Transonic flow around the leading edge of a thin airfoil with a parabolic nose
Transonic flow around the leading edge of a thin airfoil with a parabolic nose
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DOI：
10.1017/s0022112093000667
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发表时间：
1993-03
影响因子：
3.7
通讯作者：
Z. Rusak
中科院分区：
文献类型：
--
作者：
Z. Rusak
分析了具有抛物线机头的二维薄翼型前缘的跨声速势流。速度势函数的渐近展开式是在一个固定的跨音速相似参数(K)下，根据翼型在翼型周围的外部区域和靠近机头的内部区域的厚度比构造的。这些展开式是渐进匹配的。外展开由跨音速小扰动理论和它的二阶问题组成，其中出现前沿奇异性。内部膨胀解释了机头周围的流动，在那里存在停滞点。给出了内渐近展开式和外渐近展开式的第一项解析表达式。采用对称远场近似，在无环流的情况下，在内区建立了二维抛物线零攻角均匀声速绕流的边值问题。对内区域流动进行数值求解，得到抛物线鼻翼上的对称压力分布。利用外部小扰动解和机头解，可以得到整个翼型表面上均匀有效的压力分布。在前导项中，对于每一跨音速迎流和翼型形状及小攻角，机头周围的流动是对称的，驻点位于前缘。翼型上、下表面的压力分布在翼缘点附近是对称的，不对称偏差增大，只有当翼型前缘的距离超过内区时才变得明显。在前缘区域，本文解与全势流方程和欧拉方程的数值解有很好的一致性。
Transonic potential flow around the leading edge of a thin two-dimensional general airfoil with a parabolic nose is analysed. Asymptotic expansions of the velocity potential function are constructed at a fixed transonic similarity parameter (K) in terms of the thickness ratio of the airfoil in an outer region around the airfoil and in an inner region near the nose. These expansions are matched asymptotically. The outer expansion consists of the transonic small-disturbance theory and it second-order problem, where the leading-edge singularity appears. The inner expansion accounts for the flow around the nose, where a stagnation point exists. Analytical expressions are given for the first terms of the inner and outer asymptotic expansions. A boundary value problem is formulated in the inner region for the solution of a uniform sonic flow about an infinite two-dimensional parabola at zero angle of attack, with a symmetric far-field approximation, and with no circulation around it. The numerical solution of the flow in the inner region results in the symmetric pressure distribution on the parabolic nose. Using the outer small-disturbance solution and the nose solution a uniformly valid pressure distribution on the entire airfoil surface can be derived. In the leading terms, the flow around the nose is symmetric and the stagnation point is located at the leading edge for every transonic Mach number of the oncoming flow and shape and small angle of attack of the airfoil. The pressure distribution on the upper and lower surfaces of the airfoil is symmetric near the edge point, and asymmetric deviations increase and become significant only when the distance from the leading edge of the airfoil increases beyond the inner region. Good agreement is found in the leading-edge region between the present solution and numerical solutions of the full potential-flow equations and the Euler equations.