Boundary layer sensitivity and receptivity

Airiau, Christophe; Walther, Steeve; Bottaro, Alessandro

doi:10.1016/s1631-0721(02)01450-x

Cited by 13 publications

(8 citation statements)

References 10 publications

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“…This behavior was also observed in the FRNT results by Ng & Crouch (1999). Tempelmann (2009) considered a refined, nonlocal receptivity model combining the direct and adjoint LPSE (see also Airiau et al 2002). This approach was combined here with a NPSE solution in order to compute the receptivity and growth of the crossflow vortex.…”

Section: Roughness-induced Crossflow Vorticessupporting

confidence: 60%

Numerical study of boundary-layer receptivity on a swept wing

Tempelmann

Schrader

Hanifi

et al. 2011

6th AIAA Theoretical Fluid Mechanics Conference

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Direct numerical simulations (DNS) of the flow over a wing with 45• sweep and −4• angle-of-attack are presented. This flow configuration was investigated in a series of wind-tunnel experiments at the Arizona State University (ASU). On the upper wing side, the flow develops a substantial crossflow and is therefore ideally suited for a study of the receptivity mechanisms of crossflow vortices. Here, we examine the boundary-layer receptivity to surface roughness and to single vortical free-stream modes. The roughness is modeled by a shallow circular disk and is identical with one single element of the spanwise roughness array considered in the ASU experiments. The boundary layer develops a steady crossflow mode downstream of the roughness. The spatial evolution of the modal amplitude obtained by the DNS is in excellent agreement with a solution to the nonlinear parabolized stability equations (NPSE) while being lower than that measured in the experiments. The reasons for this discrepancy are yet to be determined. Possible explanations are the idealization of the roughness array by spanwise periodic boundary conditions in our simulations, or the presence of traveling crossflow waves due to background free-stream turbulence in the experiments. We demonstrate that the boundary-layer receptivity to roughness can be successfully predicted by a nonlocal, adjoint-based receptivity model. Stationary crossflow vortices can also be triggered by zero-frequency free-stream vortical modes. We consider two types of mode, carrying streamwise and chordwise vorticity. Both modes give rise to nonmodal disturbances near the leading edge, which soon evolve into a steady crossflow mode. The boundary layer is found to be somewhat more receptive to the streamwisevorticity mode than to the chordwise vorticity.

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Section: Roughness-induced Crossflow Vorticessupporting

confidence: 60%

Numerical study of boundary-layer receptivity on a swept wing

Tempelmann

Schrader

Hanifi

et al. 2011

6th AIAA Theoretical Fluid Mechanics Conference

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“…Since PSE are mathematically PDE, it is simple to solve them by adding various boundary conditions and source terms. This leads to use them for receptivity and sensitivity analysis, 14 in optimal flow control approaches 13 and for weakly nonlinear stability studies. 15 In the following, all the variables are made non-dimensional.…”

Section: Pse and Adjoint-pse In Jet Stability And Sensitivity Anamentioning

confidence: 99%

PSE-based sensitivity analysis of turbulent and supersonic single stream jet

Ansaldi

Airiau

Arroyo

et al. 2016

22nd AIAA/CEAS Aeroacoustics Conference

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Reducing noise emission from jet is a major topics of aeroacoustics. Recently, it has been shown that the large coherent structures of a turbulent single-stream jet, which are parts of the noise generation mechanisms, can be interpreted as instability of the mean turbulent flow, especially in the region of the potential core. Reducing noise will be probably only achieved with some new control strategy on the underlying physics of the acoustic wave generation. The present work deals with the last investigations associated to the sensitivity analysis of the single and dual-stream jet instability to any local forcing. Sensitivity is a first step of any aeroacoustic or flow control approach and it is performed by the Parabolized Stability Equations and their adjoint counter part. Validation is first made on a simple semi-analytical supersonic jet. Then sensitivity functions to a source of momentum, mass or energy forcing are given in a supersonic single (M = 1.15) and dualstream jets (Mp = 0.89 and Ms = 1.20). The base-flow is obtained from accurate Large Eddy Simulations and included some shock cells. Highest sensitivities are found inside the shear layer close to the external boundary of the potential core and close to the jet inlet, similar to the previous results found in incompressible single stream jet. The growth rate and wave number of the Kelvin-Helmhotz instability and the acoustic (pressure) perturbation are strongly influenced by the shock cell positions.

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“…Previous adjoint-based investigations into BL type flows can be grouped into investigation with respect to either BL receptivity, 3,9 modal sensitivity, 8,10 or BL stability 15,18 considering the perturbationbased excitation of Tollmien-Schlichting waves 1,2 or the linearized Orr-Sommerfeld equation. 6,9 Hill 16,17 was the first who investigated the adjoint Orr-Sommerfeld operator and subsequently extended his study toward the adjoint to a parabolic stability equation.…”

Section: Introductionmentioning

confidence: 99%

Continuous adjoint complement to the Blasius equation

2021

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This manuscript is concerned with a continuous adjoint complement to two-dimensional, incompressible, first-order boundary-layer equations for a flat plate boundary layer. The text is structured into three parts. The first part demonstrates that the adjoint complement can be derived in two ways, following either a first simplify then derive or a first derive and then simplify strategy. The simplification step comprises the classical boundary-layer (BL) approximation, and the derivation step transfers the primal flow equation into a companion adjoint equation. The second part of the paper comprises the analyses of the coupled primal/adjoint BL framework. This leads to similarity parameters, which turn the partial-differential-equation (PDE) problem into a boundary value problem described by a set of ordinarydifferential-equations (ODEs) and support the formulation of an adjoint complement to the classical Blasius equation. Opposite to the primal Blasius equation, its adjoint complement consists of two ODEs, which can be simplified depending on the treatment of advection. It is shown that the advective fluxes, which are frequently debated in the literature, vanish for the investigated self-similar BL flows. Differences between the primal and the adjoint Blasius framework are discussed against numerical solutions, and analytical expressions are derived for the adjoint BL thickness, wall shear stress, and subordinated skin friction and drag coefficients. The analysis also provides an analytical expression for the shape sensitivity to shear driven drag objectives. The third part assesses the predictive agreement between the different Blasius solutions and numerical results for Navier-Stokes simulations of a flat plate BL at Reynolds numbers between 10 3 Re L 10 5 . It is seen that the reversal of the inlet and outlet locations and the direction of the flow, inherent to the adjoint formulation of convective kinematics, poses a challenge when investigating real finite length (finite Re-number) flat plate boundary layer problems. Efforts to bypass related issues are discussed.

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Boundary layer sensitivity and receptivity

Cited by 13 publications

References 10 publications

Numerical study of boundary-layer receptivity on a swept wing

Numerical study of boundary-layer receptivity on a swept wing

PSE-based sensitivity analysis of turbulent and supersonic single stream jet

Continuous adjoint complement to the Blasius equation

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