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Progress Towards a Cartesian Cut-Cell Method for Viscous Compressible Flow

机译:粘性可压缩流的直角切线法的研究进展

摘要

We present preliminary development of an approach for simulating high Reynolds number steady compressible flow in two space dimensions using a Cartesian cut-cell finite volume method. We consider both laminar and turbulent flow with both low and high cell Reynolds numbers near the wall. The approach solves the full Navier-Stokes equations in all cells, and uses a wall model to address the resolution requirements near boundaries and to mitigate mesh irregularities in cut cells. We present a quadratic wall model for low cell Reynolds numbers. At high cell Reynolds numbers, the quadratic is replaced with a newly developed analytic wall model stemming from solution of a limiting form of the Spalart-Allmaras turbulence model which features a forward evaluation for flow velocity and exactly matches characteristics of the SA turbulence model in the field. We develop multigrid operators which attain convergence rates similar to inviscid multigrid. Investigations focus on preliminary verification and validation of the method. Flows over flat plates and compressible airfoils show good agreement with both theoretical results and experimental data. Mesh convergence studies on sub- and transonic airfoil flows show convergence of surface pressures with wall spacings as large as approx.0.1% chord. With the current analytic wall model, one or two additional refinements near the wall are required to obtain mesh converged values of skin friction.
机译:我们目前提出一种使用笛卡尔割池有限体积法在两个空间维度上模拟高雷诺数稳定可压缩流的方法的初步开发。我们考虑层流和湍流,壁附近有低细胞和高细胞雷诺数。该方法解决了所有像元中的完整Navier-Stokes方程,并使用墙模型来解决边界附近的分辨率要求并减轻切割像元中的网格不规则性。我们提出了低细胞雷诺数的二次壁模型。在高单元雷诺数下,二次方程式被新开发的解析壁模型取代,该模型基于对Spalart-Allmaras湍流模型的极限形式的求解,该模型具有对流速的正向评估,并且与SA湍流模型的特征完全匹配。领域。我们开发的多网格运算符可以达到与无粘性多网格相似的收敛速度。研究集中于该方法的初步验证和确认。平板和可压缩翼型上的流动与理论结果和实验数据均显示出良好的一致性。对亚音速和跨音速翼型流的网格收敛研究表明,壁间距高达约0.1%弦的表面压力收敛。使用当前的分析墙模型,需要在墙附近进行一两个附加的细化,以获得蒙皮摩擦的网格收敛值。

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