On predicting receptivity to surface roughness in a compressible infinite swept wing boundary layer

Abstract

The receptivity of crossflow disturbances on an infinite swept wing is investigated using solutions of the adjoint linearised Navier-Stokes equations. The adjoint based method for predicting the magnitude of stationary disturbances generated by randomly distributed surface roughness is described, with the analysis extended to include both surface curvature and compressible flow effects. Receptivity is predicted for a broad spectrum of spanwise wavenumbers, variable freestream Reynolds numbers and subsonic Mach numbers. Curvature is found to play a significant role in the receptivity calculations, while compressible flow effects are only found to marginally affect the initial size of the crossflow instability. A Monte-Carlo type analysis is undertaken to establish the mean amplitude and variance of crossflow disturbances generated by the randomly distributed surface roughness. Mean amplitudes are determined for a range of flow parameters that are maximised for roughness distributions containing a broad spectrum of roughness wavelengths, including those that are most effective in generating stationary crossflow disturbances. A control mechanism is then developed where the short scale roughness wavelengths are damped, leading to significant reductions in the receptivity amplitude.

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

“…Choudhari 18 addressed this problem although he did not proceed to study any particular roughness distributions. This was done for stationary cross-flow instabilities over swept wings by Mughal & Ashworth 47 and Thomas et al 37 The former work reconstructed the power spectral density (PSD) of a painted panel and an unpainted aluminum plate and showed that energy tends to be concentrated in the small wavenumbers. To overcome the issues of randomness existing in the surface roughness field distribution and spectral content description, Mughal & Ashworth 47 used a Monte-Carlo (MC) based uncertainty quantification analysis in their receptivity modeling.…”

“…The large point distribution thus ensured that all fine roughness scales (i.e. constrained by N max ) were resolved in the numerical discretization of the simulated roughness field; ramifications of underresolving the roughness scales is discussed in some detail by Thomas et al 37 Receptivity amplitudes are calculated at the lower-branch of neutral stability according to Eq. (31), where h * = √ 2h * RMS is the amplitude of a wavy wall for a given r.m.s height.…”

Stabilization of crossflow instability with plasma actuators: Linearized Navier–Stokes simulations

“…2 As described in some detail in Mughal & Ashworth 21 and Thomas, Mughal & Ashworth. 22 the LNS equations are solved for spanwise periodic disturbances in a spanwise homogeneous base flow with a computational domain that encloses one period of the disturbance inducing roughness or plasma forcing as indicated in Figure 2.…”

“…The details of our numerical approach may be found in the paper of Thomas, Mughal & Ashworth, 22 below we focus on aspects of the plasma model and demonstrate the efficacy of our LNS model with comparisons with the experiment. The basis of our methodology is as follows: we utilise the LNS model for capturing the plasma induced crossflow generation of the killer mode; and the amplitude of the killer mode predicted by the LNS model is then used to force the significantly more efficient nonlinear PSE solver to investigate the control aspects of the study.…”

Acoustic Receptivity of Compressible Tollmien-Schlichting Waves with an Efficient Time-Harmonic Linearized Navier-Stokes Method

“…The work reported here builds on previous work on time-harmonic LNS and applications to acoustic receptivity [23][24][25], but addresses additional challenges such as the modeling of the compressible Stokes layer. Ultimately, the problem of interest in the aeronautics sector is that of an airfoil operating in transonic flow conditions with acoustic waves incident at a generalized angle.…”