Abstract
This paper concerns the implementation and evaluation of high-order reconstruction schemes for predicting three well established hovering rotor flows i.e. Caradonna and Tung, PSP and UH-60A. Monotone Upstream Centred Scheme for Conservation Laws (MUSCL) and Weighted Essentially Non-Oscillatory (WENO) spatial discretisation schemes, up to fourth-order, are employed to approximate the compressible Reynolds Averaged Navier-Stokes (RANS) equations in a rotating reference frame, on mixed-element unstructured grids. Various flow speed conditions are simulated including subsonic and transonic, with the latter stretching the discontinuities capturing abilities of the numerics. We consistently evaluate the accuracy, cost and robustness of the developed numerical framework by analysing the discretisation error with respect to the grid resolution. A thorough validation is conducted for all cases by comparing the obtained numerical solutions with experimental data points and relevant literature.
Highlights
In the not-so-distant past, academic codes were the backbone of high-order method development, these codes generally lacked the robustness and efficiency of low-order methods (≤ 2)
This paper introduces the work related to the implementation of high-order Monotone Upstream Centred Scheme for Conservation Laws (MUSCL) and Weighted Essentially NonOscillatory (WENO) spatial discretisation schemes, up to fourth-order of accuracy, on a rotating reference frame, based on the k-exact finite volume formulation of the compressible Reynolds Averaged Navier-Stokes equations
The MOGE formulation of the MUSCL limiter version employed in this study exhibits high-order of accuracy at significant reduced computational cost compared to WENO schemes
Summary
In the not-so-distant past, academic codes were the backbone of high-order method development, these codes generally lacked the robustness and efficiency of low-order methods (≤ 2). For fluid dynamics problems the finite volume method provides several benefits; flexibility, the ease of formulating transport equation systems, conservation properties on arbitrary-defined spatial elements, extensibility to multi-physics systems and robust numerical frameworks including schemes, solvers and limiters for hyperbolic systems. An example of these is the Weighted Essentially Non-Oscillatory scheme (WENO) and Monotone Upstream-Centred Scheme for Conservation Laws (MUSCL). This paper introduces the work related to the implementation of high-order MUSCL and WENO spatial discretisation schemes, up to fourth-order of accuracy, on a rotating reference frame, based on the k-exact finite volume formulation of the compressible Reynolds Averaged Navier-Stokes equations. The conclusions of the present work are outlined in the last section
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