Efficient thermal management is a critical pillar for the safety, performance, and longevity of large-scale energy storage systems. The operational temperature range for a typical lithium-ion energy storage cell is strictly between 20°C and 40°C, with a maximum allowable temperature difference among cells of 5°C to prevent accelerated aging and potential thermal runaway. To address this challenge for a commercially relevant 43 kWh battery pack comprising 48 large-format cells, this work presents a systematic investigation into the design and optimization of a multi-channel serpentine liquid cooling plate. The core objective is to maintain the temperature of every energy storage cell within the ideal window while simultaneously minimizing the pumping power required by the cooling system through flow resistance reduction.
1. Mathematical and Geometrical Foundation
1.1 Governing Mathematical Models
The analysis is built upon fundamental principles of fluid mechanics and heat transfer, which govern the cooling plate’s performance.
1.1.1 Flow Resistance Model
The total pressure drop \(\Delta P_{total}\) across the cooling plate is the sum of frictional (major) losses along the channel length and local (minor) losses due to geometrical changes like bends, expansions, and contractions.
Major Loss (Darcy-Weisbach Equation):
The pressure drop due to wall friction in a channel of constant cross-section is given by:
$$\Delta P_{\lambda} = \lambda \frac{l}{d_h} \cdot \frac{\rho v^2}{2}$$
where \(\lambda\) is the Darcy friction factor (dependent on flow regime and channel roughness), \(l\) is the channel length, \(d_h\) is the hydraulic diameter, \(\rho\) is the coolant density, and \(v\) is the average flow velocity.
Minor Loss:
The pressure drop from local disturbances is expressed as:
$$\Delta P_{\zeta} = \zeta \frac{\rho v^2}{2}$$
where \(\zeta\) is the local loss coefficient, specific to the geometry of the disturbance (e.g., a sharp turn or sudden contraction).
1.1.2 Heat Transfer Model
Heat transfer from the energy storage cell to the coolant involves two primary modes: conduction through the solid plate and convection to the flowing liquid.
Conduction (Fourier’s Law):
The heat flux through the solid cooling plate contacting the energy storage cell is:
$$\Phi_{cond} = -\lambda_s A \frac{dT}{dx}$$
where \(\lambda_s\) is the thermal conductivity of the plate material, \(A\) is the contact area, and \(dT/dx\) is the temperature gradient.
Convection (Newton’s Law of Cooling):
The heat removed by the coolant is:
$$\Phi_{conv} = h A_s (T_w – T_f)$$
where \(h\) is the convective heat transfer coefficient, \(A_s\) is the internal wetted surface area, \(T_w\) is the channel wall temperature, and \(T_f\) is the local coolant bulk temperature.
The convective coefficient \(h\) is crucial and is correlated with flow conditions via the Nusselt number \(Nu\):
$$h = \frac{\lambda_l Nu}{d_h}$$
where \(\lambda_l\) is the thermal conductivity of the coolant. For turbulent flow within the channels, which is typical for effective cooling, the Gnielinski correlation provides a highly accurate prediction for \(Nu\):
$$Nu = \frac{(f/8)(Re – 1000)Pr}{1 + 12.7(f/8)^{1/2}(Pr^{2/3} – 1)} \left[1 + \left(\frac{d_h}{l}\right)^{2/3}\right]$$
where \(Pr\) is the Prandtl number of the coolant, and \(f\) is the Darcy friction factor, often calculated using the Konakov correlation for smooth tubes:
$$f = (1.8\log_{10}Re – 1.5)^{-2}$$
The Reynolds number \(Re\), defining the flow regime, is:
$$Re = \frac{\rho v d_h}{\mu}$$
where \(\mu\) is the dynamic viscosity of the coolant.
1.2 Geometrical Model Development
1.2.1 Battery Pack Assembly
The study focuses on a practical energy storage battery pack module. Each energy storage cell is a large-format 280 Ah Lithium Iron Phosphate (LFP) cell. The key thermal properties of this energy storage cell are anisotropic due to its layered electrode construction, significantly impacting heat spreading. The relevant parameters are summarized below.
| Parameter | Value | Unit |
|---|---|---|
| Nominal Capacity | 280 | Ah |
| Internal Resistance | 0.22 | mΩ |
| Dimensions (x, y, z) | 173 × 208 × 72 | mm |
| Density | 2219 | kg/m³ |
| Specific Heat Capacity | 1000 | J/(kg·K) |
| Thermal Conductivity (x, y, z) | 2.5, 12, 12 | W/(m·K) |
| Max. Continuous Discharge Rate | 1C | – |
The full pack consists of two modules, each with 24 such energy storage cells, totaling 48 cells. For simulation efficiency, the model is simplified to include only the essential thermal masses: the 48 energy storage cells and the cooling plate, bonded together with thermal interface material.
1.2.2 Serpentine Cooling Plate Design Variants
A parallel multi-channel serpentine configuration is proposed. Its key feature is the inclusion of inlet and outlet manifolds (converging/diverging zones) at both ends of the plate, allowing all flow channels to be interconnected in a single, continuous “M”-shaped serpentine path. This design places both coolant ports on the same side, simplifying plumbing in a packed battery enclosure. To investigate the influence of channel count, six distinct designs with 3, 4, 5, 6, 7, and 8 parallel channels were created. The basic channel width and depth were held constant at 20 mm and 6 mm, respectively, across all designs to ensure a consistent comparative baseline. The primary variable was the number of parallel channels splitting the total coolant flow.
2. Cooling Performance Analysis of Design Variants
2.1 Numerical Methodology and Setup
Computational Fluid Dynamics (CFD) simulations were performed using a finite volume-based solver. The energy storage cell was modeled as a volumetric heat source with a uniform heat generation rate of 17 W per cell, corresponding to a 1C discharge rate for the 280 Ah energy storage cell. The coolant was water-glycol, with an inlet temperature of 25°C and a fixed mass flow rate of 0.05 kg/s. The outlet boundary was set to a zero-static-pressure condition. The external surfaces of the battery pack were subject to a natural convection boundary condition with a heat transfer coefficient of 5 W/(m²·K).
A poly-hexcore meshing strategy was employed to efficiently capture the thin cooling plate geometry and the larger energy storage cell volumes. A rigorous grid independence study was conducted, as summarized below, leading to the selection of a mesh with approximately 18 million elements, ensuring solution accuracy was not compromised by discretization.
| Mesh Case | Number of Elements | Battery Pack Maximum Temperature (°C) |
|---|---|---|
| Coarse | ~4.26 million | 38.6 |
| Medium 1 | ~13.68 million | 38.4 |
| Medium 2 | ~16.30 million | 38.2 |
| Selected | ~17.97 million | 38.1 |
| Fine | ~19.56 million | 38.1 |
2.2 Comparative Results and Discussion
The simulations for all six cooling plate designs yielded several key findings regarding thermal performance and hydraulic characteristics.
2.2.1 Thermal Performance: Temperature Control
All six cooling plate designs successfully maintained the temperature of every energy storage cell within the safe operating limit. The results, consolidated in the table below, reveal a critical insight: the number of flow channels has a remarkably negligible impact on the overall cooling effectiveness.
| Number of Channels | Pack Max. Temp. T_max (°C) | Pack Avg. Temp. T_avg (°C) | Max. Cell-to-Cell ΔT (°C) |
|---|---|---|---|
| 3 | 38.55 | 34.33 | 2.13 |
| 4 | 38.60 | 34.37 | 2.12 |
| 5 | 38.45 | 34.28 | 2.11 |
| 6 | 38.35 | 34.22 | 2.11 |
| 7 | 38.30 | 34.18 | 2.10 |
| 8 | 38.25 | 34.14 | 2.10 |
The maximum temperature varied within a band of only 0.35°C, and the average temperature within 0.23°C. The maximum temperature difference between any two energy storage cells remained consistently around 2.1°C, well below the 5°C threshold. This consistency stems from two competing effects: designs with fewer channels have higher coolant velocity (increasing \(h\)), but smaller total contact area (\(A_s\) in \(\Phi_{conv}=hA_s\Delta T\)). Designs with more channels have lower velocity but larger area. For this specific geometry and operating condition, these effects nearly cancel each other out from a net heat removal perspective. The serpentine path ensures a long flow length, promoting temperature uniformity among energy storage cells along the flow path.
2.2.2 Hydraulic Performance: Flow Resistance
In stark contrast to the thermal results, the hydraulic performance showed a strong and clear dependence on the channel count. The total pressure drop across the cooling plate decreased significantly as the number of parallel channels increased.
| Number of Channels | Total Pressure Drop ΔP (Pa) | Relative Reduction vs. 3-channel |
|---|---|---|
| 3 | 1512.4 | 0.0% |
| 4 | 1308.7 | -13.5% |
| 5 | 1101.0 | -27.2% |
| 6 | 985.3 | -34.9% |
| 7 | 915.8 | -39.5% |
| 8 | 1058.1* | -30.0% |
*Note: The 8-channel design shows a slight increase from the 7-channel trend, likely due to more complex local losses in the compact manifold.
This trend is directly explained by the flow resistance equations. The total mass flow rate is constant. Increasing the number of channels \(N\) reduces the flow rate per channel proportionally (\( \dot{m}_{channel} = \dot{m}_{total} / N \)), leading to a lower flow velocity \(v\) in each channel. Since both major and minor losses are proportional to the square of the velocity (\(\Delta P \propto v^2\)), the pressure drop per channel decreases sharply. Although there are more channels and potentially more minor loss points, the dominant effect is the reduction in \(v^2\), leading to a net decrease in total system pressure drop. Lower pressure drop translates directly to lower pumping power requirement for the coolant circulation system, enhancing overall energy efficiency.
2.2.3 Design Selection for Optimization
Based on the analysis, the 5-channel cooling plate was selected as the optimal baseline for further geometric optimization. This choice represents a balanced compromise: its thermal performance is virtually identical to the best-performing designs (T_max ~38.45°C, ΔT ~2.1°C), while offering a substantial 27% reduction in flow resistance compared to the 3-channel design. Furthermore, from a manufacturing perspective, a 5-channel plate presents a simpler and potentially more robust structure than designs with 7 or 8 channels, which have thinner supporting ribs between channels.
3. Flow Resistance Optimization Using Advanced Algorithms
With the 5-channel configuration selected, the next phase focused on minimizing its flow resistance without degrading its excellent thermal performance. The strategy was to optimize the geometry of the inlet/outlet manifold regions, where flow separation and recirculation were identified as major contributors to local (minor) pressure losses.
3.1 Optimization Framework Setup
A simulation-driven optimization workflow was implemented using integrated software tools. The goal was a multi-objective optimization: Minimize Flow Resistance (\(\Delta P\)) while Constraining Thermal Performance (Coolant Outlet Temperature, \(T_{out}\)).
Design Variables (X1-X6): Six key dimensions defining the manifold and channel transition zones were chosen as variables. These parameters control the smoothness of flow expansion and contraction, influencing the local loss coefficients \(\zeta\). Their bounds were set based on spatial constraints.
Objective & Constraint:
– Objective: Minimize \(Y_2 = \Delta P\) (Total Pressure Drop).
– Constraint: \(Y_1 = T_{out} \leq 29.5^\circ C\) (Ensuring cooling capacity is not compromised).
A simplified CFD model, replacing the energy storage cells with a constant heat flux boundary condition equivalent to the total pack heat load, was used for rapid evaluation within the optimization loop.
Process:
1. Design of Experiments (DOE): A Latin Hypercube Sampling (LHS) method was used to generate 43 spatially well-distributed sample points within the 6-dimensional design space. This provides a high-quality dataset for model building.
2. Surrogate Model Construction: A Response Surface Methodology (RSM) model, specifically a quadratic model with cross-terms, was fitted to the DOE data. This creates a fast mathematical approximation (metamodel) of the complex, computationally expensive CFD simulations.
The accuracy of the surrogate models was high, as indicated by their coefficients of determination:
– For \(T_{out}\) (\(Y_1\)): \(R^2 = 0.91064\)
– For \(\Delta P\) (\(Y_2\)): \(R^2 = 0.98779\)
3. Optimization Algorithm: The Non-dominated Sorting Genetic Algorithm II (NSGA-II) was employed on the surrogate models. NSGA-II is a powerful multi-objective evolutionary algorithm effective at finding a Pareto-optimal front—a set of solutions where no objective can be improved without worsening another. The crowding distance calculation in NSGA-II, which helps maintain diversity among solutions, is given by:
$$I_{distance}(i) = \sum_{k=1}^{m} \frac{z_k(i+1) – z_k(i-1)}{z_k^{max} – z_k^{min}}$$
where for solution \(i\), \(z_k(i)\) is its value for the \(k\)-th objective, and \(z_k^{max}\) and \(z_k^{min}\) are the maximum and minimum values for that objective in the population.
3.2 Optimization Results and Validation
The NSGA-II algorithm successfully identified an optimized set of geometry parameters from the Pareto front that prioritized flow resistance reduction. The optimized design featured enlarged and smoother transition zones in the manifolds.
Performance Improvement:
– Predicted by Surrogate Model: \(\Delta P_{opt} = 590.9 \, \text{Pa}\)
– Validated by Full CFD Simulation: \(\Delta P_{CFD} = 640.6 \, \text{Pa}\)
The discrepancy (~7.8%) is within an acceptable range for engineering optimization using surrogate models. This represents a dramatic 41.8% reduction in flow resistance compared to the original 5-channel baseline (1101 Pa).
A final, full-scale CFD simulation of the complete battery pack (with all 48 energy storage cells modeled) was conducted to conclusively verify that the thermal management performance was preserved. The results confirmed success:
| Metric | Original 5-Channel Design | Optimized 5-Channel Design | Change |
|---|---|---|---|
| Flow Resistance, ΔP | 1101.0 Pa | 640.6 Pa | -41.8% |
| Pack Maximum Temperature | 38.45 °C | 38.40 °C | -0.05 °C |
| Pack Average Temperature | 34.28 °C | 34.25 °C | -0.03 °C |
| Max. Cell-to-Cell ΔT | 2.11 °C | 2.10 °C | -0.01 °C |
The optimized cooling plate successfully maintains the temperature of every energy storage cell well within the safe zone (max < 39°C, ΔT ~2.1°C) while requiring significantly less pumping power. Flow field analysis confirmed that the optimization successfully reduced the size and intensity of vortices in the manifold regions, leading to the lower pressure losses.
4. Conclusions
This comprehensive study on the thermal management of a large-scale energy storage battery pack through serpentine liquid cooling plates yields several significant conclusions for engineering design:
- Channel Count vs. Thermal Performance: For the parallel multi-channel serpentine design with a fixed total coolant flow rate, the number of channels has a minimal impact on the pack’s thermal state. All designs from 3 to 8 channels maintained the maximum temperature of the energy storage cells below 39°C and the cell-to-cell temperature difference at approximately 2.1°C. The competing effects of convective coefficient and heat transfer area balance each other in this configuration.
- Channel Count vs. Hydraulic Performance: Flow resistance is highly sensitive to channel count. Increasing the number of parallel channels reduces the flow velocity per channel, leading to a quadratic reduction in pressure drop. This is a primary lever for improving the energy efficiency of the thermal management system.
- Design Trade-off and Selection: The 5-channel design was identified as a balanced choice, offering excellent cooling performance (on par with designs having more channels) coupled with substantially lower flow resistance than designs with fewer channels, and without the increased manufacturing complexity of higher channel counts.
- Effectiveness of Shape Optimization: Strategic optimization of the manifold and transition zone geometries is a highly effective method for reducing flow resistance. Using a surrogate-model-based approach with the NSGA-II algorithm, the pressure drop of the selected 5-channel plate was reduced by 41.8% (from 1101 Pa to 640.6 Pa) without any compromise in its ability to keep the energy storage cell temperatures within the optimal operating range.
This work demonstrates a practical and effective design optimization pathway for liquid cooling systems in large-format energy storage battery packs. The methodology balances high-fidelity simulation with efficient optimization algorithms to achieve a system that ensures both the thermal safety of the energy storage cell and the operational efficiency of the cooling system itself.