Numerical mesh

On the basis of the domain presented in the previous section, the numerical mesh was prepared. All the domain fluid and solid elements were divided into smaller grid elements allowing for the domain discretization.

The final numerical mesh generated within the computational domain included more than 8 million elements. Due to the domain complexity, the mesh consisted of hybrid ele-ments connecting tetrahedrons, quadrilateral pyramids, triangular prisms and hexahedrons.

Moreover, due to the geometry complexity, it was decided to use non-conformal mesh be-tween solid and fluid elements. It allowed building mesh in the connection regions bebe-tween the small dimension elements, e.g., air gap and bigger solid elements, e.g., stator core.

Outlet

Inlet Motor elements

Generator surfaces Coupling

Figure 3.2: Computational domain of Thermal Model I

Due to the domain complexity, the process of numerical mesh creation was a challenging task. Therefore, the mesh independency test was conducted only for two different meshes which were coarser and finer comparing to the one finally selected. The region, where the number of elements varied during the test, was located in the vicinity of surface connecting surrounding air with external motor elements. Moreover, the tested region of the mesh in-fluence was within the back part of motor where the LDA measurements were recorded. The finer mesh consisted of 10 million elements. Finally, the selected mesh, as presented above, reached 8 million elements and showed similar results as for the finer mesh.

The visualisation of the final mesh is presented in Fig. 3.3 on a vertical cross-section cutting the main motor components across the shaft axis. In the figure, on the left-hand side,

the cross-section through all fluid and solid domain is presented. In Fig.3.3(a), the mesh in a cross-section through the whole domain is presented. On the right-hand side of the figure, three zooms of the mentioned cross-section are presented with the mesh without air domain around the investigated machine. In Fig. 3.3(b), the zoomed view of half of the motor is presented. This view is consistent with the yellow frame marked in Fig.3.3(a). In Fig.3.3(c), the internal elements of the motor are zoomed and their image is presented in Fig. 3.3(b) using a red frame. The last zoomed view illustrates the air gap between stator and rotor in Fig.3.3(d). This image is pointed out using a green frame in Fig.3.3(c). Using orange colour, the windings were pointed out and the remaining solid elements are in grey colour. The fluid was presented using blue colour. On the right-hand side of the figure, the numerical mesh without an external air is illustrated, while two zoom views are shown in colour frames. In the figure, the mesh details are displayed on the side of the motor. However, the generator side is not included in this view but the mesh resolution in the generator vicinity was similar to on the motor side. The semi-transparent view through solid motor elements is presented in Fig.3.1.

(a)

(b)

(c) (d)

Figure 3.3: Mesh of Thermal Model I displayed in the vertical cross-section of the motor in four views: (a) whole domain with air around motor within the acrylic cover, (b) motor elements with external surfaces, (c) internal motor elements, (d) zoom to the air gap

The details of the mesh type, number of elements and its orthogonal quality are pre-sented in Fig. 3.4. In the figure, the group representing the highest quality elements in-cluded 2 million hexahedral cells and it is double amount when compared to the tetrahedral elements in this group. The tetrahedral elements dominate in the cell groups representing orthogonal quality in the ranges between 0.63 and 0.88 and their sum was approx. 3 mil-lion elements. In this range, the hexahedral elements constituted 0.7 milmil-lion cells. In the groups representing lower orthogonal quality than 0.5, the hexahedral elements were domi-nant. The rest of the elements were the cells of quadrilateral pyramids and triangular prisms.

The orthogonal quality of each cell in the domain reached more than 0.09. The meshing strategy was based on the implementation of the highest number of hexahedral elements, while tetrahedral elements were used in the most complex regions. The quadrilateral pyra-mids and triangular prisms were used to connect the zones of hexahedral and tetrahedral elements.

Orthogonal quality

Number o f elements

2.1M 1.6M 1.2M 0.8M 0.4M

0.0 0.09 0.25 0.38 0.5 0.63 0.75 0.88 1.00

tetrahedral hexahedral prism pyramid

Figure 3.4: Mesh orthogonal quality

The distribution of the skewness parameter within the mesh elements is presented in Fig.3.5. The lowest skewness value, characterising the highest quality of the cell, can be no-ticed for more than 2 million hexahedral and 0.5 million tetrahedral elements. The skewness parameter reaching higher values was dominant in the tetrahedral elements. The highest skewness values were reported for limited tetrahedral elements.

The quality of the presented mesh was improved within the Fluent software using inte-grated algorithm of the nodes moving. The mentioned algorithm was applied for the selected

pyramid

Skewness

Number o f elements

2.0M 1.6M 1.2M 0.8M 0.4M 0.0 2.25M

0.0 0.13 0.25 0.38 0.5 0.63 0.75 0.88 0.99

pyramids

tetrahedral hexahedral prism pyramids

Figure 3.5: Mesh skewness

cells that were characterised by the lowest quality. Therefore, the applied mesh in the calcu-lation process was of a higher quality than that discussed in the previous paragraphs.