Theoretical Modeling of Porous Coatings with Simple Microstructures for Hypersonic Boundary-Layer Stabilization (original) (raw)
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Effects of Passive Porous Walls on Hypersonic Boundary Layers
2009
A theoretical linear stability analysis is used to consider the effect of a porous wall on the first mode of a hypersonic boundary layer on a sharp slender cone. The effect of curvature and of the attached shock are included. The flow in the hypersonic boundary layer is coupled to the flow in the porous layer. The theoretical model of a porous wall developed by Fedorov and his co-workers is used for regular microstructures. The resulting transcendental equations are solved numerically. Neutral solutions are presented, indicating a destabilizing effect of the porous wall. The spatial growth rates determined demonstrate that the porous wall leads to a significant increase in growth rates.
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Journal of Applied Mechanics and Technical Physics, 2005
The possibility of controlling the laminar-turbulent transition in hypersonic shock layers by means of porous coatings is considered. The linear stability of the shock layer to acoustic disturbances is analyzed. A dispersion relation is derived in an analytical form and analyzed for different characteristic values of porosity of the wall, which allows one to study the spectrum of acoustic disturbances in the shock layer. Analytical expressions for the growth rate of instability of acoustic disturbances are presented as functions of the reflection factor. Their structure indicates that the porous coating effectively decreases acoustic instability of the shock layer.
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A second-mode stability analysis has been performed for a hypersonic boundary layer on a wall covered by a porous coating with equally spaced cylindrical blind microholes. Massive reduction of the second mode amplication is found to be due to the disturbance energy absorption by the porous layer. This stabilization effect was demonstrated by experiments recently conducted on a sharp cone in the T-5 high-enthalpy wind tunnel of the Graduate Aeronautical Laboratories of the California Institute of Technology. Their experimental con rmation of the theoretical predictions underscores the possibility that ultrasonically absorptive porous coatings may be exploited for passive laminar ow control on hypersonic vehicle surfaces.
Instability of Hypersonic Boundary Layer on a Wall with Resonating Micro-Cavities
49th AIAA Aerospace Sciences Meeting including the New Horizons Forum and Aerospace Exposition, 2011
Ultrasonically absorptive coatings (UAC) can stabilize the Mack second mode and thereby increase the laminar run on configurations where laminar-turbulent transition is second-mode dominated. Theory indicates that the stabilization effect can be essentially enhanced by increasing the UAC porosity. However, direct numerical simulations (DNS) showed that coatings having closely spaced grooves can trigger a new instability whose growth rate can be larger than that of Mack' second mode. The nature of the new instability is investigated theoretically and numerically. 2D linear DNS and stability analysis are performed for the temporally evolving boundary layer on a flat wall at the outer-flow Mach number 6. The wall is covered by UAC comprising equally-spaced spanwise grooves. It is shown that the new mode is associated with acoustic resonances in the grooves. Disturbance fields near mouths of resonating cavities are coupled such that the boundary-layer disturbance is decelerated and becomes unstable. To avoid this detrimental effect the coating should have sufficiently small porosity and/or narrow pores of sufficiently small aspect ratio. Restrictions on these parameters can be estimated using the linear stability theory with the impedance boundary conditions. Nomenclature
2013
Passive porous coatings have been proposed in literature as a means of delaying transition to turbulence in hypersonic boundary layers. The nonlinear stability of hypersonic viscous flow over a sharp slender cone with passive porous walls is investigated in this study. Hypersonic flows are unstable to viscous and inviscid disturbances, and following Mack (1984) these have been called the first and second Mack modes. A weakly nonlinear analysis of the instability of the flow to axisymmetric and non-axisymmetric viscous (first Mack mode) disturbances is performed here. The attached shock and effect of curvature are taken into account. Asymptotic methods are used at large Reynolds number and large Mach number to examine the viscous modes of instability, which may be described by a triple-deck structure. Various porous wall models have been incorporated into the stability analysis. The eigenrelations governing the linear stability of the problem are derived.
Modeling The Drag Forces Of Porous Media Acoustics
1992
The drag forces controlling the amount of relative flow induced in a fluid-saturated porous material by a mechanical wave are modeled here from first principles. Specifically, analytical expressions are derived for the drag force in material models that possess variable-width pores; Le., pores that have widths that vary with distance along their axis. The dynamic (complex, frequency-dependent) permeability determined for such a variable-width pore model is compared to estimates made using the models of Johnson, Koplik, and Dashen (JKD) and of Biot. Both the JKD model and the Biot model underestimate the imaginary part of the dynamic permeability at low frequencies with the amount of discrepancy increasing with the severity of the convergent/divergent flow; Le., increasing with the magnitude of the maximum pore-wall slope relative to the channel axis. It is shown how to modify the JKD model to obtain proper lowfrequency behavior; however, even with this modification, discrepancies st...
Effects of Passive Porous Walls on the First Mode of Hypersonic Boundary Layers Over a Sharp Cone
2013
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Journal of The Acoustical Society of America, 2003
A model for the propagation of high amplitude continuous sound through hard-backed rigid-porous layers has been developed which allows for Forchheimer's correction to Darcy's law. The nonlinearity associated with this is shown to be particularly important in the range of frequencies around layer resonance. The model is based on the introduction of particle velocity dependent flow resistivity into the equivalent fluid model expression for complex tortuosity. Thermal effects are accounted for by means of a linear complex compressibility function. The model has been used to derive analytical expressions for surface impedance and reflection coefficient as a function of incident pressure amplitude. Depending on the material parameters, sample thickness, and frequency range the model predicts either growth or decrease of reflection coefficient with sound amplitude. Good agreement between model predictions and data for three rigid-porous materials is demonstrated.