RANS Data Assimilation Techniques for Wind-Tunnel Wall Interference Corrections

Abstract

Among all the interference effects contaminating wind-tunnel experiments, those due to the presence of the walls are particularly challenging to account for. Their influence becomes hard to quantify in the non-linear flow regime, for which classical linear correction methodologies are inadequate. This work proposes to use a variational data assimilation framework to tackle the problem of wall interference corrections in the presence of non-linear flow phenomena. The main idea is to use a gradient-based optimization technique to minimize the difference between an experimentally measured quantity of interest and the same quantity obtained by means of a RANS simulation. The control parameters contain the free-stream angle of attack and Mach number, and terms correcting the approximations introduced by eddy viscosity turbulence models. The former return the corrections to the angle of attack and Mach number, while the latter treat the main source of error in RANS simulations. Two parameterizations of the turbulence model are presented in this paper, each one correcting the error introduced by the turbulence model in its own way. One re-calibrates the balance of terms within the turbulent transport equations, while the other directly assimilates the Reynolds stress anisotropy tensor, thus bypassing the limitations introduced by the Boussinesq hypothesis. The two methodologies are tested on transonic 2D cases, and are shown to yield more accurate corrections than traditional methods.