Towards a Rational Approach to Transition Modeling

Existing transition sensitized RANS models rely on ad-hoc ramping functions and fits to experimental data. We propose a new modeling approach which takes on the fact that the exact, unclosed, second-order moment equations are valid for all flows, including those in transition. In order to develop a closure which is valid in the transition region, we attempt to impose the constraint that the linear response of the model equations to small disturbances should match the predictions of linear stability theory. Our analysis results in two critical conclusions. First, the scaling of the turbulent kinetic energy production is not physically consistent with the common intermittency scaling. Second, the non-local behavior of the Orr-Sommerfeld equation must arise in the model through a properly behaved explicit rapid-pressure diffusion model. In addition, we show that the normal rapid pressure-strain term, which assumes homogeneity, is a poor model for linear instability waves. Finally, we present a new model for transition in Rayleigh-Taylor and Kelvin-Helmholtz unstable flows.