Data assimilation for turbulent mean flow and scalar fields with anisotropic formulation

This work presents an anisotropic formulation for data assimilation (DA) of turbulent flows using the continuous adjoint system. This DA scheme serves as a tool to complement flow measurement data (the observations), which are usually limited in spatial range and measurable quantities, with the help of a predictive model in the framework of the Reynolds-averaged Navier–Stokes approach (the estimator). Herein, the measured data profiles at several locations are used as observations. In the estimator, a forcing term \({\varvec{F}}\) is added to the momentum equation to compensate for the contribution of the anisotropic eddy viscosity, whilst the isotropic part of the eddy viscosity is determined by conventional turbulence models. \({\varvec{F}}\) is optimised using the continuous adjoint equations, driving the predicted flow quantities towards the observations. Similar treatments are conducted for the scalar prediction. Three test cases are used for assessment and validation of the present DA scheme. The results of a circular jet demonstrate that the mean flow and scalar fields can be perfectly reproduced from the observations due to the \({\varvec{F}}\) optimisation. The flow over a blunt plate demonstrates the ability of the present DA scheme to reconstruct global flow fields from several measured velocity profiles. The flow and heat transfer on a ribbed wall reveal that once the global flow field is well recovered, the wall heat transfer characteristics can be correctly determined with a limited number of observations. The present anisotropic DA approach is quite practical for complex flow applications, serving as a complement to our previous isotropic adjoint-based data assimilation for further DA work.