Thermal management has become one of the most critical bottlenecks for the rapid development of new energy vehicles, especially for the vehicle traction battery systems. The continuous growth in production and sales of new energy vehicles has highlighted the urgent need for efficient and reliable thermal control solutions for vehicle traction battery packs. Among the various energy storage technologies, lithium-ion batteries are widely adopted because of their high specific energy, low self-discharge rate, long cycle life, and negligible memory effect. However, the heat generation of lithium-ion batteries during high-rate charging and discharging can be substantial. If the generated heat is not removed promptly, the temperature of the cells may exceed the allowable limit, causing capacity fade, internal resistance growth, thermal runaway, and even fire hazards. Therefore, an effective thermal management system is indispensable to maintain the operating temperature of a vehicle traction battery within its optimum range, typically between 298.15 K and 318.15 K, while ensuring that the temperature difference across the module stays below 5 K.
The research status of battery thermal management has evolved through several mainstream cooling methods. Air cooling, liquid cooling, phase change material cooling, heat pipe cooling, and spray evaporative cooling have each been investigated extensively. Air cooling is advantageous for its simple structure, low weight, and low cost, but the low heat transfer coefficient of air limits its capacity, especially for high energy density vehicle traction battery packs. Liquid cooling provides better heat transfer performance but suffers from a more complex system, higher pump power consumption, and potential leakage risks. Phase change materials can absorb heat passively, but their low thermal conductivity necessitates the addition of fins, metal foams, or expanded graphite. Heat pipes are efficient passive heat spreaders but often require integration with other active cooling elements to maintain their condensing section at a low temperature. Spray cooling, on the other hand, exploits the large latent heat of water evaporation, which can be several times higher than the sensible heat capacity of conventional coolants, and can achieve excellent surface temperature uniformity without requiring complex cold plates or heat exchangers.
In this study, a novel hybrid cooling strategy is proposed for the vehicle traction battery, which combines forced convective air flow with water spray directly injected into the air flow channels. The spray droplets travel with the airstream, absorb heat from the air, evaporate near the battery surfaces, and therefore enhance the heat transfer between the battery and the cooling medium. Compared with conventional methods, the proposed spray-and-ventilation coupled cooling system can simplify the system architecture while improving the cooling performance.
The primary objective of this work is to investigate the heat transfer characteristics of this coupled cooling approach for a prismatic lithium-ion battery module. The study follows a comprehensive path consisting of experimental discharge tests, numerical model construction, model validation, and parametric simulations. First, the thermal behavior of the battery is characterized experimentally, and a volume heat source model is derived. Then, a computational fluid dynamics model, based on the Eulerian-Lagrangian approach, is established for the spray and ventilation coupled cooling process. The model is verified against a specifically designed experimental platform that uses an equivalent aluminum block heater to mimic the battery heat generation. After satisfactory agreement is obtained, the validated numerical model is used to analyze the influence of several critical factors, including inlet air velocity, inlet air temperature, nozzle type, nozzle arrangement and spacing, spray mass flow rate, droplet diameter, battery gap spacing, discharge C-rate, ambient temperature, and ambient relative humidity. These analyses provide substantial insight for the design and optimization of spray-assisted air cooling systems for vehicle traction battery modules.
Thermal Characteristics of the Vehicle Traction Battery
The vehicle traction battery selected for this study is a prismatic lithium iron phosphate cell. Compared with cylindrical and pouch cells, prismatic cells provide a higher packing density and more convenient surface mounting, which is beneficial for experimental instrumentation and thermal management module integration. Table 1 lists the main physical parameters of the battery used in this study.
| Property | Unit | Value |
|---|---|---|
| Dimensions | mm | 20 × 100 × 140 |
| Mass | kg | 0.588 |
| Nominal voltage | V | 3.2 |
| Operating voltage | V | 2.0 – 3.65 |
| AC resistance | mΩ | 0.8 – 1.2 |
| DC resistance | mΩ | ≤3.0 |
| Nominal capacity | Ah | 27 |
The internal structure of the prismatic lithium-ion cell is composed of a positive electrode, a negative electrode, a separator, and an electrolyte. The positive electrode consists of lithium iron phosphate coated on an aluminium foil, while the negative electrode is graphite coated on a copper foil. During discharge, lithium ions deintercalate from the anode and migrate through the electrolyte and separator to intercalate into the cathode. This process simultaneously transports electrons through the external circuit, generating power. The heat produced inside the cell originates mainly from reaction heat, polarization heat, ohmic heat, and side-reaction heat. In lithium-ion phosphate batteries, side-reaction heat is usually negligible because of the stable electrochemical system and low self-discharge rate.
The constituent materials of the battery have different thermo-physical properties, which are summarized in Table 2. The overall heat capacity and anisotropic thermal conductivity of the cell are difficult to calculate precisely from a detailed layered structure. Therefore, the cell is treated as a homogeneous heat-generating solid in the numerical model, with equivalent thermal properties obtained from a simplified composite rule.
| Component | Material | Specific heat J/(kg·K) | Thermal conductivity W/(m·K) | Density kg/m³ |
|---|---|---|---|---|
| Positive electrode | LiFePO4 | 830 | 1.58 | 1523 |
| Positive collector | Aluminium | 903 | 238 | 2702 |
| Negative electrode | Graphite | 1437 | 1.04 | 1455 |
| Negative collector | Copper | 385 | 398 | 8933 |
| Separator | PP/PE/PP | 1978 | 0.3344 | 492 |
| Electrolyte | LiPF6 solution | 1545 | 0.6 | 1290 |
The heat generation rate of the cell is experimentally identified by means of a discharge test. The prismatic cell is placed inside an isothermal chamber, and the surrounding air temperature is maintained at 300 K. Five T-type thermocouples are attached to the surface of the cell, and the average temperature is recorded by an Agilent 34972A data acquisition unit. The battery tester Neware BTS-8000 controls the charge and discharge cycles. Discharge experiments are conducted at 1C, 2C, and 3C rates. Figure 1 depicts the typical experimental setup for acquiring the transient surface temperature of a single cell.
During each discharge test, the cell is initially fully charged and then rested until thermal equilibrium is established. The temperature histories show that at all three C-rates the temperature increases slowly at first and then rises more sharply near the end of discharge. The rise is more pronounced at higher discharge currents because the ohmic and polarization heat increases quadratically with current. For the thermal modeling, the widely used Bernardi heat generation model is adopted. According to this model, the total heat generation rate can be written as:
$$q_{\text{gen}} = I\left(U_{\text{OC}} – U\right) – IT_b \frac{dU_{\text{OC}}}{dT_b}$$
where \(I\) is the current, \(U_{\text{OC}}\) is the open-circuit voltage, \(U\) is the terminal voltage, \(T_b\) is the battery temperature, and \(dU_{\text{OC}}/dT_b\) is the temperature coefficient of the open-circuit voltage. The first term accounts for ohmic and polarization heat, while the second term represents entropic heat. In practice, the heat generation rate can be expressed as:
$$Q_{\text{gen}} = I^2 R_j + I T_b \frac{\partial U_{\text{OC}}}{\partial T_b}$$
The absorbed heat by the battery during the discharge is:
$$Q_{\text{abs}} = m_b c_{p,b} \frac{dT_b}{dt}$$
By combining the above equations and using the measured temperature rise curve, the following linear relationship is fitted:
$$\frac{1}{I}\cdot\frac{dT_b}{dt} = \frac{R_j}{m_b c_{p,b}} \cdot I + \frac{1}{m_b c_{p,b}} \cdot T_b \cdot \frac{\partial U_{\text{OC}}}{\partial T_b}$$
From the experimental data, the battery heat generation power is obtained as:
$$Q_{\text{gen}} = 1.06 \times 10^{-3} I^2 + 0.085 I$$
Considering the equivalent volume of the prismatic cell, the volumetric heat source is expressed as:
$$q_{\text{gen}} = 3.42 I^2 + 274.19 I$$
The unit of current is ampere, and the resulting heat source has units of watts per cubic metre. Table 3 summarizes the volume heat sources for the three discharge rates considered in this work.
| Discharge rate (C) | Volumetric heat source (W/m³) |
|---|---|
| 1 | 9893 |
| 2 | 24777 |
| 3 | 44626 |
The heat source data listed above are essential for establishing the numerical cooling model of the vehicle traction battery module. In the subsequent simulations, the battery internal structure is simplified into a homogeneous cuboid with dimensions of 140 mm × 100 mm × 20 mm. The cell is assumed to have uniform volumetric heat generation. This simplification is acceptable because the focus of the present work is the external cooling performance rather than the internal electrochemical status of the cell.
Numerical Model of the Spray-and-Ventilation Coupled Cooling System
Physical Model Description
The physical model of the coupled cooling system is built in SpaceClaim 2022. As illustrated in the model diagram, the computational domain contains a battery module composed of 24 prismatic cells, a ventilation duct, and multiple spray nozzles arranged in the gaps between adjacent cells. Each battery cell has dimensions of 140 mm × 100 mm × 20 mm, and the default gap between cells is 10 mm unless otherwise stated. The inlet of the duct provides a uniform air flow, while the nozzles inject finely atomized water droplets into the channels. A schematic view of the entire vehicle traction battery cooling configuration is displayed by the figure shown above, which represents the typical layout of a prismatic vehicle traction battery pack used in this study.
Governing Equations
The air phase is treated as a continuous phase, and the water droplets are treated as a discrete phase. The Eulerian-Lagrangian approach is employed to couple the two phases. For an incompressible flow with evaporation, the continuity equation is:
$$\frac{\partial \rho}{\partial t} + \nabla \cdot \left(\rho \vec{v}\right) = S_m$$
where \(\rho\) is the air density, \(\vec{v}\) is the air velocity vector, and \(S_m\) is the mass source term caused by droplet evaporation. The momentum equation is:
$$\frac{\partial \left(\rho \vec{v}\right)}{\partial t} + \nabla \cdot \left(\rho \vec{v}\vec{v}\right) = -\nabla p + \nabla \cdot \overline{\overline{\tau}} + \rho \vec{g} + \vec{F}$$
The stress tensor is defined as:
$$\overline{\overline{\tau}} = \mu \left[\nabla \vec{v} + \nabla \vec{v}^T – \frac{2}{3}\nabla \cdot \vec{v} I \right]$$
where \(\mu\) is the dynamic viscosity and \(I\) is the unit tensor. The energy equation for the continuous phase is:
$$\frac{\partial \left(\rho E\right)}{\partial t} + \nabla \cdot \left[\vec{v}\left(\rho E + p\right)\right] = \nabla \cdot \left[k_{\text{eff}} \nabla T – \sum_j h_j \vec{J}_j\right] + \Phi + S_h$$
where \(k_{\text{eff}}\) is the effective thermal conductivity, \(E = h – p/\rho + v^2/2\), and \(S_h\) accounts for the energy contribution from the discrete phase. The species transport equation for water vapor in air is written as:
$$\frac{\partial \left(\rho Y_m\right)}{\partial t} + \nabla \cdot \left(\rho \vec{v} Y_m\right) = \nabla \cdot \left(\rho D_{m,\text{mix}} \nabla Y_m\right) + S_i$$
where \(Y_m\) is the mass fraction of component \(m\), \(D_{m,\text{mix}}\) is the diffusion coefficient, and \(S_i\) is the vapor source from the evaporating droplets.
Because the Reynolds number of the air flow through the channels is in the transition and turbulent range, the realizable \(k\)-\(\varepsilon\) model is selected. The transport equations for turbulent kinetic energy \(k\) and turbulent dissipation rate \(\varepsilon\) are:
$$\frac{\partial (\rho k)}{\partial t} + \frac{\partial (\rho k u_i)}{\partial x_i}
= \frac{\partial}{\partial x_j}\left[\left(\mu + \frac{\mu_t}{\sigma_k}\right)\frac{\partial k}{\partial x_j}\right]
+ P_k + G_b – \rho \varepsilon – Y_M$$
$$\frac{\partial (\rho \varepsilon)}{\partial t} + \frac{\partial (\rho \varepsilon u_i)}{\partial x_i}
= \frac{\partial}{\partial x_j}\left[\left(\mu + \frac{\mu_t}{\sigma_\varepsilon}\right)\frac{\partial \varepsilon}{\partial x_j}\right]
+ C_1 S \varepsilon – C_2 \rho \frac{\varepsilon^2}{k + \sqrt{\nu \varepsilon}} + C_3 \frac{G_b \varepsilon}{k}$$
The enhanced wall treatment is used to resolve the viscous sublayer near the battery surfaces and duct walls. This treatment is especially important because the spray droplets significantly alter the near-wall heat and mass transfer.
Discrete Phase Model
The trajectories of individual droplets are calculated by integrating the force balance on the droplet. The droplet motion equation is:
$$\frac{d \vec{u}_p}{dt} = F_D \left(\vec{u} – \vec{u}_p\right) + \frac{\vec{g}\left(\rho_p – \rho\right)}{\rho_p} + \vec{F}_{\text{other}}$$
where \(\vec{u}_p\) is the droplet velocity, \(\rho_p\) is the droplet density, and \(F_D\) is the drag force coefficient. For a spherical droplet, the drag coefficient is evaluated using the Schiller-Naumann correlation:
$$C_D = \frac{24}{Re_d}\left(1 + 0.15 Re_d^{0.687}\right)$$
with the droplet Reynolds number defined as:
$$Re_d = \frac{\rho d_p \left|\vec{u}_p – \vec{u}\right|}{\mu}$$
The evaporation of the droplet is modeled through a two-stage process. When the droplet temperature is below the saturation temperature, only heat transfer occurs. The droplet heat balance is integrated over a time step to update the temperature. Once the droplet reaches the evaporation temperature, the mass transfer rate is controlled by the gradient of vapor concentration between the droplet surface and the gas phase:
$$N_{H_2O} = k_c \left(C_{H_2O,s} – C_{H_2O,\infty}\right)$$
where \(k_c\) is the mass transfer coefficient and \(C_{H_2O,s}\) and \(C_{H_2O,\infty}\) are the vapor concentrations at the droplet surface and in the bulk gas, respectively. The droplet diameter distribution is described by the Rosin-Rammler expression:
$$Y_d = e^{-\left(\frac{d}{\bar{d}}\right)^{n^*}}$$
where \(\bar{d}\) is the mean droplet diameter and \(n^*\) is the spread parameter. The TAB model is used for secondary droplet breakup because of its reasonable accuracy for low-speed atomization sprays.
Two-Way Coupling and Solver Settings
The interaction between the continuous air phase and the discrete droplets is accounted for by a two-way coupling strategy. The momentum, mass, and energy source terms are exchanged during each coupling iteration. These source terms can be expressed as:
$$\vec{F} = \sum \left[\frac{18 \mu C_D Re}{\rho_p d_p^2 24}\left(\vec{u}_p – \vec{u}\right) + \vec{F}_{\text{other}}\right] \dot{m}_p \Delta t$$
$$Q = \frac{\dot{m}_{p,0}}{m_{p,0}}\left[\left(m_{p,\text{in}} – m_{p,\text{out}}\right)\left(-H_{\text{lat}}^{\text{ref}}\right) – m_{p,\text{out}} \int_{T_{\text{ref}}}^{T_{p,\text{out}}} c_{p,p} dT + m_{p,\text{in}} \int_{T_{\text{ref}}}^{T_{p,\text{in}}} c_{p,p} dT \right]$$
$$M = \frac{\Delta m_p}{m_{p,0}} \dot{m}_{p,0}$$
The model is solved using the commercial CFD solver Fluent. The pressure-based coupled algorithm is used for the pressure-velocity coupling. Second-order upwind schemes are applied for the spatial discretization of momentum, energy, turbulence, and species equations. The calculations are considered converged when the scaled residuals fall below \(10^{-6}\) for the energy equation and \(10^{-4}\) for the other transport equations.
Mesh Independence Analysis
A structured mesh is generated with ICEM software. Six grid systems, ranging from 0.89 million to 5.74 million cells, are tested. The maximum battery temperature is used as the monitored parameter. The grid independence analysis results are presented in Table 4.
| Number of cells (millions) | Maximum battery temperature (K) |
|---|---|
| 0.894 | 315.51 |
| 1.433 | 314.95 |
| 2.815 | 314.61 |
| 3.455 | 314.46 |
| 4.560 | 314.39 |
| 5.744 | 314.31 |
When the mesh size increases from 2.815 million to 3.455 million cells, the maximum temperature changes by only 0.15 K. Therefore, the mesh with 2.815 million cells is adopted for all subsequent simulations because it provides a good trade-off between computational accuracy and resource consumption.
Experimental Validation of the Numerical Model
To evaluate the reliability of the CFD model, a dedicated experimental platform is built. Because the direct use of a real battery cell under violent spray may raise safety issues, a simplified equivalent heat source is designed. An aluminium block with the same dimensions as the prismatic battery cell is heated by cartridge heaters, and its heat generation rate is set according to the fitted battery heat-generation model. This approach allows precise control of the heating power and ensures repeatable experiments.
The experimental system includes several major components: an adjustable DC power supply, a transformer, an ultrasonic atomizer, a variable-speed DC fan, an anemometer, an Agilent 34972A data acquisition module, and T-type thermocouples. Table 5 lists the equipment specifications.
| Instrument | Model or specification |
|---|---|
| Atomizer | W0403-2 |
| Variable-speed fan | DC 12 V |
| Data acquisition unit | Agilent 34972A |
| T-type thermocouple | TT-T-320 |
| Voltage regulator | TDGC2-0.2 |
The uncertainty of the temperature measurement is evaluated by combining the data acquisition unit error of ±0.06 K and the thermocouple error of ±0.1 K, yielding a combined uncertainty of ±0.16 K.
The experimental procedure includes the following steps. First, the instruments are connected according to the schematic diagram. The ambient temperature and relative humidity are recorded. Then, the variable-speed fan is switched on and its rotational speed is adjusted to achieve the desired inlet air velocity, which is verified with the anemometer. The atomizer is started, and the amount of water used for atomization is determined by weighing before and after each test. The DC power supply is turned on, and the heating power is adjusted to the desired level. For the validation tests, a power of 12.5 W, corresponding to 3C discharge, is used. The transient temperature of the aluminium block is recorded for 1200 seconds, after which the power, fan, and atomizer are switched off.
Several validation cases are conducted with inlet air velocities of 1.0 m/s, 1.5 m/s, and 2.0 m/s, either without spray or with a spray mass flow rate of 0.15 g/s. The ambient temperature is 298.4 K. The experiment and simulation temperatures are compared in Table 6, which reports the final average surface temperatures for each case.
| Case | Air velocity (m/s) | Spray rate (g/s) | Experimental temperature (K) | Simulated temperature (K) | Difference (K) |
|---|---|---|---|---|---|
| 1 | 1.0 | 0 | 316.87 | 315.06 | 1.81 |
| 2 | 1.5 | 0 | 312.85 | 310.58 | 2.27 |
| 3 | 2.0 | 0 | 309.86 | 308.12 | 1.74 |
| 4 | 1.0 | 0.15 | 313.28 | 311.45 | 1.83 |
| 5 | 1.5 | 0.15 | 310.93 | 308.53 | 2.40 |
| 6 | 2.0 | 0.15 | 308.74 | 306.78 | 1.96 |
The root mean square error between all measured and simulated temperatures is calculated as:
$$RMSE = \sqrt{\frac{1}{30}\sum_{i=1}^{30}\left(y_i – \hat{y}_i\right)^2}$$
The resulting RMSE is approximately 1.57 K, while the maximum single-point deviation is about 1.9 K. The simulation consistently underpredicts the measurements by a small margin. This discrepancy may be attributed to the unavoidable environmental humidity fluctuation during the experiments and the ideal assumptions in the evaporation model. Also, the heat losses through the insulation and non-uniform contact of thermocouples contribute to the deviations. Overall, the model reproduces the trend with acceptable accuracy, confirming its reliability for further parametric studies.
Results and Discussion
Influence of Inlet Air Velocity under Pure Air Cooling
To establish a baseline, the pure forced-air cooling performance is simulated for the vehicle traction battery module at 3C discharge with an inlet air temperature of 300 K. The inlet air velocity is varied from 0.5 m/s to 3.0 m/s. Figure data show that the maximum battery temperature decreases from 321.7 K at 0.5 m/s to 307.3 K at 3 m/s. Higher velocity not only strengthens the convective heat transfer coefficient but also carries away more sensible heat from the module. Nevertheless, the associated pressure drop rises rapidly, as shown in Table 7, which affects the fan power demand.
| Inlet velocity (m/s) | Maximum temperature (K) | Maximum temperature difference (K) | Pressure drop (Pa) |
|---|---|---|---|
| 0.5 | 321.7 | 10.9 | 2.4 |
| 1.0 | 318.0 | 6.6 | 9.2 |
| 1.5 | 311.5 | 5.4 | 18.5 |
| 2.0 | 309.6 | 4.7 | 30.4 |
| 3.0 | 307.3 | 3.8 | 61.9 |
The pressure drop increases from 2.4 Pa to 61.9 Pa as the velocity increases from 0.5 to 3.0 m/s. Therefore, for practical applications of the vehicle traction battery, the recommended air velocity range is 1–2 m/s, which achieves a reasonable balance between cooling performance and fan power.
Influence of Inlet Air Temperature
Keeping the inlet velocity at 1 m/s and the discharge rate at 3C, simulations are performed at inlet temperatures of 290, 295, 300, 305, and 310 K. The maximum battery temperature increases from about 306 K to about 326.2 K as the inlet temperature increases from 290 K to 310 K, a total rise of around 20.2 K. In contrast, the maximum temperature difference changes only slightly, remaining between 6.3 and 6.6 K across this inlet temperature range. This indicates that the inlet temperature has a strong effect on the absolute cell temperature but a minimal effect on the temperature uniformity under a fixed velocity because the flow rate and convective heat transfer distribution are essentially unchanged.
Influence of Nozzle Type and Arrangement
Spray cooling is then activated in the coupled system. Three nozzle types are compared: cone, cone-back, and surface. The total mass flow rate is fixed at 0.7 g/s for all types, the droplet mean diameter is 20 μm, and the ambient relative humidity is 50%. The simulation results are compared with the pure-air cooling case in Table 8.
| Case | Air velocity (m/s) | Spray rate (g/s) | Maximum temperature (K) | Maximum temperature difference (K) |
|---|---|---|---|---|
| Pure air | 1.0 | 0 | 318.0 | 6.6 |
| Surface nozzle | 1.0 | 0.7 | 314.8 | 7.2 |
| Cone-back nozzle | 1.0 | 0.7 | 314.5 | 7.0 |
| Cone nozzle | 1.0 | 0.7 | 314.1 | 5.2 |
| Two cone nozzles | 1.0 | 0.7 | 313.6 | 4.8 |
All spray configurations lower the maximum cell temperature compared with pure air cooling. However, the surface nozzle and cone-back nozzle increase the module temperature difference because their wide spray coverage concentrates too many droplets on the first row of cells, causing local overcooling and insufficient cooling downstream. The cone nozzle, which injects droplets mainly into the gaps between neighboring cells, yields both a lower maximum temperature and a better temperature uniformity.
In order to further improve the uniformity in the vertical direction, two cone nozzles are installed symmetrically in every gap instead of one. Figure 5 shows the nozzle layout concept. With the total spray flow rate in each gap kept at 0.1 g/s, the distance between the two nozzles is optimized from 30 mm to 130 mm. Table 9 lists the maximum temperatures and maximum temperature differences for the different nozzle spacings.
| Nozzle spacing (mm) | Maximum temperature (K) | Maximum temperature difference (K) |
|---|---|---|
| 30 | 314.6 | 5.1 |
| 50 | 314.4 | 4.9 |
| 70 | 314.2 | 4.7 |
| 90 | 314.0 | 4.5 |
| 110 | 313.8 | 4.4 |
| 130 | 314.3 | 4.8 |
The optimal nozzle spacing is 110 mm, which yields the lowest maximum temperature and minimum temperature difference. At this spacing, the droplets are distributed more uniformly over the entire height of the cell surfaces. Thus, all subsequent simulations are carried out using two cone nozzles per gap with a spacing of 110 mm.
Influence of Spray Mass Flow Rate
At an inlet air velocity of 1 m/s, the total spray mass flow rate is varied from 0 g/s (pure air) to 0.5 g/s. The percentage of each nozzle pair is set equally. Table 10 summarizes the results.
| Spray flow rate (g/s) | Maximum temperature (K) | Maximum temperature difference (K) |
|---|---|---|
| 0 | 318.0 | 6.6 |
| 0.1 | 315.1 | 4.8 |
| 0.2 | 314.6 | 4.7 |
| 0.3 | 314.2 | 4.6 |
| 0.4 | 314.1 | 4.6 |
| 0.5 | 314.1 | 4.6 |
Increasing the spray flow rate from 0.1 to 0.2 g/s reduces the maximum temperature by about 0.5 K. Beyond 0.3 g/s, the additional benefit is marginal because the air stream gradually becomes saturated with vapor, and the evaporation potential is limited. Therefore, for an inlet velocity of 1 m/s, the optimal spray flow rate is around 0.2–0.3 g/s, considering water consumption and cooling gain.
Influence of Droplet Diameter
Keeping the total spray mass flow rate at 0.2 g/s, the droplet diameter is changed from 20 μm to 100 μm. Table 11 presents the results.
| Droplet diameter (μm) | Maximum temperature (K) | Maximum temperature difference (K) |
|---|---|---|
| 20 | 314.4 | 4.7 |
| 40 | 315.6 | 5.6 |
| 60 | 316.3 | 6.1 |
| 80 | 316.8 | 6.4 |
| 100 | 317.3 | 6.6 |
Smaller droplets provide a much larger interfacial area per unit volume, which accelerates evaporation and promotes better distribution inside the channel. Consequently, a droplet diameter of 20 μm is found to be the most effective among the tested values. These findings are important for selecting the appropriate atomization method for the vehicle traction battery cooling system.
Coupled Effect of Air Velocity and Spray Flow Rate
The interplay between air velocity and spray flow rate is studied at an ambient temperature of 300 K and relative humidity 50%. The inlet velocity ranges from 0.5 to 3 m/s, while the spray flow rate ranges from 0 to 0.5 g/s. Table 12 lists the maximum battery temperatures for this matrix of simulations.
| Velocity (m/s) | Spray rate 0 g/s | 0.1 g/s | 0.2 g/s | 0.3 g/s | 0.4 g/s | 0.5 g/s |
|---|---|---|---|---|---|---|
| 0.5 | 327.3 | 321.2 | 320.2 | 319.6 | 319.3 | 319.1 |
| 1.0 | 318.0 | 315.1 | 314.6 | 314.2 | 314.1 | 314.1 |
| 1.5 | 311.5 | 310.5 | 310.0 | 309.9 | 309.8 | 309.8 |
| 2.0 | 309.6 | 308.9 | 308.7 | 308.6 | 308.5 | 308.5 |
| 3.0 | 307.3 | 306.9 | 306.8 | 306.8 | 306.7 | 306.7 |
At a low velocity of 0.5 m/s, increasing the spray rate from 0.1 to 0.2 g/s lowers the maximum temperature by 1 K. When the velocity is raised to 2 m/s, the same increase in spray rate only lowers the temperature by 0.2 K. Thus, the benefit of increasing spray flow diminishes with air velocity because the droplets have less residence time to evaporate before being swept downstream. The practical recommendation for achieving a maximum temperature below 310 K at high ambient temperatures would be a velocity of about 1.5 m/s combined with a spray flow rate between 0.2 and 0.3 g/s.
Influence of Battery Gap Spacing
Battery gap spacing is crucial for both thermal performance and airflow resistance. In this study, gap spacings of 5, 10, 15, and 20 mm are simulated. The pressure drop results for different spacings and velocities are listed in Table 13.
| Battery spacing (mm) | Pressure drop at 0.5 m/s (Pa) | Pressure drop at 1 m/s (Pa) | Pressure drop at 2 m/s (Pa) | Pressure drop at 3 m/s (Pa) |
|---|---|---|---|---|
| 5 | 16.01 | 41.58 | 129.55 | 258.09 |
| 10 | 4.82 | 10.24 | 29.73 | 63.82 |
| 15 | 1.52 | 4.56 | 15.72 | 30.55 |
| 20 | 0.76 | 2.15 | 8.24 | 17.26 |
The maximum temperatures under various spacings, velocities, and spray flow rates are presented in Table 14. Only the cases with spray rates of 0, 0.2, and 0.5 g/s are shown for brevity.
| Spacing (mm) | Velocity (m/s) | Tmax at 0 g/s (K) | Tmax at 0.2 g/s (K) | Tmax at 0.5 g/s (K) |
|---|---|---|---|---|
| 5 | 0.5 | 315.2 | 312.8 | 311.9 |
| 1 | 308.9 | 306.5 | 305.8 | |
| 2 | 305.4 | 304.1 | 303.8 | |
| 3 | 302.7 | 301.9 | 301.4 | |
| 10 | 0.5 | 318.0 | 314.6 | 314.1 |
| 1 | 310.8 | 308.5 | 307.7 | |
| 2 | 306.3 | 305.0 | 304.6 | |
| 3 | 303.6 | 302.8 | 302.4 | |
| 15 | 0.5 | 320.6 | 316.8 | 316.2 |
| 1 | 312.3 | 310.0 | 309.3 | |
| 2 | 307.7 | 306.3 | 305.8 | |
| 3 | 304.5 | 303.7 | 303.3 | |
| 20 | 0.5 | 323.6 | 319.6 | 318.8 |
| 1 | 314.5 | 312.1 | 311.5 | |
| 2 | 308.8 | 307.5 | 307.1 | |
| 3 | 305.8 | 304.8 | 304.4 |
Smaller spacing leads to higher local air velocity inside the gap for the same volumetric flow rate, which enhances convection. However, a narrow gap dramatically increases the pressure drop and can impair droplet dispersion, leading to larger temperature differences between the front and rear rows. In the 5 mm spacing case, the maximum temperature difference is reduced when the spray flow rate increases because the high-speed airflow prevents droplet accumulation and the increased amount of spray helps wet more surfaces. In contrast, for 15 mm and 20 mm spacing at a low inlet velocity of 0.5 m/s, increasing the spray flow from 0.2 to 0.5 g/s leads to droplet accumulation and slightly worsens the temperature uniformity. When the inlet velocity is raised above 2 m/s, increasing the spray flow consistently improves uniformity for all spacings. Considering pressure drop, thermal performance, and packaging compactness, a 10 mm gap spacing is recommended for the studied vehicle traction battery module.
Effect of Discharge Rate on Coupled Cooling Performance
Simulations are performed at discharge rates of 1C, 2C, and 3C with a fixed spray flow rate of 0.2 g/s. Table 15 lists the maximum temperature and temperature difference for two representative inlet velocities.
| Discharge rate | Velocity (m/s) | Maximum temperature (K) | Maximum temperature difference (K) |
|---|---|---|---|
| 1C | 0.5 | 303.1 | 2.4 |
| 1C | 3.0 | 301.4 | 1.2 |
| 2C | 0.5 | 310.5 | 5.0 |
| 2C | 3.0 | 303.9 | 1.3 |
| 3C | 0.5 | 320.1 | 8.2 |
| 3C | 3.0 | 307.4 | 3.7 |
At 1C discharge, the battery temperature remains below 305 K even with a low air velocity of 0.5 m/s, indicating that the spray may be unnecessary in low-load conditions. Therefore, an adaptive control strategy that can adjust the spray rate according to the actual discharge C-rate would be advantageous to reduce water consumption and parasitic power.
Influence of Ambient Temperature and Humidity
The cooling performance of the spray-and-ventilation system depends strongly on ambient conditions. With an inlet air velocity of 1 m/s and a spray flow rate of 0.2 g/s, simulations are conducted at ambient temperatures of 290, 295, 300, 305, and 310 K and a fixed relative humidity of 50%. Table 16 displays the maximum temperatures and temperature differences.
| Ambient temperature (K) | Tmax at 1 m/s (K) | ΔT at 1 m/s (K) | Tmax at 3 m/s (K) | ΔT at 3 m/s (K) |
|---|---|---|---|---|
| 290 | 306.0 | 5.5 | 297.8 | 1.8 |
| 295 | 310.0 | 5.6 | 302.4 | 2.1 |
| 300 | 314.6 | 5.8 | 306.8 | 2.4 |
| 305 | 317.1 | 5.9 | 310.3 | 2.8 |
| 310 | 323.2 | 6.0 | 316.7 | 3.3 |
The maximum temperature increases by roughly 17 K over the temperature range from 290 to 310 K. The temperature difference also increases with ambient temperature because higher temperatures accelerate the evaporation of droplets at the upstream cells, causing less liquid and vapor concentration downstream.
The relative humidity is varied from 20% to 80% at a constant ambient temperature of 300 K. Table 17 lists the key results.
| Relative humidity (%) | Tmax at 1 m/s (K) | ΔT at 1 m/s (K) | Tmax at 3 m/s (K) | ΔT at 3 m/s (K) |
|---|---|---|---|---|
| 20 | 313.5 | 4.2 | 306.9 | 2.8 |
| 30 | 313.9 | 4.6 | 307.1 | 2.9 |
| 40 | 314.3 | 5.0 | 307.2 | 3.1 |
| 50 | 314.6 | 5.8 | 307.3 | 3.2 |
| 60 | 314.9 | 5.9 | 307.4 | 3.3 |
| 70 | 315.2 | 6.0 | 307.4 | 3.3 |
| 80 | 315.4 | 5.3 | 307.5 | 3.3 |
At 1 m/s, the maximum temperature increases by about 1.9 K when the relative humidity rises from 20% to 80%. This is because high humidity reduces the vapor concentration gradient and weakens the evaporation of droplets. At 3 m/s, the influence of humidity is much smaller because convective heat transfer dominates over evaporative cooling. The outlet water-vapor mass fraction grows from about 0.0092 at 20% RH to 0.0202 at 80% RH, confirming that the evaporation capacity of the air stream is largely controlled by its inlet humidity.
Conclusion and Outlook
The present study has systematically investigated the heat transfer characteristics of a coupled spray and ventilation cooling system for a prismatic vehicle traction battery module. Based on experimental discharge data, a simplified volumetric heat source model was established for the battery. A sophisticated CFD model that accounts for droplet evaporation, two-way coupling, and turbulent dispersion was validated against experiments, showing a root mean square error of approximately 1.57 K. The validated model was then used to analyze the cooling performance under various operating and design parameters.
The main conclusions are summarized as follows.
First, pure air cooling can reduce the maximum battery temperature from 321.7 K at 0.5 m/s to 307.3 K at 3 m/s under 3C discharge. However, the pressure drop increases drastically from 2.4 Pa to 61.9 Pa, imposing a significant penalty on fan power. The recommended inlet air velocity for the vehicle traction battery is therefore in the range of 1–2 m/s. The inlet air temperature has a strong linear effect on the maximum cell temperature but a negligible influence on the module temperature uniformity.
Second, among the evaluated nozzle types, the cone nozzle exhibits the best cooling performance and temperature uniformity. The cone-back nozzle and surface nozzle cause excessive cooling of the upstream cells and increase the maximum temperature difference. By installing two horizontally opposed cone nozzles in each gap with a vertical spacing of 110 mm, the droplets are distributed more uniformly, and the battery temperature difference is minimized.
Third, increasing the spray mass flow rate from 0 to 0.2 g/s at an inlet velocity of 1 m/s reduces the maximum temperature by 3.4 K. Beyond 0.3 g/s, the additional temperature reduction becomes negligible. Thus, the optimal spray rate is controlled by the saturation limit of the air stream. Smaller droplet diameters are clearly beneficial since 20 μm droplets yield the lowest temperature and temperature difference compared with droplets of 40–100 μm.
Fourth, the interaction between air velocity and spray rate is important. At low velocities, spray cooling is more effective because the droplets remain in the channel for a longer time and evaporate completely. When the inlet velocity exceeds 2 m/s, the droplets are swept away too quickly, and the benefit of increasing the spray rate is diminished. Consequently, an adaptive system that combines low or moderate air velocity with a moderate spray rate is favorable for reducing energy consumption while maintaining cell temperatures below the critical threshold.
Fifth, battery gap spacing has a dual effect. Reducing the gap from 20 mm to 5 mm enhances the local air velocity and reduces the maximum temperature, but it also increases the pressure drop and can create droplet accumulation patterns that worsen temperature uniformity. For the current module, the 10 mm gap spacing offers the best compromise. The influence of spray rate on temperature difference depends on the gap spacing and air velocity: at narrow gaps, spray improves uniformity, whereas at wide gaps and low velocity, excessive spray may lead to droplet pooling and non-uniform cooling.
Finally, ambient temperature and humidity significantly affect the coupled cooling system. An increase in ambient temperature reduces the convective driving temperature difference, while an increase in relative humidity reduces the evaporation potential of the spray droplets. These effects should be considered when applying the spray-and-ventilation cooling strategy to vehicle traction battery packs in different climatic zones.
Future research may extend the present model by considering transient driving cycles and real-time variation of the heat generation rate. The use of phase change materials or heat pipe elements in combination with the spray ventilation concept can also be investigated to further improve thermal uniformity. Moreover, an adaptive control algorithm that adjusts the spray flow rate based on the battery temperature, current rate, and ambient humidity would be valuable for practical implementation in electric vehicles. Reliable long-term durability and anti-clogging performance of the nozzles are another essential issue that must be addressed before commercialization of spray-assisted thermal management systems for vehicle traction battery packs.