Investigation of Dynamic Stability Regimes for Axisymmetric Bodies in Supersonic Flow

The problem of supersonic flow past a slender blunt cone with allowance for the reverse boundary-layer effect on the outer flow is solved with the aim of studying the influence of the boundary layer on the damping coefficient of axisymmetric body oscillations. It is assumed that the body executes plane angular, both low-amplitude and low-velocity, oscillations about a center of rotation. A modified version of the method [1] is applied for calculating the time-dependent flow past a body with the viscosity effect taken into account. The high accuracy of the flow parameter determination provided by this technique is confirmed by wind- tunnel experiments on a large-scale cone model (L1 m) at Mach numbers M=4 and 6. The agreement between the calculated and measured data forms the basis for the numerical investigation of the blunt-cone damping coefficient over a wide range of freestream Mach (M=4–20) and Reynolds (Re _L =10⁶–10⁸) numbers. At moderate freestream Mach numbers (M=4 and 6) an appreciable Re _L effect on the damping coefficient was not detected. However, on the hypersonic range this effect manifests itself more strongly, especially when there is gas injection into the boundary layer from the vehicle surface.     

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.     

Correlation of the separation region length in shock wave/channel boundary layer interaction

 Results of an experimental investigation of the characteristics of a separation region induced by the interaction of an externally generated oblique shock with the turbulent boundary layer formed in a rectangular half channel are discussed. The experiments were carried out in the supersonic wind tunnel of the Institute of Theoretical and Applied Mechanics SB RAS at a free-stream Mach number M _∞=3.01 over a range of Reynolds numbers Re ₁=(9.7–47.5)×10⁶ m^-1 and at zero incidence and zero yaw of the model. Particular attention is paid to the size of the zone of the upstream propagation of disturbances (upstream influence region) under different experimental conditions: with varied values of the shock wave strength, half channel width, and Reynolds number. It is shown, in particular, that the normalized upstream influence region length as a function of inclination angle of the shock generator in a rectangular half channel is readily approximated by a simple exponential function. In support of the known reference data obtained for supersonic numbers M _∞ and moderate Re in other configurations, it is also shown that the upstream influence region length decreases with increasing Reynolds number. Generalization of experimental data on the length of the upstream influence region formed in similar geometric configurations is possible using an additional reference linear scale which is the distance from the leading edge of the shock generator to the exposed surface. A substantial dependence of the reference dimensions of separation region on the half channel width is also established. Received: 20 January 1997/Accepted: 30 June 1997     

Laminar boundary layer on blunt bodies with account for vorticity of the external flow

This paper presents the technique for and results from numerical calculations of the hypersonic laminar boundary layer on blunted cones with account for the vorticity of the external flow caused by the curved bow shock wave. It is assumed that the air in the boundary layer is in the equilibrium dissociated state, but the Prandtl number is assumed constant, =0.72. The calculations were made in the range of velocities 3–8 km/sec, cone half-angles _k=0°–20°. With account for the vortical interaction of the boundary layer with the external flow, the distribution of the thermal flux and friction will depend on the freestream Reynolds number (other conditions being the same). In the calculations the Reynolds number R, calculated from the freestream parameters and the radius of the spherical blunting, varies from 2.5·10³ to 5.10⁴. For the smaller Reynolds numbers the boundary layer thickness on the blunting becomes comparable with the shock standoff, and for R<2.5·10³ it is apparent that we must reconsider the calculation scheme. With R>5·10⁴ for cones which are not very long the vortical interaction becomes relatively unimportant. The results of the calculations are processed in accordance with the similarity criteria for hypersonic viscous gas flow past slender blunted cones [1, 2].     

Numerical simulation of receptivity of a hypersonic boundary layer to acoustic disturbances

Direct numerical simulations of the evolution of disturbances in a viscous shock layer on a flat plate are performed for a free-stream Mach number M _∞ = 21 and Reynolds number Re _L = 1.44 · 10⁵. Unsteady Navier-Stokes equations are solved by a high-order shock-capturing scheme. Processes of receptivity and instability development in a shock layer excited by external acoustic waves are considered. Direct numerical simulations are demonstrated to agree well with results obtained by the locally parallel linear stability theory (with allowance for the shock-wave effect) and with experimental measurements in a hypersonic wind tunnel. Mechanisms of conversion of external disturbances to instability waves in a hypersonic shock layer are discussed. __________ Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, Vol. 48, No. 3, pp. 84–91, May–June, 2007.     

Effect of sound-absorbing materials on intensity of disturbances in the shock layer on a flat plate aligned at an angle of attack

Results of a numerical and experimental study of characteristics of disturbances in a hypersonic shock layer on a flat plate covered by a sound-absorbing coating and aligned at an angle of attack are presented. Experiments and computations are performed for the free-stream Mach number M _∞ = 21 and Reynolds number Re _L = 6 · 10⁴. A possibility of suppressing pressure fluctuations in the shock layer at frequencies of 20–40 kHz with the use of tubular and porous materials incorporated into the plate surface is demonstrated. Results of numerical simulations are found to be in good agreement with experimental data.     

Experimental study and direct numerical simulation of the evolution of disturbances in a viscous shock layer on a flat plate

The evolution of disturbances in a hypersonic viscous shock layer on a flat plate excited by slow-mode acoustic waves is considered numerically and experimentally. The parameters measured in the experiments performed with a free-stream Mach number M _∞ = 21 and Reynolds number Re _L = 1.44 · 10⁵ are the transverse profiles of the mean density and Mach number, the spectra of density fluctuations, and growth rates of natural disturbances. Direct numerical simulation of propagation of disturbances is performed by solving the Navier-Stokes equations with a high-order shock-capturing scheme. The numerical and experimental data characterizing the mean flow field, intensity of density fluctuations, and their growth rates are found to be in good agreement. Possible mechanisms of disturbance generation and evolution in the shock layer at hypersonic velocities are discussed. __________ Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, Vol. 47, No. 5, pp. 3–15, September–October, 2006.     

An experimental investigation of the ELAC 1 configuration at supersonic speeds

Supersonic flight of aerospace planes is of marked interest since several flow regimes characterized by different local flow structures have to be flown through. This problem was investigated experimentally for the hypersonic research configuration ELAC 1. The aim of the study was to detect the influence of the rounded leading edge, of the thickness distribution prescribed, and of the Reynolds number, especially on the flow on the leeward side of the configuration. The experiments were carried out in the transonic wind tunnel of Aerodynamisches Institut of RWTH Aachen, at a freestream Mach number Ma _∞=2, a unit Reynolds number of Re _∞=13×10⁶, angles of attack between ?3°?α?10°, and in a wind tunnel of the Institute for Theoretical and Applied Mechanics of the Russian Academy of Sciences in Novosibirsk. The freestream Mach numbers covered in these experiments were varied between 2?Ma _∞?4, freestream Reynolds numbers per unit length between 25×10⁶?Re _∞?56×10⁶ and angles of attack between ?3°?α?10°. Flow visualization studies, measurements of surface pressure distributions and of aerodynamic forces were used to analyze the flow. The results, which will also be compared with numerical data, clearly indicate marked differences in the location of the separation and reattachment lines, and the formation of the primary, secondary and tertiary vortices, for the flow regimes investigated.     

Upstream roughness and Reynolds number effects on turbulent flow structure over forward facing step

This paper presents results of experiments conducted to investigate the effects of Reynolds number and upstream wall roughness on the turbulence structure in the recirculation and recovery regions of a smooth forward facing step. A reference smooth upstream wall and a rough upstream wall made from sand gains were studied. For the smooth upstream wall, experiments were conducted at Reynolds number based on the freestream velocity and step height (h), Re_h = 4940, 8400 and 8650. The rough wall experiments was performed at Re_h = 5100, 8200 and 8600 to closely match the corresponding Re_h experiment over the smooth wall. The reattachment lengths in the smooth wall experiments were L_r/h ≈ 2.2, but upstream roughness significantly reduced these values to L_r/h ≈ 1.3. The integral scales within the recirculation bubbles were independent of upstream roughness and Reynolds number; however, upstream roughness significantly increased the spatial coherence and integral scales outside the recirculation bubbles and in the recovery region. Irrespective of the upstream wall condition, the redeveloping boundary layer recovered at 25h from reattachment.     

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.     

Development of a turbulent boundary layer after a step from smooth to rough surface

The flow developing downstream of a step change from smooth to rough surface condition is studied in the light of Townsend’s wall similarity hypothesis. Previous studies seem to support the hypothesis for channel and pipe flows, but there are considerable controversies about its application to boundary layers and in particular to surface roughness formed by spanwise bars. It has been suggested that this controversy arises from insufficient separation of scales between the boundary layer thickness and the roughness length scale. An experimental investigation has therefore been undertaken where the flow evolves from a fully developed smooth wall boundary layer at high Reynolds numbers over a step in surface roughness (Re _θ = 13,400 at the step). The flow is mapped through the development of the internal layer until the flow is fully developed over the rough wall. The internal layer is found to grow as δ ∼ X ^0.73, and after about 15 boundary layer thicknesses at the step, the internal layer has reached the outer edge of the incoming layer. At the last rough wall measurement station, the Reynolds number has grown to Re _θ ≈ 32,600 and the ratio of boundary layer to roughness length scales is δ/k ≈ 140. The outer layer differences between the smooth and the rough wall data were found to be sufficiently small to conclude that for this setup the Townsend’s wall similarity hypothesis appears to hold.     

Laminar heat exchange on sharp and blunt plates in a hypersonic air flow

The results of an experimental investigation and numerical simulation of heat exchange are given for sharp and blunt plates in a hypersonic air flow. The experiments were carried out in a Ludwig-type wind tunnel at hypersonic Mach numbers and a Reynolds number Re_L which varied over the range from 0.24 10⁶ to 1.31 10⁶. The bluntness radius r was varied over the range from 0.008 mm (almost sharp plate) to 4 mm (the corresponding Reynolds numbers Re_r from 15 to 4 10⁴). The numerical simulation was carried out by solving the complete two-dimensional Navier-Stokes equations. The experimental data were correlated using the well-known viscous hypersonic interaction parameters.__________Translated from Izvestiya Rossiiskoi Academii Nauk, Mekhanika Zhidkosti i Gaza, No. 1, 2005, pp. 168–180. Original Russian Text Copyright © 2005 by Borovoi, Egorov, Skuratov and Struminskaya.     

Influence of Mach and Reynolds numbers on heat transfer to the leeward surface of a half-cone at hypersonic speed

Results are given of an investigation of heat transfer on the flat surface of a blunted half-cone, washed at zero angle of attack by a helium flow at high Mach number (up to 23.5). A correlation is given for the experimental data obtained over a wide range of Mach numbers (M = 3–23.5) and Reynolds numbers (Re_a = 10⁴–3.5·⁵, wherea is the nose radius).Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 5, pp. 105–109, September–October, 1976.     

Investigation of the influence of the unit Reynolds number on the transition of a boundary layer on a sharp cone

To establish the influence of the unit Reynolds number on the transition of a boundary layer on the side surface of a cone, the transition was investigated on a model of a sharp cone with half-angle = 7.5 ° and lengths from 150 to 400 mm. The experiments were made in a shock tube at Mach number M = 6.1 in the wide range of Reynolds numbers Re_eL = 1.3·10⁶-5.5·10⁷. The position of the transition region was determined from the results of measurement of the local heat flux by calorimetric thermocouple converters. Data were obtained on the influence on the transition of the unit Reynolds number at large values. It was also shown that under the investigated conditions the base region does not influence the transition of the boundary layer on the surface of the cone.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 4, pp. 32–38, July–August, 1982.     

Nature of the surface heart transfer fluctuation in a hypersonic separated turbulent flow

This paper presents the results of an experimental study of the unsteady nature of a hypersonic separated turbulent flow. The nomimal test conditions were a freestream Mach number of 7.8 and a unit Reynolds number of 3.5×10⁷/m. The separated flow was generated using finite span forward facing steps. An array of flush mounted high spatial resolution and fast response platinum film resistance thermometers was used to make multi-channel measurements of the fluctuating surface heat trtansfer within the separated flow. Conditional sampling analysis of the signals shows that the root of separation shock wave consists of a series of compression wave extending over a streamwise length about one half of the incoming boundary layer thickness. The compression waves converge into a single leading shock beyond the boundary layer. The shock structure is unsteady and undergoes large-scale motion in the streamwise direction. The length scale of the motion is about 22 percent of the upstream influence length of the separation shock wave. There exists a wide band of frequency of oscillations of the shock system. Most of the frequencies are in the range of 1–3 kHz. The heat transfer fluctuates intermittently between the undisturbed level and the disturbed level within the range of motion of the separation shock wave. This intermittent phenomenon is considered as the consequence of the large-scale shock system oscillations. Downstream of the range of shock wave motion there is a separated region where the flow experiences continuous compression and no intermittency phenomenon is observed. The project supported by National Natural Science Foundation of China     

Laminar-turbulent transition in the boundary layer on cones in a hypersonic flow at high Reynolds numbers per meter

The laminar-turbulent transition is experimentally studied in boundary-layer flows on cones with a rectangular axisymmetric step in the base part of the cone and without the step. The experiments are performed in an A-1 two-step piston-driven gas-dynamic facility with adiabatic compression of the working gas with Mach numbers at the nozzle exit M _∞ = 12–14 and pressures in the settling chamber P₀ = 60–600 MPa. These values of parameters allow obtaining Reynolds numbers per meter near the cone surface equal to Re _1e = (53–200) · 10⁶ m ⁻¹. The transition occurs at Reynolds numbers Re _tr = (2.3–5.7) · 10⁶. __________ Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, Vol. 48, No. 3, pp. 76–83, May–June, 2007.     

Nonmonotonic relationship between the Reynolds number and the lift coefficient of a plate in a hypersonic rarefied gas flow

The aerodynamic coefficients of a plate in a hypersonic stream at low Reynolds numbers are studied over a wide range of similarity parameters. The dependence of the lift coefficientC _Y on the tangential force coefficient, the finite Mach number at the outer edge of the boundary layer and the velocity-slip and temperature-jump boundary conditions is taken into consideration. The nonmonotonic character of the relationship betweenC _Y and the Reynolds number, revealed previously in experiments, is explained within the framework of the viscous hypersonic interaction model.Moscow. Translated from Izvestiya Rossiiskoi Akademii Nauk, Mekhanika Zhidkosti i Gaza, No. 1, pp. 186–189, January–February, 1996.     

Some Reynolds number effects on two- and three-dimensional turbulent boundary layers

Experimental data for a two-dimensional (2-D) turbulent boundary layer (TBL) flow and a three-dimensional (3-D) pressure-driven TBL flow outside of a wing/body junction were obtained for an approach Reynolds number based on momentum thickness of Re _θ =23,200. The wing shape had a 3:2 elliptical nose, NACA 0020 profiled tail, and was mounted on a flat wall. Some Reynolds number effects are examined using fine spatial resolution (Δy ⁺=1.8) three-velocity-component laser-Doppler velocimeter measurements of mean velocities and Reynolds stresses at nine stations for Re _θ =23,200 and previously reported data for a much thinner boundary layer at Re _θ =5,940 for the same wing shape. In the 3-D boundary layers, while the stress profiles vary considerably along the flow due to deceleration, acceleration, and skewing, profiles of the parameter correlate well and over available Reynolds numbers. The measured static pressure variations on the flat wall are similar for the two Reynolds numbers, so the vorticity flux and the measured mean velocities scaled on wall variables agree closely near the wall. The stresses vary similarly for both cases, but with higher values in the outer region of the higher Re _θ case. The outer layer turbulence in the thicker high Reynolds number case behaves similarly to a rapid distortion of the flow, since stream-wise vortical effects from the wall have not diffused completely through the boundary layer at all measurement stations. Received: 9 June 2000/Accepted: 26 January 2001     

Experimental study of compressible boundary layer on a cone at angles of attack

Experimental study was conducted for boundarylayers on a sharp 5° half-angle cone of 400mm length at angles of attack. The model was tested in the T-326 hypersonic wind tunnel （ITAM） at freestream Mach number M = 5.95. Mean and fluctuation wall characteristics of the boundary layer are measured at 0°, 2°, 3° and 4° angles of attack for different stagnation pressures. Pulsation measurements are carried out by means of ALTP sensor. Pressure and temperature distributions along the model are obtained, and transition beginning and end locations have been found. Boundary layer stabilization with the increase of angle of attack and the decrease of stagnation pressure is observed. High frequency pulsations inherent to hypersonic boundary layer （second mode） have been detected.     

Interaction of intersecting shocks with a flat-plate boundary layer in the presence of an entropy layer

Gas flow and heat transfer on the surfaces of sharp and blunt plates is experimentally investigated in the presence of two forward-looking wedges at the Mach numbers M = 5, 6, and 8 and the Reynolds numbers up to Re_∞L = 27×10⁶. It is shown that the entropy layer generated by a small bluntness of the leading edge of the plate can considerably change the heat transfer, the gas pressure, and the friction in the zone of interference of the shock with the plate boundary layer. Under certain conditions a small plate bluntness can also lead to a qualitative change in the flow structure. The effect of constriction of the channel between the wedges on the interference flow is studied.