In my research, I systematically investigated the cooling performance of a traction battery pack under the coupled effect of spray evaporation and forced ventilation. The rapid growth of electric vehicles has made the thermal management of traction battery packs one of the most critical bottlenecks for further improvement. Lithium-ion batteries are widely adopted because of their high energy density, low self-discharge, and stable cycle life. However, during high-rate charging or discharging, these batteries generate a large amount of heat, which can lead to excessive temperature rise and uneven temperature distribution. An overheated traction battery pack not only suffers from accelerated capacity fade but also faces severe safety risks such as thermal runaway.
In the first part of this dissertation, I reviewed the existing thermal management techniques for traction battery packs, including air cooling, liquid cooling, phase-change-material cooling, heat pipe cooling, and spray evaporative cooling. Air cooling has the advantages of simple structure, low weight, and low cost, but its heat transfer coefficient is limited. Liquid cooling can provide a much higher heat transfer rate, but the system complexity and potential leakage issues remain challenging. Phase change materials are passive and effective in buffering temperature fluctuations, yet their low thermal conductivity often requires the addition of fins or high-conductivity fillers. Heat pipe cooling offers superior effective thermal conductivity, but its performance relies on the capillary limit and condenser section design. Spray cooling is particularly attractive because the evaporation latent heat of water is extremely high, and the spray droplets can directly interact with both the heated surface and the mainstream air. Therefore, I proposed a coupled spray and ventilation cooling scheme for a traction battery pack. In this scheme, fine water droplets are injected into the battery air-flow channels, where they absorb heat from the battery surfaces and the surrounding air through convective heat transfer and evaporation, thereby providing a stronger cooling effect than conventional forced air cooling alone.
To obtain reliable heat generation data for the numerical model, I first selected a prismatic lithium-ion cell with dimensions of 20 mm × 100 mm × 140 mm and a rated capacity of 27 Ah. The main physical parameters of the cell are summarized in the following table.
| Parameter | Value |
|---|---|
| Dimensions (mm) | 20 × 100 × 140 |
| Mass (kg) | 0.588 |
| Nominal voltage (V) | 3.2 |
| Operating voltage (V) | 2.0 – 3.65 |
| AC impedance (mΩ) | 0.8 – 1.2 |
| DC impedance (mΩ) | ≤ 3.0 |
| Nominal capacity (Ah) | 27 |
The heat generation mechanisms inside a lithium-ion cell include reaction heat, polarization heat, Joule heat, and side-reaction heat. During normal operation, the side-reaction heat is often negligible because lithium-ion cells have a very low self-discharge rate. The total heat generation rate can be evaluated using the Bernardi model:
$$Q_{\mathrm{gen}} = I(U_{\mathrm{OC}} – U) – I T_b \frac{\mathrm{d}U_{\mathrm{OC}}}{\mathrm{d}T_b}$$
where \(I\) is the current, \(U_{\mathrm{OC}}\) is the open-circuit voltage, \(U\) is the terminal voltage, \(T_b\) is the battery temperature, and the term \(\mathrm{d}U_{\mathrm{OC}}/\mathrm{d}T_b\) accounts for the entropic heat. By assuming that the battery is a homogeneous equivalent heat source with uniform volumetric heat generation, the model can be simplified. I conducted discharge experiments on a single cell inside a constant-temperature chamber at 300 K. The battery was discharged at 1C, 2C, and 3C rates while the surface temperature was monitored by five T-type thermocouples connected to an Agilent 34972A data acquisition system. The measured temperature rise curves were then used to derive the heat generation power as a function of current.
$$Q_{\mathrm{gen}} = 1.06 \times 10^{-3} I^2 + 0.085 I$$
Dividing by the cell volume gives the volumetric heat source:
$$q_{\mathrm{gen}} = 3.42 I^2 + 274.19 I$$
For the three discharge rates, the corresponding volumetric heat sources are listed in Table 2.
| Discharge rate (C) | Volumetric heat source (W/m³) |
|---|---|
| 1 | 9 893 |
| 2 | 24 777 |
| 3 | 44 626 |
Using these volumetric heat sources, I established a three-dimensional numerical model of a traction battery pack containing 24 cells. The computational domain consisted of a ventilation duct, the battery pack, and several spray nozzles. In the model, air was treated as a continuous phase, whereas the spray droplets were treated as discrete particles using the Eulerian–Lagrangian approach. The continuity, momentum, and energy equations for the continuous phase are written as follows:
$$\frac{\partial \rho}{\partial t} + \nabla \cdot (\rho \vec{v}) = S_m$$
$$\frac{\partial (\rho \vec{v})}{\partial t} + \nabla \cdot (\rho \vec{v} \vec{v}) = -\nabla p + \nabla \cdot \boldsymbol{\tau} + \rho \vec{g} + \vec{F}$$
$$\frac{\partial (\rho E)}{\partial t} + \nabla \cdot [\vec{v}(\rho E + p)] = \nabla \cdot \left(k_{\mathrm{eff}} \nabla T – \sum_j h_j J_j \right) + \Phi + S_h$$
Since the droplets experience evaporation, a species transport equation was also solved for the water vapor mass fraction \(Y_m\):
$$\frac{\partial (\rho Y_m)}{\partial t} + \nabla \cdot (\rho \vec{v} Y_m) = \nabla \cdot (\rho D_m \nabla Y_m) + S_i$$
For the turbulent flow in the cooling channels, I employed the realizable \(k\)-\(\varepsilon\) model. This model provides better predictions for planar and round jets, which is important for spray-induced flows. The transport equations for turbulent kinetic energy \(k\) and turbulent dissipation rate \(\varepsilon\) are:
$$\frac{\partial (\rho k)}{\partial t} + \frac{\partial (\rho k u_i)}{\partial x_i} = \frac{\partial}{\partial x_j} \left[\left(\mu + \frac{\mu_t}{\sigma_k}\right)\frac{\partial k}{\partial x_j}\right] + P_k + G_b – \rho \varepsilon – Y_M$$
$$\frac{\partial (\rho \varepsilon)}{\partial t} + \frac{\partial (\rho \varepsilon u_i)}{\partial x_i} = \frac{\partial}{\partial x_j} \left[\left(\mu + \frac{\mu_t}{\sigma_\varepsilon}\right)\frac{\partial \varepsilon}{\partial x_j}\right] + C_1 S \varepsilon – C_2 \rho \frac{\varepsilon^2}{k + \sqrt{\nu \varepsilon}} + C_3 \frac{\varepsilon}{k} G_b$$
For the discrete phase, the droplet motion is governed by the following equation:
$$\frac{\mathrm{d}\vec{v}_p}{\mathrm{d}t} = F_D(\vec{v} – \vec{v}_p) + \frac{\vec{g}(\rho_p – \rho)}{\rho_p} + \vec{F}$$
The drag coefficient \(F_D\) was evaluated from the spherical droplet assumption. The droplet evaporation process was treated by a non-equilibrium thermal law, and the droplet size distribution was defined using the Rosin–Rammler model:
$$Y_d = \exp\left[-\left(\frac{d}{d_m}\right)^{n_s}\right]$$
where \(d_m\) is the mean diameter and \(n_s\) is the distribution index. I used the TAB break-up model for the secondary breakup of droplets.
Before performing the comprehensive parametric study, I carried out a grid-independence analysis. Six mesh counts from approximately 0.89 million to 5.74 million were generated and tested for the same cooling condition. Table 3 shows the predicted maximum temperature of the battery pack for each mesh count.
| Number of cells | Maximum temperature (K) |
|---|---|
| 893,896 | 315.51 |
| 1,433,159 | 314.95 |
| 2,815,236 | 314.61 |
| 3,455,368 | 314.46 |
| 4,560,371 | 314.39 |
| 5,744,296 | 314.31 |
The maximum temperature changed by only 0.15 K when the mesh count increased from 2.81 million to 3.46 million. Therefore, I chose the mesh size corresponding to approximately 2.81 million cells for all subsequent simulations.
In order to verify the numerical model, I built an experimental bench that mimicked the heat generation of a single battery using an aluminum block with an embedded heating rod. The block had the same dimensions as the real cell. The heating power was controlled by a variable transformer and adjusted to match the volumetric heat generation at a 3C discharge rate. The experimental setup comprised an ultrasonic atomizer, a variable-speed fan, an anemometer, a data acquisition module, and thermocouples. The test section was a rectangular duct with a cross-section identical to one battery cooling channel. Six validation cases were performed, as summarized in Table 4.
| Case | Air velocity (m/s) | Spray mass flow rate (g/s) |
|---|---|---|
| 1 | 1.0 | 0 |
| 2 | 1.5 | 0 |
| 3 | 2.0 | 0 |
| 4 | 1.0 | 0.15 |
| 5 | 1.5 | 0.15 |
| 6 | 2.0 | 0.15 |
The root-mean-square error (RMSE) between the measured and simulated average temperatures was calculated as:
$$\mathrm{RMSE} = \sqrt{\frac{1}{n}\sum_{i=1}^{n}(y_i – \hat{y}_i)^2}$$
For all thirty measured points, the RMSE was 1.566 K, and the maximum deviation did not exceed 1.9 K. The agreement between the experimental data and the numerical results was considered satisfactory, which demonstrated that the present model is sufficiently accurate for simulating the coupled spray and ventilation cooling of a traction battery pack.
After verifying the model, I first examined the effect of the inlet air velocity and inlet air temperature under pure air-cooling conditions. The battery pack was discharged at 3C, and the inlet air temperature was fixed at 300 K. The results showed that the maximum temperature of the traction battery pack dropped significantly when the inlet air velocity was increased. For example, increasing the velocity from 0.5 m/s to 3 m/s reduced the maximum temperature by about 8–19 K depending on the specific operating conditions. At the same time, the temperature difference across the cells was also reduced. However, a higher inlet velocity increased the pressure drop in the flow channel from approximately 2.4 Pa at 0.5 m/s to 61.9 Pa at 3 m/s. This means that the fan power consumption would increase rapidly if the velocity were set too high. Therefore, the inlet velocity should be kept in the range of approximately 1–2 m/s for a balanced design.
When the inlet air temperature was varied while maintaining a constant velocity of 1 m/s, the maximum temperature of the traction battery pack increased almost linearly. Specifically, when the inlet air temperature was raised from 290 K to 310 K, the battery maximum temperature increased by 20.2 K, while the maximum temperature difference remained around 6.3–6.6 K. This indicates that the inlet air temperature has a much stronger influence on the absolute temperature than on the temperature uniformity.
I then investigated the influence of the nozzle type. Three typical nozzle configurations were compared: surface nozzles, cone-back nozzles, and cone nozzles. These nozzles were placed at the inlet side of the battery gaps. Among them, the cone nozzle gave the best overall performance because it directed droplets into the gaps between neighboring cells more effectively. The surface-type and cone-back-type nozzles tended to wet the upstream cells more heavily, producing a larger front-to-rear temperature difference. To further improve the temperature uniformity in the vertical direction, I modified the layout by using two symmetric cone nozzles at each gap instead of one single nozzle. The vertical distance between the two nozzles was then optimized.
Table 5 shows the comparison of the maximum temperature and maximum temperature difference under the base operating condition (air velocity = 1 m/s, total spray mass flow rate = 0.7 g/s, droplet diameter = 20 μm, relative humidity = 50%) for five nozzle configurations. The notation “2 cone” refers to two nozzles per gap arranged vertically.
| Configuration | Maximum temperature trend | Maximum temperature difference trend |
|---|---|---|
| Air only | Reference (highest) | Medium |
| Surface type | Lower than air | Higher than cone type |
| Cone-back type | Lower than air | Higher than cone type |
| Cone type (one per gap) | Low | Lower |
| Two cone nozzles per gap | Lowest | Lowest |
By increasing the spacing between the two vertically opposed cone nozzles from 30 mm to 130 mm, I found that a spacing of 110 mm provided both the lowest maximum temperature and the smallest temperature difference. When the spacing was too small, the droplets overlapped near the center and could not cover the whole vertical surface. When the spacing reached 130 mm, the nozzles were too close to the duct boundaries, causing some droplets to impinge on the walls and become ineffective. Consequently, I adopted the two-cone-nozzle arrangement with a 110 mm spacing for the remainder of the parametric investigation.
The effect of total spray mass flow rate was then studied under an inlet air velocity of 1 m/s. The total spray flow rate varied from 0.1 to 0.5 g/s. The maximum temperature of the traction battery pack decreased from about 315.1 K at 0.1 g/s to about 314.1 K at 0.5 g/s. The temperature difference varied in a narrow range of 4.6–4.8 K. The cooling improvement weakened considerably after the spray flow rate exceeded 0.2 g/s. This saturation behavior can be explained by the limited evaporation capacity of the air and by the fact that extra droplets could not fully evaporate before leaving the channel. Therefore, an optimal spray flow rate of approximately 0.2 g/s was selected for further analysis when the air velocity was 1 m/s.
I also examined the influence of the droplet diameter using fixed values of 20, 40, 60, 80, and 100 μm while the spray mass flow rate was held constant at 0.2 g/s. The cooling performance improved as the droplet diameter decreased. Smaller droplets possess a larger total surface area per unit mass, which intensifies the evaporation rate and produces a more uniform spatial distribution of liquid phase in the channel. The 20 μm droplets yielded the lowest maximum temperature and the best temperature uniformity. From an application point of view, generating ultra-fine droplets may be more energy-consumptive, but the results suggest that a mean diameter below 40 μm is preferred for the proposed spray ventilation cooling system.
The coupling effect of air velocity and spray rate was also analyzed. I simulated combinations of inlet velocities from 0.5 m/s to 3 m/s and spray mass flow rates from 0 to 0.5 g/s in increments of 0.1 g/s. The results are summarized in Figure trends described as follows: at a low air velocity of 0.5 m/s, the spray effect was particularly effective. When the spray rate increased from 0.1 to 0.2 g/s, the maximum temperature was reduced by about 1 K. At 1 m/s, the same increment produced a reduction of about 0.5 K. However, at 2 m/s, the reduction was only 0.17 K. The reason is that a high air velocity reduces the residence time of the droplets in the channel, so they have less time to evaporate and interact with the heated battery surfaces. Thus, the marginal cooling benefit obtained from increasing the spray rate diminishes at high inlet velocities. For a compact and energy-efficient traction battery pack thermal management system, the optimum combination appears to be a moderate air velocity around 1 m/s and a spray flow rate around 0.2 g/s.
I further explored the influence of battery spacing. Four spacings, namely 5 mm, 10 mm, 15 mm, and 20 mm, were considered. The pressure drop across the flow channels increased significantly with decreasing spacing. At an inlet velocity of 3 m/s, the pressure drop at 5 mm spacing was as high as 258.09 Pa, whereas at 20 mm spacing it was only about 17.26 Pa. Smaller battery spacing increased the local air velocity in the channels and thereby improved convective cooling, but it also increased the flow resistance and tended to produce a less uniform air distribution. As a result, the maximum temperature of the traction battery pack decreased as the spacing was reduced, while the temperature difference became larger. The effect of spray flow rate on the temperature difference also depended on the spacing. At a small spacing of 5 mm, increasing the spray flow rate decreased both the maximum temperature and the maximum temperature difference. In contrast, at larger spacings such as 15 mm or 20 mm and low air velocities, increasing the spray rate caused the temperature difference to increase because the droplets tended to accumulate and evaporate unevenly. This phenomenon disappeared when the air velocity was increased to 2 m/s, because the airflow was strong enough to carry the droplets and distribute them more uniformly. Overall, a battery spacing of 10 mm provided a good compromise between thermal performance and pressure drop.
In addition, I evaluated the performance of the spray ventilation cooling system under three different discharge rates. The simulated conditions used the same spray flow rate of 0.2 g/s. At an inlet velocity of 0.5 m/s, the maximum temperature of the traction battery pack for a 3C discharge was about 320.1 K, while for 2C and 1C the values decreased to approximately 310.5 K and 303.1 K, respectively. At a higher inlet velocity of 3 m/s, the corresponding maximum temperatures were about 307.4 K, 303.9 K, and 301.4 K. The maximum temperature differences also decreased significantly at lower discharge rates. These results suggest that a full spray cooling capacity is only necessary for high-rate operations such as fast charging or aggressive driving. During normal low-rate discharge, reducing the spray flow rate or using only forced air could save power while still maintaining the battery temperature within the desired range.
Finally, I studied the impact of ambient temperature and relative humidity on the cooling effectiveness. The ambient temperature was varied from 290 K to 310 K, and the relative humidity was varied from 20% to 80%. For an inlet velocity of 1 m/s, increasing the ambient temperature from 290 K to 310 K raised the maximum battery temperature from about 306 K to 323.2 K. The maximum temperature difference also increased but to a smaller degree. When the ambient relative humidity increased from 20% to 80% at a constant air temperature of 300 K, the maximum battery temperature increased from about 313.5 K to 315.4 K at 1 m/s, and the maximum temperature difference grew from 4.2 K to 5.3 K. This is because higher humidity reduces the driving force for mass transfer of water vapor from the droplet surface to the surrounding air, thus suppressing evaporation. Conversely, dry air promotes stronger evaporation and enhances the spray cooling effect. These findings highlight that spray ventilation cooling is particularly attractive in hot and dry climates, whereas its effectiveness may be reduced in humid environments.
From the results of this research, I can draw several important conclusions. First, the coupled spray and ventilation cooling system can effectively control the maximum temperature and improve the temperature uniformity of a traction battery pack when compared with pure forced air cooling. Second, the nozzle configuration plays a crucial role in distributing the droplets evenly among the cells. The cone-type nozzles placed in the battery gaps with two nozzles per gap and a vertical distance of 110 mm were found to be the best design among the tested options. Third, the spray mass flow rate should be optimized based on the inlet air velocity because an excessive amount of water droplets cannot fully evaporate and does not further improve the cooling performance. Fourth, the battery spacing should be carefully selected because it affects the flow velocity, pressure drop, droplet transport, and temperature uniformity simultaneously. Fifth, environmental temperature and humidity have a strong influence on the spray cooling performance. Higher temperatures reduce the driving force for convective heat transfer, while higher humidities suppress droplet evaporation. The numerical model and the parametric analysis provided in this study can be used as a reference for the future design of thermal management systems for traction battery packs using spray ventilation coupled cooling.