*2.3. Lattice Boltzmann Method*

The simulation was conducted using LBM that discerned air at its mesoscopic scale. LBM has an advantage in its excellent numerical stability and can be solved efficiently on parallel computers [38]. Furthermore, due to its diffusive particle modeling, LBM could handle the simulation of complex topology [39]. In LBM, the motion of the air particles is modeled in a completely disordered direction and random manner whose velocities are distributed around the mean value. In this study, the structure is introduced as the Bhatnagar–Gross–Krook (BGK) (Equation (4)) model is discretized in the lattice unit of space *x* and time *t* [40].

$$f\_i(\mathbf{x} + e\_i \Delta t, t + \Delta t) - f\_i(\mathbf{x}, t) = \Delta t \frac{1}{\tau} (f\_i^{eq}(\mathbf{x}, t) - f\_i(\mathbf{x}, t)) + \Delta t e\_i \mathbf{F}\_k \tag{4}$$

where *fi* is the distribution function of air particles, Δ*t* is the lattice time step, *Fk* is the external force, *ei* is the discrete lattice velocity vector of a particle in a link, *τ* is the single relaxation time, *f eq <sup>i</sup>* is the local equilibrium distribution function, and *i* represents the air particle in specified lattice point.

The LBM simulation was conducted using ANSYS Discovery Live to generate instant results of the velocity and temperature distribution within the battery pack. The model used in the LBM simulation was created using ANSYS Space Claim that was integrated with ANSYS Discovery Live. The dimension of each inlet was 40 mm × 40 mm, and the outlet dimension was 240 mm × 40 mm. The volume of the fluid was then extracted from the inlet to the outlet that enclosed the cylinders. After this process, airflow from the inlet to the outlet could be seen in real-time or live. The flow velocity at the inlet was set to 1.4 m/s according to the cooling fan characteristics, and at the outlet, the relative pressure was set to 0 MPa. The ambient temperature was 30 ◦C according to the average ambient temperature for the tropical region where the BTMS was designed to be used. The air was assumed to be dry air having low thermal conductivity to represent the worst cooling condition. The thermal condition of the battery cells was set by adjusting the heat flow for each cylinder with the calculated heat generation rate of 0.338 W. The example of the model in ANSYS Discovery Live, consisting of battery cells and the volume of the fluid within the battery pack for four inlets, is shown in Figure 2.

**Figure 2.** Example of LBM model (**a**) battery cells configuration (**b**) battery pack for 4 inlets.

The solution was created by assigning the inlet region and the outlet region enclosing the whole model. This region that enclosed the cylinders was extracted as the volume of fluid, which was the volume of air flowing. After the fluid volume was extracted, the velocity contour of the air flowing could be investigated from the maximum value or the small particles flowing within the battery packs. The number of particles flowing within the battery pack could be adjusted by setting the solution's speed or fidelity, where high-speed results reduced the fidelity, and the high fidelity reduced the speed results. This fidelity was based on the distance between the lattice points. The high speeds could generate the temperature contour within seconds, albeit not very accurately, because when

the high-speed result was chosen, fewer particles of air were flowing within the cells. In this simulation for the 3D geometry model, the setting was adjusted to have higher fidelity than the speed, so the contour of the temperature distribution would resemble the real condition more accurately. The simulation in this work was performed in two configurations. The former was varying the number of inlets into 1, 2, 3, and 4 inlets with a constant inlet air temperature of 30 ◦C to study the effect of airflow configuration on temperature distribution. The latter was varying both the number of inlets (1, 2, 3, and 4 inlets) and the inlet air temperature (20, 25, and 30 ◦C) to find the optimum cooling strategy for the air-cooled BTMS.
