Introduction
The rapid growth of the electric vehicle market has led to an increasing demand for high-power-density traction motors. However, the compact design and intense electromagnetic loading of such motors generate a considerable amount of heat within a limited space. The resulting temperature rise directly threatens the reliability of winding insulation, degrades the magnetic performance of permanent magnets, and eventually shortens the service life of the drive system. It has been widely reported that 30% to 40% of motor failures can be attributed to excessive temperature. In this context, an efficient thermal management strategy is essential for electric vehicle traction motors. Traditional air cooling and conventional liquid cooling jackets are gradually approaching their heat dissipation limits. Spray cooling, by contrast, offers remarkable heat transfer coefficients, lower coolant consumption, and better surface temperature uniformity. These features make spray cooling a promising solution for the thermal management of high-power-density electric vehicle motors. In my study, I focus on the ring-array spray cooling configuration which is particularly suitable for the stator of the electric vehicle traction motor. I investigate the heat transfer performance under vibration conditions through a combined experimental and numerical approach. The aim is to reveal the influence of vibration parameters and spray parameters on the cooling behavior of the annular stator surface.
In an electric vehicle, vibration is an unavoidable operating condition. The motor, gearbox, and road excitation all generate mechanical vibration over a wide range of frequencies and amplitudes. Vibration alters the impact dynamics of spray droplets and the distribution of the liquid film on the heated surface. Consequently, the cooling performance of a spray cooling system in an electric vehicle motor cannot be fully understood without considering the vibration effect. Several investigators have analysed droplet impact on vibrating surfaces and observed significant changes in droplet spreading and heat transfer. However, few experimental studies have considered the coupling of vibration with the ring-shaped stator surface of an electric vehicle motor. Moreover, direct measurements of the transient liquid film thickness and velocity are difficult to obtain from experiments. Therefore, numerical simulation is a valuable tool for revealing the underlying mechanisms.
In the present work, I first build an experimental platform for spray cooling on a circular arc vibrating surface. The effects of vibration frequency, vibration amplitude, spray flow rate, and nozzle height on the heat flux, heat transfer coefficient, and heat transfer enhancement ratio are investigated. Then I develop a transient numerical model using the Eulerian-Lagrangian framework, which is validated against the measured data. The simulation is employed to explain the liquid film behaviour in terms of film thickness and film velocity. Finally, a stator ring numerical model is constructed to investigate the influence of the nozzle number, the total spray flow rate, and the nozzle height on the maximum surface temperature and the maximum temperature difference under vibration conditions. The results obtained in this work can provide valuable guidance for the design of robust spray cooling systems in electric vehicle drive motors.
Experimental System and Test Conditions
I designed a closed-loop spray cooling test bench with an arc-shaped vibrating heated surface. The test system consisted of four main modules: the spray module, the vibration module, the heating module, and the data acquisition module. The spray loop was composed of a lubricant reservoir, a gear pump, a throttle valve, a filter, a solenoid valve, a solid-cone nozzle, a spray chamber, and a condenser. The coolant was pumped from the reservoir and filtered before entering the nozzle. The nozzle produced a full-cone spray with droplet diameters roughly in the range of 50 to 100 µm. The heated block was mounted inside the spray chamber and rigidly attached to the vibration exciter. The vibration module employed an electrodynamic shaker controlled in a closed loop with an accelerometer and a power amplifier. The maximum dynamic force was 500 N, the frequency range was 5 to 5000 Hz, and the maximum displacement amplitude was 10 mm. The heating module consisted of a copper block, nine cartridge heaters, an insulating sleeve, and a DC power supply. The heating power could be adjusted up to 800 W. K-type thermocouples installed at different depths inside the copper block were used to obtain the temperature gradient. All sensor signals were recorded by a data acquisition card connected to LabVIEW software.
The coolant used in my experiments was a commercially available electric-vehicle transmission lubricant, which provides a high flash point and suitable viscosity for motor spraying. I used the same lubricant in the experiments and the simulations. The relevant thermophysical properties of the copper block and the coolant are listed in Tables 1 and 2.
| Property | Value |
|---|---|
| Distance from nozzle to copper surface (mm) | 10, 15, 20 |
| Copper block diameter (mm) | 20 |
| Effective heat transfer area (m²) | 0.000628 |
| Thermal conductivity (W·m⁻¹·K⁻¹) | 398 |
| Property | Value |
|---|---|
| Flash point (°C) | above 210 |
| Boiling point (°C) | above 250 |
| Kinematic viscosity at 40 °C (mm²·s⁻¹) | 27.38 |
| Kinematic viscosity at 100 °C (mm²·s⁻¹) | 5.916 |
| Specific heat capacity (J·kg⁻¹·K⁻¹) | 2149.3 |
| Surface tension (N·m⁻¹) | 0.025 |
| Density (kg·m⁻³) | 786.65 |
| Pour point (°C) | −51 |
In each experiment, the copper surface was cleaned with acetone to remove oxides and contaminants. The coolant temperature was kept at 40 °C. The heating power was adjusted from 200 W to 800 W. The vibration parameters and spray parameters are summarized in Table 3. The vibration amplitude was 0.0005 mm when the frequency was varied, while the frequency was fixed at 20 Hz when the amplitude was varied. For the spray parameter tests, the spray flow rate ranged from 150 to 250 mL/min and the nozzle height ranged from 10 to 20 mm. Every test was repeated at least three times to guarantee repeatability.
| Amplitude (mm) | Frequency (Hz) |
|---|---|
| 0.0005 | 1000 |
| 0.0005 | 2000 |
| 0.0005 | 3000 |
| 0.0005 | 4000 |
| 1 | 20 |
| 2 | 20 |
| 3 | 20 |
| 4 | 20 |
Data Reduction and Uncertainty
Because the periphery and the bottom of the copper block were thermally insulated, I assumed one-dimensional steady-state heat conduction inside the copper block. According to Fourier’s law, the heat flux can be calculated from the temperature difference measured by the two thermocouples:
$$q = \lambda \frac{dT}{dx} = \lambda \frac{T_2 – T_1}{x_2}$$
where \( \lambda \) is the thermal conductivity of copper, \(T_1\) is the temperature measured by the upper thermocouple, \(T_2\) is the temperature measured by the middle thermocouple, and \(x_2 = 6~\mathrm{mm}\) is the spacing between these two thermocouples.
The cooled surface temperature cannot be measured directly. It was obtained by extrapolation using Fourier’s law:
$$T_s = T_1 – \frac{q}{\lambda} x_1$$
where \(x_1 = 16~\mathrm{mm}\) is the distance from the upper thermocouple to the sprayed surface. The average spray cooling heat transfer coefficient is
$$h = \frac{q}{T_s – T_{in}}$$
where \(T_{in}\) is the initial coolant temperature. In addition, I introduced the heat transfer enhancement ratio to quantify the influence of vibration:
$$\varepsilon = \frac{h}{h_{st}}$$
where \(h_{st}\) denotes the heat transfer coefficient measured without vibration. The Sauter mean diameter \(d_{32}\) is used to characterize the spray droplet size:
$$d_{32} = \frac{\sum_i n_i d_i^3}{\sum_i n_i d_i^2}$$
The uncertainty propagation was evaluated with the standard error-propagation method. The resulting uncertainties were estimated as ±1.4% for the surface temperature, ±2.3% for the heat flux, ±2.6% for the heat transfer coefficient, and ±3.7% for the enhancement ratio.
Experimental Results and Discussion
Effect of Vibration on Spray Cooling Heat Transfer
Table 4 summarizes the measured heat flux, heat transfer coefficient, and enhancement ratio at representative vibration conditions. The results were obtained at a heating power of 800 W, a spray flow rate of 250 mL/min, and a nozzle height of 20 mm.
| Condition | Heat flux (W/cm²) | h (W·cm⁻²·K⁻¹) | ε |
|---|---|---|---|
| Static | ≈ 90.8 | 0.30 | 1.00 |
| 1000 Hz, 0.0005 mm | ≈ 103.1 | ≈ 0.32 | ≈ 1.06 |
| 4000 Hz, 0.0005 mm | 114.5 | 0.38 | 1.26 |
| 1 mm, 20 Hz | 97.4 | 0.29 | 0.98 |
| 4 mm, 20 Hz | 70.4 | 0.20 | 0.67 |
When the vibration frequency was increased from 1000 Hz to 4000 Hz at a constant amplitude of 0.0005 mm, the heat flux and heat transfer coefficient both increased. At 4000 Hz, the heat flux reached 114.5 W/cm², which was 11.1% higher than that at 1000 Hz. The heat transfer coefficient at 4000 Hz was 0.38 W·cm⁻²·K⁻¹, which was 18.8% higher than the value measured at 1000 Hz. This behaviour can be explained as follows. A higher vibration frequency increases the relative impact velocity between the droplets and the heated surface. The enhanced droplet momentum disrupts the thermal boundary layer and promotes direct liquid-surface interaction. The liquid film is also disturbed more frequently, which accelerates the renewal of the film layer and improves heat exchange.
In contrast, increasing the vibration amplitude has an adverse effect. When the amplitude was increased from 1 mm to 4 mm at a fixed frequency of 20 Hz, the heat flux decreased from 97.4 W/cm² to 70.4 W/cm², a reduction of 27.7%. The heat transfer coefficient decreased from 0.29 W·cm⁻²·K⁻¹ to 0.20 W·cm⁻²·K⁻¹. The enhancement ratio dropped from 0.98 to 0.67. Large-amplitude vibration causes severe oscillation of the liquid film. The film becomes unstable and periodically accumulates at certain locations. The effective contact between the coolant film and the heating surface is reduced. Therefore, large vibration amplitudes suppress the spray cooling heat transfer instead of improving it.
Effect of Spray Flow Rate
I also performed tests at three spray flow rates: 150 mL/min, 200 mL/min, and 250 mL/min. The heating power was 800 W and the nozzle height was 20 mm. In the frequency vibration group, the amplitude was kept at 0.0005 mm. In the amplitude vibration group, the frequency was kept at 20 Hz. The results are shown in Tables 5 and 6.
| Flow rate (mL/min) | Heat flux at 4000 Hz (W/cm²) | Increase compared with 150 mL/min |
|---|---|---|
| 150 | ≈ 92.2 | — |
| 200 | — | — |
| 250 | 114.5 | +24.2% |
| Flow rate (mL/min) | Heat flux at 1 mm (W/cm²) | h at 1 mm (W·cm⁻²·K⁻¹) | ε at 1 mm |
|---|---|---|---|
| 150 | 81.5 | 0.21 | 0.88 |
| 250 | 97.4 | 0.29 | 0.98 |
The experimental data show that increasing the spray flow rate raises the heat flux, the heat transfer coefficient, and the enhancement ratio under both frequency-vibration and amplitude-vibration conditions. At a frequency of 4000 Hz, the heat flux obtained at 250 mL/min was 24.2% higher than that obtained at 150 mL/min. In the amplitude-vibration group at 1 mm amplitude, the heat flux rose from 81.5 W/cm² to 97.4 W/cm² when the flow rate increased from 150 to 250 mL/min. The heat transfer coefficient increased by 38.1%. This enhancement can be attributed to the larger impact velocity and greater droplet kinetic energy associated with a larger spray flow rate. The droplets are more capable of penetrating the liquid film and reaching the heated surface directly. At the same time, the enhanced droplet flux promotes spreading of the liquid film, which produces a thinner film and reduces the conduction resistance through the film.
Effect of Nozzle Height
Three nozzle heights were evaluated: 10 mm, 15 mm, and 20 mm. The maximum nozzle height corresponded to a spray footprint that was tangent to the circular heating surface. The cooling results are shown in Table 7.
| Frequency condition | Nozzle height (mm) | Heat flux (W/cm²) | h (W·cm⁻²·K⁻¹) | ε |
|---|---|---|---|---|
| 4000 Hz, 0.0005 mm | 10 | 102.4 | 0.29 | 1.21 |
| 4000 Hz, 0.0005 mm | 20 | 114.5 | 0.38 | 1.26 |
| 20 Hz, 1 mm | 10 | 80.4 | 0.20 | 0.86 |
| 20 Hz, 1 mm | 20 | 97.4 | 0.29 | 0.98 |
In the frequency-vibration group, increasing the nozzle height from 10 mm to 20 mm raised the heat flux from 102.4 W/cm² to 114.5 W/cm², representing an increase of 11.8% at 4000 Hz. Under the amplitude-vibration condition at 1 mm amplitude, the heat flux increased by 21.1% when the nozzle height was changed from 10 mm to 20 mm. The heat transfer coefficient increased from 0.20 to 0.29 W·cm⁻²·K⁻¹, which is a 45.0% improvement. A larger nozzle height allows the spray to cover a wider area of the heated surface. The liquid film is thinner and more uniform, while the splashing of droplets is suppressed. These factors reduce the thermal resistance and enhance the convective heat transfer. It should be noted that if the nozzle height is too large, the spray becomes overly dispersed and the cooling performance can decline. Therefore, an optimum nozzle height needs to be determined for each practical configuration.
Numerical Simulation of Spray Cooling on a Vibrating Arc Surface
To reveal the underlying mechanisms of the experimentally observed trends, I developed a transient numerical model of spray cooling on a vibrating arc surface. The model was built in Star CCM+. The computational domain was a cubic region of 60 mm side length. A half-cylindrical copper block of 20 mm diameter and 20 mm height was placed at the centre of the domain. The solid-cone nozzle was located above the centre of the specimen. The simulation relied on an Eulerian-Lagrangian framework. The liquid droplets were treated as a discrete phase, while the continuous gaseous phase was solved with the Reynolds-averaged Navier-Stokes equations. The \(k-\varepsilon\) turbulence model was used to close the equations. The primary atomization was modelled using the Huh model, and the secondary breakup was modelled using the Kelvin-Helmholtz/Rayleigh-Taylor approach. The droplet size distribution was described by the Rosin-Rammler function. The liquid film formed on the heated surface was calculated by a thin-film model solving the mass, momentum, and energy conservation equations in the film. Table 8 lists the boundary conditions used in the simulation.
| Parameter | Value |
|---|---|
| Spray flow rate (mL/min) | 150, 200, 250 |
| Nozzle height (mm) | 10, 15, 20 |
| Gravity (m/s²) | 9.8 |
| Injection velocity (m/s) | 8.8, 11.8, 14.8 |
| Droplet diameter (µm) | 100 |
| Oil temperature (°C) | 40 |
| Heating power (W) | 800 |
| Vibration frequency (Hz) | 1000 to 4000 at 0.0005 mm |
| Vibration amplitude (mm) | 1 to 4 at 20 Hz |
The governing equations for the turbulence model can be written as
$$\frac{\partial}{\partial t}(\rho k) + \frac{\partial}{\partial x_j}(\rho k u_j) = \frac{\partial}{\partial x_j}\left[\left(\mu + \frac{\mu_t}{\sigma_k}\right)\frac{\partial k}{\partial x_j}\right] + G_b + G_k – \rho \varepsilon – Y_M$$
$$\frac{\partial}{\partial t}(\rho \varepsilon) + \frac{\partial}{\partial x_j}(\rho \varepsilon u_j) = \frac{\partial}{\partial x_j}\left[\left(\mu + \frac{\mu_t}{\sigma_\varepsilon}\right)\frac{\partial \varepsilon}{\partial x_j}\right] + \rho C_1 S \varepsilon – \rho C_2 \frac{\varepsilon^2}{k + \sqrt{\nu \varepsilon}} + C_{1\varepsilon} C_{3\varepsilon} \frac{\varepsilon}{k} G_b$$
For the discrete phase, the droplet motion is described by Newton’s second law:
$$\frac{d\vec{u_p}}{dt} = F_D(\vec{u_l} – \vec{u_p}) + \frac{\vec{g}(\rho_p – \rho_l)}{\rho_p} + \vec{F}$$
$$F_D = \frac{18\mu}{\rho_p d_p^2}\frac{C_d Re}{24}$$
The droplet heat balance is calculated as follows:
$$m_p C_p \frac{dT_p}{dt} = Q_t + Q_{rad} + Q_s$$
$$Q_t = h_p A_s (T_\infty – T_p)$$
where the Nusselt number correlation is used to obtain the droplet heat transfer coefficient:
$$Nu_p = \frac{h_p d_p}{k_\infty} = 2\left(1 + 0.3 Re_p^{1/2} Pr_\infty^{1/3}\right)$$
The thin liquid film conservation equations are:
$$\frac{\partial}{\partial t}\int_V \rho_f dV + \int_A \rho_f u_f dA = \int_V \frac{S_m}{H_f} dV$$
$$\frac{\partial}{\partial t}\int_V \rho_f u_f dV + \int_A \rho_f u_f u_f dA = \int_A \tau_f dA – \int_A P_f dA + \int_V \left(F_b + \frac{s_{ui}}{H_f}\right)dV$$
$$\frac{\partial}{\partial t}\int_V \rho_f E_f dV + \int_A \rho_f E_{nf} u_f dA = \int_A q_f^{”}dA + \int_A P_f u_f dA + \int_V F_b u_f dV + \int_V \frac{S_h}{H_f}dV$$
A grid independence test was performed with three mesh resolutions containing 175,760; 306,959; and 954,382 cells. The predicted heat flux changed by less than 5.8% between the coarse and fine meshes. Therefore, the medium mesh with 306,959 cells was selected for all subsequent simulations. The numerical model was validated against the experimental data obtained in the previous chapter. Sixteen representative cases covering different vibration frequencies and amplitudes were compared. The maximum deviation between the predicted and measured heat flux was within 10.3%, confirming that the numerical model was able to capture the spray cooling behaviour under vibration conditions.
Liquid Film Characteristics under Different Vibration Parameters
For a spray flow rate of 250 mL/min and a nozzle height of 20 mm, the simulated maximum film thickness remained nearly constant when the vibration frequency increased from 1000 Hz to 4000 Hz at an amplitude of 0.0005 mm. The maximum film thickness was about 0.91 mm at 1000 Hz and about 0.90 mm at 4000 Hz. The film velocity increased by only 0.35 m/s over this frequency range. This confirms that high-frequency vibration at small amplitude does not distort the liquid film; instead, the film remains stable and uniformly distributed.
The effect of the vibration amplitude was much more pronounced. At a frequency of 20 Hz, the maximum liquid film thickness increased from 0.98 mm at 1 mm amplitude to 2.11 mm at 4 mm amplitude. This represents an increase of 1.13 mm. The maximum film velocity also increased from 7.64 m/s to 9.18 m/s. Large-amplitude vibration imposes an additional inertial force on the liquid film, causing the film to gather and form thicker regions near the centre or at the periphery. These results explain why the measured heat flux in the amplitude tests decreased with increasing amplitude.
Liquid Film Behaviour under Different Spray Flow Rates
The simulation results showed that increasing the spray flow rate significantly reduced the liquid film thickness. In the frequency-vibration group at 4000 Hz, the maximum film thickness was 0.90 mm at 250 mL/min. When the flow rate was reduced to 150 mL/min, the maximum film thickness was 1.31 mm, i.e. 0.41 mm larger. A larger flow rate increases the droplet impact velocity and the momentum transfer to the liquid film. The film spreads more easily and becomes thinner. The simulated maximum film velocity rose from 5.22 m/s at 150 mL/min to 7.11 m/s at 250 mL/min, representing an increase of 1.89 m/s.
In the amplitude-vibration group, the trend was similar. At 4 mm amplitude and 20 Hz, the maximum film thickness decreased by 0.98 mm when the spray flow rate increased from 150 to 250 mL/min. Meanwhile, the maximum film velocity increased from 6.81 m/s to 9.18 m/s. Although a larger amplitude increases the film velocity, the film fluctuation becomes more severe, which is detrimental to the heat transfer.
Liquid Film Behaviour under Different Nozzle Heights
Increasing the nozzle height caused the film thickness to decrease and the film velocity to decrease. At 4000 Hz and a spray flow rate of 250 mL/min, the maximum film thickness was 0.90 mm at a nozzle height of 20 mm, which was 0.46 mm smaller than that at 10 mm. The maximum film velocity decreased from 9.34 m/s at a nozzle height of 10 mm to 7.11 m/s at a nozzle height of 20 mm. This result indicates that a larger nozzle height allows the spray droplets to spread over a wider area, leading to a more uniform film and less droplet splashing. Although the local film velocity is reduced, the more uniform coverage improves the overall cooling performance.
Numerical Simulation of Spray Cooling on the Stator Ring Surface
In order to apply the spray cooling technology to an actual electric vehicle motor, I established a three-dimensional numerical model of the motor stator ring surface. The geometry of the stator was provided by an industrial partner in the electric vehicle motor sector. The model included the complete annular structure of the stator. The stator outer surface was treated as the main cooling surface. Polyhedral meshes were used and local refinement was applied around the stator surface and the spray impact regions. The total number of mesh cells was 15,876,488.
In this model, the spray nozzles were distributed in a uniform ring array around the stator annulus. The total spray flow was evenly divided among the nozzles. The stator was modelled as a heat-generating body with a total heating power of 3000 W. The stator was prescribed with sinusoidal vibration motion. The coolant temperature was 40 °C. I first evaluated the effect of the number of nozzles, then the effect of the total spray flow rate, and finally the effect of the nozzle height. The operating parameters are summarized in Table 9.
| Case | Nozzle number | Total flow (mL/min) | Nozzle height (mm) | Injection velocity (m/s) |
|---|---|---|---|---|
| Nozzle number series | 12, 15, 18 | 8000 | 30 | 26.2, 31.4, 39.3 |
| Flow rate series | 18 | 4000, 6000, 8000 | 30 | 13.1, 19.6, 26.2 |
| Nozzle height series | 18 | 8000 | 20, 25, 30 | 26.2 |
These cases were run under two groups of vibration conditions. The frequency-vibration group used a frequency range of 1000 to 4000 Hz with a fixed amplitude of 0.0005 mm. The amplitude-vibration group used an amplitude range of 1 to 4 mm with a fixed frequency of 20 Hz.
Effect of Nozzle Number
Table 10 summarizes the simulated maximum surface temperature and maximum temperature difference for different nozzle numbers at 4000 Hz and at 4 mm amplitude.
| Vibration condition | Nozzles | T_max (°C) | ΔT_max (°C) |
|---|---|---|---|
| 4000 Hz, 0.0005 mm | 12 | 120.8 | 12.5 |
| 4000 Hz, 0.0005 mm | 15 | — | — |
| 4000 Hz, 0.0005 mm | 18 | 95.5 | 4.1 |
| 20 Hz, 4 mm | 12 | 169.6 | 26.5 |
| 20 Hz, 4 mm | 18 | 135.9 | 15.3 |
The simulation results demonstrate that increasing the number of nozzles from 12 to 18 improves the cooling performance significantly. At 4000 Hz and 0.0005 mm amplitude, the maximum stator surface temperature was 95.5 °C with 18 nozzles, compared with 120.8 °C with 12 nozzles. The maximum temperature difference dropped by 8.4 °C. The maximum liquid film thickness was also reduced by 0.23 mm. This improvement is attributed to the smaller angular spacing between adjacent nozzles. The spray footprints overlap more effectively and provide a more continuous liquid film over the whole ring surface. The film becomes more uniform and the dry hotspots are eliminated.
At an amplitude of 4 mm and a frequency of 20 Hz, the maximum temperature with 18 nozzles was 135.9 °C, i.e. 33.7 °C lower than with 12 nozzles. The maximum temperature difference decreased from 26.5 °C to 15.3 °C. Therefore, adding more nozzles is an effective approach for improving cooling uniformity on the electric vehicle motor stator under vibration conditions.
Effect of Total Spray Flow Rate
With 18 nozzles and a fixed nozzle height of 30 mm, the total spray flow rate was increased from 4000 to 8000 mL/min. Table 11 lists the simulated values.
| Vibration condition | Total flow (mL/min) | T_max (°C) | ΔT_max (°C) |
|---|---|---|---|
| 4000 Hz, 0.0005 mm | 4000 | 134.3 | 15.5 |
| 4000 Hz, 0.0005 mm | 8000 | 95.5 | 4.1 |
| 20 Hz, 4 mm | 4000 | 197.3 | 30.2 |
| 20 Hz, 4 mm | 8000 | 135.9 | 15.3 |
The simulation shows that the maximum stator temperature decreases considerably as the total spray flow rate is raised. At 4000 Hz, increasing the flow rate from 4000 to 8000 mL/min reduced the maximum temperature from 134.3 °C to 95.5 °C, i.e. by 38.8 °C. The maximum temperature difference was reduced by 11.4 °C. At 4 mm amplitude and 20 Hz, the maximum temperature was reduced by 61.4 °C when the flow rate was increased to 8000 mL/min. The maximum film thickness also dropped by 1.35 mm in this case.
Physically, the higher flow rate produces a larger liquid volume flux and higher droplet impact velocity. The droplets can break through the liquid film and directly cool the stator surface. A higher flow rate also corresponds to a larger spray cone angle, which improves the coverage area over the annular stator surface. As a result, the film is thinner and the heat removal is more efficient. I therefore concluded that the spray flow rate is a key parameter in the design of an electric vehicle motor spray cooling system and must be sufficiently high to suppress hotspots.
Effect of Nozzle Height
For 18 nozzles and a total flow rate of 8000 mL/min, I compared nozzle heights of 20 mm, 25 mm, and 30 mm. The results are shown in Table 12.
| Vibration condition | Nozzle height (mm) | T_max (°C) | ΔT_max (°C) |
|---|---|---|---|
| 4000 Hz, 0.0005 mm | 20 | 108.6 | 21.5 |
| 4000 Hz, 0.0005 mm | 30 | 95.5 | 4.1 |
| 20 Hz, 4 mm | 20 | 163.2 | 48.5 |
| 20 Hz, 4 mm | 30 | 135.9 | 15.3 |
At 4000 Hz, increasing the nozzle height from 20 mm to 30 mm lowered the maximum stator surface temperature by 13.1 °C. The maximum temperature difference decreased by 17.4 °C. At the amplitude of 4 mm, the maximum temperature was reduced by 27.3 °C and the maximum temperature difference by 33.2 °C. A larger nozzle height expands the spray footprint on the stator surface and improves the overlap between neighbouring nozzles. The liquid film is distributed more uniformly and the splashing loss is reduced. The maximum film thickness decreased from 4.49 mm to 3.36 mm at the large-amplitude condition. Therefore, the nozzle height should be chosen carefully so that the spray can fully cover the stator annulus without causing excessive liquid accumulation.
Conclusions
In this work, I carried out a combined experimental and numerical investigation of ring-array spray cooling for an electric vehicle motor stator. The heat transfer behaviour was analysed under frequency vibration and amplitude vibration conditions. The main conclusions are drawn as follows.
First, the experimental results on the vibrating arc surface showed that a high vibration frequency promotes heat transfer while a large vibration amplitude impairs it. At an amplitude of 0.0005 mm, increasing the frequency from 1000 Hz to 4000 Hz increased the heat flux by 11.1% and the heat transfer coefficient by 18.8%. At a fixed frequency of 20 Hz, increasing the amplitude from 1 mm to 4 mm caused the heat flux to decrease by 27.7% and the heat transfer coefficient by 31.0%.
Second, increasing the spray flow rate improved the heat transfer under all tested vibration conditions. At 4000 Hz, the heat flux at 250 mL/min was 24.2% higher than that at 150 mL/min. The numerical simulation confirmed that a higher spray flow rate reduces the film thickness because the droplet impact kinetic energy is increased, and the liquid film becomes thinner and more uniform.
Third, increasing the nozzle height improved the coverage uniformity of the liquid film and reduced droplet splashing. Under frequency-vibration conditions at 4000 Hz, the heat flux at a nozzle height of 20 mm was 11.8% higher than that at 10 mm. The simulation indicated that the maximum film thickness decreased from 1.36 mm to 0.90 mm when the nozzle height increased from 10 mm to 20 mm.
Fourth, for the electric vehicle motor stator ring model, increasing the nozzle number from 12 to 18 significantly improved the temperature uniformity and reduced the maximum surface temperature. At 4000 Hz, the maximum temperature was lowered by 25.3 °C and the maximum temperature difference by 8.4 °C. Increasing the total spray flow rate from 4000 to 8000 mL/min decreased the maximum stator temperature by 38.8 °C and the maximum temperature difference by 11.4 °C. Finally, increasing the nozzle height from 20 mm to 30 mm reduced the maximum temperature by 13.1 °C at 4000 Hz and by 27.3 °C at large amplitude.
These findings demonstrate that ring-array spray cooling can provide highly efficient and uniform thermal management for electric vehicle motors. The optimal selection of nozzle number, spray flow rate, and nozzle height must consider the actual vibration environment of the electric vehicle. The present study offers practical guidance for developing robust and efficient spray cooling systems for next-generation electric vehicle drive motors.