Optimization of the Adaptability of the Fuel Cell Vehicle Waste Heat Utilization Subsystem to Extreme Cold Environments

Abstract

In extremely cold environments, the fuel cell vehicle (FCV) waste heat utilization subsystem can only exchange a small amount of proton exchange membrane fuel cell (PEMFC) waste heat into the warm air circuit for cab heating, which has poor adaptability to extremely cold environments. The first step in this study was to build a test bench for the waste heat utilization subsystem of fuel cell vehicles. Secondly, the PEMFC heating capacity and liquid–liquid exchanger heat transfer capacity were analyzed using experimental data to assess the ability of FCV waste heat utilization subsystems with different rated powers to adapt to extremely cold environments. Then, the optimization mathematical model of the liquid–liquid exchanger was established, and the heat transfer performance of the liquid–liquid exchanger was orthogonally optimized based on the Taguchi method. Finally, the optimized liquid–liquid exchanger was installed in the waste heat utilization subsystem for experimental tests. The results show that when the ambient temperature is −20 °C, −25 °C or −30 °C, in the optimized waste heat utilization subsystem, the inlet and outlet temperatures of the PEMFC are reduced, and the power consumption of the positive temperature coefficient (PTC) is reduced by 57.6% and 48% and 34.3%, respectively, improving the utilization rate of PEMFC waste heat, and thereby improving the adaptability of FCV in extremely cold environments.

1. Introduction

In the current context of global decarbonization, the development and utilization of renewable energy are increasing rapidly. However, renewable energy is often unstable and intermittent in the power generation process. To solve this problem, the utilization and stability of renewable energy can be greatly improved by using certain energy storage and power generation systems [1]. The combination of water electrolysis hydrogen production and proton exchange membrane fuel cells (PEMFCs) will become a very important technology for green hydrogen energy utilization and renewable energy peak regulation. The high energy conversion efficiency, high specific power, quick start, and zero greenhouse gas emissions are all advantages of PEMFCs [2,3,4]. The electric efficiency of a PEMFC is about 40–50% [5]. The heat generated is greater than or equal to the generated electric energy [6,7]. The actual calculation shows that only 3% to 5% of the waste heat energy is taken away through the exhaust heat of the PEMFC, and the radiative heat dissipation accounts for about 1% of the PEMFC’s waste heat. The rest of the waste heat should be recycled through its cooling system or waste heat utilization subsystem [8]. PEMFC waste heat utilization research is a new area of study in PEMFC thermal management that can help improve PEMFC performance [9,10] and total fuel consumption [11]. With the technical improvement of fuel cell shutdown and purge control strategy, external auxiliary heating and no auxiliary heating, fuel cell vehicles currently on the market can start quickly and run stably in an extremely cold environment of −30 °C. On this basis, the research on the adaptability optimization of energy-saving fuel cell vehicle waste heat utilization subsystems in extreme cold environments has become a hot spot and key point of study [12].

Direct and indirect waste heat usage are the two types of waste heat utilization for PEMFCs. Indirect utilization is defined as the conversion of waste heat generated by PEMFCs into electric energy using thermoelectric generators (TEG) in order to achieve waste heat recovery and utilization [13,14]. Gigliucci et al. [15] investigated a PEMFC-based residential cogeneration system in the lab. The results demonstrate that the cogeneration system’s primary energy usage is reduced by up to 10% when compared to electricity and thermal separation production. Chen et al. [16] simulated the performance of each thermoelectric module for the thermal recovery of 1 kW PEMFCs using a three-dimensional CFD model. In the study of whole systems, however, the three-dimensional model has some drawbacks. For the waste heat recovery of PEMFCs, Gao et al. [17] developed a thermoelectric generator computational model with a compact plate-fin heat exchanger. A waste heat indirect utilization subsystem comprising a PEMFC, a thermoelectric generator, and a regenerator was proposed by Chen et al. [18]. PEMFC, thermoelectric generator, and hybrid power system efficiency and power outlet expressions were developed, and the hybrid power system’s ideal area was found. The findings will help researchers better understand the mixed waste heat utilization subsystem’s performance and operation. This information was used by Yang et al. [19] to deduce the basic relationship between the PEMFC’s working current density and the thermoelectric generator’s dimensionless current, from which the thermoelectric generator’s working current density range was determined. According to the modeling results, the PEMFC’s equivalent maximum power density may be increased by 23% using this hybrid system. Parise et al. [20] created a model for using thermoelectric coolers to manage the temperature of PEMFCs. The results revealed that thermoelectric coolers can be replaced by feed gases chilled by internal liquid or externally humidified. Sulaiman et al. [21] proposed an energy recovery method for ultra-low-waste heat temperature proton exchange membrane fuel cells using a combined thermoelectric generator, heat pipe and radiator system, and achieved good results. Hwang [22] et al. built a MATLAB/Simulink model to examine the performance of steam reformer-powered PEMFC cogeneration systems. The results reveal that the cogeneration system may reach an 80.6 percent cogeneration efficiency. To build and optimize a micro cogeneration housing system based on PEMFC, Arsalis et al. [23] used a genetic algorithm optimization technique. The single objective optimization strategy’s objective function is the micro cogeneration system’s net power efficiency. Through the change in nine choice factors, the optimization software aims to maximize the objective function. The ideal design configuration’s objective function value is much greater than the initial value, up 20.7 percent. Romdhane et al. [24] developed a PEMFC and single-effect lithium absorber-based miniaturized refrigeration, heating, and power supply system. Numerous control strategies were devised, and their advantages were examined based on different operation metrics such as thermal efficiency and total efficiency, hydrogen consumption and self-consumption rate, and fuel energy saving rate as a performance index.

The direct use of PEMFC waste heat for automobile heating in the winter is referred to as PEMFC waste heat consumption [25]. Hasani et al. [26] created a waste heat recovery system that uses a PI controller to accomplish maximal heat recovery while sacrificing the PEMFC’s operational temperature. Hwang et al. [27] devised an intelligent control method to regulate the waste heat utilization system, which controls the waste heat utilization of the PEMFC while controlling the PEMFC’s working temperature. Alijanpour [28] developed a system model for direct waste heat utilization in a PEMFC with metal hydride memory, as well as an analysis of the effect of coolant flow rate and pressure ratio on waste heat utilization in a PEMFC. To investigate the influence of PEMFC waste heat utilization on hydrogen heating systems in low-temperature environments, Xu [29] et al. built a PEMFC waste heat direct utilization system for heavy trucks. Jin et al. [30] developed a waste heat utilization system for PEMFCs that uses a constant temperature controller to keep the PEMFC at 50 degrees Celsius and uses the remaining heat to heat the cab. Antonio [31] created a waste heat direct utilization system for a fuel cell vehicle (FCV) that uses waste heat from the power cells to heat the cab while lowering power cell energy usage. The mileage of vehicles has grown. Sun and colleagues [32] developed a direct waste heat utilization system that included a PEMFC, radiator, liquid–liquid exchanger, positive temperature coefficient (PTC) heater, and warm air core. The impacts of various factors on system energy usage and waste heat exchange rate were determined by the study of key parameter elements, and the waste heat utilization subsystem of an FCV was then constructed. The energy-saving effects of the new and old matching methods were tested at −3 °C and −6 °C. However, the aforementioned study did not address the use of waste heat by PEMFCs in extremely cold temperatures.

This paper uses the FCV’s waste heat utilization system as the research object, and sets up an experimental bench for the waste heat utilization subsystem of the FCV at various environmental temperatures in order to fully utilize the PEMFC’s waste heat in low-temperature environments and improve the FCV’s performance in low-temperature environments. The effect of PEMFC radiator and PTC energy consumption on the adaptability of the waste heat utilization subsystem of a truck with varying rated powers to extremely cold environments is investigated experimentally. Based on the experimental data, the effects of PEMFC heating capacity and liquid–liquid exchanger heat transfer capacity on the extremely cold environment adaptability of the truck waste heat utilization subsystem with different rated powers are analyzed, and the optimization mathematical model of the liquid–liquid exchanger is established. Optimization of the heat transfer performance of a liquid–liquid exchanger is performed using the Taguchi method. The optimized liquid–liquid exchanger is inserted into the waste heat utilization subsystem for experimental testing to confirm the optimized waste heat utilization subsystem’s superiority. In addition, the following is a description of the research’s contribution: (1) experiments with a FCV waste heat utilization subsystem reveal that in extremely cold environments, a vehicle with a PEMFC rated power of 60 kW has a very low level of heat generation from the PEMFC, and the waste heat utilization subsystem cannot use the PEMFC waste heat to heat the cab. As a result, the waste heat utilization subsystem is not suited to extremely cold temperatures; after increasing the PEMFC’s rated power to 90 kW, the PEMFC creates more heat, but the heat transferred via the liquid–liquid exchanger is rather low. Only a limited portion of the waste heat from the PEMFC can be transferred to the warm air loop for cab heating, making the waste heat utilization subsystem less suited to extreme cold situations. (2) Taking the fin height H of the liquid–liquid exchanger, the core length L_h, the core width L_w, and the total number of fluid layers N as the optimization variables, the heat exchange performance of the liquid–liquid exchanger is optimized based on the Taguchi method. The excess heat from the PEMFC is swapped to the warm air loop for heating the cab when the liquid–liquid exchanger is placed in the waste heat utilization subsystem. The waste heat utilization subsystem boosts the efficiency of PEMFC waste heat, improves its adaptation to extreme cold, and boosts the performance of PEMFC cars in low-temperature conditions.

2. Experimental Research on Waste Heat Utilization Subsystem of FCVs

2.1. Experimental Equipment

(a)

Environmental Chamber and Chassis Dynamometer

(1) Figure 1a depicts the PEMFC experimental sample vehicle, while Figure 1b depicts the test environment chamber. The environmental chamber’s temperature can be adjusted from −40 to 70 degrees Celsius, with temperature uniformity of less than or equal to 2 throughout; the air intake flow rate is greater than 8 Nm³ per minute; the volume size is greater than 5 m (length) × 4 m (width) × 3 m (height); the maximum load-bearing capacity is between 1.5 and 2 t, it operates stably with a power of 100 kW, and the continuous operation time is not less than 0.5 h; all of the above meet the requirements of this experiment. (2) Figure 1c shows the chassis dynamometer, which replicates the running road of the PEMFC test prototype.

(b)

Test and Acquisition Equipment

(1) Sensors: Six T-type thermocouples for monitoring the PEMFC’s inlet and outlet coolant temperatures, as well as the hot and cold sides of the liquid–liquid exchanger’s inlet and outlet coolant temperatures, and 1 current sensor for detecting the PTC inlet current. (2) A data acquisition card was used to capture the data acquired by each sensor. (3) A computer was used to summarize and process the data recorded by the data acquisition card. (4) Wire harness for connecting sensor and data acquisition card. (5) Wire harness for data acquisition card, PC and data transmission. As shown in Figure 2, 3 temperature sensors located at the hot side inlet and outlet of the liquid–liquid exchanger and the cold measurement outlet were added, and the data collector, PC, low-voltage wiring harness, USB wiring harness, and inverter in the signal acquisition system were added. Other equipment included the original car part.

2.2. Experimental Subjects

The auxiliary system of the PEMFC consists of an air supply system, hydrogen supply system, thermal management system and control system. The waste heat utilization subsystem belongs to the thermal management system. The FCV waste heat utilization subsystem is shown in Figure 3. The waste heat utilization subsystem consists of the PEMFC, radiator, plate-fin liquid–liquid exchanger, PTC, heat, air ventilation, and cooling (HAVC) and a variable pump. Through the use of its control system software, the PEMFC’s rated power, which is now 60 kW, may be increased to 90 kW. The variable pump is the hot side water pump of the liquid–liquid exchanger of the waste heat utilization subsystem, and the quantitative pump is the cold side water pump of the liquid–liquid exchanger.

2.3. PEMFC Heating Analysis

When a vehicle with a PEMFC rated power was tested in an extremely cold environment with ambient temperatures of −20 °C, −25 °C, and −30 °C, the inlet and outlet water temperatures of the PEMFC fell as the external environment temperature decreased, as shown in Figure 4. When the ambient temperature was −20 °C, the PEMFC outlet water temperature was kept at 69.5 °C, when the ambient temperature was −25 °C, it was kept at 66.1 °C, and when the temperature of the surroundings was −30 °C, it was kept at 63.9 °C. The coolant flow rate was almost unchanged, reaching 111 L/min, and the outlet water temperature of the fuel cell at all ambient temperatures did not reach the threshold value of 70 °C for the opening of the electric water valve in the hot side of the liquid–liquid exchanger, so that there was no coolant flowing through the hot side of the liquid–liquid exchanger. All the heat needed for heating the cab was provided by the PTC. From the above analysis, it can be seen that the PEMFC with a rated power of 60 kW generates a small amount of heat, so that the waste heat reuse system cannot be applied in an extremely cold environment.

When the truck with the PEMFC’s rated power set to 90 kW was tested in an extremely cold environment with ambient temperatures of −20 °C, −25 °C, and −30 °C, the inlet and outlet water temperatures of the PEMFC dropped as well, but the temperature was higher, as shown in Figure 5. When the ambient temperature was −20 °C, the PEMFC outlet water temperature was controlled at 85 °C. When the ambient temperature was −25 °C, the PEMFC outlet water temperature was controlled at 85 °C. The coolant flow through the PEMFC was substantial, up to 186 L/min, and the outlet water temperature was maintained at 83.9 °C at −30 °C. At all ambient temperatures, when the PEMFC outlet water temperature approached 70 °C, the electric water valve of the hot fluid circuit of the liquid–liquid exchanger opened, and a small amount of coolant flowed through the hot fluid circuit. The PEMFC radiator fan was also turned on during the experiment, allowing more heat from the PEMFC to be dispersed into the air via the radiator. The PEMFC with a rated power of 90 kW has greater excess heat at various ambient temperatures, which can be used for cab heating by the waste heat utilization subsystem, as shown in the above analysis.

2.4. Analysis of Heat Exchange of Liquid–Liquid Exchanger

When the FCV with a PEMFC rated power of 90 kW was tested at temperatures of −20 °C, −25 °C, and −30 °C, it can be concluded from Figure 6 that under the conditions where the environmental temperature is −20 °C and the PEMFC output is stable with high power, the hot side inlet coolant temperature of the liquid–liquid exchanger is 85 °C, the maximum temperature difference (∆T_max) is 3.3 °C, the cold side inlet temperature is 65.7 °C, and the maximum temperature difference (∆T_max) is 8 °C. At an environment temperature of −25 °C, the inlet coolant temperature of the liquid–liquid exchanger hot side is 85 °C, and as the ambient temperature decreases, the cold side inlet temperature decreases, so the inlet temperature difference of the cold side and hot side increases relatively, and the inlet temperature difference is 3.8 °C and 9.2 °C, respectively. At an environmental temperature of −30 °C, due to the relatively low ambient temperature, the inlet coolant temperature of the liquid–liquid exchanger hot and cold side is also relatively small, so the inlet temperature of the hot side of the liquid–liquid exchanger at this environmental temperature is 82.9 °C, the maximum temperature difference (∆T_max) is 2.9 °C, the inlet temperature of the cold side is 62.5 °C, and the maximum temperature difference (∆T_max) is 9 °C. The above analysis can be summarized by observing that the temperature difference of the liquid–liquid exchanger hot side inlet and outlet and the temperature difference of the liquid–liquid exchanger cold side inlet and outlet are small at various ambient temperatures, and so the amount of heat exchanged by the liquid–liquid exchanger is small.

From the above analysis, it can be seen that under the extremely cold environment with the ambient temperature of −20 °C, −25 °C and −30 °C for the FCV with a PEMFC rated power of 90 kW, the PEMFC has more waste heat that can be used by the waste heat utilization subsystem, but since the heat exchange of the liquid–liquid exchanger is small, the waste heat reuse system cannot fully utilize the PEMFC waste heat. Therefore, it is necessary to optimize the liquid–liquid exchanger heat exchange performance to increase the utilization rate of the PEMFC waste heat by the waste heat utilization subsystem, enhance its adaptability to the extreme cold environment, and then promote FCV performance in the low-temperature environment.

From the above analysis, it can be seen that in an extremely cold environment with an ambient temperature of −20 °C, −25 °C and −30 °C for the vehicle with a PEMFC rated power of 90 kW, the PEMFC has more waste heat that can be used by the waste heat utilization subsystem, but since the heat exchange of the liquid–liquid exchanger is small, the waste heat utilization subsystem cannot fully utilize the waste heat of the PEMFC. It is essential to optimize the heat exchange performance of the liquid–liquid exchanger in order to increase the utilization rate of the PEMFC’s waste heat by the waste heat utilization subsystem, improve its adaptability to the extreme cold environment, and then improve the performance of the FCV in low-temperature surroundings.

3. Optimization of the Heat Exchange Performance of the Liquid–Liquid Exchanger

3.1. Mathematical Model for Optimization of Heat Transfer Performance of Liquid–Liquid Exchanger

3.1.1. Optimization Goal of Heat Transfer Performance of Liquid–Liquid Exchanger

(a)

Liquid–liquid exchanger heat exchange

The average temperature difference approach is utilized in this study to determine the total heat exchange of the liquid–liquid exchanger, and one of the optimization objectives is to achieve the maximum total heat exchange. In ideal settings, the liquid–liquid exchanger should function under stable conditions, with all fluids on the hot and cold sides being liquid. The following formula can be used to compute the total heat exchange:

$$Q=ϵ\left(A_c+A_h\right)\mathsf{\Delta }{t}_m$$

(1)

where ϵ is the coefficient of complete heat exchange, the liquid–liquid exchanger’s hot and cold sides, A_c and A_h, represent the heat transfer region’s size, and ∆t_m is the average heat transfer temperature difference. The calculation formulas of A_c and A_h are as follows [33]:

$$A_c=L_{hc}{L}_{wc}{N}_c\left[1+2n_c\left(H_c-{\delta }_{pc}\right)\right]$$

(2)

$$A_h=L_{hh}{L}_{wh}{N}_h\left[1+2n_h\left(H_h-{\delta }_{ph}\right)\right]$$

(3)

where L_hc and L_hh are the core lengths of the hot and cold sides of the liquid–liquid exchanger, respectively, L_wc and L_wh are the widths of the cores on the hot and cold sides, respectively, N_c and N_h are the total number of fluid layers on both the hot and cold sides, and n_c and n_h are the hot and cold sides’ fin frequencies, respectively, while H_c and H_h are the cold and hot side fins’ respective heights; δ_pc and δ_ph are the plate thicknesses, respectively.

(b)

Flow resistance on the liquid–liquid exchanger’s cold side

The flow resistance of the liquid–liquid exchanger is one of the most key parameters influencing the heat exchange achievement of the exchanger; lowering the flow resistance of the exchanger reduces the total resistance to flow of the waste heat utilization subsystem, lowering the pump’s energy consumption. The second optimization goal is to achieve the lowest flow resistance feasible on the device’s cold side, which can be expressed as:

$$\mathsf{\Delta }{P}_c=\frac{2f_c{m}_c{}^2}{{\rho }_c}\times \frac{L_c}{D_{h,c}{L}_h{}^2{N}_c{}^2{\left(H_C-t_c\right)}^2{\left(1-n_c{t}_c\right)}^2}$$

(4)

The cold side hydraulic diameter D_hc is expressed as:

$$D_{hc}=\frac{2\left(s_h-t_h\right)\left(H_h-t_h\right)}{\left[s_h+\left(H_h-t_h\right)\right]+\frac{\left(H_h-t_h\right)t_h}{l_h}}$$

(5)

where f_c is the cold-side fin friction coefficient, m_c is the cold-side fluid mass flow, ρ_c is the cold-side fluid density, L_c is the length of the cold-side core, t_c is the cold-side fin thickness, and l_c is the cold-side fin length, while s_c is the cold-side fin spacing.

(c)

Flow resistance on the liquid–liquid exchanger’s hot side

The flow resistance on the hot side of the liquid–liquid exchanger has the same effect as the fluid viscosity on the cooling coil in the heat exchange and waste heat utilization subsystems. As a result, the final optimization goal on the hot side is to obtain the lowest flow resistance. The flow resistance on the hot side is calculated as follows:

$$\mathsf{\Delta }{P}_h=\frac{2f_h{m}_h{}^2}{{\rho }_h}\times \frac{L_h}{D_{h,h}{L}_c{}^2{N}_h{}^2{\left(H_h-t_h\right)}^2{\left(1-n_h{t}_h\right)}^2}$$

(6)

The hydraulic diameter D_hc is expressed as:

$$D_{hh}=\frac{2\left(s_h-t_h\right)\left(H_h-t_h\right)}{\left[s_h+\left(H_h-t_h\right)\right]+\frac{\left(H_h-t_h\right)t_h}{l_h}}$$

(7)

where f_h is the hot-side fin friction coefficient, m_h is the hot-side fluid mass flow, ρ_h is the hot-side fluid density, L_h is the length of the hot-side core, t_h is the hot-side fin thickness, and l_h is the hot-side fin length, while s_h is the hot-side fin spacing.

3.1.2. Constraints on the Optimization of the Heat Transfer Performance of the Liquid–Liquid Exchanger

(a)

Constraint conditions for optimization of heat exchange of the liquid–liquid exchanger

Because the PTC’s maximum heating power in the FCV waste heat utilization subsystem is 13.8 kW, the liquid-to-liquid exchanger’s maximum heat exchange rate is 13.8 kW, which means that the heat exchanged from the PEMFC waste heat to the warm loop can replace the PTC, and the remaining waste heat from the PEMFC is used to heat the warm loop. It can be utilized to heat the batteries, so the heat exchange constraint condition of the liquid–liquid exchanger can be written as:

$$Q\le 13.8$$

(8)

(b)

Optimal restriction conditions for flow resistance on the cooling coil of the liquid–liquid exchanger

The flow resistance of the cooling coil of the liquid–liquid exchanger cannot exceed 2 KPa based on the total cost of the service and the energy usage of the water pump in the waste heat utilization subsystem. Thus, its optimization constraint can be expressed as:

$$\mathsf{\Delta }{P}_c\le 2$$

(9)

(c)

Optimal flow resistance restrictions on the hot side of the liquid–liquid exchanger

Considering the total cost of the service and the energy usage of the waste heat utilization subsystem water pump, the flow resistance of the hot side of the liquid–liquid exchanger cannot exceed 18 KPa, thus the optimization constraint may be expressed as:

$$\mathsf{\Delta }{P}_c\le 18$$

(10)

3.1.3. Optimization Variables for the Heat Transfer Performance of the Liquid–Liquid Exchanger

In this paper, the hot and cold sides of the liquid–liquid exchanger used have the same core length and the same core width (L_hc = L_hh, L_wc = L_wh), the cold and hot side fins have the same height (H_c = H_h), and the cold and hot side fluid layers are equal (N_c = N_h), so we choose the fin height (H), liquid–liquid exchanger core length (L_h), core width (L_w), and total fluid layers (N) as the optimization parameters. Changing these optimization factors can not only boost the heat exchange of the liquid–liquid exchanger, but also reduce the flow resistance, lowering the pump’s energy consumption and lowering the system’s overall energy consumption [34]. In accordance with the orthogonal optimization principle of the Taguchi method [35,36,37], the corresponding relationship between different optimization variables and different level values is shown in

Table 1. Different optimization variables and different levels of values.

Level Factor	Fin Height H (mm)	Core Length Lh (mm)	Core Width Lw (mm)	Total Fluid Layers (N)
1	3	200	70	12
2	4	215	80	14
3	5	230	90	16
4	6	245	100	18
5	7	260	110	20

.

3.2. The Optimization Process of the Heat Exchange Performance of the Liquid–Liquid Exchanger

3.2.1. Obtaining Orthogonal Experiment Results

The number of experimental optimization variables designed in this paper is four, and the number of levels is five. The orthogonal experiment table is created using the Taguchi method’s omnidirectional optimization principle.

Table 2. Orthogonal test table and experimental results.

Number of Experiments	Fin Height H/(mm)	Core Length Lh/(mm)	Core Width Lw/(mm)	Fluid Layers (N)	Heat Exchange/(kW)	Hot Side Flow Resistance/(KPa)	Cold Side Flow Resistance/(KPa)
1	1	1	1	1	5.163	18.492	0.942
2	1	2	2	2	6.861	19.882	1.013
3	1	3	3	3	8.864	21.272	1.082
4	1	4	4	4	10.238	22.665	1.152
5	1	5	5	5	14.100	24.058	1.22
6	2	1	2	3	7.265	16.319	0.826
7	2	2	3	4	8.964	17.546	0.887
8	2	3	4	5	11.453	18.775	0.948
9	2	4	5	1	8.541	19.992	1.012
10	2	5	1	2	7.212	21.212	1.074
11	3	1	3	5	10.156	14.524	0.733
12	3	2	4	1	7.293	15.609	0.789
13	3	3	5	2	9.044	16.702	0.843
14	3	4	1	3	7.632	17.786	0.899
15	3	5	2	4	10.376	18.880	0.953
16	4	1	4	2	7.727	13.847	0.699
17	4	2	5	3	10.442	14.889	0.751
18	4	3	1	4	7.915	15.923	0.804
19	4	4	2	5	10.700	16.966	0.856
20	4	5	3	1	7.725	17.999	0.909
21	5	1	4	4	10.741	13.030	0.657
22	5	2	1	5	8.107	14.004	0.707
23	5	3	2	1	6.474	14.977	0.762
24	5	4	3	2	8.276	15.957	0.806
25	5	5	4	3	12.833	16.938	0.854

shows the omnidirectional experiment table and experimental findings of various factors corresponding to various levels.

3.2.2. Analysis of Orthogonal Test Results

(a)

The total average value of each optimization objective of the liquid–liquid exchanger

The total average value of each optimization objective of the liquid–liquid exchanger is determined using the Taguchi method’s perpendicular optimization concept, using the data in Table 2. The following is the calculating formula:

$$y=\frac{1}{n}\sum _n^{i=1}{y}_i$$

(11)

where n is the number of simulation experiments and $y_i$ is the result of the i simulation experiment.

The total average value of heat exchange is 8.964 kW, the total average value of flow resistance on the hot side is 17.530 KPa, and the total average value of fluid viscosity on the cold side is 0.887 KPa, as estimated by Formula (11).

(b)

The average value of each optimization objective of the liquid–liquid exchanger under different optimization variables and levels

The approximate value of each liquid–liquid exchanger optimization objective is derived using the data in Table 2 for various optimization factors and levels. The following is the calculating formula:

$$y(X)=\frac{1}{5}\left(y_{X,1}+y_{X,2}+y_{X,3}+y_{X,4}+y_{X,5}\right)$$

(12)

where y_X,1~y_X,5 are the results of five different experiments under the same value of an optimized variable.

Table 3. The average value of each optimization objective of the liquid–liquid exchanger under different optimization variables and levels.

Parameter	Level Factor	Heat Exchange/(kW)	Hot side Flow Resistance/(KPa)	Cold Side Flow Resistance/(KPa)
Fin height H	1	7.781	21.274	1.082
	2	8.687	18.769	0.949
	3	8.901	16.700	0.843
	4	8.902	15.925	0.804
	5	9.286	14.981	0.757
Core length Lh	1	8.210	15.243	0.771
	2	8.334	16.386	0.829
	3	8.750	17.530	0.888
	4	9.078	18.673	0.945
	5	10.449	19.817	1.002
Core width Lw	1	7.206	17.484	0.885
	2	8.335	17.405	0.882
	3	8.777	17.460	0.883
	4	9.909	17.567	0.891
	5	10.574	17.734	0.897
Fluid layers N	1	7.039	17.414	0.883
	2	7.824	17.520	0.887
	3	9.407	17.441	0.882
	4	9.647	17.609	0.891
	5	10.903	17.665	0.893

shows the outcomes of the calculations. The heat exchange of the liquid–liquid exchanger is positively correlated with the fin height H, the core length L_h, the core width L_w, and the total number of fluid layers, reaching a maximum of 10.903 kW when the number of fluid layers is five. The fin height and core length are adversely linked with flow resistance on both the hot and cold sides. The increased viscosity on the hot and cold sides reduces first, then increases in terms of core width. When the fin height level is 5, the flow resistance on the hot and cold sides displays a trend of first growing, then reducing, and then increasing, and reaches a minimum value of 0.757 KPa and 14.981 KPa, respectively, when the fin height level is 5.

(c)

Weight analysis of the influence of different optimization variables on the optimization objectives of the liquid–liquid exchanger

We calculate the variance of an optimized variable of the liquid–liquid exchanger through the above two average values, and the calculation formula is expressed as:

$$S_x=\frac{1}{5}\sum _5^{i=1}{[y{\left(X\right)}_i-y]}^2$$

(13)

where y(X)_i is the average value of the optimization target of a certain optimization variable at the level of i and y is the total average value of a certain optimization target.

The influence weights of different optimization variables on the optimization objectives of liquid–liquid exchanger are shown in

Table 4. The influence weights of different optimization variables on the optimization objectives of the liquid–liquid exchanger.

Optimization Variable	Heat Exchange		Hot Side Flow Resistance		Cold Side Flow Resistance
	Value/(kW)2	Percentage/%	Value/(KPa)2	Percentage/%	Value/(KPa)2	Percentage/%
Fin height H	0.317413	7.47	5.062703	65.74	0.013502394	66.83
Core length Lh	0.646011	15.20	2.615916	33.97	0.006654138	32.94
Core width Lw	1.401179	32.97	0.013181	0.17	0.000029162	0.14
Fluid layers N	1.885592	44.36	0.009225	0.12	0.000017066	0.09

. The influence weights of different optimization variables on the liquid–liquid exchanger are different. The fin height H on the hot and cold sides of the liquid–liquid exchanger has the greatest influence on flow resistance, and the weight on the heat exchange has the least influence. However, the total number of fluid layers N has the opposite influence on the liquid–liquid exchanger. The core length L_h has a larger influence on the resistance of the cold and hot side, and a smaller influence on the heat exchange. The core width L_w has a larger influence on the heat transfer, but has a small influence on the resistance of the hot and cold sides.

3.3. Optimization Results of the Heat Exchange Performance of the Liquid–Liquid Exchanger

Because the goal of this article’s optimization is to reduce the flow resistance of the liquid–liquid exchanger as much as possible while increasing the heat exchange rate, the above analysis shows that a larger core width should be considered when increasing the heat exchange rate of the liquid–liquid exchanger. When considering reducing the flow resistance of liquid–liquid exchanger, a larger fin length and smaller core length should be selected. Therefore, the optimal combination of each level factor is: H(5), L_h(1), L_w(5), N(5)—that is, the height of the fin, the length of the core, the width of the core and the total number of fluid layers are, respectively, 7 mm, 200 mm, 110 mm, 20.

After optimization, the heat exchange of the liquid–liquid exchanger increased from 4.774 kW before optimization to 12.724 kW, an increase of 62.5%; the resistance of the hot side was reduced from 21.605 KPa to 13.642 KPa, and the resistance of the cold side was reduced from 1.102 KPa to 0.687 KPa, representing reductions of 38.5% and 36.9%, respectively. The optimized liquid–liquid exchanger is installed in the waste heat utilization subsystem, and due to the increase in the heat exchange of the liquid–liquid exchanger, more waste heat of the PEMFC is exchanged to the warm air loop, which will reduce the PTC energy, and the flow resistance of the liquid–liquid exchanger is reduced, so that the flow resistance of the entire system is reduced, thereby reducing the energy consumption of the water pump.

4. Validation of the Optimization Results for the Adaptability of the FCV Waste Heat Utilization Subsystem to Extreme Cold Environments

The optimized liquid–liquid exchanger is installed in the FCV waste heat utilization subsystem, and the FCV with a PEMFC rated power of 90 kW is tested again in accordance with the operating conditions described in Section 2. The experimental results displayed in Figure 7 show that at varied ambient temperatures, the PEMFC’s intake and outlet coolant temperatures are lowered. The PEMFC’s inlet and outlet coolant temperatures both drop slightly when the temperature of the environment drops to −20 °C. The reason for this is that the PEMFC radiator fan is frequently turned on before the waste heat utilization subsystem is optimized, and more heat of the PEMFC is dissipated into the air through the radiator. After optimization, the heat exchange of the liquid–liquid exchanger is increased, the PEMFC radiator fan is disabled, and the waste heat utilization subsystem uses more of the PEMFC’s residual heat to heat the cab, reducing PTC energy use. When the temperature of the surroundings reaches −25 °C and −30 °C, the PEMFC’s intake and outlet coolant temperatures drop even more. The reason for this is that before the optimization of the waste heat utilization subsystem, the opening frequency of the radiator fan is relatively small, and relatively less heat from the PEMFC is dissipated into the air by the radiator. After optimization, the PEMFC radiator fan will no longer be turned on, and the waste heat utilization subsystem will provide more PEMFC waste heat to warm the cab, reducing the heat supply of the PTC. From the above analysis, it can be seen that the optimized waste heat utilization subsystem can improve the utilization of PEMFC waste heat, enhance the adaptability to extreme cold environments, and improve the performance of FCV in low-temperature environments.

It can be concluded from Figure 8 that in an extremely cold environment with an environment temperature of −20 °C, the PEMFC radiator fan is frequently turned on before the waste heat utilization subsystem is optimized, and more heat from the PEMFC is dissipated into the air through the radiator. After optimization, the radiator fan is not turned on, and the coolant flowing through the radiator only exchanges heat with the outside low-temperature environment through heat radiation. The waste heat utilization subsystem uses the PEMFC heat that is mostly dissipated into the air by the radiator to heat the cab, reducing the PTC’s energy consumption; at a temperature of −25 °C, the radiator fan will also turn on when the PEMFC releases a higher amount of energy before the waste heat utilization subsystem is optimized, dissipating a large amount of heat from the PEMFC into the air. After optimization, when the PEMFC releases a large amount of energy, the radiator fan will no longer be turned on, and the waste heat utilization subsystem will utilize more waste heat from the PEMFC; at an environmental temperature of −30 °C, the PEMFC radiator fan will not be turned on before and after the waste heat utilization subsystem is optimized. The PEMFC heat dissipated into the air is also relatively small. Due to the increase in the heat exchange of the liquid–liquid exchanger, more PEMFC waste heat is used by the waste heat utilization subsystem for heating the cab, which reduces the heat supply of the PTC. The optimized waste heat utilization subsystem can reduce the energy consumption of PEMFC radiators and PTC, improve the utilization of PEMFC waste heat, improve the adaptability to extreme cold environments, and improve the performance of FCV in low-temperature environments, as shown in the above analysis.

It can be seen from Figure 9 that under the ambient temperature of −20 °C, the temperature difference between the inlet and outlet coolants on the cold and hot sides of the liquid–liquid exchanger is the largest, at 8.9 °C and 25.7 °C, respectively, compared with those before the optimization of the waste heat utilization subsystem. The improvements are 62.9% and 68.9%, respectively, indicating that the liquid–liquid exchanger transfers more heat from the PEMFC to the cab, thereby reducing the PTC energy consumption. At an environmental temperature of −25 °C, the inlet and outlet coolant temperature differences on the liquid–liquid exchanger’s cold and hot side are 8.9 °C and 8.9 °C, respectively, which is 57.3% and 61.8% higher than before the optimization. The waste heat utilization subsystem at this ambient temperature can also use more heat from the PEMFC to heat the cab. At an ambient temperature of −30 °C, the temperature differences between the inlet and outlet coolants on the cold side and the hot side of the liquid–liquid exchanger are 8.9 °C and 22.9 °C, respectively, which are 67.4% and 60.7% higher than before. The results of the optimization of the waste heat utilization subsystem show that the warm air loop obtains more waste heat from the PEMFC. At each ambient temperature, the temperature difference between the inlet and outlet water on the hot side of the liquid–liquid exchanger is the same as that of the PEMFC, indicating that the optimized liquid–liquid exchanger is more suitable for the PEMFC cooling system. The energy usage of the PTC in the optimized waste heat recycling system is reduced, the optimized waste heat utilization subsystem improves the consumption of the PEMFC waste heat and enhances its adaptability to the extreme cold environment, and the FCV performance in a low-temperature environment is improved, as can be seen from the above analysis.

From Figure 10, it can be concluded that the PTC energy consumption changes can be divided into five stages. The PEMFC releases less energy in stage ①, and the PEMFC waste heat cannot be used by the waste heat utilization subsystem. Only PTC is utilized to heat the cab at this time. The PTC energy consumption change begins in stage ② after a certain amount of time. At this time, the PEMFC outlet water temperature is higher than 70 °C, when the electric water valve is opened, a temperature differential exists between the hot and cold sides of the coolant when it passes through the hot side inlet of the liquid–liquid exchanger, the PEMFC waste heat is transferred to the warm air loop, and the PTC energy consumption decreases. Due to the increased heat exchange of the liquid–liquid exchanger in the optimized waste heat utilization subsystem, more of the waste heat from the PEMFC is transferred to the warm air loop, and as a result, the improved waste heat utilization subsystem’s PTC energy consumption is lower than the PTC energy consumption of the waste heat utilization subsystem before optimization. In stage ③, when the inlet coolant temperature of the liquid–liquid exchanger cold and hot side is equal, no heat exchange occurs in the liquid–liquid exchanger. At this stage, only the PTC is still used to provide heat to the cab. With the increase in PEMFC outlet power, the inlet coolant of the liquid–liquid exchanger’s cold and hot sides begins to display a certain temperature difference, and the PTC energy consumption change enters stage ④. The PTC energy consumption of the optimized waste heat utilization subsystem is smaller because the inlet and outlet coolant temperature differences on the liquid–liquid exchanger’s cold and hot side are both increased after the optimization of the waste heat utilization subsystem, and the warm air loop obtains more PEMFC waste heat. PTC energy consumption is significantly reduced and is maintained in a low-energy state. PTC energy consumption was reduced by 57.6 percent, 48 percent, and 34.3 percent in extreme cold temperatures of −20 °C, −25 °C, and −30 °C, respectively, indicating that the optimized waste heat utilization subsystem can increase the utilization rate of waste heat in PEMFCs and improve their adaptability to extreme cold.

5. Conclusions

This article firstly studies the influence of PEMFC radiator and PTC energy consumption on the adaptability of the vehicle waste heat utilization subsystem of different rated power PEMFCs to extreme cold environments through experiments under different ambient temperatures, and then uses the experimental data to analyze the PEMFC heating capacity and liquid–liquid exchanger heat exchange capacity to adapt to the extreme cold environment of different rated power FCV waste heat utilization subsystems. Then, the optimization mathematical model of the liquid–liquid exchanger was established, and the heat transfer performance of the liquid–liquid exchanger was orthogonally optimized based on the Taguchi method. Finally, the optimized liquid–liquid exchanger was fitted in the waste heat utilization subsystem, and the vehicle experiment confirmed the superiority of the optimized waste heat utilization subsystem. The conclusions are as follows:

(1)

In an extremely cold environment with an ambient temperature of −20 °C, −25 °C, and −30 °C, for the vehicle with a PEMFC rated power of 60 kW, because its PEMFC generates a small amount of heat, all the heat required to heat the cab is provided by PTC, indicating that its waste heat utilization subsystem cannot utilize the waste heat of PEMFC and is not suitable for extremely cold environments. The adaptability of the automobile waste heat utilization subsystem with a PEMFC rated power of 90 kW is low in extreme cold environments. The reason for this is that the PEMFC with a rated power of 90 kW has more waste heat, but the heat exchange of the liquid–liquid exchanger is small. Most of the heat from the PEMFC is dissipated into the air through the radiator, which is not utilized by the waste heat utilization subsystem, resulting in the high power consumption of the PTC.

(2)

After the liquid–liquid exchanger is optimized by the Taguchi method orthogonally, the optimal combination of each level factor is: H(5), L_h(1), L_w(5), N(5)—that is, the fin height H, core length L_h, core width L_w, and the total fluid layer N of the liquid–liquid exchanger are 7 mm, 200 mm, 110 mm, and 20, respectively. After optimization, the heat transfer capacity of the liquid–liquid exchanger increased by 62.5% from 4.774 kW before optimization to 12.724 kW after optimization; the hot side resistance decreased from 21.605 KPa to 13.642 KPa, and the cold side resistance decreased from 1.102 KPa to 0.687 KPa, decreasing by 38.5% and 36.9%, respectively.

(3)

In an extremely cold environment with an ambient temperature of −20 °C, −25 °C, −30 °C, after the waste heat utilization subsystem is optimized, the PEMFC radiator fan is not turned on, the radiator energy consumption is reduced, and the flow resistance of the waste heat utilization subsystem is reduced. Water pump energy consumption is reduced; at various ambient temperatures, the warm air loop receives extra waste heat from the PEMFC, which is used to heat the cab. The energy consumption of PTC is lowered by 57.6%, 48%, and 34.3%, respectively; the utilization rate of PEMFC waste heat of the optimized waste heat utilization subsystem increases and its adaptability to extreme cold environments is enhanced, which improves the performance of FCVs in low-temperature environments.