3.3. Thermal Analysis
The integration of power converters on the machine housing could increase the temperature of the WRSM. Note that, if the temperature is too high, this can cause problems and thus shorten the life of the converters and the whole machine. In this study, a limit on the temperature inside the coils is fixed to 105 °C. Hence, the temperature distribution of the new corrected machine has to be determined.
The temperature can be computed following two approaches: lumped-parameter thermal analysis or numerical methods. Using lumped-parameter thermal models, this is possible to estimate some key temperatures inside an electrical machine much more quickly than numerical methods. However, the computation of the lumped parameters can be very difficult to perform for some complex geometrical parts of the WRSM [
20].
On the contrary, the use of 3D numerical simulations makes it possible to predict the temperature of complex structures, but with an enormous calculation time; FE or CFD methods can be used.
FE simulations enable the computation of the temperature accurately inside solid bodies. However, in order to consider the effect of the fluid on the solid, convection heat transfer coefficients need to be applied at the boundaries between the solid zone and the moving fluid. These coefficients are provided by using analytical approaches or some experimental tests. Using CFD simulation, the solid and the fluid regions can be modeled and the machine temperature is then analyzed with a high accuracy. The exact evaluation of the temperature, at different locations inside the machine, is an extremely high CPU time consuming task because of the complicity of the fluid velocity and of the surface properties of the machine [
20,
21]. In this paper, the CFD method is selected to analyze the temperature of the WRSM without a cooling system by using ANSYS Fluent software.
The family of the Reynolds-Averaged Navier-Stokes (RANS) models has been chosen because they are widely used to consider the field of turbulence. RANS is the most widely used method for thermal analysis of electrical machines. Based on turbulent kinetic energy and dissipation rate or length scale transport equations, RANS models are commonly used for developing the turbulences arising from buoyancy, shear, or shocks.
For incompressible fluids, the density does not change with the pressure. The RANS equations can be described for fluid flow of an incompressible fluid by the following equations, see [
22]:
where
is the density, U is average velocity field,
is the pressure, μ is the dynamic viscosity, and
is the volumetric force.
A simplified model of all the parts in the new corrected machine is created in 3D by using ANSYS–Maxwell software. The complete model is required due to the lack of symmetry in the geometry of this machine. The thermal modeling of some parts, such as winding, bearing is a challenging task. The bearing is thus not modeled in this study. In order to simplify the CFD model, some assumptions are made as follows, see [
23]: —the ambient temperature is constant, —there is no influence of the temperature rise on the thermal property of materials, —the lamination is modeled as an orthotropic composite material, which has different thermal conductivities in different directions, —air is blown in and out perpendicular to the inlet and the outlet faces, —heat sources are uniformly distributed in the corresponding parts of the machine.
Since the stator and the rotor are laminated, the eddy current losses are reduced. A low thermal conductivity insulation separates the lamination. Hence, the thermal conductivity of the rotor and stator (in the axial direction) is computed as the equivalent conductivity of insulation and lamination [
24]. In addition, the winding insulation is simplified and consists only of the copper and wire insulation.
Table 7 shows the thermal properties of the different materials used.
Regarding the inlet and outlet regions, these are faces through which air enters and exits the simulation domain. Moreover, the inlet pressure and outlet pressure are used to define the boundary conditions of the inlet and outlet flow, respectively; zero
Pascal is taken as the relative pressure of natural convection, [
25]: inlet pressure is equal to
with
; outlet pressure is equal to
) with
; wall of moving fluid are taken as moving wall; -Contact interfaces are taken into account as coupling surfaces.
The rotation of the WRSM owns a direct effect on the fluid flow and the pressure distribution. Two main techniques can be used in order to simulate the machine rotation: Moving Reference Frame (MRF) and Sliding Mesh (SM). Therefore, the MRF technique is used for a steady state analysis, and the SM technique is used for a transient analysis [
26].
In this work, the MRF technique is used to simulate the relative motion of the rotor and stator. The fluid region is divided into two regions (inner and outer), as it is shown in
Figure 8. The internal fluid area surrounding the rotor part rotates at motor speed. The outer fluid area is stationary. The area, where the MRF technique is applied, does not move. However, all walls in the MRF region are rotated to account for the generation of a constant grid flux. The grid flux is computed from the properties of the reference frame. Hence, the forces due to rotation are introduced in the MRF region. This approach is suitable for steady-state analysis and solves for most flow behaviors, such as mass flow and pressure rise, through rotating components [
27].
The k-ε realizable model with Enhanced Wall Treatment is used here because of its robustness, and the resolution methods are parametrized as second order [
28]. Cellular zone conditions govern the material, heat generation, and rotational properties of the solid and fluid zones. The volumetric heat production rates represent the copper and iron losses. In natural convection, fluid movement is provided by density differences due to temperature differences. Consequently, air is considered as an ideal incompressible gas with specific operating conditions. In order to obtain those following results, 13 h of CPU-time were required using a PC-server with 16 processors (2.6 GHz and 128 GB).
Figure 9 and
Figure 10 show the temperature distribution of the WRSM. The field winding temperature (113.80 °C) is the maximum temperature. The surface temperature is about 104.48 °C. The difference in the surface temperature of the frame between the analytical equation of the temperature and the CFD simulation is about 8.05% (with the same losses from 3D electromagnetic simulations). Nevertheless, only natural convection is investigated in this study, and the radiation should be considered at the surface of the machine frame for electrical machines without cooling systems.
Note that the limit on the coil temperature was previously fixed to 105 °C in order to guarantee the perfect functioning of the machine. Hence, to provide that temperature at the end of this complete design methodology (see
Figure A1), a limit of 85 °C had to be set for our design problem. Hence, the coil temperature of the new corrected WSRM obtained using the CFD method, is 113.48 °C; which is a bit more than the limit (+8.48 °C). This should not be a problem, as some dissipation, due to the shaft and bearings of the machine, is expected and this will lower the temperature of the coils.