Precise estimation of the location and magnitude of boundary layer transition is essential for the exact computation of aero-thermodynamics and the performance of hypersonic vehicles.Compared with resource-intensive m...Precise estimation of the location and magnitude of boundary layer transition is essential for the exact computation of aero-thermodynamics and the performance of hypersonic vehicles.Compared with resource-intensive methods such as large eddy simulation,direct numerical simulation,and experimental approaches,Reynolds-averaged Navier-Stokes(RANS)-based models offer an efficient and cost-effective solution for engineering applications.Therefore,this review focuses on the capabilities of various RANS-based models for prediction of boundary layer transition in hypersonic flows.The formulation and underlying assumptions of these models are described and their predictive performance in terms of transition initiation and length in hypersonic regimes is examined.Critical gaps and limitations of existing models are outlined and a framework is established for future development of RANS-based transition models,with the aim of developing more robust,reliable,and cost-effective techniques for prediction of hypersonic boundary layer transition that are suitable for use in current state-of-the-art computational codes.展开更多
We study for a class of symmetric Levy processes with state space R^n the transition density pt（x） in terms of two one-parameter families of metrics, （dt）t〉o and （δt）t〉o. The first family of metrics describes...We study for a class of symmetric Levy processes with state space R^n the transition density pt（x） in terms of two one-parameter families of metrics, （dt）t〉o and （δt）t〉o. The first family of metrics describes the diagonal term pt （0）; it is induced by the characteristic exponent ψ of the Levy process by dr（x, y） = √tψ（x - y）. The second and new family of metrics 6t relates to √tψ through the formula exp（-δ^2t（x,y））=F[e^-tψ/pt（0）]（x-y）,where Y denotes the Fourier transform. Thus we obtain the following ＂Gaussian＂ representation of the tran- sition density： pt（x） = pt（O）e^-δ^2t（x,0） where pt（O） corresponds to a volume term related to √tψ and where an ＂exponential＂ decay is governed by 5t2. This gives a complete and new geometric, intrinsic interpretation of pt（x）.展开更多
基金supported by a National Research Foundation of Korea(NRF)grant funded by the Korean Government-(No.RS-2025-00557769).
文摘Precise estimation of the location and magnitude of boundary layer transition is essential for the exact computation of aero-thermodynamics and the performance of hypersonic vehicles.Compared with resource-intensive methods such as large eddy simulation,direct numerical simulation,and experimental approaches,Reynolds-averaged Navier-Stokes(RANS)-based models offer an efficient and cost-effective solution for engineering applications.Therefore,this review focuses on the capabilities of various RANS-based models for prediction of boundary layer transition in hypersonic flows.The formulation and underlying assumptions of these models are described and their predictive performance in terms of transition initiation and length in hypersonic regimes is examined.Critical gaps and limitations of existing models are outlined and a framework is established for future development of RANS-based transition models,with the aim of developing more robust,reliable,and cost-effective techniques for prediction of hypersonic boundary layer transition that are suitable for use in current state-of-the-art computational codes.
文摘We study for a class of symmetric Levy processes with state space R^n the transition density pt（x） in terms of two one-parameter families of metrics, （dt）t〉o and （δt）t〉o. The first family of metrics describes the diagonal term pt （0）; it is induced by the characteristic exponent ψ of the Levy process by dr（x, y） = √tψ（x - y）. The second and new family of metrics 6t relates to √tψ through the formula exp（-δ^2t（x,y））=F[e^-tψ/pt（0）]（x-y）,where Y denotes the Fourier transform. Thus we obtain the following ＂Gaussian＂ representation of the tran- sition density： pt（x） = pt（O）e^-δ^2t（x,0） where pt（O） corresponds to a volume term related to √tψ and where an ＂exponential＂ decay is governed by 5t2. This gives a complete and new geometric, intrinsic interpretation of pt（x）.
