Adaptive mesh refinement method based investigation of the interaction between shock wave, boundary layer, and tip vortex in a transonic compressor

Abstract

Shock wave and tip leakage are important flow features at small length scales. These flow phenomena and their interactions play important roles in the performance of modern transonic fans and compressors. In most numerical predictions of these features, mesh convergence studies are conducted using overall performance data as criteria. However, less effort is made in assessing the quality of the predicted small-scale features using a mesh that yields a fairly accurate overall performance. In this work, this problem is addressed using the adaptive mesh refinement (AMR) method, which automatically refines the local mesh and provides very high resolution for the small-scale flow feature, at much less cost compared with globally refining the mesh. An accurate and robust AMR system suitable for turbomachinery applications is developed in this work and the widely studied NASA Rotor-37 case is investigated using the current AMR method. The complex interactions between the shock wave and the boundary layer, as well as those between the shock wave and the tip vortex, are accurately captured by AMR with a very high local grid resolution, and the flow mechanisms are analyzed in detail. The baseline mesh, which is considered to be “acceptable” according to the commonly used mesh convergence study, is unable to capture the detailed interaction between the shock wave and the boundary layer. Moreover, it falsely predicts the tip leakage vortex breakdown, which is a consequence of inadequate resolution in the tip region. Current work highlights the importance of a careful check of the mesh convergence, if small-scale features are the primary concern. The AMR method developed in this work successfully captures the flow details in the transonic compressor in an automatic fashion, and has been verified to be efficient compared with the globally mesh refinement or manually mesh regeneration.

A mesh adaptation strategy for complex wall-modeled turbomachinery LES

“…Similarly, Vivarelli et al [73] proposed both a Hessian-based and an adjoint-based anisotropic mesh adaptation procedure for the NASA rotor 37, to then consider a mesh adaptation strategy based on adjoint quantities only, and considering the total pressure ratio, total temperature ratio, and adiabatic efficiency (Vivarelli et al [74] ). Finally, a methodology to adapt a mesh accounting for shocks and vorticity is presented in Gou et al [31] for the rotor 37 configuration specifically targeting the interactions between shock waves, boundary layers and tip leakage flows.…”

Numerical simulation of aerodynamic problems based on adaptive mesh refinement method

“…If it is necessary to refine the mesh to the peculiarities of the physical solution of the problem (for example, in the areas of discontinuities, rapid parameter changes), then dynamically adaptive meshes are used. Dynamically adaptive mesh, depending on the method of its construction, can be adaptively embedded or adaptively movable [10][11][12].…”

Combining ensemble Kalman filter and multiresolution analysis for efficient assimilation into adaptive mesh models

“…AMR enables the simulated mesh to adapt both in space and time, assigning high spatial resolution to the areas in which the solution varies rapidly, and coarsening the mesh in regions of mild variations. This makes AMR particularly useful in capturing sharp fronts or shock formation [5,19]. By limiting the fine mesh resolution to regions in which it is required, AMR-based simulations significantly reduce computational complexity and accordingly enhance computational performance.…”