Norman D. Malmuth

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

7^{\circ}

Problems in high speed flow prediction relevant to control

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.

Acoustic properties of rarefied gases inside pores of simple geometries

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.

Influence of a counterflow plasma jet on supersonic blunt-body pressures

Three flow problems are discussed whose solutions suggest flow control schemes. These are 1) unsteady hypersonic flow over bodies in the Newtonian approximation, 2) a mechanism of hypersonic flow stabilization over acoustically semi-transparent walls and 3) store separation from cavities. Simplified systematic approximations based on asymptotic frameworks lead to compact computational models that elucidate the flow structure and opportunities for control. Besides generalizing the steady model of Cole, the Newtonian approximation in the unsteady context shows that unsteady body perturbations can lead to inflectional velocity profiles that can produce instabilities and boundary layer transition to enhance mixing in combustors and inlets. The absorbing wall illustrates a mechanism that can be exploited to damp 2 mode hypersonic instabilities. Simplified flow modeling based on systematic asymptotics for store separation from cavities shows the influence of the cavity shear layer on apparent mass effects that are important to damping in pitch and clearance from the parent body. Comparisons with free drop experiments are used for initial validations of the analytical models. * Senior Scientist, Fellow, AIAA f Principal Researcher, Member, AIAA * Margaret Damn Distinguished Professor, Mathematical Sciences, Fellow, AIAA § Professor ** Professor, Associate Fellow Copyright© 1998, American Institute of Aeronautics and Astronautics, Inc. 1. Unsteady Newtonian thin shock layers and hypersonic flow stability 1.11ntroduction Although the stability of high speed flows has received much attention in the recent literature, major complicating aspects have not been treated in a unified way. These features include the combined effects of the finite shock displacement on the boundary layer, the nonparallelism of the flow and the vorticity introduced by the shock curvature. The relevant structure of the shock and boundary layers has been treated in [1][9]. In [6] and [7], the aforementioned stability issues were discussed within the Hypersonic Small Disturbance approximation for the inviscid deck strongly interacting with the hypersonic boundary layer. Equations of motion for the mean and fluctuating small amplitude flows were analyzed. Because of nonparallelism in this framework, the spatial part of the waves cannot be treated by the usual Fourier decomposition and an initial value rather than eigenproblem for spatial stability is obtained. The initial value problem leads to partial rather than ordinary differential equations that require a numerical marching method for their solution. Results indicate that the specific heat ratio 7 plays a major role in the stability of flow since it controls the reflection of waves from the shock and the radiation of energy in the shock layer whose thickness scales with 7 -1. Early experiments such as those described in [2] showed that for a practically interesting class of flows, the shock layer becomes very thin compared to the boundary layer near the nose of hypersonic flat plates. This feature and the desire to further understand the shock and boundary layer structure encourage the use of the Newtonian approximation 7 —> 1. The connection with flow stability motivates the study of this approximation in an unsteady context. In this chapter, limit process expansions will be discussed relevant to unsteady viscous interactions as a prelude to the analysis of hypersonic stability and transition. The application of these limits is an unsteady extension of the steady state analysis of [3]. Although the focus here is the treatment of viscous interaction, boundary layer stability, receptivity and transition, the results derived are useful in inviscid hypersonic unsteady aerodynamic methodology and load prediction as well. 1.2 Analysis Figure 1 schematically indicates strong interaction flow near the leading edge of a hypersonic body. The viscous boundary layer which is usually thin, occupies an appreciable fraction of the distance between the shock and body that will be considered without undue loss of generality a flat plate in what follows. Accordingly F(x,f} = Q, in the notation of Fig. 1. The results in this chapter will be expressed in terms of the boundary layer thickness function A(3c,r) = 0, which in the interpretation mentioned in the Introduction could be the body shape in an inviscid context. Copyright© 1998, American Institute of Aeronautics and Astronautics, Inc. The unsteady form of the Hypersonic Small Disturbance Theory (HSDT) equations [9] are applicable and are obtained as in [7] from limit process expansions of hatted variables defined as quantities normalized by their freestream counterparts, with p,T,u,v,fJL the density, temperature, horizontal, vertical components of the velocity vector, and viscosity respectively. If the freestream density, pressure and velocity are denoted as U,p^ and p^ respectively, then a pressure coefficient used in these expansions is defined as p = (P-PJ/P-U. Fig. 1 Schematic of hypersonic strong interaction flow. With these definitions and the coordinate system in Fig. 1 as well the normalization of the Cartesian dimensional coordinates x and y to the unit reference length L and the reference time scale L/U for the time t, unbarred dimensionless normalized counterparts of these independent variables are defined. If M^ and R^ are respectively the freestream Mach and Reynolds numbers, and 5 is a characteristic flow deflection angle, then the expansions are p=a(x,y,t;H,y)+--(1.1) T=T+— p = 8p+M = l+v =• §v+• • (1.2) (1.3) (1.4) (1.5) (1.6) where y = y/(L8}. These expansions are valid in the HSDT limit x, y, t, H = M o are fixed as 8 — > 0 ,

Hypersonic Laminar Flow Control Using a Porous Coating of Random Microstructure

Analytical solutions describing propagation of monochromatic acoustic waves inside long pores of simple geometries and narrow flat slits are obtained with accounting for gas rarefaction effects. It is assumed that molecular nature of gas is important in Knudsen layers near solid boundaries. Outside the Knudsen layers, the continuum approach is used. This model allows for extension of acoustic analysis to regions of low pressures and microscopic cross-sectional sizes of channels. The problem is solved using linearized Navier-Stokes equations with the boundary conditions that resulted from the first-order approximation with respect to small Knudsen number Kn. For slits and pores of circular and square cross sections, the theoretical dependencies of the dynamic density in the low-frequency range are compared with those that resulted from known experimental data on steady-state flows of rarefied gases in uniform channels. Despite the formal restriction Kn << 1 of asymptotic analysis, the theoretical model agrees well with experiments up to Kn approximately 5. It is shown that the molecular phenomena affect acoustic characteristics of micro-channels and pores starting from relatively small Knudsen numbers Kn > 0.01, especially at low frequencies. The obtained results may be used for analyses of acoustic properties of waveguides, perforated panels, micro-channels and pores in wide range of gas pressures as well as for stationary flows of rarefied gases through long uniform pipes etc.

Parametric studies of hypersonic laminar flow control using a porous coating of regular microstructure

Aerodynamic augmentation in the presence of a thin high-temperature onboard plasma jet directed upstream of a slightly blunted cone was studied experimentally and numerically. The flow around a truncated cone cylinder at zero incidence was considered for Mach numbers M∞ = 2.0, 2.5, and 4.0. For the first time, computationally validated experimental pressure distributions over the model surface in the presence of the plasma jet were obtained. As in the conventional (nonplasma) counterflow jet, two stable operational regimes of the plasma jet were found. These were a short penetration mode and a long penetration mode (LPM) aerospike into the opposing supersonic freestream. The greatest drag reduction occurred in the moderate LPM regime. LPM strong overblowing reduces the benefits. The experimental pressure results were approximately validated against an Euler computational fluid dynamics simulation, modeling a perfect gas hot jet, counterflowing against a perfect gas supersonic freestream. Plasma effects such as electron pressure, radiation, electric field interactions, Joule heating, and induced vorticity, streamers, and plasmoids have been identified that, if accounted for, may improve the comparison. Procedures for the use of these experimental results have been outlined as a baseline that will be useful in separating fluid dynamic/thermal effects from plasma processes in understanding the physics of onboard plasma jets for aerodynamic augmentation.

Dynamics of Slender Bodies Separating from Rectangular Cavities

It is shown that a passive porous coating of random structure (felt metal) significantly delays transition on a sharp cone at zero angle of attack in the Mach=12 wind tunnel. A semi-empirical method is developed to predict acoustic properties of randomly structured coatings including effects of gas rarefaction. This method simplifies calculations of the boundary conditions on the porous coating and solving the boundary-layer stability problem. The transition onset points on coated and uncoated cone surfaces are calculated using the -method. With this approach theoretical predictions agree satisfactorily with the experimental data. For the first time it is demonstrated that porous coatings of random microstructure, which are synergistic with fiber-ceramic thermal protection systems (TPS), can be used for hypersonic laminar-flow control. This provides symbiotic reduction of aeroheating and reduced skin friction drag. It also leads to a new family of lightweight TPS. N e

Theoretical Aerodynamics in Today's Real World: Opportunities and Challenges

To aid in the design of an ultrasonically absorptive coating (UAC) to be tested on a 7degree half-angle sharp cone in the CUBRC LENS I shock tunnel, parametric studies of the coating laminar-flow-control performance are conducted for Mach=7 and Mach=10 freestream conditions. The second-mode amplification factors, N, are calculated using the reduced-order computational package that includes the compressible Blasius mean flow and the local-parallel linear stability solver. These N-factors agree well with those predicted by the STABL solver that opens up an opportunity to conduct quick turn-around computations of the UAC performance. Stability calculations are carried out for the uncoated (solid) and coated (porous) wall. A porous coating of regular microstructure, which comprises equally spaced vertical cylindrical blind micro-holes of fixed radius, spacing and depth, is analyzed. The UAC parameters, at which the coating massively suppresses the second mode and can lead to significant (more than twice) increase of the laminar run, are predicted. Estimates of the UAC roughness effect indicate that the coating can be treated as aerodynamically smooth in the unit Reynolds number range required for transition experiments. It is shown that the UAC performance strongly increases with porosity. In this connection, it is suggested to investigate a rectangular or honeycomb patterns, which allow for coatings of substantially higher porosity compared with pores of circular cross-section.