An all-speed formulation using a modified γ-model for the prediction of boundary layer transition and heat transfer

Abstract

• Effect of Mach number and temperature is added in the modified γ -model to find the transition onset for all speed flows. • Algebraic correlation is derived for the scaling constant of F onset1 based on the Mach number and temperature ratio. • Compressibility correction is added to the R e θ c correlation. • Effect of inlet viscosity ratio on transition and an existing correlation for it is identified to use with modified γ -model . Menter’s one-equation transition model, known to predict all types of boundary layer transition in low-speed flows, does not include the effect of Mach number and temperature, predominant at high speeds. This work uses an algebraic correlation based on a self-similar solution of compressible boundary layer equations to predict the transition onset location at all speed regimes ranging from incompressible to hypersonic speeds at different temperature ratios. Since Menter’s model is highly susceptible to inflow conditions (viscosity ratio and turbulence intensity), the modified model uses correlations related to the experimental conditions for inlet turbulence quantities. A two-dimensional in-house solver based on the finite volume method is developed for this study and validated with standard test cases (flat plate, ramp) in different speed regimes for the turbulence model and a low-speed test case for Menter’s transition model. Transition location is predicted from the heat transfer rate for high-speed flows and skin friction co-efficient for low-speed flows. Numerical results obtained from Menter’s and modified model for various test cases are compared against the experimental and DNS data. Computational results show that modified γ -model could predict the transition onset location more accurately than Menter’s model in all speed regimes.