle configuration is shown in Figure 1. This arrangement for utilizing the energy of exhaust gases from the engine has not been previously studied to the best of authors’ knowledge. The system is comprised of two centrifugal pumps and one expander with two inputs and one output, i.e., a dual expander. The working fluid leaves the condenser at state point 1 and flows in two separate parallel paths. First Step: In this step, the working fluid from the condenser exit is directed into Pump 1 and then enters the heat recovery steam generator (HRG) 1. The rejected heat from the engine coolant system changes the phase of the working fluid to steam which leaves HRG 1 at point 4 and enters the expander as a low-pressure steam. Second Step: In this step, the working fluid flows in parallel with the first step and enters Pump 2 where the pressure increases. This high-pressure liquid enters HRG 2 which utilizes the energy of the exhaust gas and then turns into high-temperature vapor that expands in the dual expander to generate electricity. Since the temperature of the exhaust gas (even at speeds as low as 1000 rpm) is usually higher than the engine coolant, the working fluid is hotter at point 5 than 4. Since it is the same working fluid, with a reasonable matching of the inlet pressures of the two streams with the local pressure of the expander or turbine, it is advantageous and energy-efficient to expand both the streams in a single expander or
turbine with multiple stages by injecting the hot stream at the first stage and the cold stream at a later stage. Such dual expander or turbine designs have been proposed previously where the fuel and the oxidizer were designed to be introduced through two input ports. The dual expander is proposed in this paper as an option to save space (one multi-stage expander vs. two expanders) and detailed design of this expander or other components such as the pumps is not focused upon.
Figure 1: Schematic of the pursued two-parallel-step organic Rankine cycle for waste heat recovery from ICE
2.3 Assumptions Key assumptions used in this work are discussed here. Exergy is the potential tool to assess the energy systems. Exergy has different forms similar to energy. Magnetic and nuclear forms of exergy were neglected in this analysis. The other four major exergies are kinetic, potential, physical, and chemical exergy. It was assumed that the variation in velocity and elevation is not considerable in the ORC and hence the kinetic and potential exergies were considered negligible especially compared to the physical and chemical exergies as the. This assumption is reasonable since the considered ORC design does not include components such as nozzles and/or diffusers that cause large changes in velocity. Furthermore, it is assumed that the exhaust gases do not react and only transfer heat in the HRG. Accordingly, chemical exergy is neglected as well. The isentropic efficiencies of the dual expander and the two pumps were assumed constant. In addition, the exhaust gas temperature after waste heat recovery and the condenser temperature were also assumed constant as their variation is usually very small due to constant engine speed assumed (Table 1) and the phase change processes
respectively. The pursued analysis can be considered reasonable as these assumptions are not expected to particularly alter the qualitative findings. 2.4. Cycle working fluid Working fluids play a significant role in low-grade heat recovery systems. These fluids can be classified into three categories according to the slope of the saturation vapor line in a T-s diagram. They are: a dry fluid with a positive slope; a wet fluid with a negative slope, and an isentropic fluid with infinitely large slope. Liu et al. [25] derived an expression to compute the slope of the saturation vapor curve on a T-s diagram (dT/ds). Defining , the type of the working fluid can be classified among the three aforementioned types. As : a wet fluid.
: a dry fluid,
: an isentropic fluid, and
(1)
Where n was suggested to be 0.375 or 0.38 [25],
represents
, and
denotes enthalpy of
evaporation. Some criteria for working fluid selection for heat recovery ORC were presented in Ref. [23]. In this study, R-123, water, and R-134a were considered. From the T-s diagram (Figure 2) showing the saturated liquid and vapor curves for these fluids, they can be categorized as dry (R-123), wet (water), and isentropic (R-134a) according to the equation 1 in the operating temperature range of a typical heat recovery ORC. Table 2 shows the considered thermodynamic and practical criteria for these fluids. It must be noted that these three fluids also have different values of latent phase change enthalpies with water having the highest value of the three. Thus, their selection also provides scope to consider the impact of the phase change enthalpy on the two chosen objective functions. Table 2. Physical and Thermodynamic properties of the considered working fluids [26] Parameter Working fluid Chemical formula Type ritical temperature C) Critical pressure (MPa) Ozone depletion potential (-) Global warming potential (-) Flammability
R-123
Amount Water
R-134a
C2HCl2F3
H2O
C3H3F5
Dry
Wet
Isentropic
183.7
373.9
101.1
3.66
22.06
4.06
0.01
0.00
0.00
120
0.00
1430
Non-flammable
Non-flammable
Non-flammable
Figure 2. Temperature-entropy diagram of the considered working fluids
3. Exergy Analysis Exergy analysis is a combination of the first and second law of thermodynamics. Many researchers and practicing engineers refer to exergy methods as powerful tools for analyzing, assessing, designing, improving, and optimizing systems and processes. For a control volume in the steady state flow condition, the conservation of mass and energy equations as well as the exergy balance equation are provided below[11, 27, 28]: =
(2) (3) (4)
Net transferred exergy through heat and work can be calculated as follows:
(5)
(6) where ex is specific exergy and is expressed as: (7) Subscript 0 represents the reference condition, which is considered as the ambient condition in this study (i.e. and . Exhaust gas and cooling fluid are the exergy sources of the considered system (8) Exergy destruction in this system occurs in the various components of the heat recovery part including expander, condenser, and pump. The exergy destruction rate for each component of the ORC cycle is defined in Table 3. Table 3. Expression for exergy destruction rate for components of the system Component
Exergy destruction rate
Heat recovery steam generator (hrg) Expander (expd) Condenser (cond) Pump (pmp) Exergy efficiency is another significant indicator which provides a finer understanding of the performance than energy efficiency for system level analysis. Exergy efficiency shows the performance of a system relative to an ideal system. It is defined as the maximum reversible thermal efficiency under equal conditions and is estimated as follows: (8) 4. Results and discussion 4.1. Exergy-based analysis and optimization In this section, the model was used to identify the optimal operating conditions of the system for the three different working fluids through a statistical optimization. The exergy efficiency and the net output power were considered as the objective functions. The first and second step pressures of the cycle i.e., p2 and p3 respectively after the pumps, were considered as the decision variables; the operating ranges of which are tabulated in Table 4. The pinch point limitation and the critical point of the working fluid were the two main considerations that imposed limits on the operating ranges of these decision variables. The critical point limit was imposed as the working fluid does not show distinct liquid and vapor phases above this pressure. This point is the peak of each of the liquid-
vapor saturation curves shown in figure 2. The pinch point is the minimum temperature difference between the available heat source (e.g., exhaust gas) and sink (e.g., ambient air) for the system (or ORC) and the working fluid temperatures in HRGs and the condenser (figure 1) respectively. Imposing this limitation is important as heat exchange between the system and the surroundings is not possible with a lower temperature difference than the pinch point limitation. In other words, if a system (with a constant size) operates very close to the pinch point limit, its performance decreases. Table 4. Confine of decision variables
Operating Range
Decision variable Working fluid R123
(kPa)
Water R134a R123
(kPa)
Water R134a
(200,360) (10,28) (1200,2100) (400, 3600) (100,2500) (2100,3400)
Reason for Limits on the Operating Range
Pinch point limitation
Pinch point & critical point limitation
The values of the expander and pump efficiencies, the exhaust gas and the condenser temperatures are provided in Table 5. Table 5. The value of constant parameters assumed in the optimization Parameter
Value
(%)
80
(%)
80
(°C)
100
(°C)
40
Figure 3 shows the effect of low pressure, p2, on both output power and exergy efficiency of the first step of the cycle for R-123. It can be observed that an increase in this pressure results in an increase in both the output power and the exergy efficiency. Hence, the value of 360 kPa, which is the maximum possible value (Table 4), was selected for p2. Figure 4 demonstrates the effect of the high pressure, p3, on exergy efficiency and net output power of the second stage of the cycle for R-123. With an increase in this pressure, both these quantities exhibited a change of slope and their corresponding maximum values were found to be attained at a pressure of ~2760 kPa. The change of slope in figure 4 can be attributed to the decreasing power and exergy efficiency as the system operates closer to the pinch point limit for R-123. Such decrease was not observed in figure 3 because p2 was much lower than p3.
Figure 3. Net output power and exergy efficiency of low-pressure step for R-123 as the working fluid
Figure 4. Net output power and exergy efficiency of high-pressure step for R-123 as the working fluid Figures 5 and 6 are provided for the first and second stage pressures considering water as the working fluid. Similar trends were observed in this case with water as for the previous case with R123. The optimized pressure for the first and second stages was found to be 28 kPa and 2500 kPa respectively. As thermosphysical properties of water differ from R-123 especially with regards to its very high liquid-vapor phase change enthalpy, a change of slope was not observed in this case even when p3 approaches the pinch point limit. Nevertheless, a decreasing slope was still observed. Figure 7 and 8 show the variation of p2 and p3 on the exergy efficiency and the net output power for R-134a. The trend for p2 was the same as before. However, for increasing p3, the system showed a decreased performance as p3 approached the limiting pressure value (it must be noted that among the three fluids, R-134a has the lowest enthalpy of liquid-vapor phase change). The optimal values for p2 and p3 in this case were found to be 2100 kPa and 2246 kPa, respectively.
Table 6 provides the thermodynamic properties of the considered working fluids at different state points of the cycle for the optimum operating conditions identified for each of these fluids. A particularly interesting observation is the low values of pressures at state points 1, 2, and 4 of the cycle for water and high values of the pressures at the same state points for R-134a. State point 1 corresponds to the condenser exit and state points 2 and 4 correspond to the pressures in the first step. For water, these low pressures might lead to leakage of outside air into the system. For R-134a, the very high operating pressures might cause component damage unless bulky components that could withstand the resulting stresses are employed, which will increase the system weight in the automobile.
Figure 5. Net output power and exergy efficiency of low-pressure step for water as the working fluid
Figure 6. Net output power and exergy efficiency of high-pressure step for water as the working fluid
Table 7 lists the expander power output, pump power input, and exergy efficiency of the cycle for each of the three working fluids. The highest values of the net output power and the exergy efficiency were observed for R-123. Therefore, the ensuing exergy analysis results are presented with R-123 as the working fluid.
Of particular note in this table is the lowest pump power consumption for water. This could be attributed to the following reasons: the mass flow rate of water is much lower than the other two fluids and the density of water in the saturated liquid state is much higher than the other two fluids. Therefore, high density of the liquid phase accompanied with a low density of the vapor phase for working fluid of the ORC can be considered as an advantage. However, because a very small portion of net power output is consumed by the pumping process, the low density of vapor phase can be considered a more important parameter.
Figure 7. Net output power and exergy efficiency of low-pressure step for R-134a as the working fluid
Figure 8. Net output power and exergy efficiency of high-pressure step for R-134a as the working fluid.
Table 6. Thermodynamic property data at different state points of the two-parallel-step ORC for the three working fluids Working Fluid
R-123
Water
R-134a
Property/ Parameter
1
2
3
4
5
6
181.9 45 247.2
360 45.1 247.3
2760 360 2760 46.47 68.22 166 249 424.1 468.6
181.9 56.24 412.5
1.16
1.16
1.16
1.68
1.71
1.75
19.96 9.59 45 188.4 0
11.88 28 45
8.08 2500 45.2
11.88 28 67.51
8.08 2500 224
19.96 9.59 44.97
188.40 190.8
2622
2802
2464
0.64
0.64
0.64
7.79
6.26
7.94
1.50 1161
0.86 2100
0.64 2245
0.86 2100
0.64 2245
1.50 1161
45 115.8
45.85 116.6
45.98 69.61 72.61 116.8 280.4 280.7
45 269.1
0.42
0.42
0.42
0.91
23.06
12.84
10.22 12.84 10.22
0.9
0.9
23.06
Table 7. Expander and pump power and system exergy efficiency for different working fluids. Working Fluid
Parameter
Amount 448.1 20.32
R-123 (%)
21.01 282.6 2.035
Water (%)
13.16 211.2
R-134a
25.65 8.703
Figures 12 and 13 show the exergy destruction rate or anergy rate in different components of the cycle as a function of the pressures in the two steps of the ORC with R-123 as the working fluid. The highest exergy destruction rate can be observed to occur in the HRGs followed by the condenser. Also, the anergy rates for the dual expander and pumps are considerably lower than the components that transfer heat between the system and the sources/sinks to the ORC (i.e., HRGs and the condenser). In general, the total anergy rate was found to decrease with increasing pressure in either step (in accordance with the increase in the exergy efficiency with increasing pressure in figures 3 and 4 for the same working fluid). In both the figures, it can also be observed that with an increasing operating pressure, the anergy rate in the HRGs and the condenser decreased while it showed an increase in the pumps and the dual expander. This is because of the fact that increasing the working fluid pressure increases its temperature and allows for a more isothermal operation in the heat exchange components while it results in increasing the operating temperature range for the pumps and the dual expander. The effect of increasing either p2 or p3 was found to be more pronounced on the dual expander than on the pump, which also affected the total anergy rate causing a change in its slope This could be attributed to the additional entropy generation in the dual expander due to the mixing of the two working fluid streams at different pressures.
Figure 9. Exergy destruction rate vs. pressure for low-pressure stage with R-123 as the working fluid
Figure 10. Exergy destruction rate vs. pressure for high-pressure stage with R-123 as the working fluid.
4.2. Sensitivity analysis In this section, R-123 was assumed as the working fluid with the optimum values of p2, p3, and the state points. The effect of parameters that are not specific to the proposed two-parallel-step ORC such as the expander and pumps’ isentropic efficiencies on the net output power and exergy efficiency are investigated. The aim of this analysis is to understand the importance of these parameters on the two objective functions (i.e., the considered performance metrics) by varying their values since they were kept constant for the optimization study. Figures 14 shows the effect of expander isentropic efficiency on both the net output power and exergy efficiency. As expected, an increase in the expander isentropic efficiency from 60% to 90% (a 30% increase) showed an increase in both these quantities; more specifically, the net output power and the exergy efficiency of the system improved from 331 kW to 506.6 kW (a ~53% increase) and from 15.52% to 23.76% respectively (a ~8% increase).
Exergy efficiency
Net output power
600 Net output power (kW) & Exergy efficiency (%)
506.6 500
448.1 389.5
400
331
300 200 100
15.52
18.27
21.01
23.76
0 60
70
80
90
Expander isentropic efficiency (%)
Figure 11. Effect of expander isentropic efficiency on the net output power and the exergy efficiency of the cycle
Figure 15 illustrates the effect of pump isentropic efficiency on the net output power and the exergy efficiency of the cycle. Again, as expected, with increasing pump isentropic efficiency by 30%, both the quantities showed an increase; however, there is no considerable improvement in these quantities especially when compared to the improvements in figure 14.
Net output power (kW) & Exergy efiiciency (%)
Exergy efficiency 500 450 400 350 300 250 200 150 100 50 0
60
21.01
20.9 70
449.9
448.1
445.7
442.5
20.75
Net output power
80
21.1 90
Pump isentropic efficiency (%)
Figure 12. Effect of pumps isentropic efficiency on net output power and exergy efficiency of the system Comparatively, it is observed that the benefit of improving the expander isentropic efficiency is more conspicuous than increasing the pump isentropic efficiency.
4. Conclusions In this paper, thermodynamic modeling and optimization of a novel two-parallel-step ORC configuration for heat recovery from an ICE heat recovery is presented. The decision variables for the optimization were chosen as the first and second step pressures in the system, which are specific to this new ORC configuration and hence were not studied before. Three different working fluids were studied (a dry, a wet, and an isothermal fluid on the T-s diagram) and the optimal values for these two chosen decision variables were obtained. Using the optimal values, the net output power and the exergy efficiency for each of the three fluids were obtained. Some of the major concluding remarks based on this work are as follows: • Under the chosen conditions, R-123 was found to have the best performance among the three working fluids even though water has the highest value of the liquid-vapor phase change enthalpy. In general, from a thermodynamic perspective, it can be concluded that using a dry fluid on the T-s diagram (here, R-123 whose saturated vapor entropy increases with increasing temperature) as the working fluid for this application could have the potential to realize maximum useful power and exergy efficiencies. From a practical perspective, R-123 has acceptable physical properties to prevent the formation of liquid drops in expander outlet, and environmental properties like low ozone depletion potential, global warming, non-flammability, and non-toxicity. • The pressure of the second step (i.e., the exhaust gas heat recovery step) was found to impact the ORC performance more than the pressure of the first step (i.e., the engine coolant heat recovery step).
The highest exergy destruction rate was found to occur in the heat recovery generators of the ORC. • A sensitivity analysis was also performed to understand the impact of improving the expander and pump efficiencies on the performance. This analysis showed that pursuing improvements to the pump isentropic efficiency is not worthwhile. However, it was observed from the results that a 30% improvement in the isentropic efficiency of the dual expander could result in a 53% increase in the net output power and ~8% increase in the cycle exergy efficiency. This implies that future designs of ORC for this application should consider using high efficiency expanders.
Funding: This research did not receive any specific grant or award from funding agencies in the public, commercial, or not-for-profit sectors.
Nomenclature
CP ex
h P T s
specific heat at constant pressure, [kJ.kg–1·K–1] specific exergy [kJ.kg–1] exergy flow rate [kW] exergy destruction rate [kW] specific enthalpy [kJ.kg–1] mass flow rate [kg·s–1] pressure [kPa] heat transfer rate [kW] temperature [°C] specific entropy [kJ/kg·K–1] work rate [kW]
Greek symbols efficiency [%]
Subscripts C cond e exh expd H HP hrg i LP o pmp Q W 0
cold condenser exit condition exhaust gas expander hot high pressure Heat recovery steam generator inlet condition low pressure output pump heat transfer work reference environment condition
Acronyms HRG ICE RPM ORC
heat recovery steam generator internal combustion engine round per minute (engine speed) organic Rankine cycle
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Highlights 1. A novel two-parallel-step organic Rankine cycle (ORC) is proposed for waste heat recovery from internal combustion engines, where step 1 recovers heat from the engine coolant while step 2 simultaneously recovers heat from the engine exhaust gas 2. Three different working fluids were analyzed and it was observed from the results that the fluid with the highest enthalpy of liquid-vapor phase change may not always be the optimum choice. 3. It was found that increasing the isentropic efficiency of the proposed dual expander offers a great benefit to the ORC performance.