In the context of global carbon neutrality and peak carbon targets, the energy storage industry has experienced explosive growth. The safe and efficient operation of energy storage battery packs is a critical issue, especially under high charge/discharge rates. The thermal runaway of energy storage battery cells can lead to catastrophic fires and explosions. Therefore, an effective battery thermal management system (BTMS) is essential to maintain the temperature of energy storage battery packs within an ideal range of 20–40 °C and to keep the temperature difference among cells below 5 °C. Liquid cooling, particularly the use of cold plates with serpentine channels, offers superior heat transfer performance and structural simplicity. However, the flow resistance inside the cold plate directly affects the pumping power and system efficiency. In this study, I systematically investigate the influence of the number of flow channels on the cooling performance and flow resistance of a multi-channel serpentine liquid cooling plate for a 43 kWh energy storage battery pack. A parameter optimization is then performed using the NSGA-II algorithm to minimize flow resistance while maintaining adequate cooling capability.
1. Model Setup and Methodology
1.1 Geometry and Assumptions
I constructed a simplified 3D model of an energy storage battery pack consisting of 48 prismatic lithium‑iron‑phosphate cells (280 Ah each) arranged in two modules. The cells are bonded by thermally conductive adhesive and tightened with metal straps, with negligible gap between cells. The liquid cooling plate is placed at the bottom of the pack. The key parameters of a single cell are listed in Table 1.
| Parameter | Value |
|---|---|
| Nominal capacity (Ah) | 280 |
| Internal resistance (mΩ) | 0.22 |
| Dimensions (x, y, z) (mm) | (72, 208, 173) |
| Density (kg/m³) | 2219 |
| Specific heat capacity (J/(kg·K)) | 1000 |
| Thermal conductivity (x, y, z) (W/(m·K)) | (2.5, 12, 12) |
| Maximum charge/discharge rate | 1 C |
The heat generation of each cell at 1 C discharge is 17 W. The initial temperature of the whole pack is set to 25 °C. The cold plate is made of aluminum (thermal conductivity ~202 W/(m·K)), and the coolant is a 50/50 water‑glycol mixture. The inlet mass flow rate is 0.05 kg/s, and the outlet is set as pressure outlet (0 Pa gauge). A natural convection coefficient of 5 W/(m²·K) is applied on the external surfaces of the pack.
1.2 Governing Equations
The flow inside the cold plate is turbulent (Re ≈ 5273 at inlet). The k‑ε turbulence model is used. The pressure‑velocity coupling is handled by the COUPLED algorithm, and second‑order upwind schemes are adopted for spatial discretization. The key equations describing flow resistance and heat transfer are summarized below.
Flow resistance: The total pressure drop ΔP consists of frictional loss and local loss:
$$
\Delta P_{\lambda} = \lambda \frac{l}{d} \cdot \frac{\rho v^{2}}{2}
$$
$$
\Delta P_{r} = \zeta \frac{\rho v^{2}}{2}
$$
where λ is the Darcy friction factor, ζ is the local loss coefficient, l is channel length, d is hydraulic diameter, ρ is density, and v is velocity.
Heat transfer: Conduction inside the solid follows Fourier’s law:
$$
\Phi = -\lambda_{s} A \frac{dT}{dx}
$$
Convection between the cold plate and coolant is described by:
$$
\Phi = h A (T_{w} – T_{f})
$$
The convective heat transfer coefficient h is derived from the Nusselt number:
$$
h = \frac{\lambda_{l} Nu}{d}
$$
For turbulent flow in smooth tubes, the Gnielinski correlation is used (valid for Re = 2300–10⁶, Pr = 0.6–10⁵):
$$
Nu = \frac{(f/8)(Re-1000)Pr}{1+12.7(f/8)^{1/2}(Pr^{2/3}-1)} \left[ 1+\left(\frac{d}{l}\right)^{2/3} \right]
$$
where f is the Darcy friction factor given by the Konakov formula:
$$
f = (1.8 \log_{10} Re – 1.5)^{-2}
$$
Re is the Reynolds number:
$$
Re = \frac{\rho v d}{\mu}
$$
1.3 Mesh Independence Study
I generated poly‑hexcore meshes with cell counts ranging from 4.26 million to 19.56 million. The maximum temperature of the energy storage battery pack was monitored. As shown in Table 2, when the mesh count exceeds 17.97 million, the temperature variation becomes negligible. Therefore, a mesh of 17.97 million cells (minimum size 1 mm, maximum size 16 mm) was selected for all subsequent simulations.
| Number of cells (million) | Maximum temperature (°C) |
|---|---|
| 4.26 | 40.5 |
| 13.68 | 39.8 |
| 16.30 | 39.5 |
| 17.97 | 38.6 |
| 19.56 | 38.5 |
2. Effect of Number of Flow Channels
Six liquid cooling plates with 3, 4, 5, 6, 7, and 8 parallel serpentine channels were designed. All channels have a width of 20 mm and a height of 6 mm. The inlet/outlet diameter is 12 mm. The coolant flows in an “M‑shaped” serpentine path. The simulation results for the energy storage battery pack at 1 C discharge are summarized in Table 3.
| Number of channels | Max temperature (°C) | Average temperature (°C) | Max cell temperature difference (°C) | Flow resistance (Pa) |
|---|---|---|---|---|
| 3 | 38.55 | 34.30 | 2.1 | 1455 |
| 4 | 38.52 | 34.28 | 2.1 | 1280 |
| 5 | 38.45 | 34.25 | 2.1 | 1101 |
| 6 | 38.42 | 34.22 | 2.1 | 1035 |
| 7 | 38.40 | 34.20 | 2.1 | 985 |
| 8 | 38.38 | 34.19 | 2.1 | 958 |
From Table 3, it is evident that the number of channels has a negligible effect on the heat transfer performance: the maximum temperature varies only by about 0.17 °C, and the average temperature remains around 34.3 °C. The temperature difference among cells is consistently about 2.1 °C, which is within the safe limit. This is because the overall coolant flow path (the serpentine route) remains unchanged; only the number of parallel branches changes. However, the flow resistance decreases significantly as the channel count increases, from 1455 Pa (3 channels) to 958 Pa (8 channels). The reason is that more channels reduce the coolant velocity in each branch, thereby lowering both frictional and local losses.
Considering the trade‑off between flow resistance and manufacturing complexity (more channels increase the difficulty of machining), the 5‑channel design emerges as the optimal candidate for further optimization. Its cooling performance is already satisfactory, and its flow resistance (1101 Pa) is moderate.
3. Optimization of the 5‑Channel Cold Plate
3.1 Design Variables and Sampling
I identified six geometric variables: the gaps between adjacent channels at the inlet/outlet plenum regions (X1–X4) and the two gaps at the serpentine turns (X5, X6), as illustrated in the original study. Based on the velocity field, the recirculation zones at the ends have a maximum size of about 60 mm. Hence, the variable ranges were set to 20–60 mm. A Latin Hypercube Design (LHD) was used to generate 43 sample points. The responses (coolant outlet average temperature Y1 and flow resistance Y2) were computed via CFD. A subset of the samples is shown in Table 4.
| Sample | X1 (mm) | X2 (mm) | X3 (mm) | X4 (mm) | X5 (mm) | X6 (mm) | Y1 (°C) | Y2 (Pa) |
|---|---|---|---|---|---|---|---|---|
| 1 | 58.2 | 30.2 | 52.6 | 31.8 | 50.6 | 38.6 | 29.5 | 720.1 |
| 2 | 28.2 | 21.8 | 34.6 | 41.4 | 31.8 | 25.4 | 29.4 | 813.1 |
| 3 | 37.0 | 47.8 | 25.4 | 21.8 | 59.0 | 23.0 | 29.8 | 860.8 |
| 4 | 47.4 | 36.2 | 29.8 | 25.4 | 25.8 | 55.4 | 29.3 | 803.1 |
| 5 | 50.2 | 31.8 | 22.6 | 29.0 | 32.2 | 44.2 | 29.3 | 786.5 |
| … | … | … | … | … | … | … | … | … |
| 43 | 49.0 | 39.0 | 43.0 | 41.0 | 45.0 | 36.6 | 29.6 | 692.6 |
3.2 Response Surface Model
A second‑order response surface (RSM) was fitted to approximate the relationships between the six variables and the two responses. The coefficients of determination (R²) are 0.9106 for Y1 and 0.9878 for Y2, indicating good accuracy. The simplified polynomial models (with only significant terms) are:
For outlet temperature Y1:
$$
\begin{aligned}
Y1 &= 28.73179 + 0.09230X1 – 0.03492X2 – 0.00056X1^{2} – 0.00127X5^{2} \\
&\quad – 0.00095 X1 X5 – 0.00025 X1 X6 + 0.00018 X2 X3 – 0.00039 X2 X5 \\
&\quad – 0.00021 X3 X5 + 0.00017 X3 X6 – 0.00032 X4 X6 – 0.00032 X5 X6 \\
&\quad + 2.72158 X2^{3} + 1.70040 X4^{3} + 7.70745 X5^{3} + 3.47272 X6^{3} \\
&\quad – 3.02769 X2^{4} – 2.34748 X4^{4} – 7.52310 X5^{4}
\end{aligned}
$$
For flow resistance Y2:
$$
\begin{aligned}
Y2 &= 2496.45732 – 40.56239 X1 – 5.94390 X2 – 36.50450 X5 – 27.26761 X6 \\
&\quad + 1.04921 X1^{2} + 0.07542 X2^{2} – 0.12362 X4^{2} + 0.86664 X5^{2} + 0.61137 X6^{2} \\
&\quad – 0.03183 X1 X2 – 0.08958 X1 X5 – 0.03242 X3 X5 – 0.05027 X4 X6 \\
&\quad – 0.00823 X1^{3} + 0.00402 X4^{3} – 0.00627 X5^{3} – 0.00432 X6^{3} \\
&\quad + 2.51225 X3^{4} – 3.16500 X4^{4}
\end{aligned}
$$
3.3 Multi‑Objective Optimization Using NSGA‑II
Since the cooling performance (Y1) varies only slightly among samples, I set a constraint: Y1 ≤ 29.5 °C (coolant outlet temperature). The objective is to minimize Y2 (flow resistance). The NSGA‑II algorithm was employed with a population size of 100 and 200 generations. The Pareto front was obtained, and the optimal solution satisfying the constraint was selected: X1 = 54 mm, X2 = 44 mm, X3 = 52 mm, X4 = 52 mm, X5 = 56 mm, X6 = 60 mm, with a predicted flow resistance of 590.9 Pa.
3.4 CFD Validation
The optimized geometry was simulated using Fluent. The actual flow resistance was 640.6 Pa, with a relative error of 7.8% compared to the RSM prediction. The velocity streamlines (not shown here) indicate that the recirculation zones at the plenum regions are significantly reduced, and the flow distribution among channels is more uniform. The cooling performance of the optimized cold plate was then evaluated with the full energy storage battery pack model. The maximum temperature of the pack remained at 38.4 °C, and the cell temperature difference was still 2.1 °C. The flow resistance decreased from 1101 Pa to 640.6 Pa, a reduction of 41.8%. This directly lowers the pumping power required for the liquid cooling system, enhancing overall system efficiency.
4. Conclusion
In this study, I have systematically analyzed the thermal performance and flow resistance of a multi‑channel serpentine liquid cooling plate for a 43 kWh energy storage battery pack. The key findings are:
- The number of flow channels (3 to 8) has a negligible effect on the temperature distribution of the energy storage battery pack. All designs maintain the maximum temperature below 39 °C and the cell temperature difference around 2.1 °C.
- Flow resistance decreases monotonically with increasing channel count, due to reduced coolant velocity in each branch.
- The 5‑channel cold plate was selected as the best compromise for further optimization. Using a response surface model combined with the NSGA‑II algorithm, the flow resistance was reduced from 1101 Pa to 640.6 Pa (a 41.8% reduction) without sacrificing cooling performance.
- The optimized cold plate exhibits a “crescent‑shaped” gap distribution, which minimizes flow recirculation at the plenum ends.
These results demonstrate that careful geometric optimization of the liquid cooling plate can significantly reduce energy consumption while maintaining the safe operation of energy storage battery packs. The methodology presented here can be readily extended to other energy storage battery configurations and cooling plate designs.