DNS of leading-edge receptivity to sound

The Quarterly Journal of Mechanics and Applied Mathematics

2012

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.

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

The Quarterly Journal of Mechanics and Applied Mathematics

2012

“…Saric et al (1995) eliminated this problem by using an elliptic leading edge machine drilled onto a flat plate, called a Modified Super Ellipse (MSE), to eliminate any discontinuity, and further experiments were carried out by Saric & White (1998). Fuciarelli et al (1998) and Wanderley & Corke (2001) both computed their respective numerical calculations for the MSE in order to compare their results with those of Saric & White. Excellent agreement of the T-S wave amplitude at lower branch is found between Wanderley & Corke and the experiments, however in this paper we are not able to make comparisons with these results, due to the significance of non-zero pressure gradients along a MSE.…”

Section: Comparison With Previous Numerical Studiesmentioning

confidence: 99%

“…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%

See 1 more Smart Citation

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

Hammerton

2006

J. Fluid Mech.

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).

“…Fuciarelli et al (1998) discuss such DNS results for a flat plate with an elliptical leading edge while the alternative approach of Corke and coworkers linearises about the basic flow, which then decouples the steady and unsteady flow fields that can then be solved separately. Haddad & Corke (1998) consider parabolic bodies at a zero angle of attack to the mean flow, while Erturk & Corke (2001) and Haddad et al (2005) extend this to consider parabolic bodies with non-zero angle of attack.…”

Section: Introductionmentioning

confidence: 99%

Analysis of the unstable Tollmien–Schlichting mode on bodies with a rounded leading edge using the parabolized stability equation

Hammerton

2009

J. Fluid Mech.

The interaction between free-stream disturbances and the boundary layer on a body with a rounded leading edge is considered in this paper. A method which incorporates calculations using the parabolized stability equation (PSE) in the Orr-Sommerfeld region along with an upstream boundary condition derived from asymptotic theory in the vicinity of the leading edge, is generalised to bodies with an inviscid slip velocity which tends to a constant far downstream. We present results for the position of the lower branch neutral stability point and the magnitude of the unstable Tollmien-Schlichting (T-S) mode at this point for both a parabolic body and the Rankine body. For the Rankine body, which has an adverse pressure gradient along its surface far from the nose, we find a double maximum in the T-S wave amplitude for sufficiently large Reynolds numbers.