Non-Parallel Receptivity and the Adjoint PSE

Airiau, Christophe; Walther, Steeve; Bottaro, Alessandro

doi:10.1007/978-3-662-03997-7_6

Cited by 9 publications

(10 citation statements)

References 6 publications

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“…9-12, amongst others͒ and solutions using the adjoint of the parabolized stability equations. [13][14][15][16] DNS solutions are accurate, but computationally expensive and need a nontrivial amount of postprocessing work to yield the depth of understanding of the physical mechanisms that a Fourier analysis does. The adjoint method is accurate and computationally efficient, and offers information on the flow regions most receptive to forcing.…”

Section: Introductionmentioning

confidence: 99%

Receptivity of three-dimensional boundary-layers to localized wall roughness and suction

Bertolotti

2000

Physics of Fluids

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The receptivity of three-dimensional, incompressible, boundary-layer flows to localized roughness or suction is studied theoretically and numerically. Three-dimensional boundary-layer flows have a strong “nonparallel” component due to the curvature of the potential-flow streamlines. Our theoretical model extends the Fourier-transform methodology to nonparallel flows using a Taylor expansion of the laminar mean-flow at the location of the roughness. Both the near-field and the far-field solutions are contained in the model. Additionally, the use of MacLaurin expansions in the complex plane leads quickly to the receptivity factors of eigenmodes. The theoretical results are validated with solutions to the linearized Navier–Stokes equations efficiently obtained by replacing the actual wall forcing with a smoother, but equivalent, forcing. We find that the far-field response is proportional to both H̃(αe) and dH̃(αe)/dα, where H̃(α) is the Fourier transform of the forcing distribution, and αe is the eigenmode’s wave number. The receptivity coefficient for H̃(αe) decreases when nonparallelism is included in our models, while that for dH̃(αe)/dα increases.

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Section: Introductionmentioning

confidence: 99%

Receptivity of three-dimensional boundary-layers to localized wall roughness and suction

Bertolotti

2000

Physics of Fluids

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“…These authors then went on to perform adjoint-based receptivity studies of the Blasius and the Falkner-Skan fl at-plate boundary layers and demonstrated the very close agreement of the results obtained and those of the previous adjoint local analysis of Hill (1995). In parallel developments, Airiau et al (2000), Pralits et al (2000), and Walther et al (2001) have also presented receptivity prediction methodologies based on direct and adjoint PSE equations. In parallel developments, Airiau et al (2000), Pralits et al (2000), and Walther et al (2001) have also presented receptivity prediction methodologies based on direct and adjoint PSE equations.…”

Section: 5-d: Developing Background Flowsmentioning

confidence: 82%

Fundamentals and Applications of Modern Flow Control

Joslin¹,

Miller²,

Miller³

2009

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“…(12) in terms of the efficiency function that relates the disturbance amplitude to the Fourier geometry factor due to the surface nonuniformity. Hence, Eq.…”

Section: (2)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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Non-Parallel Receptivity and the Adjoint PSE

Cited by 9 publications

References 6 publications

Receptivity of three-dimensional boundary-layers to localized wall roughness and suction

Receptivity of three-dimensional boundary-layers to localized wall roughness and suction

Fundamentals and Applications of Modern Flow Control

Boundary-Layer Receptivity and Integrated Transition Prediction

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