Alexander V. Fedorov

Stabilization of Hypersonic Boundary Layers by Porous Coatings

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 amplification 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 confirmation of the theoretical predictions underscores the possibility that ultrasonically absorptive porous coatings may be exploited for passive laminar flow control on hypersonic vehicle surfaces.

Stabilization of a hypersonic boundary layer using an ultrasonically absorptive coating

Experimental and theoretical studies of the effect of an ultrasonically absorptive coating (UAC) on hypersonic boundary-layer stability are described. A thin coating of fibrous absorbent material (felt metal) was selected as a prototype of a practical UAC. Experiments were performed in the Mach 6 wind tunnel on a

Experiments on Passive Hypervelocity Boundary-Layer Control Using an Ultrasonically Absorptive Surface

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Receptivity of a high-speed boundary layer to acoustic disturbances

half-angle sharp cone whose longitudinal half-surface was solid and other half-surface was covered by a porous coating. Hot-wire measurements of ‘natural’ disturbances and artificially excited wave packets were conducted on both solid and porous surfaces. Stability analysis of the UAC effect on two- and three-dimensional disturbances showed that the porous coating strongly stabilizes the second mode and marginally destabilizes the first mode. These results are in qualitative agreement with the experimental data for natural disturbances. The theoretical predictions are in good quantitative agreement with the stability measurements for artificially excited wave packets associated with the second mode. Stability calculations for the cooled wall case showed the feasibility of achieving a dramatic increase of the laminar run using a thin porous coating of random microstructure.

Receptivity of a hypersonic boundary layer over a flat plate with a porous coating

Recently performed linear stability analyses suggested that transition could be delayed in hypersonic boundary layers by using an ultrasonically absorptive surface to damp the second mode (Mack mode). Boundary-layer transition experiments were performed on a sharp 5.06-deg half-angle round cone at zero angle of attack in the T5 Hypervelocity Shock Tunnel to test this concept. The cone was constructed with a smooth surface around half the cone circumference (to serve as a control) and an acoustically absorptive porous surface on the other half. Test gases investigated included nitrogen and carbon dioxide at M∞ ≃ 5 with specific reservoir enthalpy ranging from 1.3 to 13.0 MJ/kg and reservoir pressure ranging from 9.0 to 50.0 MPa. Comparisons were performed to ensure that previous results obtained in similar experiments (on a regular smooth surface) were reproduced, and the results were extended to examine the effects of the porous surface. These experiments indicated that the porous surface was highly effective in delaying transition provided that the pore size was significantly smaller than the viscous length scale.

The Extended Görtler-Hämmerlin Model For Linear Instability of Three-Dimensional Incompressible Swept Attachment-Line Boundary Layer Flow

Receptivity of a high-speed boundary layer on a flat plate to acoustic disturbances is investigated using a combined numerical and asymptotic approach. The leading-edge receptivity problem is discussed with emphasis on physical mechanisms associated with scattering, diffraction and reflection of acoustic waves. The theoretical predictio ns are compared with experimental data and direct numerical simulation. The results of the leading-edge receptivity model are incorporated into the mult iple-modes method to account for the inter-modal exchange downstream from the leading edge. Comparative analysis of the leading-edge receptivity, distributed receptivity and the inter-modal exchange due to nonparallel effects is presented. Feasible ways of further theoretical and experimental studies of high-speed boundary layer receptivity to acoustic disturbances are discussed. Nomenclature

High-Speed Boundary-Layer Instability: Old Terminology and a New Framework

Two-dimensional direct numerical simulation (DNS) of receptivity to acoustic disturbances radiating onto a flat plate with a sharp leading edge in the Mach 6 free stream is carried out. Numerical data obtained for fast and slow acoustic waves of zero angle of incidence are consistent with the asymptotic theory. Numerical experiments with acoustic waves of non-zero angles of incidence reveal new features of the disturbance field near the plate leading edge. The shock wave, which is formed near the leading edge owing to viscous-inviscid interaction, produces a profound effect on the acoustic near field and excitation of boundary-layer modes. DNS of the porous coating effect on stability and receptivity of the hypersonic boundary layer is carried out. A porous coating of regular porosity (equally spaced cylindrical blind micro-holes) effectively diminishes the second-mode growth rate in accordance with the predictions of linear stability theory, while weakly affecting acoustic waves. The coating end effects, associated with junctures between solid and porous surfaces, are investigated.

Initial-Value Problem for Hypersonic Boundary-Layer Flows

A simple extension of the classic Gortler–Hammerlin (1955) (GH) model, essential for three-dimensional linear instability analysis, is presented. The extended Gortler–Hammerlin model classifies all three-dimensional disturbances in this flow by means of symmetric and antisymmetric polynomials of the chordwise coordinate. It results in one-dimensional linear eigenvalue problems, a temporal or spatial solution of which, presented herein, is demonstrated to recover results otherwise only accessible to the temporal or spatial partial-derivative eigenvalue problem (the former also solved here) or to spatial direct numerical simulation (DNS). From a numerical point of view, the significance of the extended GH model is that it delivers the three-dimensional linear instability characteristics of this flow, discovered by solution of the partial-derivative eigenvalue problem by Lin & Malik (1996a), at a negligible fraction of the computing effort required by either of the aforementioned alternative numerical methodologies. More significant, however, is the physical insight which the model offers into the stability of this technologically interesting flow. On the one hand, the dependence of three-dimensional linear disturbances on the chordwise spatial direction is unravelled analytically. On the other hand, numerical results obtained demonstrate that all linear three-dimensional instability modes possess the same (scaled) dependence on the wall-normal coordinate, that of the well-known GH mode. The latter result may explain why the three-dimensional linear modes have not been detected in past experiments; criteria for experimental identification of three-dimensional disturbances are discussed. Asymptotic analysis based on a multiple-scales method confirms the results of the extended GH model and provides an alternative algorithm for the recovery of three-dimensional linear instability characteristics, also based on solution of one-dimensional eigenvalue problems. Finally, the polynomial structure of individual three-dimensional extended GH eigenmodes is demonstrated using three-dimensional DNS, performed here under linear conditions.

Acoustic properties of rarefied gases inside pores of simple geometries

The discrete spectrum of disturbances in high-speed boundary layers is discussed with emphasis on singularities caused by synchronization of the normal modes. Numerical examples illustrate different spectral structures and jumps from one structure to another with small variations of basic flow parameters. It is shown that this singular behavior is due to branching of the dispersion curves in the synchronization region. Depending on the locations of the branch points, the spectrum contains an unstable mode or two. In connection with this, the terminology used for instability of high-speed boundary layers is clarified. It is emphasized that the spectrum branching may cause difficulties in stability analyses based on traditional linear stability theory and parabolized stability equations methods. Multiple-mode considerations and direct numerical simulations are needed to clarify this issue.

Stabilization of a Hypersonic Boundary Layer Using a Wavy Surface

An initial-value problem is analyzed for a two-dimensional wave packet induced by a local two-dimensional disturbance in a hypersonic boundary layer. The problem is solved using Fourier transform with respect to the streamwisecoordinateandLaplacetransform with respectto time. The temporal continuous spectrum isrevisited, and the uncertainty associated with the overlapping of continuous-spectrum branches is resolved. It is shown that thediscretespectrum’ s dispersion relationship isnonanalyticbecause of thesynchronization of thee rst mode with the vorticity/entropy waves of the continuous spectrum. However, the inverse Laplace transform is regular at the synchronism point. Characteristics of the wave packet generated by an initial temperature spot are numerically calculated. It is shown that the hypersonic boundary layer is highly receptive to vorticity/entropy disturbances in the synchronism region. The feasibility of experimental verie cation of this receptivity mechanism is discussed.