利用壓力修正法解可壓縮流

Abstract

本論文引進一個用馬赫數控制的遲滯壓力法及遲滯密度法來解決橢圓形壓力修正方程式在超音速區的問題。統御方程式是建立在非正交曲線座標及非交錯式安排的綱格點上，利用有限容積法將方程式離散化，再以SIMPLE的數值方法求解速度和壓力方程式。 不同的流場用來探討個方法的可適用性，其中包括無黏性一維及二維噴嘴，二維渠道流和通過一機翼之外流場，以及二維紊流邊界層與震波的交互作用。在無黏性流場計算中，雖然因遲滯壓力和的引進造成些微的過量人工消散，但方法仍顯出合理震波的捕捉。至於紊流流場的計算，則是使用 k-E 模式配合壁面函數來預測震波與邊界層的交互作用，在與實驗比較結果均不甚理想尤其是在迴流區的計算。

In this study a retarded pressure and a retarded density approach, controlled by a Mach-unmber-dependent monitor function, was incorporated within the pressure correction framework to ensure the hyperbolic nature in supersonic zone. The governing equations are constructed on curvilinear coordinates and the grids are arranged in a non-staggered manner. Differential equations are discretized by finite-volume method. The system of discretized equations is solved by the SIMPLE-type algorithm. Capabilities of the numerical method were examined by applying to several inviscid and turbulent transonic flows, including a quasi-one-dimensional nozzle flow with different back pressures,flows over a bump in an inviscid channel, flow over an airfoil, and a turbulent flow with shick-boundary layer interaction. In the inviscid flow calculations, is was found that the present schemes give predictions of the shock except that a slightly smearing occurs due to introduction of the excessive artificial dissipation. As regards turbulent flow computations, the k-E model and wall-function were incorporated to exam the shock wave /boundary lager interaction . It was in poor agreement with the experimental data especially in recirculating region.