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} 系统的 COP 有很大影响。然而，Wang 等人 [25] 分析了影响功耗和加热能力的运行参数。结果表明，EEV 开度的变化对耗电量和制热量的影响最小，而压缩机转速对耗电量和制热量的影响较大。Li 等人[12]通过实验研究了冷却模式下 CO_(2)ACHP\mathrm{CO}_{2} \mathrm{ACHP} 系统中 EEV 开度与充注量之间的关系。结果表明，当 EEV 开度在 30%30 \% 至 60% 之间变化时，最佳充注量出现在 550 g。
Morever, the optimal refrigerant charge can be calculated by mathematical formulas that have been previously validated in the literature [26,27][26,27]. The CO_(2)\mathrm{CO}_{2} in the gas cooler (GC) is in supercritical state, where its temperature and pressure exceed the critical point and its density increases drastically. Marques Humia et al. [28] discretized the supercritical region of GC, determined the average density of each control volume and calculated the total fluid mass. Thus the total fluid mass in GC can be obtained by multiplying the internal volume and average density. The mass of single-phase refrigerant is determined by density and internal volume [29]. However, accurately calculating the mass of 此外，最佳制冷剂充注量可通过数学公式计算得出，这些公式之前已在文献 [26,27][26,27] 中得到验证。气体冷却器 (GC) 中的 CO_(2)\mathrm{CO}_{2} 处于超临界状态，其温度和压力超过临界点，密度急剧增加。Marques Humia 等人[28] 对 GC 的超临界区域进行了离散化处理，确定了每个控制体积的平均密度，并计算了总流体质量。因此，气相色谱仪中的总流体质量可以通过内部体积和平均密度相乘得到。单相制冷剂的质量由密度和内部体积决定 [29]。然而，要准确计算单相制冷剂的质量，还需要进行大量的计算工作。
the two-phase refrigerant is challenging as it requires suitable void fraction correlation. It is proved that three mass flux-dependent methods, namely Tondan’s model, Premoli’s model and Hughmark’s model are appropriate for heat pump system [30]. Compared to other models, it is found that Hughmark provides the most accurate result when calculating CO_(2)\mathrm{CO}_{2} mass of water heater with an average error of 6.38%6.38 \% [28]. However, these mathematical models are predominantly applied in regular subcritical refrigeration cycle for the calculation of conventional refrigerant in two-phase state. The research on verification of the computation of CO_(2)\mathrm{CO}_{2} mass for automobile usage is inadequate. Therefore, these models require further theoretical verification and experimental validation for CO_(2)\mathrm{CO}_{2} transcritical ACHP system. 由于需要合适的空隙率相关性，因此对两相制冷剂进行分析具有挑战性。实践证明，三种与质量通量相关的方法，即 Tondan 模型、Premoli 模型和 Hughmark 模型，都适用于热泵系统[30]。与其他模型相比，Hughmark 模型在计算热水器的 CO_(2)\mathrm{CO}_{2} 质量时结果最为准确，平均误差为 6.38%6.38 \% [28]。不过，这些数学模型主要应用于常规亚临界制冷循环，用于计算两相状态下的常规制冷剂。对汽车使用中 CO_(2)\mathrm{CO}_{2} 质量计算的验证研究还不够。因此，这些模型需要在 CO_(2)\mathrm{CO}_{2} 跨临界 ACHP 系统中进一步进行理论验证和实验验证。
From the aforementioned literature, several issues regarding CO_(2)\mathrm{CO}_{2} ACHP system have been subject to debate. To start with, many studies investigate the refrigerant charge by adding refrigerant at fixed interval of 50 g or even 100 g . It will induce inaccurate optimal charge plateau for compact system with moderate charge amount. Secondly, the criteria of charge determination in transcritical refrigeration cycle remains controversial in the latest studies. And further validation is required for theoretical models used to calculate the optimal charge in CO_(2)ACHP\mathrm{CO}_{2} \mathrm{ACHP} systems. 从上述文献来看，有关 CO_(2)\mathrm{CO}_{2} ACHP 系统的几个问题一直备受争议。首先，许多研究通过以 50 克甚至 100 克的固定间隔添加制冷剂来研究制冷剂充注量。 对于充注量适中的紧凑型系统来说，这会导致最佳充注量高点不准确。其次，在最新的研究中，跨临界制冷循环中制冷剂充注量的确定标准仍然存在争议。还需要进一步验证用于计算 CO_(2)ACHP\mathrm{CO}_{2} \mathrm{ACHP} 系统中最佳充注量的理论模型。
In this paper, a transcritical CO_(2)\mathrm{CO}_{2} automobile ACHP experimental system was established and experimentally tested to analyze the optimal charge amount. This study investigate the refrigerant charge by adding the refrigerant at the interval of 10 g to obtain an accurate range of optimal charge utill apporaching the optimal charge. And this study contributes to verifying and extending the criteria for charge 本文建立了跨临界 CO_(2)\mathrm{CO}_{2} 汽车冷热电联供实验系统，并通过实验测试分析了最佳充注量。本研究通过以 10 克为间隔添加制冷剂来研究制冷剂充注量，以获得最佳充注量的精确范围，直至达到最佳充注量。这项研究有助于验证和扩展充注量标准。
Table 1 表 1
The functioning of valves under different operating modes. 阀门在不同运行模式下的功能。
-: the valve is open; @\circ : the valve is close; diamond\diamond : the opening of valve can be adjusted. -：阀门打开； @\circ ：阀门关闭； diamond\diamond ：可调节阀门开度。
determination. The SH_("evap, out ")S H_{\text {evap, out }} and SH_("comp,suc ")S H_{\text {comp,suc }} (Ref. 16) are verified to successfully determine the OCPR. Besides the two calculated parameters, suction temperature, discharge temperature (Ref. 22), and discharge pressure are found to be sensitive indicators of charge amount under various compressor speed. Additionally, three different theoretical models are adopted to calculate different optimal refrigerant charge, allowing for further analysis of mass inventory in all system components. Summarily, this paper can serve as a comprehensive guidance for analyzing charge characteristics and determining the optimal refrigerant charge in CO_(2)ACHP\mathrm{CO}_{2} \mathrm{ACHP} system. 确定。经验证， SH_("evap, out ")S H_{\text {evap, out }} 和 SH_("comp,suc ")S H_{\text {comp,suc }} （参考文献 16）可成功确定 OCPR。除了这两个计算参数外，吸气温度、排气温度（参考文献 22）和排气压力也是不同压缩机转速下充注量的敏感指标。此外，本文还采用了三种不同的理论模型来计算不同的最佳制冷剂充注量，从而进一步分析了所有系统组件的质量库存。总之，本文可为分析 CO_(2)ACHP\mathrm{CO}_{2} \mathrm{ACHP} 系统的充注特性和确定最佳制冷剂充注量提供全面指导。
2. Experimental setup 2.实验装置
2.1. System description 2.1.系统描述
The schematic diagram of transcritical CO_(2)\mathrm{CO}_{2} ACHP system and flow circuit in cooling mode is illustrated in Fig. 1.As depicted in Fig. 1(a), the transcritical ACHP system contains following components: a compressor, an outdoor heat exchanger (ODHX), an intermediate heat exchanger/accumulator (IHX/A), two EEVs, a heating, ventilation and air conditioning(HVAC) unit, and four solenoid valves (SV). The HVAC unit consists of two heat exchangers (IDHX1 and IDHX2) and a blower that supples fresh air from the ambient environment to the heat exchange surface. Pressure and temperature sensors are arranged in the specific positions of system to obtain the crucial data in specific positions to evaluate the performance of system and obtain state parameters of refrigerant. The working modes are controlled by SVs and EEVs, as illustrated in Table 1. The HVAC unit consisting of two heat exchangers can supply both heating capacity and cooling capacity by adjusting the opening of valves. Eventually, the physical system and components are displayed in Fig. 2, which corresponds with the schematic diagram. 如图 1（a）所示，跨临界 ACHP 系统包含以下组件：一台压缩机、一个室外热交换器 (ODHX)、一个中间热交换器/蓄热器 (IHX/A)、两个 EEV、一个加热、通风和空调（HVAC）装置以及四个电磁阀 (SV)。暖通空调设备由两个热交换器（IDHX1 和 IDHX2）和一个鼓风机组成，鼓风机将周围环境中的新鲜空气输送到热交换表面。压力和温度传感器布置在系统的特定位置，以获取特定位置的关键数据，从而评估系统性能并获取制冷剂的状态参数。工作模式由 SV 和 EEV 控制，如表 1 所示。由两个热交换器组成的暖通空调设备可以通过调节阀门的开度来提供制热量和制冷量。最终，物理系统和组件如图 2 所示，与原理图相对应。
The flow circuit diagram of cooling mode is demonstrated in Fig. 1 (b). In this mode, the SV1, SV3, and EEV1 are open, as shown in Table 1. The refrigerant is compressed in the compressor and then enters ODHX served as external GC. The high pressure, medium temperature refrigerant continues to exchange heat in the intermediate heat exchanger with the refrigerant vapor. Then the refrigerant throttles in the EEV1 and then absorbs heat from the cabin in IDHX2 served as evaporator. Eventually, the refrigerant vapor gains a certain degree of superheat in the intermediate heat exchanger and flows back into the compressor. The accumulator can prevent liquid refrigerant from flowing into compressor until its filling level exceeds the upper limitation in the overcharged condition. 冷却模式的流程电路图如图 1 (b) 所示。在该模式下，SV1、SV3 和 EEV1 开启，如表 1 所示。制冷剂在压缩机中被压缩，然后进入作为外部 GC 的 ODHX。高压、中温制冷剂继续在中间热交换器中与制冷剂蒸汽进行热交换。然后，制冷剂在 EEV1 中节流，然后在作为蒸发器的 IDHX2 中吸收来自机舱的热量。最终，制冷剂蒸气在中间热交换器中获得一定的过热度，流回压缩机。蓄能器可以防止液态制冷剂流入压缩机，直到其充注水平超过过充状态下的上限。
Table 2 illustrates the specifications of several crucial components. The scroll compressor has a displacement of 5.3cm^(3)//rev5.3 \mathrm{~cm}^{3} / \mathrm{rev} with the range of rotary speed from 600r*min^(-1)600 \mathrm{r} \cdot \mathrm{min}^{-1} to 8600r*min^(-1)8600 \mathrm{r} \cdot \mathrm{min}^{-1}. Its discharge pressure should not exceed 16 MPa . Three heat exchangers are all parallel flow microchannel fin-tube type with their internal volumes as shown in the table. The EEVs can manually adjust the opening by the stepping motor from 0 to 1000. The operating data are recorded by Agilent every 2s. 表 2 列出了几个关键部件的规格。涡旋式压缩机的排量为 5.3cm^(3)//rev5.3 \mathrm{~cm}^{3} / \mathrm{rev} ，转速范围为 600r*min^(-1)600 \mathrm{r} \cdot \mathrm{min}^{-1} 至 8600r*min^(-1)8600 \mathrm{r} \cdot \mathrm{min}^{-1} 。其排气压力不应超过 16 兆帕。三个热交换器均为平行流微通道翅片管式，其内部容积如表所示。EEV 可以通过步进电机在 0 到 1000 之间手动调节开度。安捷伦每 2 秒记录一次运行数据。
2.2. Experiment conditions 2.2.实验条件
The experiment bench is established in the outdoor environmental chamber of Psychometric Room where adjustable temperature ambient can be provided. The air tunnel regulates the volumetric flow rate of the air through the ODHX, and two temperature sensors can detect the temperatures of air before and behind the ODHX. The humidity sensor can obtain the relative humidity. And the humidifier can change the relative humidity in accordance with the feedback of the sensor. Experimental conditions are designed to investigate the determination method of OCPR under the nominal refrigeration conditions for vehicle usage (GB/T 21361-2017 [31]) and the variation of optiaml charge under different rotary speed, as shown in Table 3. During the experiment, ambient temperature is fixed at 35^(@)C35^{\circ} \mathrm{C} with a relative humidity of 50% in cooling mode.This determines the inlet conditions of air in both ODHX and HVAC unit since the fresh air mode is selected for supplying air. In the fresh air mode, the temperature and relatively humidity of 实验台设在心理测量室的室外环境室中，可提供可调节的环境温度。空气隧道可调节通过 ODHX 的空气容积流量，两个温度传感器可检测 ODHX 前后的空气温度。湿度传感器可获得相对湿度。加湿器可根据传感器的反馈改变相对湿度。实验条件设计为研究车用名义制冷条件（GB/T 21361-2017[31]）下 OCPR 的测定方法以及不同转速下光电开关充注量的变化，如表 3 所示。实验期间，在制冷模式下，环境温度固定为 35^(@)C35^{\circ} \mathrm{C} ，相对湿度为 50%，这决定了 ODHX 和 HVAC 设备的进气条件，因为选择的是新风模式供气。在新风模式下，ODHX 和 HVAC 设备的温度和相对湿度均为 50%。
Table 2 表 2
Specification of experimental apparatuses. 实验设备的规格。
indoor condition are the same as the outdoor condition. And the indoor air flow is regulated by blower at the constant speed of 2000rev//min2000 \mathrm{rev} / \mathrm{min}. The compressor speed is considered as a variable that varies from 3000 to 4500r*min^(-1)4500 \mathrm{r} \cdot \mathrm{min}^{-1}. The volume flow rates at the inlet of outdoor heat exchanger is fixed at 3000m^(3)//h3000 \mathrm{~m}^{3} / \mathrm{h}. And the opening of EEV1 is fixed at 50%. 室内条件与室外条件相同。室内空气流量由鼓风机以 2000rev//min2000 \mathrm{rev} / \mathrm{min} 的恒定速度调节。压缩机转速被视为变量，在 3000 到 4500r*min^(-1)4500 \mathrm{r} \cdot \mathrm{min}^{-1} 之间变化。室外热交换器入口处的体积流量固定为 3000m^(3)//h3000 \mathrm{~m}^{3} / \mathrm{h} 。EEV1 的开度固定为 50%。
2.3. Data reduction 2.3.数据缩减
Test data was recorded by the data collection equipment. The thermal properties of refrigerant were calculated by NIST REFPROP 10.0. 测试数据由数据采集设备记录。制冷剂的热性能由 NIST REFPROP 10.0 计算得出。
In the cooling mode, the cooling capacity can be calculated by multiplying the mass flow rate of CO_(2)\mathrm{CO}_{2} and the enthalpy difference of refrigerant between the inlet and the outlet of evaporator, as shown in equation (1). And the flow rate can be obtained by the First Law of Thermodynamics (equation (2)) in the GC. The power consumption ( W_("comp ")W_{\text {comp }} ) is obtained by equation (3). 在制冷模式下，制冷量可通过 CO_(2)\mathrm{CO}_{2} 的质量流量与蒸发器入口和出口之间制冷剂的焓差相乘来计算，如式（1）所示。根据热力学第一定律（公式 (2)），可求得气相色谱仪中的流量。功耗（ W_("comp ")W_{\text {comp }} ）由公式 (3) 得出。 Q_(e)=m_(co_(2))(h_("evap, out ")-h_("evap, in "))Q_{\mathrm{e}}=m_{\mathrm{co}_{2}}\left(h_{\text {evap, out }}-h_{\text {evap, in }}\right) m_("co "2)(h_(GC," in ")-h_(GC," out "))=m_("air ")c_(p," air ")(T_("air,out ")-T_("air,in "))m_{\text {co } 2}\left(h_{\mathrm{GC}, \text { in }}-h_{\mathrm{GC}, \text { out }}\right)=m_{\text {air }} c_{p, \text { air }}\left(T_{\text {air,out }}-T_{\text {air,in }}\right)
where Q_(e)Q_{\mathrm{e}} is the cooling capacity, kW ; m_("air ")m_{\text {air }} is the mass flow rate of moist air, kg//s;h_("evap, out ")\mathrm{kg} / \mathrm{s} ; h_{\text {evap, out }} and h_("evap, in ")h_{\text {evap, in }} are the specific enthalpy of evaporator outlet and inlet, kJ//kg\mathrm{kJ} / \mathrm{kg}. 其中， Q_(e)Q_{\mathrm{e}} 为制冷量，千瓦； m_("air ")m_{\text {air }} 为湿空气的质量流量， kg//s;h_("evap, out ")\mathrm{kg} / \mathrm{s} ; h_{\text {evap, out }} 和 h_("evap, in ")h_{\text {evap, in }} 分别为蒸发器出口和入口的比焓， kJ//kg\mathrm{kJ} / \mathrm{kg} 。 W_("comp ")=m_(CO_(2))(h_("comp,dis ")-h_("comp, suc "))W_{\text {comp }}=m_{\mathrm{CO}_{2}}\left(h_{\text {comp,dis }}-h_{\text {comp, suc }}\right)
where h_("comp, dis ")h_{\text {comp, dis }} is the specific enthalpy of compressor discharge, kJ//kg\mathrm{kJ} / \mathrm{kg}; h_("comp, suc ")h_{\text {comp, suc }} is the specific enthalpy of compressor suction, kJ//kg;W_("comp ")\mathrm{kJ} / \mathrm{kg} ; W_{\text {comp }} is the compression work, kW . 其中， h_("comp, dis ")h_{\text {comp, dis }} 为压缩机排气比热， kJ//kg\mathrm{kJ} / \mathrm{kg} ； h_("comp, suc ")h_{\text {comp, suc }} 为压缩机吸气比热， kJ//kg;W_("comp ")\mathrm{kJ} / \mathrm{kg} ; W_{\text {comp }} 为压缩功，千瓦。
The COP is determined by Q_(e)Q_{\mathrm{e}} and W_("comp ")W_{\text {comp }}. COP 由 Q_(e)Q_{\mathrm{e}} 和 W_("comp ")W_{\text {comp }} 决定。 COP=(Q_(e))/(W_("comp "))\mathrm{COP}=\frac{Q_{\mathrm{e}}}{W_{\text {comp }}}
The SH_("evap, out ")S H_{\text {evap, out }} is defined as the deviation between the outlet temperature of evaporator and the outlet saturated temperature of evaporator at the evaporation pressure. The SH_("evap, out ")S H_{\text {evap, out }} equals 0^(@)C0^{\circ} \mathrm{C} when the state of refrigerant at the outlet of evaporator falls into two-phase region. SH_("evap, out ")S H_{\text {evap, out }} 定义为蒸发压力下蒸发器出口温度与蒸发器出口饱和温度之间的偏差。当蒸发器出口处的制冷剂状态进入两相区时， SH_("evap, out ")S H_{\text {evap, out }} 等于 0^(@)C0^{\circ} \mathrm{C} 。
The SH_("comp, suc ")S H_{\text {comp, suc }} represents the difference between the suction temperature and the saturated temperature at suction pressure. Similar to the SH_("evap, out, ")SH_("comp, suc ")S H_{\text {evap, out, }} S H_{\text {comp, suc }} equals 0^(@)C0^{\circ} \mathrm{C} when the state of refrigerant at the compressor inlet falls into two-phase region. SH_("comp, suc ")S H_{\text {comp, suc }} 表示吸气温度与吸气压力下的饱和温度之差。当压缩机入口处的制冷剂状态进入两相区时， SH_("evap, out, ")SH_("comp, suc ")S H_{\text {evap, out, }} S H_{\text {comp, suc }} 等于 0^(@)C0^{\circ} \mathrm{C} 。
2.4. Error analysis 2.4.误差分析
Table 4 demonstrates the accuracy of the measuring instruments. The accuracy of platinum resistance sensor is +-0.3^(@)C\pm 0.3^{\circ} \mathrm{C} with the working range from -200^(@)C-200^{\circ} \mathrm{C} to 400^(@)C400{ }^{\circ} \mathrm{C}. The pressure sensor has the accuracy of +-0.5%\pm 0.5 \%. 表 4 显示了测量仪器的精度。铂电阻传感器的精度为 +-0.3^(@)C\pm 0.3^{\circ} \mathrm{C} ，工作范围为 -200^(@)C-200^{\circ} \mathrm{C} 至 400^(@)C400{ }^{\circ} \mathrm{C} 。压力传感器的精度为 +-0.5%\pm 0.5 \% 。
Based on the accuracy the of sensors in the table, the uncertainty of cooling capacity and COP is calculated by Kline and McClintock method [21]: 根据表中传感器的精度，采用 Kline 和 McClintock 方法计算制冷量和 COP 的不确定性[21]： omega_(R)=[((del R)/(delx_(1))omega_(1))^(2)+((del R)/(delx_(2))omega_(2))^(2)+dots+((del R)/(delx_(n))omega_(n))^(2)]^((1)/(2))\omega_{R}=\left[\left(\frac{\partial R}{\partial x_{1}} \omega_{1}\right)^{2}+\left(\frac{\partial R}{\partial x_{2}} \omega_{2}\right)^{2}+\ldots+\left(\frac{\partial R}{\partial x_{n}} \omega_{\mathrm{n}}\right)^{2}\right]^{\frac{1}{2}}
3. Theoretical model for charge amount calculation 3.电荷量计算的理论模型
Refrigerant is distributed in every system component including the compressor, ODHX, IHX/A, IDHX2 in HVAC unit and pipes with different states. The refrigerant in single-phase (liuqid or vapor), for example, high pressure pipes, low pressure pipe, GC and compressor, is straightforward to calculate by condsidering the average density and internal volume of componets. However, the calculation becomes more challenging for two-phase regions in heat exchangers where the proportions of vapor and liquid are unknown. Therefore, the concept of void fraction needs to be introduced. 制冷剂分布在每个系统组件中，包括压缩机、暖通空调设备中的 ODHX、IHX/A、IDHX2 以及不同状态的管道。单相（液态或气态）制冷剂，例如高压管道、低压管道、气相色谱仪和压缩机，可以通过考虑组件的平均密度和内部容积来直接计算。然而，对于热交换器中的两相区域，由于蒸汽和液体的比例未知，计算变得更具挑战性。因此，需要引入空隙率的概念。
As shown in Equation (6), the total charge amount consists of seven parts. The high pressure pipes contain four parts: from compressor to ODHX (L_(1))\left(L_{1}\right), from ODHX to IHX/A (L_(2))\left(L_{2}\right), from IHX/A to EEV1 (L_(3))\left(L_{3}\right) and from EEV1 to evaporator (L_(4))\left(L_{4}\right). While the low pressure pipe is from evaporator to IHX/A ( L_(5)L_{5} ). The refrigerant mass in pipe from IHX/A to compressor is negligible due the short length of the pipe. According to the above literature [28], refrigerant charge in GC can be estimated by equation (7) that is also applicable to IHX and compressor. It is noteworthy that the refrigerant amount in IHX consists of low-pressure side and high-pressure side. The remaining refrigerant mass in corresponding components is evaluated by equations (7)-(11) 如公式 (6) 所示，总充气量由七个部分组成。高压管道包括四个部分：从压缩机到 ODHX (L_(1))\left(L_{1}\right) ，从 ODHX 到 IHX/A (L_(2))\left(L_{2}\right) ，从 IHX/A 到 EEV1 (L_(3))\left(L_{3}\right) ，从 EEV1 到蒸发器 (L_(4))\left(L_{4}\right) 。而低压管道是从蒸发器到 IHX/A ( L_(5)L_{5} )。由于管道长度较短，从 IHX/A 到压缩机的管道中的制冷剂质量可以忽略不计。根据上述文献 [28]，GC 中的制冷剂充注量可通过公式 (7) 估算，该公式同样适用于 IHX 和压缩机。值得注意的是，IHX 中的制冷剂量由低压侧和高压侧组成。相应组件中剩余的制冷剂质量可通过公式 (7)-(11) 进行估算 m_("sum ")=m_("comp ")+m_("ODHX ")+m_("accu ")+m_(IHX)+m_("evap ")+m_(pl)+m_(ph)m_{\text {sum }}=m_{\text {comp }}+m_{\text {ODHX }}+m_{\text {accu }}+m_{\mathrm{IHX}}+m_{\text {evap }}+m_{\mathrm{pl}}+m_{\mathrm{ph}}
Charge amount in compressor ( m_("comp ")m_{\text {comp }} ), accumulator ( m_("accu ")m_{\text {accu }} ), intermediate heat exchanger ( m_(IHX)m_{\mathrm{IHX}} ), evaporator ( m_("evap ")m_{\text {evap }} ), ODHX ( m_(ODHX)m_{\mathrm{ODHX}} ), and high and low pressure pipes ( m_(ph),m_(pl)m_{\mathrm{ph}}, m_{\mathrm{pl}} ) constitutes the refrigerant charge amount ( m_("sum ")m_{\text {sum }} ). 压缩机 ( m_("comp ")m_{\text {comp }} ) 、蓄能器 ( m_("accu ")m_{\text {accu }} ) 、中间热交换器 ( m_(IHX)m_{\mathrm{IHX}} ) 、蒸发器 ( m_("evap ")m_{\text {evap }} ) 、ODHX ( m_(ODHX)m_{\mathrm{ODHX}} ) 和高低压管道 ( m_(ph),m_(pl)m_{\mathrm{ph}}, m_{\mathrm{pl}} ) 中的充注量构成制冷剂充注量 ( m_("sum ")m_{\text {sum }} ) 。 m_("comp ")=(rho_("in ")+rho_("out "))/(2)V_("comp ")m_{\text {comp }}=\frac{\rho_{\text {in }}+\rho_{\text {out }}}{2} V_{\text {comp }}
In terms of the calculation of mass in compressor, it is calculated by multiplying the average density of inlet ( rho_("in ")\rho_{\text {in }} ) and outlet ( rho_("out ")\rho_{\text {out }} ) by internal volume of itself. The rho_("in ")\rho_{\text {in }} and rho_("out ")\rho_{\text {out }} refer to the suction and discharge density of compressor respectively. And V_("comp ")V_{\text {comp }} is the volume of compressor. 压缩机质量的计算方法是将入口（ rho_("in ")\rho_{\text {in }} ）和出口（ rho_("out ")\rho_{\text {out }} ）的平均密度乘以自身的内部容积。 rho_("in ")\rho_{\text {in }} 和 rho_("out ")\rho_{\text {out }} 分别指压缩机的吸气密度和排气密度。而 V_("comp ")V_{\text {comp }} 则是压缩机的体积。 m_(ph)=pi((D_(1))/(2))^(2)(L_(1)rho_(1)+L_(2)rho_(2)+L_(3)rho_(3)+L_(4)rho_(4))m_{\mathrm{ph}}=\pi\left(\frac{D_{1}}{2}\right)^{2}\left(L_{1} \rho_{1}+L_{2} \rho_{2}+L_{3} \rho_{3}+L_{4} \rho_{4}\right)
Refrigerant amount of high-pressure pipes consists of four parts. D_(1)D_{1} is the internal diameter of high-pressure pipes. 高压管道的制冷剂量由四部分组成。 D_(1)D_{1} 是高压管道的内径。 m_(pl)=pi((D_(2))/(2))^(2)rho_(v)L_(5)m_{\mathrm{pl}}=\pi\left(\frac{D_{2}}{2}\right)^{2} \rho_{v} L_{5}
The refrigerant charge in low-pressure pipe is gained by multiplying density of refrigerant vapor and its volume. D_(2)D_{2} is the internal diameter of low-pressure pipe. 低压管道中的制冷剂充注量由制冷剂蒸气的密度与其体积相乘得出。 D_(2)D_{2} 是低压管道的内径。 m_("evap ")=m_("two-phase ")+nA_(i)L_(v)rho_(v)m_{\text {evap }}=m_{\text {two-phase }}+n A_{\mathrm{i}} L_{\mathrm{v}} \rho_{\mathrm{v}}
The total mass in evaporator is divided into two segments: two-phase mass, gaseous mass. For the gaseous mass, it is calculated by number of micro-channels ( nn ), cross sectional area of single channel ( A_(i)A_{i} ), the length of superheated refrigerant in minichannels (L_(v))\left(L_{v}\right) and the density of gaseous refrigerant (rho_(v))\left(\rho_{v}\right). 蒸发器中的总质量分为两部分：两相质量和气体质量。气态质量由微通道数（ nn ）、单通道横截面积（ A_(i)A_{i} ）、过热制冷剂在微通道中的长度 (L_(v))\left(L_{v}\right) 和气态制冷剂的密度 (rho_(v))\left(\rho_{v}\right) 计算得出。
In terms of estimation of m_("two-phase ")m_{\text {two-phase }}, the konwledge of void fraction is required. Initially, a void fraction (epsi_(v))\left(\varepsilon_{v}\right), representing the gas fraction in total refrigerant, is defined as shown in Equation (11). Thus the refrigerant can be calculated by the coefficient and Equation (12) 在估算 m_("two-phase ")m_{\text {two-phase }} 时，需要用到空隙率。最初，空隙率 (epsi_(v))\left(\varepsilon_{v}\right) 的定义如公式 (11) 所示，它代表总制冷剂中的气体比例。因此，制冷剂可以通过系数和公式 (12) 计算得出 epsi_(v)=(dV_(v))/(dV)=(dA_(v))/(dA)\varepsilon_{\mathrm{v}}=\frac{d V_{\mathrm{v}}}{d V}=\frac{d A_{\mathrm{v}}}{d A} V_(v)V_{\mathrm{v}} and VV are the volumes of gaseous and total refrigerant; A_(v)A_{v} and AA are the cross sectional area of gaseous and total refrigerant. V_(v)V_{\mathrm{v}} 和 VV 是气态制冷剂和总制冷剂的体积； A_(v)A_{v} 和 AA 是气态制冷剂和总制冷剂的横截面积。
Table 5 表 5
Three different models to determine void fraction. 确定空隙率的三种不同模型
Z=(Re(1)/(6)Fr(1)/(8))/((1-epsi_(hom))^((1)/(4)))quad(14)quadepsi_(hom)=(1)/(1+(1-x)/(x)(rho_(v))/(rho_(1)))(15)Z=\frac{\operatorname{Re} \frac{1}{6} F r \frac{1}{8}}{\left(1-\varepsilon_{\mathrm{hom}}\right)^{\frac{1}{4}}} \quad(14) \quad \varepsilon_{\mathrm{hom}}=\frac{1}{1+\frac{1-x}{x} \frac{\rho_{\mathrm{v}}}{\rho_{1}}}(15)
F_(1)=1.578 Re^(-0.19)((rho_(1))/(rho_(v)))^(0.22)quad(20)quadF_(2)=0.0273 WeRe^(-0.19)((rho_(1))/(rho_(v)))^(-0.08)F_{1}=1.578 R e^{-0.19}\left(\frac{\rho_{1}}{\rho_{\mathrm{v}}}\right)^{0.22} \quad(20) \quad F_{2}=0.0273 W e R e^{-0.19}\left(\frac{\rho_{1}}{\rho_{\mathrm{v}}}\right)^{-0.08}
The mass in two-phase region is computed by integrating the sum of the products of the densities of the gaseous phase and the liquid phase and the corresponding void fraction across the volume of the two-phase region ( V_("two-phase ")V_{\text {two-phase }} ). 气相和液相的密度乘积之和以及两相区域体积内相应的空隙率（ V_("two-phase ")V_{\text {two-phase }} ）的积分计算两相区域的质量。
There are different way to determine the void fraction. This paper primarily studies three of them: Tandon’s. Premoli’s and Hughmark’s models. Hughmark’s correlation is derived from Homogeneous model. Compared to the other model, Hughmark correlation incorporates the flow characteristics because the correlation contains Re,Fr\mathrm{Re}, \mathrm{Fr}, as shown in Equation (14) [26]. And Hughmark’s model needs iterative computation, rendering it more complex. Premoli correlation [30], Tandon 确定空隙率的方法多种多样。本文主要研究其中三种：Tandon模型、Premoli模型和Hughmark模型。Premoli模型和Hughmark模型。Hughmark 相关性源自均质模型。与其他模型相比，Hughmark 相关性包含了流动特性，因为相关性包含 Re,Fr\mathrm{Re}, \mathrm{Fr} ，如公式（14）所示[26]。而且 Hughmark 模型需要迭代计算，因此更加复杂。Premoli 相关性 [30]、Tandon
correlation [32] and Hughmark correlation [26] are listed in Table 5. 表 5 列出了相关性 [32] 和休马克相关性 [26]。
4. Result and discussion 4.结果和讨论
4.1. Experimental results discussion 4.1.实验结果讨论
4.1.1. The effect of charge amount 4.1.1.收费金额的影响
Refrigerant charge is one of the determining factors that affect the performance of the transcritical CO_(2)\mathrm{CO}_{2} ACHP system. As listed out in Table 2, the experiment was conducted at the ambient temperature of 35^(@)C35{ }^{\circ} \mathrm{C}, the compressor speed of 3000r*min^(-1)3000 \mathrm{r} \cdot \mathrm{min}^{-1}, the EEV opening at 50%50 \% with the relative humidity of 50%50 \%. The refrigerant was charged into the system from the initial amount of 420 g to the maximum amount of 590 g with the interval of 50g,10g50 \mathrm{~g}, 10 \mathrm{~g} or 30 g to search for the charge amount. The refrigerant was charged with 50 g when the refrigerant mass in the system significantly deviated from the optimal value. As the refrigerant 制冷剂充注量是影响跨临界 CO_(2)\mathrm{CO}_{2} ACHP 系统性能的决定性因素之一。如表 2 所示，实验在环境温度为 35^(@)C35{ }^{\circ} \mathrm{C} 、压缩机转速为 3000r*min^(-1)3000 \mathrm{r} \cdot \mathrm{min}^{-1} 、EEV 开启度为 50%50 \% 和相对湿度为 50%50 \% 的条件下进行。将制冷剂从初始量 420 克充入系统至最大量 590 克，以 50g,10g50 \mathrm{~g}, 10 \mathrm{~g} 或 30 克为间隔寻找充注量。当系统中的制冷剂质量明显偏离最佳值时，注入 50 克制冷剂。由于制冷剂
Fig. 3. The effects of varied charge on system characteristics (a) pressure, (b) temperature and superheat. 图 3.不同充注量对系统特性的影响（a）压力，（b）温度和过热度。
Fig. 4. The effects of varied charge on COP and cooling capacity. 图 4.不同充注量对 COP 和制冷量的影响。
amount approached the optimal level, subsequent charges were reduced to 10 g to ensure the precise starting point and ending point of OCPR. Then the refrigerant was charged with 30 g per time after entering the OCPR. However, excessive charge results in serious system stability degradation. Once the system is over-charged, the SH_("comp,suc ")S H_{\text {comp,suc }} would plunge to considerably low value, which furtherly threatened the safe operation of compressor. 为确保 OCPR 起点和终点的精确性，制冷剂注入量在接近最佳水平时减少到 10 克。然后，在进入 OCPR 后，每次注入 30 克制冷剂。然而，过量充注会导致系统稳定性严重下降。一旦系统充注过量， SH_("comp,suc ")S H_{\text {comp,suc }} 就会骤降到相当低的值，进一步威胁压缩机的安全运行。
Different refrigerant charge induces significant variation of pressure and temperature, which furtherly affects the cooling capacity and performance of the system. Fig. 3 (a) and (b) depicts the varying tendency of pressure, temperature, and superheat degree with the growing of charge amount. Fig. 4 demonstrates the variation of COP and cooling capacity with charge amount. 不同的制冷剂充注量会引起压力和温度的显著变化，从而进一步影响系统的冷却能力和性能。图 3 (a) 和 (b) 描述了压力、温度和过热度随充注量增加而变化的趋势。图 4 显示了 COP 和冷却能力随充注量的变化。
Generally, the refrigerant charge amounts tested in the experiments can be divided into three categories: insufficient charge, optimal charge, and excessive charge. Initially, the system operates with an insufficient charged state, characterized by relative low refrigerant mass. In this state, it is evident from Fig. 3 (b) that the SH_("comp, suc ")SH_("evap,out, ")S H_{\text {comp, suc }} S H_{\text {evap,out, }}, suction temperature ( T_("suc ")T_{\text {suc }} ) and discharge temperature ( T_("dis ")T_{\text {dis }} ) peak at 27.3^(@)C27.3^{\circ} \mathrm{C}, 10.3^(@)C,33.9^(@)C,93.8^(@)C10.3^{\circ} \mathrm{C}, 33.9^{\circ} \mathrm{C}, 93.8^{\circ} \mathrm{C} respectively. Because the inadequate refrigerant flowing in the system causes diminished cooling capacity and COP. Besides, the suction pressure ( P_("suc ")P_{\text {suc }} ), evaporation pressure ( P_("evap ")P_{\text {evap }} ) and discharge pressure (P_("dis "))\left(P_{\text {dis }}\right) are at the lowest points of the lines at 4.14 MPa , 4.36 MPa and 8.08 MPa respectively in Fig. 3 (a). With the increment of refrigerant amount in insufficient charge, the T_("suc ")T_{\text {suc }} and T_("dis ")T_{\text {dis }} continue to decline by 10.0^(@)C10.0^{\circ} \mathrm{C} and 17.8^(@)C17.8{ }^{\circ} \mathrm{C} respectively. Meanwhile, SH_("comp, suc ")S H_{\text {comp, suc }} and SH_("evap, out ")S H_{\text {evap, out }} descend by 12.5^(@)C12.5^{\circ} \mathrm{C} and 9.4^(@)C9.4^{\circ} \mathrm{C}. Moreover, suction pressure, evaporation pressure and discharge pressure rise by 0.27MPa,0.28MPa0.27 \mathrm{MPa}, 0.28 \mathrm{MPa} and 0.1 MPa . As the refrigerant charge grows, there is increasing liquid refrigerant absorbing heat from the outside air in IDHX2. Meanwhile, the power consumption of compressor witnesses a slight increase. Thus, the COP and cooling capacity continue to increase, provided that more refrigerant is added to the system in the insufficient charge condition. 一般来说，实验中测试的制冷剂充注量可分为三类：充注量不足、充注量最佳和充注量过多。最初，系统运行在充注量不足的状态，其特点是制冷剂质量相对较低。在这种状态下，从图 3 (b) 可以看出， SH_("comp, suc ")SH_("evap,out, ")S H_{\text {comp, suc }} S H_{\text {evap,out, }} 、吸气温度 ( T_("suc ")T_{\text {suc }} ) 和排气温度 ( T_("dis ")T_{\text {dis }} ) 分别在 27.3^(@)C27.3^{\circ} \mathrm{C} 和 10.3^(@)C,33.9^(@)C,93.8^(@)C10.3^{\circ} \mathrm{C}, 33.9^{\circ} \mathrm{C}, 93.8^{\circ} \mathrm{C} 处达到峰值。由于系统中制冷剂流量不足，导致制冷量和 COP 下降。此外，吸气压力（ P_("suc ")P_{\text {suc }} ）、蒸发压力（ P_("evap ")P_{\text {evap }} ）和排气压力（ (P_("dis "))\left(P_{\text {dis }}\right) ）在图 3 (a) 中分别为 4.14 兆帕、4.36 兆帕和 8.08 兆帕，处于管路的最低点。随着制冷剂充注量的增加， T_("suc ")T_{\text {suc }} 和 T_("dis ")T_{\text {dis }} 继续下降，分别为 10.0^(@)C10.0^{\circ} \mathrm{C} 和 17.8^(@)C17.8{ }^{\circ} \mathrm{C} 。同时， SH_("comp, suc ")S H_{\text {comp, suc }} 和 SH_("evap, out ")S H_{\text {evap, out }} 分别下降 12.5^(@)C12.5^{\circ} \mathrm{C} 和 9.4^(@)C9.4^{\circ} \mathrm{C} 。此外，吸气压力、蒸发压力和排气压力分别上升了 0.27MPa,0.28MPa0.27 \mathrm{MPa}, 0.28 \mathrm{MPa} 和 0.1 MPa。随着制冷剂充注量的增加，IDHX2 中的液态制冷剂从外部空气中吸收的热量也在增加。同时，压缩机的功耗也略有增加。因此，只要在充注量不足的情况下向系统添加更多的制冷剂，COP 和制冷量就会继续增加。
After the SH_("evap,out ")S H_{\text {evap,out }} decreases to 0^(@)C0^{\circ} \mathrm{C} at the refrigerant mass of 500 g , the COP and cooling capacity reach their peaks at 1.481 and 1.669 kW . Then they will remain almost constant prior to the ending point of OCPR, as shown in Fig. 4. Meanwhile pressure and temperature parameters also remain steady, for example discharge pressure, suction temperature, discharge temperature, superheat of evaporator outlet and compressor suction. This steadiness is facilitated by the accumulator, which reserves the extra refrigerant until its capacity is exceeded. In addition, the refrigerant from IDHX2 exchanges heat with low-pressure side, causing relative high superheat at compressor suction. Consequently, the pressure and temperature parameters of system slightly 当制冷剂质量为 500 g 时， SH_("evap,out ")S H_{\text {evap,out }} 下降到 0^(@)C0^{\circ} \mathrm{C} 后，COP 和制冷量分别达到 1.481 和 1.669 kW 的峰值。如图 4 所示，在 OCPR 结束点之前，它们几乎保持不变。同时，压力和温度参数也保持稳定，例如排气压力、吸气温度、排气温度、蒸发器出口过热度和压缩机吸气过热度。这种稳定性得益于蓄能器，它可以储备额外的制冷剂，直到超出其容量。此外，IDHX2 的制冷剂与低压侧进行热交换，导致压缩机吸气处的过热度相对较高。因此，系统的压力和温度参数略有下降。
Fig. 5. pp-h diagrams under varied refrigerant charge in experimental test. 图 5.实验测试中不同制冷剂充注量下的 pp -h 图。
change after entering the optimal charge from 500 g to 580 g . Essentially, the performance of system is minimally affected by the charge of refrigerant in OCPR. Because the heat exchange surface in IDHX2 is completely utilized. And the outlet of IDHX2 consists of a mixture of gaseous and liquid CO_(2)\mathrm{CO}_{2}. 在最佳充注量从 500 克增加到 580 克之后，系统的性能发生了变化。从根本上说，OCPR 中制冷剂充注量对系统性能的影响很小。因为 IDHX2 中的热交换面已被完全利用。而 IDHX2 的出口由气态和液态的混合物 CO_(2)\mathrm{CO}_{2} 组成。
However, when the volume of liquid CO_(2)\mathrm{CO}_{2} in accumulator exceeds that of accumulator, the suction superheat of compressor will drop drastically. This reduction negatively impacts both compressor and system performance. Worse yet, the orbiting scroll will be damaged by the flowing liquid refrigerant, causing a decline of the volumetric efficiency and isentropic efficiency. The excessive charge occurs when more than 580 g of refrigerant circulates in the system. During the excessive charge, the SH_("comp,suc ")\mathrm{SH}_{\text {comp,suc }} drastically falls from 11.8^(@)C11.8^{\circ} \mathrm{C} at 580 g to 7.6^(@)C7.6^{\circ} \mathrm{C} at 590 g , and COP and cooling capacity begin to substantially decrease from 1.469 to 1.234 and from 1.581 kW to 1.456 kW respectively. 但是，当蓄能器中的 CO_(2)\mathrm{CO}_{2} 液体体积超过蓄能器的体积时，压缩机的吸气过热度将急剧下降。这种下降会对压缩机和系统性能产生负面影响。更严重的是，流动的液态制冷剂会损坏轨道涡旋，导致容积效率和等熵效率下降。当系统中循环的制冷剂超过 580 克时，就会出现过量充注。在过量充注期间， SH_("comp,suc ")\mathrm{SH}_{\text {comp,suc }} 从 580 g 时的 11.8^(@)C11.8^{\circ} \mathrm{C} 急剧下降到 590 g 时的 7.6^(@)C7.6^{\circ} \mathrm{C} ，COP 和制冷量开始大幅下降，分别从 1.469 降至 1.234 和从 1.581 kW 降至 1.456 kW。
The pressure and enthalpy diagram ( p-hp-h diagram) depicted in Fig. 5 can explicitly elucidate the principle of the aforementioned phenomena. Apparently, the entire cycle tends to move to the up and left direction along with the increment of refrigerant, which shows the consistent tendency as Ref. 21. More specifically, the discharge pressure increases from 8.08 MPa at 420 g to 8.32 MPa at 590 g . Meanwhile, suction pressure presents the similar trend from 4.14 MPa at 420 g to 4.67 MPa at 590 g . From the initial stage, the length of two-phase line in IDHX2 gradually extends until reaching the optimal charge condition. Meanwhile, the compression work exhibits a mild upward trend. Therefore, both the COP and cooling capacity show an upward trend. In addition, the refrigeration cycles of optimal charge condition are considerably compact with minimal change, which can verify the appropriateness of refrigerant charge. When entering the excessive charge phase, the cycle continues to move to left more noticeably. And the refrigerant state at compressor inlet is less superheated because the flux of excessive liquid refrigerant beyond the capacity of accumulator. Hence the compression work begins to increase and cooling capacity declines, causing the drop of COP. 图 5 所示的压力和焓图（ p-hp-h 图）可以明确阐明上述现象的原理。显然，随着制冷剂的增加，整个循环趋向于向上和向左移动，这与参考文献 21 中的趋势一致。21.更具体地说，排气压力从 420 克时的 8.08 兆帕增加到 590 克时的 8.32 兆帕。同时，吸气压力也呈现出类似的趋势，从 420 克时的 4.14 兆帕增加到 590 克时的 4.67 兆帕。从初始阶段开始，IDHX2 中的两相线长度逐渐延长，直至达到最佳充填状态。与此同时，压缩功呈现出温和的上升趋势。因此，COP 和制冷量都呈上升趋势。此外，最佳充注量条件下的制冷循环相当紧凑，变化极小，这可以验证制冷剂充注量的适当性。当进入过量充注阶段时，循环会更明显地继续向左移动。由于过量液态制冷剂的流量超出了蓄能器的容量，压缩机入口处的制冷剂过热度降低。因此，压缩功开始增加，制冷量下降，导致 COP 下降。
In insufficient charge condition from 420 g to 500 g , all pressure, temperature, and performance parameters vary tremendously. In optimal charge condition from 500 g to 580 g , there is a flat region for most of the parameters. Especially, the COP and cooling capacity peak at 1.469 and 1.581 kW . In excessive charge condition starting from 580 g , the temperature and performance parameters continue to fall. Particularly the suction temperature and suction superheat decrease more significantly. However, the pressure parameters gain an upward trend. 在 420 克至 500 克的充气不足条件下，所有压力、温度和性能参数都有很大变化。在 500 g 至 580 g 的最佳充注条件下，大部分参数都处于平缓区域。特别是 COP 和制冷量的峰值分别为 1.469 和 1.581 kW。在从 580 克开始的过量充注条件下，温度和性能参数继续下降。尤其是吸气温度和吸气过热度下降更为明显。然而，压力参数却呈上升趋势。
Taken together, the total mass of refrigerant in the system 综上所述，系统中制冷剂的总质量为
Fig. 6. The influence of varied charge on system characteristics under different compressor speed (a) pressure, (b) temperature. 图 6.不同压缩机转速下不同充注量对系统特性的影响 (a) 压力，(b) 温度。
Fig. 7. The influence of varied charge on COP and cooling capacity under different compressor speed. 图 7.不同压缩机转速下不同充注量对 COP 和制冷量的影响。
Fig. 8. The results comparison of different theoretical calculations with experiments. 图 8.不同理论计算与实验结果的对比。
substantially influences the operational performance of individual component and whole system. Thus, the determination of optimal refrigerant in specific working conditions is extremely crucial. On the basis of the above analysis, it is effective that SH_("evap, out ")S H_{\text {evap, out }} and SH_("comp,out ")S H_{\text {comp,out }} can confirm the OCPR, which is consistent with the result of Ref 16. Additionally, P_("dis "),T_("dis "),T_("suc ")P_{\text {dis }}, T_{\text {dis }}, T_{\text {suc }}, COP, cooling capacity and pp-h diagram can provide further verification on whether the OCPR is accurate or not. 在很大程度上影响着单个部件和整个系统的运行性能。因此，确定特定工况下的最佳制冷剂极为关键。根据上述分析， SH_("evap, out ")S H_{\text {evap, out }} 和 SH_("comp,out ")S H_{\text {comp,out }} 可以有效确认 OCPR，这与参考文献 16 的结果一致。此外， P_("dis "),T_("dis "),T_("suc ")P_{\text {dis }}, T_{\text {dis }}, T_{\text {suc }} 、COP、冷却能力和 pp -h 图可以进一步验证 OCPR 是否准确。
4.1.2. Influence of different speed of compressor on OCPR 4.1.2.压缩机不同转速对 OCPR 的影响
While driving, the passengers have different demand for the cooling capacity, which is modulated by adjustments in the rotating speed of compressor. Therefore, it is imperative to investigate the effect of compressor speed on OCPR. In essence, the optimal charges under different compressor speeds need to be investigated. 在驾驶过程中，乘客对制冷量的需求各不相同，而压缩机转速的调节可以调节制冷量。因此，必须研究压缩机转速对 OCPR 的影响。实质上，需要研究不同压缩机转速下的最佳制冷量。
During the test, the ambient temperature is fixed at 35^(@)C35{ }^{\circ} \mathrm{C} with a relative humidity of 50%50 \% and the opening of EEV1 is set at 50%50 \%. The speed of compressor varies from 3000 to 4500r*min^(-1)4500 \mathrm{r} \cdot \mathrm{min}^{-1} with the interval of 500r*min^(-1)500 \mathrm{r} \cdot \mathrm{min}^{-1} as shown in Table 3. 测试期间，环境温度固定为 35^(@)C35{ }^{\circ} \mathrm{C} ，相对湿度为 50%50 \% ，EEV1 的开度设定为 50%50 \% 。如表 3 所示，压缩机的转速在 3000 到 4500r*min^(-1)4500 \mathrm{r} \cdot \mathrm{min}^{-1} 之间变化，间隔时间为 500r*min^(-1)500 \mathrm{r} \cdot \mathrm{min}^{-1} 。
More specifically, it can be observed from Fig. 6 (a) that the discharge pressure varies significantly corresponding to the compressor speed with the maximum value of roughly 8.52 MPa and the minimum value of 8.24 MPa under the condition of optimal charge. Whereas the suction pressure exhibits the opposite trend. It reaches minimum value at 4500r*min^(-1)4500 \mathrm{r} \cdot \mathrm{min}^{-1} and the maximum value at 3000r*min^(-1)3000 \mathrm{r} \cdot \mathrm{min}^{-1}. 更具体地说，从图 6 (a) 可以看出，排气压力随压缩机转速的变化而显著变化，在最佳充气条件下，最大值约为 8.52 兆帕，最小值为 8.24 兆帕。而吸气压力则呈现出相反的趋势。它在 4500r*min^(-1)4500 \mathrm{r} \cdot \mathrm{min}^{-1} 时达到最小值，在 3000r*min^(-1)3000 \mathrm{r} \cdot \mathrm{min}^{-1} 时达到最大值。
From Fig. 6 (b), the discharge temeprature at 4500r*min^(-1)4500 \mathrm{r} \cdot \mathrm{min}^{-1} and refrigerant of 420 g peaks at 114^(@)C114^{\circ} \mathrm{C}. Subsequently, it falls by nearly 16.1^(@)C16.1^{\circ} \mathrm{C} at the ending point of insufficient charge condition. Meanwhile, the discharge temperature at 3000r*min^(-1)3000 \mathrm{r} \cdot \mathrm{min}^{-1} shows the lowest value at 93.8^(@)C93.8^{\circ} \mathrm{C}, then declines by 18.4^(@)C18.4^{\circ} \mathrm{C}. During the optimal charge condition, the discharge temperatures of the four compressor speeds exhibit the milder decline compared to the insufficient charge condition. The discharge temperature experience a notable fall in the excessive charge condition. However, the suction temperature of 3000r*min^(-1)3000 \mathrm{r} \cdot \mathrm{min}^{-1} is the highest with 33.9^(@)C33.9^{\circ} \mathrm{C}, subsequently falling by 9.3^(@)C9.3^{\circ} \mathrm{C}; the suction temperature of 4500r*min^(-1)4500 \mathrm{r} \cdot \mathrm{min}^{-1} records its lowest value at 27.9^(@)C27.9^{\circ} \mathrm{C}, followed by a decline of 6.4^(@)C6.4^{\circ} \mathrm{C}. Likewise, four discharge temperatures almost remain stable in the optimal charge condition but decline significantly in the excessive charge condition. 从图 6 (b)可以看出，在 4500r*min^(-1)4500 \mathrm{r} \cdot \mathrm{min}^{-1} 和制冷剂为 420 g 时，放电温度在 114^(@)C114^{\circ} \mathrm{C} 时达到峰值。随后，在充注不足状态的终点，温度下降了近 16.1^(@)C16.1^{\circ} \mathrm{C} 。同时， 3000r*min^(-1)3000 \mathrm{r} \cdot \mathrm{min}^{-1} 处的放电温度在 93.8^(@)C93.8^{\circ} \mathrm{C} 处达到最低值，然后在 18.4^(@)C18.4^{\circ} \mathrm{C} 处下降。在最佳充注条件下，与充注不足条件相比，四个压缩机转速的排气温度下降幅度较小。在过量充气条件下，排气温度明显下降。然而， 3000r*min^(-1)3000 \mathrm{r} \cdot \mathrm{min}^{-1} 的吸气温度在 33.9^(@)C33.9^{\circ} \mathrm{C} 时最高，随后在 9.3^(@)C9.3^{\circ} \mathrm{C} 时下降； 4500r*min^(-1)4500 \mathrm{r} \cdot \mathrm{min}^{-1} 的吸气温度在 27.9^(@)C27.9^{\circ} \mathrm{C} 时达到最低值，随后在 6.4^(@)C6.4^{\circ} \mathrm{C} 时下降。同样，在最佳充电条件下，四个放电温度几乎保持稳定，但在过量充电条件下则显著下降。
The optimal charge decreases with the increment of compressor speed in accordance with Fig. 7. The optimal charge is from 500 g to 580 g at 3000r*min^(-1)3000 \mathrm{r} \cdot \mathrm{min}^{-1}; it is roughly from 495 g to 575 g at 3500r*min^(-1)3500 \mathrm{r} \cdot \mathrm{min}^{-1}; it is from 490 g to 570 g at 4000r*min^(-1)4000 \mathrm{r} \cdot \mathrm{min}^{-1}; it is from 485 g to 565 g at 4500 r*min^(-1)\mathrm{r} \cdot \mathrm{min}^{-1}. Remarkably, the range of optimal charge is almost constant with around 80 g despite the variation of compressor speed. This varying 与图 7 一致，最佳充注量随压缩机转速的增加而减少。在 3000r*min^(-1)3000 \mathrm{r} \cdot \mathrm{min}^{-1} 时，最佳充注量为 500 g 至 580 g；在 3500r*min^(-1)3500 \mathrm{r} \cdot \mathrm{min}^{-1} 时，最佳充注量大致为 495 g 至 575 g；在 4000r*min^(-1)4000 \mathrm{r} \cdot \mathrm{min}^{-1} 时，最佳充注量为 490 g 至 570 g；在 4500 r*min^(-1)\mathrm{r} \cdot \mathrm{min}^{-1} 时，最佳充注量为 485 g 至 565 g。值得注意的是，尽管压缩机转速不同，但最佳充注量的范围几乎恒定在 80 克左右。这种变化
Furthermore, in Fig. 7, cooling capacity increases with the growing compressor speed because of the incremental mass flow of refrigerant. On the contrary, COP presents a reversed tendency. Because the growing trend of compression work outweighs the increase in cooling capacity. 此外，在图 7 中，由于制冷剂质量流量的增加，制冷量随着压缩机转速的增加而增加。相反，COP 却呈现出相反的趋势。因为压缩功的增长趋势超过了制冷量的增长。
4.2. Calculating optimal refrigerant charge with different prediction models 4.2.用不同预测模型计算最佳制冷剂充注量
The refrigerant amount in each component is calculated by using the method of void fraction correlations and other equations, which incorporate the geometric parameters of each part and state parameters of refrigerant. Three points, the starting point, the intermediate point and the ending point of the OCPR ( 500g,540g,580g500 \mathrm{~g}, 540 \mathrm{~g}, 580 \mathrm{~g} ), are selected under the condition of 35^(@)C35{ }^{\circ} \mathrm{C} ambient temperature, 3000r*min^(-1)3000 \mathrm{r} \cdot \mathrm{min}^{-1}. The experimental data under specific condition serve as references to compare the results of different void fraction correlations as depicted in Fig. 8. From the bar chart, the results of three void fraction correlations roughly align with the experiments, which facilitates the practical estimation. Specifically, Hughmark’s model is the most accurate among three models with a maximum error of approximately 6.09%6.09 \% under 580 g refrigerant charge and a minimum error of 3.2%3.2 \% at the starting point of OCPR (500 g). And the errors of Tandon’s model and Premoli’s model are below 8.54%8.54 \% and 8.28%8.28 \% respectively. Consequently, Hughmark’s model proves to be the most appropriate method for the system. And this conclusion is consistent with Ref 28, 29 and 30. 利用空隙率相关法和其他方程，结合各部件的几何参数和制冷剂的状态参数，计算出各部件中的制冷剂量。在 35^(@)C35{ }^{\circ} \mathrm{C} 环境温度、 3000r*min^(-1)3000 \mathrm{r} \cdot \mathrm{min}^{-1} 条件下，选择 OCPR 的起点、中间点和终点（ 500g,540g,580g500 \mathrm{~g}, 540 \mathrm{~g}, 580 \mathrm{~g} ）三个点。如图 8 所示，特定条件下的实验数据可作为比较不同空隙率相关性结果的参考。从柱状图来看，三种空隙率相关性的结果与实验结果基本一致，这为实际估算提供了便利。具体来说，Hughmark 模型是三种模型中最准确的，在制冷剂充注量为 580 克时，最大误差约为 6.09%6.09 \% ，而在 OCPR 起点（500 克）时，最小误差为 3.2%3.2 \% 。而 Tandon 模型和 Premoli 模型的误差分别低于 8.54%8.54 \% 和 8.28%8.28 \% 。因此，休马克模型被证明是最适合该系统的方法。这一结论与参考文献 28、29 和 30 一致。
4.3. Mass inventory 4.3.质量清单
Fig. 9 presents the distribution of refrigerant mass in each 图 9 显示了每种制冷剂质量的分布情况。
component of the system under the above working conditions. Taking the results of Hughmark’s model as example. From the pie chart, it indicates that the high-pressure pipe has the largest mass of refrigerant, accounting for 26.31%26.31 \% of the total in 500 g of refrigerant, followed by IHX/A that holds the secondly largest mass of refrigerant with approximately 26.29%26.29 \%. In contrast, compressor possesses the least mass of refrigerant, comprising roughly 0.15%0.15 \% of the total. Therefore, it is recommended that shortening the length and diameter of high-pressure pipe and optimization of heat exchangers are the main research orientations to minimize the refrigerant charge. Moreover, the refrigerant mainly flows into accumulator and high-pressure pipe with the growth proportion of 1.82%1.82 \% and 0.72%0.72 \% respectively when the charge amount increases from 500 g to 580 g . Additionally, the charged refrigerant in optimal charge condition is mostly stored in the accumulator. 在上述工作条件下的系统组件。以 Hughmark 模型的结果为例。饼图显示，高压管中的制冷剂质量最大，占 500 克制冷剂总量的 26.31%26.31 \% ，其次是 IHX/A，制冷剂质量约为 26.29%26.29 \% 。相比之下，压缩机的制冷剂质量最小，约占总量的 0.15%0.15 \% 。因此，建议将缩短高压管道的长度和直径以及优化热交换器作为最大限度减少制冷剂充注量的主要研究方向。此外，当充注量从 500 g 增加到 580 g 时，制冷剂主要流入蓄能器和高压管，其增长比例分别为 1.82%1.82 \% 和 0.72%0.72 \% 。此外，在最佳充注状态下，充注的制冷剂主要储存在蓄能器中。
5. Conclusions 5.结论
In this paper, an experimental study on the determination of refrigerant charge was conducted by establishing a transcritical CO_(2)\mathrm{CO}_{2} automobile ACHP system. The effects of refrigerant charge on system characteristics were investigated, and the influence of compressor speed on optimal charge and system characteristics were analyzed. The novel principle for determining the optimal charge plateau was verified, and the range of optimal charge for the tested CO_(2)ACHP\mathrm{CO}_{2} \mathrm{ACHP} system was proposed. Some main conclusions are drawn as follows: 本文通过建立一个跨临界 CO_(2)\mathrm{CO}_{2} 汽车 ACHP 系统，对制冷剂充注量的确定进行了实验研究。研究了制冷剂充注量对系统特性的影响，分析了压缩机转速对最佳充注量和系统特性的影响。验证了确定最佳充注量高原的新原理，并提出了测试的 CO_(2)ACHP\mathrm{CO}_{2} \mathrm{ACHP} 系统的最佳充注量范围。主要结论如下：
(1) The system performance of insufficient charge and excessive charge can not reach the optimum compared to that of optimal charge. The SH_("evap,out ")S H_{\text {evap,out }} and SH_("comp,suc ")S H_{\text {comp,suc }} are verified to accurately predict the OCPR, while discharge temperature, suction temperature and discharge pressure are appropriate indicators of OCPR. (1) 与最佳充注相比，充注不足和充注过量的系统性能无法达到最佳。经过验证， SH_("evap,out ")S H_{\text {evap,out }} 和 SH_("comp,suc ")S H_{\text {comp,suc }} 可以准确预测 OCPR，而排气温度、吸气温度和排气压力则是 OCPR 的合适指标。
(2) Considering the operating conditions in the experiments, the optimal charge plateu initates at the charge of 500 g and ends at 565 g , where the COP, cooling capacity, pressure and temperature barely change. The optimal charge declines slightly with the increase of compressor speed. (2) 考虑到实验中的运行条件，最佳充气量排位从充气量 500 克开始，到 565 克结束，其 COP、制冷量、压力和温度几乎没有变化。随着压缩机转速的增加，最佳充注量略有下降。
(3) Three void fraction correlations to calculate optimal charge are verified for the system. Hughmark’s model, with a maximum error of 6.09%6.09 \%, proves to be the most appropriate for the calculating the optimal charge. And the errors of Tandon model and Premoli model are below 8.54%8.54 \% and 8.28%8.28 \% respectively. (3) 验证了计算系统最佳电荷的三种空隙率相关性。休马克模型的最大误差为 6.09%6.09 \% ，被证明是最适合计算最佳电荷的模型。而 Tandon 模型和 Premoli 模型的误差分别低于 8.54%8.54 \% 和 8.28%8.28 \% 。
(4) The refrigerant mainly distributes in high pressure pipe and IHX/ A in the optimal charge condition, taking up about 52.6%55.14%55.14 \%. And the compressor accounts for the lowest proportion. It is advisable to reduce the refrigerant in these components to lower the refrigerant charge amount. (4) 在最佳充注状态下，制冷剂主要分布在高压管和 IHX/ A 中，约占 52.6% 55.14%55.14 \% 。而压缩机所占比例最低。建议减少这些部件中的制冷剂，以降低制冷剂充注量。
Nevertheless, determination of optimal charge amount is a prerequisite for refrigeration system research. In practical applications, the CO_(2)\mathrm{CO}_{2} AHCP system performance was influenced by all kinds of operating parameters. Thus, the control strategy in the thermal manegemant system for EVs was a complex issue and needs further study. Further investigation on the coupled effect of varied compressor speed and EEV openning will be conducted in our future work, as well as the system performance in both cooling and heat pump mode. 然而，确定最佳充注量是制冷系统研究的先决条件。在实际应用中， CO_(2)\mathrm{CO}_{2} AHCP 系统的性能受到各种运行参数的影响。因此，电动汽车热动力系统的控制策略是一个复杂的问题，需要进一步研究。我们将在今后的工作中进一步研究压缩机转速变化与电动汽车开度的耦合效应，以及冷却和热泵模式下的系统性能。
The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper. 作者声明，他们没有任何可能会影响本文所报告工作的已知经济利益或个人关系。
Data availability 数据可用性
Data will be made available on request. 数据将应要求提供。
Acknowledgement 鸣谢
This work was supported and sponsored by National Natural Science Foundation of China (Grant No. 52206016 and No. 51206022) and the Central Guidance on Local Science and Technology Development Fund of Shanghai City, China ( No. YDZX20213100003002). 本研究得到了国家自然科学基金（52206016 号和 51206022 号）和中央地方科技发展引导基金（YDZX20213100003002 号）的支持和资助。
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Corresponding author. School of Energy and Power Engineering, University of Shanghai for Science and Technology, Shanghai 200093, China. 通讯作者：上海科技大学能源与动力工程学院上海科技大学能源与动力工程学院，中国上海 200093。
