Evaluation of Adjoint Based Methods for the Prediction of Receptivity

Collis, S. Scott; Dobrinsky, Alexander

doi:10.1007/978-3-662-03997-7_14

Cited by 7 publications

(8 citation statements)

References 5 publications

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“…However, in contrast to the efficiency function based prediction methods, calculations must be repeated when the geometry of the nonuniformities changes unless one uses the adjoint form of LNS equations as described in Ref. [13]. To improve the efficiency of the LNS formulation, this study also examines a new LNS formulation based on the existing PSE method.…”

Section: T 7 T I T I\mentioning

confidence: 99%

Boundary-Layer Receptivity and Integrated Transition Prediction

Chang

Choudhari²

2005

43rd AIAA Aerospace Sciences Meeting and Exhibit

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The adjoint p a r a b o l d stability equations (BE) formulation is used to calculate the boundary layer receptivity to localized surface roughness and suction for compressible boundary layers. Receptivity efficiency functions predicted by the adjoint PSE approach agree well with results based on other nonparallel methods including linearized Navier-Stokes equations for both Tollmien-Schlichting waves and crossflow instability in swept wing boundary layers. The receptivity efficiency function can be regarded as the Green's function to the disturbance amplitude evolution in a nonparallel (growing) boundary layer. Given the Fourier transformed geometry factor distribution along the chordwise direction, the linear disturbance amplitude evolution for a finite size, distributed nonuniformity can be computed by evaluating the integral effects of both disturbance generation and linear amplification. The synergistic approach via the linear adjoint PSE for receptivity and nonlinear PSE for disturbance evolution downstream of the leading edge forms the basis for an integrated transition prediction tool. Eventually, such physics-based, high fdelity prediction methods could simulate the transition process from the disturbance generation through the nonlinear breakdown in a holistic manner.

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Section: T 7 T I T I\mentioning

confidence: 99%

Boundary-Layer Receptivity and Integrated Transition Prediction

Chang

Choudhari²

2005

43rd AIAA Aerospace Sciences Meeting and Exhibit

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“…Rather than one solution with each dataset k = 1, · · ·, only a single solution of the dual formulation given in equation (6) is required, followed by repeated evaluation of the dual cost function given by equation (8).…”

Section: -39mentioning

confidence: 99%

“…Note that in the continuous approach the discretization of the equations is explicitly performed on the dual equations given in (6) and (8). The discretized continuous adjoint equations (i.e.…”

Section: -39mentioning

confidence: 99%

“…Potentially substantial effects of surface curvature and mean-flow nonparallelism were pointed out in Ref. 8 and the effects of nonlinear roughness height were recently addressed in Ref. 9.…”

Section: Introductionmentioning

confidence: 99%

“…9. References 8,[10][11][12][13][14][15][16][17][18][19] describe the various applicable prediction methodologies (ranging from the inhomogeneous form of linear stability equations, parabolized stability equations, and linearized or full Navier-Stokes equations) and their application to a broader class of flows. Much of this work, however, pertains to a single, spanwise periodic array of roughness elements, while studies reporting the receptivity to spatially nonlocalized roughness distributions are less common.…”

Section: Introductionmentioning

confidence: 99%

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Excitation of Crossflow Instabilities in a Swept Wing Boundary Layer

Carpenter

Choudhari

et al. 2010

48th AIAA Aerospace Sciences Meeting Including the New Horizons Forum and Aerospace Exposition

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The problem of crossflow receptivity is considered in the context of a canonical 3D boundary layer (viz., the swept Hiemenz boundary layer) and a swept airfoil used recently in the SWIFT flight experiment performed at Texas A&M University. First, Hiemenz flow is used to analyze localized receptivity due to a spanwise periodic array of small amplitude roughness elements, with the goal of quantifying the effects of array size and location. Excitation of crossflow modes via nonlocalized but deterministic distribution of surface nonuniformity is also considered and contrasted with roughness induced acoustic excitation of Tollmien-Schlichting waves. Finally, roughness measurements on the SWIFT model are used to model the effects of random, spatially distributed roughness of sufficiently small amplitude with the eventual goal of enabling predictions of initial crossflow disturbance amplitudes as functions of surface roughness parameters.

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Acoustic receptivity and transition modeling of Tollmien-Schlichting disturbances induced by distributed surface roughness

2018

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Acoustic receptivity to Tollmien-Schlichting waves in the presence of surface roughness is investigated for a flat plate boundary layer using the time-harmonic incompressible linearized Navier-Stokes equations. It is shown to be an accurate and efficient means of predicting receptivity amplitudes, and therefore to be more suitable for parametric investigations than other approaches with DNS-like accuracy. Comparison with literature provides strong evidence of the correctness of the approach, including the ability to quantify non-parallel flow effects. These effects are found to be small for the efficiency function over a wide range of frequencies and local Reynolds numbers. In the presence of a two-dimensional wavy-wall, non-parallel flow effects are quite significant, producing both wavenumber detuning and an increase in maximum amplitude. However, a smaller influence is observed when considering an oblique Tollmien-Schlichting wave. This is explained by considering the non-parallel effects on receptivity and on linear growth which may, under certain conditions, cancel each other out. Ultimately, we undertake a Monte-Carlo type uncertainty quantification analysis with two-dimensional distributed random roughness. Its power spectral density (PSD) is assumed to follow a power law with an associated uncertainty following a probabilistic Gaussian distribution. The effects of the acoustic frequency over the mean amplitude of the generated two-dimensional Tollmien-Schlichting waves are studied. A strong dependence on the mean PSD shape is observed and discussed according to the basic resonance mechanisms leading to receptivity. The growth of Tollmien-Schlichting waves is predicted with non-linear parabolized stability equations computations to assess the effects of stochasticity in transition location.

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Evaluation of Adjoint Based Methods for the Prediction of Receptivity

Cited by 7 publications

References 5 publications

Boundary-Layer Receptivity and Integrated Transition Prediction

Boundary-Layer Receptivity and Integrated Transition Prediction

Excitation of Crossflow Instabilities in a Swept Wing Boundary Layer

Acoustic receptivity and transition modeling of Tollmien-Schlichting disturbances induced by distributed surface roughness

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