Numerical modeling of the stabilization of a supersonic flat-plate boundary layer by a porous coating

2011

AIAA Journal

In the laminar-turbulent transition of boundary-layer flows, the spatial development of boundary-layer waves, especially that of unstable waves, is important and indispensable. In this paper, the response of a Mach 8 flow over a 5.3 half-angle sharp wedge to wall blowing-suction is studied by numerical simulations. Steady base flow is obtained by solving the compressible Navier-Stokes equations with a combination of a fifth-order shock-fitting method and a second-order total-variation-diminishing scheme. In stability simulations, wall blowing-suction is introduced through an actuator on the wedge surface. The unsteady flow simulation is carried out using the shock-fitting method. The results show that mode F, mode S, acoustic waves, and entropy/vorticity waves are simultaneously excited by wall blowing-suction and coexist in the boundary layer just downstream of the actuator. For blowing-suction at a specific frequency, the results also show that mode S is strongly excited when the actuator is located upstream of the corresponding synchronization point. There is no significant amplification of pressure perturbation when the actuator is downstream of the synchronization point. This result represents a mixture of the receptivity and the downstream growth of mode S. The exact cause and mechanism of this result are not clear. However, such a result is obtained for wall blowing-suction at all frequencies considered in the current study. To excite a strong mode S at a specific frequency, the result indicates that it is necessary to place the blowing-suction actuator upstream of the corresponding synchronization point. Further theoretical analysis is needed to reveal the mechanism behind the numerical results.

Section: Introductionsupporting

confidence: 83%

Section: Introductionsupporting

confidence: 80%

Response of a Hypersonic Boundary Layer to Wall Blowing-Suction

2011

AIAA Journal

“…It was found that there was a good agreement between normal-mode amplitudes calculated with the help of the theoretical receptivity model and those obtained from projecting the numerical results onto the normal modes. Egorov et al 26 studied stability and receptivity of a Mach 6 flow over a flat plate with a porous coating by numerically solving two-dimensional Navier-Stokes equations. Their numerical results were in a good agreement with theoretical analysis based on LST.…”

Section: Introductionmentioning

confidence: 99%

Effect of wall perturbations on the receptivity of a hypersonic boundary layer

2009

Physics of Fluids

The receptivity of a Mach 5.92 flat plate boundary layer to periodic two-dimensional wall perturbations is studied by numerical simulations and linear stability theory ͑LST͒. Free stream flow conditions are the same as the leading edge receptivity experiment of Maslov et al., J. Fluid Mech. 426, 73 ͑2001͒. Steady base flow is simulated by solving compressible Navier-Stokes equations with a combination of a fifth-order shock-fitting method and a second-order total variation diminishing scheme. The accuracy of the steady base flow is validated by comparisons with the experimental measurements of Maslov et al. and self-similar boundary-layer solution. In receptivity simulations, streamwise velocity perturbation, blowing suction, and temperature perturbation are introduced to the steady base flow with a forcing slot on flat plate. A model of wall perturbation is proposed based on physical properties of the electric pulse generator used in the experiment of Maslov et al. Stability characteristics of boundary-layer waves are identified and evaluated by comparing the results of LST and numerical simulation. Numerical simulation results show that all three types of wall perturbations eventually result in the same type of instability wave ͑mode S͒ in the boundary layer, which indicates that receptivity mechanism of the hypersonic boundary layer to wall perturbation is independent of specific perturbation type. On the other hand, the hypersonic boundary layer is found to be most sensitive to blowing-suction and least sensitive to temperature perturbation.

“…It was found that there was a good agreement between normal-mode amplitudes calculated with the help of the theoretical receptivity model and those obtained by projecting the numerical results onto the normal modes. Egorov et al [43] studied the stability and receptivity of a Mach 6 flow on a flat plate with a porous coating by numerically solving the two-dimensional Navier-Stokes equations. Their numerical results were in good agreement with the theoretical analysis based on LST.…”

Section: Introductionmentioning

confidence: 99%

Receptivity of a Hypersonic Flat-Plate Boundary Layer to Surface Roughness

46th AIAA Aerospace Sciences Meeting and Exhibit

2008

The receptivity of a hypersonic flat-plate boundary layer to small surface roughness is investigated by series of numerical simulations. The main objectives of the current paper are to study the receptivity process of a Mach 5.92 flow over a flat plate to surface roughness and the effect of spanwise wave number on the receptivity. The free-stream flow conditions are the same as those of Maslov et al.'s leading-edge receptivity experiment [1]. Two-dimensional steady base flow is firstly achieved by solving compressible Navier-Stokes equations with a combination of a fifthorder shock-fitting method and a second-order TVD scheme. The accuracy of the numerical steady base flow is validated by comparisons with the theoretical self-similar boundary-layer solution and Maslov et al.'s experimental measurements. The three-dimensional base flow is directly extended from two-dimensional base flow due to the fact that the base flow over the flat plate is independent of spanwise coordinate. In receptivity simulations, small surface roughness, periodic in spanwise direction, is introduced on the flat plate. The subsequent responses of the hypersonic boundary layer are simulated by solving three-dimensional Navier-Stokes equations with a fifth-order shock-fitting method and a Fourier collocation method. Due to small height of roughness element, boundary conditions of temperature and velocities on the rough surface are transferred to original smooth surface by linear extrapolation. The effect of spanwise wave number on the receptivity is studied by considering six cases of receptivity simulations. The numerical results show that counter rotating streamwise vortices and transient growth are induced by surface roughness. The spanwise wave number has a strong effect on the excitation of transient growth. For the six cases considered in current study, surface roughness with the spanwise wave number being 0.0101 has the strongest excitation of transient growth.