The relentless global pursuit of carbon neutrality has catalyzed an unprecedented expansion of the energy storage industry. At the heart of this infrastructure lies the lithium-ion battery pack, whose safety, efficiency, and longevity are paramount. A critical factor governing these attributes is temperature. Energy storage cells operate optimally within a narrow temperature window, typically 20°C to 40°C, with a maximum temperature difference between individual cells of less than 5°C to ensure uniform aging and performance. Exceeding safe thermal limits, especially approaching 70°C, can trigger thermal runaway—a catastrophic cascade of exothermic reactions leading to fire or explosion. Therefore, developing an efficient, reliable, and energy-conscious Battery Thermal Management System (BTMS) is not merely an engineering challenge but a fundamental requirement for large-scale energy storage deployment.
Among various cooling methodologies, liquid cooling has emerged as a superior solution for high-power-density applications due to its high heat capacity and superior thermal conductivity compared to air. The liquid cold plate, a key component, is prized for its structural simplicity, cost-effectiveness, and high heat exchange performance. Its operation is based on convective heat transfer, where a coolant circulated by a pump absorbs heat from the battery pack. While maximizing cooling performance is often the primary focus, the hydraulic power required to drive the coolant—directly related to the flow resistance within the cold plate—significantly impacts the overall system efficiency. An optimal design must therefore achieve a delicate balance: maintaining the energy storage cell temperatures within the ideal range with minimal cell-to-cell variation, while simultaneously minimizing pumping power. This article, from a design engineering perspective, details the thermal analysis and multi-objective optimization of a multi-channel serpentine liquid cooling plate for a large-capacity 43 kWh energy storage battery pack.
The design challenge escalates significantly when moving from small battery modules to full-scale packs. Many prior studies utilize simplified models with a handful of cells, resulting in reported temperature differences that are often unrealistically low for practical, densely-packed energy storage battery packs containing dozens of cells. Our work addresses this gap by modeling a complete pack containing 48 large-format 280 Ah Lithium Iron Phosphate (LFP) energy storage cells. LFP chemistry is favored for stationary storage due to its intrinsic safety and long cycle life, but effective thermal management remains essential. Each energy storage cell generates heat during operation (charge/discharge), modeled as a volumetric heat source. The anisotropic thermal conductivity of the cell, a result of its laminated internal structure, is a critical parameter: heat conducts more easily along the plane of the electrodes (y-z plane) than across them (x-direction).
We selected a serpentine channel cold plate design for its proven effectiveness and manufacturability. To improve upon traditional single-path serpentine designs, we proposed a parallelized multi-channel serpentine configuration. This design features multiple parallel flow channels connected by common inlet and outlet manifolds on the same side of the plate, forcing the coolant into a longer, tortuous “M-shaped” path. This approach aims to combine the good temperature uniformity of a long serpentine path with potentially reduced flow resistance from parallel channels. The core investigation began by evaluating six distinct cold plate designs, varying only the number of parallel channels (N = 3, 4, 5, 6, 7, 8). All other geometric parameters, such as channel width (20 mm), depth (6 mm), and inlet/outlet diameter (12 mm), were held constant. The simplified battery pack model, consisting solely of the 48 cells and the cold plate attached to their base, was subjected to a 1C continuous discharge rate, a standard and demanding operational condition.
The governing physics for this system are captured by a set of fundamental equations. The heat generation within each energy storage cell is conducted to the cold plate. This conductive heat transfer is governed by Fourier’s Law:
$$ \Phi_{cond} = – \lambda_s A \frac{dT}{dx} $$
Where $\Phi_{cond}$ is the conductive heat flux (W), $\lambda_s$ is the thermal conductivity of the solid (W/m·K), $A$ is the cross-sectional area (m²), and $dT/dx$ is the temperature gradient (K/m).
The heat is then removed by the flowing coolant via convection, described by Newton’s Law of Cooling:
$$ \Phi_{conv} = h A_s (T_w – T_f) $$
Here, $h$ is the convective heat transfer coefficient (W/m²·K), $A_s$ is the solid-fluid contact area (m²), $T_w$ is the wall temperature, and $T_f$ is the bulk fluid temperature. The convective coefficient $h$ is a crucial parameter dependent on fluid properties and flow regime. For the turbulent flow in our system (Reynolds number, $Re > 4000$), we employ the Gnielinski correlation, renowned for its accuracy:
$$ Nu = \frac{(f/8)(Re – 1000)Pr}{1 + 12.7(f/8)^{1/2}(Pr^{2/3} – 1)} \left[ 1 + \left(\frac{d_h}{L}\right)^{2/3} \right] $$
$$ h = \frac{Nu \cdot \lambda_l}{d_h} $$
Where $Nu$ is the Nusselt number, $f$ is the Darcy friction factor, $Re = \frac{\rho u d_h}{\mu}$ is the Reynolds number, $Pr$ is the Prandtl number, $\lambda_l$ is the fluid thermal conductivity, $d_h$ is the hydraulic diameter, and $L$ is the flow length. The friction factor $f$ for smooth tubes under turbulent conditions can be approximated by the Konakov formula: $f = (1.8\log Re – 1.5)^{-2}$.
The hydraulic performance, dictating pumping power, is determined by the total pressure drop $\Delta P_{total}$. It comprises major (frictional) losses and minor (local) losses:
$$ \Delta P_{total} = \Delta P_{major} + \Delta P_{minor} = \sum \left( f \frac{L}{d_h} \frac{\rho u^2}{2} \right) + \sum \left( \zeta \frac{\rho u^2}{2} \right) $$
Where $\zeta$ represents the local loss coefficient at features like bends, expansions, and contractions in the manifold regions.
We established a Computational Fluid Dynamics (CFD) model using ANSYS Fluent, applying the realizable k-ε turbulence model for the coolant flow. A grid independence study was meticulously conducted to ensure solution accuracy, culminating in a mesh of approximately 18 million elements. The boundary conditions are summarized in the table below:
| Parameter | Value | Description |
|---|---|---|
| Battery Heat Rate | 17 W/cell | 1C discharge for 280Ah cell |
| Initial Temperature | 25 °C | Uniform pack initial condition |
| Coolant Inlet | 0.05 kg/s, 25°C | Water-Ethylene Glycol mixture |
| Coolant Outlet | Pressure-outlet (0 Pa gauge) | Atmospheric pressure reference |
| Ambient Convection | 5 W/m²·K | Natural convection on exposed surfaces |
The simulation results for the six channel-number variants yielded fascinating and somewhat counter-intuitive insights regarding cooling performance. As the table below illustrates, the maximum temperature of the energy storage battery pack showed remarkably little variation, staying within a 0.3°C band across all designs.
| Number of Channels (N) | Max. Pack Temp. (°C) | Avg. Pack Temp. (°C) | Max. Cell ΔT (°C) | Flow Resistance (Pa) |
|---|---|---|---|---|
| 3 | 38.60 | 34.33 | 2.13 | 1455.2 |
| 4 | 38.55 | 34.25 | 2.11 | 1290.8 |
| 5 | 38.48 | 34.19 | 2.10 | 1101.0 |
| 6 | 38.40 | 34.14 | 2.11 | 980.5 |
| 7 | 38.35 | 34.10 | 2.10 | 875.4 |
| 8 | 38.32 | 34.07 | 2.09 | 1000.9 |
All configurations successfully maintained the energy storage cell temperatures well within the safe operating limit (below 39°C). The average temperature showed a gradual decreasing trend with increasing channel count, which can be attributed to a larger effective contact area between the coolant and the plate. However, the law of diminishing returns is evident; the gain from adding channels beyond five becomes minimal. Most importantly, the maximum temperature difference between any two energy storage cells in the pack remained consistently around 2.1°C, satisfying the critical uniformity criterion (<5°C). This consistency is a direct consequence of the preserved “M-shaped” serpentine flow path. Regardless of channel count, the coolant is forced to traverse the entire length and width of the plate, ensuring that each section of the pack is serviced by coolant at a similar stage of its thermal soak. This design elegantly addresses the uniformity challenge in large packs.
The most pronounced and predictable effect was on hydraulic performance. Flow resistance dropped significantly as the number of channels increased from 3 to 7. This is directly explained by fluid mechanics principles. For a constant total inlet mass flow rate, increasing the number of parallel channels reduces the average flow velocity $u$ in each channel. Since pressure drop is proportional to the square of velocity ($\Delta P \propto u^2$), the reduction in $u$ leads to a substantial decrease in both frictional and local losses. The anomalous slight increase for the 8-channel design is likely due to increased complexity and more severe local losses in the manifold regions, where flow splitting and combining occur. The 5-channel design presented itself as the balanced candidate, offering near-optimal thermal performance (second-lowest max temperature) with a flow resistance 24% lower than the 3-channel design and avoiding the diminishing thermal returns and manufacturing complexity of higher channel counts.
We therefore selected the 5-channel cold plate for further parametric optimization, with the singular goal of minimizing flow resistance without compromising its proven cooling efficacy. The optimization variables were the geometric dimensions of the flow distribution manifolds—the spaces between channel turns, labeled X1 through X6. These regions are primary contributors to local pressure losses due to sudden expansions, contractions, and vortices. To reduce computational cost for the optimization loop, we created a simplified yet physically representative model: the battery pack was replaced by a constant heat flux boundary condition on the top surface of the cold plate, equivalent to the total heat generation of the pack. The objective function was to minimize flow resistance (Y2=$\Delta P$), with a constraint that the average coolant outlet temperature (Y1=$T_{out,avg}$) did not exceed 29.5°C, ensuring cooling capacity was preserved.
The optimization workflow integrated several advanced engineering methodologies. A space-filling Latin Hypercube Sampling (LHS) design was used to generate 43 design points within the defined variable bounds (20-60 mm). For each point, a CFD simulation was performed to obtain the response values (Y1, Y2). A Response Surface Methodology (RSM) meta-model was then constructed to approximate the functional relationship between the design variables (X) and the responses (Y). The accuracy of these surrogate models was validated using the coefficient of determination R²:
$$ R^2 = 1 – \frac{\sum_{i=1}^{n} (y_i – \hat{y}_i)^2}{\sum_{i=1}^{n} (y_i – \bar{y})^2} $$
Where $y_i$ is the actual simulation value, $\hat{y}_i$ is the meta-model predicted value, and $\bar{y}$ is the mean of actual values. The models for pressure drop and outlet temperature achieved excellent R² values of 0.988 and 0.911, respectively, confirming their fidelity.
Finally, the Non-dominated Sorting Genetic Algorithm II (NSGA-II), a powerful multi-objective evolutionary algorithm, was employed to search the design space. NSGA-II excels at finding a Pareto-optimal frontier—a set of solutions where no objective can be improved without worsening another. It uses non-dominated sorting and a crowding distance metric to maintain population diversity. The crowding distance $idistance$ for solution $i$ is calculated as:
$$ idistance = \sum_{k=1}^{m} \frac{z_k(i+1) – z_k(i-1)}{z_k^{max} – z_k^{min}} $$
Where $m$ is the number of objectives, and $z_k$ is the objective function value. This process efficiently navigated the complex, nonlinear design space defined by the RSM models.
The optimization algorithm converged on an optimal geometry characterized by enlarged, crescent-shaped manifold regions. The final dimensions were: X1=54 mm, X2=44 mm, X3=52 mm, X4=52 mm, X5=56 mm, X6=60 mm. A subsequent full CFD simulation of the complete battery pack with this optimized cold plate confirmed the results. The flow resistance was dramatically reduced from the original 1101 Pa to 640.6 Pa—a reduction of 41.8%. This translates directly to a potential for significantly lower pumping power and higher system efficiency. Crucially, the thermal performance was unaffected: the maximum energy storage cell temperature remained at 38.4°C, and the critical maximum temperature difference between cells was unchanged at 2.1°C. Examination of the flow field revealed the reason for the hydraulic improvement: the enlarged manifolds smoothed the flow, reducing flow velocities and eliminating aggressive vortices in the turning regions, thereby curtailing local pressure losses.
In conclusion, this systematic study underscores several key principles for designing liquid cooling systems for large-scale energy storage battery packs. First, for serpentine-style plates, the number of parallel channels has a minimal impact on the ultimate cooling performance and temperature uniformity of a large, dense pack, provided the overall serpentine flow path is maintained. The primary thermal challenge is adequately removing the total heat load, which all configurations achieved. Second, hydraulic efficiency is profoundly sensitive to channel count and manifold geometry. Optimizing manifold design is a highly effective lever for reducing system energy consumption without sacrificing cooling performance. The successful 41.8% reduction in pressure drop via geometric optimization highlights this potential. Third, a balanced design approach is essential. The 5-channel optimized cold plate represents a pragmatic optimum, offering robust thermal management for the energy storage cells, excellent temperature uniformity, substantially reduced flow resistance, and relative ease of manufacturing compared to more complex biomimetic or topology-optimized structures. This work provides a validated, practical framework for the thermal-hydraulic co-design of efficient and reliable liquid cooling solutions, contributing to the safer and more sustainable deployment of large-capacity energy storage systems vital for the global energy transition.