Investigation of a hypersonic crossing shock wave/turbulent boundary layer interaction

A combined theoretical and experimental study is presented for the interaction between crossing shock waves generated by (10°, 10°) sharp fins and a flat plate turbulent boundary layer at Mach 8.3. The theoretical model is the full 3-D mean compressible Reynolds-averaged Navier-Stokes RANS) equations incorporating the algebraic turbulent eddy viscosity model of Baldwin and Lomax. A grid refinement study indicated that adequate resolution of the flowfield has been achieved. Computed results agree well with experiment for surface pressure and surface flow patterns and for pitot pressure and yaw angle profiles in the flowfield. The computations, however, significantly overpredict surface heat transfer. Analysis of the computed flowfield results indicates the formation of complex streamline and wave structures within the interaction region.This article was processed using Springer-Verlag T_EX Shock Waves macro package 1.0 and the AMS fonts, developed by the American Mathematical Society.     

Bispectral analysis of numerical simulations of wave processes in hypersonic shock layers

Results of numerical simulations of the evolution of disturbances in a hypersonic shock layer on a flat plate at high Mach numbers (M_∞ = 21) and moderate Reynolds numbers (Re _L = 1.44 · 10⁵) are analyzed by an adapted method of bispectral analysis. All basic types of nonlinear interactions are obtained. The calculated results are compared with experimental data.     

Viscous shock layer on a plate in hypersonic flow

The results of theoretical and experimental investigations of the hypersonic flow around a plate with a shap leading edge are presented. Step-by-step verification of the numerical model of the full viscous shock layer is performed: the calculated density profiles, shock wave inclinations, and the Stanton numbers are compared with experimental data obtained using the method of electron-beam fluorescence, calorimetric gages and IR imaging system.     

Radiation in a hypersonic shock layer generated around a projectile

Radiation emitted from the shock layer generated around a hypersonic flight model is experimentally investigated by using a ballistic range (two-stage light-gas gun). A polyethylene projectile of 1.2 cm in diameter is launched in this facility at the velocity of 5 km/sec (M=15), and the emission from the induced shock layer around the projectile is observed with a spectroscope. As a result, molecular band-spectra from NO and N₂ are detected along with those from carboncontaining molecules. Total emission power is measured with a diode-type powermeter. In addition, dimension effect of the flight model is theoretically and numerically examined, and a scaling law on thermochemical structure of the shock layer is developed. It shows that the thickness of thermal boundary-layer formed on the model surface does not follow the conventional scaling law based on the reaction distance and on the energy relaxation distance. Finally, the radiative field around the projectile is numerically computed, and the total power emitted from the shock layer is estimated. From the comparison between computed and measured results, the validity of the calculation model is discussed.     

Blowing of a foreign gas in a hypersonic viscous shock layer

We consider the problem of a hypersonic viscous flow of a nonreactive mixture of ideal gases around smooth thick bodies in the framework of a two-layer model of a thin shock layer for moderately small Reynolds numbers. We investigate the effect of blowing of a foreign gas through a permeable surface in the bow region of a spherical blunt body. We introduce a transformation of variables that gives a number of important advantages in the numerical solution of the problem under consideration. The problem of mass blowing from the surface of a body into a boundary layer has an extensive literature. The effect of blowing for moderately small Reynolds numbers has been considerably less studied [1–5], and in the majority of papers on this question either the critical point of a blunt body or the blowing of a gas homogeneous with the gas in the incoming flow is investigated.Moscow. Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 4, pp. 110–116, July–August, 1972.     

Nonlinear development of a wave in a boundary layer

In recent years definite progress has been achieved in the construction of theoretical models of nonlinear wave processes which lead to a transition from laminar to turbulent flow [1, 2]. At the same time, there is a shortage of actual experimental material, especially for flows in a boundary layer. Fairly thorough experimental studies have been carried out only on the initial stage of the development of disturbances in a boundary layer, which is satisfactorily describable by the linear theory of hydrodynamic stability. In evaluating the theoretical models of subsequent stages of the transition, investigators have been forced to turn chiefly to much earlier experiments carried out by the United States National Bureau of Standards [3, 4], in which the main attention was concentrated on the three-dimensional structure of the transition region. The present investigation was undertaken for the purpose of obtaining detailed data on the structure of the flow in the transition region when there is disturbance in the laminar boundary layer of a two-dimensional wave. In order to make the two-dimensional nonlinear effects stand out more clearly, the amplitude of the wave was specified to be fairly large from the very outset. In contrast to earlier investigations, the main attention was centered on the study of the spectral composition of the disturbance field.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 3, pp. 49–58, May–June, 1977.     

Study of the shock motion in a hypersonic shock system/turbulent boundary layer interaction

Wall pressure fluctuations and surface heat transfer signals have been measured in the hypersonic turbulent boundary layer over a number of compression-corner models. The distributions of the separation shock oscillation frequencies and periods have been calculated using a conditional sampling algorithm. In all cases the oscillation frequency distributions are of broad band, but the most probable frequencies are low. The VITA method is used for deducing large scale disturbances at the wall in the incoming boundary layer and the separated flow region. The results at present showed the existence of coherent structures in the two regions. The zero-cross frequencies of the large scale structures in the two regions are of the same order as that of the separation shock oscillation. The average amplitude of the large scale structures in the separated region is much higher than that in the incoming boundary layer. The length scale of the separation shock motion region is found to increase with the disturbance strength. The results show that the shock oscillation is of inherent nature in the shock wave/turbulent boundary layer interaction with separation. The shock oscillation is considered to be the consequence of the coherent structures in the separated region.This work was supported by the Chinese National Science Foundation. Thanks for Prof. Z. B. Lin and Miss X. Y. Feng for their helps. The authors wish to express thanks to Professor W. Merzkirch who has helped us to check the paper again and again.     

Behavior of sonic lines in a shock layer behind a detached shock wave

A numerical investigation is made into the formation of local supersonic zones in the subsonic flow region between a detached shock wave and the surface of the body in the case of supersonic three-dimensional flow over conical bodies with opening angle _k = 120 ° of the cone in the range of Mach numbers M = 2.5–15.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No.4 pp. 143–145, July–August, 1979.We thank G. I. Petrov for suggesting the problem and for helpful advice and O. M. Belotserkovskii for constant interest in the work.     

Experimental study of vortex structures in a hypersonic shock layer on a flat plate

The characteristics of travelling perturbations of density in a hypersonic shock layer on a flat plate for the Mach number M_∞=21 and unit Reynolds numberRe ₁=6·10⁵ m⁻¹ were experimentally studied by the method of electron-beam fluorescence. The perturbations were generated by interaction of the shock layer behind an oblique gas-dynamic whistle and the leading edge of the plate. The cases of unsteady and quasi-steady interaction were considered. In both cases, vortex disturbances of finite amplitude were generated. The measurements were performed at the fundamental frequency F=0.6·10⁻⁴ and at the harmonic; the streamwise phase velocities, the growth rates of the disturbances, and the angles of wave propagation were obtained. The measurement results are compared with some experimental data for subsonic flows, some particular results of the linear stability theory for compressible flows, and the results obtained on the basis of a simple model of the nonlinear stage of disturbance evolution in a hypersonic boundary layer. Institute of Theoretical and Applied Mechanics, Siberian Division, Russian Academy of Sciences, Novosibirsk 630090. Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, Vol. 40, No. 6, pp. 41–47, November–December, 1999.     

Model of a viscous nonequilibrium shock layer with a thin shock wave

It is shown that the concept of a viscous shock layer with boundary conditions specified in a thin shock wave is unsuitable for analyzing the flow of a chemically reacting gas, even in the case of high Reynolds numbers; it may produce a finite error when determining the parameters of the shock layer.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 5, pp. 175–178, September–October, 1973.     

On shock layer method for the hypersonic flow problems

Chernyi’s series method[1] is not proper for the case that(γ-l)/(γ+l)<<2/(γ+1)×M²sin²β (γ=c_p/c_v-adiabatic index number, M-Much number, β-shock incidence). In this paper, we only suppose that in the neighbour of the shock, there exists a shock layer in which the density of the gas is very big, but we do not remove the case that (γ-1)/(γ+1)<<2/(γ+1)M²sin²β.     

Nonlinear instability of a spontaneously radiating shock wave

A self-consistent integrodifferential equation is derived for weakly nonlinear perturbations of the surface of a spontaneously radiating shock wave. This equation can have solutions that increase unboundedly with the time.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 3, 110–118, May–June, 1984.I am very grateful to A. G. Kulikovskii, whose suggested the problem and put forward a number of valuable ideas that helped in the successful completion of the work, and also to A. A. Barmin and the participants of G. G. Chernyi's seminar for helpful discussions.     

Control of disturbances of a hypersonic viscous shock layer on a flat plate

Receptivity of a viscous shock layer on a flat plate aligned at an angle of attack to external multiwave acoustic perturbations is studied. It is shown that external acoustic waves and periodic controlled perturbations introduced from the surface of the plate mounted at an angle of attack smaller than 20° generate entropy-vortex disturbances with a similar spatial distribution in the viscous shock layer. This result allows numerical implementation of the interference method of controlling disturbances generated in the viscous shock layer on the plate by external acoustic waves at one frequency and at a spectrum of frequencies by introducing blowing-suction perturbations on the plate surface with appropriate amplitudes and phases.     

On the influence of elevated surface temperatures on hypersonic shock wave/boundary layer interaction at a heated ramp model

Although important flow parameters as Mach number, Reynolds number and total enthalpy can be reproduced in most hypersonic experiments quite well, due to different surface temperature effects in wind tunnel and flight, scaling as well as specific flow properties of shock wave/boundary layer interactions are different. This especially holds for short-duration facilities like, e.g. shock tunnels where due to short running times the models remain more or less at ambient temperature. To overcome this shortcoming, an experimental study has been conducted using a preheatable ramp model with 15° ramp angle. This allowed us to adjust the surfaces to an arbitrary temperature just before the experiment started. Pressure and heat flux measurements clearly showed the effect of varying surface and free stream temperatures. These results are supported by schlieren pictures and infrared measurements. The comparison of the measurements with theoretical and numerical results shows a good agreement. Separation bubble scaling laws proposed by Katzer and Davis have been applied and partially confirmed using the local conditions of the boundary layer at separation.     

Investigation of the hypersonic viscous shock layer around blunt bodies in a nonuniform flow

Unseparated viscous gas flow past a body is numerically investigated within the framework of the theory of a thin viscous shock layer [13–15]. The equations of the hypersonic viscous shock layer with generalized Rankine-Hugoniot conditions at the shock wave are solved by a finite-difference method [16] over a broad interval of Reynolds numbers and values of the temperature factor and nonuniformity parameters. Calculation results characterizing the effect of free-stream nonuniformity on the velocity and temperature profiles across the shock layer, the friction and heat transfer coefficients and the shock wave standoff distance are presented. The unseparated flow conditions are investigated and the critical values of the nonuniformity parameter a_k [10] at which reverse-circulatory zones develop on the front of the body are obtained as a function of the Reynolds number. The calculations are compared with the asymptotic solutions [10, 12].Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 3, pp. 154–159, May–June, 1987.     

A hypersonic chemically nonequilibrium viscous shock layer oh wings with a catalytic surface

Within the framework of the theory of a hypersonic viscous shock layer a study is made of flow round wings of infinite span with blunt leading edges at various angles of attack and slip. Account is taken of multicomponent diffusion, and homogeneous chemical reactions, including dissociation-recombination reactions and exchange reactions. On the shock wave the generalized Rankine-Hugoniot conditions are given, and on the surface of the body conditions which allow for heterogeneous catalytic reactions of the first order with reaction rate constants depending [1] or not depending [2] on the temperature. The cases of an ideally catalytic and a noncatalytic surface are also considered. The surface of the body is assumed to be heatinsulated. A numerical study was made of the problem in a broad range of variation in the angles of attack and slip for different cases of prescribed constants representing the rates of the heterogeneous reactions. The conditions of the flow corresponded to the motion of a body which possess a lifting force along the trajectory of entry into the Earth's atmosphere [3]. The dependences are given of the equilibrium temperature of the surface along the stagnation line of the wing on the height of the flight and the distribution of this temperature along the surface of wings with parabolic and hyperbolic contours. It is shown that for flow regimes with a relatively high degree of dissociation in cases when the proportion of atoms recombined on the surface of the body is small, the dependences of the heat flow and the temperature of the surface on the angle of slip are of a nonmonotonic nature.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhldkosti i Gaza., No. 6, pp. 127–135, November–December, 1984.