利用壓力法之非結構性網格可壓縮流計算

Abstract

本論文引用預測不可壓縮流之SIMPLE壓力修正法，以有限容積積分法、重置變數安排之非結構性網格，來離散穩態的統御方程式，求解可壓縮流。將密度及速度的變動導入壓力修正方程式中，推導出馬赫數控制因子，來自動調整壓力修正方程式在次音速為橢圓型式及在超音速為雙曲線型式之流場特性，可有效處理穿、超音速流場之問題。本文對於擴散項之離散採用中央差分來近似；而對流項之近似則採用二階中央差分及一階上風差分混合法，除了可準確捕捉震波之位置與強度，並可消除震波附近之數值震盪，具有計算模擬全速流流場之能力。 以不同之流場及任意邊形之非結構網格，來探討本方法之可適用性，其中包括非黏性流體之一維/二維漸縮-漸擴噴嘴及二維渠道流，以及黏性流體之二維渠道流。並進一步探討密度混合因子對計算解之影響情況。

In this thesis an extended pressured-correction method using SIMPLE algorithm is developed for the computations of two-dimensional steady compressible flow. The correction of pressure in pressure-correction equation is correlated to the density and velocity in terms of a “Mach control factor” so that it can automatically adopt elliptic or hyperbolic characteristics according to either subsonic or supersonic flow condition. An unstructured finite volume method with collocated variables arrangement is employed in space discretization where the diffusion fluxes are discretized using central difference scheme (CDS), and the convection terms are discretized using a blended central difference and upwind difference scheme (UDS). The blended scheme is so incorporated to increase the accuracy of the captured shock position and strength while eliminating the oscillations near shock wave. The method is verified by a series of test problems including invicid flows in a one-dimensional and a two-dimensional converging-diverging nozzle, viscous and invicid flows past a circular arc bump in a channel. Both quadrilateral and triangular cells are used in the computations to illustrate the unstructured capability and grid flexibility of the unstructured flow solver. Some effects of the “density-blending factor” to the numerical solutions are discussed and conclusions are drawn from the verification process. The accuracy and stability properties of the current method demonstrate its capability and potential in the computation of compressible flow past arbitrary body shapes at all flow speeds.