Super fast charging for EVs generally adopts the DC charging mode, where the dielectric loss of the medium can be neglected, and its heat source only includes the Ohmic loss on the conductor. During the cable charging process, Ohmic loss is generated due to the presence of resistance, and part of the energy is converted into thermal energy, causing the cable temperature to rise. The Ohmic loss power is proportional to the square of the current.

$P=\frac{1}{2{\sigma }_e}{\displaystyle \underset{V}{\int }{J}^2}\text{d}V$ (1)

where P stands for Ohmic loss power, σ_e is electrical conductivity, V is heat source volume, J refers to current density.

Meanwhile, since the signal wires, control wires, and grounding wires in the cable carry very small currents—negligible compared with the charging current—it is therefore considered that all the heat in the cable is generated by the charging current.

When the liquid-cooled cables are in service, the Ohmic loss heat on the conductors will be transferred to the coolant via three processes: thermal conduction, fluid convection heat transfer, and thermal radiation.

1) Thermal Conduction

Thermal conduction is dominant in the solid region. Heat transfer occurs between objects that are in contact with each other and have different temperatures, or between different temperature regions within a single object. The thermal conduction process can be described by Fourier’s Law in terms of the heat transfer efficiency in solids.

$\nabla \cdot \left(k\nabla T\right)+Q=\rho c\frac{\partial T}{\partial t}$ (2)

where k is the thermal conductivity of the solid, $\nabla T$ is the spatial gradient of temperature, Q is the heat source, referring to the heat generated by the Ohmic loss on the conductor when the charging cable is in operation. The ρ and c refer to the density and specific heat capacity of the solid, respectively. The $\partial T/\partial t$ is the time rate of change of temperature. According to the structural characteristics of the cable, thermal conduction mainly occurs in the direction perpendicular to the cable axis, dissipating heat from the cable conductor to other surrounding media. This in turn causes the temperature rise of the surrounding media.

2) Fluid Convection Heat Transfer

Convective heat transfer occurs between a fluid and a solid; it refers to the heat transfer phenomenon that takes place when there is relative motion between the fluid and the solid wall, as well as a temperature difference between the both. The heat transfer between the core of a liquid-cooled cable and the coolant falls into the category of forced convection, while that between the cable’s outer surface and the air is natural convection. The coolant is driven and cooled by the pile-side refrigeration unit, forming a liquid-cooling channel. This method utilizes the high specific heat capacity and thermal conductivity of the liquid, and can achieve more efficient heat dissipation compared with air cooling.

Throughout the entire physical process, fluid flow and heat transfer are coupled with each other, and this complies with the law of conservation of energy.

$\rho C_p\frac{\partial T}{\partial t}+\rho C_{p}u\cdot \nabla T=\nabla \cdot \left(k\nabla T\right)+Q$ (3)

where ρ is the mass density of the coolant, c_p is the specific heat capacity of the coolant at constant pressure; u and k are the velocity and thermal conductivity of the liquid, respectively. Q stands for the internal heat source, which is zero in this problem.

At the wall of the liquid cooling channel, the thermal boundary condition complies with Newton’s Law of Cooling.

$q=-h\Delta T$ (4)

where, h refers to the convective heat transfer coefficient, which is related to fluid velocity, temperature difference, and interface characteristics. The h-value is a key parameter in the design of liquid cooling systems since it has a positive correlation with the heat transfer efficiency between the wall surface and the fluid.

3) Thermal Radiation.

Thermal radiation refers to the process in which radiant energy is emitted outward due to the thermal motion of microscopic particles in a substance. Radiative heat transfer, on the other hand, is the phenomenon where heat transfer occurs between objects through the emission and absorption of thermal radiation. During the operation of the cable, the cable temperature rises due to Ohmic loss, and heat radiates to the surrounding environment through the outer sheath of the cable. Radiative heat dissipation complies with the Stefan-Boltzmann Law.

$P={\sigma }_T\epsilon \left(T_1^4-T_0^4\right)$ (5)

where, σ_T = 5.67*10⁻⁸ (W/m²K⁴) is the product of the Stefan-Boltzmann constant; T₁ and T₀ are the temperature of the emitter and receiver, respectively. When the external shape of the cable is fixed, its thermal radiation power is determined solely by the temperature of its outer surface and the ambient temperature.

As shown in Figure 1 , when the charging system is in operation, current is transmitted from the DC power supply to the charging gun via power lines. The charging gun is connected to the vehicle side through the vehicle-mounted charging socket. The Ohmic loss heat generated by the charging current is carried away by the coolant that runs parallel to the power lines inside cable, enabling temperature rise management of the cables. Low-temperature coolant is pumped out by the cooling system and delivered directly to the charging gun end through the coolant inlet pipe. It is then split into two paths by the liquid distribution terminal at the gun end, entering the cooling pipes of the positive and negative power lines respectively, and finally flows back to the cooling system, completing the fluid cooling cycle.

During the manufacturing of liquid-cooled cables, power lines, control lines, signal lines, ground lines, and liquid-cooled pipes are usually stranded together into a single cable, and encapsulated with a flexible outer sheath. As shown in Figure 2 is a cross-sectional diagram of the “water-immersed copper” type liquid-cooled charging pile cable. The conductor is bunched copper wires covered with a tinned copper wire braid. It has good flexibility and is not easy to loosen, which helps maintain the cooling tube unobstructed. The braided copper conductor is placed into the liquid-cooled pipe, where the coolant acts as the conductor insulation. The liquid-cooled pipe and the independent water inlet pipe form a coolant circulation path. The cooling system on the charging pile side continuously supplies low-temperature liquid with constant pressure and flow rate to the cooling pipe. The entire cable consists of 2 liquid-cooled power conductors, 1 grounding wire, 1 water inlet pipe, and several signal wires. By adding appropriate filler materials, comprehensive cabling is completed through co-directional bunch stranding.

In this paper, the heat dissipation capacity and thermal distribution state of liquid-cooled pipes under the condition of cable conductor eccentricity were studied. By optimizing the pipe structure, it improves the uniformity of the pipe’s temperature field distribution and reduces local temperature rise. This paper took a section of cable as the research object to establish a simulation model, as shown in Figure 3(a) . This paper mainly studies the influence of the internal structure optimization of liquid-cooled pipes on convective heat dissipation. Therefore, a single liquid-cooling unit was taken as the research object to study the flow field and temperature field in a section of cable. For the convenience of comparative study, three types of cooling pipe models are established, as shown in Figure 3(b) , namely spiral internal grooved pipes, straight internal grooved pipes, and traditional non-grooved pipe structures. They are referred to as Type 1, Type 2, and Type 3 respectively hereinafter. The material properties of each component are shown in Table 1 .

The operating parameters of the fluid can be calculated from the model dimensions and coolant properties. When the fluid inlet pressure is 0.8 MPa, the outlet pressure is 0.75 MPa, and the fluid flow rate is 15 L/min, the average flow velocity of the fluid in the pipe is approximately 40 mm/s. The dynamic viscosity of the dimethyl silicone oil used for cooling in the liquid-cooled cable is about 0.1 Pa·s; the calculated Reynolds number of the fluid is approximately 1500, indicating that the flow of the fluid in the pipe conforms to the laminar flow model.

The power curve of a certain brand of electric vehicle during the cold-vehicle charging process is shown in Figure 4 . In a complete charging operation, the current duration is much shorter than the steady-state temperature rise time constant of the cable, so the thermal field calculation should adopt a transient field model. For the convenience of analysis, the current in the cable was equated to the form of a step function to study the cable heat dissipation and structural optimization driven by a typical charging current sequence. The charging voltage is 1000 V, the maximum charging current is 1000 A, and the charging duration is approximately 20 minutes with the maximum charging power at 1 MW. The cold-vehicle charging capacity is 300 kWh.

In the multi-physics field coupling calculation of this paper, a single liquid-cooled power line was taken as the research object, and the multi-physics field coupling computational method involving the electromagnetic field, flow velocity field, and temperature field was adopted to analyze its heat dissipation performance. In the simulation, the coupling interface between the electromagnetic field and the temperature field is “electromagnetic-thermal”, with the Ohmic loss of the current field taken as the heat source for the temperature field. The “non-isothermal flow” was taken as the coupling interface between the flow field and the temperature field; the velocity fluid in the temperature field was obtained through the calculation of the flow velocity field. The computational domain of the current field module only includes conductors. The two ends of the conductor serve as the inflow and outflow ports for current. Inside the conductor, the current lines are parallel to the conductor’s axis. The transient current waveform is shown in Figure 4 . The fluid was calculated employing the laminar flow module, with the calculation domain including only the coolant. The fluid flow rate is 15 L/min according to the operating parameters of the charging pile. The solid and fluid heat transfer module was adopted to solve the temperature field, covering the entire model domain. The coolant was set as fluid, with a given pressure at the inlet. To facilitate the comparative study on the heat dissipation efficiency of different pipeline structures, the outer surface of the cooling pipe was set as a thermal insulation boundary, and the lateral heat exchange between the cooling pipe and other components of the cable is not considered. The boundary condition of the fluid field was set as a no-slip boundary.

The bottom surfaces at both ends of the model are set as symmetric boundaries since the calculation model is a local part of the cable line.

Generally, the length of high-power charging cables ranges from 4.5 m to 7 m. Taking 6 m as a typical length of charging pile cable as an example, when the pressure difference between the coolant outlet and inlet is 0.05 MPa, the pressure difference between the fluid outlet and inlet in the cable segment model studied in this paper is 833 Pa, assuming that the fluid pressure is uniformly distributed along the cable.

The calculated results of fluid velocity for the three types of pipes under the same inlet pressure condition were as shown in Figure 5 , which indicates that the average coolant velocity was in the region of 150~160 mm/s. The fluid streamlines are parallel to the pipe axis with no transverse component in the Type 1 and Type 2 pipes. Simultaneously, the flow lines of the fluid are no longer parallel to the pipe axis in the Type 3 pipe due to the structure induction. The coolant velocity includes both longitudinal and transverse components. The magnitude of the transverse flow velocity is shown in Figure 5(b) . The transverse velocity of coolant in the Type 1 and Type 2 pipes is zero, while the transverse velocity in the Type 3 pipe is 12 mm/s in average and a maximum value of 32 mm/s, respectively.

When the conductor is coaxial with the pipe, the spatial distribution and circulation of the fluid exhibit good symmetry, and the pipe structure has little impact on the temperature field distribution. When conductor eccentricity occurs, the longitudinal velocity will decrease due to reduced local fluid volume on the eccentric side of the conductor, and the longitudinal velocity will increase on the opposite side, as shown in Figure 6(a) . The transverse velocity components as shown in Figure 6(b) . There are no transverse velocity components in the Type 1 and Type 2 pipes. The transverse velocity components of coolant velocity in the Type 3 pipe are related to the eccentric position of the conductor. The transverse velocity decreases in the direction of conductor eccentricity, while it increases in the direction opposite to the eccentricity. The helical grooves inside the pipe induce the local circulation pattern of the fluid through the geometric structure and promote the transverse convection of the fluid.

For the three pipeline models in Figure 3(b) , the temperature field variation during a single cold-start charging process was investigated. In this problem, room temperature (293.15 K) was taken as the initial temperature, and the outer boundary of the model was set as a thermally insulated boundary. The temperature rise-time response curves of the outer surface of the power line conductor are shown in Figure 7 with the charging current sequence as shown in Figure 4 . It can be seen from the figure that the three models show similar temperature distribution trends. At 22.7 minutes after the start of charging, the temperature rise reached its maximum value; and then, as the charging current decreased until the end of charging, the temperature rise of the conductor surface gradually decreased. Furthermore, compared with non-grooved pipes, grooved pipes have an increased fluid cross-sectional area, which leads to a higher flow rate. This improves the heat dissipation efficiency to a certain extent and reduces the conductor temperature rise.

Since the size of the fluid channel between the outer surface of the power line and the inner wall of the cooling pipe varies with the position of the conductor, when power line conductor eccentricity occurs, the fluid volume on the side close to the conductor decreases and the flow velocity decreases. This leads to local temperature rise on the eccentric side of the conductor, thereby resulting in uneven temperature rise distribution on the cross-section.

This section studies the temperature field distribution on the inner side of different pipe structures under the condition of power line conductor eccentricity, and the conductor eccentricity coefficient is defined.

$\eta =\frac{\Delta r}{R-r_{con}}\times 100\%$ (6)

where, Δr is the distance by which the power line conductor deviates from the center of the cooling pipe, R is the minimum radius of the cooling pipe; r_con is the radius of the power line conductor.

The impact of different pipe structures on pipe temperature rise was studied when the eccentricity of the power line conductor was 80%. The temperature distribution diagram of the cooling pipe at the coolant outlet cross-section is shown in Figure 8 . As can be seen from Figure 8(a) , when the conductor is eccentric, the spatial distribution of the coolant and the change in local flow velocity cause the temperature rise on the inner surface of the pipeline near the conductor to be significantly higher than that on the surface far from the conductor, resulting in an uneven temperature distribution across the same cross-section. Among them, the local temperatures of the circular pipe (traditional non-grooved pipe) and straight-grooved pipe are higher than that of helical-grooved pipe, which because the effect of the structure-induced transverse fluid flow, enabling the rapid transverse diffusion of local high temperatures and reducing local temperature rise.

The temperatures along the transverse cross-sectional lines on the inner wall of the pipe were extracted, as shown in Figure 8(b) . At the same conductor eccentricity, the temperature distribution on the inner wall of the non-grooved pipe shows a sinusoidal-like distribution along the circumference. For the straight-grooved pipe, due to the cooling effect of the fluid in the grooves on the side where the power line deviates, its maximum temperature is lower than that of the non-grooved pipe. For the helical-grooved liquid-cooled pipe, the maximum temperature is much lower than that of the other two structures. Moreover, on the side opposite to the power line’s eccentricity, the minimum temperature of the pipe wall is higher than that of the other two structures, resulting in higher temperature uniformity across the pipe’s cross-section.

From the above analysis, it can be concluded that the helical-grooved structure could enhance the transverse heat dissipation efficiency by inducing forced transverse convection of the coolant through its structural design. The ratio of the helical-groove pitch to the average inner diameter of the pipe was defined as the pitch-diameter ratio, denoted as μ. The characteristics of the flow field and temperature field with the value of μ in the range of 5~15 were studied in this paper. By comprehensively considering parameters including the longitudinal-transverse fluid velocity, heat dissipation efficiency, and temperature uniformity, the selection principle for the helical-grooved structure is determined.

As shown in Figure 9 , as the helical-groove pitch decreases, the transverse fluid velocity increases approximately linearly, while the longitudinal fluid velocity remains basically unchanged; the fluid vorticity also increases approximately linearly, which effectively improves the transverse heat transfer efficiency. However, under the same inlet pressure condition, an excessively small pitch will increase the longitudinal flow resistance to a certain extent.

Set the eccentricity of the power line to 80%. Under the same load and fluid pressure conditions, study the influence of the pitch-diameter ratio of the spiral channel on the temperature field distribution. Extract the maximum temperature T_max and minimum temperature T_min of the inner wall of the pipeline at the fluid outlet, and define the temperature uniformity coefficient as the ratio of the maximum temperature difference on the outlet plane of the cooling fluid to the algebraic mean value of temperatures.

$\lambda =\frac{2\left(T_{\text{max}}-T_{\text{min}}\right)}{T_{\text{max}}+T_{\text{min}}}\times 100\%$ (7)

The smaller the value of μ, the more uniform the temperature distribution tends to be on the same cross-section. As shown in Figure 10 , this is the variation trend of temperature on the same plane corresponding to different pitch-diameter ratios of the helical groove. The transverse fluid velocity is relatively high with a small value of μ, which is conducive to the transverse convective heat dissipation of the coolant, thereby improving the transverse temperature uniformity.

With the pitch-diameter ratio increases, the transverse fluid velocity decreases, and the transverse heat exchange of the fluid weakens. The value of T_max in the pipe and temperature difference in the same cross-section increase.

It can be seen from the figure that when the pitch-diameter ratio is small, the helical groove structure has a more obvious temperature homogenization effect. When the pitch-diameter ratio of the groove is greater than 12, the structure has little or even no impact on the transverse temperature. With reference to the processing technology and material properties of the cooling pipe, it is advisable to select a pitch-diameter ratio of around 10.