Boundary Layer Receptivity to Free-stream Sound on Elliptic Leading Edges of Flat Plates

Wanderley, Juan B. V.; Corke, Thomas

doi:10.1007/978-3-662-03997-7_8

Cited by 17 publications

(39 citation statements)

References 1 publication

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“…This extrapolation is marked as the dotted line in figure 16 (cf figure 10 of Wanderley & Corke (2001)) for = 0.194 (F = 54.0 × 10 −6 ). However this analysis does have some possible flaws.…”

Section: Comparison With Previous Numerical Studiesmentioning

confidence: 91%

“…An alternative approach taken by Corke and co-workers is based on linearisation about the base flow, that leads to decoupling of the base and unsteady flows which can then be solved separately. Haddad & Corke (1998) considered parabolic bodies with axis of symmetry parallel to the mean flow, Erturk & Corke (2001) and Haddad et al (2005) extended the analysis to parabolic bodies at an angle-of-attack to the mean flow, while Wanderley & Corke (2001) considered bodies with elliptical leading edges in order to compare with the results of Fuciarelli et al (1998).…”

Section: Introductionmentioning

confidence: 99%

“…A modified super ellipse has the leading edge directly machined onto a flat plate, which moves the pressure minimum closer to the leading edge, and removes the curvature discontinuity associated with an ellipse stuck onto a flat plate, which contributes additional receptivity. The results of Saric & White (1998) are compared to numerical results in Wanderley & Corke (2001). The aim of the present paper is to show how results from receptivity theory can be combined with stability calculations in order to allow comparison with experimental measurements and numerical simulation.…”

Section: Introductionmentioning

confidence: 99%

“…We compare our results with the numerical computations of Haddad & Corke (1998), in the limiting case of a parabola with zero nose radius. Finally we compare our results with the methods used by Wanderley & Corke (2001) in their attempt to extrapolate numerical results, close to the neutral stability point, back to the receptivity region at the leading edge.…”

Section: Introductionmentioning

confidence: 99%

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Asymptotic receptivity analysis and the parabolized stability equation: a combined approach to boundary layer transition

Turner

Hammerton

2006

J. Fluid Mech.

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We consider the interaction of free-stream disturbances with the leading edge of a body and its effect on the transition point. We present a method which combines an asymptotic receptivity approach, and a numerical method which marches through the Orr-Sommerfeld region. The asymptotic receptivity analysis produces a three deck eigensolution which in its far downstream limiting form, produces an upstream boundary condition for our numerical Parabolized Stability Equation (PSE). We discuss the advantages of this method against existing numerical and asymptotic analysis and present results which justifies this method for the case of a semi-infinite flat plate, where asymptotic results exist in the Orr-Sommerfeld region. We also discuss the limitations of the PSE and comment on the validity of the upstream boundary conditions. Good agreement is found between the present results and the numerical results of Haddad & Corke (1998).

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Section: Comparison With Previous Numerical Studiesmentioning

confidence: 91%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

Asymptotic receptivity analysis and the parabolized stability equation: a combined approach to boundary layer transition

Turner

Hammerton

2006

J. Fluid Mech.

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“…Haddad & Corke (18) developed their code for a parabolic body so as to eliminate the discontinuous curvature issue of the elliptical body studied by Reed et al (31), see (10) for a more detailed discussion. This DNS method was extended to parabolic bodies at non-zero angles of attack by Ertuck & Corke (35) and Haddad et al (36), and to the MSE by Wanderley & Corke (37). The results of (37) were compared to the DNS results of Fuciarelli et al (38) and the experiments of Saric & White (39).…”

Section: Introductionmentioning

confidence: 99%

Tollmien-schlichting wave amplitudes on a semi-infinite flat plate and a parabolic body: comparison of a parabolized stability equation method and direct numerical simulations

Turner

2012

The Quarterly Journal of Mechanics and Applied Mathematics

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SummaryIn this paper the interaction of free-stream acoustic waves with the leading edge of an aerodynamic body is investigated and we compare two different methods for analysing this interaction. Results are compared for a method which incorporates Orr-Sommerfeld calculations using the parabolized stability equation (PSE) to those of direct numerical simulations (DNS). By comparing the streamwise amplitude of the Tollmien-Schlichting (T-S) wave it is found that non-modal components of the boundary-layer response to an acoustic wave can persist some distance downstream of the lower branch. The effect of nose curvature on the persisting non-modal eigenmodes is also considered, with a larger nose radius allowing the non-modal eigenmodes to persist farther downstream.

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A numerical evaluation of the asymptotic theory of receptivity for subsonic compressible boundary layers

Tullio

Ruban

2015

J. Fluid Mech.

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The capabilities of the triple-deck theory of receptivity for subsonic compressible boundary layers have been thoroughly investigated through comparisons with numerical simulations of the compressible Navier-Stokes equations. The analysis focused on the two Tollmien-Schlichting wave linear receptivity problems arising due to the interaction between a low amplitude acoustic wave and a small isolated roughness element and the low amplitude, time-periodic vibrations of a ribbon placed on the wall of a flat plate. A parametric study was carried out to look at the effects of roughness element and vibrating ribbon longitudinal dimensions, Reynolds number, Mach number and TollmienSchlichting wave frequency. The flat plate is considered isothermal, with a temperature equal to the laminar adiabatic-wall temperature. Numerical simulations of the full and the linearised compressible Navier-Stokes equations have been carried out using highorder finite differences to obtain, respectively, the steady basic flows and the unsteady disturbance fields for the different flow configurations analysed. The results show that the asymptotic theory and the Navier-Stokes simulations are in good agreement. The initial Tollmien-Schlichting wave amplitudes and, in particular, the trends indicated by the theory across the whole parameter space are in excellent agreement with the numerical results. An important finding of the present study is that the behaviour of the theoretical solutions obtained for Re → ∞ holds at finite Reynolds numbers and the only conditions needed for the theoretical predictions to be accurate are that the receptivity process be linear and the free stream Mach number be subsonic.

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Boundary Layer Receptivity to Free-stream Sound on Elliptic Leading Edges of Flat Plates

Cited by 17 publications

References 1 publication

Asymptotic receptivity analysis and the parabolized stability equation: a combined approach to boundary layer transition

Asymptotic receptivity analysis and the parabolized stability equation: a combined approach to boundary layer transition

Tollmien-schlichting wave amplitudes on a semi-infinite flat plate and a parabolic body: comparison of a parabolized stability equation method and direct numerical simulations

A numerical evaluation of the asymptotic theory of receptivity for subsonic compressible boundary layers

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