Effect of turbulence-closure consistency on airfoil identification

We consider an inverse flow problem in which the airfoil shape is identified from its wake signature, namely the velocity field in the wake of a target airfoil. This is an ill-posed problem and highly sensitive to the accuracy and consistency of the employed turbulence closure. We first demonstrate that shape identification based on a single flow condition is ill-posed, whereas incorporating multiple wake signatures obtained at different angles of attack substantially mitigates this ill-posedness. We then compare the inferred geometries obtained using different turbulence closures and find that inconsistencies among the models lead to markedly divergent shapes. Consequently, we directly compare the geometric sensitivities obtained from different models at fixed shapes, and find up to 250% difference among these sensitivities. These findings underscore that turbulence-closure consistency is essential for reliable shape identification and further suggest that effective turbulence models must ensure not only accurate predictions but also physically consistent sensitivities—a principle that should guide the development of both classical and data-driven closure models.