In the pursuit of greener maritime transportation, all-electric ships have emerged as a pivotal technology, often conceptualized as “floating microgrids.” At the heart of these systems lies the cell energy storage system, predominantly composed of lithium-ion batteries, which ensures power quality and operational reliability by mitigating load fluctuations. However, the inherent heat generation during charge-discharge cycles poses significant thermal management challenges. In the confined, enclosed spaces typical of ships, effective heat dissipation from the cell energy storage system is critical not only for performance and longevity but also for preventing thermal runaway and ensuring vessel safety. This study focuses on the thermal design of a shipboard cell energy storage system, employing Icepak software to numerically simulate and evaluate two primary cooling strategies: air-based and liquid-based systems. By analyzing the impact of key design parameters on temperature distribution and uniformity, we aim to provide foundational insights for selecting and optimizing thermal management solutions for maritime cell energy storage systems.
The core of our analysis begins with establishing a mathematical model for heat transfer within the cell energy storage system. For a single lithium iron phosphate (LiFePO₄) cell, the three-dimensional heat conduction governing equation, derived from energy conservation and Fourier’s law, is expressed in Cartesian coordinates as:
$$ \rho c \frac{\partial T}{\partial t} = \nabla \cdot (\lambda \nabla T) + \dot{Q} $$
where \( \rho \) is density, \( c \) is specific heat, \( \lambda \) is thermal conductivity tensor, \( T \) is temperature, \( t \) is time, and \( \dot{Q} \) is the volumetric heat generation rate. For the fluid domains involved in both cooling methods, the coupled fluid flow and heat transfer are governed by the conservation equations for mass, momentum, and energy. The continuity, momentum (Navier-Stokes), and energy equations for incompressible flow are given respectively:
$$ \frac{\partial \rho_f}{\partial t} + \nabla \cdot (\rho_f \mathbf{U}) = 0 $$
$$ \frac{\partial \mathbf{U}}{\partial t} + (\mathbf{U} \cdot \nabla) \mathbf{U} = \mathbf{F} – \frac{1}{\rho_f} \nabla p + \nu \nabla^2 \mathbf{U} $$
$$ \frac{\partial (\rho_f T)}{\partial t} + \nabla \cdot (\rho_f \mathbf{U} T) = \nabla \cdot \left( \frac{\lambda_f}{c_{p,f}} \nabla T \right) + S_T $$
Here, \( \rho_f \) is fluid density, \( \mathbf{U} \) is velocity vector, \( p \) is pressure, \( \nu \) is kinematic viscosity, \( \lambda_f \) is fluid thermal conductivity, \( c_{p,f} \) is fluid specific heat, and \( S_T \) encompasses heat sources. The cell energy storage system’s thermal behavior is simulated by solving these coupled equations within the Icepak environment.
The physical cell energy storage system under investigation is constructed from a commercial 3.2V/12.8Ah LiFePO₄ prismatic cell. Ten such cells are connected in parallel to form a module, and sixteen identical modules are connected in series to constitute the complete battery pack for the shipboard application.
The thermal properties of the cell components are essential inputs for an accurate simulation. We summarize these material properties in the following table:
| Component | Material | Density, ρ (kg/m³) | Specific Heat, c (J/(kg·K)) | Thermal Conductivity, λ (W/(m·K)) |
|---|---|---|---|---|
| Core | Composite | 2194 | 1083.75 | Anisotropic: λ_x=0.91, λ_y=λ_z=2.69 |
| Case | Polyethylene | 962 | 1956 | 0.35 |
| Positive Tab | Aluminum | 2700 | 880 | 237 |
| Negative Tab | Copper | 8960 | 390 | 386 |
The internal heat generation rate \( \dot{Q} \) for a single cell under a 1C continuous discharge rate is calculated using the Bernardi model, which assumes uniform heat generation within the cell core:
$$ \dot{Q} = \frac{I}{V_b} \left[ I R_{int} + T \frac{dE_0}{dT} \right] $$
Where \( I = 12.8 \, \text{A} \) is the discharge current, \( V_b = 2.7125 \times 10^{-4} \, \text{m}^3 \) is the cell volume, \( R_{int} = 5.05 \, \text{mΩ} \) is the internal resistance, and \( \frac{dE_0}{dT} = 0.5 \, \text{mV/K} \) is the entropic coefficient. This yields a volumetric heat generation rate of approximately 9964 W/m³, which is applied to the cell core domain in our simulations for the entire cell energy storage system.
We first designed a forced air cooling system for the cell energy storage system. The battery pack is housed in an enclosure with an axial fan installed at the bottom center to draw in ambient air (20°C), while exhaust vents are positioned at the top. The initial design featured a single fan with a radius of 7.5 cm and an inlet air velocity of 5 m/s. A hybrid meshing strategy in Icepak resulted in a computational grid of over 530,000 cells, balancing accuracy and efficiency. The steady-state simulation for the 1C discharge scenario revealed a highly non-uniform temperature field. The maximum temperature within the cell energy storage system reached 64.27°C, located in the peripheral modules, while the minimum was 37.88°C near the fan inlet, resulting in a maximum temperature difference (\(\Delta T_{max}\)) exceeding 25°C. This performance is unacceptable for a reliable cell energy storage system, which typically requires a maximum temperature below 50°C and a \(\Delta T_{max}\) under 5°C among modules.
To improve the air cooling performance for the cell energy storage system, we systematically investigated the effects of three key parameters: inlet air velocity, fan radius, and the number of fans. The results are consolidated in the table below.
| Case Description | Inlet Velocity (m/s) | Fan Radius (cm) | Number of Fans | Max. Temp. (°C) | Min. Temp. (°C) | \(\Delta T_{max}\) (°C) |
|---|---|---|---|---|---|---|
| Baseline Design | 5 | 7.5 | 1 | 64.27 | 37.88 | |
| Increased Velocity | 15 | 7.5 | 1 | 48.22 | 29.77 | |
| Increased Radius | 15 | 10 | 1 | 43.33 | 28.36 | |
| Increased Fan Count | 15 | 10 | 3 | 33.94 | 27.45 |
The analysis clearly shows that merely increasing the airflow velocity or the fan radius reduces the overall temperature of the cell energy storage system but fails to adequately address temperature uniformity. The modules farthest from the single fan inlet remain significantly hotter. Only by distributing the cooling effort using three fans could we achieve a \(\Delta T_{max}\) of about 6°C, bringing the cell energy storage system closer to acceptable operational limits, though still slightly above the ideal 5°C threshold. The governing heat removal rate in such a system can be approximated by Newton’s law of cooling:
$$ \dot{q}_{air} = h A (T_{surface} – T_{air}) $$
where \( h \) is the convective heat transfer coefficient, which increases with airflow velocity, explaining the observed temperature reduction. However, achieving uniform \( h \) across all modules in a complex geometry is challenging with a simple single-inlet design.
We then designed an indirect liquid cooling system for the same cell energy storage system. This system utilizes aluminum cold plates with an S-shaped channel and high-density fins, placed beneath each battery module. The heat from the cells conducts into the cold plate and is carried away by circulating coolant (water). The initial simulation conditions were set with coolant inlet velocity of 1 m/s and temperature of 20°C. The steady-state temperature distribution demonstrated superior performance compared to air cooling. The maximum temperature of the cell energy storage system was limited to 26.69°C, and the minimum was 21.46°C, resulting in a \(\Delta T_{max}\) of 5.23°C. The temperature gradient followed the coolant flow path, with cooler modules near the inlet.
We proceeded to evaluate the sensitivity of the liquid-cooled cell energy storage system to coolant flow velocity and inlet temperature. The following table summarizes the findings:
| Parameter Variation | Coolant Velocity (m/s) | Inlet Temp. (°C) | Max. Temp. (°C) | Min. Temp. (°C) | \(\Delta T_{max}\) (°C) |
|---|---|---|---|---|---|
| Baseline Liquid Cooling | 1.0 | 20 | 26.69 | 21.46 | 5.23 |
| Increased Velocity | 1.5 | 20 | 24.85 | 20.89 | 3.96 |
| Further Increased Velocity | 2.0 | 20 | 23.77 | 20.61 | 3.16 |
| Reduced Inlet Temperature | 1.0 | 15 | 21.69 | 16.46 | 5.23 |
The data indicates that increasing the coolant flow rate effectively lowers both the maximum temperature and the temperature spread within the cell energy storage system. This is because higher flow rates reduce the coolant temperature rise along the channel, promoting more uniform cooling. The relationship can be linked to the energy balance for the coolant stream:
$$ \dot{m} c_{p,c} (T_{out} – T_{in}) = \dot{Q}_{total} $$
where \( \dot{m} \) is the mass flow rate, \( c_{p,c} \) is coolant specific heat, and \( \dot{Q}_{total} \) is the total heat dissipated from the cell energy storage system. A higher \( \dot{m} \) results in a smaller \( (T_{out} – T_{in}) \), leading to a lower and more uniform cold plate temperature. Conversely, lowering the inlet temperature from 20°C to 15°C reduced the absolute temperature levels but did not improve the temperature uniformity (\(\Delta T_{max}\) remained ~5.23°C). This is because the uniformity is primarily governed by the flow field and thermal resistance distribution, not the absolute inlet temperature.
The comparative analysis between the two cooling methods for the shipboard cell energy storage system reveals distinct advantages and trade-offs. The liquid cooling system demonstrates significantly higher cooling efficiency and excellent temperature uniformity, easily meeting the sub-5°C \(\Delta T_{max}\) requirement with optimized flow rates. Its performance is less dependent on the internal pack geometry for airflow distribution. The heat transfer capability is fundamentally higher due to the superior thermophysical properties of water compared to air. The overall heat transfer process in the liquid system involves conduction through multiple layers and convection to the coolant, which can be modeled as a series of thermal resistances:
$$ R_{total} = R_{cond,cell} + R_{contact} + R_{cond,plate} + \frac{1}{h_{liquid} A_{channel}} $$
Minimizing \( R_{total} \) is key to enhancing performance. In contrast, the air cooling system, while simpler, cheaper, and easier to maintain, struggles with heat removal density and achieving temperature uniformity in a densely packed cell energy storage system without a sophisticated multi-fan or ducted design. Its effectiveness is highly sensitive to the arrangement of modules and the airflow path. For a maritime application where reliability, safety, and space constraints are paramount, the liquid cooling system presents a more robust solution for thermal management of the cell energy storage system, despite its increased complexity and potential corrosion concerns in a marine environment.
In conclusion, through detailed numerical simulation using Icepak, we have comprehensively analyzed the heat dissipation characteristics of a shipboard cell energy storage system under both air-cooled and liquid-cooled configurations. The liquid cooling system consistently outperforms air cooling in maintaining lower maximum temperatures and superior temperature homogeneity within the cell energy storage system. Parameter studies show that for air cooling, a combination of high airflow, large fan area, and multiple inlets is necessary to approach acceptable performance. For liquid cooling, increasing coolant flow rate is the most effective means to enhance both cooling capacity and uniformity, while lowering inlet temperature mainly reduces the absolute temperature level. The selection of an appropriate thermal management system for a maritime cell energy storage system must therefore balance cooling performance, system complexity, maintenance requirements, lifecycle cost, and marine environmental adaptability. This work provides a simulation-based framework and quantitative insights to guide the design and optimization of thermal management systems for the safe and reliable operation of cell energy storage systems in all-electric ships.