Modification of a differential Reynolds-stress turbulence model for flows around aircrafts using experimental and theoretical methods

The accurate prediction of decelerated turbulent boundary layer flows and flow separation is still an important question of computational fluid mechanics for the design of a fuel-efficient (and hence competitive) wing for commercial aircrafts. As the Reynolds number Re is very high (Re around 50 Million for an Airbus A350 in cruise flight, Re based on the wing mean chord), there is still interest in the improvement of statistical turbulence models based on the statistically averaged (Reynolds-averaged) Navier-Stokes (RANS) equations, used as a part of a numerical optimization loop for wing design.
This talk reports on an initiative pursued at DLR in the departments of numerical methods (CAS) and the department of experimental methods (EXV) to improve RANS turbulence models for turbulent boundary layer flows in an adverse pressure gradient (APG) by building a large data base available in literature, by designing and performing an own wind-tunnel experiment (in cooperation with Universität der Bundeswehr München), by developing a new wall law for the mean velocity, and by developing and calibrating a modification of the SSG/LRR-omega differential Reynolds stress model (DRSM) to account for the wall law.
The development of the RANS modification uses the classical approach by Prandtl to consider a suitable boundary layer approximation of the full partial differential equations of a RANS model to derive a simplified ordinary differential equation, which can be solved analytically. This leads to an inverse problem, as the supposed theoretical solution does not solve the RANS model equations, and from this a RANS model modification term is inferred.
As an outline and as a topic for possible joint future research between CAS and NAM, an alternative approach for RANS turbulence modelling (the so-called Field-Inversion/Machine-Learning, proposed by Duraisamy in 2014) is described. The RANS model modification term is determined by solving the above inverse problem numerically as a minimization problem given reference data from experiment or numerical simulation, and to determine the RANS model modification term by some inference method used in data science methods. This leads to many questions from the view point of inverse problems and interpolation theory.