Marine decarbonization has changed the way onboard energy systems are designed. In this context, the traction battery pack has become one of the most relevant components for electric and hybrid ships. Unlike stationary storage systems, the traction battery pack experiences high discharge rates, frequent load variations and constrained installation volumes. These conditions increase heat generation and impose severe requirements on the thermal management system. During discharge, the temperature of the traction battery pack gradually increases, and the discharge performance follows the temperature change. Therefore, temperature control of the traction battery pack is essential to guarantee safety, cycle life and energy efficiency.
The present investigation was carried out from the perspective of liquid cooling, with a focus on the internal structure of a cooling plate. A bionic liquid-cooled plate was designed by combining the hexagonal pattern found in leaf veins and the branching behaviour of tree roots. The cooling performance was evaluated under the heat generation of a 16.18 kWh marine traction battery pack. Fluid flow and heat transfer were simulated using CFD. The effects of geometrical parameters, coolant velocity, coolant inlet temperature, fluid-domain thickness and heat-generation rate were examined.
1 Introduction
International regulations on greenhouse-gas emissions have accelerated the transition toward low-carbon and zero-carbon ships. Electric propulsion is widely accepted as a practical alternative to conventional internal-combustion engines. Compared with diesel-powered vessels, electric vessels reduce CO2, NOx and particulate emissions in port areas. They also generate less noise and vibration, which is beneficial for underwater ecosystems. However, the traction battery pack remains the bottleneck that determines the reliability and cost of an electric vessel because its electrochemical performance strongly depends on operating temperature.
Lithium-ion batteries suffer from capacity degradation and safety hazards when they are operated outside the recommended temperature range. Previous studies indicate that the optimal operating window for a lithium-ion traction battery pack is roughly 25 andamp;deg;C to 40 andamp;deg;C, while the temperature difference inside the module should be kept below 5 andamp;deg;C. If the battery is overheated, solid-electrolyte interphase decomposition, electrolyte oxidation and internal short circuit can occur, leading to thermal runaway. Thermal runaway events have been reported in consumer electronics, electric vehicles, cargo aircraft and marine installations. These events are caused by mechanical abuse, electrical abuse or thermal abuse. Mechanical abuse usually triggers an internal short circuit, and electrical abuse, such as overcharging, also releases heat. When the heat is not dissipated fast enough, the temperature of the traction battery pack rises and accelerates cell degradation.
Several thermal management technologies for the traction battery pack have been studied in the literature: air cooling, phase-change-material cooling, immersion cooling and indirect liquid cooling. Air cooling is attractive because of its simple structure and low cost, but its heat-transfer coefficient is limited. Phase-change materials absorb heat during melting, but their long-term stability, leakage and low thermal conductivity are problematic. Immersion cooling offers very high heat-transfer performance, but its implementation requires careful management of dielectric fluids and sealing systems. Indirect liquid cooling is a good compromise because the liquid coolant has a high heat-transfer coefficient and the cold plate can be integrated directly with the battery module.
In indirect liquid cooling, the channel layout inside the cold plate determines the temperature distribution, maximum temperature and pressure drop of the whole system. Different channel designs have been proposed, such as straight channels, serpentine channels, fractal channels and bionic channels. Many studies improve the cooling effect by increasing the contact area between the coolant and the heated surface. However, the pressure drop is not always reported. Since pressure drop determines the pump head, a cooling plate with excessive pressure drop consumes more parasitic energy and reduces the overall efficiency of the marine traction battery pack. Therefore, this research does not merely aim to decrease the maximum temperature. It also attempts to reduce the pressure drop so that the cooling system can achieve better performance with less energy.
2 Physical model and numerical method
2.1 Geometry and design concept
The bionic liquid-cooled plate was inspired by two natural structures. First, the leaf vein of a dicotyledonous leaf contains a network of small hexagonal meshes. The honeycomb-like mesh distributes water and nutrients efficiently across the whole leaf blade. Second, the root system of a tree divides repeatedly and distributes fluid through a hierarchical network. When a coolant enters the cooling plate, it encounters hexagonal obstacles. The coolant is split, redirected and merged in a manner similar to water travelling through tree roots. This flow path creates repeated boundary-layer interruption and redevelopment, which is beneficial for convective heat transfer. In the present design, the region containing the hexagonal obstacles is called the enhanced heat-transfer region, while the rest of the plate is treated as a normal heat-transfer region.
The total dimensions of the cooling plate are 773 mm andtimes; 634 mm andtimes; 6 mm. The inlet height is 2 mm and the inlet width is 32 mm. The fluid-domain thickness is equal to the inlet height unless stated otherwise. The material of the cooling plate is aluminium. Water is used as the coolant because it has high specific heat and thermal conductivity. The heat source is the bottom face of the cell stack, represented by a constant heat flux of 785 W/m2, which corresponds to the measured heat release of a 16.18 kWh marine traction battery pack during continuous discharge. Geometrical parameters describing the internal layout are defined as follows: a is the size of each hexagon, b is the transverse distance between two adjacent hexagons, c is the longitudinal distance between two adjacent hexagons, and d is the distance between the hexagon and the outlet. These four parameters determine the performance of the bionic cooling plate.
2.2 Governing equations
In this numerical simulation, the flow is assumed steady, incompressible and laminar. The corresponding Reynolds number at the inlet is about 680, so a laminar viscosity model is appropriate. Gravity, viscous dissipation and thermal radiation are neglected. Thermophysical properties of the aluminium and water are considered constant.
The governing equations are the conservation of mass, momentum and energy. For an incompressible steady flow, the continuity equation can be expressed as
$$ \frac{\partial u_x}{\partial x} + \frac{\partial u_y}{\partial y} + \frac{\partial u_z}{\partial z} = 0 \tag{1} $$
where \(u_x\), \(u_y\) and \(u_z\) are the velocity components in the Cartesian coordinates.
The momentum equations are given by the Navier–Stokes equation:
$$ \rho \left( u_x \frac{\partial \mathbf{u}}{\partial x} + u_y \frac{\partial \mathbf{u}}{\partial y} + u_z \frac{\partial \mathbf{u}}{\partial z} \right) = -\nabla p + \mu \nabla^2 \mathbf{u} \tag{2} $$
where \(p\) is the pressure, \(\rho\) is the density and \(\mu\) is the dynamic viscosity.
The energy equation is:
$$ \rho c_p \left( u_x \frac{\partial T}{\partial x} + u_y \frac{\partial T}{\partial y} + u_z \frac{\partial T}{\partial z} \right) = \lambda \nabla^2 T \tag{3} $$
where \(c_p\) is the specific heat and \(\lambda\) is the thermal conductivity. The Reynolds number is calculated as:
$$ Re = \frac{\rho V d_h}{\mu} \tag{4} $$
where \(V\) is the average inlet velocity and \(d_h\) is the hydraulic diameter of the inlet channel. The hydraulic diameter is calculated from the inlet height and width.
2.3 Boundary conditions
The boundary conditions were set as follows. The inlet is a velocity inlet with a temperature of 30 andamp;deg;C and a velocity of 0.2 m/s, unless the effect of the inlet condition is being studied. The outlet is a pressure outlet at atmospheric pressure. The upper plate surface is a constant heat-flux boundary. All other external surfaces are adiabatic. The inlet temperature is the same as the coolant temperature at the inlet. The initial temperature of the whole computational domain is 30 andamp;deg;C.
The thermophysical properties adopted in the simulation are listed in Table 1.
| Item | Material | Density (kg/m3) | Dynamic viscosity (kg/(m s)) | Thermal conductivity (W/(m K)) | Specific heat (J/(kg K)) |
|---|---|---|---|---|---|
| Coolant | Water | 998.2 | 0.001003 | 0.6 | 4182 |
| Solid plate | Aluminium | 2719 | — | 1555 | 3485 |
2.4 Numerical algorithm and discretisation
The commercial CFD solver ANSYS Fluent was used to solve the governing equations. The pressure-based solver was selected because the coolant velocity is low and the flow can be regarded as incompressible. The pressure–velocity coupling was treated with the coupled algorithm. The pressure and momentum equations were discretised with a second-order upwind scheme. The energy equation was also discretised with a second-order upwind scheme. Convergence was monitored by examining the residuals of continuity, momentum and energy equations. The convergence criterion was set to 1 andtimes; 10-5 for the continuity and momentum equations and 1 andtimes; 10-8 for the energy equation.
3 Mesh and validation
3.1 Mesh generation
Structured hexahedral meshes were generated with ICEM CFD. The computational domain was divided into blocks so that a smooth hexahedral mesh could be obtained in the complex hexagonal channels. After two-dimensional blocking, the mesh was extruded in the thickness direction to produce a three-dimensional hexahedral mesh. More than 88% of the cells have a quality greater than 0.9. The mesh quality is considered sufficient for accurate numerical simulation.
To eliminate the dependence of the numerical results on cell number, five different mesh densities were tested. Table 2 summarises the mesh independence study. When the cell count is increased from about 0.99 million to 9.55 million, the maximum temperature decreases gradually and the pressure drop increases gradually. However, the variation becomes very small when the cell count is larger than about 4.74 million. Further refinement changes the maximum temperature by less than 0.2 andamp;deg;C and the pressure drop by an almost negligible amount. Therefore, the mesh with 4,740,770 cells was selected as the baseline mesh for the rest of this study.
| Mesh number | Maximum temperature (andamp;deg;C) | Pressure drop (Pa) |
|---|---|---|
| 987,282 | Reference + 0.54 | Reference − 12.4 |
| 2,157,634 | Reference + 0.31 | Reference − 5.6 |
| 3,896,452 | Reference + 0.12 | Reference − 2.1 |
| 4,740,770 | Baseline | Baseline |
| 9,548,515 | Baseline − 0.08 | Baseline + 0.7 |
3.2 Model validation
To verify the numerical model, a separate liquid-cooled plate with a known experimental configuration was simulated under exactly the same operating conditions as those reported in the published experimental study. The validation plate has the same overall size, the same channel thickness and a similar channel pattern. A constant heat flux of 3412 W/m2 was applied to the heating surface, and the inlet temperature was fixed at 25 andamp;deg;C. The inlet mass flow rate was varied from 0.5 g/s to 2.0 g/s. The simulated maximum temperatures were compared with the measured temperatures. The relative error in all cases is below 5%. This confirms that the present numerical model and method are sufficiently accurate for the investigation of the bionic liquid-cooled plate used in the marine traction battery pack.
4 Effect of external parameters
4.1 Fluid-domain thickness
The total thickness of the cooling plate is fixed in the actual battery module. If the fluid-domain thickness is changed, the upper and lower aluminium layers also change. The fluid-domain thickness influences both the heat conduction path and the coolant mass flow rate. In the same inlet velocity and temperature condition, four fluid-domain thicknesses were compared: 1 mm, 2 mm, 3 mm and 4 mm.
The results are shown qualitatively in Table 3. As the fluid-domain thickness increases, the maximum temperature first decreases and then increases. When the thickness is increased from 1 mm to 2 mm, the mass flow rate doubles, which strengthens convective heat transfer and reduces the maximum temperature. When the thickness is increased further to 3 mm and 4 mm, the additional coolant does not compensate for the increased thermal resistance caused by the thinner aluminium face sheets. Therefore, the lowest maximum temperature appears at a fluid-domain thickness of 2 mm. The pressure drop decreases monotonically with increasing thickness because the hydraulic diameter is enlarged and the flow resistance is reduced. The reduction becomes slower as the thickness grows. A fluid-domain thickness of 2 mm was selected as the baseline because it offers the best temperature control and also maintains enough aluminium thickness for structural stability.
| Fluid-domain thickness (mm) | Maximum temperature | Pressure drop |
|---|---|---|
| 1 | Highest | Highest |
| 2 | Lowest | Moderate |
| 3 | Intermediate | Low |
| 4 | High | Lowest |
4.2 Coolant inlet velocity
Coolant velocity is another external parameter that affects both heat transfer and pumping power. The maximum temperature of three different cooling plates was compared at velocities of 0.1 m/s, 0.15 m/s, 0.2 m/s, 0.25 m/s and 0.3 m/s. The fluid-domain thickness was fixed at 2 mm. As the velocity increases, the maximum temperature of each plate decreases. The reason is that the higher velocity increases the coolant mass flow rate and improves the convective heat-transfer coefficient. However, the temperature drop becomes less obvious beyond 0.2 m/s. At this point the thermal resistance is dominated by heat conduction in the aluminium and by the thermal boundary layer rather than by the available mass flow rate. Since pumping power increases continuously with velocity, the marginal loss is no longer justified by the small temperature reduction. Therefore, 0.2 m/s was selected as the baseline velocity for subsequent structural optimisation.
5 Orthogonal experimental design of the bionic structure
5.1 Design variables and test matrix
The internal geometry of the bionic liquid-cooled plate is controlled by four variables: hexagonal size \(a\), transverse distance \(b\), longitudinal distance \(c\), and outlet distance \(d\). A complete parametric study covering all combinations of four levels would require 256 cases. To reduce the computational cost, an orthogonal array L16(4 andtimes; 4 andtimes; 4 andtimes; 4) was used. The levels of each parameter are listed in Table 4.
| Factor | Level 1 (mm) | Level 2 (mm) | Level 3 (mm) | Level 4 (mm) |
|---|---|---|---|---|
| a: hexagonal size | 20 | 26 | 32 | 38 |
| b: transverse spacing | 8 | 12 | 16 | 20 |
| c: longitudinal spacing | 30 | 40 | 50 | 60 |
| d: outlet distance | 80 | 90 | 100 | 110 |
Sixteen different configurations were modelled with the baseline inlet velocity and coolant temperature. The maximum temperature and pressure drop obtained from each simulation are listed in Table 5. It can be seen that the maximum temperature and pressure drop have opposite tendencies in general. The case with the lowest temperature often has a relatively high pressure drop. The physical reason is that a more compact hexagonal layout creates more heat-transfer area and more flow disturbance, but it also introduces more flow resistance.
| Case | a (mm) | b (mm) | c (mm) | d (mm) | Tmax (andamp;deg;C) | Pressure drop (Pa) |
|---|---|---|---|---|---|---|
| 1 | 20 | 8 | 30 | 80 | 35.43 | 173.47 |
| 2 | 20 | 12 | 40 | 90 | 36.08 | 158.21 |
| 3 | 20 | 16 | 50 | 100 | 36.14 | 157.52 |
| 4 | 20 | 20 | 60 | 110 | 36.33 | 153.46 |
| 5 | 26 | 8 | 50 | 90 | 35.46 | 171.68 |
| 6 | 26 | 12 | 60 | 80 | 35.88 | 158.92 |
| 7 | 26 | 16 | 30 | 110 | 36.06 | 157.39 |
| 8 | 26 | 20 | 40 | 100 | 36.35 | 157.34 |
| 9 | 32 | 8 | 60 | 100 | 35.45 | 167.94 |
| 10 | 32 | 12 | 50 | 110 | 35.84 | 165.11 |
| 11 | 32 | 16 | 40 | 80 | 36.16 | 170.11 |
| 12 | 32 | 20 | 30 | 90 | 36.13 | 154.75 |
| 13 | 38 | 8 | 40 | 110 | 35.47 | 180.66 |
| 14 | 38 | 12 | 30 | 100 | 35.81 | 158.73 |
| 15 | 38 | 16 | 60 | 90 | 35.91 | 158.69 |
| 16 | 38 | 20 | 50 | 80 | 35.96 | 158.38 |
5.2 Range analysis
A range analysis was conducted to identify the significance of each structural parameter. Let \(k_i\) be the sum of the results corresponding to level \(i\) of a specific factor, and \(K_i\) be the average value of \(k_i\). The range \(R\) is defined as the maximum of \(K_i\) minus the minimum of \(K_i\):
$$ R = \max(K_1, K_2, K_3, K_4) – \min(K_1, K_2, K_3, K_4) \tag{5} $$
A larger range indicates that the corresponding factor has a more significant influence on the result. The range analysis results are presented in Table 6.
| Level statistics | Maximum temperature | Pressure drop | ||||||
|---|---|---|---|---|---|---|---|---|
| a | b | c | d | a | b | c | d | |
| K1 | 36.00 | 35.45 | 35.86 | 35.86 | 160.67 | 173.44 | 161.09 | 165.22 |
| K2 | 35.94 | 35.90 | 36.02 | 35.90 | 161.33 | 160.24 | 166.58 | 160.83 |
| K3 | 35.90 | 36.07 | 35.85 | 35.94 | 164.48 | 160.93 | 163.17 | 160.38 |
| K4 | 35.79 | 36.19 | 35.89 | 35.93 | 164.12 | 155.98 | 159.75 | 164.16 |
| R | 0.21 | 0.74 | 0.17 | 0.08 | 3.81 | 17.46 | 6.83 | 4.84 |
For the maximum temperature, the order of significance is:
$$ b > a > c > d \tag{6} $$
For the pressure drop, the order of significance is:
$$ b > c > a > d \tag{7} $$
The transverse spacing \(b\) is the dominant parameter for both objectives. This is physically reasonable because the transverse spacing controls the width of the flow passage between two adjacent hexagonal obstacles. When \(b\) is small, the coolant is accelerated in the gap and the boundary layer is repeatedly interrupted, which improves heat transfer but also increases the pressure drop. The outlet distance \(d\) has the weakest influence on both temperature and pressure drop. Based on the temperature distribution, all sixteen simulated configurations show a common characteristic: the highest temperature appears at the two corners near the outlet. This is caused by the flow direction from the inlet to the outlet; the coolant gradually warms up as it travels through the cooling plate, and the corners far away from the main flow receive less coolant.
6 Multi-objective optimisation
6.1 Regression model
Because the orthogonal test only evaluates a limited number of combinations, it is not sufficient to identify the exact optimum. A regression model was therefore constructed from the sixteen simulation results. Let \(x_1 = a\), \(x_2 = b\), \(x_3 = c\) and \(x_4 = d\). The linear regression for the pressure drop \(y_p\) is:
$$ y_p = 0.224917 x_1 – 1.292 x_2 – 0.07405 x_3 – 0.03645 x_4 + 181.0079 \tag{8} $$
The linear regression for the maximum temperature \(y_t\) is:
$$ y_t = -0.01108 x_1 + 0.059625 x_2 – 0.0006 x_3 + 0.00245 x_4 + 35.18467 \tag{9} $$
The coefficient of determination \(r^2\) is calculated as:
$$ r^2 = 1 – \sum_{i=1}^{n} \left( \frac{Z_i – Z_{i,\mathrm{CFD}}}{Z_{i,\mathrm{CFD}}} \right)^2 \tag{10} $$
The computed \(r^2\) is 0.81 for temperature and 0.63 for pressure drop. Although the pressure drop regression is not perfect, the coefficient is still acceptable for guiding the optimisation at the conceptual stage.
6.2 NSGA-II optimisation
The two objectives are conflicting because a lower maximum temperature is generally accompanied by a higher pressure drop. In order to handle both objectives simultaneously, the non-dominated sorting genetic algorithm NSGA-II was adopted. The optimisation problem is expressed as:
$$ \min F(x_1, x_2, x_3, x_4) = \begin{cases} \min f_1(x_1,x_2,x_3,x_4) \\ \min f_2(x_1,x_2,x_3,x_4) \end{cases} \tag{11} $$
subject to
$$ 20 \le x_1 \le 38, \quad 8 \le x_2 \le 20, \quad 30 \le x_3 \le 60, \quad 80 \le x_4 \le 110 \tag{12} $$
The algorithm was implemented with a population size of 50, 150 generations and a fitness tolerance of 0.0001. After the optimisation run, a Pareto front was obtained. The results show a clear trade-off between maximum temperature and pressure drop. Along the Pareto front, it is possible to reduce the maximum temperature by roughly 0.8 andamp;deg;C, but the reduction is accompanied by a pressure-drop rise of about 25 Pa.
From the Pareto front, a solution with \(a=30\) mm, \(b=8\) mm, \(c=50\) mm and \(d=90\) mm was selected. This solution gives the best balance between thermal performance and pumping power. The predicted maximum temperature is 35.49 andamp;deg;C and the predicted pressure drop is 170.08 Pa. To confirm the accuracy of the regression and optimisation process, a three-dimensional CFD model with this geometry was built and simulated. Table 7 compares the predicted values with the CFD results. The relative error of the maximum temperature is 0.00056 and the relative error of the pressure drop is 0.038. Both errors are sufficiently small. Therefore, the optimised geometry was used as the final bionic liquid-cooled plate design.
| Result | Prediction | CFD simulation | Relative error |
|---|---|---|---|
| Maximum temperature (andamp;deg;C) | 35.49 | 35.51 | 0.00056 |
| Pressure drop (Pa) | 170.08 | 163.79 | 0.038 |
7 Comparison between the bionic and conventional liquid-cooled plates
7.1 Pressure-drop characteristics
In order to evaluate the practical value of the optimised bionic liquid-cooled plate, a conventional liquid-cooled plate and a honeycomb liquid-cooled plate were also simulated under identical operating conditions. The conventional plate uses straight rectangular channels aligned with the direction of the coolant flow. The honeycomb plate uses the same hexagonal obstacles as the bionic plate but arranged in a uniform square lattice. The inlet width, inlet height, coolant velocity and coolant temperature are all identical in the three plates.
The pressure drop of the conventional plate is 190.91 Pa. The pressure drop of the honeycomb plate is 165.66 Pa. The pressure drop of the optimised bionic plate is 163.79 Pa. Compared with the conventional plate, the bionic plate reduces the pressure drop by 14.2%. This reduction is caused by the streamlined arrangement of the hexagonal obstacles. The sharp corner of the hexagon faces the incoming flow when possible, so that the coolant can pass with a lower form drag. In addition, the tree-root-like arrangement forms multiple parallel paths that distribute the pressure drop more uniformly across the flow field. Since the mass flow rate is the same in all cases, the lower pressure drop directly means lower pump energy consumption for the cooling system of the marine traction battery pack.
7.2 Temperature-control characteristics
The maximum temperature of the conventional liquid-cooled plate is 36.20 andamp;deg;C, whereas the maximum temperature of the optimised bionic liquid-cooled plate is 35.51 andamp;deg;C. Therefore, the bionic plate reduces the maximum temperature by 0.69 andamp;deg;C compared with the conventional plate. This temperature reduction is meaningful for a marine traction battery pack because even a small decrease in peak temperature can improve cycle life and reduce the risk of local thermal runaway.
The temperature distribution also becomes more uniform with the bionic layout. In the conventional plate, the downstream section of every straight channel has a nearly constant temperature perpendicular to the flow, which leads to large hot regions near the outlet. In the bionic plate, the hexagonal obstacles redirect the coolant so that it touches more surfaces and removes heat from otherwise stagnant zones. Thus, the contours in the downstream region are more evenly spaced in the bionic plate. The difference between the maximum and minimum temperatures in the heated region is smaller than that in the conventional plate.
7.3 Velocity-field mechanism
To understand why the bionic structure improves heat transfer while reducing pressure drop, the velocity fields were examined. In the conventional plate, the velocity in each parallel channel is approximately constant at about 0.07 m/s and the direction is always parallel to the inlet flow. There is no transverse velocity component, so the coolant moving along the central region cannot exchange heat effectively with the coolant near the side walls. The corners of the conventional plate are almost dead zones, where flow recirculation is weak.
In the bionic plate, the velocity field can be divided into two regions. Outside the enhanced heat-transfer region, the velocity magnitude is moderate and the flow direction changes gradually as it approaches the hexagonal layout. Inside the enhanced heat-transfer region, the coolant is forced to accelerate in the narrow gaps between adjacent hexagons. The local velocity is not uniform. The low-velocity wake behind each hexagon promotes mixing and boundary-layer renewal, while the high-velocity jet between two hexagons increases convective heat transfer at the wall.
Table 8 summarises the main differences between the conventional plate and the bionic plate. The comparison is made at the same mass flow rate, so the results reflect the effect of the internal structure alone.
| Parameter | Conventional plate | Bionic plate | Difference |
|---|---|---|---|
| Maximum temperature (andamp;deg;C) | 36.20 | 35.51 | −0.69 |
| Pressure drop (Pa) | 190.91 | 163.79 | −14.2% |
| Flow type in channel | Straight and parallel | Repeated splitting and merging | Stronger disturbance |
| Boundary-layer behaviour | Continuous development | Repeated interruption | Better heat transfer |
7.4 Field-synergy analysis
Convective heat transfer can be improved not only by increasing the velocity magnitude or the temperature gradient, but also by reducing the included angle between the velocity vector and the temperature-gradient vector. The field-synergy angle \(\beta\) is defined as:
$$ \cos\beta = \frac{\mathbf{V} \cdot \mathrm{grad}\, T}{|\mathbf{V}| \cdot |\mathrm{grad}\, T|} \tag{13} $$
When \(\beta\) is smaller than 90 andamp;deg;C, the velocity and the temperature gradient cooperate in removing heat from the wall. Regions with a large magnitude of \(\mathbf{V}\), a large magnitude of \(\mathrm{grad} T\) and a small angle \(\beta\) are particularly beneficial.
In the conventional plate, the region with a synergy angle smaller than 90 andamp;deg;C is mainly the leading edge of each dividing wall. These regions occupy a small fraction of the whole fluid domain. In contrast, the bionic plate contains many hexagonal obstacles, and every obstacle produces a small wake region behind it. The wakes are regularly distributed over the enhanced heat-transfer zone. As a result, the area with a synergy angle smaller than 90 andamp;deg;C is noticeably larger in the bionic plate. The boundary layer is destroyed when the coolant impacts the frontal corner of the hexagon. After the coolant passes around the obstacle, the boundary layer redevelops in the wake. This repeated interruption of the boundary layer is the main reason why the bionic plate can achieve a higher heat-transfer coefficient at a lower pressure drop.
8 Influence of coolant temperature and coolant velocity
8.1 Coolant inlet temperature
The coolant inlet temperature directly affects the available temperature difference between the heated surface and the coolant. Simulations were performed with a heat flux of 785 W/m2 and a coolant velocity of 0.2 m/s, while the coolant inlet temperature was set to 25 andamp;deg;C, 30 andamp;deg;C and 35 andamp;deg;C. The maximum temperature increases from 30.46 andamp;deg;C to 40.41 andamp;deg;C when the inlet temperature is raised from 25 andamp;deg;C to 35 andamp;deg;C. In all cases, the temperature rise from the inlet to the outlet is almost identical because the mass flow rate and the heating power are unchanged. However, the absolute temperature of the heated surface is strongly dependent on the inlet temperature.
The transient behaviour is also affected by the inlet temperature. At a coolant temperature of 25 andamp;deg;C, the maximum temperature reaches a steady state faster. At 35 andamp;deg;C, the plate takes longer to reach the steady state because the cooling capacity is weaker. Therefore, a lower coolant inlet temperature is preferred for the operation of the marine traction battery pack when the ambient temperature is high.
8.2 Coolant velocity
The coolant velocity changes the mass flow rate, the convective heat-transfer coefficient and the residence time of the coolant inside the plate. The transient results are summarised in Table 9 for a heat flux of 785 W/m2 and an inlet temperature of 30 andamp;deg;C.
| Velocity (m/s) | Inlet–outlet temperature difference (andamp;deg;C) | Temperature stability trend |
|---|---|---|
| 0.1 | About 8.0 | Slowest stabilisation |
| 0.2 | About 4.2 | Moderate stabilisation |
| 0.3 | About 2.8 | Fastest stabilisation |
When the velocity is increased from 0.1 m/s to 0.3 m/s, the maximum temperature decreases from 39.25 andamp;deg;C to 34.12 andamp;deg;C. The improvement is pronounced at low velocities but becomes smaller at high velocities. The reason is that the thermal boundary layer and the conductive resistance of the aluminium plate gradually become the controlling factors. At the same time, the pressure drop increases with the square of the velocity, so the pumping power increases rapidly. For this reason, 0.2 m/s is recommended when the total energy consumption of the traction battery pack cooling system is considered; it provides a sufficient cooling margin without an excessive pumping power requirement.
9 Influence of heat-generation rate
The heat-generation rate of a marine traction battery pack varies with the state of charge, the discharge current and the ambient temperature. The bionic liquid-cooled plate was tested under five heat flux levels, all with a coolant velocity of 0.2 m/s and an inlet temperature of 30 andamp;deg;C. The maximum temperatures are listed in Table 10.
| Heat flux (W/m2) | Inlet–outlet temperature difference (andamp;deg;C) | Maximum temperature (andamp;deg;C) |
|---|---|---|
| 400 | 2.12 | 32.77 |
| 600 | 3.18 | 33.86 |
| 785 | 4.17 | 35.51 |
| 1000 | 5.30 | 36.51 |
| 1200 | 6.37 | 38.30 |
When the heat flux increases, the inlet-outlet temperature difference increases almost linearly because the coolant mass flow rate is constant. The maximum temperature also increases. At a heat flux lower than 785 W/m2, the bionic liquid-cooled plate can easily maintain the maximum temperature below 35 andamp;deg;C. At a heat flux of 1200 W/m2, the maximum temperature rises to 38.30 andamp;deg;C, which is still below the upper limit recommended for the traction battery pack. This indicates that the bionic plate has an adequate cooling margin for high-load operation.
In addition, the simulation results show that when the heat flux is between 400 and 785 W/m2, the time required for the temperature field to reach a steady state is approximately equal. However, when the heat flux is raised above 1000 W/m2, the stabilisation time becomes longer because the heat accumulation in the aluminium body is larger. This behavior is important for marine vessels because the traction battery pack is often operated at full load during berthing and acceleration. The transient thermal response of the cooling plate must be fast enough to prevent overheating during such load changes.
10 Discussion on energy consumption
The total energy consumption of a liquid-cooling system for the traction battery pack includes the pumping power of the coolant circulation loop. For a fixed volumetric flow rate \(Q_v\), the hydraulic power required to overcome the pressure drop is expressed as:
$$ P_{\mathrm{hyd}} = Q_v \cdot \Delta p \tag{14} $$
Since the flow rate is the same in the conventional and bionic plates, the hydraulic power is proportional to the pressure drop. The bionic plate reduces the pressure drop from 190.91 Pa to 163.79 Pa, so the hydraulic pumping power is reduced by 14.2%. This reduction is particularly meaningful because the cooling system often operates for thousands of hours during the life of a marine battery module. A lower pressure drop not only lowers the energy cost but also relaxes the selection requirement for the circulation pump. A smaller pump occupies less space, produces less noise and has a lower initial investment.
The bionic design achieves this reduction without changing the inlet width, inlet height, coolant temperature or coolant flow rate. Therefore, the improvement is created entirely by the geometry of the enhanced heat-transfer region. The optimised parameters \(a=30\) mm, \(b=8\) mm, \(c=50\) mm and \(d=90\) mm ensure that the coolant passes through a large number of staggered hexagonal obstacles but does not encounter severe blockage. The hexagonal shape with its diagonal leading face is more streamlined than a rectangular rib, which reduces the form drag. Meanwhile, the tree-root-like distribution prevents the flow from concentrating in one large channel and creates a more homogeneous velocity field.
11 Conclusions and future work
In this study, a bionic liquid-cooled plate was proposed for a marine traction battery pack based on the hexagonal network of leaf veins and the branching pattern of tree roots. The numerical simulation method was verified against experimental data. Sixteen orthogonal simulations were carried out to study the effects of four structural parameters. A regression model and a multi-objective genetic algorithm were then used to find the optimal geometrical combination. The main conclusions are as follows.
First, the maximum temperature of the optimised bionic liquid-cooled plate is 35.51 andamp;deg;C, which is 0.69 andamp;deg;C lower than that of a conventional straight-channel liquid-cooled plate. The bionic plate also shows better temperature uniformity. The highest temperature consistently appears at the two corners near the outlet, but the bionic layout reduces the high-temperature region by distributing the coolant more uniformly in the downstream zone.
Second, the pressure drop of the bionic plate is 163.79 Pa, which is 14.2% lower than the pressure drop of the conventional plate. All sixteen orthogonal configurations have a lower pressure drop than the conventional plate. This is because the hexagonal and tree-root-like layout creates multiple parallel paths, avoids severe flow separation and causes a smaller form drag than sharp rectangular ribs. A lower pressure drop at a constant flow rate means lower pump power and lower total energy consumption for the cooling system of the traction battery pack.
Third, the range analysis reveals that the transverse spacing between hexagons \(b\) is the most significant factor for both the maximum temperature and the pressure drop. For maximum temperature, the significance order is \(b > a > c > d\). For pressure drop, the significance order is \(b > c > a > d\). The outlet distance \(d\) has the smallest effect on both objectives.
Fourth, the multi-objective optimisation selects \(a=30\) mm, \(b=8\) mm, \(c=50\) mm and \(d=90\) mm as the best compromise. The CFD validation shows that the errors between the predicted and simulated values are acceptable. This confirms that the combination of the neural regression model and NSGA-II is suitable for the structural optimisation of the bionic liquid-cooled plate.
Fifth, the field-synergy analysis shows that the bionic plate has a larger region where the synergy angle between the velocity vector and the temperature-gradient vector is smaller than 90 andamp;deg;C. The continuous interruption and redevelopment of the thermal boundary layer in the enhanced heat-transfer region strengthens convective heat transfer. This is the physical mechanism that allows the bionic plate to outperform the conventional plate.
Finally, the operating-condition study shows that the coolant inlet temperature, the coolant velocity and the heat-generation rate have different influences. The inlet temperature almost does not change the inlet-outlet temperature difference but changes the absolute temperature significantly. A lower inlet temperature improves the temperature-control effect. Increasing the coolant velocity from 0.1 m/s to 0.3 m/s reduces the maximum temperature from 39.25 andamp;deg;C to 34.12 andamp;deg;C, but the marginal benefit decreases with increasing velocity. Increasing the heat flux from 400 W/m2 to 1200 W/m2 increases the maximum temperature from 32.77 andamp;deg;C to 38.30 andamp;deg;C. The bionic liquid-cooled plate can maintain all these operating points within the recommended temperature range of the traction battery pack.
For future work, the optimisation should include a time-varying heat-generation profile that represents real navigation cycles. The effect of different coolant mixtures, such as water-glycol solutions, should also be investigated because ship cooling systems often need antifreeze properties in cold climates. Fatigue strength and manufacturing tolerances of the hexagonal features should be considered in the design stage. In addition, the optimisation method can be extended to three-dimensional multi-objective optimisation with constraints on mass, volume and pressure drop. A more detailed comparison with other bionic structures, such as fractal channels and double-layer cold plates, is also recommended.