A Semi-Unstructured Turbomachinery Meshing Library With Focus on Modeling of Specific Geometrical Features

Abstract

Abstract. Computational Fluid Dynamics is widely used for the analysis and the design of turbomachinery blade rows. A well established method is the application of semi-unstructured meshes, that uses a combination of structured meshes in the radial direction and unstructured meshes in the axial as well as the tangential direction. This takes advantage of the approximately two dimensional flow field through the blade rows, whereby a fine radial discretization, excepting the near wall region, is not necessary. Otherwise, it is possible to discretize particular regions, e.g. the leading and trailing edge regions, in the axial and tangential direction without generating unnecessary nodes in the far field. The meshing approach is based on the projection of a two dimensional unstructured mesh defined at a reference surface. Once, the two dimensional mesh is generated the projection is achieved by transfinite interpolation from the reference surface to further radial surfaces using a structured mesh. Due to the modeling of geometrical features, especially fillets, advanced methods for the generation of structured meshes and mesh smoothing algorithms are required.The paper presents two different approaches for the generation of an appropriate structured mesh. The first is based on the solution of elliptic partial differential equations. The second approach is based on the split of the domain into fourteen appropriately arranged blocks. Furthermore, two smoothing methods for two dimensional unstructured meshes, a constrained Laplace smoothing and an optimization based approach, are presented. Regarding a more realistic representation of the geometry, methods for the modeling of cavities, variable clearance sizes and fillets are presented. Finally, a comparison of the smoothing techniques applied to a rotor passage is presented and the influence of chosen geometrical features on the flow solution is evaluated.

Design of Radial-Inflow Turbines for Low-Temperature Organic Rankine Cycle

“…The newly generated ξ-η coordinate is called a body-fitted curvilinear coordinate, and its main advantage is that it makes the discretization of PDEs and imposing the boundary conditions more straightforward and simpler compared to solving PDEs on the r-z plane. Using Equation ( 56), all the mesh point coordinates can be obtained through transfinite interpolation [37]. The curves 𝑐 ⃗ 𝜉 and 𝑐 ⃗ 𝜉 are one pair of opposite sides of the physical domain, and 𝑐 ⃗ 𝜂 and 𝑐 ⃗ 𝜂 are another pair shown in Figure 1.…”

“…Equation ( 32) is transformed into: Using Equation ( 56), all the mesh point coordinates can be obtained through transfinite interpolation [37]. The curves…”

“…The number of streamwise grid points (along ξ direction) in each region is proportional to its averaged meridional length, which will result in a relatively uniform grid size along the streamwise direction. Using Equation ( 56), all the mesh point coordinates can be obtained through transfinite interpolation [37]. The curves 𝑐 ⃗ 𝜉 and 𝑐 ⃗ 𝜉 are one pair of opposite sides of the physical domain, and 𝑐 ⃗ 𝜂 and 𝑐 ⃗ 𝜂 are another pair shown in Figure 1.…”

Analysis of mistuned forced response in an axial high-pressure compressor rig with focus on Tyler–Sofrin modes

“…The used meshes are semiunstructured i.e. structured in the spanwise direction but each layer contains an unstructured mesh, compare ( 19 , 20 ) for a more detailed description of the meshing philosophy. Fillets and varying gap sizes are taken into account, compare also ( 9 , 20 ) .…”

“…structured in the spanwise direction but each layer contains an unstructured mesh, compare ( 19 , 20 ) for a more detailed description of the meshing philosophy. Fillets and varying gap sizes are taken into account, compare also ( 9 , 20 ) . Measured radial total pressure and total temperature profiles are applied at the inlet of the domain and a choked nozzle with variable area is attached to the outlet of the domain to adjust the working line of the compressor.…”