The transient thermal response of a 15-cell, 48 V, lithium-ion battery pack for an unmanned ground vehicle (UGV) was simulated using ANSYS fluent. Heat generation rates and specific heat capacity of a single cell were experimentally measured and used as input to the thermal model. A heat generation load was applied to each battery, and natural convection film boundary conditions were applied to the exterior of the enclosure. The buoyancy-driven natural convection inside the enclosure was modeled along with the radiation heat transfer between internal components. The maximum temperature of the batteries reached 65.6 °C after 630 s of usage at a simulated peak power draw of 3600 W or roughly 85 A. This exceeds the manufacturer's maximum recommended operating temperature of 60 °C. We present a redesign of the pack that incorporates a passive thermal management system consisting of a composite expanded graphite (EG) matrix infiltrated with a phase-changing paraffin wax. The redesigned battery pack was similarly modeled, showing a decrease in the maximum temperature to 50.3 °C after 630 s at the same power draw. The proposed passive thermal management system kept the batteries within their recommended operating temperature range.
A 48 V lithium-ion battery pack was designed and fabricated for use in an unmanned ground vehicle (UGV). The battery pack is assembled from 15 high-capacity cylindrical lithium iron phosphate (LiFePO4) batteries (Headway model H-40152 S, 3.2 V, 15 Ah, 40 mm in diameter and 152 mm tall). The batteries are supported by plastic spacer frames arranged in a close-packed hexagonal array inside a closed aluminum battery box, see Figs. 1 and 2. The battery box panels were welded together to form a trapezoid-shaped enclosure. Since the UGV is designed to operate in all-weather conditions, the battery pack must be sealed from the outside environment. Since the batteries generate a significant amount of heat during discharge and the sealed enclosure isolates them from the external air, there is concern that the operating temperatures could rise substantially inside the battery pack. The batteries are designed to operate at a maximum temperature of 60 °C.
Though lithium iron phosphate batteries provide the necessary power density required by the UGV, they have high heat generation rates which can limit safe application and battery life [1,2]. Vehicle performance and space considerations require the cells to be packed closely together leading to the possibility of high battery temperatures that degrade battery life and, potentially, lead to thermal runaway . Heat is generated in the cell by two factors: entropy change from electrochemical reactions and irreversible effects such as ohmic heating due to current flow across internal resistance [4,5]. Thermal management becomes more critical with larger batteries as surface area to volume ratio decreases with increasing battery size, leading to lower heat transfer rates per unit heat generation rate .
The vehicle features hot-swappable battery packs which can be removed from the vehicle and charged off platform. Charging can be done at a controlled rate to limit thermal effects on performance. The goal of this analysis was to determine the maximum temperatures the batteries would experience under a prescribed high power loading of 240 W per battery or about 85 A. Since the initial design of the battery pack did not focus on thermal constraints, it was subsequently desired to perform a thermal analysis of the pack to determine the maximum temperatures under the prescribed loading, as well as support design options to control the resulting temperatures.
We present a comprehensive study that includes both laboratory experiments and computer simulations on a new battery system arranged in a unique geometry. Earlier efforts reported in the literature focused on two-dimensional simulation of largely different sized, non-LiFePO4 batteries, under low current draw profiles in packs of rectangular geometry. There is a need to optimize the more specific LiFePO4 chemistry pack parameters presented here to improve vehicle performance. A novel fluid-thermal coupled three-dimensional computational model of a lithium iron phosphate battery pack is developed with the objective of understanding the various heat transfer mechanisms that contribute to battery and vehicle performance. The model incorporates a unique three-dimensional closed-packed hexagonal geometry, a shape factor that was derived from the imposed design constraints. Additionally, the model features a novel, high amperage, loading that is not presented in previous research, showing how extreme use profiles might lead to degradation. Previous research has studied numerical modeling of phase-change material (PCM) based thermal management systems, but does not compare the thermal performance of systems with and without the phase-change material in the same model space, as presented in this study. This study establishes that heat transport can be controlled effectively by a sealed phase-change material with expanded graphite matrix (PCM/EG) for the given geometry and current draw. Some new interesting phenomena are found, for example, the PCM/EG composite substantially lowers the maximum battery temperature, but the conductivity of the composite needs to be increased to gain full benefit of the added phase-change material.
Following Mills and Al-Hallaj, the battery was insulated in polyurethane foam to reduce convection heat transfer during the experiments. A polyurethane foam block was cut such that the battery could be placed in the center, see Fig. 3. Two metal cylinders, one copper and one 6061 aluminum, were machined to the same cylindrical dimensions as the battery. These cylinders were used to determine the heat loss, or UA value, of the foam insulation block setup. Three T-type thermocouples were used to measure the temperature at the surface of the battery or metal cylinder as well as the external air temperature. An Agilent 34972 A Data Acquisition/Switch Unit, BK Precision XLN3640 Programmable direct current (DC) Power Supply, and BK Precision 8518 Programmable Electronic Load were used for the experiments.
Calibration and Heat Capacity.
The natural log of the temperature difference over time, shown in Fig. 4, yields a linear cooling trend. The slope of this line is −UA/mCP. The heat capacity of the cylinder, mCP, is known from the material properties of copper and the measured mass of the cylinder. The heat loss, or UA value, of the foam insulated setup was determined from the cooling plot using the known heat capacity of the cylinder. This procedure was performed three times for each of the cylinders to characterize the uncertainty of the UA value, resulting in a UA value of 0.0283 ± 0.0005 W/K. The procedure was similarly performed using the battery in place of the metal cylinders to determine the heat capacity of the subject Li-ion batteries. In these experiments, the heat capacity of the battery was found using the slope of the cooling plot with the previously determined UA value of the foam setup providing an experimentally measured specific heat capacity for the batteries of 950 ± 20 J/kg K. The calibration results are shown in Table 1.
Heat Generation Rates—Experimental Method.
Heat generation rates of a single battery were determined by performing three constant power discharges for each of the three different power levels, 144 W, 192 W, and 240 W or 3 P, 4 P, and 5 P, respectively. Plots of measured voltage and current as a function of depth of discharge (DOD) are shown in Figs. 5 and 6. Two T-type thermocouples were attached with electrical tape to the middle of the battery on the opposite sides and one was placed in air 3 ft away, as described for the previous experiments. Temperatures, voltage, and current were recorded every 5 s during each discharge experiment. In each case, heat generation rates of the battery were determined using Eq. (2) with the previously determined UA and battery heat capacity value. The heat generation rates for each discharge power level and their curve fit lines are shown in Fig. 7. The total heat generated during each run (shown in Table 2) was calculated by integrating the heat generation rate with respect to time. The highest constant power discharge rate of 5 P, or 240 W, was chosen to represent the maximum expected current draw, about 85 A, required by the robotic vehicle during service. This is the power level used for subsequent simulations of the battery pack temperatures during vehicle operation.
Heat Generation Rates—Entropy Method.
The entropy coefficient of the battery, shown in Fig. 8, was determined using the measured discharge characteristics from each run. The entropy coefficient was modeled as a linear fit of all the heat generation data points between the 0.1 and 0.9 depth of discharge. The black line shows the linear fit for all of the trials for all the P-rates. Each light gray line shows the linear fit for all the three trials from each respective P-rate. The entropy coefficient curve fit was used with Eq. (4) to calculate the theoretical heat generation rates. A comparison of experimentally measured and predicted heat generation rates is shown in Fig. 9. It can be seen that there is a good general agreement between the predicted and measured rates. The 5 P discharge rate represents the worst-case current draw expected in application. For each constant power discharge, there is a dramatic increase in the heat generation rate at the end of the battery discharge. This arises from the drop in operating voltage and related increase in current at the end of each constant power discharge.
Radiation heat transfer between the batteries and enclosure was accounted for with the fluent surface-to-surface radiation model. This accounted for the radiation exchange in the enclosure of gray-diffuse surfaces by calculating a view factor for each internal surface. This model assumed that all the surfaces were gray and that any absorption, emission, or scatter of radiation by the air could be ignored. Emissivity values of 0.90 , 0.84 , and 0.92 were assigned to the aluminum, plastic, and battery surfaces, respectively.
A Flir Thermacam SC300 infrared camera was used to measure the emissivity of the batteries. A piece of black electrical tape with a known emissivity of 0.97 was attached to the battery such that it had the same temperature as the battery. The camera was set to measure surface temperatures with an emissivity of 0.97, and the infrared radiation of the tape was compared to the radiation from the battery material. Figure 10 shows a typical infrared image of the battery. An emissivity of 0.92 was calculated for the battery coating material using this technique. Emissivity is a function of wavelength and temperature for any material. The emissivity value required by fluent for the surface-to-surface radiation model should be a representative average of the varying emissivities for the material over all the wavelengths. The infrared camera captures radiation over the 7.5–13 μm wavelength range. As such, the camera can detect a fraction of the radiation wavelengths being emitted by the battery. Wein's displacement law predicts that the wavelength of peak intensity at a temperature of 60 °C occurs at 8.7 μm, which falls within the detectable range of the infrared camera. The result is an approximation for the emissivity of the battery using the detectable wavelengths and this emissivity is extended to apply to all the wavelengths for the material.
Thermal properties of the batteries including specific heat and heat generation rates were determined from the aforementioned experiments, while the thermal conductivity was taken from the published literature . The volume of the subject battery was determined using caliper measurements of the battery diameter and length. The small amount of material associated with the protruding terminals at each end was neglected. The battery was weighed on a scale, and the density was calculated by dividing the weight by the measured volume of the battery. The properties of each battery were assumed to be isotropic and homogeneous [4,7]. Table 3 shows the material properties for the batteries, aluminum, plastic, and air at 20 °C . The viscosity of the air in the model was 1.85 × 10−5 kg/ms, and the air thermal expansion coefficient was 0.00343 1/K. Heat generation in the batteries was modeled as uniformly distributed [7,10]. The average of the experimentally measured heat generation rates for a 5 P discharge was divided by the volume of the battery to yield a curve for the average body heat flux load in W/m3 over the discharge of the battery. A polynomial curve fit to the average heat generation rates was applied as a heat load to each battery in the simulation.
Boundary and Initial Conditions
A no-slip wall condition was imposed at the inner enclosure walls, battery walls, and plastic walls where the enclosed air comes in contact with a solid surface. At the start of the simulation, all the components of the system were initialized to atmospheric pressure and a temperature of 25 °C. The external free surfaces of the enclosure were given surface film boundary conditions to simulate free convection on the vertical and horizontal surfaces. The sink temperatures for the film boundary conditions were set to an ambient temperature of 25 °C. Convection coefficients were determined using experiment correlations from Incropera et al. . Dirt and debris are likely to settle on the pack, effectively adding a thin layer of insulation to the pack and reducing the heat convection to the ambient air. To be conservative, a smaller than predicted, uniform convection coefficient boundary condition of 2 W/m2 K was applied to the exterior surfaces of the pack.
An unstructured mesh was generated for this study using 1,733,072 tetrahedral elements with a global maximum size measuring 4 mm. Gravity was defined as acting downward toward the bottom of the pack. The grid independence plot showed that at a flow time of 630 s, the temperature at one point in the model converges to a specific value as the grid is refined. The global maximum size parameter was chosen because it generated a mesh that provided accurate results without substantially increasing the computational expense of the simulation. Tetrahedral elements were used throughout the entire model because they readily conformed to the complex geometry of the components in the pack.
A transient analysis was required in the present case since the simulation only reached steady state long after the battery pack would be depleted. Experiments showed that the batteries were depleted after 630 s at the 5 P rate. A fixed time step of 0.5 s was used to run a 630 s flow time study. This small time step ensured accuracy of the results and was based on the characteristic time of the modeled system. A comparison of results using a 0.5 s time step and a 0.1 s time step showed negligible differences in the heat transfer rate and battery temperatures in the pack. The Boussinesq approximation was used by assigning the modeled air an operating density of 1.205 kg/m3. The Boussinesq approximation neglects any changes in density of the fluid, except when the density terms appear multiplied by the gravity term. This leads to the conclusion that inertia differences are negligible while gravity is large enough to create a buoyancy-driven flow. The second-order upwind scheme was used for the momentum and energy equations. The pressure equation was set to body force weighted. Second-order implicit and noniterative time advancement was used for the transient formulation. Pressure–velocity coupling was set to pressure-implicit with splitting operators, and the gradient calculation was set to least squares cell based.
Computational Fluid Dynamics (CFD) Results
The temperature distribution after 630 s at a 5 P discharge rate is shown in Figs. 11 and 12. The batteries were initialized to a temperature of 25 °C and were found to increase to 65.6 °C in 630 s under a 5 P discharge. This exceeded the maximum design operating temperature of 60 °C for these batteries. These elevated temperatures lead to degraded battery life and can create unsafe operating conditions. Figure 12 illustrates that the aluminum enclosure stayed at a relatively uniform and near ambient temperature throughout the battery discharge. This result is significant as it illustrates the lack of heat flow to the enclosure that would have transferred thermal energy away from the batteries.
Figure 13 shows an image of the buoyancy-driven flow in the pack, plotted as vectors. For the sake of clarity, the batteries are removed from this image. One can see a plume of hot air collecting at the top of the enclosure and relatively cooler air at the bottom. Additionally, as one would expect, this figure shows that the air rises along the battery walls and flows downward along the relatively cool inside walls of the enclosure. This forms thin convection cells along the enclosure walls with the air circling in the space at the top of the batteries and falling down as it cools from convection with the colder aluminum enclosure walls. The vertical component of air velocity is largest near the walls of the batteries and enclosure. In contrast, the center of the convection cell between the vertical walls is nearly stagnant.
Figure 14 illustrates that, with the air gap model, the temperature is relatively uniform along a horizontal line, perpendicular to the longitudinal axis of the batteries, through the center of the back row of batteries. This trend continues throughout the battery discharge with only small temperature gradients through the pack interior along the horizontal line. Maximum temperatures in the batteries occur near the vertical midpoint of the pack, with relatively cooler temperatures at the top and bottom.
The CFD model was validated by comparing the surface temperature of the battery at the center of the pack to the experimentally measured surface temperature of the battery performing the same discharge profile while insulated by polyurethane. Figure 15 shows that the surface temperature in the model followed the same trend and had a slightly smaller magnitude compared to the experimentally measured temperature. The temperature rise at the end of the simulation was 1.2 °C smaller for the model surface than the insulated experimentally measured surface. The results matched closely as expected since the modeled battery pack has near insulating conditions due to the close proximity of other batteries and the weak buoyancy-driven flow predicted by the low Rayleigh number.
Since the current pack design is not sufficient to protect the batteries from thermal damage during worst-case loading, a passive thermal management system was designed to exploit the energy absorption of a phase-change material (PCM). Following pioneering work on the use of phase-change materials for thermal management in batteries [7,11], we chose to utilize a paraffin wax with an expanded graphite matrix. The PCM composite is designed to fill the open space surrounding each battery and along the inside of the aluminum enclosure walls. This design for a passive cooling system allows the battery pack to be fully sealed from the environment without any intruding cooling elements .
High performing phase-change materials are characterized by their high latent heat of fusion, but typically suffer from low thermal conductivity [12,13]. The thermal conductivity of the PCM can be improved by creating an expanded graphite (EG) matrix impregnated with a PCM [14,15]. This composite PCM/EG material combines the high specific latent heat of fusion of the PCM and the high thermal conductivity of the expanded graphite to create a highly thermally conductive and energy-absorptive composite material.
The PCM absorbs the heat generated from the batteries while minimizing temperature changes in the pack. The effectiveness of the PCM is governed by the melting point and latent heat of the material. Paraffin wax (Rubitherm RT-42) was used as the PCM in this study due to its high specific latent heat of fusion and its melting point, 42 °C, in the operating temperature range of the battery pack.
The expanded graphite matrix is formed from flake graphite by a heat-treatment process . The process increases the porosity of the graphite and thus decreases the bulk density. The expanded graphite particles are then compacted to form a graphite matrix. Compacting the particles increases the thermal conductivity, both perpendicular and parallel to the compaction while decreasing the porosity of the resulting matrix . The expanded graphite matrix is submerged into liquid PCM to form the PCM/EG composite material. Capillary forces draw the liquid PCM into the matrix where it remains after the matrix is removed. The mass of PCM left in the matrix is a function of soaking time and is characterized in the work of Ref. .
Modeling the phase-change process of materials can be complicated and computationally expensive. A modeling method developed by Farid et al.  was used to treat the phase-change process of the paraffin as a temperature-dependent change in the specific heat of the composite material. A differential scanning calorimetry (DSC) curve fit of the paraffin is used from the method described in Ref. . The curve was used to convert the latent heat of fusion of the paraffin to an effective specific heat over the melting temperature range. The curve has been normalized such that the area under the large peak, from 35 °C to 55 °C, is equal to one so the curve can be scaled to the latent heat of fusion of the paraffin. The specific heat of the PCM/EG composite material was input to the fluent model as a piecewise linear function and is the sum of the effective specific heat due to the latent heat of the paraffin and the specific heat of the composite material. Any density change of the phase-change material from the solid to liquid phase was neglected. Realistically achievable thermophysical properties for the PCM/EG composite  used in the fluent simulation are shown in Table 4. The model can be adapted to accommodate other phase-change materials. Phase-change materials with known density, heat capacity, conductivity, and latent heat can be modeled using the same assumptions in the place of PCM/EG.
Figure 16 shows how the PCM/EG passive thermal management system substantially reduced the maximum temperature of the batteries compared to the original pack with natural convection cooling. Without the passive thermal management system, the maximum temperature of the batteries increases beyond the 60 °C threshold to 65.6 °C. In stark contrast, the passive thermal management system reduced the maximum temperature of the batteries to 50.3 °C, keeping all of the batteries within the design operating temperature range. Figure 14 shows the temperature fluctuations across the width of the pack through the back row of batteries with PCM/EG. This plot shows clearly the radial temperature fluctuation across each individual battery. The highest temperature occurs in the radial center of the middle back row battery. Temperature deviations between the centermost cell and the two outermost cells on the graph are minor, less than 3 °C.
The temperature comparison for the two models under the worst-case loading condition of 3600 W or roughly 85 A for 630 s is shown in Fig. 16. For the case of air-convection cooling, the maximum battery temperature reached 65.6 °C and exceeded the maximum design operating temperature of 60 °C. This analysis indicates that the batteries in the pack are likely operating outside of their optimal temperature range if the UGV is drawing a sustained 85 A or more for 630 s. This increase in operating temperature does lead to an increase in the electrical performance of the batteries arising from the increased rate of chemical reactions, but decreases the life expectancy of the battery due to increased corrosion rates [4,19]. Furthermore, if overheated, Li-ion batteries may suffer from thermal runaway and, in extreme cases, cell rupture or combustion.
The temperature distribution results presented here provide insight into how the pack performs under maximum loading, what the maximum temperatures are, and how evenly distributed the heat is throughout the battery. This is an important and useful check to ensure that the current design can implement safety protocols to prevent thermal runaway in the batteries. It is known that cells within the pack will be charged or discharged slightly differently during each cycle if they are at different temperatures. Under these conditions, the cells eventually become unbalanced with cycles, which degrades pack performance [4,19]. Temperature variation among the cells in the pack can cause differences in impedance which can amplify capacity differences between the cells. Capacity differences can cause some cells to become overcharged or overdischarged which can lead to accelerated capacity fading or thermal runaway . Thermal balancing ensures that the batteries wear out as evenly as possible and certain batteries do not need to be replaced prematurely. In short, battery management is simpler if thermal management is controlled and uniform. This study suggests that future packs group the batteries together in a manner that provides a more uniform battery temperature distribution.
In the passive thermal management model, the air surrounding the batteries was replaced with a composite expanded graphite matrix embedded with paraffin wax. This configuration exploits the large heat capacity and latent heat of fusion of the wax as well as the high thermal conductivity of the graphite matrix. This increase in conductivity around the batteries conducted heat more effectively to the exterior of the pack. Most importantly, the wax provided significant heat storage through its latent heat of fusion during phase change. The PCM/EG system provided significant heat storage and reduced the temperature of the batteries substantially as shown in Fig. 16. Table 5 shows that the maximum temperature of the batteries was reduced from 65.6 °C to 50.3 °C by this passive thermal management system. Figure 17 shows that the PCM/EG itself did not get hot enough to completely melt the wax. The temperature reduction performance would be improved further by starting the battery discharge at a higher ambient temperature or alternatively, by lowering the melting temperature of the PCM. The PCM/EG would be better utilized by increasing the gap size between batteries at the cost of space between the batteries and the enclosure walls.
The maximum temperature over time with PCM/EG (Fig. 16) is relatively linear. The linearity is in part due to the alignment of trends near the end of discharge. The effective heat capacity of the PCM/EG is nonlinear over the temperature range as modeled and increases sharply at temperatures seen near the end of the simulation. Similarly, the heat generation rates increase sharply as current levels increase at the end of discharge. The increasing effective heat capacity of the PCM/EG and increasing heat generation rates have the effect of mitigating each other near the end of discharge.
The spaces for the air to circulate between the batteries and the enclosure are small and lead to significant friction, which limits advection. Replacing the air space with a highly conductive material with a high heat capacity and high latent heat, such as the expanded graphite phase-change material, proved to significantly improve the thermal performance of the pack. The bulk density of the composite PCM/EG material is low compared to other highly conductive materials and will only add 1.4 kg to the mass of each battery pack while still providing substantial thermal performance enhancement. The passive system modeled here provides excellent thermal performance improvements without siphoning any of the battery pack power as would an active thermal management solution. The temperature reduction of the system allows the UGV to operate in hotter environments and draw higher currents, if necessary, without the risk of thermal runaway.
fluent was used to run simulations of the transient temperatures in a 15-cell lithium iron phosphate battery pack for an unmanned ground vehicle under worst-case power draw conditions. These simulations were conducted to determine the risk of thermal runaway and to explore what changes might be made to better manage the battery pack temperatures. The CFD simulation adequately modeled the worst-case heat generation scenario with a power draw of 3600 W at roughly 85 A and determined the temperature distribution in the pack over time. The analysis revealed that the batteries reached 65.6 °C after 630 s of peak power usage. This temperature exceeds the maximum recommended operating temperature of 60 °C. Input for the simulation came from a series of experiments to determine individual cell heat generation as a function of depth of discharge over a broad range of current draws. After finding that the air-convection cooled pack would not properly protect the batteries, the model was adapted to simulate a passive cooling system utilizing an expanded graphite phase-change material composite. The PCM/EG system provided a substantial maximum temperature reduction of 15.3 °C, a 37.7% reduction in temperature rise. The maximum battery temperature was reduced to 50.3 °C for the largest expected power draw during UGV operation. The simulated passive thermal management system restored the batteries to the design operating temperature range and allowed for a sealed battery pack without intrusive cooling elements.
The authors thank the Center for Renewable Energy and Alternative Transportation Technologies at Cal Poly, funded through the Department of Energy, Award Number No. EE-0004178, managed by Dr. Chris Johnson. The authors also acknowledge the critical guidance and support provided by Dr. John Dunning. His experience and knowledge made this research possible.