翼型跨音速定常及非定常粘性绕流的数值模拟

A Different N.S.Method for Calculating Steady andUnsteady Transonic Viscous Flows around Airfoils

发展了一种计算翼型跨音速定常及非定常粘性绕流的数值方法。采用ＬＵ分解隐式三阶迎风格式求解二维非定常可压ＮＳ方程组，紊流模型采用ＢａｌｄｗｉｎＬｏｍａｘ双层代数模型。计算网格采用相对翼型固定的贴体运动网格。数值模拟了ＮＡＣＡ００１２翼型的几种跨音速定常及非定常粘性绕流状态。

N.S.(NavierStokes) equations are necessary for accurate calculations needed in highgrade engineering projects. We present an N.S. method that is about as accurate as but is simpler and more convenient than other N.S. methods. The flowfield around airfoil was analyzed by solving the 2dimensional timeaveraged compressible N.S. equations with the BaldwinLomax turbulence model. An implicit LowerUpperFactorized algorithm(eq.3) was constructed in a bodyfitted coordinate system. In the algorithm, a simple thirdorder upwind scheme(eq.4) was adopted. The grid of type C that was generated by an algebraic method was visualized to be rigidly attached to the airfoil so as to save computation time. Some examples for the steady and unsteady transonic viscous flows around NACA 0012 airfoil were calculated. Fig.1 shows the part of the grid of type C for NACA 0012 airfoil. Figs.3 and 4 show characteristics of the variations of coefficients C N and C M with angle of attack α for two different unsteady transonic flows. Numerical results are in good agreement with experimental data.