Thermal management has become one of the most critical bottlenecks in the development of electric vehicles. The rapid growth of new-energy vehicles in recent years has brought the thermal management of power batteries into sharp focus. Among all the available energy-storage technologies, lithium-ion batteries are preferred because of their high energy-storage density, low capacity degradation rate, and stable cycling behaviour. They nevertheless release substantial heat whenever they are operated, particularly during high-rate charge and discharge. If that heat cannot be removed effectively, the temperature of a high-voltage battery pack may increase sharply, leading to accelerated ageing, capacity fade, and even catastrophic thermal runaway. Conventional air cooling is simple but limited in its cooling capacity, whereas liquid cooling can improve heat transfer but introduces complexity, additional mass, and higher parasitic energy consumption. Spray cooling, by contrast, provides outstanding heat dissipation and temperature-uniformity control and has therefore emerged as an attractive solution for battery thermal management. The purpose of this paper is to investigate the heat-transfer characteristics of a spray-and-ventilation coupled cooling scheme applied to a prismatic lithium-ion high-voltage battery pack, with the aid of calorimetric experiments, CFD simulation, and validation experiments.
In this work, I first measured the discharge performance and heat-generation behaviour of a selected prismatic cell, developed a heat-generation model from the experimental data, and then built a numerical model of spray-ventilation coupled cooling using computational-fluid-dynamics software. The numerical model treats air as the continuous phase and water droplets as the discrete phase; droplets injected into the airflow channel absorb heat from both the air and the battery surfaces, thereby suppressing the temperature rise. To validate the model, I constructed an experimental setup reproducing the same geometry, flow rate, and heat-generation rate as the simulation. The predicted temperatures were compared with the experimental readings under several air velocities with and without spray. The root-mean-square error was approximately 1.57 K, which indicates that the numerical model is sufficiently accurate for further parametric studies.
After validation, I systematically examined the effects of inlet air velocity, inlet air temperature, nozzle type, nozzle spacing, spray mass-flow rate, droplet diameter, battery spacing, discharge C-rate, ambient temperature, and relative humidity on the cooling performance. The results show that the proposed coupled cooling solution can reduce the maximum cell temperature significantly and can also improve temperature uniformity across the module when the nozzle arrangement and spray rate are chosen appropriately. The remainder of the paper is organized as follows: Section 1 introduces the background and reviews the evolution of battery thermal-management technologies; Section 2 analyses the heat-generation mechanisms of lithium-ion batteries and quantifies the heat-generation rate of the test cell; Section 3 describes the physical model, mathematical formulation, numerical details, and experimental validation; Section 4 presents the simulated results and discusses the influence of each parameter; Section 5 summarizes the conclusions.
1. Background and Research Status
The transport sector consumes approximately one-third of the global oil supply and contributes roughly 25% of global carbon-dioxide emissions. Electric vehicles offer an obvious route towards decarbonization because their well-to-wheel greenhouse-gas emissions are about 40% lower than those of an equivalent internal-combustion-engined vehicle, and their powertrain efficiency can exceed 90%. Global electric-vehicle sales surpassed ten million units in 2022, and the stock of electric vehicles is expected to reach 230 million by 2030. The performance of those vehicles is strongly dependent on the battery pack, whose gravimetric energy density has increased from about 100 Wh/kg in 2010 to approximately 350 Wh/kg nowadays. With such high energy densities, the thermal-load problem of the high-voltage battery has become more and more prominent.
Numerous cooling technologies have been studied for managing the temperature of the high-voltage battery, including forced-air cooling, liquid cooling, phase-change-material cooling, heat-pipe cooling, and evaporation/spray cooling. Air cooling is attractive because of its low cost, simple structure, and light weight. For example, wind-tunnel tests and simulations have shown that a carefully designed Z-type or U-type duct can substantially reduce the maximum cell temperature and the maximum temperature difference in a module. However, because air has a low heat-transfer coefficient and a small specific heat, pure air cooling is not sufficient for the high heat fluxes generated under fast charging or aggressive driving. Liquid cooling provides a much higher convective heat-transfer coefficient, but the required pump, cold plate, piping, and heat exchanger increase the complexity, weight, and cost, and also introduce the risk of leakage. Phase-change materials absorb heat through latent heat and can smooth the transient temperature response, yet their low thermal conductivity usually necessitates the addition of metal foam, expanded graphite, fins, or nano-particles. Heat pipes are excellent heat spreaders and can transfer large quantities of heat over a short distance, but a separate heat sink is still required at the condenser section and the overall thermal resistance is often controlled by that sink.
Spray evaporative cooling is an alternative scheme with a very high heat-removal capability. The latent heat of water evaporation is about 2400 kJ/kg, which is nearly an order of magnitude larger than the sensible heat absorbed by air. When a fine water mist is injected into the air stream of a battery module, the droplets evaporate and absorb heat from the surrounding air and the heated surfaces. This mechanism simultaneously reduces the air temperature, increases the local heat-transfer coefficient, and provides a direct evaporative-cooling effect at the cell surface. Previous work has demonstrated that spray cooling can keep the cells of a battery module below 40 °C with a more uniform temperature distribution than dry air cooling. Several investigators have combined spray cooling with other techniques, such as heat pipes or phase-change materials, to cool pouch cells. Spray pre-cooling of the inlet air has also been investigated by adding water droplets upstream of the battery module. Nevertheless, there are still very few systematic attempts to inject the fog directly into the narrow airflow gaps between prismatic cells and to optimize the cooling system parameters for a high-voltage battery pack. The present study aims to fill that gap.
2. Thermal Behaviour and Heat-Generation Model of the High-Voltage Battery
Lithium-ion batteries are available in cylindrical, prismatic, and pouch form. Among these, the prismatic cell offers the best compromise among packaging density, structural rigidity, durability, and manufacturability. I therefore chose a prismatic lithium-iron-phosphate cell as the research object. The positive electrode is typically LiFePO₄ on an aluminium-foil current collector; the negative electrode is graphite on a copper-foil current collector; and a porous polyolefin separator separates the two electrodes. During discharge, lithium ions leave the graphite lattice, migrate through the electrolyte, and are inserted into the iron-phosphate lattice, while electrons travel through the external circuit and perform work. The idealized charge/discharge reactions can be written as:
$$
\mathrm{LiFePO_4} – x\mathrm{Li^+} – x\mathrm{e^-} \rightarrow x\mathrm{FePO_4} + (1-x)\mathrm{LiFePO_4}
$$
$$
\mathrm{FePO_4} + x\mathrm{Li^+} + x\mathrm{e^-} \rightarrow x\mathrm{LiFePO_4} + (1-x)\mathrm{FePO_4}
$$
The internal materials govern the effective physical properties of the cell. Table 1 summarizes the thermophysical properties of the main cell components.
| Component | Material | Specific Heat (J kg⁻¹ K⁻¹) | Thermal Conductivity (W m⁻¹ K⁻¹) | Density (kg m⁻³) |
|---|---|---|---|---|
| Positive electrode | LiFePO₄ | 830 | 1.58 | 1523 |
| Positive current collector | Aluminium | 903 | 238 | 2702 |
| Negative electrode | Graphite | 1437 | 1.04 | 1455 |
| Negative current collector | Copper | 385 | 398 | 8933 |
| Separator | PP/PE/PP | 1978 | 0.3344 | 492 |
| Electrolyte | LiPF₆ | 1545 | 0.6 | 1290 |
The heat generated during charging and discharging arises from four sources: reaction heat \(Q_r\), polarisation heat \(Q_p\), Joule heat \(Q_j\), and side-reaction heat \(Q_s\). The total heat-generation rate is:
$$
Q = Q_r + Q_j + Q_p + Q_s
$$
The reaction heat is related to the entropy change of the electrode reactions. For a cell operating at current \(I\), Faraday’s law gives:
$$
Q_r = \frac{n m Q I}{M F}
$$
where \(n\) is the number of electrons transferred per mole of active species, \(m\) is the mass of active material, \(M\) is the molar mass, and \(F\) is Faraday’s constant. The Joule heat caused by the ohmic resistance \(R_e\) is:
$$
Q_j = I^2 R_e
$$
The polarisation heat, caused by the interfacial charge-transfer overpotential and concentration polarisation, can be written as:
$$
Q_p = I^2 R_p
$$
Side-reaction heat is usually negligible in a healthy lithium-ion battery because self-discharge and electrolyte decomposition are very small in the normal temperature window. Therefore, the total heat-generation rate can be obtained from the Bernardi model:
$$
Q_{gen} = I(U_{OC} – U) – I T_b \frac{dU_{OC}}{dT_b}
$$
For practical purposes, this equation can be rearranged as:
$$
Q_{gen} = I^2 R_j + I T_b \frac{\partial U_{OC}}{\partial T_b}
$$
The heat-absorption rate of the cell is related to its temperature-rise rate by:
$$
Q_{abs} = m_b c_{p,b}\frac{dT_b}{dt}
$$
Combining these expressions, the temperature-rise rate divided by the current becomes:
$$
\frac{1}{I}\frac{dT_b}{dt} = \frac{R_j}{m_b c_{p,b}}I + \frac{1}{m_b c_{p,b}}T_b\frac{\partial U_{OC}}{\partial T_b}
$$
Table 2 lists the physical specifications of the prismatic test cell used in the experiments.
| Attribute | 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 |
3. Experimental Measurement of Heat Generation
To acquire realistic heat-generation data, I performed discharge tests using a Neware BTS-8000 battery test station. The cell was placed inside a temperature-controlled chamber at 300 K. Five T-type thermocouples were attached to the cell surface at distributed locations, and an Agilent 34972A data-acquisition unit recorded the temperature every few seconds. Discharge experiments were conducted at 1C, 2C, and 3C constant-current rates until the cut-off voltage was reached. The measured temperature-rise curves showed a similar shape: the temperature increased slowly and almost linearly during the early part of discharge, then accelerated near the end of discharge because the cell impedance increases when the state of charge becomes low.
By differentiating the temperature-time data and fitting the linear relationship between \((1/I)(dT_b/dt)\) and the discharge current \(I\), I obtained the following heat-generation expression for the test cell:
$$
Q_{gen} = 1.06 \times 10^{-3} I^2 + 0.085 I
$$
$$
q_{gen} = 3.42 I^2 + 274.19 I
$$
where \(Q_{gen}\) is the heat-generation power in watts and \(q_{gen}\) is the volumetric heat-generation rate in W/m³. Table 3 lists the corresponding volumetric heat-source values used in the simulation.
| Discharge Rate (C) | Volumetric Heat Source (W/m³) | Heat-generation Power (W) |
|---|---|---|
| 1 | 9893 | 2.77 |
| 2 | 24777 | 6.94 |
| 3 | 44626 | 12.50 |
4. Spray-Ventilation Coupled Cooling System
4.1 Physical Model and Computational Domain
Figure 2 shows the physical model built in SpaceClaim 2022. The computational domain consists of a rectangular airflow channel and a battery module containing 24 prismatic cells arranged in two rows. Each cell has dimensions of 140 mm × 100 mm × 20 mm. Water mist is injected by nozzles into the vertical airflow gaps between adjacent cells. In the baseline layout, one nozzle is placed in each gap. Because the cells are electrically connected in series, the entire module is a high-voltage battery pack, and the central cells are thermally the most unfavourable because they exchange heat mainly through the narrow gaps. In the numerical model, the battery module is simplified as a homogeneous equivalent thermal body with orthotropic thermal conductivity. The polar tabs are ignored, since they contribute little to the overall heat-transfer surface. The heat-generation rate is assumed to be spatially uniform in each cell and is applied as a volumetric source term.
A structured hexahedral mesh was generated with ICEM. A grid-independence study was performed by increasing the mesh count from about 0.89 million to 5.74 million. Table 4 shows the predicted maximum temperature of the module at steady state. The maximum temperature changed by only 0.15 K when the cell count increased from 2.81 million to 3.46 million. Therefore, a mesh of approximately 2.81 million cells was chosen for all subsequent simulations, as it gives a good compromise between accuracy and computational cost.
| Mesh Count | 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 |
4.2 Governing Equations for the Continuous Phase
The air flow is treated as the continuous phase using the Eulerian approach. The conservation equations of mass, momentum, energy, and species can be written as:
$$
\frac{\partial \rho}{\partial t} + \nabla \cdot (\rho \vec{v}) = S_m
$$
$$
\frac{\partial (\rho \vec{v})}{\partial t} + \nabla \cdot (\rho \vec{v} \vec{v}) = -\nabla p + \nabla \cdot \boldsymbol{\tau} + \rho \vec{g} + \vec{F}
$$
$$
\frac{\partial (\rho E)}{\partial t} + \nabla \cdot [\vec{v}(\rho E+p)] = \nabla \cdot (k_{eff}\nabla T – \sum_j h_j \vec{J}_j) + \Phi + S_h
$$
$$
\frac{\partial (\rho_m)}{\partial t} + \nabla \cdot (\rho \vec{v} Y_m) = \nabla \cdot (\rho D_m \nabla Y_m) + S_i
$$
In these equations, \(\rho\) is the air density, \(\vec{v}\) is the velocity vector, \(S_m\) is the mass source due to droplet evaporation, \(\boldsymbol{\tau}\) is the viscous stress tensor, \(E\) is the total energy, \(S_h\) is the energy source, and \(Y_m\) is the mass fraction of water vapour in the air. The source terms in the mass and energy equations couple the continuous phase to the discrete phase by accounting for the evaporated mass and the associated latent heat.
4.3 Turbulence Model
For the flow in narrow channels, I adopted the realizable \(k\)-\(\varepsilon\) model, which performs better than the standard \(k\)-\(\varepsilon\) model for the simulation of round jets, planar jets, and flows with strong streamline curvature. The transport equations for the turbulent kinetic energy \(k\) and the dissipation rate \(\varepsilon\) are:
$$
\frac{\partial (\rho k)}{\partial t} + \frac{\partial (\rho k u_i)}{\partial x_i} = \frac{\partial}{\partial x_j}\left[\left(\mu+\frac{\mu_t}{\sigma_k}\right)\frac{\partial k}{\partial x_j}\right] + P_k + G_b – \rho\varepsilon – Y_M
$$
$$
\frac{\partial (\rho \varepsilon)}{\partial t} + \frac{\partial (\rho \varepsilon u_i)}{\partial x_i} = \frac{\partial}{\partial x_j}\left[\left(\mu+\frac{\mu_t}{\sigma_\varepsilon}\right)\frac{\partial \varepsilon}{\partial x_j}\right] + C_1 S \varepsilon – C_2 \rho\frac{\varepsilon^2}{k+\sqrt{\nu\varepsilon}} + C_3 G_b \frac{\varepsilon}{k}
$$
Enhanced wall treatment was used in the near-wall region to avoid the inaccuracies of standard wall functions when \(y^+\) is small.
4.4 Discrete-Phase Model
The water droplets are tracked in a Lagrangian frame. The droplet motion equation is:
$$
\frac{d\vec{u}_p}{dt} = F_D(\vec{u}-\vec{u}_p) + \frac{\rho_p-\rho}{\rho_p}\vec{g} + \vec{F}_{other}
$$
where \(\vec{F}_{other}\) represents additional forces such as thermophoretic force, Saffman lift force, and virtual-mass force. The drag force coefficient is:
$$
C_D = \frac{24}{Re}(1+0.15Re^{0.687})
$$
with the droplet Reynolds number defined as:
$$
Re = \frac{\rho d_p |\vec{u}-\vec{u}_p|}{\mu}
$$
The droplet size distribution was prescribed by a Rosin-Rammler distribution:
$$
Y_d = \exp\left[-\left(\frac{d}{\bar{d}}\right)^{n^*}\right]
$$
where \(\bar{d}\) is the mean droplet diameter and \(n^*\) is the spread parameter. The two-phase coupling is treated as a two-way interaction: the air flow influences the trajectory and evaporation of the droplets, and the droplets simultaneously affect the air flow through momentum, mass, and energy source terms. The coupling source terms can be expressed as:
$$
\vec{F} = \sum\left[\frac{18\mu C_D Re}{\rho_p d_p^2 24}(\vec{u}_p-\vec{u}) + \vec{F}_{other}\right]\dot{m}_p \Delta t
$$
$$
Q = \frac{\dot{m}_{p,o}}{m_{p,o}}\left[(m_{p,in}-m_{p,out})(-H_{lat}^{ref}) – m_{p,out}\int_{T_{ref}}^{T_{p,out}} c_{p,p}\,dT + m_{p,in}\int_{T_{ref}}^{T_{p,in}}c_{p,p}\,dT\right]
$$
$$
M = \frac{\Delta m_p}{m_{p,o}}\dot{m}_{p,o}
$$
4.5 Experimental Validation
To validate the numerical model, I built an experimental platform using an aluminium block with embedded heating cartridges as the equivalent heat source. The block had the same external dimensions as the prismatic cell, and the heating power was adjusted with an autotransformer to match the heat-generation rate of the cell at the corresponding discharge rate. Five T-type thermocouples were attached to the block surfaces. A variable-speed fan supplied air through a rectangular duct at a controlled velocity. A commercial ultrasonic atomizer was used to atomize water into fine droplets, and the total spray mass-flow rate was obtained by measuring the mass loss of water in the atomizer over the test duration. The ambient temperature was approximately 298.4 K. Table 5 defines the six test cases used for validation.
| 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 |
Each case was run for 1200 s, corresponding to a 3C discharge. The experimental and simulated temperatures agreed closely. The comparison was quantified using the root-mean-square error (RMSE):
$$
RMSE = \sqrt{\frac{1}{n}\sum_{i=1}^{n}(y_i-\hat{y}_i)^2}
$$
The calculated RMSE over the acquired temperature data was about 1.57 K, with the maximum deviation being about 1.9 K. The differences can be attributed to the simplification of the cell as a uniform heat source, the uncertainty of the thermocouples and data-acquisition unit, and the slight drift of ambient humidity during the repeated experiments. Overall, the model is sufficiently accurate for parametric analysis.
5. Results and Discussion
5.1 Effect of Air-Cooling Parameters
Before activating the spray, I evaluated the pure-air-cooling performance of the high-voltage battery module at different inlet-velocity and inlet-temperature conditions. The simulations were performed at a 3C discharge rate with an inlet temperature of 300 K. When the inlet air velocity was increased from 0.5 m/s to 3 m/s, the maximum battery temperature decreased from 321.7 K to 307.3 K. The improvement, however, is not linear. Doubling the velocity from 0.5 m/s to 1 m/s produced a large temperature drop, whereas a further increase from 2 m/s to 3 m/s brought a much smaller benefit. At the same time, the pressure drop across the module increased sharply from approximately 2.4 Pa at 0.5 m/s to around 61.9 Pa at 3 m/s. Therefore, from an energy-consumption point of view, an inlet air velocity in the range of 1–2 m/s is recommended.
The inlet air temperature also has a strong effect. When the inlet temperature rose from 290 K to 310 K at a fixed velocity of 1 m/s, the maximum battery temperature increased by 20.2 K. The maximum temperature difference remained nearly constant within 6.3–6.6 K because the inlet-temperature change did not affect the airflow pattern significantly.
5.2 Effect of Nozzle Type and Nozzle Spacing
Three spray nozzle types were compared: a cone nozzle injecting droplets downwards into each battery gap, a cone-back nozzle injecting droplets against the incoming airflow, and a surface nozzle releasing droplets uniformly along the flow direction. In all three cases, the total sprayed water mass-flow rate was equal to 0.7 g/s and the air velocity was 1 m/s. The results show that spray cooling in any form reduced the maximum temperature compared with pure air cooling. The cone-back and surface nozzles, however, produced a larger maximum temperature difference because their wide spray cones wetted the first row of cells immediately, locally cooled the first cells, and left less water for the downstream cells. The cone nozzle, which directed the fog into the gaps, gave the best uniformity. To improve the temperature distribution further, I replaced the single nozzle in each gap by two vertically mounted nozzles while keeping the total spray flow rate per gap at 0.1 g/s. With the twin-nozzle arrangement, the droplets were distributed more uniformly along the vertical direction, and the maximum temperature decreased below that obtained with a single nozzle.
Nozzle spacing between the two vertical nozzles was then optimized. Six values were studied: 30 mm, 50 mm, 70 mm, 90 mm, 110 mm, and 130 mm. When the spacing was very small, the two sprays overlapped and the behaviour was similar to that of a single nozzle. Increasing the spacing improved the uniformity until the spacing reached 130 mm. At 130 mm, the nozzles were located only 5 mm from the top and bottom walls, so that part of the spray impinged onto the wall and reduced the droplet concentration in the middle of the channel. Consequently, the 110 mm spacing yielded the lowest maximum temperature and the smallest temperature difference. All subsequent simulations were therefore performed with the twin-nozzle configuration and 110 mm nozzle spacing.
5.3 Effect of Spray Flow Rate and Droplet Diameter
The spray flow rate is one of the most important operating parameters. Figure 3 and Figure 4 summarize the results for the maximum temperature and the maximum temperature difference as functions of the total spray flow rate at different air velocities. At an air velocity of 1 m/s, the maximum temperature of the high-voltage battery module was about 318 K without spray. With a total spray flow rate of only 0.1 g/s, the maximum temperature decreased to 315.1 K. Increasing the spray flow rate to 0.2 g/s reduced the maximum temperature by a further 0.5 K, to about 314.6 K. A further increase from 0.3 g/s to 0.5 g/s reduced the temperature by only another 0.15 K. This indicates that the evaporative-cooling capacity of the air flow approaches saturation at a relatively small liquid flow rate; the extra water cannot evaporate fast enough and instead accumulates on the cell surfaces or is swept out of the channel.
The maximum temperature difference also decreased slightly with increasing spray flow rate under the baseline conditions, remaining between 4.6 K and 4.8 K at 1 m/s. The droplet diameter is another key parameter. Holding the spray flow rate at 0.2 g/s, I compared droplet diameters of 20 μm, 40 μm, 60 μm, 80 μm, and 100 μm. Smaller droplets provided both a lower maximum temperature and a lower maximum temperature difference, because the total surface area of the spray increases when the droplet diameter is reduced. A droplet of 20 μm diameter therefore produced the best cooling effect. The trend suggests that atomization quality is critical for achieving a high cooling efficiency in the narrow airflow gaps of a high-voltage battery pack.
| Air Velocity (m/s) | Tmax Reduction (K) |
|---|---|
| 0.5 | 1.00 |
| 1.0 | 0.50 |
| 2.0 | 0.17 |
5.4 Coupled Effect of Air Velocity and Spray Flow Rate
The interaction between the ventilation rate and the spray flow rate is important for the practical design of the cooling system. Table 6 shows the temperature reduction obtained when the spray flow rate was increased from 0.1 g/s to 0.2 g/s. At a low air velocity of 0.5 m/s, this increase reduced the maximum battery temperature by about 1 K. At 1 m/s, the reduction was approximately 0.5 K, and at 2 m/s it was only 0.17 K. High-velocity air carries the droplets out of the module before they have sufficient residence time to evaporate fully; consequently, the benefit of increasing the spray flow rate diminishes as the air velocity increases. In other words, there is a clear interaction between the two control variables. For a fixed spray flow rate, increasing the air velocity always improves the cooling performance, but the relative gain is largest when the spray flow rate is small. Conversely, for a fixed air velocity, increasing the spray flow rate produces a larger temperature reduction at low air velocities than at high air velocities.
5.5 Effect of Battery Spacing
The gap width between cells affects the flow cross-sectional area, the local air velocity, the pressure drop, and the residence time of the droplets. I examined four battery spacings: 5 mm, 10 mm, 15 mm, and 20 mm. At 0.5 m/s, the pressure drop decreased from about 16.0 Pa at 5 mm spacing to 0.76 Pa at 20 mm spacing. At 1 m/s, the corresponding values were 41.6 Pa and 2.2 Pa; at 3 m/s, they reached 258.1 Pa and 17.3 Pa, respectively. Therefore, reducing the battery spacing can greatly increase the pressure loss and the pumping-power consumption.
The simulation results show that the maximum temperature of the high-voltage battery pack decreases as the battery spacing is reduced, because the reduced cross-section increases the airflow velocity inside the gaps and strengthens the convective heat transfer. However, the maximum temperature difference follows the opposite trend. At a small spacing of 5 mm, the temperature difference is larger because the narrow channels make it difficult for the air and droplets to distribute uniformly in the streamwise direction. Meanwhile, the effect of the spray flow rate on the maximum temperature difference depends on the battery spacing and the air velocity. For example, at 5 mm spacing, increasing the spray flow rate reduces both the maximum temperature and the maximum temperature difference. At 15 mm and 20 mm spacings and a low air velocity, however, increasing the spray rate can slightly increase the maximum temperature difference, because the droplets are not carried away quickly enough and tend to accumulate, causing locally stronger evaporative cooling in the upstream region. When the air velocity is increased to 2 m/s, the droplets are swept away faster, and increasing the spray flow rate again reduces the maximum temperature difference at all battery spacings. In view of both thermal performance and the hydraulic penalty, a 10 mm gap provides a reasonable compromise and is recommended for practical design.
5.6 Effect of Discharge C-Rate
Different operating conditions of an electric vehicle correspond to different discharge rates of the high-voltage battery. I evaluated the cooling system under 1C, 2C, and 3C discharge conditions. Table 7 lists the maximum temperatures and temperature differences obtained at both 0.5 m/s and 3 m/s. As expected, the highest temperature and the largest non-uniformity occur at the highest discharge rate. At 0.5 m/s and 1 m/s the maximum temperature under 3C discharge was 320.1 K, while in 1C discharge it was only 303.1 K. The corresponding maximum temperature differences were 8.2 K at 3C and 2.4 K at 1C. When the air velocity was increased to 3 m/s, the maximum temperature of the 3C case was suppressed to 307.4 K, and the temperature difference was 3.7 K. The 1C case can be cooled adequately with pure air at a fairly low fan speed; spray is then unnecessary and may be switched off to save water and pumping energy.
| Air Velocity (m/s) | Discharge Rate | Tmax (K) | ΔTmax (K) |
|---|---|---|---|
| 0.5 | 1C | 303.1 | 2.4 |
| 0.5 | 2C | 310.5 | 5.0 |
| 0.5 | 3C | 320.1 | 8.2 |
| 3.0 | 1C | 301.4 | 1.2 |
| 3.0 | 2C | 303.9 | 1.3 |
| 3.0 | 3C | 307.4 | 3.7 |
5.7 Effect of Ambient Temperature
The external environment can vary over a wide range in vehicle operation. I therefore varied the ambient temperature from 290 K to 310 K while keeping the spray parameters fixed. The maximum temperature of the module increased with ambient temperature because the air entering the module is hotter and the convective heat-transfer driving force is smaller. At an air velocity of 1 m/s, the maximum temperature increased from about 306 K at 290 K ambient temperature to about 323.2 K at 310 K. At the same time, the maximum temperature difference increased from 5.5 K to approximately 6 K. When the air velocity was raised to 3 m/s, the maximum temperatures were 297.8 K and 316.7 K at the two extremes, and the temperature differences were 1.8 K and 3.3 K, respectively. At high ambient temperatures, the locally intense evaporation of droplets near the first rows of the module can create stronger temperature gradients, making the temperature uniformity slightly worse.
5.8 Effect of Relative Humidity
Air humidity has a decisive influence on the evaporation process. I varied the relative humidity from 20% to 80% while keeping the temperature at 300 K and the spray flow rate at 0.2 g/s. When the relative humidity rises, the partial pressure of water vapour in the air increases, and the partial-pressure difference between the droplet surface and the surrounding air is reduced. Therefore, the mass-transfer driving force and the evaporation rate both decrease, weakening the spray-cooling effect. Table 8 summarizes the results. At 1 m/s, the maximum temperature increased from 313.5 K at 20% relative humidity to 315.4 K at 80% relative humidity, while the temperature difference increased from 4.2 K to 5.3 K. At 3 m/s, the humidity effect was smaller but still observable: the maximum temperature rose from 306.9 K to 307.5 K. The water-vapour mass fraction in the outlet air increased with humidity from approximately 0.0092 at 20% RH to about 0.0202 at 80% RH. These results imply that the proposed spray-ventilation cooling system is especially effective in dry climates, where evaporative cooling is enhanced by the large humidity deficit of the air.
| Air Velocity (m/s) | Relative Humidity (%) | Tmax (K) | ΔTmax (K) |
|---|---|---|---|
| 1.0 | 20 | 313.5 | 4.2 |
| 1.0 | 80 | 315.4 | 5.3 |
| 3.0 | 20 | 306.9 | 2.8 |
| 3.0 | 80 | 307.5 | 3.3 |
6. Conclusion
In this work, I developed an experimentally validated numerical model of a spray-ventilation coupled cooling system for a prismatic lithium-ion high-voltage battery pack and used this model to investigate the heat-transfer characteristics under a wide range of operating parameters. The main conclusions are as follows:
(a) The proposed numerical model, which solves the continuous-phase equations for air and the discrete-phase equations for evaporating water droplets, agrees well with the experimental data. The root-mean-square error is about 1.57 K, confirming that the model is suitable for engineering design and optimization.
(b) Pure air cooling with an inlet velocity of 0.5 m/s to 3 m/s is capable of reducing the maximum battery temperature from 321.7 K to 307.3 K under a 3C discharge, but the associated pressure drop increases from 2.4 Pa to 61.9 Pa. An inlet velocity in the range of 1–2 m/s gives a good balance between cooling performance and fan power.
(c) Spray cooling reduces the maximum temperature of the high-voltage battery much further than air cooling. A cone nozzle injecting the spray into the battery gaps produces the best temperature uniformity. Replacing the single nozzle with two vertically stacked nozzles improves the vertical uniformity, and a nozzle spacing of 110 mm gives the lowest maximum temperature and temperature difference. The cooling benefit of increasing the spray flow rate saturates at roughly 0.2 g/s for an air velocity of 1 m/s; droplets with a smaller diameter, such as 20 μm, provide the best cooling performance.
(d) The interaction between air velocity and spray rate is significant. When the spray flow rate is increased from 0.1 g/s to 0.2 g/s, the maximum temperature drop is about 1 K at 0.5 m/s but only 0.17 K at 2 m/s. High air velocities shorten the residence time of the droplets, reducing the amount of water that can evaporate before leaving the module.
(e) Battery spacing changes the trade-off between thermal performance and pumping power. Smaller gaps improve convective cooling and reduce the maximum temperature but increase the pressure drop and the maximum temperature difference. When the battery spacing is large and the air velocity is low, increasing the spray rate may worsen temperature uniformity; this drawback disappears when the air velocity is raised above about 2 m/s. A gap width of 10 mm appears to be the recommended design compromise for the module considered here.
(f) The cooling system is sensitive to external conditions. Higher ambient temperature and higher relative humidity both weaken the cooling effect because the former reduces the convective heat-transfer driving force and the latter reduces the evaporation driving force. The proposed spray-ventilation coupled cooling strategy is most effective in hot and dry climates and can be switched off at low discharge rates to save energy and water.
Overall, the spray-ventilation coupled cooling system offers an effective and relatively simple solution for the thermal management of high-voltage battery packs. The results provide quantitative guidance for the selection of nozzle type, nozzle layout, spray flow rate, droplet size, and battery spacing, and they clarify the influence of ambient conditions on the achievable cooling performance.