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Optimal aerodynamic design of airfoils in unsteady viscous flows

机译:非稳态粘性流中翼型的最佳空气动力学设计

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A continuous adjoint formulation is used to determine optimal airfoil shapes in unsteady viscous flows at Re= 1 × 10~4. The Reynolds number is based on the free-stream speed and the chord length of the airfoil. A finite element method based on streamline-upwind Petrov/Galerkin (SUPG) and pressure-stabilized Petrov/ Galerkin (PSPG) stabilizations is used to solve both the flow and adjoint equations. The airfoil is parametrized via a Non-Uniform Rational B-Splines (NURBS) curve. Three different objective functions are used to obtain optimal shapes: maximize lift, minimize drag and minimize ratio of drag to lift. The objective functions are formulated on the basis of time-averaged aerodynamic coefficients. The three objective functions result in diverse airfoil geometries. The resulting airfoils are thin, with the largest thickness to chord ratio being only 5.4%. The shapes obtained are further investigated for their aerodynamic performance. Maximization of time-averaged lift leads to an airfoil that produces more than six times more lift compared to the NACA 0012 airfoil. The excess lift is a consequence of the large peak and extended region of high suction on the upper surface and high pressure on the lower surface. Minimization of drag results in an airfoil with a sharp leading edge. The flow remains attached for close to 70% of the chord length. Minimization of the ratio of drag to lift results in an airfoil with a shallow dimple on the upper surface. It leads to a fairly large value of the time-averaged ratio of lift to drag (~ 17.8). The high value is mostly achieved by a 447% increase in lift and 16% reduction in drag, compared to a NACA 0012 airfoil. Imposition of volume constraint, for the cases studied, is found to result in airfoils that have lower aerodynamic performance.
机译:在Re = 1×10〜4的情况下,采用连续的伴随公式确定非恒定粘性流中的最佳翼型形状。雷诺数基于自由流速度和翼型的弦长。基于流线上风彼得罗夫/加勒金(SUPG)和压力稳定彼得罗夫/加勒金(PSPG)稳定的有限元方法用于求解流动方程和伴随方程。通过非均匀有理B样条曲线(NURBS)曲线对机翼进行参数化。使用三种不同的目标函数来获得最佳形状:最大化升力,最小化阻力以及最小化升力比。目标函数是基于时间平均空气动力学系数制定的。这三个目标函数导致了不同的机翼几何形状。所得的机翼很薄,最大的弦厚比仅为5.4%。进一步研究了获得的形状的空气动力学性能。时间平均升力的最大化导致机翼产生的升力是NACA 0012机翼的六倍以上。过量的升程是由于上表面的高吸力和下表面的高压导致大的峰值和扩展区域的结果。阻力最小化会导致机翼的前缘锋利。气流保持接近弦长的70%。阻力与升力之比的最小化导致机翼的上表面带有浅浅的凹坑。它导致升力与阻力的时间平均比率值相当大(〜17.8)。与NACA 0012机翼相比,升力主要是增加了447%,阻力减少了16%,从而获得了较高的价值。对于所研究的情况,施加体积约束会导致机翼的空气动力学性能降低。

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