Modeling the transition region

The calculation of engineering flows undergoing laminar-turbulent transition presents special problems. Mean-flow quantities obey neither the fully laminar nor the fully turbulent correlations. In addition, local maxima in skin friction, wall temperature, and heat transfer often occur near the end of the transition region. Traditionally, modeling this region has been important for the design of turbine blades, where the transition region is long in relation to the chord length of the blade. More recently, the need for better transition-region models has been recognized by designers of hypersonic vehicles where the high Mach number, the low Reynolds number, and the low-disturbance flight environment emphasize the importance of the transition region. Needless to say, a model that might work well for the transitional flows typically found in gas turbines will not necessarily work well for the external surface of a hypersonic vehicle. In Section 2 of this report, some of the important flow features that control the transition region will be discussed. In Section 3, different approaches to the modeling problem will be summarized and cataloged. Fully turbulent flow models will be discussed in detail in Section 4; models specifically designed for transitional flow, in Section 5; and the evaluation of models, in Section 6.