2.1.2. Mathematical Model
In the present study, a standard k-ε turbulence model was adopted to conduct a flow field analysis in an automobile cabin [
34]. To fully accommodate the physical characteristics and corresponding calculation time, the following assumptions were made: (1) the effects of gravity and buoyancy on the flow field are accounted for; (2) the fluid is a Newtonian fluid; (3) the flow field is a transient, turbulent flow; (4) viscous dissipation is overlooked; and (5) the fluid at the inlet is moving at a uniform velocity. The dominance equations for numerical analysis in this study are as follows:
(c) Energy equation:
where
E is the total energy,
is the effective thermal conductivity, and
is the effective stress tensor, whose definition is as follows:
denotes the turbulent thermal conductivity coefficient, which is defined as follows:
(d) Buoyancy:
When density changes, fluid moves due to buoyancy. This study used the Boussinesq buoyancy approximation to derive the movement, which is defined as follows:
Equation (6) shows that the coefficient of thermal expansion substantially influences the fluid density change and the degree of fluidity, and Equation (7) shows that gas β is the reciprocal of temperature
T; the definition of β is as follows:
(e) External radiation heat:
This study adopted the fair weather condition [
33], and the transmissivity of solar radiation is as follows:
The reflectivity of solar radiation is defined as follows:
In Equation (13),
A is the solar radiation parameter when the air mass is zero;
B is the atmospheric extinction coefficient when the air mass is zero;
β is the degree to which the Sun is above the horizon (deg); and
Edn is the direct radiation of the sun on the Earth during fair weather conditions. The equation for solar radiation shining vertically on a surface is as follows:
C is a constant, and
Y is the ratio of diffused radiation on a vertical surface compared with a horizontal surface. Thus,
Ed becomes:
where
is the obliquity of the Earth’s surface. Therefore, the ground reflection of the solar radiation is defined as follows:
where
is the rate of ground reflection.
(f) Turbulence equation
Turbulence kinetic
k can be obtained using Equation (17), and the turbulence dissipation rate
can be obtained using Equation (18):
where
denotes the turbulent Prandtl coefficient in the kinetic equation
k [
35];
is the turbulent Prandtl coefficient of dissipation rate in the
equation;
is the turbulence viscosity;
is the turbulence kinetics generated from the average speed gradient; and
is the turbulence kinetics generated from buoyancy. Furthermore,
is calculated from the standard
equation, where
= 0.09,
= 1.44,
= 1.92,
= 1, and
= 1.3.
(g) Standard wall function:
This equation was established based on the hypothesis of Launder and Spalding [
36]. When the space-control nodes on the adjacent walls satisfy y+ >11.63 and the fluid movement is located at the logarithmic rate layer, the fluid speed can be shown as follows:
where
and
.
denotes the Karman constant, and
= 0.41;
E is the experience constant, and
E = 9.81;
is the average speed of the fluid at point
p;
is the turbulence kinetic of point
p;
is the distance between point
p to the wall; and
is the kinetic viscosity coefficient of the fluid.
2.1.4. Regional AC System Simulation Settings
The boundary conditions of the automobile cabin, including the various units such as the cabin AC inlet, outlet, and walls were as listed
Table 1. The cabin regional AC system was simulated and analyzed using two cases involving different inlet and outlet boundary conditions. The inlet and outlet simulation settings are listed in
Table 2.
Case A was for the integrated regional AC system in the driver’s seat. In the simulated cabin, only the driver required AC, and therefore only the inlet and outlet at the driver’s seat were open. The boundary of the cabin inlet was set as the velocity inlet. The wind speeds at Inlet 1 and Inlet 2 were 2.5 and 2 m/s, respectively; the temperature at both was 278 K, and the inlet angles were 10° and 55°, respectively (
Figure 3a). For the outlet, the boundary condition was set as the pressure outlet, and the outlet pressure was −75 Pa (
Figure 3b).
Case B was for the driver’s seat with no integrated regional AC system. Case B was similar to Case A in that only the driver required AC. However, Case B was different from Case A in that there was no integrated regional AC system, and therefore only the inlet at the driver’s seat and outlet at the blower were open. The cabin inlet boundary condition was set as the velocity inlet. The wind speeds at Inlet 1 and Inlet 2 were 2.5 and 2 m/s, respectively; the temperature at both was 278 K, and the inlet angles were 10° and 55°, respectively (
Figure 3c). For the outlet, the boundary condition was set as the pressure outlet, and the outlet pressure was −75Pa (
Figure 3d).
Regarding the cabin boundary conditions, given that when the fluid passed the wall, the no-permeability and no-slip conditions were satisfied, the flow field was fixed to the wall. For example, the boundary conditions of the interior of the cabin and the window adopted the no-slip conditions. Therefore, the velocity of the flow field in all three directions was 0 (υ = ν = ω = 0). Likewise, the fluxes of the turbulence kinetic energy, turbulent kinetic dissipation rate, and turbulence density that were vertical to the wall were all assumed to be zero (∂T⁄∂n = ∂ε⁄∂n = ∂c⁄∂n = 0). Regarding the external radiation, the ANSYS/FLUENT solar load model [
33] was adopted using the typical fair weather conditions at the latitude and longitude of Taipei City. For the car, a BC type with an opaque body was adopted, and the windows were semitransparent. Detailed information is listed in
Table 3 and
Table 4.
The initial condition assumed that the temperature in the cabin was 308 K and the car was idle. The AC operated at the set speed, temperature, angle, and inlet pressure in each case. The relaxation factors of Multiphysics were as follows: pressure = 0.3, body forces = 1, momentum = 0.7, turbulence kinetic energy = 0.5, turbulence dissipation rate = 0.5, turbulence viscosity = 1, and energy = 1. Regarding the convergent conditions, the continuity, momentum, and turbulent equations were set to 10−3, whereas the energy equation was set to 10−6.