A dedicated heat exchanger model is introduced for the optimization of heavy-duty diesel engines. The model is a prerequisite for the execution of CFD simulations, which are used to improve waste heat recovery in these systems. Several optimization methods coupled with different types of working fluids are compared in terms of exergy efficiency and heat exchanger complicity. The three considered optimization methods all lead to significant improvements in the R245fa and R1233zd systems with a comparatively low evaporation temperature. The optimal R245fa system has the highest efficiency increase (77.49%). The cyclopentane system displays the highest efficiency among the optimized ORC (Organic Rankine Cycle) systems, yet achieved by using a much heavier evaporator HEC (Heat Exchanging Core). In contrast, the 96.84% efficiency increase for the optimized R1233zd is achieved with only 68.96% evaporator weight.

Transportation contributed a large proportion of the total greenhouse gas emission each year, of which road transportation has the highest energy consumption amount [_{2} emissions. For road vehicles, the ORC system also requires considerations of compact and robustness, alongside high-efficiency. A simple diesel engine exhaust ORC system is shown in

Therefore, heat exchangers, especially the evaporator, determine the quantity of recovered energy and affect its quality, thus critical to the ORC system. The detailed analysis of Holik et al. [

The thermal efficiency of the ORC system is largely determined by the expansion ratio within the expander. With the evaporate pressure and the condense temperature remaining constant, the expansion ratio is determined by condense temperature thus, working fluid with lower condense pressure has better thermal efficiency. On the other hand, working fluid with lower condense pressure usually has higher evaporate temperature; comparatively low-temperature differences within the evaporator requires more heat exchanging area, which further increases the weight and the capital cost. The exhaust temperature of the diesel engine is considerably lower than the gasoline engine. Therefore, working fluids with extremely high evaporate temperature, such as water, benzene and toluene, are less effective due to evaporate pressure limitation and will not be taken into further comparison. Working fluids with moderately high evaporate temperature, such as ethanol [_{2} transcritical ORC system of Li et al. [

The scheme of the ORC system varies greatly in terms of heat sources. Besides engine exhaust, utilizing waste heat from the coolant, the exhaust gas recirculation (EGR) cooler and the charge intercooler have also been taken into experimental consideration and possible application. Coolant contained a large quantity of waste heat with limited quality, the usage of the coolant waste heat and other low-quality heat sources can be difficult in applications. Lu et al. [

The evaporator affects the ORC system performance, the simple system of Holik et al. [

This paper’s objective is to increase the exergy efficiency of the ORC system while containing the system weight at an appropriate level for road vehicles. This work analyzed various factors that affect the evaporator and the ORC system output, namely evaporation pressure, condensing temperature and supercooling degree, and preheating system schemes. Different working fluids are also compared within the process. The major consideration is to evaluate the ORC system complicity (in terms of heat exchanging area and weight) increase along with system efficiency increase and achieve high system output with a limited weight increase. The comprehensive analysis is both a supplement of former research, and a suggestion for future application and optimization.

The heat absorption process of the ORC system can be divided in to preheating, evaporation and superheating. The evaporation process requires a heat source with both high quality and large quantity, and the evaporate temperature largely determines the thermal efficiency of the ORC system. The low-temperature fluid of the preheating process can absorb waste heat from low-quality heat sources such as the coolant and the charge inter cooler, and the superheating requires heat source with a high energy quality instead of a large energy quantity, thus the EGR cooler is ideal for superheating. The heat source of the ORC system model is generalized into two parts, low-quality heat sources and the engine exhaust. The engine exhaust exchanges heat within the evaporator, and low-quality heat sources exchange heat before the evaporator. The EGR waste heat is not considered in this paper, mainly because of practical difficulties such as high temperature lubrication and heat exchanger reliability.

A simplified ORC system model has been constructed for thermal and exergy efficiency analysis, with the system structure shown in

where _{s}_{r} stands for mass flow,_{s} and _{r} stands for the enthalpy change of the source and the fluid within the evaporator, _{eva} stands for the thermal efficiency of the evaporator.

Methods that increase system output either increase the system efficiency or increase the system energy input, as defined as

where _{exp} and _{pump} stand for the thermal efficiency of the expander and pump.

where

Parameters of the evaporator, namely heat transfer loss, working fluid side pressure drop and narrow temperature difference range, are taken from a heat exchanger bench test [

Simple | High-efficiency | |
---|---|---|

Exhaust temperature (°C) | 391 | |

Exhaust mass flow (kg/s) | 0.23 | |

Heat exchanger efficiency | 0.95 | |

Evaporate pressure (MPa) | 2 | 3 |

Superheating degree (°C) | 20 | |

Undercooling degree (°C) | 20 | 5 |

Environment temperature (°C) | 25 | |

Preheating temperature (°C) | None | 100 |

Expander efficiency | 0.6 | |

Pump efficiency | 0.4 |

The following assumptions are made for the system:

(1) 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.

(2) The working fluid can be fully expanded in the expander, and the efficiency of the expander and working fluid pump is constant.

(3) The pressure drop and heat transfer loss of the evaporator and other heat exchangers are determined concerning experimental data, and the pressure drop and heat transfer loss of pipelines and other components are ignored.

A heat exchanger model is applied for detailed evaporator analysis. To achieve higher working pressure then, a tube-fin heat exchanger is used as the evaporator of the ORC system. The evaporator’s heat exchanging core (HEC) is divided into two parts, the evaporation part and the preheating part.

The exhaust side of the tube-fin heat exchanger model is taken from Li et al. [

where s is the distance between fins, s_{2} is the vertical distance between tubes, d_{3} is the fin thickness, N is the number of fins.

The single-phase flow within the fluid side is calculated through the renowned Gnielinski equation [

The preheating of the working fluid happens in the preheating part, the superheating of the fluid happens in the evaporation part.

The two-phase zone, or the evaporation of the fluid, is calculated through

After the heat transfer coefficient of the heat exchanger calculation, the heat transfer area will be calculated via log-mean temperature difference (LMTD) method:

where K stands for the total heat transfer coefficient, A stands for the equivalent collecting area of the HEC.

The 3D model of the HEC is constructed for CFD simulation. The structure of the tube-fin evaporator is given in

Part | Preheating | Evaporation |
---|---|---|

Tube pass | 16 | 2 |

Tube | 48 | 42 |

Tube outer diameter (mm) | 10 | 10 |

Tube thickness (mm) | 0.4 | 0.4 |

Tube length (mm) | 315 | 315 |

Fin height (mm) | 90 | 60 |

Fin thickness (mm) | 0.4 | 0.4 |

Fin length (mm) | 350 | 350 |

Governing equations of continuity, momentum and energy can be listed as:

where ρ represents the density, u is the velocity, t is the time, P is the pressure, μ is the viscosity, k is the thermal conductivity, T is temperature and S is heat source. Energy generated from dissipation is ignored.

The simulation used the standard k-omega model, for lower Reynolds number situation:

where G_{k} and G_{ω} represent the generation of k and ω due to mean velocity gradients, Γ_{k} and Γ_{ω} represent the effective diffusivity of k and ω, and Y_{k} and Y_{ω} represent the dissipation of k and ω due to turbulence.

The low-Reynolds-number correction is given by a coefficient α:

The turbulent viscosity is modified by this coefficient:

The CFD model is a pressure-based solver with steady-state iterative algorithm, absolute velocity formulation and compressible fluid (exhaust), and simple pressure-velocity coupling. The simulation of compressible fluid model is similar to Giacomelli et al. [

The mesh sensitivity analysis also focused on energy transfer. Two comparison models are meshed in same geometric structure, with element quantity decreased in comparison model A and increased in B. The comparison is given in

Case | Simulation | Comparison-A | Comparison-B |
---|---|---|---|

3D elements | 4644704 | 657832 | 22134936 |

Heat transfer rate (kW) | 21.46 | 20.96 | 21.43 |

The main theme of this paper, evaporator simulation model is verified through bench test (

The ORC model is partly verified by the experiment, while other parameters are taken from follow references. The condensing temperature range is taken from Shu et al. [

The evaporation pressure directly affects both the expansion ratio of the expander and the temperature difference within the evaporator. The thermal and exergy efficiency increase through evaporation pressure increase will inevitably cause an increase in both the capital cost and weight of the evaporator, beside other changes. Detailed analysis is given in

At 3 MPa, the R245fa system required a much lighter preheating HEC, only 48.86% of the ethanol preheating HEC, the weight of the evaporator HEC is 35.73% lighter. However, the exergy efficiency of the R245fa system at 3 MPa is only 53.36% of the 3 MPa ethanol system; the condense pressure of the R245fa system requires further analysis and optimization.

Two parameters of the ORC system are mainly determined by the condenser, the condense temperature and the supercooling degree. The condensing temperature affects the expansion ratio of the expander, thus directly affecting the thermal efficiency of the ORC system. The proper supercooling degree is necessary for reliable system operation, since condenser with larger supercooling degree requires more heat in the preheating process and decreases the thermal efficiency of the ORC system. With the outlet temperature remaining at 30°C, decrease the R245fa ORC system condensing temperature from 60°C to 35°C, the system exergy efficiency increased by 52.96%. Besides, with the condensing temperature remaining at 60°C, decreasing the supercooling degree from 30°C to 5°C also increased the system exergy efficiency by 11.97%.

The condenser also affects the evaporator in terms of working fluid inlet temperature, as shown in

The condense temperature of ethanol at ambient pressure is 78.09°C, which is comparatively easy to achieve. Further decreasing the condense pressure may cause negative pressure within the ORC system; therefore, the condenser of the ethanol ORC system will not further decrease these two parameters.

The simple ORC system recovers waste heat solely from the exhaust evaporator, yet the low-temperature working fluid can recover waste heat from the engine coolant, charge intercooler and even working fluid steam before condensing. The effect of the ORC system scheme, namely additional preheating heat exchangers, is simulated through inlet temperature change. As the working fluid absorbs waste heat from other sources before entering the evaporator, the fluid inlet temperature of the exhaust evaporator increases accordingly.

As shown in

For the R245fa system, the effect of the complex system scheme is more significant and positive. In the ethanol system, the enthalpy of evaporation is 50.34% of the total enthalpy increase within the evaporator, while the R245fa system is only 31.94%. A much larger proportion of waste heat is recovered in the preheating process. Besides, the low condense temperature retained a large temperature difference for low-quality heat recovery. The larger temperature difference within the evaporator is less affected by the inlet temperature increase. In contrast, the larger proportion of heat in the preheating process further increases the system exergy efficiency. As shown in

The comparison of the five working fluids in Li et al. [

The optimization result of the five systems is given in

As shown in

The analysis of this paper focused on the evaporator of the ORC system, to achieve high-efficiency waste heat recovery from heavy-duty diesel engines. Several optimization methods coupled with different types of working fluids are compared in terms of exergy efficiency and heat exchanger weight and cost.

(1) At the same evaporate pressure, the HEC weight is determined by the evaporating temperature of working fluids, fluids with high evaporate temperature requires a larger evaporator, and optimization methods also causes a significant HEC weight increase. The weight of ethanol evaporator HEC increased by 12.76% in the optimal system, and the final HEC weight is 163.51% of the R245fa evaporator at the same system parameter.

(2) Effect of evaporate pressure and condense temperature have significant effect on ORC system efficiency and power output, ranges from 9%–17%, while the increase in HEC weight is below 3% in all cases, insignificant in terms of total system cost and weight increase. Reliability and availability is the major concern of the two parameters.

(3) Add an extra heat source, either through preheating or recuperating, inevitably requires extra equipments and has significant effect in system complicity. Beside other requirements, the increase of inlet temperature will significantly increase the HEC of evaporator, especially for the preheating HEC of fluids with high condense temperature. The 12.03% output increase of ethanol system is achieved at the cost of increase evaporator HEC by 9.71%.

(4) The ethanol system has the highest efficiency among the simple ORC systems. The cyclopentane system has the highest efficiency among the optimal ORC systems. The optimal R245fa system has the highest efficiency increase of the five, while the optimal R1233zd system achieved 96.84% efficiency of the cyclopentane system with only 68.96% evaporator HEC weight.

Heat exchanging area, m^{2}

Diameter, mm

k-ω generation (-)

Enthalpy, kJ/kg

Heat transfer coefficient, W/m^{2}·K

Turbulence kinetic energy, J

Mass, kg

Nusselt number (-)

Prandtl number (-)

Heat flux, kW

Reynolds number (-)

Distance, mm

Low-Reynolds-Number coefficient (-)

Effective diffusivity (-)

Turbulent viscosity, m^{2}/s

Efficiency, %

Specific dissipation rate

Computational Fluid Dynamics

_{2}

Carbon Dioxide

Exhaust Gas Recirculation

Evaporator

Expander

Heat Exchanging Core

Log-Mean Temperature Difference

Organic Rankine Cycle

Exergy

I personally appreciate the editors and reviewers for their constructive and detailed critiques contributed to the quality of this paper.

This work was funded by

The authors declare that they have no conflicts of interest to report regarding the present study.