Finding Transition Models using Dimensional Analysis Gene Expression Programming

Abstract

Data-driven turbulence modeling has become an emerging field, aiming to overcome the weaknesses of classical Reynolds Averaged Navier-Stokes (RANS) models. One branch is Gene Expression Programming (GEP), which tries to find symbolic expressions for unknown functional dependencies. As an evolutionary algorithm it typically relies on many function evaluations. To reduce the computational cost, prior knowledge should be included where possible. When modeling functional dependencies in a physical context, the classical GEP is unaware of the physical dimensions of the involved quantities. Nevertheless, the validity of an expression in terms of its dimensions is a valuable hint towards its suitability and may improve the algorithms’ performance. Therefore, in this work, we propose a new approach to consider physical dimensions within GEP. The new algorithm is evaluated and compared against existing approaches and applied on well-described turbomachinery test cases at transitional flow conditions.