I designed and numerically investigated a novel miniature liquid cooling plate that combines a bionic leaf-vein flow network with reverse Tesla valve units, specifically intended for thermal management of an electric vehicle battery pack. The motivation for this work is straightforward: high-power and fast-charging operation of an electric vehicle battery pack generates substantial heat, and although liquid cooling is one of the most practical and widely deployed cooling strategies, conventional cold-plate channels often suffer from either insufficient heat transfer enhancement or excessive pressure drop. Tesla valve structures have attracted attention because they can intensify fluid mixing and improve heat dissipation, but their unique geometry often increases flow resistance. In an electric vehicle battery pack, that additional flow resistance translates directly into higher pump power, greater parasitic energy consumption, and potentially poorer flow distribution among parallel channels. I therefore sought a hybrid architecture that preserves the heat-transfer advantage of the Tesla valve while reducing the pressure-drop penalty through a bionic leaf-vein main path and carefully selected Tesla valve angles.
The electric vehicle battery pack considered in this study consists of prismatic lithium-ion cells that are stacked in a highly symmetrical module. I simplified the module as a repeating sandwich structure in which each cell is separated from its neighbor by a liquid cooling plate. The cooling plate is 135.3 mm long, 185.3 mm wide, and 8 mm thick. The channel cross-section is 6 mm by 4 mm. The plate material is 6061 aluminum alloy because it offers a favorable combination of high thermal conductivity, low density, adequate mechanical strength, and mature manufacturability. The coolant is a 20% ethylene glycol aqueous solution, selected for its low freezing point, low viscosity, and reasonable thermal conductivity. The inlet and outlet are arranged in a one-inlet and two-outlet configuration, which I found beneficial for reducing pressure drop and improving flow mobility compared with a conventional one-inlet and one-outlet layout.
The core idea of my design is to use a biomimetic leaf-vein pattern as the global flow distributor and to embed reverse Tesla valve units along selected branches as local heat-transfer enhancers. The leaf-vein structure provides a naturally inspired hierarchy of main and secondary channels, which helps distribute coolant more evenly and reduces the risk of maldistribution in an electric vehicle battery pack. The reverse Tesla valve introduces repeated flow separation, impingement, and recombination, which enhances convective heat transfer. However, because the Tesla valve also creates additional local losses, I systematically studied three geometric parameters: the contraction ratio of the main leaf-vein path, the branch angle of the Tesla valve, and the convergence angle of the Tesla valve. My objective was to identify a configuration that minimizes pressure drop with only negligible degradation in maximum temperature and maximum temperature difference across the electric vehicle battery pack.
Table 1. Basic properties of the coolant.
| Property | Value |
|---|---|
| Density (kg/m³) | 1027.93 |
| Composition | 20% ethylene glycol + water |
| Thermal conductivity (W/m·°C) | 0.498 |
| Dynamic viscosity (kg/m·s) | 0.00146 |
| Freezing point (°C) | −7.8 |
| Boiling point (°C) | 102.2 |
| Specific heat capacity (J/kg·°C) | 3826 |
Table 2. Basic parameters of the lithium-ion cell used in the electric vehicle battery pack.
| Parameter | Value |
|---|---|
| Nominal capacity (Ah) | 50 |
| Dimensions (mm) | 135.3 × 29.3 × 185.3 |
| Density (kg/m³) | 1899.04 |
| Mass (g) | 1395 |
| Specific heat capacity (J/kg·°C) | 1100 |
| Nominal voltage (V) | 3.65 |
| Thermal conductivity (W/m·°C) | 3.3 |
For the thermal model of the electric vehicle battery pack, I adopted the Bernardi heat-generation framework. The total volumetric heat-generation rate of a cell is expressed as the sum of irreversible Joule heating and reversible entropic heating divided by cell volume:
$$ q = \frac{Q_{irr} + Q_{rev}}{V_b} $$
$$ Q_{irr} = I (E_{ocv} – U) = I^2 R_0 $$
$$ Q_{rev} = I T \frac{dE_{ocv}}{dT} $$
Here, \(I\) is the charge or discharge current, \(V_b\) is the cell volume, \(E_{ocv}\) is the open-circuit voltage, \(U\) is the terminal voltage, \(T\) is the cell temperature, and \(R_0\) is the ohmic internal resistance. In my simulations, the reversible heat was small relative to the irreversible heat under high-rate operation, especially at 3C discharge. The irreversible Joule heat grows with the square of current, so it dominates the thermal load in the electric vehicle battery pack under fast discharge or fast charging. This is precisely why an efficient cold-plate design is necessary.
Heat transfer from the cell to the cooling plate is described by Fourier’s law for conduction, and heat transfer from the plate wall to the coolant is described by Newton’s law of cooling:
$$ Q_1 = -\lambda A \frac{dT}{dx} $$
$$ Q_2 = h A (T_w – T_f) $$
In these equations, \(Q_1\) and \(Q_2\) are heat flow rates, \(\lambda\) is thermal conductivity, \(A\) is the effective heat-transfer area, \(dT/dx\) is the temperature gradient along the conduction direction, \(h\) is the convective heat-transfer coefficient, \(T_w\) is the wall temperature, and \(T_f\) is the coolant bulk temperature. The negative sign in Fourier’s law indicates that heat flows opposite to the temperature gradient.
For the coolant flow, I assumed steady, incompressible, single-phase flow. The continuity equation reduces to:
$$ \nabla \cdot \vec{v} = 0 $$
Neglecting gravity and body forces, the momentum equation for the coolant becomes the simplified Navier–Stokes equation:
$$ \rho (\vec{v} \cdot \nabla \vec{v}) = -\nabla p + \mu \nabla^2 \vec{v} $$
Here, \(\vec{v}\) is the velocity vector, \(\rho\) is density, \(p\) is pressure, and \(\mu\) is dynamic viscosity. For the solid cold plate and the coolant, the energy equations are:
$$ \nabla \cdot (\lambda_s \nabla T_s) = 0 $$
$$ \nabla \cdot (\rho_l c_l \vec{v} T_l) = \nabla \cdot (\lambda_l \nabla T_l) $$
where the subscript \(s\) denotes the solid cold plate, and the subscript \(l\) denotes the liquid coolant. These equations were solved numerically for the electric vehicle battery pack module and its integrated cooling plates.
Table 3. Fixed simulation conditions and geometric parameters.
| Parameter | Value |
|---|---|
| Cooling plate size (mm) | 135.3 × 185.3 × 8 |
| Channel cross-section (mm × mm) | 6 × 4 |
| Cold plate material | 6061 aluminum alloy |
| Coolant | 20% ethylene glycol aqueous solution |
| Coolant volumetric flow rate (m³/s) | 4 × 10⁻⁵ |
| Ambient temperature (°C) | 25 |
| Discharge rate | 3C |
| Reynolds number | 5636 |
| Mesh count for independence | approximately 4.9 × 10⁵ |
| Time step for independence | 1 s |
I checked grid independence and time-step independence before performing the parametric study. The pressure drop and maximum temperature converged when the mesh count reached approximately 490,000 cells. The time-step study showed that a step of 1 s was sufficient for stable and accurate transient predictions. Based on these checks, I used 490,000 cells and a 1 s time step as the baseline for all subsequent simulations of the electric vehicle battery pack cooling plate.
Table 4. Model assumptions used in the numerical simulation.
| Assumption | Description |
|---|---|
| Coolant compressibility | Incompressible, constant density |
| Thermal radiation | Neglected |
| Channel surface roughness | Smooth wall assumed |
| Contact resistance | Perfect contact between cell and cold plate |
| Flow regime | Turbulent at Re = 5636 |
The first geometric parameter I examined was the contraction ratio of the main leaf-vein path. I defined the inlet channel width as \(a\), the terminal channel width as \(b\), and the contraction ratio as:
$$ i = \frac{b}{a} $$
I tested \(i = 0.25, 0.5, 0.75, 1.0\). A value of 1.0 means no contraction, so the main path remains uniform along its length. The leaf-vein analogy suggests that a certain degree of contraction may help distribute flow in a natural branching system, but in a compact liquid cooling plate for an electric vehicle battery pack, the penalty in pressure drop must be weighed against any thermal benefit. My results showed that the thermal effect of the contraction ratio was very small. The maximum temperature difference remained close to 2.8 °C, and the maximum temperature remained around 28.3 °C over the entire range. These values are acceptable for an electric vehicle battery pack operating under a 3C discharge condition. The pressure drop, however, changed significantly. As the contraction ratio increased from 0.25 to 1.0, the pressure drop decreased monotonically. The best pressure-drop performance occurred at \(i = 1.0\).
Table 5. Effect of main-path contraction ratio on thermal and hydraulic performance.
| Contraction ratio \(i\) | Maximum temperature difference ΔTmax (°C) | Maximum temperature Tmax (°C) | Pressure drop ΔP (Pa) |
|---|---|---|---|
| 0.25 | 2.54 | 27.81 | 319.38 |
| 0.50 | 2.51 | 27.83 | 261.99 |
| 0.75 | 2.48 | 27.87 | 219.61 |
| 1.00 | 2.48 | 27.92 | 179.59 |
When \(i\) increased from 0.25 to 0.50, the maximum temperature difference barely changed, the maximum temperature increased by about 0.71%, and the pressure drop decreased by about 21.91%. From 0.50 to 0.75, the maximum temperature difference increased by about 1.21%, the maximum temperature increased by about 1.41%, and the pressure drop decreased by about 19.30%. From 0.75 to 1.00, the maximum temperature difference increased by about 1.20%, the maximum temperature increased by about 1.74%, and the pressure drop decreased by about 22.38%. In terms of the overall conclusion for this parameter, selecting \(i = 1.0\) allowed the maximum temperature difference and maximum temperature to increase by at most 2.42% and 0.40%, respectively, while the pressure drop could be reduced by as much as 77.84% relative to the most restrictive contraction case. The pressure field also became more uniform as \(i\) increased, and the inlet pressure was effectively relieved. Therefore, I selected a non-contracted main path, \(i = 1.0\), for the electric vehicle battery pack cooling plate.
The second parameter was the Tesla valve branch angle θ. This angle strongly affects the local flow pattern inside the Tesla valve units. A smaller branch angle tends to guide the flow more smoothly into the branch, whereas a larger branch angle increases the intensity of flow turning and local separation. In my simulations, θ was varied from 10° to 20° in increments of 2.5°: 10°, 12.5°, 15°, 17.5°, and 20°. The main-path contraction ratio was fixed at the previously selected value \(i = 1.0\). The ambient temperature was 25 °C, the coolant flow rate was \(4 \times 10^{-5}\) m³/s, and the ethylene glycol concentration was 20%.
The maximum temperature difference varied within only about 0.4 °C over the entire branch-angle range. The maximum temperature also changed only slightly. The pressure drop, however, exhibited a clear trend. It increased overall as the branch angle increased from 10° to 20°. The detailed values are summarized in Table 6. At θ = 10°, the maximum temperature difference was about 2.60 °C, the maximum temperature was about 28.02 °C, and the pressure drop was about 172.44 Pa. At θ = 20°, the pressure drop rose to about 179.21 Pa. Although the differences are not enormous, they matter for pump power and energy consumption in an electric vehicle battery pack, especially when many cooling plates operate in parallel.
Table 6. Effect of Tesla valve branch angle on thermal and hydraulic performance.
| Branch angle θ (°) | Maximum temperature difference ΔTmax (°C) | Maximum temperature Tmax (°C) | Pressure drop ΔP (Pa) |
|---|---|---|---|
| 10.0 | 2.60 | 28.02 | 172.44 |
| 12.5 | 2.57 | 27.96 | 175.48 |
| 15.0 | 2.56 | 27.93 | 177.23 |
| 17.5 | 2.48 | 27.92 | 179.45 |
| 20.0 | 2.54 | 27.98 | 179.21 |
I fitted the average pressure drop as a function of branch angle. The result followed a fourth-order polynomial:
$$ \Delta P = -0.005\theta^4 + 0.295\theta^3 – 6.4398\theta^2 + 62.455\theta – 53.315 $$
with \(R^2 = 1\). This fit confirms that the pressure drop increases with branch angle over the studied range. Comparing θ = 10° with θ = 20°, the maximum temperature difference and maximum temperature increased by only about 2.36% and 0.36%, respectively, while the pressure drop decreased by about 3.78%. When considering the penalty relative to other angles, θ = 10° provided the best compromise. Pressure contours also showed that the pressure impact at the Tesla valve corners in the tail channels was smaller at θ = 10°, and each branch exhibited a more uniform pressure distribution. For these reasons, I selected θ = 10° for the electric vehicle battery pack cooling plate.
The third parameter was the Tesla valve convergence angle α. This angle controls how the branch flow rejoins the main flow. I selected three representative values: 45° for an acute angle, 90° for a right angle, and 135° for an obtuse angle. The main-path contraction ratio was fixed at \(i = 1.0\), and the Tesla valve branch angle was fixed at θ = 10°. The ambient temperature, coolant flow rate, and coolant concentration were kept the same as before. The maximum temperature difference and maximum temperature were almost insensitive to α. The curves nearly overlapped, so the thermal effect of the convergence angle was negligible. The pressure drop, however, was noticeably affected. The acute and right angles produced almost identical pressure-drop curves, while the obtuse angle of 135° produced a clearly lower pressure drop.
Table 7. Effect of Tesla valve convergence angle on thermal and hydraulic performance.
| Convergence angle α (°) | Maximum temperature difference ΔTmax (°C) | Maximum temperature Tmax (°C) | Pressure drop ΔP (Pa) |
|---|---|---|---|
| 45 | 2.59 | 28.02 | 172.61 |
| 90 | 2.60 | 28.02 | 172.44 |
| 135 | 2.60 | 28.03 | 161.67 |
When α was set to 135°, the maximum temperature difference was about 2.60 °C, which was roughly 0.38% higher than the right-angle case and essentially the same as the acute-angle case. The maximum temperature was about 28.03 °C, only about 0.04% higher than both the right-angle and acute-angle cases. However, the pressure drop was reduced by about 6.34% and 6.25% relative to the right-angle and acute-angle cases, respectively. A second-order polynomial captured the pressure-drop trend as a function of convergence angle, and the minimum occurred at α = 135° with a value of about 161.67 Pa. The pressure contours also showed that the overall pressure was lower at the obtuse angle, and the tail-channel pressure was smaller, indicating smoother coolant flow. In the context of an electric vehicle battery pack, this means that a larger convergence angle can reduce pumping effort without sacrificing thermal performance. I therefore selected α = 135°.
After selecting the three key parameters sequentially, I evaluated the cumulative effect of the structural evolution. The process began with a baseline configuration and then applied \(i = 1.0\), followed by θ = 10°, and finally α = 135°. The thermal performance remained within a narrow band. The maximum temperature difference increased by only 2.36%, and the maximum temperature increased by only 0.39%. At the same time, the pressure drop decreased by about 9.98%. This is a favorable outcome for an electric vehicle battery pack because the cooling plate can maintain the battery pack within safe operating temperatures while reducing the parasitic power required to circulate coolant.
Table 8. Cumulative structural optimization and performance change.
| Optimization step | Selected parameter | ΔTmax change | Tmax change | ΔP change |
|---|---|---|---|---|
| Main-path contraction | i = 1.0 | up to +2.42% | up to +0.40% | up to −77.84% |
| Tesla valve branch angle | θ = 10° | up to +2.36% | up to +0.36% | up to −3.93% |
| Tesla valve convergence angle | α = 135° | up to +0.04% | up to +0.04% | up to −6.66% |
| Overall optimized design | i = 1.0, θ = 10°, α = 135° | up to +2.36% | up to +0.39% | up to −9.98% |
Several physical mechanisms explain these trends. The leaf-vein main path without contraction reduces the bulk flow acceleration and deceleration losses along the main channel. When the main path contracts, the flow must accelerate in the narrower section, which increases the dynamic pressure and viscous dissipation. The resulting pressure drop is not compensated by a meaningful thermal improvement because the coolant flow rate and the total heat-transfer area remain essentially unchanged. In a compact electric vehicle battery pack, where many cooling plates may be connected in parallel, even a modest reduction in pressure drop per plate can produce a substantial reduction in total pump power. The Tesla valve branch angle affects the local turning losses. A smaller branch angle allows the flow to enter the branch with less separation, so the local loss coefficient is lower. A larger branch angle forces the flow to turn more sharply, creating stronger recirculation zones and higher local pressure losses. The convergence angle works in a similar way at the reattachment point. An obtuse convergence angle smooths the merging flow and reduces the intensity of the recirculation zone, which lowers the pressure drop.
It is important to emphasize that the thermal performance of this miniature cooling plate is not highly sensitive to these geometric variations. The reason is that the cell-to-plate contact area, the channel hydraulic diameter, and the coolant flow rate remain fixed in the parametric study. The Tesla valve units enhance local mixing, but in a small plate the flow path is short, so the bulk temperature rise of the coolant is modest. As a result, the maximum temperature and maximum temperature difference are governed more by the overall thermal resistance and the total flow rate than by the detailed branch angle or convergence angle. This is actually advantageous for design: it means that I can tune the geometry for lower pressure drop without compromising the thermal safety margin of the electric vehicle battery pack.
The maximum temperature difference is a key indicator of thermal uniformity in an electric vehicle battery pack. A large temperature difference can accelerate cell-to-cell imbalance, reduce usable capacity, and shorten pack life. In my optimized design, the maximum temperature difference remained around 2.6 °C under 3C discharge. The maximum temperature remained around 28 °C, which is well below the typical safe operating limit for lithium-ion cells. The coolant flow rate of \(4 \times 10^{-5}\) m³/s per plate, combined with the 6 mm × 4 mm channel cross-section, produced a Reynolds number of 5636. This is in the turbulent regime, which is beneficial for convective heat transfer. The turbulence also helps suppress hot spots near the cell tabs and edges, although the compact plate geometry limits the development of fully developed turbulent flow.
I also considered the flow distribution among the parallel branches. The leaf-vein architecture is inherently symmetric, and the one-inlet and two-outlet arrangement helps balance the flow. In a conventional one-inlet and one-outlet serpentine cold plate, the pressure gradient along the main path can cause uneven flow among parallel branches, leading to poor thermal uniformity. The leaf-vein design mitigates this problem by providing multiple branching levels and a more uniform pressure field. The Tesla valve units introduce local flow resistance, but because they are placed in a symmetric arrangement, they do not create a systematic bias in flow distribution. The pressure contours showed that the pressure field became more uniform as the contraction ratio increased to 1.0 and as the branch angle decreased to 10°. The convergence angle of 135° further reduced the tail-channel pressure, which is often a region of poor flow in compact cooling plates.
From an energy-management perspective, the pressure drop is directly related to pumping power. For a given volumetric flow rate \(Q\), the ideal pumping power is:
$$ P_{pump} = \Delta P \cdot Q $$
Using this relation, a 9.98% reduction in pressure drop corresponds to approximately a 9.98% reduction in pumping power at the same flow rate. If the electric vehicle battery pack contains many cooling plates, the total saving can be significant over a drive cycle. This is especially relevant for fast-charging scenarios, where the coolant pump may operate at high speed for extended periods. A lower pressure-drop design also gives the system more hydraulic margin, which can be used to increase flow rate during extreme fast charging or to reduce pump size and cost.
I further summarized the relationship between the geometric parameters and the performance metrics in a qualitative table. This table is intended to guide future design iterations for electric vehicle battery pack cooling plates.
Table 9. Qualitative influence of geometric parameters on performance.
| Parameter | Effect on ΔTmax | Effect on Tmax | Effect on ΔP | Recommended value |
|---|---|---|---|---|
| Main-path contraction ratio i | Very weak | Very weak | Strong; lower i increases ΔP | i = 1.0 |
| Tesla valve branch angle θ | Weak | Weak | Moderate; larger θ increases ΔP | θ = 10° |
| Tesla valve convergence angle α | Negligible | Negligible | Moderate; obtuse angle reduces ΔP | α = 135° |
The numerical results also indicated that the pressure field is more sensitive to geometry than the temperature field. This is because pressure drop is governed by local losses, flow separation, recirculation, and wall shear, all of which are strongly influenced by channel shape. Temperature, on the other hand, is governed by the overall energy balance, the total heat-transfer area, and the coolant flow rate. Since these latter quantities were fixed, the temperature field remained relatively stable. This insight is valuable for electric vehicle battery pack thermal design: if the cooling system is already thermally adequate, geometric optimization can focus on pressure-drop reduction, which improves system efficiency without compromising safety.
In the optimized design, the maximum temperature difference was about 2.60 °C, and the maximum temperature was about 28.03 °C. The pressure drop was about 161.67 Pa. These values are based on a 3C discharge condition, an ambient temperature of 25 °C, and a coolant flow rate of \(4 \times 10^{-5}\) m³/s per plate. The Reynolds number of 5636 indicates turbulent flow, which is desirable for heat transfer but also contributes to pressure loss. The Tesla valve units enhance mixing, but their local losses are mitigated by the selected angles. The leaf-vein main path ensures that the flow is distributed evenly across the plate, and the one-inlet and two-outlet configuration reduces the overall pressure drop relative to a single-outlet design.
I also examined the transient behavior of the electric vehicle battery pack cooling plate. The maximum temperature difference and maximum temperature evolved over time and reached quasi-steady values after a few hundred seconds. The pressure drop reached steady state almost immediately because the flow field is dominated by the fixed geometry and the imposed flow rate. The thermal time constant is set by the cell heat capacity and the thermal resistance between the cell and the coolant. The cold plate itself has a low thermal mass compared with the cells, so its temperature responds quickly. The transient results confirmed that the optimized geometry does not introduce any thermal oscillation or instability. The system remains well-behaved under the 3C discharge condition.
For the electric vehicle battery pack, another important consideration is manufacturability. The 6061 aluminum alloy is easy to machine and braze, and the channel dimensions are compatible with common stamping, milling, or brazing processes. The Tesla valve units can be formed by casting or machining, and the leaf-vein pattern can be produced by die-sinking or additive manufacturing. The one-inlet and two-outlet manifold can be integrated into the plate or connected through standard fittings. The coolant, a 20% ethylene glycol aqueous solution, is widely used in automotive thermal management and is compatible with aluminum alloys when proper inhibitors are used. The freezing point of −7.8 °C and boiling point of 102.2 °C provide an adequate operating window for most climates.
I also compared the optimized design with a baseline Tesla valve cold plate without the leaf-vein main path. The baseline suffered from higher pressure drop and less uniform flow distribution. The hybrid design reduced the pressure drop by nearly 10% relative to the baseline while maintaining essentially the same maximum temperature and maximum temperature difference. This confirms that the leaf-vein architecture and the selected Tesla valve angles work synergistically. The leaf-vein structure handles global flow distribution, while the Tesla valve units handle local heat-transfer enhancement. Neither alone would achieve the same balance.
The results of this study lead to several practical design guidelines for liquid cooling plates in electric vehicle battery packs. First, avoid unnecessary contraction of the main flow path unless there is a clear thermal benefit. In the compact plate studied here, a uniform main path minimized pressure drop with negligible thermal penalty. Second, use small Tesla valve branch angles to reduce turning losses. A branch angle of 10° provided the best compromise between heat-transfer enhancement and pressure drop. Third, use an obtuse convergence angle at the Tesla valve outlet. The 135° convergence angle reduced pressure drop without degrading thermal performance. Fourth, maintain a symmetric flow network with multiple outlets if possible. The one-inlet and two-outlet configuration improved flow distribution and reduced pressure drop. Fifth, verify grid and time-step independence before trusting small percentage differences in performance metrics, because the geometric effects studied here are subtle relative to the overall thermal resistance.
In terms of thermal safety, the optimized electric vehicle battery pack cooling plate keeps the maximum temperature below 30 °C under 3C discharge. This is a comfortable margin for lithium-ion cells, which typically have a recommended operating range up to 45–60 °C depending on chemistry. The maximum temperature difference of about 2.6 °C is also favorable because it limits cell-to-cell imbalance. A lower temperature difference helps the battery management system estimate state of charge and state of health more accurately and reduces the risk of premature aging. The pressure drop of about 161.67 Pa is low enough that the coolant pump does not need to work excessively, which improves the overall energy efficiency of the electric vehicle battery pack.
I should note that the present study focused on a single cooling plate between two cells. In a full electric vehicle battery pack, the cooling plates would be connected in parallel or in series, and the manifold design would affect the overall flow distribution. The pressure drop of the plate itself is a key input for manifold sizing. A lower plate pressure drop provides more flexibility in manifold design and reduces the risk of maldistribution. If the plate pressure drop is too high, the manifold must be carefully tuned to ensure that every plate receives adequate coolant flow. The optimized design presented here therefore contributes to a more robust and scalable thermal management architecture for an electric vehicle battery pack.
Table 10. Summary of optimized thermal and hydraulic performance.
| Metric | Optimized value |
|---|---|
| Main-path contraction ratio i | 1.0 |
| Tesla valve branch angle θ | 10° |
| Tesla valve convergence angle α | 135° |
| Maximum temperature difference ΔTmax | approximately 2.60 °C |
| Maximum temperature Tmax | approximately 28.03 °C |
| Pressure drop ΔP | approximately 161.67 Pa |
| Change in ΔTmax versus baseline | up to +2.36% |
| Change in Tmax versus baseline | up to +0.39% |
| Reduction in ΔP versus baseline | up to −9.98% |
The broader implication of this work is that geometric optimization of liquid cooling plates for electric vehicle battery packs should consider both thermal and hydraulic objectives. In many practical systems, the thermal performance is already adequate, and the limiting factor is pump power or flow distribution. By carefully selecting the main-path contraction, branch angle, and convergence angle, it is possible to reduce pressure drop by nearly 10% without sacrificing thermal safety. This is a meaningful improvement because it directly reduces parasitic energy consumption and can extend the driving range of an electric vehicle battery pack. It also reduces the thermal load on the coolant pump and allows for a more compact and lightweight thermal management system.
I also explored the sensitivity of the results to the coolant flow rate. At higher flow rates, the pressure drop increases, and the relative benefit of the optimized geometry becomes even more important. At lower flow rates, the thermal performance degrades, but the pressure drop is less of a concern. The selected flow rate of \(4 \times 10^{-5}\) m³/s per plate is a reasonable compromise for a 50 Ah cell under 3C discharge. If a higher discharge rate is required, the flow rate can be increased, and the optimized geometry will still provide a pressure-drop advantage over the baseline. This makes the design scalable across different electric vehicle battery pack sizes and discharge requirements.
I verified that the simulation results are consistent with the expected physics. The Reynolds number of 5636 confirms turbulent flow, which enhances heat transfer but also increases pressure loss. The pressure drop is dominated by local losses at the Tesla valve units and the manifold, while the main-path contraction adds distributed losses. By removing the contraction and selecting favorable Tesla valve angles, I reduced the local and distributed losses. The temperature field remained stable because the total heat-transfer area and coolant flow rate were unchanged. The maximum temperature difference remained small because the flow distribution was uniform. These physical arguments support the numerical findings and give confidence in the optimized design.
In conclusion, I designed a Tesla-valve-based composite liquid cooling plate for an electric vehicle battery pack and optimized its key geometric parameters. The design integrates a bionic leaf-vein main path with reverse Tesla valve units. The main-path contraction ratio, Tesla valve branch angle, and Tesla valve convergence angle were systematically studied. The optimal configuration is \(i = 1.0\), θ = 10°, and α = 135°. The maximum temperature difference and maximum temperature increased by at most 2.36% and 0.39%, respectively, while the pressure drop decreased by up to 9.98%. The optimized design maintains the electric vehicle battery pack within safe thermal limits under 3C discharge and reduces pumping power. The results provide practical guidelines for the thermal management of electric vehicle battery packs and demonstrate that pressure-drop reduction can be achieved with minimal thermal penalty through careful geometric design.