Diesel engine waste heat recovery system comprehensive optimization based on system and heat exchanger simulation

Da Li; Qiang Sun; Ke Sun; Guodong Zhang; Shuzhan Bai; Guoxiang Li

doi:10.1515/phys-2021-0039

Open Access Published by De Gruyter Open Access July 2, 2021

Diesel engine waste heat recovery system comprehensive optimization based on system and heat exchanger simulation

Da Li , Qiang Sun , Ke Sun , Guodong Zhang , Shuzhan Bai and Guoxiang Li

From the journal Open Physics

https://doi.org/10.1515/phys-2021-0039

Abstract

To further improve the thermal efficiency of diesel engines, a waste heat recovery system model utilizing organic Rankine cycle (ORC) is constructed and verified through system bench test and heat exchanger bench test. To recover waste heat from diesel engine exhaust, ethanol, cyclopentane, cyclohexane, R1233zd (E), and R245fa were selected for comparison. The quality of heat source, the quality of evaporator, the system output, and the system complicity were taken as variables for comparison. Analysis shows that for ORC systems without recuperator, ethanol system has the best system output of the five in a wide operation temper range, with the highest exergy efficiency of 24.1%, yet the exergy efficiency increase after the application of recuperator, 9.0%, is limited. For low temperature exhaust, cyclopentane system has the best performance with or without recuperator, and the cyclopentane system with recuperator has the best performance in terms of exergy efficiency, 27.6%, though complex heat exchangers are also required for high power output. The system output of the R1233zd system is better than the R245fa system, yet the advantage of low evaporate temperature can be better utilized for low quality waste heat recovery.

Keywords: organic Rankine cycle; exhaust; working fluid; recuperator

Nomenclature

E: power output, kW
m: mass flow rate, kg/s
Q: heat flux, kW
h: enthalpy, kJ/kg
η: efficiency
out: outlet
s: heat source
r: working fluid
re: recuperated

Subscripts and superscripts

eva: evaporator
exp: expander
in: inlet

Acronyms

ORC: organic Rankine cycle
EGR: exhaust gas recirculation
PTD: pinch point temperature difference
CO₂: carbon dioxide

1 Introduction

As the most favorable power source for heavy-duty road vehicles, the thermal efficiency of diesel engines has increased significantly in recent decades. However, other methods of waste heat recovery also need to be applied, to further increase system exergy efficiency and meet new or upcoming regulations of CO₂ emission. A large proportion of combustion energy would inevitably be lost through engine cooling system and exhaust emissions. The waste heat recovery system using organic Rankine cycle (ORC) can effectively recover waste heat from low quantity heat sources [1]. The ORC system structure is shown in Figure 1. High pressure working fluid recovers waste heat in the evaporation process, exchanging heat within the evaporator, with or without separate preheater and superheater. Then the high pressure gas expands in the expander and generates kinetic power output through the expansion process. After expansion, working fluid condenses in the condenser and flows back to the fluid tank, ready for another cycle.

Figure 1

ORC system structure.

Conditions of heat sources are essential for ORC system working fluid selection. Studies of stationary ORC systems [2,3], though valuable for system analysis and simulation, still have much difference with ORC systems for road vehicles. To recover waste heat from heavy-duty diesel engines, Preißinger et al. [4] examined 3,000 promising working fluid candidates and rank ethanol as the best ORC working fluid for heavy-duty trucks, as well as passenger cars. Amicabile et al. [5] propose a comprehensive design methodology to optimize the ORC system, and separate evaporator and superheater were applied to recover waste heat from engine exhaust and Exhaust Gas Recirculation (EGR) cooler. Among ethanol, pentane, and R245fa, Amicabile suggests ethanol has both the best performance and the minimum capital cost. Other researches focused on dry fluids with low evaporate temperature, to recover waste heat from low quality heat sources. Yang et al. [6] suggested R1233zd (E) and other fluids as better replacement, while Talluri et al. [7] investigated an ORC Tesla turbine through experiment using R1233zd (E) as working fluid. Chen et al. [8] proposed a confluent cascade expansion ORC system for engine waste heat recovery, using single fluid for both high-temperature and low temperature recovery, and cyclopentane is analyzed to be regarded as the most suitable working fluid for this novel system. Li et al. [9] created a CO₂ transcritical power cycle using single working fluid with low evaporate temperature; the system has utilized 48.9% of the exhaust and 72.8% of the coolant energy.

Heat exchangers are essential components of ORC systems. Preheater, evaporator, superheater, and recuperator determined the total waste heat recovery, and efficiencies of heat exchangers are important for ORC system structure design. For simple and compact ORC system structure, Holik et al. [10] implemented a two-objective optimization based on the maximization of power output and minimization of the total heat exchanger surface area and suggested that recuperator is not advisable for compact ethanol ORC system. Amicabile et al. [5] considered layout with and without recuperator and also suggested that the ethanol system lay out without recuperator has the minimum capital cost. The complicate systems of Shu et al. [11] and Li et al. [9] both take recuperator into consideration.

Turbine expander [12], though promising for ORC system, is less advisable for wet fluid expansion. Song et al. [13] studied and summarized the application of a scroll expander in ORC system with higher efficiency in single working condition and droplet tolerance. When using ethanol and other wet working fluids with relatively large expansion, the piston expander has the advantage of sufficient energy recovery. Li et al. [14] analyzed the output of the free single-piston expander used in the compact ORC system and optimized the control strategy. Han et al. [15] conducted an experimental study on the application of the rotary piston expander in the ORC system. Piston expander can achieve large expansion ratio without significant efficiency loss, and the scroll expander can achieve higher isentropic efficiency at lower expansion ratio. As suggested by Chen et al. [8], large expansion ratio and high expander efficiency can be both achieved by using multiple high efficiency expanders, yet the cost of the system will increase significantly. The paper chose piston expander with wide expansion ratio.

Study on plate heat exchangers has progressed greatly in recent years; magnetic field [16], nanoparticles [16,17,18], and heat transfer within pipes [17,18,19] have been much considered. However, due to high evaporate pressure and limits in experiments, tube-fin heat exchangers are utilized in this paper. Though recover heat from low temperature heat sources has certain methods for stationary waste recovery systems [20], much practical difficulties restrain them for road vehicles.

Former researches either exclude recuperater due to using wet fluids, or include recuperator in a complex system. To further increase the thermal and exergy efficiency of ORC system, other typical working fluids, especially dry fluid with similar evaporate temperature of ethanol, need comprehensive examination. This paper used a certain type of hybrid diesel engine for heavy-duty trucks as the heat source and selected the exhaust at typical operating points as the heat input of the ORC system. Beside ethanol, cyclopentane, cyclohexane, R1233zd (E), and R245fa were also selected for comparison. In order to achieve efficient waste heat recovery, working fluids of the ORC system need to evaporate at proper temperature. The selection of high-temperature heat exchangers and expanders also needs to be adjusted accordingly. Comprehensively optimizing the recuperator and evaporator can provide reference for future vehicle ORC system working fluid selection.

2 Methods

The ORC system model, a simple system with or without recuperator, has been constructed for analysis, with the system structure shown in Figure 1. The objective of the optimization process is to achieve high power output with limited system complexity and cost.

2.1 System construction

The T–s diagram of an ethanol ORC system is shown in Figure 2. With fixed evaporation temperature and the condensing temperature, the thermal efficiency of the system is largely determined by the expansion process (4–5). Therefore, the optimal working fluid shall have a large expansion ratio, which means high evaporate pressure and low condense pressure within the operation temperature range, since larger proportion of energy will be recovered. However, the exergy efficiency of the system is also affected by the amount of energy recovery in waste heat exchanging of preheating, evaporation, and superheating (1–2–3–4). The working fluid largely determines both the expansion ratio and the heat exchanging within the evaporator, thus the selection of the working fluid is essential to both the thermal efficiency and exergy efficiency of the ORC system.

Figure 2

T–s diagram of the ethanol ORC system.

To recover waste heat from diesel engine exhaust, the working fluid of the ORC system shall properly operate within the heat source temperature range. Ethanol, cyclopentane, cyclohexane, R245fa, and R1233zd (E) were selected for comparison, and the T–s diagram of these fluids is shown in Figure 2, and related properties are given in Table 1. R245fa and R1233zd have much lower evaporating temperatures, thus the temperature difference within the evaporator will remain large at wide heat source temperature range; yet the condensing temperatures of the two fluids are also low, resulting in relatively low condensing pressure and expansion ratio. Ethanol, cyclopentane, and cyclohexane have higher evaporating temperatures, with the evaporating temperature of cyclohexane slightly higher than the other two; the thermal efficiency of the three fluids will be larger. The major disadvantage of the three systems will be the evaporation process, as high evaporation temperature may reduce the proportion of waste heat recovery within the evaporator, thus decreases exergy efficiency. The T–s diagram of selected working fluids and related working fluid properties (include latent heat) are given in Figure 3 and Table 1.

Table 1

Working fluid properties

	Ethanol	Cyclopentane	R245fa	Cyclohexane	R1233zd
Evaporate temperature (°C)	200.4	208.5	143.3	256.3	155.4
Condense pressure (MPa)	0.10	0.17	0.53	0.10	0.45
Latent heat (kJ/kg)	505.5	185.1	73.8	157.6	71.36

Figure 3

T–s Diagram of selected working fluids.

In order to focus on the simulation analysis of the heat exchanger part, it is necessary to simplify the heat source and other parts of the system to reduce secondary variables and reduce the complexity of the model. To this end, the following assumptions are made for the system:

The operating conditions in the ORC system model are all steady state, and the heat source inlet temperature and flow rate at each operating point are constant.
The condenser of the system is parallel to the engine cooling system. The superheat degree and the undercooling degree are both constant.
The pressure drop and heat transfer loss of the evaporator and recuperator are determined with reference to experimental data, and the pressure drop and heat transfer loss of pipelines and other components are ignored.
The working fluid can be fully expanded in the expander, and the efficiency of the expander and working fluid pump is constant.

2.2 System modeling

The power output of the ORC system without recuperator can be defined as equation (1):

(1) E = Q eva ⋅ η − W pump = η eva ⋅ m s ⋅ ( h in − h out ) ⋅ h 4 − h 5 h 4 − h 1 ⋅ η exp − m r ⋅ h 1 − h 9 η pump

where η _eva stands for the thermal efficiency of the evaporator, η _exp stands for the expander isentropic efficiency, η _pump stands for the pump efficiency, m _s stands for heat source (exhaust) mass flow, m_r stands for working fluid mass flow, h _in and h _out stand for the enthalpy of the heat source at the inlet and the outlet, h ₁, h ₄, and h ₅ stand for the enthalpy of the working fluid at each point in Figure 2, the same below.

With recuperator applied, the working fluid after expansion will preheat the working fluid after pump. The modified power output can be defined as equation (2):

(2) E re = Q eva ⋅ η − W pump = η eva ⋅ m s ⋅ ( h in − h ̇ out ) ⋅ h 4 − h 5 h 4 − h 1 re ⋅ η exp − m r ⋅ h 1 − h 9 η pump

The power output gain can be defined as equation (3):

(3) η ̇ = E re E ≈ η eva ⋅ m s ⋅ ( h in − h ̇ out ) ⋅ h 4 − h 5 h 4 − h 1 re ⋅ η exp η eva ⋅ m s ⋅ ( h in − h out ) ⋅ h 4 − h 5 h 4 − h 1 · η exp = ( h in − h ̇ out ) ⋅ ( h 4 − h 1 ) ( h in − h out ) ⋅ ( h 4 − h 1 re )

Therefore, the exhaust outlet temperature of the evaporator and the recuperate rate are the critical factors of the power output gain.

The largely simplified ORC system model is used to calculate system output and thermal or exergy efficiency. For system complicity analysis, an additional heat exchanger model is applied for detailed evaporator and recuperator calculation. Equations of heat exchanger model are given in Table 2.

Table 2

Equations of heat exchanger model

Heat exchanger	Equations [21,22,23,24]
Exhaust side	Nu = 0.982 ⋅ Re 0.424 ⋅ s d 3 − 0.0887 ⋅ N · s 2 d 3 − 0.159 ( 4 )
Cold side (Single phase)	Nu = f 8 ⋅ ( Re − 1000 ) ⋅ Pr / 12.7 · f 8 0.5 ⋅ ( Pr 2 / 3 − 1 ) + 1.07 ( 5 ) f = ( 1.82 ⋅ lg Re − 1.5 ) − 2 ( 6 )
Two phase zone	h tp = 30 ⋅ Re lo 0.857 ⋅ Bo 0.714 · ( 1 − x ) − 0.143 · k l d ( 7 )

As both the evaporator and the recuperator are compact tube-fin heat exchangers, the single phase turbulent flow within the tube, namely in the recuperator and in the preheating section and superheating section of the evaporator, is calculated with equations (5) and (6); the two phase turbulent flow of the evaporator is calculated with equation (7). The exhaust side of the evaporator is calculated with equation (4). The condenser is simplified.

The heat exchanger model is verified by the heat exchanger experiment. Parameters of the evaporator and the recuperator are also mainly taken from the heat exchanger bench test. The system model is verified by the ORC system experiment, and other parameters of the ORC system are determined through the ORC system bench test with the recuperator. The relevant boundary conditions are shown in Table 3.

Table 3

Boundary conditions

Boundary conditions	Parameters
Exhaust temperature (°C)	391
Exhaust mass flow (kg/s)	0.23
Evaporate pressure (MPa)	3
Heat exchanger efficiency	0.9
Expander efficiency	0.65
Pump efficiency	0.8
Superheat degree (K)	40
Undercooling degree (K)	20
Evaporator PTD (K)	20
Condenser PTD (K)	20
Environment temperature (°C)	25
Recuperate rate	0.5

Heat source conditions are taken from the bench test of a certain diesel engine, namely, the exhaust conditions at the minimum fuel consumption point. The parameters of expanders are taken from The test bench (Figure 4) and use electric heated or water cooled exhaust to simulate actual engine exhaust at each working point, with a water cooling condenser. The evaporator test used 95% ethanol as working fluid, while the recuperator test used R245fa. The heat exchanger model is also verified by the heat exchanger experiment.

Figure 4

Heat exchanger test bench.

The ORC system optimization process is shown in Figure 5. In the preliminary analysis, a largely simplified model is utilized to perform simplified calculations. Parameters are entirely preset to acquire a qualitative analysis result of the ORC system, namely, the thermal efficiency of systems with different working fluids. The coupled analysis utilized the detailed heat exchanger model related in Table 2, to optimize the simplified heat exchanger calculation data in the system model and to achieve a comprehensive optimization of the system complicity and power output, in terms of both heat exchanging area and exergy efficiency.

Figure 5

System optimization process.

3 Result and analysis

3.1 Preliminary analysis

Thermal efficiencies of simple ORC systems without (light grey) and with recuperator (dark grey) are shown in Figure 6. The thermal efficiency of R245fa system is the lowest, which is 7.7% without recuperator and 10.0% with recuperator. R1233zd shows a slightly better performance of 8.9 and 11.1%, yet still no better than the other three fluids. Ethanol system without recuperator has the highest thermal efficiency of 13.2%, while cyclohexane system has the best performance of 16.6% among recuperated systems. As for dry fluids, waste heat after expansion process is proportionally larger than wet fluids; with proportionally larger temperature difference within the recuperator, the thermal efficiency increase will be more significant. Ethanol is the only wet fluid of the five, and the latent heat at 3 MPa is also proportionally the largest; recuperator will be less effective in the ethanol system.

Figure 6

Thermal efficiencies of ORC systems with different working fluids.

The energy flow and mass balances of the cyclopentane ORC system are given in Figure 7. The configuration of system units is given in Table 4. As shown in Table 4, the exergy loss of the evaporator, 45.4%, is much higher than other system components. While the recuperator, though, has only slight direct influence on system exergy loss, yet in Figure 7, has shown much influence on system output, as it increased system thermal efficiency. Therefore, these two components need specific analysis during the ORC system working fluid selection.

Figure 7

Energy flow of the cyclopentane ORC system.

Table 4

Configuration of system units

System unit (%)	Evaporator	Expander	Condenser	Pump	Recuperator
Thermal efficiency	90	65	—	80	90
Heat loss	10	—	—	—	1.2
Exergy loss	45.4	8.6	14.5	1.3	2.5

3.2 Effect of heat source

The system exergy efficiency without recuperator at different exhaust temperature is shown in Figure 8. With evaporate pressure fixed at 3 MPa, the exergy efficiency of all systems increases as exhaust temperature increases. At middle or high conditions, exhaust temperature of conventional diesel engines is above 350°C. In this temperature range, ORC system with ethanol, cyclopentane, and cyclohexane all benefit from the large expansion ratio, and ethanol system has the highest ORC system exergy efficiency of 24.5% at 350°C. However, at lower exhaust temperature, temperature difference within the evaporator will inevitably be smaller; the three systems with high evaporate temperature, though retained the higher thermal efficiencies, cannot achieve complete heat exchanging within the evaporator, due to design limitation. For cyclohexane, with the highest evaporate temperature of the five working fluids, the decrease at low temperature is most significant; the exergy efficiency at 300°C (8.6%) is only 37.8% of the exergy efficiency at 360°C (22.9%). R245fa system and R1233zd system are less affected by evaporator design limitation at low exhaust temperature. However, both systems have significantly smaller exergy efficiency at high temperature, mainly due to the high condensing pressure hindering the expansion process.

Figure 8

ORC system (without recuperator) efficiency at different exhaust temperature.

The exergy efficiency of ORC system with recuperator at different exhaust temperature is shown in Figure 9. The recuperate rate is fixed at 0.5. With exhaust temperature above 350°C, the application of recuperator increased the exergy efficiency of all five systems, yet to ethanol, the only wet fluid of the five, the benefit is rather limited. The exergy efficiency of cyclopentane system surpassed ethanol system after the application of recuperator, and the maximum exergy efficiency, 27.8%, occurred at 350°C. As the recuperator increased the working fluid inlet temperature of the evaporator, the temperature difference will inevitably decrease; the exergy efficiency decrease of systems with the three high evaporate temperature fluid is more drastic. At 300°C, the exergy efficiency of the recuperated cyclopentane ORC system (21.9%) reduced to only 79.0% of the maximum efficiency, and the exergy efficiency increase compared to system without recuperator is below 0.1%. The output of R245fa system and R1233zd system also significantly benefited from the recuperator, while the low evaporate temperature of the two is advantageous at both low exhaust temperature and increased recuperate rate, though the exergy efficiency at high exhaust temperature is still rather low.

Figure 9

ORC system (with recuperator) efficiency at different exhaust temperature.

3.3 System complicity analysis

Before the detailed analysis of ORC system efficiency and complicity, the arrangement of heat exchangers also requires explanation. The application of recuperator will increase the working fluid temperature at the evaporator inlet, thus the evaporator, especially the preheating section, needs comprehensive analysis along with the recuperator.

A certain heat exchanging core is used in both the preheating section of the evaporator and the recuperator, to evaluate the effect of the recuperator and the evaporator on the ORC system exergy efficiency. The preheating section and the recuperator of the cyclopentane ORC system both have fixed heat exchanging cores, rather than achieving a preset pinch point temperature difference or recuperate rate. The simulation result is shown in Figure 10, with the amount of heat exchanging cores (E) in the preheating section of the evaporator and the amount of heat exchanging cores (R) of the recuperator varies in each points. Of the simple cyclopentane ORC system without recuperator, the amount of heat exchanging cores in the preheating section of the evaporator is 3. On this basis, simply increase the core amount of the recuperator, although the exergy efficiency indeed increased accordingly, yet as the temperature difference within the recuperator gradually decreases, the thermal efficiency increase brought by additional cores gradually decreases, and as the temperature of the working fluid at the evaporator inlet increases, the temperature difference in the preheating section decreases, hindering the waste heat recovery of the evaporator, thus the total increase of exergy efficiency is relatively limited. When the total number of cores is 10, the exergy efficiency is only increased by 7.09%. If the optimization priority from the recuperator to the preheating section is switched, the optimized scheme with seven heat exchanging cores in the preheating section of the evaporator and three heat exchanging cores in the recuperator increased the system exergy efficiency by 14.59%, which is 2.06 times of the comparison scheme. Therefore, to optimize the heat exchangers of ORC system with recuperator, achieve higher exergy efficiency and power output with same or similar system complicity and cost; the priority of the preheating section of the evaporator should be higher than the recuperator.

Figure 10

Effect of heat exchanger optimization priority on ORC system efficiency.

The system exergy efficiency (light grey) and the total heat exchanging area of the evaporator and the recuperator (dark grey) are shown in Figure 11. For ORC systems without recuperator, the ethanol system has the highest exergy efficiency of 24.1%, while the cyclopentane system achieved 96.4% efficiency of the ethanol system, with only 85.2% of the heat exchanging area. The R1233zd system also achieved 67.1% efficiency of the ethanol system with only 58.5% of the heat exchanging area, which is again better than the R245fa system, yet the power output will be rather small. After the application of recuperator, cyclopentane system still requires only 98.7% heat exchanging area of the ethanol system, while the exergy efficiency increased by 18.9%; therefore the exergy efficiency, 27.6%, is also the highest of the five. The exergy efficiency increase of recuperated ethanol system, 9.0%, is the lowest of the five. In terms of both complicity and efficiency, cyclohexane has no advantage to either ethanol or cyclopentane.

Figure 11

Comparison of simple ORC system with and without recuperator.

With recuperate rate at 0.5, complicity of all systems increased significantly as the heat exchanging area increased, which is more significant for the R1233zd system (574.7%) and the R245fa system (562.6%). The increase of the cyclopentane system (197.7%), though much smaller, is still rather large, compared to the exergy efficiency increase of only 18.9%. The recuperate rate can be further investigated and optimized, to achieve higher system output without the need of complex heat exchangers.

4 Conclusion

This paper constructed an ORC system simulation model, and five working fluids were selected for comparison as the working fluid of a simple diesel engine ORC system. The quality of heat source, the quality of evaporator, the system output, and the system complicity were taken as variables for comparison. Of the five working fluids:

For systems without recuperator, ethanol system has the best system output of the five in a wide operation temper range. However, at low heat source temperature, the output of cyclopentane system is higher than the ethanol system. Also, as wet fluid, the recuperator is less effective for ethanol system. Cyclopentane and cyclohexane have similar parameters, yet at most conditions considered in this paper, the performance of the cyclopentane system is better than the cyclohexane system. The cyclopentane system has the best exergy efficiency after the application of recuperator. The system output of the R1233zd system is better than the R245fa system, and both systems have better performance at low temperature. Yet the exergy efficiency is still limited compared to either the simple ethanol system or the recuperate cyclopentane system, and both systems have the disadvantage of high complicity after the application of recuperator. The advantage of low evaporate temperature can be better utilized for low quality waste heat recovery.
In the exhaust temperature range of 300–500°C, ethanol and cyclopentane have better performance than the other three. Without recuperator, the ethanol system has the highest exergy efficiency of 24.1%, while the cyclopentane system achieved 96.4% efficiency of the ethanol system, with only 85.2% of the heat exchanging area. After the application of recuperator, cyclopentane system has the highest exergy efficiency of 27.6%, while requires only 98.7% heat exchanging area of the ethanol system.
At recuperate rate of 0.5, the system complicity in terms of heat exchanging area of all five system increased significantly, while the power output increase is limited compared to complicity increase. The recuperate rate of ORC system requires further investigation.

Acknowledgement

I appreciate the reviewers for their constructive and detailed critique contributed to the quality of this paper. And I am also thankful to the editors for their kind and helpful supports.

Funding information: This work was supported by the National Key Research and Development Project of China [grant numbers 2017YFB0103504].
Conflicts of interest: The authors declare that they have no conflicts of interest to report regarding the present study.
Data availability statement: The datasets generated and analyzed during the current study are available from the corresponding authors on reasonable request.

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Received: 2021-02-04

Revised: 2021-05-06

Accepted: 2021-05-11

Published Online: 2021-07-02

This work is licensed under the Creative Commons Attribution 4.0 International License.

Diesel engine waste heat recovery system comprehensive optimization based on system and heat exchanger simulation

Abstract

Nomenclature

Subscripts and superscripts

Acronyms

1 Introduction

2 Methods

2.1 System construction

2.2 System modeling

3 Result and analysis

3.1 Preliminary analysis

3.2 Effect of heat source

3.3 System complicity analysis

4 Conclusion

Acknowledgement

References

Journal and Issue

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