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Adjoint wall functions: A new concept for use in aerodynamic shape optimization

机译：伴随壁功能：用于空气动力学形状优化的新概念

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摘要

The continuous adjoint method for the computation of sensitivity derivatives in aerodynamic optimization problems of steady incompressible flows, modeled through the k-ε turbulence model with wall functions, is presented. The proposed formulation leads to the adjoint equations along with their boundary conditions by introducing the adjoint to the friction velocity. Based on the latter, an adjoint law of the wall that bridges the gap between the solid wall and the first grid node off the wall is proposed and used during the solution of the system of adjoint (to both the mean flow and turbulence) equations. Any high Reynolds turbulence model, other than the k-ε one used in this paper, could also profit from the proposed adjoint wall function technique. In the examined duct flow problems, where the total pressure loss due to viscous effects is used as objective function, emphasis is laid on the accuracy of the computed sensitivity derivatives, rather than the optimization itself. The latter might rely on any descent method, once the objective function gradient has accurately been computed.
机译：提出了利用壁函数的k-ε湍流模型对连续不可压缩空气动力学优化问题中灵敏度导数进行计算的连续伴随方法。通过将伴随关系引入摩擦速度，所提出的公式导致伴随方程及其边界条件。基于后者，提出了一种壁的伴随定律，该定律弥合了实壁与壁之外的第一个网格节点之间的间隙，并在求解伴随系统（对于平均流量和湍流）方程组时使用了该伴随定律。除了本文使用的k-ε模型外，任何高雷诺湍流模型都可以从提出的伴随壁函数技术中受益。在所检查的管道流动问题中，由于粘性效应而导致的总压力损失被用作目标函数，因此重点放在计算出的灵敏度导数的准确性上，而不是优化本身。一旦目标函数梯度已正确计算，后者就可以依靠任何下降方法。

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