The SED-SL~T Model Applied To Transitional Hypersonic Boundary Layers Around A Sharp Cone

Current engineering transition models are built upon the concept of intermittency fac-tor 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 hypersonic flows,leading to great uncertainties in prediction.This situation begins to change after the structural ensemble dynamics(SED)theory.In the SED’s proposal the TBL flow domains are 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 en-ergy transport have characteristic(stress)lengths which locally behave in power law with wall distance(y).With a generalized dilation invariance assumption describing a universal transi-tion 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 com-putations.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 study to develop an SED-SL transition model for describing the hypersonic transitional boundary layers around a sharp cone.Such transitional boundary layers have not been well-predicted by previous tran-sition models.By cooperating with the infrared thermal image data of a Ma 6,7 degree half-angle cone at moderate attack angles,we specify the multi-layer parameters of the hypersonic transitional boundary layer on the cone surface.The boundary layer evolutions with the streamwise and circumferential coordinates,and with the attack angles,are studied and described with the multi-layer parameters.Relationships between the transition center locations and the local flow parameters are proposed for empirically determining the transition onsets.A prelimi-nary SED-SL model thus is established for simulating the hypersonic transitional boundary layers around the cone,which has given rather accurate descriptions for the current experi-mental cases.The model paves a way for an SED-SL~T(stress length transition)model with full-parameter prediction capacity to achieve engineering applications,which has to be done in a future study.The methodology we have developed in this study is worth pointing out,which is valuable to researchers working on modeling complex boundary layer flows.It consists of three steps.1.Specify the streamwise variation of the multi-layer parameters of boundary layer before solving the Reynolds averaged Navier-Stokes equations.Then,compare the simulation results with experimental and numerical data of high fidelity,and use the discrepancies to revise the settings of the multi-layer parameters,until the discrepancies are minimised,which leads to the correct multi-layer parameters.2.Conduct a series of simulations under different situations,and use the data to determine the variations of the multi-layer parameters with control param-eters and environmental factors.3.Assess and apply the SED-SL model in more flows.It should be noted that the method is effective only because the multi-layer parameters are phys-ically meaningful and describe the similarities of boundary layers when control parameters vary,which is not satisfied by the parameters in other transition models.