Acoustic receptivity of distributed micron-sized roughness elements is investigated for a swept-wing boundary layer by means of direct numerical simulations (DNS) and parabolised stability equations (PSE) computations. The geometry and flow configuration follow the experiments by [4] and DNS calculations by [7]. Acoustic wave has been modeled by superposing a periodic fluctuation εcos(ωt) to the inflow streamwise velocity component. A range of amplitudes and frequencies are considered to perform simulations and to study acoustic wave-roughness elements interaction. 

Application of ring-type plasma actuators for control of laminar-turbulent transition in a swept-wing boundary layer is investigated thorough direct numerical simulations. These actuators induce a wall-normal jet in the boundary layer and can act as virtual roughness elements. The flow configuration resembles experiments by Kim et al. (2016 Technical Report. BUTERFLI Project TR D3.19, http://eprints.nottingham.ac.uk/id/eprint/46529). The actuators are modelled by the volume forces computed from the experimentally measured induced velocity field at the quiescent air condition. Stationary and travelling cross-flow vortices are triggered in the simulations by means of surface roughness and random unsteady perturbations. Interaction of vortices generated by actuators with these perturbations is investigated in detail. It is found that, for successful transition control, the power of the actuators should be increased to generate jet velocities that are one order of magnitude higher than those used in the experiments by Kim et al. (2016) mentioned above.

With the motivation of determining the critical roughness size, a global stability and sensitivity analysis of a three-dimensional Falkner-Skan-Cooke (FSC) boundary layer with a cylindrical surface roughness is performed. The roughness size is chosen such that breakdown to turbulence is initiated by a global version of traditional secondary instabilities of the cross-flow (CF) vortices instead of an immediate flow tripping at the roughness. The resulting global eigenvalue spectra of the systems are found to be very sensitive to numerical parameters and domain size. This sensitivity to numerical parameters is quantified using the epsilon-pseudospectrum, and the dependency on the domain is analysed through an impulse response, structural sensitivity analysis and an energy budget. It is shown that while the frequencies remain relatively unchanged, the growth rates increase with domain size, which originates from the inclusion of stronger CF vortices in the baseflow. This is reflected in a change in the rate of advective energy transport by the baseflow. It is concluded that the onset of global instability in a FSC boundary layer as the roughness height is increased does not correspond to an immediate flow tripping behind the roughness, but occurs for lower roughness heights if sufficiently long domains are considered. However, the great sensitivity results in an inability to accurately pinpoint the exact parameter values for the bifurcation, and the large spatial growth of the disturbances in the long domains eventually becomes larger than can be resolved using finite-precision arithmetic.

We present results of numerical simulations of leading-edge acoustic receptivity for acoustic waves impinging on the leading edge of a finite-thickness flat plate. We use both compressible and incompressible flow solvers fitted with high-order high-accuracy numerical methods and independent methods of estimating the receptivity coefficient. The results show that the level of acoustic receptivity in the existing literature appears to be one order of magnitude too high. Our review of previous numerical simulations and experiments clearly identifies some contradictory trends. In the limit of an infinitely thin flat plate, our results are consistent with asymptotic theory and numerical simulations.

Acoustic receptivity of a two-dimensional boundary layer on a flat plate with elliptic leading edge is studied through direct numerical simulation (DNS). Sound waves are modelled by a uniform oscillation of freestream boundaries in time which results to an infinite-wavelength acoustic wave. Acoustic disturbances interact with strong streamwise gradients at the leading edge or surface non- homogeneities and create Tollmien-Schlichting (TS) waves inside the boundary layer. Measuring amplitude of TS waves created by sound waves is challenging due to presence of Stokes wave (acoustic boundary layer) with the same temporal frequency of TS waves. In this study biorthogonal eigenfunction system of local linear stability equations has been utilised to extract TS wave amplitudes. This method is based on the concept of using adjoint mode as a projector where the TS amplitude is obtained by projecting the DNS solution onto adjoint TS modes. However, the computed TS wave amplitude employing this method found to be modulated. It is shown that the modulation is due to existence of a small amplitude wave in the DNS data that is not expandable onto the basis of local linear stability equations. 

E↵ect of acoustic waves on the control performance of distributed micron-sized roughness elements in a swept-wing boundary layer is investigated through direct numerical simulations. The flow configuration conforms to experiments by Kachanov et al. (2015) who observed either no significant influence of acoustic waves on the transition location or small stabilisation e↵ect. In this work, a base set up for natural transition scenario is first established by introducing unsteady background noise in the boundary layer. The natural transition is then delayed using control roughness elements. Introduction of acoustic waves to the controlled flow promotes the transition location. In all these flow cases, stationary primary crossflow vortices dominate the disturbance environment and unsteady disturbances experience an explosive growth prior to transition. The spatial distribution of the energy production associated with z-type modes shows an increase in the local transfer of energy from the modified mean flow to perturbations. Simulation of flow with control roughness elements and acoustic waves as the only source of unsteady disturbances shows no influence of acoustic wave in transition to turbulence. 

This work is concerned with stability and receptivity analysis as well as studies on control of the laminar-turbulent transition in boundary-layer flows through direct numerical simulations. Various flow configurations are considered to address flow around straight and swept wings. The aim of this study is to contribute to a better understanding of stability characteristics and different means of transition control of such flows which are of great interest in aeronautical applications.

Acoustic receptivity of flow over a finite-thickness flat plate with elliptic leading edge is considered. The objective is to compute receptivity coefficient defined as the relative amplitude of acoustic disturbances and TS wave. The existing results in the literature for this flow case plot a scattered image and are inconclusive. We have approached this problem in both compressible and incompressible frameworks and used high-order numerical methods. Our results have shown that the generally-accepted level of acoustic receptivity coefficient for this flow case is one order of magnitude too high.

The continuous increase of computational power has enabled us to perform global stability analysis of three-dimensional boundary layers. A swept flat plate of FSC type boundary layer with surface roughness is considered. The aim is to determine the critical roughness height for which the flow becomes turbulent. Global stability characteristics of this flow have been addressed and sensitivity of such analysis to domain size and numerical parameters have been discussed.

The last flow configuration studied here is infinite swept-wing flow. Two numerical set ups are considered which conform to wind-tunnel experiments where passive control of crossflow instabilities is investigated. Robustness of distributed roughness elements in the presence of acoustic waves have been studied. Moreover, ring-type plasma actuators are employed as virtual roughness elements to delay laminar-turbulent transition.

With the motivation of determining the critical roughness size, a global stability and sensitivity analysis of a three-dimensional Falkner–Skan–Cooke (FSC) boundary layer with a cylindrical surface roughness is performed. The roughness size is chosen such that breakdown to turbulence is initiated by a global version of traditional secondary instabilities of the crossflow (CF) vortices, instead of an immediate flow tripping at the roughness. The resulting global eigenvalue spectra of the systems are found to be very sensitive to numerical parameters and domain size. This sensitivity to numerical parameters is quantified using the "-pseudospectrum, and the dependency on the domain is analysed through an impulse response and an energy budget. It is shown that the growth rates increase with domain size, which originates from the inclusion of stronger CF vortices in the baseflow. This is reflected in a change in the rate of advective energy transport by the baseflow. It is concluded that the onset of global instability in a FSC boundary layer as the roughness height is increased does not correspond to an immediate flow tripping behind the roughness, but occurs for lower roughness heights if su ciently long domains are considered. However, the great sensitivity results in an inability to accurately pinpoint the exact parameter values for the bifurcation, and the large spatial growth of the disturbances in the long domains eventually becomes larger than what can be resolved using finite precision arithmetics. 

A three-dimensional linear global stability analysis of a Falkner–Skan–Cooke boundary layer with distributed three-dimensional surface roughness is performed. The Falkner–Skan–Cooke boundary layer models the flow over swept airplane wings, and investigation of the critical roughness size for which a global instability emerges is thus of great importance within aeronautical applications. The study considers high-order direct numerical simulations and shows that such a critical roughness height exists for the Falkner–Skan–Cooke boundary layer. The roughness Reynolds number and roughness element aspect ratio for which this happens is comparable to the transition data reported in the literature for two-dimensional boundary layers. This demonstrates the importance of the local flow conditions in the vicinity of the roughness for triggering a global instability, although the resulting breakdown scenario is completely different from that of two-dimensional boundary layers. This breakdown scenario is studied in detail, and a global energy analysis is used to reveal the structures and mechanisms responsible for production and dissipation of perturbation energy.

Application of the ring-type plasma actuators for passive control of laminar- turbulent transition in a swept-wing boundary layer is investigated thorough direct numerical simulations. These actuators induce a wall-normal jet in the boundary layer and can act as virtual roughness elements. The flow configuration resembles experiments of Kim et al. (2016). The actuators are modelled by the volume forces computed from the experimentally measured induced velocity filed at the quiescent air condition. The natural surface roughness and unsteady perturbations are also included in the simulations. The interaction of generated vortices by the actuators with these perturbations is investigated in details. It is found that for a successful transition control the power of the actuator should be increased to generate a jet velocity one order of magnitude higher than that in the considered experiments.