Analysis of Transition-Sensitized Turbulent Transport Equations

Abstract

The dynamics of an ensemble of linear disturbances in boundary-layer flows at various Reynolds numbers is studied through an analysis of the transport equations for the mean disturbance kinetic energy and energy dissipation rate. Effects of adverse and favorable pressure-gradients on the disturbance dynamics are also included in the analysis. Unlike the fully turbulent regime where nonlinear phase scrambling of the fluctuations affects the flow field even in proximity to the wall, the early stage transition regime fluctuations studied here are influenced across the boundary layer by the solid boundary. The dominating dynamics in the disturbance kinetic energy and dissipation rate equations are described. These results are then used to formulate transitionsensitized turbulent transport equations, which are solved in a two-step process and applied to zero-pressuregradient flow over a flat plate. Computed results are in good agreement with experimental data.

A modular RANS approach for modeling hypersonic flow transition on an air-breathing configuration

“…Thus a separate transport equation for k L is proposed, albeit in the same manner as the conventional form for k T 14 . However, the work of Rumsey et al 15 demonstrates that the employment of two separate equations for k T and k L is not necessary. It is found that a single equation for the total fluctuating kinetic energy K is more cost-effective, which is adopted in the present work as…”

Current trends in modelling research for turbulent aerodynamic flows

“…The basis for many of the models being used today originated with the ideas of Emmons (1951) (see also Dhawan & Narasimha 1958). The desire to account for transitional effects in RANS models has been given renewed emphasis and has been ongoing for some time (Schmidt & Patankar 1991;Stock & Haase 1999;Walters & Leylek 2004; see also Rumsey et al (2005) for a more complete list). These efforts have mainly focused on engineering approaches rather than on approaches that are more theoretically based.…”

“…The latter approaches have received much less attention (e.g. Thacker et al 1999a,b;Jovanović & Pashtrapanska 2004;Rumsey et al 2005) and as yet have not reached a point where extensive flow field predictions have been made. It is worth pointing out some characteristics that a predictive transition-sensitized turbulence model should possess.…”

Prediction of Separation-Induced Transition on the SD7003 Airfoil Using Algebraic Transition Triggering

“…Although low-Reynolds multiequation turbulence models were originally introduced to predict transition [10], it is now established that they are not sufficiently precise [13][14][15][16]. Therefore various specific transition models have been introduced for use in conjunction with RANS models [17].…”