Interaction between a supersonic boundary layer and acoustic disturbances

45th AIAA Fluid Dynamics Conference

2015

Boundary-layer receptivity to two-dimensional acoustic and vortical disturbances for hypersonic flows over two-dimensional and axi-symmetric geometries were numerically investigated. The role of bluntness, wall cooling, and pressure gradients on the receptivity and stability were analyzed and compared with the sharp nose cases. It was found that for flows over sharp nose geometries in adiabatic wall conditions the instability waves are generated in the leading-edge region and that the boundary layer is much more receptive to slow acoustic waves as compared to the fast waves. The computations confirmed the stabilizing effect of nose bluntness and the role of the entropy layer in the delay of boundarylayer transition. The receptivity coefficients in flows over blunt bodies are orders of magnitude smaller than that for the sharp cone cases. Wall cooling stabilizes the first mode strongly and destabilizes the second mode. However, the receptivity coefficients are also much smaller compared to the adiabatic case. The adverse pressure gradients increased the unstable second mode regions. Nomenclaturea = speed of sound C recpt = receptivity coefficient c v = specific heat E = total energy e = internal energy F = flux vector in the x-direction, non-dimensional frequency f = frequency in Hz G = flux vector in the r-direction k = thermal conductivity M = Mach number N = N factor Pr = Prandtl number p = pressure p s = surface pressure Q = conserved flow variables vector R = gas constant Re = Reynolds number, per meter Re s = Reynolds number based on the distance s, per meter r = radial coordinate r 0 = nose radius S = source term s = distance along the surface T = temperature t = time U = mean axial velocity u = axial velocity 1 Research Scientist, AIAA Associate Fellow Downloaded by CARLETON UNIVERSITY LIBRARY on July 17, 2015 | http://arc.aiaa.org | American Institute of Aeronautics and Astronautics 2 V = radial velocity X = axial coordinate x 0 = reference x location α = wavenumber in the x-direction η = curvilinear coordinate in the radial direction, boundary-layer similarity coordinate δ = boundary layer thickness µ = viscosity ξ = curvilinear coordinate in the axial direction ρ = density ω = frequency in radian Subscripts ac = acoustic e = boundary-layer edge conditions max = maximum n = normal to the surface, neutral point ∞ = freestream quantities

Section: Introductionmentioning

confidence: 99%

Receptivity of Hypersonic Boundary Layers to Acoustic and Vortical Disturbances (Invited)

45th AIAA Fluid Dynamics Conference

2015

“…The interaction of acoustic waves with a supersonic boundary layer using inhomogeneous stability equations was investigated in Ref. [5][6]. One important finding was that due to the interaction, the acoustic waves excite disturbances inside the boundary layer, which are much larger than that in the free stream.…”

Section: Introductionmentioning

confidence: 99%

Acoustic receptivity of Mach 4.5 boundary layer with leading-edge bluntness

Malik

Theor. Comput. Fluid Dyn.

2007

Boundary layer receptivity to two-dimensional slow and fast acoustic waves is investigated by solving Navier-Stokes equations for Mach 4.5 flow over a flat plate with a finite-thickness leading edge. Higher order spatial and temporal schemes are employed to obtain the solution whereby the flat-plate leading edge region is resolved by providing a sufficiently refined grid. The results show that the instability waves are generated in the leading edge region and that the boundary-layer is much more receptive to slow acoustic waves (by almost a factor of 20) as compared to the fast waves. Hence, this leading-edge receptivity mechanism is expected to be more relevant in the transition process for high Mach number flows where second mode instability is dominant. Computations are performed to investigate the effect of leading-edge thickness and it is found that bluntness tends to stabilize the boundary layer. Furthermore, the relative significance of fast acoustic waves is enhanced in the presence of bluntness. The effect of acoustic wave incidence angle is also studied and it is found that the receptivity of the boundary layer on the 'windward' side (with respect to the acoustic forcing) decreases by more than a factor of 4 when the incidence angle is increased from 0 to 45 deg. However, the receptivity coefficient for the 'leeward' side is found to vary relatively weakly with the incidence angle.

“…The interactions of acoustic waves with a supersonic boundary layer at finite incident angles using inhomogeneous stability equations are investigated in Ref. 2,3. One important finding was that due to the interaction, the acoustic waves excite disturbances inside the boundary layer, which are much larger than that in the free stream.…”

Section: Secondary Instability and Breakdown To Turbulencementioning

confidence: 99%

Transition in a Supersonic Boundary Layer Due to Acoustic Disturbances

43rd AIAA Aerospace Sciences Meeting and Exhibit

2005

The boundary layer receptivity process due to the interaction of threedimensional slow and fast acoustic disturbances with a blunted flat plate is numerically investigated at a free stream Mach number of 3.5 and at a high Reynolds number of 10 6 /inch. The computations are performed with and without two-dimensional isolated roughness element located near the leading edge. Both the steady and unsteady solutions are obtained by solving the full Navier-Stokes equations using the 5 th -order accurate weighted essentially non-oscillatory (WENO) scheme for space discretization and using third-order total-variation-diminishing (TVD) Runge-Kutta scheme for time integration. The simulations showed that the linear instability waves are generated very close to the leading edge. The wavelength of the disturbances inside the boundary layer first increases gradually and becomes longer than the wavelength for the instability waves within a short distance from the leading edge. The wavelength then decreases gradually and merges with the wavelength for the Tollmien_Schlichting wave. The initial amplitudes of the instability waves near the neutral points, the receptivity coefficients, are about 1.20 and 0.07 times the amplitude of the free-stream disturbances for the slow and the fast waves respectively. It was also revealed that small isolated roughness element does not enhance the receptivity process for the given nose bluntness.