Research on simplification of simulating the heat conduction in the lithium-ion battery core

This paper discusses the model simplifing issue in battery thermal simulation. The paper verifies that for the large power battery simplifying the multilayer battery core as a lumped cuboid is reasonable. So when doing simulation, building a multilayer core is unnecessary. And the calculation cost can be reduced by the lumped model. Specific power battetry of 70Ah is dissembled to be modeld. Thermal models of are established, including models with a lumped core and with multilayer cores. For the lumped core, the anisotropic thermal conductivities are got by equations calculating series and parallel equivalent thermal conductivity. While for the multilayer core models, the core contains numbers of unit cells and the volume of which is equal to that of the lumped. In addition, under the boundary conditions of inner heat source and surface heating, steady state simulations are performed. Simulation results indicate that the temperature distributions of the lumped model and the multilayer model are almost the same. For one thing, large number of multilayers and low shell thermal conductivity contribute to a uniform temperature distribution within the core, so it is reasonable to simplify the multilayer core as a lumped cuboid. For another, due to the size of the battery and the shell property, it is difficult to find a simple curve to fit the simulation temperature on the battery surface. Although minor differences still exist, the lumped core can well subsitute the multilayer core in battery thermal simulation.


Introduction
Under the pressure of energy crisis and environmental protection, electric vehicle is attracting wide spread interest. Lithium-ion battery is a promising power source for the electric vehicle. Since thermal condition greatly influences the performance of the lithium-ion battery, there is a need for a good understanding of lithium-ion battery thermal issues [1]. Thermal modeling is a prevailing method to do research on battery thermal issues. The battery consists of the core, the shell, the terminal, the safety vent etc [2,3]. Core modeling is the crucial part of thermal modeling. There are two common types of battery core: the prismatic type [2][3][4][5][6] and the cylinder type [7][8][9][10][11][12][13]. The battery has a layered core. To guarantee the capacity of the battery, each battery consists of some unit cells.
Simulation model of multilayer structure requires larger amount of calculation than that of lumped cuboid. In many cases when building a model of lumped cuboid, the equivalent thermal conductivity in perpendicular and parallel directions are calculated by classic heat transfer equations of series and parallel equivalent thermal conductivity for composite slabs [2][3][4]10].
However, in the text books of heat transfer, the equations for calculating equivalent thermal conductivity works only when the thermal conductivities of different layers have little difference [14,15]. While in battery core modeling, the thermal conductivity of different materials differ on several times. Therefore there is a need to verify the reasonableness of the simplifying method by the equations of series and parallel thermal conductivity for composite slabs.
In this paper, 3D numerical models of battery core with different number of unit cells are established to do simulations. Three different thermal boundary conditions are set to perform the simulation. Simulation results are analyzed to come to a conclusion that it is reasonable to simplify the multilayer core into a lumped cuboid with anisotropic thermal conductivity.  Before dissembled, the battery is discharged to 0 SOC(State of Charge) to ensure safety. The geometry parameters of the core is measured by a micrometer ( Table 1). The measured size of the core is 50.192*100*170 mm. To simplify the model, the size of the core is normalized to 50*100*170 mm. The "Normalization" in Table   1 means the thicknesses of different materials are all normalized to meet total thickness of 50mm.

Parameters
To eliminate the influence of the terminals and make reasonable boundary conditions of the battery core, the model only has a core surrounded by a nylon shell with a thickness of 5mm (Fig. 1b, Fig. 1c). The physical parameters collected from references [1,16,17] are listed in Table 2. By employing equation (1) and (2), the anisotropic thermal conductivity both in series and in parallel direction can be calculated.
In addition, calculating the specific density and the specific heat capacity of the lumped core: Both the multilayer and lumped core models are founded in GAMBIT ® . The multilayer model contains numbers of unit cells. A unit cell contains layers of graphite, copper foil, separator,  The number of unit cell for the lumped core is 0.
While the numbers employed in multilayer modeling are 1, 2, 10 and 20 ( Fig. 2). It should be noted that we can not apply more multilayer numbers to do such a simulation, because the thickness of each layer will be too small to be meshed for simulation. In the following part, it can be seen that the temperature distribution for the 20-layer core is quite uniform without fluctuation, and the simulation results for 10-layer core and 20-layer core is quite similar, so simulations for more multilayer number is meaningless.

Boundary conditions
The control function can be described as (5)  (2) and (3), the isothermal temperature of the heater is 323K.
Because the heat flow under condition (2) or (3) may spread from graphite to LiFePO 4 , or from

Data Processing
As mentioned in Section 2, 5 cores with different numbers of unit cells and 3 boundary conditions lead to 15 groups of simulation results (Table 3)

Results and discussions
In Table 3, it can be seen that the average

Results under inner heat source (1) Relationship between number of unit cells and the temperature fluctuations
In simulation, when the number of unit cells is small, the temperature fluctuations are obvious. However, fluctuations recede when the number of unit cell increase (Fig. 4).

(2) Relationship between the number of unit cells and the peak temperature
Despite the temperature fluctuations, when the x coordinate is zero, the temperature reaches a maximum value. But the maximum value decreases as the number of unit cells increases.
(a) (b) (c) Figure 6 Difference between the lumped core and the multilayer cores when inner heated In spite of the temperature fluctuations in multilayer cores, the average temperature on the surface with norm x of the lumped model is less than that of the multilayer cores (Fig. 6). That result means that the thermal conductivity in x direction of the lumped core is a little less than that of the multilayer core. In other words, the thermal conductivity in y&z direction of the lumped core is relatively bigger than that of the multilayer core.

Results under surface heating (1) Difference between heating from positive or negative x direction
When the heat source is set at the x positive direction on the shell surface, the heat flow will pass from the LiFePO 4 layer to the graphite.
While for heater at the x negative direction, the heat flow will start at the graphite layer, the thermal conductivity of which is higher than that of the LiFePO 4 layer. However, the temperature difference is very small alone line x, with a 0.3 o C average temperature difference.

(2) Spread of the heat flow in y&z direction
Although the heat source is set at the terminal surface alone the x direction, the heat flow also spreads in y&z direction (Fig. 7). In  an order less than 7 (Fig. 9).

(2)Model adjustments
In  Table 4. In conclusion, the difference between the lumped core and the multilayer core cannot be eliminated by adjusting thermal conductivity.
What's more, the temperature difference between the lumped core and the multilayer core becomes larger as the magnitude of the uniform heat source goes bigger. However, the maximum temperature difference is relatively low ( Table 5).

Conclusion
This paper discusses the model simplifing issue in battery thermal simulation. The paper verifies that simplifying the multilayer battery core as a lumped cuboid is reasonable. So when doing simulation, building a multilayer core is unnecessary. And the calculation cost can be reduced by the lumped model.