A NEW INTERMITTENCY TRANSPORT EQUATION FOR BYPASS TRANSITION

Abstract

The new transport equation for intermittency is developed and proposed in this research work, based on the definition of intermittency and the existing transport equations of laminar and turbulent kinetic energy. Its performance is compared with the two existing transition models used in commercial CFD software: L k model and Reθ γ − model, in case of bypass transition. It is found that the proposed model can accurately predict the mean streamwise velocity in the transition zone. For f C , k and u v ′ ′ − , the proposed model has the same performance as the Reθ γ − model. INTRODUCTION During the last decade, there have been two RANSbased transition models used in commercial CFD software: L k model (Walters and Cokljat, 2008) and Reθ γ − model (Langtry and Menter, 2009). The Reθ γ − model was constructed based on correlations obtained from experimental data so that it is reliable only within a range of flow conditions that the experiment is set up to obtain such correlations. The L k model was developed based on basic physical mechanisms and their interaction to capture the flow transition, e.g. redistribution term (process) to model energy transfer from laminar to turbulent stages so that it is more attractive in such a way that it can be applied to a wider range of flow conditions. However, γ , k and L k are strongly related to each other by the definition of γ . Therefore, their transport equations should be developed in an interconnected manner. This research work is aimed to identify the incomplete modeling scheme of the L k model which requires one more transport equation for γ to complete the relationship among γ , k and L k , according to the definition of γ . Finally, the new transport equation for γ will be developed and proposed here. DERIVATION OF A NEW INTERMITTENCY TRANSPORT EQUATION To begin with, γ or the intermittency of laminar-toturbulent flow transition is defined as the fraction of time in which the flow is turbulent at a fixed point (Schneider, 1995). According to its definition, γ can be formulated as follows: