For free Mach numbers M_∞ < 0.65, the standard methods for subsonic potential flows break down when the flow becomes supersonic locally. The transition of the potential equation from elliptic to hyperbolic indicates that the flow changes from a diffusive character to a propagation behavior. The elliptic numerical operators for the subsonic flow will not be able to correctly simulate the propagation properties of supersonic flow regions, which are governed by the equation of hyperbolic type. The presence of local supersonic regions significantly influences the aerodynamic characteristics of airfoil when compared to the predicted results using the standard methods for subsonic flows. To evaluate this transonic effect, the paper presents a method of solving the full potential equation using central and backward finite difference schemes corresponding to the subsonic and supersonic regions. The rotated difference scheme consists in differencing all the derivatives in the normal direction centrally, while the derivatives in the local flow direction are upwind differenced at supersonic points. The transonic effects on airfoil aerodynamics depending on the free Mach number, incidence angle and airfoil geometry were evaluated.

免费的马赫数_M∞<0.65，当亚音速势流局部变为超音速时，其标准方法就会失效。势方程从椭圆形到双曲线型的过渡表明流量从扩散特性变为传播行为。亚音速流的椭圆数值算子将无法正确地模拟由双曲型方程控制的超音速流区域的传播特性。与使用亚音速流的标准方法得出的预测结果相比，局部超音速区域的存在会显着影响机翼的空气动力特性。为了评估这种跨音速效应，本文提出了一种使用亚音速和超音速区域对应的中央和后向有限差分方案求解全势方程的方法。旋转差分方案是在法线方向上对所有导数进行中心差分，而局部流动方向上的导数在超音速点处是迎风差分。评估了跨音速对翼型空气动力学的影响，具体取决于自由马赫数，入射角和翼型几何形状。