Galilean-Invariant Stability-Based Transition Transport Modeling Framework

Abstract

A new stability-based transition transport modeling framework for unstructured computational fluid dynamics is introduced. Based on a four-equation model published recently by the authors of this paper, new model formulations are derived being Galilean invariant and fully local. Moreover, the complexity of the four-equation model is reduced, yielding a one-equation model that is based on a local pressure-gradient parameter and a three-equation model that is based on an averaged pressure-gradient parameter considering convection (history) effects. Since the model versions are identical except the pressure-gradient parameter, the implementation effort is reduced. To be able to compute test cases in adverse pressure gradient flow regions at low Reynolds numbers, a method was developed to accelerate the turbulence production (downstream of the point of transition onset) that can also be used inside laminar separation bubbles. The models were implemented into the DLR TAU code, the unstructured compressible finite-volume flow solver of the German Aerospace Center (DLR) for external flows. For verification and validation purposes different test cases are shown capturing a wide range of parameters and flow conditions. This includes a test case verifying that the model yields identical results with and without uniform motion (Galilean invariance). Additionally, industrially relevant three-dimensional test cases were computed. This includes a helicopter rotor in vertical flight.