Alexander Fedorov

Problems in high speed flow prediction relevant to control

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

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

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

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.

Reflection of acoustic disturbances from a porous coating of regular microstructure

Laminar flow control (LFC) technologies reduce heat-transfer rates as well as the weight and complexity of thermal protection systems (TPS). Previous theoretical and experimental hypersonic wind tunnel studies showed that the laminar run could be substantially increased using an ultrasonically absorptive coating (UAC) that suppresses the second mode instability. In order to design and fabricate porous materials providing integrated UAC and TPS functions, theoretical and experimental tools are needed to perform quick and economical assessments of the UAC characteristics associated with reflection and absorption of the boundary-layer disturbances. Nature of the second mode instability suggests that basic features of the second mode interaction with a porous coating can be captured by considering the reflection of acoustic disturbances from the UAC surface without external boundary-layer flow. In this connection, the reflection of acoustic waves from a flat plate surface covered by a UAC with a regular micro-structure is studied experimentally and theoretically. An experimental setup was assembled to perform benchmark (no flow) measurements of the reflection coefficient at various ambient pressures with emphasis on low pressures relevant to high-altitude hypersonic flights. The theoretical reflection coefficients are in good agreement with the benchmark measurements conducted at an ultrasonic frequency of 180 kHz in the range of ambient pressures from 20 to 800 mbar. This new testing technique provides an economical method to evaluate the robustness of UACTPS articles prior to their testing in hypersonic wind tunnels.

Experimental study of transition in hypersonic boundary layer on ultrasonically absorptive coating with random porosity

Experimental studies of laminar -turbulent transition on the randomly structured ultrasoni cally absorptive coating (UAC) are conducted on a sharp cone at zero angle of attack in the impulse hypersonic wind tunnel at Mach = 6. The UAC comprises a thin layer of felt metal that mimics microstructures of fibrous materials commonly used for thermal protection on actual hypersonic vehicles. A new ultra fast heat flux sensors were used for stability measurements. Special attention is paid to late stages of transition associated with nonlinear breakdown and turbulent boundary layer. It is shown that tra nsition is caused by the second mode instability . The coating effectively s uppresses th is mode and higher -frequency disturbances , while it slightly enhances the low -frequency disturbances. The transition was not detected on the coated surface provid ing mor e than 17% increase of the transition end Reynolds number . It is shown that the porous coating significantly affects disturbance spectra in the turbulent boundary layer. On the porous surface, the low -frequency disturbances are marginally increased, while the high -frequency disturbances are strongly suppressed compared with the solid surface. The two major factors that could cause these effects are distributed roughness and porosity. First -cut estimates showed that the UAC roughness should not impact the tu rbulent flow under the experimental conditions discussed herein. It is conjecture d that the

Stability of hypersonic boundary layer on porous wall with regular microstructure

Theoretical and experimental studies of hypersonic boundary-layer stabilization using a passive porous coating of regular microstructure are discussed. Propagation of disturbances inside pores is simulated with linear acoustic theory including the gas rarefaction effect. This model provides boundary conditions for stability analysis of boundary-layer disturbances on the porous wall. Experiments were conducted in the Mach 6 wind tunnel on a 7-deg half-angle sharp cone whose longitudinal half-surface is solid and whose other half-surface is covered by a perforated sheet comprising equally spaced cylindrical blind microholes. Hot-wire measurements of natural disturbances and artificially excited wave packets are conducted on both solid and porous surfaces. Natural disturbance spectra indicate that the second mode is a dominant instability. The porous coating stabilizes the second mode and weakly affects the first mode. Measurements of artificially excited wave packets show that the porous coating leads to substantial decrease of the wave-packet growth. The experimental data on phase speeds and amplitudes of the second-mode disturbances are compared with theoretical predictions. Satisfactory agreement is obtained for both solid and porous surfaces. This study confirms the concept of hypersonic boundary-layer stabilization by passive porous coatings, which can be used for laminar flow control.

PLASMA CONTROL OF FOREBODY NOSE VORTEX SYMMETRY BREAKING

Flight vehicle forebody vortex symmetry breaking and control of resulting yaw departure by surface plasma discharges are considered. To assess effectiveness of this control concept, stability of the vortex pairing over slender bodies at incidence is analyzed. For this purpose, the stability of the separation saddle point at the origin of the feeding sheet in the cross flow plane is assessed. A discrete point vortex model and slender body theory are used identify key dimensionless parameters and model the basic physics. Computations are performed for a circular cone. The analysis can be extended to arbitrary-shaped bodies using appropriate scaling and conformal mapping. It is shown that the symmetric vortex structure arising in the model is absolutely unstable to small but finite disturbances that are governed by the Ginzburg-Landau equation. Although the vortex system is stable in a linear approximation applicable to infinitesimal perturbations, it is unstable to finite disturbances due to nonlinear effects. Spatial and temporal evolution of the perturbations is studied and critical initial amplitudes of the instability are obtained. Stability of the point vortices to small symmetric and asymmetric displacements is analyzed. Theoretical results are validated against experimental data. Parametric studies show that the vortex structure can be controlled by artificial displacements of the separation locus. A new method to achieve such vortex flow control using a plasma discharge on the body surface is considered. The effect of the discharge is simulated as a volumetric heat source interacting with the turbulent boundary layer. Theoretical estimates from this model indicate that this approach can control stall-spin departure due to forebody symmetry breaking.

Stability Analysis of High-Speed Boundary-Layer Flow with Gas Injection

Abstract : Stability analyses of high-speed boundary-layer flow past a 5 deg half angle sharp cone with the wall-normal injection of air through a porous strip are performed using Navier-Stokes solutions for the mean flow and linear stability theory. The configuration and free-stream parameters are chosen to be similar to the experiments, which were carried out at Caltechs T5 shock tunnel to investigate the effect of CO2 injection on laminar-turbulent transition. The analysis is focused on pure aerodynamic effects in the framework of perfect gas model. It is shown that the injection leads to destabilization of the Mack second mode in the nearfield relaxation region and its stabilization in the far-field relaxation region. To reduce the destabilization effect it was suggested to decrease the injector surface slope or use suction blowing of zero net injection. However, the eN computations showed that these modifications did not improve the injector performance in the near-filed region in general. For special cases of low injection rates in which the N-factors in the near field region are below the critical level, shaping can produce a significant stabilization in the mid- and far-field regions.

Investigations of laminar-turbulent transition on a sharp cone with localized heating or cooling in high-spee d flow

A localized heating or cooling effect on stability and transition of the boundary layer flow on a sharp cone at zero angle of attack at the free -stream Mach number 6 is analyzed using the linear stability theory. Three different locati ons of the heating/cooling strip are considered. The steady-state laminar flow solution is calculated using the axisymmetric Navier-Stokes equations to provide the mean flow fi eld. The spatial stability analysis is performed for two-dimensional disturbances associated with the Mack first and second modes. The transition onset points are estimated us ing the e N method. In this framework, the heating/cooling effect on the transition onset is i nconclusive. The heater (or cooler) may cause earlier or later transition depending on the choice of critical N-factor. Direct numerical simulations and experiments are needed to clarify this situation.

Numerical and theoretical modeling of supersonic boundary-layer receptivity to temperature spottiness

A two-dimensional direct numerical simulation (DNS) of receptivity of a flat-plate boundary layer to temperature spottiness in Mach 6 free stream is carried out. The influence of spottiness parameters to the receptivity process is studied. It is shown that the temperature spots propagating near the upper boundary-layer edge generate mode F. Further downstream mode F is synchronized with unstable mode S (Mack second mode) and excites the latter via the inter-modal exchange mechanism. A theoretical model describing the excitation of mode F by the temperature spots is developed using the biorthogonal eigenfunction decomposition method. The DNS results agree with the theoretical predictions. If the temperature spots are initiated in the free stream and pass through the bow shock, the dominant receptivity mechanism is different. The spot-shock interaction leads to excitation of acoustic waves, which penetrate into the boundary layer and excite mode S. Numerical simulations shows that this mechanism provides the instability amplitudes an order of magnitude higher than in the case of receptivity to the temperature spots themselves.