An adjoint-based approach for the accurate estimation of pressure of steady turbulent flows is developed and validated using both numerical and experimental data. The approach considers a simple algorithm to correct for the pressure in the domain solely based on sensor measurements at the wall. Adjoint looping is shown to provide both an accurate and fast algorithm where only minor modifications are required to implement the present procedure in an existing pressure solver. The algorithm is first validated using a set of time-averaged unsteady Reynolds-averaged Navier–Stokes equation in the wake of a D-shaped bluff body. The effect of noise is also investigated and shows that combining both a Helmholtz decomposition to recover a divergence-free velocity field and the adjoint-based correction provides consistent results for the pressure field. The approach is then applied to a wind-tunnel experiment for the same geometry. An independent comparison of drag, estimated between pressure measurements at the wall and the corrected pressure field shows good agreement. Finally, the role of domain size for the adjoint-based approach is addressed. The present algorithm naturally extends to time-dependent measurements without additional modifications.

中文翻译：

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基于平面粒子图像测速和稀疏传感器测量的最优压力重建

使用数值和实验数据开发并验证了一种基于伴随的方法，用于准确估计稳定湍流的压力。该方法考虑了一种简单的算法来仅基于壁上的传感器测量值来校正域中的压力。伴随循环被证明提供了一种准确和快速的算法，其中只需要很小的修改就可以在现有的压力求解器中实现当前的程序。该算法首先使用一组时间平均非定​​常雷诺平均 Navier-Stokes 方程在 D 形钝体之后进行验证。还研究了噪声的影响，并表明结合亥姆霍兹分解来恢复无发散速度场和基于伴随的校正为压力场提供一致的结果。然后将该方法应用于相同几何形状的风洞实验。在壁上的压力测量值和校正压力场之间估计的阻力的独立比较显示出良好的一致性。最后，解决了基于伴随方法的域大小的作用。本算法自然地扩展到与时间相关的测量而无需额外修改。