Abstract
A high-order Navier-Stokes solver based on the flux reconstruction (FR) or the correction procedure via reconstruction (CPR) formulation is employed to perform a direct numerical simulation (DNS) and large eddy simulations (LES) of a well-known benchmark problem – transitional flow over the low-pressure T106C turbine cascade. Hp-refinement studies are carried out to assess the resolution requirement. A 4th order (p3) simulation on the fine mesh is performed with a DNS resolution to establish a "converged" solution, including the mean pressure and skin-friction distributions, and the power spectral density in the wake. Then LES on the coarse and fine meshes with lower order schemes are conducted to assess the mesh and order dependence of the solution. In particular, we study the error in the transition location, the mean skin-friction distribution, and the mean lift and drag coefficients. These h- and p-refinement studies provide a much-needed guideline in h- and p- resolutions to achieve a certain level of accuracy for industrial LES applications.
Highlights
Large eddy simulation [1] has received increased attention for industrial applications over the past decade for challenging vortex-dominated turbulent flows [2,3,4,5,6]
Direct numerical simulations have been used to study interesting flow physics at low Reynolds numbers, e.g. [7]. This is in part due to the advancements in computational algorithms and computing power of modern computers which paved the way for simulating more practical flow problems
3.1 Case definition The T106C case is selected as a challenging transitional flow problem for computational fluid dynamics (CFD) simulations and has been widely used in assessing both numerical discretization accuracy and studying turbulent flow physics associated with such types of flows [12, 13, 16, 21, 54,55,56]
Summary
Large eddy simulation [1] has received increased attention for industrial applications over the past decade for challenging vortex-dominated turbulent flows [2,3,4,5,6]. A number of adaptive high-order methods capable of handling unstructured grids have been developed over the past few decades [22, 23] These methods offer higher than 2nd order accuracy in space in addition to the compact/local nature of the required stencils. These methods are well suited for modern computing architectures such as GPUs or hybrid CPU/GPU due to their inherent element-local structure. We employ an in-house FR/CPR solver called hpMusic for the compressible Navier-Stokes equations to conduct DNS and LES simulations of a wellknown benchmark problem from one of the International Workshops on HighOrder CFD Methods [42], flow over the low-pressure turbine blade T106C cascade [43]. LU-SGS (BLU-SGS) [52, 53] solver
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