A data assimilation model for wall pressure-driven mean flow reconstruction

Abstract

This study establishes a continuous adjoint data assimilation model (CADA) for the reproduction of global turbulent mean flow from a limited number of wall pressure measurements. The model-form error induced by the Boussinesq assumption is corrected by a body force vector, which reinforces the eddy viscosity-based Reynolds force vector. The Stokes–Helmholtz decomposition is applied to this Reynolds force vector to isolate the crucial information contained with the Reynolds stress, and the primary-adjoint system is solved only for the anisotropic components. The CADA model is theoretically derived to minimize discrepancies between the wall pressure measurements and the numerical predictions of the primary-adjoint system. This minimization reveals the optimal anisotropic contribution of the Reynolds force vector. Four test cases are used for the assessment and validation of our CADA model. First, simulation of the wake in a flow over a cylinder demonstrates the ability of our CADA model to accurately recover the global fields from different regions of local synthetic wall measurements. Second, simulation of the flow over a backward-facing step illustrates that our CADA model can reconstruct a detached flow with a high Reynolds number. Third, simulation of the flow in a converging–diverging channel shows that our CADA model can reconstruct a strong adverse pressure-gradient flow. Fourth, simulation of the periodic hill flow further showcases the ability of our CADA model to predict complex flows. The method demonstrated here opens up possibilities for assimilating realistic observations, serving as a complement to our anisotropic DA scheme for future DA work.