Prediction of compressible turbulent boundary layer via a symmetry-based length model

A recently developed symmetry-based theory is extended to derive an algebraic model for compressible turbulent boundary layers (CTBL)-predicting mean profiles of velocity, temperature and density-valid from incompressible to hypersonic flow regimes, thus achieving a Mach number invariant description. The theory leads to a multi-layer analytic form of a stress length function which yields a closure of the mean momentum equation. A generalized Reynolds analogy is then employed to predict the turbulent heat transfer. The mean profiles and the friction coefficient are compared with direct numerical simulations of CTBL for a range of from 0 (e.g. incompressible) to 6.0 (e.g. hypersonic), with an accuracy notably superior to popular current models such as Baldwin-Lomax and Spalart-Allmaras models. Further analysis shows that the modification is due to an improved eddy viscosity function compared to competing models. The results confirm the validity of our-invariant stress length function and suggest the path for developing turbulent boundary layer models which incorporate the multi-layer structure.