Robust Generation of the Parabolized Stability Equation (PSE) Inflow Conditions for Automation of Transition Analysis

摘要

The IAI CFD Department has developed a system of codes for stand-alone prediction of 3D boundary-layertransition on swept wings surface. The stability prediction method adopted relies on the most advanced mathematicalmodel Parabolized Stability Equations (PSE) [1,2,3,4,5]. The PSE approach is more accurate and consistent than theprevious classical Orr-Sommerfeld equation derived in the Linear Stability Theory (LST) of instabilities. Contrarilyto the LST theory, the PSE methodology removes the parallel flow assumption of the boundary layer flow takinginto account the dominant non-parallel effects in the mean-flow and in the perturbed quantities. Moreover anotherimportant feature of the PSE approach is that it considers the history of the longitudinal evolution of the disturbancesand wavenumber. The PSE technology enables the analysis of both Tollmien-Schlichting (TS) and Crossflow (CF)instabilities of 3D boundary-layers flows. The PSE initial solution relies on non yet automatic LST code (LSTGlobal Eigenvalue Solver) based on Chebyshev polynomials decomposition for which a tremendous amounts ofinformation, knowledge, and interaction from the user is required. Namely the user has to 1) locate and identify theinstabilities present in the flow, 2) select the instabilities that are susceptible of triggering transition, and 3) trackproperly the amplification maxima in the integration of the N factor. This is not acceptable in an industrialengineering environment. Since there is not automatic LST code, simplified models have been developed for anautomatic transition prediction capability for the industry, relying mainly on the ONERA database method [12, 13],where stability characteristics are precomputed for self-similar laminar boundary layer profiles and not for theNavier-Stokes profiles due to the lack of accuracy of most RANS codes, to serve as input to the equations ofstability. In contrast to this approach, in this work, a new way to generate automatically (with no user intervention)the initialization of PSE marching procedure is exposed. The solution of the linear stability equations at initializationis done now by converging iteratively the linear stability solver starting from new inflow empirical approximationformulas as initial guess obtained in special natural basis for CF and TS respectively. Moreover in this work onebenefits from the high accuracy of the RANS code NES which enables to overcome the well known major drawbackfor the direct coupling of most industrial RANS codes with linear stability programs (PSE or LST). Hence thisdevelopment permits an automatic use of the PSE solver coupled with the NES code, which is a real breakthrough inan industrial context.