Research on refrigerant charge determination under different compressor speed and its effects on the performance of transcritical CO_(2)\mathrm{CO}_{2} air-conditioning heat pump system in electric vehicle 不同压缩机转速下制冷剂充注量的确定及其对电动汽车跨临界 CO_(2)\mathrm{CO}_{2} 空调热泵系统性能的影响研究
Ziqi Jiang ^(a){ }^{\mathrm{a}}, Yafen Tian ^(a,b,^(**)){ }^{\mathrm{a}, \mathrm{b},{ }^{*}}, Kang Li^(a,b)\mathrm{Li}^{\mathrm{a}, \mathrm{b}}, Zhaorui Zhao ^(a,b){ }^{\mathrm{a}, \mathrm{b}}, Ni Liu ^(a,b){ }^{\mathrm{a}, \mathrm{b}}, Hua Zhang ^(a,b){ }^{\mathrm{a}, \mathrm{b}} 蒋子琪 ^(a){ }^{\mathrm{a}} 、田亚芬 ^(a,b,^(**)){ }^{\mathrm{a}, \mathrm{b},{ }^{*}} 、康晓明 Li^(a,b)\mathrm{Li}^{\mathrm{a}, \mathrm{b}} 、赵兆瑞 ^(a,b){ }^{\mathrm{a}, \mathrm{b}} 、刘妮 ^(a,b){ }^{\mathrm{a}, \mathrm{b}} 、张华 ^(a,b){ }^{\mathrm{a}, \mathrm{b}}^(a){ }^{a} School of Energy and Power Engineering, University of Shanghai for Science and Technology, Shanghai 200093, China ^(a){ }^{a} 上海科技大学能源与动力工程学院，中国上海 200093^("b "){ }^{\text {b }} Shanghai Key Laboratory of Multiphase Flow and Heat Transfer in Power Engineering, Shanghai 200093, China ^("b "){ }^{\text {b }} 上海动力工程多相流与传热重点实验室，中国上海 200093
CO_(2)\mathrm{CO}_{2} is assumed to be one of the most potential refrigerant alternatives for electric vehicles for its excellent properties. However, the charge determination of CO_(2)\mathrm{CO}_{2} in current studies remain controversial. In this study, a transcritical CO_(2)\mathrm{CO}_{2} air-conditioning heat pump system was established and experimentally tested to analyze the optimal charge amount. Based on two conflicting methods of charge determining proposed by the preceding research, this paper substantiated the existing controversy and subsequently proposed a more comprehensive method. The effects of different refrigerant charge on the system characteristics were investigated. The influence of the compressor speed on the optimal refrigerant charge and system characteristics was also analyzed. It was found that the optimal charge plateau occurred from refrigerant of 500g-580g500 \mathrm{~g}-580 \mathrm{~g} at the compressor speed of 3000 r*min^(-1)\mathrm{r} \cdot \mathrm{min}^{-1}. However, the optimal charge declined with the increment of compressor speed from 3000r*min^(-1)3000 \mathrm{r} \cdot \mathrm{min}^{-1} to 4500r*min^(-1)4500 \mathrm{r} \cdot \mathrm{min}^{-1}. Among three models, Hughmark’s model was proved to be the most appropriate for the theoretical calculation of optimal charge within an error of 6.09%6.09 \%. Further study illustrates that refrigerant mass in highpressure pipe and intermediate heat exchanger/accumulator (IHX/A) accounted for the main proportion about 52.6%-55.14%. CO_(2)\mathrm{CO}_{2} 因其优异的性能被认为是电动汽车最有潜力的制冷剂替代品之一。然而，在目前的研究中， CO_(2)\mathrm{CO}_{2} 的充注量确定仍存在争议。本研究建立了一个跨临界 CO_(2)\mathrm{CO}_{2} 空调热泵系统，并进行了实验测试，以分析最佳充注量。在前人提出的两种充注量确定方法相互矛盾的基础上，本文证实了现有的争议，并随后提出了一种更全面的方法。研究了不同制冷剂充注量对系统特性的影响。还分析了压缩机转速对最佳制冷剂充注量和系统特性的影响。研究发现，当压缩机转速为 3000 r*min^(-1)\mathrm{r} \cdot \mathrm{min}^{-1} 时， 500g-580g500 \mathrm{~g}-580 \mathrm{~g} 的制冷剂充注量达到最佳充注量高点。然而，随着压缩机转速从 3000r*min^(-1)3000 \mathrm{r} \cdot \mathrm{min}^{-1} 到 4500r*min^(-1)4500 \mathrm{r} \cdot \mathrm{min}^{-1} 的增加，最佳充注量有所下降。在三种模型中，Hughmark 模型被证明最适合最佳充注量的理论计算，误差在 6.09%6.09 \% 范围内。进一步研究表明，高压管道和中间热交换器/蓄热器（IHX/A）中的制冷剂质量占主要比例，约为 52.6%-55.14% 。
1. Introduction 1.导言
As the increasingly stricter regulations on the emission of exhaust gas are implemented, electric vehicles (EVs) have received much attention from experts worldwide. From the perspective of the environment and economy, EVs emit less polluted gas than conventional vehicles (CVs), making EVs to be the most promising substitutions of CVs [1,2]. However, the operation performance of lithium-ion batteries is considerably relative to ambient temperature [3,4]. Inappropriate temperature conditions can exacerbate battery aging issues and capacity reduction [5,6]. Therefore, an efficient thermal management system (TMS) for both battery packs and passenger cabins becomes imperative to ensure both optimal battery operation and passenger comfort. And it will contribute to enhanced energy efficiency and environmental protection [7]. 随着废气排放法规的日益严格，电动汽车（EV）受到了全球专家的广泛关注。从环境和经济的角度来看，电动汽车比传统汽车（CV）排放更少的污染气体，因此电动汽车是最有希望取代传统汽车的交通工具[1,2]。然而，锂离子电池的运行性能与环境温度有很大关系[3,4]。不适当的温度条件会加剧电池老化和容量下降问题[5,6]。因此，必须为电池组和客舱提供高效的热管理系统（TMS），以确保电池的最佳工作状态和乘客的舒适度。这将有助于提高能源效率和保护环境[7]。
As EVs equipped with TMS have become prevalent in the market, the use of conventional refrigerants like R134a, R32, and R410A has aggravated global warming. Therefore, carbon dioxide (R744), a natural gas with a relatively low Global Warming Potential (GWP), has been 随着配备 TMS 的电动汽车在市场上的普及，R134a、R32 和 R410A 等传统制冷剂的使用加剧了全球变暖。因此，全球升温潜能值（GWP）相对较低的天然气二氧化碳（R744）已被广泛使用。
extensively studied in the field of automobile air-conditioning. Besides, R744 has good thermodynamic properties that are especially advantageous in cold regions. In other words, R744 has considerably larger heating capacity compared with other refrigerants [8-11]. In addition, CO_(2)\mathrm{CO}_{2} operates in the refrigeration system in a supercritical state due to the low critical temperature ( {:31.1^(@)C,7.38MPa)\left.31.1^{\circ} \mathrm{C}, 7.38 \mathrm{MPa}\right), which enhances the heat transfer efficiency in high-pressure side. 在汽车空调领域已被广泛研究。此外，R744 还具有良好的热力学特性，这在寒冷地区尤为有利。换句话说，与其他制冷剂相比，R744 的加热能力要大得多 [8-11]。此外， CO_(2)\mathrm{CO}_{2} 由于临界温度（ {:31.1^(@)C,7.38MPa)\left.31.1^{\circ} \mathrm{C}, 7.38 \mathrm{MPa}\right) ）较低，在制冷系统中以超临界状态运行，从而提高了高压侧的传热效率。
The refrigerant charge amount is widely recognized as a crucial factor that significantly influences the performance of transcritical CO2 air-conditioning heat pump systems (ACHP) [12,13]. Researchers have been substantially studying the effects of refrigerant charge on various parameters and explored the methods to determine the optimal refrigerant charge in the system for the past decades. He et al. [14] found that the variations of ambient temperature and water inlet temperature influence the optimal charge in transcritical CO_(2)\mathrm{CO}_{2} heat pump water heater (HPWH). The optimal charge could soar by 70%70 \% along with the increase of ambient temperature, primarily due to the evaporator’s influence ( 90%90 \% ). Conversely, an increase in water inlet temperature results in a 28% decrease in the optimal charge. Zhang et al. [15] experimentally 制冷剂充注量被公认为是显著影响跨临界二氧化碳空调热泵系统（ACHP）性能的关键因素 [12,13]。过去几十年来，研究人员一直在大量研究制冷剂充注量对各种参数的影响，并探索确定系统中最佳制冷剂充注量的方法。He 等人[14]发现，环境温度和进水温度的变化会影响跨临界 CO_(2)\mathrm{CO}_{2} 热泵热水器（HPWH）的最佳充注量。主要由于蒸发器的影响（ 90%90 \% ），最佳充注量会随着环境温度的升高而增加 70%70 \% 。相反，进水温度升高会导致最佳充注量减少 28%。Zhang 等人[15]在实验中
Nomenclature 术语
A cross section area ( m^(2)\mathrm{m}^{2} ) 横截面积 ( m^(2)\mathrm{m}^{2} ) c_(p)quadc_{p} \quad specific heat at constant pressure ( J//(kg*K)\mathrm{J} /(\mathrm{kg} \cdot \mathrm{K}) ) 恒压下的 c_(p)quadc_{p} \quad 比热 ( J//(kg*K)\mathrm{J} /(\mathrm{kg} \cdot \mathrm{K}) ) D quadD \quad diameter (m) D quadD \quad 直径（米） G quadG \quad mass flux ( kg//(s*m^(2):}\mathrm{kg} /\left(\mathrm{s} \cdot \mathrm{m}^{2}\right. ) )) G quadG \quad 质量通量 ( kg//(s*m^(2):}\mathrm{kg} /\left(\mathrm{s} \cdot \mathrm{m}^{2}\right. ) )) g quadg \quad acceleration of gravity (m//s^(2))\left(\mathrm{m} / \mathrm{s}^{2}\right) g quadg \quad 重力加速度 (m//s^(2))\left(\mathrm{m} / \mathrm{s}^{2}\right) h quadh \quad specific enthalpy (J//kg(\mathrm{J} / \mathrm{kg} ) h quadh \quad 比热 (J//kg(\mathrm{J} / \mathrm{kg} ) H quadH \quad height (m) H quadH \quad 高度（米） L quadL \quad Length (m) L quadL \quad 长度（米） m quadm \quad refrigerant mass (g) m quadm \quad 制冷剂质量（克） nquad\mathrm{n} \quad number of microchannels nquad\mathrm{n} \quad 微通道数量 Q quadQ \quad heat capacity of heat exchanger ( kW)) Q quadQ \quad 换热器的热容量（千瓦 )) S quadS \quad slip ratio S quadS \quad 滑动比
SH superheat (^(@)C)\left({ }^{\circ} \mathrm{C}\right) SH 过热 (^(@)C)\left({ }^{\circ} \mathrm{C}\right) T quadT \quad Temperature ( ^(@)C{ }^{\circ} \mathrm{C} ) T quadT \quad 温度 ( ^(@)C{ }^{\circ} \mathrm{C} ) V quadV \quad volume (m^(3))\left(\mathrm{m}^{3}\right) V quadV \quad 音量 (m^(3))\left(\mathrm{m}^{3}\right) W quadW \quad power consumption (kW) W quadW \quad 功率消耗（千瓦） x quadx \quad vapor quality x quadx \quad 蒸汽质量
air, in inlet of air side at heat exchanger 空气，在热交换器空气侧入口处
air, out outlet of air side at heat exchanger 空气，从热交换器的空气侧出口排出
comp, suc suction pipe of compressor 压缩机吸气管
comp, dis discharge pipe of compressor 压缩机排气管
e evaporation e 蒸发
evap, in inlet of evaporator 蒸发，在蒸发器入口内
evap, out outlet of evaporator 蒸发器出口
GC, in inlet of GC 气相色谱仪，在气相色谱仪入口处
GC, out outlet of GC 全球控制中心，全球控制中心出口 hquad\mathrm{h} \quad hydraulic hquad\mathrm{h} \quad 液压
hom Homogeneous model 同质模型
1 liquid 1 液体
ph high-pressure pipe ph 高压管
pl low-pressure pipe pl 低压管
two-phase two-phase region of heat exchanger 热交换器的两相区域
v vapor 蒸汽
Abbreviation 缩写
ACHP air-conditioning heat pump ACHP 空调热泵
COP coefficient of performance COP 性能系数
CV conventional vehicle CV 传统车辆
EEV electronic expansion valve EEV 电子膨胀阀
EV electric vehicle EV 电动汽车
GC gas cooler 气相色谱仪气体冷却器
GWP global warming potential GWP 全球升温潜能值
HPWH Heat pump water heater HPWH 热泵热水器
HVAC heating ventilation and air-conditioning HVAC 暖通空调系统
IDHX indoor heat exchanger IDHX 室内热交换器
IHX/A Intermediate heat exchanger/accumulator IHX/A 中间热交换器/蓄热器
OCPR optimal charge plateau region OCPR 最佳电荷高原区
ODHX outdoor heat exchanger ODHX 室外热交换器
SV Solenoid valve SV 电磁阀
TMS thermal management system TMS 热管理系统
Dimensionless numbers 无量纲数
Re Reynolds number 雷诺数 Frquad\mathrm{Fr} \quad Froude number Frquad\mathrm{Fr} \quad 弗劳德数
We Weber number 我们的编号 X_(tt)quadX_{t t} \quad Lockhart-Martinelli parameter X_(tt)quadX_{t t} \quad 洛克哈特-马丁内利参数
investigated important parameters containing condensing and evaporating pressure, coefficient of performance (COP) and heating capacity varied with the change of the charge in transcritical CO_(2)HPWH\mathrm{CO}_{2} \mathrm{HPWH}. It indicated that the pressure was consistent with the variation of charge amount. The COP and heating capacity reach a peak at the charge of 1.8 kg . Wang et al. [16] proposed a method to determine the optimal charge plateau region (OCPR), where the starting point and ending point of the plateau were dependent on the superheat of evaporator ( SH_("evap, out ")S H_{\text {evap, out }} ) and the suction superheat of compressor ( SH_("comp, suc ")\mathrm{SH}_{\text {comp, suc }} ) respectively. The relation between capillary tube geometry and optimal charge amount in transcritical CO_(2)HPWH\mathrm{CO}_{2} \mathrm{HPWH} was presented by Wang et al. [17]. It suggested that the length of the capillary tube was shortened by 8.77%8.77 \% and the optimal refrigerant charge increased by about 5%5 \% under the specific conditions. Furthermore, optimizing heat exchanger structural geometry can effectively reduce refrigerant charge while maintaining system performance [18-20]. 研究了冷凝和蒸发压力、性能系数（COP）和加热能力等重要参数在跨临界 CO_(2)HPWH\mathrm{CO}_{2} \mathrm{HPWH} 中随装料量的变化而变化。结果表明，压力与充注量的变化一致。COP 和加热能力在装料量为 1.8 kg 时达到峰值。Wang 等人[16]提出了一种确定最佳充注高原区（OCPR）的方法，其中高原起点和终点分别取决于蒸发器过热度（ SH_("evap, out ")S H_{\text {evap, out }} ）和压缩机吸气过热度（ SH_("comp, suc ")\mathrm{SH}_{\text {comp, suc }} ）。Wang 等人[17]提出了跨临界 CO_(2)HPWH\mathrm{CO}_{2} \mathrm{HPWH} 中毛细管几何形状与最佳充注量之间的关系。结果表明，在特定条件下，毛细管长度缩短 8.77%8.77 \% ，最佳制冷剂充注量增加约 5%5 \% 。此外，优化热交换器结构的几何形状可有效减少制冷剂充注量，同时保持系统性能[18-20]。
The performance of transcritical the CO_(2)\mathrm{CO}_{2} cycle declines drastically in undercharged and overcharged situations, highlighting the crucial importance of determining optimal charge amount. Liu et al. and Yin et al. [21,22] discovered that insufficient charge and excessive charge would trigger the decline of COP and cooling capacity. Cho et al. [23] conducted experiments to study the impact of undercharged and overcharged situations on cooling capacity and entropy generation. Their findings revealed that the reduction in cooling capacity was more pronounced in undercharged situations compared to overcharged ones. Additionally, expansion loss and gas cooler (GC) loss were dominant in undercharged situations and overcharged situations respectively. However, inappropriate charge is common due to the inability of the 在充电不足和充电过量的情况下，跨临界 CO_(2)\mathrm{CO}_{2} 循环的性能会急剧下降，这凸显了确定最佳充电量的重要性。Liu 等人和 Yin 等人[21,22] 发现，充电不足和充电过量都会导致 COP 和制冷量下降。Cho 等人[23]通过实验研究了充电不足和充电过量对冷却能力和熵产生的影响。他们的研究结果表明，在充电不足和充电过量的情况下，冷却能力的下降更为明显。此外，膨胀损耗和气体冷却器（GC）损耗分别在充电不足和充电过量的情况下占主导地位。然而，不适当的充注很常见，这是因为气冷器不能
accumulator to fully meet refrigerant balance requirements for varying operating conditions [24]. Thus the authors present a novel control logic that concentrates on regulating the distribution of refrigerant to ensure reasonable refrigerant distribution. Consequently, the determination of appropriate refrigerant charge can guarantee the maximum COP and cooling capacity. The former two indexes ( SH_("evap,out, ")SH_("comp,suc ")S H_{\text {evap,out, }} S H_{\text {comp,suc }} ) are also two factors that distinguish whether the refrigerant charge is appropriate. With the increment of refrigerant charge, SH_("evap,out ")S H_{\text {evap,out }} exhibits a declining trend in the undercharged situation until it reaches the minimum at 0^(@)C0^{\circ} \mathrm{C}, which is regarded as the initiation point of OCPR. In other words, when the SH_("evap, out ")S H_{\text {evap, out }} equals 0^(@)C0{ }^{\circ} \mathrm{C}, it results in the longest evaporation length on the pressure-enthalpy diagram. This leads to reaching the upper limitation of cooling capacity and COP. Meanwhile, when the refrigerant charge amount enters into the overcharged situations, SH_("comp,suc ")S H_{\text {comp,suc }} is to drop because the accumulator reaches the maximum capacity. Consequently, liquid refrigerant enters into the compressor, resulting in liquid strike and subsequently reducing both cooling capacity and COP [16]. Inversely, Yin et al. [21] deemed that SH_("evap,out ")S H_{\text {evap,out }} and SH_("comp,suc ")S H_{\text {comp,suc }} are not appropriate for the judging criterion. They proposed that discharge temperature, suction temperature and the temperature before the electronic expansion valve are the most suitable parameters to judge the optimal charge condition. Therefore, the controversy surrounding the judging criterion of optimal charge condition warrants further research. 蓄能器，以完全满足不同运行条件下的制冷剂平衡要求 [24]。因此，作者提出了一种新颖的控制逻辑，集中于调节制冷剂的分配，以确保制冷剂的合理分配。因此，确定适当的制冷剂充注量可以保证最大 COP 和制冷量。前两个指标（ SH_("evap,out, ")SH_("comp,suc ")S H_{\text {evap,out, }} S H_{\text {comp,suc }} ）也是区分制冷剂充注量是否合适的两个因素。随着制冷剂充注量的增加， SH_("evap,out ")S H_{\text {evap,out }} 在充注量不足的情况下呈下降趋势，直到 0^(@)C0^{\circ} \mathrm{C} 处达到最小值，这被视为 OCPR 的起始点。换句话说，当 SH_("evap, out ")S H_{\text {evap, out }} 等于 0^(@)C0{ }^{\circ} \mathrm{C} 时，在压力-焓图上的蒸发长度最长。这将导致制冷量和 COP 达到上限。同时，当制冷剂充注量进入过充状态时， SH_("comp,suc ")S H_{\text {comp,suc }} 会因为蓄能器达到最大容量而下降。因此，液态制冷剂会进入压缩机，造成液击，从而降低制冷量和 COP [16]。相反，Yin 等人[21] 认为 SH_("evap,out ")S H_{\text {evap,out }} 和 SH_("comp,suc ")S H_{\text {comp,suc }} 不适合作为判断标准。他们提出，排气温度、吸气温度和电子膨胀阀前的温度是判断最佳充注条件的最合适参数。因此，围绕最佳充注条件判断标准的争议值得进一步研究。
Many factors, such as compressor speed, opening of electronic expansion valve (EEV) and ambient temperature, affect the operation of system. Addmittedly, the adjusting of opening of expansion valve is crucial during the operation of test. Song et al. [8] experimentally 压缩机转速、电子膨胀阀（EEV）开度和环境温度等许多因素都会影响系统的运行。诚然，在测试运行过程中，膨胀阀开度的调节至关重要。Song 等人[8]通过实验
Fig. 1. (a). The schematic diagram of transcritical CO_(2)ACHP\mathrm{CO}_{2} \mathrm{ACHP} system; (b). flow circuit diagram in cooling mode. 图 1.跨临界 CO_(2)ACHP\mathrm{CO}_{2} \mathrm{ACHP} 系统原理图； (b). 冷却模式下的流动电路图。
studied the effect of opening step of electronic expansion valve on system performance. They found that when the EEV opening reduced from 100%100 \% to 55%55 \%, the COP reached its peak at 3.17 with an opening of 55%55 \%. Meanwhile, optimum discharge pressure at the opening of 55% appears at 7.54 MPa. Liu et al. [21] assumed that the performance of system could be adjusted by discharge pressure. It is also emphasized that the system performance reduces with higher evaporation pressure under constant discharge pressure. Consequently, discharge pressure substantially influences the COP of CO_(2)\mathrm{CO}_{2} system. However, Wang et al. [25] analyzed the operation parameters that affects the power consumption and heating capacity. It is concluded that the variation of EEV opening has minimum influence on power consumption and heating capacity, while the compressor speed has a significant inflence on them. Li et al. [12] experimentally investigated the relationship between EEV opening and charge amount in CO_(2)ACHP\mathrm{CO}_{2} \mathrm{ACHP} system in cooling mode. It reveals that the optimal charge appears at 550 g when the opening of EEV varies from 30%30 \% to 60%. 研究了电子膨胀阀开启步骤对系统性能的影响。他们发现，当电子膨胀阀开度从 100%100 \% 减小到 55%55 \% 时，COP 在 55%55 \% 开度时达到峰值 3.17。同时，开度为 55% 时的最佳排放压力为 7.54 MPa。Liu 等人[21]认为系统的性能可以通过排放压力来调节。他们还强调，在恒定的排放压力下，系统性能会随着蒸发压力的升高而降低。因此，排放压力对 CO_(2)\mathrm{CO}_{2}
