Realizability of Reynolds stress and rapid pressure-strain correlation models in turbulence

Abstract

In this thesis, the issue of Reynolds stress realizability is addressed in detail. For the first time, the direct connection between the realizability of rapid pressure-strain correlation and Reynolds stress realizability is examined thoroughly. Computational evidence is used to demonstrate that realizability violation of Reynolds stress is always preceded by realizability violation of rapid pressure-strain correlation. Further, the physical failing in the model that leads at first to unrealizable rapid pressure-strain correlation and, ultimately to unrealizable Reynolds stress is also identified. It is shown that this underlying reason for the physical failure is unphysical transfer of energy (transfer of energy from low-energy components to high-energy components) over long periods of time. Thus the sequence of events leading to turbulence model failure is clearly established. Such understanding of the turbulence model dynamics is crucial to developing realizable and physically consistent turbulence models. Finally, a linear rapid pressure-strain correlation model is proposed that is based on truncation of the pressure-strain correlation model suggested by Launder, Reese and Rodi. This proposed model not only satisfies all the physical properties but also the realizability constraints of rapid pressure-strain correlation.