Automatic Transition Predictions Using Simplified Methods

Laminar-turbulent transition remains a critical issue in a number of cases, including drag reduction, performance prediction of high-lift systems, improved accuracy in general computational fluid dynamics, and reduction of computation cycles for development of optimization tools. Transition delay remains one of the most promising technologies for reducing air transport energy consumption, throughnatural or hybrid laminarflowcontrol. Theuse of linear stability theory, either local or nonlocal, remains rather demanding in terms of knowledge and user interaction. Hence, a demand exists for simplified, robust, and accurate transition prediction tools to be inserted into general flow solvers, of boundary-layer or Reynolds-averaged Navier–Stokes types. The problem can be solved by developing transition criteria or databasemethods. In this last case, characteristics of an actualfloware derived from known solutions of model flows. ONERA, the French Aerospace Laboratory, has long been involved in the development of such methods, and the present paper aims at providing a comprehensive view of the tools developed in the second category, applicable from low-speed two-dimensional to transonic three-dimensional flows, and even to three-dimensional supersonic flows. Nomenclature F = reduced frequency f = frequency Hi = incompressible shape factor Pi = characteristic parameter for the crossflow models Rk = Reynolds number based on length k Tw = wall temperature Ue,We, Te = velocity components and temperature at the boundary-layer edge Ui = velocity at the location yi of the inflection point u, w, T = velocity and temperature components of the boundary-layer profile Vg, ’g = modulus and direction of the group velocity , = complex, reduced wave numbers ( 1). Their real parts are the components of the wave vector k. = crossflow wave number. As i is usually forced to zero, represents the real part. 1 = displacement thickness = angle between the local x direction and the external velocity vector 1 = momentum thickness = wavelength of the instability