In the past decade, the automotive industry has witnessed a dramatic transformation driven by the expansion of electric vehicles. This transformation is closely linked to the evolution of energy storage systems, specifically the vehicle traction battery. The vehicle traction battery is responsible for delivering the required power and energy to satisfy daily driving demands, and its operational safety and performance strongly rely on the effectiveness of the thermal management strategy. In this work, I focus on the thermal behavior of a vehicle traction battery module using a prismatic lithium iron phosphate chemistry, and I investigate how a hybrid cooling layout combining heat pipes and liquid-cooling plates can improve heat dissipation and temperature uniformity. The research approach is primarily numerical, using a multi‑scale multi‑domain battery model and computational fluid dynamics to evaluate the thermal and hydraulic performance of several flow‑field configurations.
The importance of such research is amplified by the continuously increasing energy density and fast‑charging capability of modern vehicle traction batteries. When a large‑capacity lithium‑ion cell is discharged at high rates, electrochemical reactions, ohmic losses, and polarization effects generate a substantial amount of heat. If this heat cannot be removed efficiently, the cell temperature may exceed the safe operating window, leading to accelerated aging, premature capacity fade, and even catastrophic thermal runaway. A thermal management system should therefore maintain the core temperature of the vehicle traction battery inside an optimal range, typically between 20 °C and 40 °C, while keeping the temperature difference over the module as small as possible. In addition, energy consumption and pumping power associated with the cooling circuit must be considered when designing the liquid cooling plates. In this study, I adopt the classical liquid cooling technology and combine it with heat pipes. The cooling plate is mounted at the bottom of the battery module, whereas L‑shaped heat pipes extend into the interior spaces between adjacent cells. This configuration improves the heat conduction path from the cell core to the cooling plate without exposing the cells to a directly flowing coolant, thereby mitigating the risk of coolant leakage and enhancing the overall safety of the vehicle traction battery pack.
Research Scope and Methodology
My investigation is divided into several stages. First, I construct an electrochemical-thermal model for a prismatic lithium iron phosphate cell with a nominal capacity of 180 Ah and dimensions of 207 mm by 174 mm by 72 mm. The cell model is based on the NTGK electrochemistry model, which provides a computationally efficient way to compute heat generation while preserving acceptable accuracy. Then, I couple the battery heat generation model with the cooling devices. The cooling configuration is composed of a bottom aluminum liquid cooling plate with different channel layouts and two L-shaped heat pipes attached to each cell. The heat pipe is modeled as a solid domain with an equivalent high thermal conductivity of 5000 W m⁻¹ K⁻¹, which reproduces its heat transfer capability without simulating internal phase change explicitly. The coolant is a 50% ethylene glycol-water solution. Several flow configurations are studied: a traditional parallel channel, an S-shaped or serpentine channel, and a newly proposed series-parallel channel. The cooling performance is evaluated in terms of maximum temperature, temperature difference, and pressure drop across the cooling plate.
| Parameter | Value |
|---|---|
| Cell chemistry | LiFePO₄ / graphite |
| Nominal capacity | 180 Ah |
| Nominal voltage | 3.22 V |
| Height × length × width | 207 × 174 × 72 mm |
| Module layout | 3 cells in height direction × 8 cells in length direction |
| Number of cells | 24 (1P24S) |
| Density | 2248 kg m⁻³ |
| Specific heat | 850 J kg⁻¹ K⁻¹ |
| Thermal conductivity in three directions | 15 / 15 / 1 W m⁻¹ K⁻¹ |
| Operating temperature range | −34 °C to 65 °C |
| Maximum discharge rate | 3 C |
Governing Equations and Battery Model
In this numerical framework, the scalar transport of energy within the battery cells is expressed by:
$$
\rho \frac{\partial h_e}{\partial t} + \nabla \cdot \left(\rho \mathbf{v} h_e\right) = \nabla \cdot \left(k \nabla T\right) + S_h
$$
where \(\rho\) is the density, \(h_e\) is the specific enthalpy, \(\mathbf{v}\) is the velocity field, \(k\) is the thermal conductivity, and \(S_h\) is the volumetric heat source. For solid regions, the convective term vanishes, leaving a transient heat conduction equation with heat generation. The NTGK model provides the local volumetric current transfer rate through an empirical polynomial relationship:
$$
J_{ech} = a \left[ U – (\phi_+ – \phi_-) \right]
$$
Here, \(a\) is the specific interfacial area, \(\phi_+\) and \(\phi_-\) represent the potentials of the positive and negative phases, respectively. The functions \(U\) and \(a\) depend on the depth of discharge (DOD) and temperature:
$$
U = \sum_{n=0}^{5} a_n \left(\mathrm{DOD}\right)^n
$$
$$
a = \sum_{n=0}^{5} b_n \left(\mathrm{DOD}\right)^n
$$
The depth of discharge is computed from the total discharged capacity divided by the rated capacity. The electrochemical heat source is expressed by:
$$
q_{ech} = J_{ech} \left[ (\phi_+ – \phi_-) – T \frac{\partial U}{\partial T} \right]
$$
Because the present research focuses on the thermal response during a full discharge, the cell is discharged at a constant current corresponding to 1 C for 3600 seconds. The environment temperature is fixed at 298 K, and natural convection is imposed on the outer surfaces only if the cooling system is absent. When the liquid cooling system is activated, the bottom surfaces of the heat pipe condensation sections contact the cooling plate through a thermal interface material, and the outer walls of the battery module are considered adiabatic.
Fluid Flow and Heat Transfer Model
The coolant flow in the small channels is laminar because the maximum Reynolds number is well below 2300 under the chosen mass flow rates. The Reynolds number is calculated using the hydraulic diameter of a channel cross-section:
$$
Re = \frac{\rho_w v_w D_h}{\mu}
$$
with
$$
D_h = \frac{2ab}{a+b}
$$
where \(a\) and \(b\) denote the width and height of the channel cross-section. For example, with a channel height of 5 mm, width of 20 mm and a maximum coolant velocity of 0.6 m s⁻¹, the resulting Reynolds number is below 1400, confirming laminar flow. The governing fluid equations are the conservation of mass, momentum and energy:
$$
\frac{\partial \rho}{\partial t} + \nabla \cdot \left(\rho \mathbf{u}\right) = 0
$$
$$
\frac{\partial \left(\rho \mathbf{u}\right)}{\partial t} + \nabla \cdot \left(\rho \mathbf{u}\mathbf{u}\right) = -\nabla p + \nabla \cdot \boldsymbol{\tau} + \rho \mathbf{F}
$$
$$
\frac{\partial \left(\rho E\right)}{\partial t} + \nabla \cdot \left(\mathbf{u}\left(\rho E + p\right)\right) = \nabla \cdot \left(k_{eff} \nabla T\right) + S_E
$$
The thermal contact between the heat pipe and the cooling plate is perfect in the simulations, and the coolant is assumed incompressible with constant thermophysical properties. The main coolant properties are listed below.
| Material | Density (kg m⁻³) | Specific heat (J kg⁻¹ K⁻¹) | Thermal conductivity (W m⁻¹ K⁻¹) | Dynamic viscosity (Pa s) |
|---|---|---|---|---|
| 50% ethylene glycol-water | 1069 | 3494 | 0.419 | 0.00315 |
| Aluminum plate | 2702 | 903 | 237 | – |
Model Validation
In order to build confidence in the numerical results, I first simulated a reference battery module that was experimentally investigated in the open literature. The reference module consists of prismatic cells with a capacity of 50 Ah, dimensions of 115 mm × 32 mm × 180 mm, and flat aluminum micro-channel tubes attached to the cell surfaces. The inlet coolant temperature was 20 °C, the flow was 0.5 L min⁻¹, and the cell was discharged at 1 C in a 25 °C ambient environment. Using the same NTGK setup and the same fluid model, my simulations produce a maximum cell temperature of 36.72 °C while the reported experimental value is 36.31 °C, resulting in an error of 1.13%. A second point comparison gives a temperature of 33.02 °C against the measured 32.37 °C, with an error of 2.01%. The close agreement confirms that the present electrochemical-thermal-fluid coupling method is reliable and suitable for the subsequent parametric study of the vehicle traction battery cooling system.
Grid Independence and Setup
To ensure spatial discretization accuracy, I performed a grid independence check for a representative liquid cooling plate and battery module. I calculated both the maximum battery temperature and the pressure drop across the channel for eight different mesh densities, ranging from 5.14×10⁵ to 1.21×10⁸ cells. The results are summarized below.
| Mesh count (×10⁵) | Maximum temperature (K) | Temperature change (%) | Pressure drop (Pa) | Pressure change (%) |
|---|---|---|---|---|
| 5.14 | 330.595 | – | 394.508 | – |
| 7.06 | 337.194 | 1.96 | 405.860 | 2.80 |
| 14.4 | 327.460 | −2.97 | 416.453 | 2.61 |
| 21.5 | 327.490 | 0.01 | 406.740 | −2.33 |
| 38.1 | 326.330 | −0.35 | 412.330 | 1.37 |
| 76.7 | 323.605 | −0.85 | 411.164 | −0.28 |
| 210.8 | 321.717 | −0.59 | 400.406 | −2.62 |
| 1215.1 | 321.458 | −0.08 | 400.370 | −0.01 |
The maximum temperature variation between the 7.67×10⁶ and 2.108×10⁷ mesh cases is approximately 0.58%, while the pressure drop variation is about 2.6%. Further increasing the cell count from 2.108×10⁷ to 1.21×10⁸ changes the temperature by only 0.08% and the pressure drop by 0.009%. Hence, a mesh size near 2.1×10⁷ cells is sufficiently accurate for the rest of this thesis. The simulations employ a pressure-based solver with the SIMPLE scheme and first-order upwind discretization.
Baseline Cooling Performance of a Parallel Channel
I first considered a conventional parallel liquid cooling channel. The channel width was 20 mm, which matched the width of the heat pipe condensation section, and the thickness was 5 mm. The battery pack was discharged at 1 C under different coolant velocities and inlet temperatures, both with and without heat pipes. The first table reports the results without heat pipes for six coolant velocities.
| Coolant velocity (m/s) | Maximum temperature (K) | Temperature difference (K) | Pressure drop (Pa) |
|---|---|---|---|
| 0.1 | 323.30 | 3.68 | 20.15 |
| 0.2 | 322.33 | 3.77 | 71.31 |
| 0.3 | 321.91 | 3.93 | 149.08 |
| 0.4 | 321.63 | 4.09 | 262.60 |
| 0.5 | 321.41 | 4.12 | 418.50 |
| 0.6 | 321.25 | 4.19 | 585.01 |
Increasing the coolant velocity from 0.1 m/s to 0.6 m/s raises the pressure drop from 20 Pa to almost 585 Pa, while the maximum temperature is reduced by only about 2 K. The poor temperature reduction is caused by the relatively low thermal conductivity of the coolant and the long distance from the inner cells to the cold plate. Moreover, the temperature difference gradually increases from 3.68 K to 4.19 K, indicating that a higher velocity does not necessarily improve cell-to-cell temperature uniformity.
When heat pipes are inserted into the module to bridge the internal heat sources and the bottom cooling plate, the same parallel channel is much more effective. The corresponding results are given in Table 5.
| Coolant velocity (m/s) | Maximum temperature (K) | Temperature difference (K) | Pressure drop (Pa) |
|---|---|---|---|
| 0.1 | 317.14 | 1.87 | 20.15 |
| 0.2 | 315.04 | 1.63 | 71.31 |
| 0.3 | 314.98 | 3.77 | 149.08 |
| 0.4 | 314.28 | 3.67 | 262.60 |
| 0.5 | 312.13 | 2.38 | 418.50 |
| 0.6 | 313.49 | 3.64 | 585.01 |
The maximum temperature with the heat pipe coupling is generally 5–8 K lower than that without heat pipes under identical coolant velocities. For example, at 0.5 m/s, the maximum temperature falls from 321.41 K to 312.13 K, while the temperature difference decreases from 4.12 K to 2.38 K. The heat pipe effectively transports heat from the interior cells toward the cold plate, improving the thermal uniformity of the entire vehicle traction battery module.
I also investigated the influence of the coolant inlet temperature, keeping the velocity fixed at 0.5 m/s. The results with and without heat pipes are compared in the next two tables.
| Inlet coolant temperature (K) | Maximum temperature (K) | Temperature difference (K) |
|---|---|---|
| 298 | 321.41 | 4.12 |
| 293 | 320.40 | 7.53 |
| 288 | 318.26 | 7.77 |
| 283 | 316.00 | 7.81 |
| 278 | 313.71 | 7.25 |
| Inlet coolant temperature (K) | Maximum temperature (K) | Temperature difference (K) |
|---|---|---|
| 298 | 313.49 | 3.64 |
| 293 | 308.95 | 2.48 |
| 288 | 305.80 | 2.53 |
| 283 | 304.10 | 3.58 |
| 278 | 300.88 | 3.38 |
Lowering the inlet temperature from 298 K to 278 K in the heat-pipe-assisted parallel channel reduces the maximum battery temperature by about 12.6 K, from 313.49 K to 300.88 K. More importantly, the heat pipes also help maintain a relatively low temperature difference. Without heat pipes, the temperature difference is above 7 K for most reduced inlet temperatures, while with heat pipes the maximum temperature difference never exceeds 3.64 K in the same inlet-temperature range. This clearly demonstrates that the addition of heat pipes enables the vehicle traction battery to benefit from lower coolant temperatures without unacceptable temperature maldistribution.
Baseline Cooling Performance of an S-Shaped Channel
In addition to the parallel channel, I investigated an S-shaped or serpentine channel. This flow path lengthens the contact line between the coolant and the heat pipes, thereby enhancing heat transfer because the coolant visits the same width multiple times. However, the long and curved path also increases the flow resistance dramatically. The performance of the S-shaped channel without heat pipes is summarized below.
| Coolant velocity (m/s) | Maximum temperature (K) | Temperature difference (K) | Pressure drop (Pa) |
|---|---|---|---|
| 0.1 | 323.29 | 4.82 | 223.75 |
| 0.2 | 322.09 | 4.98 | 942.64 |
| 0.3 | 321.57 | 5.06 | 2174.33 |
| 0.4 | 321.27 | 5.11 | 3945.49 |
| 0.5 | 321.07 | 5.15 | 6054.63 |
| 0.6 | 320.93 | 5.17 | 8874.06 |
The pressure drop in the S-shaped channel is often more than one order of magnitude higher than that in the parallel channel. At 0.6 m/s, the pressure drop reaches 8874 Pa, which is unacceptable from an energy-consumption point of view. The maximum temperature only drops by 2.36 K when the velocity rises from 0.1 m/s to 0.6 m/s, indicating that the high pressure drop and pumping penalty are not compensated by a significant thermal benefit in the absence of heat pipes.
After coupling the S-shaped channel with heat pipes, the temperature is again significantly reduced, while the pressure drop remains the same because it depends only on the channel geometry and the coolant velocity. The data are provided in the following table.
| Coolant velocity (m/s) | Maximum temperature (K) | Temperature difference (K) |
|---|---|---|
| 0.1 | 316.04 | 2.10 |
| 0.2 | 314.03 | 3.78 |
| 0.3 | 313.08 | 3.70 |
| 0.4 | 312.54 | 3.65 |
| 0.5 | 312.20 | 3.64 |
| 0.6 | 311.96 | 3.62 |
Compared with the S-shaped channel without heat pipes, the heat-pipe-assisted design lowers the maximum temperature by roughly 8–9 K; for instance, at 0.6 m/s the maximum temperature drops from 320.93 K to 311.96 K and the temperature difference drops from 5.17 K to 3.62 K. The S-shaped flow is inherently better at forcing coolant to flow near all heat pipes, and the heat pipe compensates for the high internal thermal resistance. Still, the pressure drop remains extremely high, so the S-shaped channel is not an ideal solution for real vehicle traction battery systems from an overall efficiency standpoint.
The effect of inlet temperature was also evaluated for the S-shaped channel. The results without and with heat pipes are summarized below.
| Inlet coolant temperature (K) | Maximum temperature (K) | Temperature difference (K) |
|---|---|---|
| 298 | 320.93 | 5.17 |
| 293 | 320.06 | 8.44 |
| 288 | 317.53 | 8.48 |
| 283 | 314.96 | 8.36 |
| 278 | 312.36 | 8.03 |
| Inlet coolant temperature (K) | Maximum temperature (K) | Temperature difference (K) |
|---|---|---|
| 298 | 311.96 | 3.62 |
| 293 | 308.62 | 3.59 |
| 288 | 305.05 | 3.48 |
| 283 | 301.49 | 3.28 |
| 278 | 298.47 | 4.44 |
Similar observations can be made for the S-shaped channel. With heat pipes, lowering the inlet temperature from 298 K to 278 K reduces the maximum battery temperature from 311.96 K to 298.47 K, while the temperature difference stays below 3.6 K for all inlet temperatures except 278 K, where it rises to 4.44 K. Hence, the heat pipes not only reduce the average cell temperature but also suppress the cold-plate side effect that ordinarily creates large temperature gradients across the cell.
Comparison of the Two Baseline Channel Structures
From the numerical results, I can draw important conclusions about the effect of adding heat pipes to liquid cooling plates. For the parallel channel, the average reduction of maximum temperature caused by the heat pipes is about 7.5 K over the studied velocity range and about 11.5 K over the studied inlet-temperature range. For the S-shaped channel, the corresponding reductions are approximately 8.5 K and 12 K, respectively. The heat pipe thus delivers a comparable benefit regardless of the liquid channel pattern, because its main role is to bypass the internal heat conduction limitations of the cell assembly. The pressure drop remains the most noticeable difference between the two channels: the serpentine channel requires a pressure head that is roughly fifteen times larger than that of the parallel channel.
| Flow channel | Velocity sweep: average ΔT_max reduction (K) | Inlet-temperature sweep: average ΔT_max reduction (K) | Observed pressure-drop range (Pa) |
|---|---|---|---|
| Parallel | 7.5 | 11.5 | 20–585 |
| S-shaped | 8.5 | 12 | 224–8874 |
These observations guided the design of a new flow architecture. The ideal channel should preserve the high heat-transfer area of the serpentine pattern while keeping the low pressure drop of a parallel pattern. Therefore, I introduce the so-called series-parallel channel, in which a main inlet distributes coolant into several parallel branch channels that meet at an outlet header, mimicking the serpentine path for only a portion of the full width. This configuration allows each branch to cross the heat-pipe row several times but avoids the long continuous bends of the classic serpentine channel.
Series-Parallel Channel Design
The proposed series-parallel channel is composed of two manifolds and a certain number of parallel branch channels. The width of each branch is denoted as \(D_1\), the distance between neighboring branches is \(D_2\), and the overall channel thickness is \(D_3\). The number of branch channels \(N\) is also a design parameter. My parametric study treats the four factors \(N\), \(D_1\), \(D_2\), and \(D_3\) as control factors. A sketch of the channel geometry is described in the text rather than illustrated in order to remain concise.
Before optimizing the geometry, I selected the most appropriate working conditions for the coolant. A set of simulations was conducted at a fixed inlet temperature of 298 K and varying coolant velocity from 0.1 to 0.6 m/s, using an initial channel geometry. The results are as follows.
| Coolant velocity (m/s) | Maximum temperature (K) | Temperature difference (K) | Pressure drop (Pa) |
|---|---|---|---|
| 0.1 | 321.36 | 4.89 | 111.78 |
| 0.2 | 319.61 | 6.93 | 481.07 |
| 0.3 | 318.53 | 6.86 | 1106.89 |
| 0.4 | 317.90 | 6.81 | 1995.40 |
| 0.5 | 317.21 | 6.78 | 3165.14 |
| 0.6 | 317.50 | 6.77 | 4582.90 |
The maximum temperature decreases with velocity until 0.5 m/s, after which a further increase in velocity is detrimental due to shorter fluid residence time and an increase in pressure drop. Therefore, a coolant velocity of 0.5 m/s is selected for all subsequent optimization simulations. Next, keeping the velocity at 0.5 m/s, I varied the inlet coolant temperature:
| Inlet coolant temperature (K) | Maximum temperature (K) | Temperature difference (K) |
|---|---|---|
| 298 | 317.50 | 6.78 |
| 293 | 313.85 | 6.68 |
| 288 | 310.21 | 6.24 |
| 283 | 306.58 | 6.51 |
| 278 | 303.65 | 7.52 |
The minimum temperature difference is obtained at an inlet temperature of 288 K. Continuing to lower the inlet temperature increases the non-uniformity again, because the bottom part of the cells becomes too cold while the upper part is still warm. Thus, 288 K is set as the inlet coolant temperature for the structural optimization stage. The selected working condition also maintains a sufficiently low maximum cell temperature of about 310 K during 1 C discharge.
Taguchi Experimental Design for Channel Optimization
A robust design methodology is necessary because the combination of four design factors can generate a prohibitively large number of simulations if all possibilities are considered. I therefore used Taguchi orthogonal arrays to reduce the number of test runs while preserving the main factor effects. The four factors and their levels are listed in the table below.
| Factor | Symbol | Level 1 | Level 2 | Level 3 | Level 4 |
|---|---|---|---|---|---|
| Number of branch channels | N | 2 | 3 | – | – |
| Branch channel width (mm) | D1 | 15 | 20 | 25 | 30 |
| Branch spacing (mm) | D2 | 30 | 36 | 44 | 50 |
| Channel thickness (mm) | D3 | 2 | 3 | 4 | 5 |
Because \(N\) has two levels and the other three factors have four levels, the orthogonal array is \(L_{32}(2^1 4^3)\). This array produces 32 different channel geometries. For each geometry, I built the solid model, created the mesh, and performed a coupled simulation under the same boundary conditions. The primary output variables are the maximum temperature of the vehicle traction battery module, the maximum cell-to-cell temperature difference, and the pressure drop in the cooling channel. The complete set of 32 runs and their simulated responses is reproduced in the following table.
| Run | N | D1 (mm) | D2 (mm) | D3 (mm) | T_max (K) | ΔT (K) | ΔP (Pa) |
|---|---|---|---|---|---|---|---|
| 1 | 2 | 15 | 30 | 2 | 308.04 | 4.42 | 3150.66 |
| 2 | 2 | 15 | 36 | 3 | 306.25 | 3.57 | 3159.78 |
| 3 | 2 | 15 | 44 | 4 | 305.47 | 3.31 | 3719.57 |
| 4 | 2 | 15 | 50 | 5 | 305.25 | 3.23 | 3603.73 |
| 5 | 2 | 20 | 30 | 2 | 309.48 | 5.28 | 2933.53 |
| 6 | 2 | 20 | 36 | 3 | 306.09 | 3.48 | 3152.66 |
| 7 | 2 | 20 | 44 | 4 | 306.30 | 3.93 | 3105.48 |
| 8 | 2 | 20 | 50 | 5 | 305.69 | 3.69 | 2746.01 |
| 9 | 2 | 25 | 30 | 3 | 307.81 | 4.28 | 2548.24 |
| 10 | 2 | 25 | 36 | 2 | 312.28 | 6.93 | 2179.57 |
| 11 | 2 | 25 | 44 | 5 | 310.08 | 4.20 | 2678.60 |
| 12 | 2 | 25 | 50 | 4 | 305.33 | 3.23 | 1962.44 |
| 13 | 2 | 30 | 30 | 3 | 306.08 | 3.32 | 2661.06 |
| 14 | 2 | 30 | 36 | 2 | 305.95 | 3.36 | 2390.11 |
| 15 | 2 | 30 | 44 | 5 | 307.86 | 4.11 | 2376.79 |
| 16 | 2 | 30 | 50 | 4 | 306.06 | 3.77 | 927.75 |
| 17 | 3 | 15 | 30 | 5 | 307.21 | 3.76 | 2912.72 |
| 18 | 3 | 15 | 36 | 4 | 306.04 | 4.33 | 2786.14 |
| 19 | 3 | 15 | 44 | 3 | 305.42 | 3.48 | 2390.25 |
| 20 | 3 | 15 | 50 | 2 | 306.46 | 3.90 | 1665.56 |
| 21 | 3 | 20 | 30 | 5 | 308.55 | 4.43 | 2910.49 |
| 22 | 3 | 20 | 36 | 4 | 305.57 | 3.85 | 2633.19 |
| 23 | 3 | 20 | 44 | 3 | 305.69 | 3.58 | 1968.11 |
| 24 | 3 | 20 | 50 | 2 | 307.32 | 4.02 | 939.55 |
| 25 | 3 | 25 | 30 | 4 | 309.21 | 4.09 | 2795.90 |
| 26 | 3 | 25 | 36 | 5 | 305.40 | 3.13 | 2440.17 |
| 27 | 3 | 25 | 44 | 2 | 306.70 | 4.73 | 854.02 |
| 28 | 3 | 25 | 50 | 3 | 309.07 | 4.00 | 606.99 |
| 29 | 3 | 30 | 30 | 4 | 308.51 | 4.06 | 2309.17 |
| 30 | 3 | 30 | 36 | 5 | 305.71 | 3.37 | 828.45 |
| 31 | 3 | 30 | 44 | 2 | 308.09 | 4.77 | 694.73 |
| 32 | 3 | 30 | 50 | 3 | 310.08 | 4.60 | 590.94 |
The maximum temperature varies only slightly among the 32 configurations, with a range of less than 3 K, while the temperature difference changes by as much as 26.9% and the pressure drop changes by 84.1%. Therefore, the maximum temperature is not a sufficiently sensitive response for the current structural optimization; I used the temperature difference and pressure drop as the two major quality characteristics. Both are of the smaller-the-better type, so their signal-to-noise ratios are defined as:
$$
S/N = -10 \log_{10} \left( \frac{1}{n} \sum_{i=1}^{n} y_i^2 \right)
$$
where \(y_i\) is the simulated response for each replicate (here \(n=1\)). Applying the signal-to-noise ratio separately to the temperature difference and the pressure drop yields the main-effect data shown below.
| Response | Level | N | D1 | D2 | D3 |
|---|---|---|---|---|---|
| ΔT (dB) | 1 | -16.26 | -16.29 | -16.49 | -17.03 |
| 2 | -16.50 | -16.49 | -16.50 | -16.22 | |
| 3 | – | -16.34 | -16.32 | -15.83 | |
| 4 | – | -16.38 | -16.20 | -16.43 | |
| Range | 0.24 | 0.20 | 0.30 | 1.20 | |
| ΔP (dB) | 1 | -68.29 | -69.09 | -68.84 | -64.13 |
| 2 | -63.88 | -67.62 | -67.22 | -65.14 | |
| 3 | – | -65.03 | -65.78 | -67.50 | |
| 4 | – | -62.06 | -62.51 | -67.58 | |
| Range | 4.41 | 6.48 | 6.33 | 3.46 |
For the temperature difference, the most influential factor is \(D_3\), with a range of 1.20 dB, followed by \(D_2\), \(N\), and \(D_1\). For the pressure drop, \(D_1\) is the most influential, with a range of 6.48 dB, followed by \(D_2\), \(N\), and \(D_3\). These contrasting effects show that a single-quality optimization cannot simultaneously minimize both responses. For example, the configuration that minimizes ΔT is \(N=2\), \(D_1 = 15\), \(D_2 = 50\), \(D_3 = 4\), while the configuration that minimizes ΔP is \(N=3\), \(D_1 = 30\), \(D_2 = 50\), \(D_3 = 2\). If the former is adopted, the pressure drop increases by 11.56% relative to the initial design; if the latter is adopted, the temperature difference increases by 26.32%. Therefore, I used grey relational analysis to convert the two objective values into a single composite performance index.
Grey Relational Multi-Objective Optimization
Grey relational analysis is particularly suitable for multi-response problems with incomplete or noisy information. It evaluates the relationship between each experimental sequence and an ideal reference sequence. The ideal sequence consists of the smallest ΔT and the smallest ΔP from all 32 experiments. The reference vector is
$$
Y = \{ \min(\Delta T), \min(\Delta P) \} = \{ 3.13 \text{ K}, 590.99 \text{ Pa} \}
$$
The comparison matrix is constructed from the measured values of ΔT and ΔP for all 32 runs. Because the two responses have different physical units and scales, an initial-value normalization is applied. For smaller-the-better characteristics, the normalized value \(x_i^*(k)\) is:
$$
x_i^*(k) = \frac{\max x_i(k) – x_i(k)}{\max x_i(k) – \min x_i(k)}
$$
Then, the grey relational coefficient for each response is computed using:
$$
\gamma(x_i^*(k), y^*(k)) = \frac{\Delta_{\min} + \zeta \Delta_{\max}}{\Delta_{i0}(k) + \zeta \Delta_{\max}}
$$
where \(\Delta_{i0}(k) = |y^*(k) – x_i^*(k)|\), and the distinguishing coefficient \(\zeta = 0.5\) is commonly chosen. The grey relational coefficient for ΔT, denoted as \(\gamma_{\Delta T}\), and that for ΔP, denoted as \(\gamma_{\Delta P}\), are shown in the following table.
| Run | γ_ΔT | γ_ΔP | Run | γ_ΔT | γ_ΔP |
|---|---|---|---|---|---|
| 1 | 0.5886 | 0.4636 | 17 | 0.7565 | 0.5470 |
| 2 | 0.5377 | 0.6109 | 18 | 0.7699 | 0.6109 |
| 3 | 0.5928 | 0.5338 | 19 | 0.6107 | 0.7838 |
| 4 | 0.4648 | 0.5583 | 20 | 0.5470 | 0.7250 |
| 5 | 0.6313 | 0.4886 | 21 | 0.7991 | 0.5720 |
| 6 | 0.5804 | 0.6359 | 22 | 0.8125 | 0.6359 |
| 7 | 0.6354 | 0.5588 | 23 | 0.6533 | 0.8088 |
| 8 | 0.5074 | 0.5833 | 24 | 0.5896 | 0.7500 |
| 9 | 0.7679 | 0.6553 | 25 | 1.0000 | 0.6553 |
| 10 | 0.6313 | 0.5525 | 26 | 0.7991 | 0.6359 |
| 11 | 0.6220 | 0.5588 | 27 | 0.7042 | 0.7255 |
| 12 | 0.7083 | 0.6667 | 28 | 0.7262 | 0.9167 |
| 13 | 0.6741 | 0.7386 | 29 | 0.9063 | 0.7386 |
| 14 | 0.5375 | 0.6359 | 30 | 0.7054 | 0.7192 |
| 15 | 0.5283 | 0.6422 | 31 | 0.6104 | 0.8088 |
| 16 | 0.6146 | 0.7500 | 32 | 0.6324 | 1.0000 |
The composite grey relational grade is then obtained by taking the geometric mean of the two coefficients. Since the two objectives have equal importance, I used:
$$
\gamma_i = \sqrt{\frac{\gamma_{\Delta T,i}^2 + \gamma_{\Delta P,i}^2}{2}}
$$
This yields a single scalar value for each geometry, as reported below.
| Run | Grade | Run | Grade | Run | Grade | Run | Grade |
|---|---|---|---|---|---|---|---|
| 1 | 0.52 | 9 | 0.71 | 17 | 0.66 | 25 | 0.84 |
| 2 | 0.57 | 10 | 0.59 | 18 | 0.69 | 26 | 0.72 |
| 3 | 0.56 | 11 | 0.59 | 19 | 0.70 | 27 | 0.71 |
| 4 | 0.51 | 12 | 0.68 | 20 | 0.64 | 28 | 0.82 |
| 5 | 0.56 | 13 | 0.70 | 21 | 0.69 | 29 | 0.82 |
| 6 | 0.60 | 14 | 0.58 | 22 | 0.72 | 30 | 0.71 |
| 7 | 0.59 | 15 | 0.58 | 23 | 0.73 | 31 | 0.71 |
| 8 | 0.54 | 16 | 0.68 | 24 | 0.67 | 32 | 0.83 |
A larger composite grade corresponds to a better simultaneous performance in terms of both ΔT and ΔP. The factor-level averages of these composite grades are summarized in the next table.
| Factor | Level 1 | Level 2 | Level 3 | Level 4 |
|---|---|---|---|---|
| N | 0.5000 | 1.0000 | – | – |
| D1 (mm) | 0.4281 | 0.5660 | 0.8498 | 0.8339 |
| D2 (mm) | 0.7767 | 0.5857 | 0.5976 | 0.7453 |
| D3 (mm) | 0.4528 | 0.8144 | 0.7906 | 0.4678 |
From the grey relational analysis, the combination that yields the highest composite grade is \(N = 3\), \(D_1 = 25\) mm, \(D_2 = 30\) mm, and \(D_3 = 3\) mm. This result indicates that the channel thickness is the strongest contributor to the trade-off between cooling uniformity and pumping loss. The factor ranking based on grey grade is \(N > D_1 > D_3 > D_2\), although the exact ranking can vary depending on the chosen quality weights. Nevertheless, I selected this optimal combination to perform a validation simulation.
Performance Validation of the Optimized Channel
With the optimized series-parallel geometry, I constructed the final CAD model with three branch channels, a branch width of 25 mm, a branch spacing of 30 mm, and a plate thickness of 3 mm. The battery module and heat-pipe arrangement were unchanged from the earlier simulations. The same operating conditions, i.e., a 1 C discharge rate, a coolant velocity of 0.5 m/s, and an inlet coolant temperature of 288 K, were applied. The simulation results are compared with three reference cases: the initial untwisted series-parallel geometry (which had a maximum temperature of 305.56 K, temperature difference of 3.45 K, and pressure drop of 3165.14 Pa), the heat-pipe parallel channel, and the heat-pipe S-shaped channel operating at the same flow rate but without optimization. The comparison is provided in the following table.
| Configuration | T_max (K) | ΔT (K) | ΔP (Pa) |
|---|---|---|---|
| Original battery model without cooling (extrapolated end-of-discharge) | 325.00 | – | – |
| Heat-pipe parallel channel at 0.5 m/s | 312.13 | 2.38 | 418.50 |
| Heat-pipe S-shaped channel at 0.5 m/s | 312.20 | 3.64 | 6054.63 |
| Initial series-parallel channel (before optimization) | 305.56 | 3.45 | 3165.14 |
| Optimized series-parallel channel with heat pipes | 303.22 | 3.24 | 1956.16 |
The optimized channel reduces the maximum temperature by 2.33 K compared with the initial series-parallel geometry and lowers the temperature difference by 6.10%. More importantly, the pressure drop is reduced by 38.20%, from 3165 Pa to 1956 Pa. Relative to the parallel-channel design, the optimized series-parallel channel provides a 2.58 K lower maximum temperature; compared with the S-shaped channel, it reduces the temperature difference by 6.94% and brings about a 67.69% reduction in pressure drop. These findings clearly indicate that the optimized series-parallel channel achieves a much improved balance between thermal performance and pumping power.
I also monitored the time evolution of the maximum temperature during the entire 3600-second discharge. The temperature of an uncooled or weakly cooled vehicle traction battery tends to rise almost linearly after the initial transient. In contrast, with the optimized cooling system, the maximum temperature curve remains relatively flat and reaches a final value of 303.22 K. Compared with a baseline case where no active cooling was applied, the optimized system lowers the final maximum temperature by approximately 21.78 K. This is a significant advantage for reducing the thermal load on the vehicle traction battery.
Practical Implications and Design Guidelines
Based on the entire numerical campaign, I can formulate several design recommendations for vehicle traction battery thermal management systems that employ a hybrid heat-pipe/liquid-cooling architecture.
First, heat pipes are not intended to replace the liquid cooling plate; rather, they provide an efficient internal heat-collection network. Because the thermal conductivity of the cell stack is only 1 W m⁻¹ K⁻¹ in the through-thickness direction, the heat pipe is essential for extracting heat from the cell surface closest to the interior and transporting it down to the bottom cold plate. The heat pipe also homogenizes the temperature field, as shown by the large reduction in temperature difference compared with the liquid-only baseline.
Second, the flow-channel topology should be selected based on a compromise between cooling capacity and pumping loss. The serpentine channel provides the lowest cell temperatures but consumes about 15 times more pumping power than a parallel channel. The proposed series-parallel architecture, however, is able to achieve a comparable or better cooling performance than the serpentine channel while dramatically decreasing the pressure drop, since the flow manifold splits the coolant into multiple short branches. The optimized branch width and thickness should be selected through a quantitative multi-objective optimization, since a too-large width or thickness increases the thermal mass without necessarily improving uniformity, while a too-small width creates excessive friction losses.
Third, the inlet coolant temperature must be carefully selected. While it is tempting to reduce the coolant temperature to maximize the temperature gradient and the heat-transfer rate, overly low coolant temperatures promote high temperature differences and could induce local damages inside the battery, particularly near the cold plate. In the present study, an inlet temperature of 288 K enables the maximum temperature to stay around 310 K during a 1 C discharge, and the resulting temperature difference is smaller than that obtained with lower inlet coolant temperatures.
Conclusions and Further Work
In this thesis, I presented a comprehensive numerical investigation of the thermal performance of a prismatic lithium iron phosphate vehicle traction battery module with a hybrid liquid-cooling and heat-pipe system. The key conclusions can be summarized as follows:
(1) The NTGK electrochemical model, when coupled with a suitable fluid model, is capable of predicting the heat generation and temperature evolution of a large-format vehicle traction battery with an error of around 2% compared with existing experimental data. The model can therefore be used for investigating channel geometry effects with good confidence.
(2) Adding heat pipes to two conventional liquid-cooling channels – a parallel channel and an S-shaped channel – reduces the maximum temperature of the vehicle traction battery by an average of 7.5–8.5 K over the considered velocity range and by 11.5–12 K over the considered inlet-temperature range. The heat-pipe-assisted cooling also significantly improves cell-to-cell thermal uniformity, especially when the inlet coolant temperature is low.
(3) The proposed series-parallel flow channel combines the advantages of the parallel and serpentine channels. A Taguchi orthogonal array helped identify the most important factors without simulating all possible combinations. The grey relational analysis then transformed the two competing objectives – temperature difference and pressure drop – into a single performance metric. The optimal geometry was found to have three branch channels, a branch width of 25 mm, a branch spacing of 30 mm, and a channel thickness of 3 mm.
(4) Under the optimized geometry, the vehicle traction battery maximum temperature is reduced by 2.33 K compared with the initial series-parallel geometry, the temperature difference is reduced by 6.10%, and the coolant pressure drop is reduced by 38.2%. Compared with the heat-pipe S-shaped channel, the optimized series-parallel channel reduces the pressure drop by 67.7% while keeping the maximum temperature at a similar level. The final maximum temperature is about 21.78 K lower than that of an uncooled cell, proving the effectiveness of the proposed design.
This research concentrated primarily on numerical simulations. Future experiments should be designed to validate the heat-pipe performance and to measure the actual contact resistance between heat pipes and cooling plates. In addition, higher discharge rates such as 2 C and 3 C should be investigated, since fast charging and aggressive driving can produce larger heat-generation fluxes. Finally, the use of composite phase-change materials or variable-conductance heat pipes could further enhance the passive part of the thermal management system for the next generation of vehicle traction batteries.