New perspective for developing reliable engineering transition model based on the structural ensemble dynamics theory

Current engineering transition models are built upon the concept of intermittency factor whose streamwise evolution is described by phenomenology of dimensional analysis with numerous physically insignificant coefficients which are not invariant with varying physical conditions, especially for supersonic and hypersonic flows. The major bottleneck is the lack of a complete theory for turbulent boundary layer (TBL) beyond the log law, and the situation begins to change after the proposal of the structural ensemble dynamics (SED) theory, which is based on the analysis of wall-induced dilation symmetry constraint on the momentum and energy balance equations. The key assumption of the SED theory is that TBL flow domain is self-organized into a finite number of sub-regions, in each of which a structural ensemble is so formed that eddies responsible for momentum and energy transport have characteristic (stress) lengths which locally behave in power laws with wall distance (y) to preserve dilation symmetry. With a generalized dilation invariance assumption describing a universal transition across different sub-regions, the theory yields analytic multi-layer expression of the stress lengths from which the mean velocity and turbulence intensity distributions can be derived, in excellent agreement with data of canonical wall turbulence from both experiments and computations. More recent extension of the SED theory in describing streamwise evolving TBL by introducing dilation of the distance to leading edge (x) yields in a straightforward way an accurate description of laminar-turbulent transition. Here, we present a new perspective to build a reliable engineering transition model from the SED theory, which consists in specifying the streamwise variation of the multi-layer parameters before solving the Reynolds averaged Navier-Stokes equations. The model is successfully validated by computational results for free-stream turbulence induced transitional flows passing flat plate and hypersonic flows passing sharp cone with varying attack angles. New kind of promising transition model may arise with advantage of being stable and transparency for adjusting parameters which are all physically meaningful.