Three-dimensional hybrid grid generator and unstructured flow solver for compressors and turbines
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A numerical method for the simulation of compressible turbulent ﬂows is presented. This method includes a novel hybrid grid generation for airfoil cascades and an unstructured mesh ﬂow solver. The mesh tool incorporates a mapping technique and a grid smoothing method. The mapping technique is used to build an initial volume mesh and the grid smoothing method is used to improve the quality of the initial mesh. The grid smoothing is based on the optimization of mesh-quality parameters. The further improvement of the smoothed mesh is achieved by an edge-swapping and node-insertion technique. The unstructured ﬂow solver is developed for a hybrid grid. This ﬂow solver uses a rotational frame of reference. The convective and viscous ﬂuxes are numerically solved by an upwind scheme and an averaged nodal gradient. A higher-order spatial accuracy is achieved by a piece-wise linear reconstruction. An explicit multi-stage method is employed for integration in time. The Menter?s k −τ model is implemented to simulate the turbulence eﬀects. The ﬂow solver is validated against the analytical and experimental results. A parametric study is performed for a high speed centrifugal compressor.