In the past decade, electric vehicles have experienced a remarkable expansion in both market share and technological sophistication. This growth has been motivated by the urgent need to reduce fossil-fuel consumption and greenhouse-gas emissions. Nevertheless, the driving range, charging speed, and service life of an EV battery are strongly dependent on its operating temperature. Lithium-ion batteries, especially square-format cells, are widely used in modern EV battery packs because of their high energy density, low self-discharge, long cycle life, and stable electrochemical performance. However, high-rate discharge generates significant heat inside the cells, and if this heat is not removed efficiently, the temperature can exceed the recommended window of 25–45°C. Even more importantly, cell-to-cell temperature differences should generally remain smaller than 5°C. Thermal management systems therefore play a key role in ensuring safe operation and durable performance of EV battery packs.
Several cooling methods have been investigated, including air cooling, liquid cooling, phase-change-material cooling, heat-pipe cooling, and spray evaporative cooling. Air cooling is simple and lightweight, but its low heat capacity and low heat-transfer coefficient limit its use to low-energy-density battery modules. Liquid cooling is more effective but requires pumps, coolant channels, plates, and complex sealing arrangements, increasing system weight and parasitic energy consumption. Phase-change materials and heat pipes are passive solutions that can suppress temperature rise for a limited duration, but they may saturate under continuous high-rate discharge. Spray evaporation cooling, by contrast, exploits the large latent heat of water, which is roughly 2400 kJ/kg, and can be integrated directly into the airflow path of an EV battery pack. The spray droplets evaporate in the air and on warm surfaces, absorbing heat very effectively. Because spray cooling can be implemented with relatively simple hardware, it offers an attractive compromise among performance, complexity, and energy cost.
My work aims at exploring a combined spray-and-ventilation cooling strategy for an EV battery pack. In this concept, the conventional forced-air channel is retained, and atomized water droplets are injected into the airflow passages between cells. The droplets interact with the air and with the battery surfaces, producing an evaporative cooling effect that removes heat far more effectively than air alone. I first characterize the heat-generation behavior of a commercial square lithium-ion cell through discharge experiments. Then I build a computational fluid dynamics model that couples the continuous air phase with discrete water-droplet spray. The model is validated by experiments on a heated block that reproduces the heat-generation rate of the EV battery cell. Using the validated model, I systematically evaluate parameters such as inlet-air velocity, inlet-air temperature, nozzle type, nozzle spacing, spray mass-flow rate, droplet diameter, cell spacing, discharge rate, ambient temperature, and ambient humidity. I also evaluate the important interaction between air velocity and spray rate, because these two variables must be balanced to optimize evaporative cooling and avoid droplet carry-over.
2. Thermal Characterization of Square Lithium-Ion EV Battery Cells
The battery used in this research is a prismatic lithium-iron-phosphate cell typical of many EV battery modules. The selection was made because prismatic cells offer better space utilization, simpler stacking, and improved mechanical robustness compared with cylindrical cells. A prismatic cell is composed of alternating positive and negative electrode layers separated by a microporous membrane, packaged inside an aluminum housing. During discharge, lithium ions deintercalate from the negative graphite lattice, migrate through the organic electrolyte, and intercalate into the positive iron-phosphate lattice. The overall electrochemical reaction can be described by
$$ \mathrm{FePO_4} + x\mathrm{Li^+}+x e^- \rightarrow x\mathrm{LiFePO_4} + (1-x)\mathrm{FePO_4} $$
although this representation is simplified because side reactions, charge transfer, and transport limitation occur simultaneously in a real cell.
Heat generation inside an EV battery cell is usually divided into four parts: reaction heat, polarization heat, Joule heat, and side-reaction heat. Side-reaction heat, such as electrolyte decomposition and self-discharge, is negligible for lithium-ion cells under normal operation. Thus, the total heat-generation rate can be written as
$$ Q_{\rm total}=Q_r+Q_j+Q_p $$
where \(Q_r\) is the reversible entropic heat, \(Q_j\) is the Joule heat caused by ohmic resistance, and \(Q_p\) is polarization heat caused by activation and concentration overpotential. The widely used Bernardi lumped model approximates the generated heat as
$$ Q_{\rm gen}=I(U_{\rm OCV}-U)-I T_b \frac{dU_{\rm OCV}}{dT_b} $$
The first term on the right side, \((U_{\rm OCV}-U)\), is the total voltage loss caused by internal resistance and overpotential. When the cell is discharged or charged at current \(I\), this term produces Joule-type heat equal to \(I^2 R_j\), where \(R_j\) is the equivalent internal resistance. The second term represents the reversible entropic contribution. The heat absorbed by the cell is
$$ Q_{\rm abs}=m_b c_{p,b}\frac{dT_b}{dt} $$
By measuring the surface temperature of a single cell during constant-current discharge, I obtained the cell temperature rise with respect to time. Rearranging the lumped energy balance gives
$$ \frac{1}{I}\frac{dT_b}{dt} = \frac{R_j}{m_b c_{p,b}}I + \frac{1}{m_b c_{p,b}}T_b\frac{\partial U_{\rm OCV}}{\partial T_b} $$
After conducting discharge tests at 1C, 2C, and 3C in a constant-temperature chamber, I fitted the measured temperature-rise curves to the above linear relation. The resulting cell heat-generation correlation is
$$ Q_{\rm gen}=1.06\times10^{-3}I^2+0.085I $$
where \(I\) is the discharge current in amperes and \(Q_{\rm gen}\) is in watts. Because the computational model uses a uniform volumetric heat source, the heat-generation rate is converted to a volumetric form:
$$ q_{\rm gen} = \frac{Q_{\rm gen}}{V_b} = 3.42I^2 + 274.19I $$
where \(q_{\rm gen}\) is expressed in W/m³. Table 1 summarizes the physical parameters of the tested cell. Table 2 reports the corresponding volumetric heat source for three discharge rates.
| Property | Value |
|---|---|
| Cell dimensions (mm) | 20 × 100 × 140 |
| Cell mass (kg) | 0.588 |
| Rated voltage (V) | 3.2 |
| Operating voltage (V) | 2.0–3.65 |
| AC internal resistance (mΩ) | 0.8–1.2 |
| DC internal resistance (mΩ) | ≤3.0 |
| Rated capacity (Ah) | 27 |
| Discharge rate (C) | Volumetric heat source (W/m³) |
|---|---|
| 1C | 9893 |
| 2C | 24777 |
| 3C | 44626 |
These tests confirmed that high discharge rates increase both the amplitude and nonlinearity of the temperature rise. At low discharge rates the temperature rise is nearly linear, whereas at 3C the strong quadratic heat-generation term causes a pronounced acceleration near the end of discharge. The heat-generation values given in Table 2 are used as boundary data for every numerical case in this paper.
3. Numerical Model for Spray and Ventilation Coupled Cooling
3.1 Physical Model and Computational Domain
My numerical model represents an EV battery module containing 24 prismatic cells. The overall cooling channel is rectangular, and air enters from one side, flows through the gaps between adjacent cells, and exits on the opposite side. In the spray-assisted configuration, a set of atomizing nozzles is placed upstream or between the cell columns so that droplets enter the same flow passages as the cooling air. The cells measure 140 mm × 100 mm × 20 mm, and the spaces between cells are treated as the main heat-exchange passages. The computational model is deliberately simplified to reduce cost while preserving the dominant heat-transfer mechanisms. Because the cell is constructed of layered materials, it is represented as a homogeneous solid with effective thermal properties. The heat-generation rate is uniform throughout the cell volume, and the thermal properties are treated as constant over the narrow temperature range considered.
Since the volume-of-fluid interface of individual spray droplets is impractical for a full battery module, I use the Eulerian–Lagrangian approach. The gas phase is treated as a continuous phase and solved in the Eulerian frame, while each spray droplet is tracked in the Lagrangian frame. Heat, mass, and momentum exchange between the continuous gas phase and the discrete droplet phase is handled by source terms. The computational mesh was generated using structured hexahedral elements in the battery blocks and in the fluid region. A local inflation layer is used near the walls so that the enhanced wall treatment can adequately capture near-wall gradients.
3.2 Conservation Equations for the Continuous Phase
For the continuous air-and-vapor mixture, the mass-conservation equation is
$$ \frac{\partial \rho}{\partial t} + \nabla \cdot \left(\rho\vec{V}\right) = S_m $$
where \(\rho\) is the density of the gas mixture, \(\vec{V}\) is the velocity vector, and \(S_m\) represents the mass source term caused by evaporation of droplets. The momentum equation is
$$ \frac{\partial(\rho\vec{V})}{\partial t} + \nabla\cdot\left(\rho\vec{V}\vec{V}\right) = -\nabla p + \nabla\cdot\bar{\tau} + \rho\vec{g} + \vec{F} $$
where \(\bar{\tau}\) is the viscous stress tensor, \(p\) is static pressure, \(\rho\vec{g}\) is the gravitational body force, and \(\vec{F}\) is the momentum source produced by inter-phase drag. The energy equation is
$$ \frac{\partial(\rho E)}{\partial t} + \nabla\cdot\left[\vec{V}(\rho E + p)\right] = \nabla\cdot\left(k_{\rm eff}\nabla T – \sum_j h_j \vec{J}_j\right) + \Phi + S_h $$
In this expression, \(E\) is the total energy per unit mass, \(k_{\rm eff}\) is the effective thermal conductivity, \(h_j\) and \(\vec{J}_j\) are the specific enthalpy and diffusive flux of species \(j\), and \(S_h\) is the energy source caused by droplet heating and evaporation. Because the droplet evaporates into air, the gas phase also contains a water-vapor transport equation:
$$ \frac{\partial(\rho Y_m)}{\partial t} + \nabla\cdot\left(\rho\vec{V}Y_m\right) = \nabla\cdot\left(\rho D_m\nabla Y_m\right)+S_i $$
where \(Y_m\) is the mass fraction of species \(m\), \(D_m\) is the diffusion coefficient, and \(S_i\) is the species source generated by the evaporating droplets.
3.3 Turbulence Model
Accurate prediction of a spray flow requires a turbulence model that accounts for recirculation and mixing. I use the realizable \(k\)-\(\varepsilon\) model because it has been shown to give good predictions of planar and round jet spreading and therefore suits spray-cooling flows. Its two transport equations are:
$$ \frac{\partial(\rho k)}{\partial t} + \frac{\partial(\rho k u_i)}{\partial x_i} = \frac{\partial}{\partial x_j}\left[\left(\mu+\frac{\mu_t}{\sigma_k}\right)\frac{\partial k}{\partial x_j}\right]+P_k+G_b-\rho\varepsilon-Y_M $$
$$ \frac{\partial(\rho\varepsilon)}{\partial t} + \frac{\partial(\rho\varepsilon u_i)}{\partial x_i} = \frac{\partial}{\partial x_j}\left[\left(\mu+\frac{\mu_t}{\sigma_\varepsilon}\right)\frac{\partial\varepsilon}{\partial x_j}\right]+C_1 S\varepsilon – C_2 \frac{\varepsilon^2}{k+\sqrt{\nu\varepsilon}} + C_{3}\frac{\varepsilon}{k}G_b $$
where \(k\) is turbulent kinetic energy, \(\varepsilon\) is its dissipation rate, \(\mu_t\) is the turbulent viscosity, \(P_k\) is the turbulence-production term, \(G_b\) is the buoyancy-production term, and \(\sigma_k\), \(\sigma_\varepsilon\), \(C_1\), \(C_2\), and \(C_3\) are empirical constants. The enhanced wall treatment is applied so that near-wall heat transfer is computed accurately without relying on very high near-wall mesh resolution.
3.4 Discrete Droplet Phase
Each spray droplet is tracked by solving its momentum equation:
$$ \frac{d\vec{v}_p}{dt} = F_D\left(\vec{V}-\vec{v}_p\right) + \frac{\rho-\rho_p}{\rho_p}\vec{g}+\vec{F}_{\rm other} $$
where \(\vec{v}_p\) is the droplet velocity, \(\rho_p\) is the droplet density, \(F_D\) is the drag-force coefficient, and \(\vec{F}_{\rm other}\) collects other forces such as virtual mass. For spherical droplets, the drag coefficient is
$$ C_D = \frac{24}{Re}\left(1+0.15Re^{0.687}\right) $$
in which \(Re\) is the relative Reynolds number based on droplet diameter. The droplet is heated by the surrounding air and by hot battery surfaces. The convective heat-transfer coefficient is obtained from the Ranz–Marshall correlation:
$$ Nu = 2 + 0.6Re^{1/2}Pr^{1/3}, \qquad h = \frac{k}{d_p}Nu $$
where \(d_p\) is the droplet diameter, \(k\) is the thermal conductivity of the gas mixture, and \(Pr\) is molecular Prandtl number. Once the droplet temperature reaches the wet-bulb value, evaporation begins and is controlled by the concentration difference between water vapor at the droplet surface and vapor in the bulk air. The mass transfer rate can be described by
$$ \frac{dm_p}{dt} = -A_p M_w k_w\left(C_{w,s}-C_{w,\infty}\right) $$
where \(A_p\) is the droplet surface area, \(M_w\) is water molar mass, \(k_w\) is the convection mass-transfer coefficient, and \(C_{w,s}\) and \(C_{w,\infty}\) are the vapor concentrations at the droplet surface and in the gas, respectively. The initial droplet-size distribution is represented with a Rosin–Rammler expression:
$$ Y_d = \exp\left[-\left(\frac{d}{\bar d}\right)^{n^*}\right] $$
where \(\bar d\) is the mean droplet diameter and \(n^*\) is the spread parameter. The Taylor-analogy breakup model is applied to account for secondary atomization.
Because the spray interacts with the continuous air phase, a two-way coupling is employed. During each coupling iteration, the momentum, mass, and energy exchanged along each droplet trajectory are summed and converted into source terms for the gas-phase equations. The momentum source is
$$ \vec{F} = \sum\left[\frac{18\mu C_D Re}{24 \rho_p d_p^2}\left(\vec{v}_p-\vec{V}\right)\right]\dot{m}_p\Delta t $$
while the energy source includes latent heat and sensible heat:
$$ Q = \frac{\dot{m}_{p,0}}{m_{p,0}}\left[(m_{p,in}-m_{p,out})(-h_{\rm lat}) – m_{p,out}\int_{T_{\rm ref}}^{T_{p,out}}c_{p,p}dT + m_{p,in}\int_{T_{\rm ref}}^{T_{p,in}}c_{p,p}dT \right] $$
The mass source is obtained from the change in droplet mass in each computational cell.
3.5 Grid Independence
To eliminate mesh dependency, I generated six meshes with cell counts ranging from about \(8.9\times10^5\) to \(5.7\times10^6\). Each mesh was run for a representative spray-cooling case, and the predicted maximum battery temperature was recorded. The results are listed in Table 3.
| Total number of meshes | Maximum battery 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 |
When the mesh density was increased from 2.8 million to 3.5 million elements, the calculated maximum temperature changed by only 0.15 K. The 2.8-million-element mesh was therefore chosen as the optimum compromise between accuracy and computational cost. This grid resolution was used for all subsequent parametric simulations.
4. Experimental Validation of the Numerical Model
To establish confidence in the numerical model, I constructed an experimental test bench based on thermal-energy-surface equivalence. Rather than discharging a real EV battery cell, an aluminum block with the same outer dimensions as the actual battery was heated with embedded electric resistance cartridges. The heating power was controlled by an adjustable-voltage transformer and set equal to the heat-generation rate of the cell at 3C discharge, which is 12.5 W in the volume-equivalent model. The aluminum block was placed inside a rectangular duct provided with a variable-speed fan and an ultrasonic atomizer. The atomizer produced fine water droplets that were carried by the air stream to the heated surface, reproducing the spray-and-ventilation coupled cooling concept.
The measurement system included T-type thermocouples, a data-acquisition unit, an anemometer, and a digital power meter. Five T-type thermocouples were attached to the heated aluminum block surfaces. The data-acquisition unit recorded temperatures every second. The combined uncertainty of the temperature measurement system was estimated to be ±0.16 K, originating mainly from the thermocouple tolerance of ±0.1 K and the data-acquisition unit of ±0.06 K.
I performed six validation tests at an ambient temperature of 298.4 K, corresponding to the real environmental temperature during the experiment. Three airflow rates, 1 m/s, 1.5 m/s, and 2 m/s, were tested both without spray and with a water spray mass-flow rate of 0.15 g/s. The operating cases are summarized in Table 4.
| Case | Air velocity (m/s) | Spray flow rate (g/s) |
|---|---|---|
| Case 1 | 1.0 | 0 |
| Case 2 | 1.5 | 0 |
| Case 3 | 2.0 | 0 |
| Case 4 | 1.0 | 0.15 |
| Case 5 | 1.5 | 0.15 |
| Case 6 | 2.0 | 0.15 |
The simulation reproduced the same geometry, heating power, inlet velocity, spray rate, and ambient boundary conditions. Table 5 compares the measured steady-state average surface temperature and the predicted average surface temperature for each case.
| Case | Measured average temperature (K) | Simulated average temperature (K) | Absolute difference (K) |
|---|---|---|---|
| Case 1 | 316.36 | 315.06 | 1.30 |
| Case 2 | 312.34 | 310.58 | 1.76 |
| Case 3 | 309.34 | 308.12 | 1.22 |
| Case 4 | 312.49 | 311.45 | 1.04 |
| Case 5 | 310.38 | 308.53 | 1.85 |
| Case 6 | 308.19 | 306.78 | 1.41 |
To quantify the agreement, I calculated the root-mean-square error between the 30 measured point values and their corresponding simulated values using
$$ RMSE = \sqrt{\frac{1}{n}\sum_{i=1}^{n}\left(y_i-\hat{y}_i\right)^2} $$
The resulting RMSE is 1.566 K, while the largest point-wise deviation is below 1.9 K. This indicates that the spray-evaporation model can capture the cooling trend with acceptable engineering accuracy. The remaining discrepancies may be caused by environmental-humidity drift, contact resistance between the heater and aluminum block, and uncertainty in the thermocouple placement.
5. Results and Discussion
5.1 Effect of Inlet-Air Parameters under Pure Air Cooling
Before examining the coupled spray system, I analyzed pure forced-air cooling as a baseline. The inlet-air velocity was varied from 0.5 m/s to 3 m/s while the battery was discharged at 3C and the ambient air inlet temperature was 300 K. Increasing the air velocity improves the convective heat-transfer coefficient because more air comes into contact with the battery surfaces and because the higher Reynolds number enhances turbulent mixing. The maximum battery temperature decreased by roughly 19 K when the inlet-air velocity was raised from 0.5 m/s to 3 m/s. At the same time, the cell-to-cell temperature difference also decreased from a larger value to about 3–5 K at high airflow, because the boundary layer over the downstream cells becomes thinner and the temperature of the air does not rise as dramatically along the channel.
However, the benefit of increasing air velocity diminishes at high speeds, whereas the pressure-drop penalty increases sharply. In my simulation, the airside pressure drop at 3 m/s was about 61.9 Pa, while at 0.5 m/s it was only 2.4 Pa. Thus, although high-speed air can provide better cooling, it also requires more fan power and generates more acoustic noise. The optimum inlet velocity for a compact EV battery cooling system is found in the range of 1–2 m/s, where the coolant temperature suppression is still significant and the pressure-drop penalty is manageable.
The inlet-air temperature also has a strong influence. In simulations with inlet temperature varied from 290 K to 310 K at a fixed velocity of 1 m/s, the maximum battery temperature rose by about 20.2 K. The reason is direct: the lower the inlet-air temperature, the larger the temperature difference between the battery surface and the air, which increases the convective heat flux. Interestingly, the maximum temperature difference between cells remained relatively stable between 6.3 and 6.6 K when only the inlet temperature was changed. This finding implies that changing the air-inlet temperature mainly shifts the mean temperature level of the EV battery module but does not significantly improve or worsen its temperature uniformity.
5.2 Effect of Nozzle Type on Spray Cooling
For the spray-assisted configuration, I compared three typical nozzle types available in the discrete-phase model: surface, cone-back, and cone nozzles. The nozzles were installed in the battery gaps for cone-type nozzles or upstream for surface-type nozzles. A schematic representation of the spray behavior is captured by the Lagrangian particle tracks. In the surface nozzle, droplets are injected uniformly along the airflow direction, while the cone-back nozzle injects droplets against the main airflow direction. Cone nozzles introduce a conical spray into the gap between neighboring cells. All cases were run at an air velocity of 1 m/s, a droplet diameter of 20 μm, and a total spray flow rate of 0.7 g/s.
The simulation results demonstrated that all spray configurations lowered the maximum temperature compared with pure air cooling. However, the temperature-uniformity performance differed strongly among nozzle types. The cone-back and surface nozzles produced a relatively wide dispersion of droplets over the first rows of cells, causing intense evaporative cooling at the upstream side but leaving downstream cells with much less spray coverage. Consequently, although the maximum temperature decreased, the maximum temperature difference within the EV battery pack increased compared with pure air cooling. In contrast, the cone nozzle concentrates the spray inside the gaps between cells, allowing droplets to cool the cell surfaces more uniformly throughout the whole battery pack. Among the three nozzle designs, the cone nozzle provided the smallest maximum temperature and the best temperature uniformity.
After selecting the cone nozzle, I examined the number and orientation of nozzles in each gap. A single nozzle placed at the middle of the vertical gap produced a concentrated droplet core and caused local overcooling. I therefore placed two smaller cone nozzles in a vertically staggered arrangement, each delivering the same total mass flow as the single-nozzle case. The two-nozzle arrangement significantly improved vertical coverage and reduced the maximum temperature difference of the EV battery module. The distance between the two nozzles was then varied from 30 mm to 130 mm. The results reveal an optimum nozzle spacing near 110 mm. When the spacing was too small, the spray cones overlapped and behaved similarly to a single concentrated nozzle. When the spacing was too large, part of the spray approached the duct walls and transferred less heat to the battery surfaces, especially in the middle of the vertical direction. Therefore, I selected a vertical nozzle spacing of 110 mm for all subsequent investigations.
5.3 Effect of Spray Mass-Flow Rate and Droplet Diameter
With the optimum nozzle type and spacing fixed, I varied the spray mass-flow rate from 0.1 g/s to 0.5 g/s per gap. For an inlet-air velocity of 1 m/s, increasing the spray rate from zero to 0.1 g/s reduced the maximum EV battery surface temperature by roughly 3 K, from about 318 K under air alone to about 315.1 K. When the spray rate was further increased to 0.2 g/s, the maximum temperature decreased to about 314.6 K. A further increase from 0.3 g/s to 0.5 g/s reduced the maximum temperature by only another 0.15 K. This behavior indicates a saturation effect: once the air is nearly saturated with water vapor, additional droplets do not evaporate readily and therefore contribute little additional cooling. At the same time, the maximum temperature difference between cells remained around 4.6–4.8 K, which is lower than the pure-air result. This is mostly due to the uniform evaporative cooling provided by droplets in the boundary layer near the cell sides.
Droplet diameter is another essential design parameter. I studied mean droplet diameters of 20 μm, 40 μm, 60 μm, 80 μm, and 100 μm while maintaining a constant spray mass flow of 0.2 g/s. The general trend is that smaller droplets produce better cooling. Table 6 clearly shows both improved maximum-temperature suppression and reduced temperature difference as the droplet diameter is decreased. The two mechanisms are the increase in total droplet surface area for a fixed water mass, which accelerates evaporation, and the improved spatial dispersion of smaller droplets in the airflow, which makes the spray coverage more uniform.
| Droplet diameter (μm) | Maximum battery temperature (K) | Maximum temperature difference (K) |
|---|---|---|
| 20 | 314.6 | 4.6 |
| 40 | 315.2 | 4.7 |
| 60 | 316.1 | 4.9 |
| 80 | 316.9 | 5.1 |
| 100 | 317.5 | 5.3 |
From a practical standpoint, 20 μm droplets are preferable, but extremely fine atomization may require higher nozzle pressure or ultrasonic atomization. It is therefore important to match the atomizer capability to the system cooling demand.
5.4 Coupling between Air Velocity and Spray Rate
The interaction between inlet-air velocity and spray flow rate is central to designing an efficient EV battery thermal management system. I therefore performed a matrix of simulations covering air velocities of 0.5, 1, 1.5, 2, and 3 m/s and spray rates from zero to 0.5 g/s. Figure data from this matrix reveal several important features. Increasing the air velocity always improves the cooling performance because forced convection enhances heat removal from the battery surface. At zero spray, increasing the air velocity from 0.5 to 3 m/s reduced the maximum battery temperature by approximately 19 K. When spray is used, high air velocity also helps to remove the water vapor that forms around the droplet surface, refreshing the vapor-concentration boundary layer and enhancing the evaporation rate.
Nevertheless, the marginal benefit of spray becomes smaller at high air velocities. For example, at an air velocity of 0.5 m/s, increasing the spray flow rate from 0.1 g/s to 0.2 g/s reduced the maximum battery temperature by about 1 K. At 1 m/s, the same increase in spray rate reduced the maximum temperature by roughly 0.5 K. At 2 m/s, the reduction was only about 0.17 K. The explanation is that at high velocity, the air residence time in the EV battery module is shorter, so droplets are carried downstream before they have enough time to evaporate fully and release their latent heat. Thus, there is an optimum operating combination: at low speed, spray cooling is very effective; at high speed, increasing the fan power may be more effective than increasing the water-pumping power.
This coupling behavior is important for practical control strategies. If the EV battery is operating at moderate discharge and the air speed is low, increasing the spray rate can quickly suppress a hot spot. At high vehicle speeds or high fan speed, the spray rate can be reduced without sacrificing much cooling performance, so that water consumption and the risk of water carry-over are minimized.
5.5 Effect of Cell Spacing on Spray Cooling and Pressure Drop
Cell spacing is one of the main geometric parameters that determines both the thermal performance and the flow resistance in an EV battery module. I simulated cell gaps of 5, 10, 15, and 20 mm, while keeping the inlet-air velocity, inlet temperature, and spray-nozzle arrangement unchanged. The simulations show that reducing cell spacing increases the velocity in the flow passages. The higher velocity thins the thermal boundary layers on the battery surfaces and therefore improves convective heat transfer. This effect can lower the maximum battery temperature, but it also increases the pressure drop considerably.
Table 7 lists the pressure drop for different cell spacings and inlet velocities.
| Cell spacing (mm) | Pressure drop at 0.5 m/s (Pa) | Pressure drop at 1 m/s (Pa) | Pressure drop at 3 m/s (Pa) |
|---|---|---|---|
| 5 | 16.01 | 41.58 | 258.09 |
| 10 | relatively low | moderate | still acceptable |
| 15 | relatively low | moderate | still acceptable |
| 20 | 0.76 | 2.15 | 17.26 |
At a fixed inlet velocity of 0.5 m/s and a spray flow rate of 0.1 g/s, reducing the spacing from 20 mm to 5 mm decreased the maximum EV battery temperature from about 323.6 K to 315.2 K. At the same time, however, the maximum temperature difference increased from about 6.4 K to 10.9 K. The higher temperature difference is caused by nonuniform droplet dispersion in narrow passages: when the passage is narrow, the flow velocity is higher and the droplets are less able to spread across the entire vertical height of the cell surface. At a velocity of 3 m/s, the narrower 5 mm gap maintained the maximum temperature at about 305 K, while the 20 mm gap reached 310 K; in this case, the temperature difference was 4.7 K at 5 mm and 2.6 K at 20 mm.
The effect of spray rate also depends on cell spacing. In a small 5 mm gap, increasing the spray rate always reduced both the maximum temperature and the maximum temperature difference. In larger gaps of 15 mm or 20 mm, at low air velocity, increasing the spray rate could slightly increase the maximum temperature difference. This happens because droplets accumulate in the lower part of the large gap, creating a liquid film or large droplets that are no longer efficient evaporators. At higher air velocity, this adverse effect disappears because the airflow is strong enough to prevent droplet accumulation. Therefore, for the present EV battery pack, a 10 mm gap is a balanced choice: it provides acceptable pressure loss, good cooling effectiveness, and reasonable temperature uniformity while keeping the module compact.
5.6 Effect of Discharge Rate
EV battery discharge rate changes dramatically in real driving. I simulated 1C, 2C, and 3C discharge heat loads under a constant spray flow rate of 0.2 g/s. At an air velocity of 0.5 m/s, the maximum cell temperature at 3C was about 320.1 K. Reducing the discharge rate to 2C reduced the maximum temperature to about 310.5 K, while 1C brought it down to 303.1 K. The maximum temperature difference also decreased from 8.2 K at 3C to 5.0 K at 2C and 2.4 K at 1C. At a higher air velocity of 3 m/s, the corresponding maximum temperatures were 307.4 K, 303.9 K, and 301.4 K, while the maximum temperature differences were 3.7 K, 1.3 K, and 1.2 K, respectively. These results indicate that the spray-assisted cooling system is particularly useful for high-rate discharge, where air cooling alone is insufficient. For low discharge rates, the spray and fan powers can be reduced to save energy. A control system can modulate the spray flow based on the real-time heat-generation estimate of the EV battery.
5.7 Effect of Ambient Temperature and Relative Humidity
Ambient temperature and humidity play especially important roles in evaporative cooling. I varied the ambient temperature from 290 K to 310 K while keeping the spray flow rate, droplet diameter, and inlet velocity fixed. As shown in the simulations, a higher ambient temperature reduces the temperature difference between the battery surface and the air, which weakens sensible heat transfer. It also raises the wet-bulb temperature, but because the spray water temperature is equal to the ambient air temperature in these simulations, the air at 310 K can still evaporate water more rapidly. Overall, the maximum EV battery temperature increased from about 306 K at 290 K to about 323 K at 310 K under an air velocity of 1 m/s. At 3 m/s, the corresponding increase was from about 297.8 K to 316.7 K. The temperature difference also increased with ambient temperature because the local cooling created by the first cells is stronger when the driving temperature difference is larger, causing an uneven heat-removal pattern.
Humidity was varied from 20% to 80% relative humidity at a constant ambient temperature of 300 K. Table 8 summarizes the simulation results.
| Relative humidity (%) | Maximum temperature at 1 m/s (K) | Maximum temperature difference at 1 m/s (K) | Maximum temperature at 3 m/s (K) | Maximum temperature difference at 3 m/s (K) |
|---|---|---|---|---|
| 20 | 313.5 | 4.2 | 306.9 | 2.8 |
| 30 | 313.8 | 4.4 | 307.0 | 2.9 |
| 40 | 314.2 | 4.6 | 307.1 | 3.0 |
| 50 | 314.6 | 4.8 | 307.2 | 3.1 |
| 60 | 314.9 | 5.0 | 307.3 | 3.2 |
| 70 | 315.2 | 5.2 | 307.4 | 3.3 |
| 80 | 315.4 | 5.3 | 307.5 | 3.3 |
As the relative humidity rises, the vapor-pressure difference between the droplet surface and the surrounding air decreases. This reduces the mass-transfer driving force and weakens droplet evaporation. Consequently, the maximum temperature and temperature difference both increase. At high humidity, the spray cooling system is less capable of creating a large temperature decrease. Therefore, if the EV battery is operated in a humid climate, the control strategy should account for the reduced evaporation potential and may need to combine spray with a higher air flow rate or a lower-temperature cooling fluid to maintain the desired cell temperature.
6. Concluding Remarks
In this research, I have systematically investigated the heat-transfer characteristics of a coupled spray-and-ventilation cooling system for an EV battery pack. The study combined experimental thermal characterization of a lithium-ion cell, construction of a validated spray-evaporation numerical model, and extensive parametric simulations. The most important conclusions can be summarized as follows.
First, the heat-generation behavior of square lithium-ion EV battery cells can be approximated with a lumped volumetric heat source. For the 27-Ah cell used in this study, the fitted correlation \(q_{\rm gen}=3.42I^2+274.19I\) is in good agreement with discharge tests at 1C, 2C, and 3C. The strong quadratic dependence on current indicates that high-rate operation dramatically increases the thermal burden on the EV battery.
Second, forced-air cooling alone can suppress temperature rise if the inlet velocity is high enough, but the pressure-drop penalty restricts practical operation to approximately 1–2 m/s. Inlet-air temperature directly shifts the maximum temperature level but has little influence on temperature uniformity.
Third, spray cooling integrated into the ventilation channel is an effective method for reducing both peak temperature and temperature difference in an EV battery module. The cooling mechanism is threefold: evaporation of droplets in the mainstream cools the air before it reaches downstream cells; evaporation in the boundary layer changes the thermal-boundary-layer structure; and direct contact between droplets and hot battery surfaces removes heat by latent and sensible heat transfer.
Fourth, nozzle design matters. A cone nozzle placed in the gap between cells, with two vertically spaced injection points at a distance of roughly 110 mm, yields the best cooling uniformity. In contrast, surface-type and cone-back nozzles create excessive cooling at the upstream cells and increase the temperature difference.
Fifth, the spray flow rate should be selected carefully. In my simulations, 0.2 g/s per gap is close to the saturation point for an inlet velocity of 1 m/s. Above this value, additional water contributes little cooling and may even lead to surface wetting. Smaller droplet diameters down to 20 μm improve both heat transfer and temperature uniformity, but practical atomization limits need to be considered.
Sixth, the coupling between air velocity and spray rate must be considered in the system design. At low air velocity, spray evaporation has a large influence; at high air velocity, forced convection dominates and the incremental benefit of more spray is small. Therefore, a smart controller can reduce water consumption when high fan speed is used or when ambient humidity is high.
Seventh, reducing the battery spacing promotes heat transfer because the local air velocity increases, but it also raises pressure loss and worsens temperature uniformity under some spray conditions. The optimal cell spacing in the present system is approximately 10 mm, which keeps the EV battery module compact while maintaining a reasonable pressure drop.
Finally, ambient temperature and humidity strongly affect evaporative cooling. High ambient temperature reduces the sensible-cooling contribution, while high relative humidity suppresses evaporation by reducing the vapor-concentration gradient. For practical EV battery applications, the spray-and-ventilation cooling strategy must therefore be adaptive to ambient conditions and to the instantaneous discharge rate.
Overall, this work demonstrates that spray-and-ventilation coupled cooling is a feasible and efficient thermal-management concept for EV battery packs. It combines the structural simplicity of air cooling with the large heat-absorption capacity of water evaporation. The validated simulation model and the parameter maps presented in this research provide a useful basis for designing compact, energy-efficient, and climate-adaptive EV battery thermal-management systems.