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.     

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.     

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.     

Hypersonic flow past a flat-plate/beveled-whistle system

The results of an experimental and numerical investigation of unsteady hypersonic nitrogen flow (M_∞ = 21 and the unit Reynolds number Re_∞1 = 6×10⁵ m^?1) past an integrated flat-plate/beveled whistle model are presented. The calculations using the ANSYS Fluent package are carried out for different geometries of the whistle cavity and angles of incidence of the model. The conditions under which fluctuations occur in the whistle are determined and the fields of the mean flow and fluctuations in the shock layer on the plate are obtained. In the experiments performed in the T-327A hypersonic nitrogen wind tunnel of the Institute of Theoretical and Applied Mechanics of the Siberian Branch of the Russian Academy of Sciences the dependence of the pressure fluctuations on the plate surface on the angle of attack of the model are obtained. The calculated and measured results are compared.     

Numerical modeling of the receptivity of a supersonic boundary layer to entropy disturbances

Numerical modeling of the receptivity of a two-dimensional flat-plate boundary layer to entropy disturbances is carried out at the freestream Mach number M_∞ = 6. Low-intensity perturbations considered are in the form of temperature spots of various shapes and with different initial positions downstream of the shock. They are shown to be able to generate unstable disturbances in the boundary layer. This receptivity mechanism is relatively weak as compared with the receptivity to acoustic waves. When the entropy perturbations are introduced upstream of the bow shock, they first pass across the shock. Downstream of the shock this interaction generates acoustic waves which, in turn, penetrate into the boundary layer thus exciting unstable disturbances of a considerably greater amplitude than the temperature spots. Thus, the bow shock can change the receptivity mechanism.     

Nonlinear wave processes in a hypersonic shock layer

Nonlinear disturbance development in a hypersonic flat-plate shock layer (M_∞ = 21, Re _L = 1.44×10⁵) exposed to external-flow slow-mode acoustic perturbations at one or several frequencies is studied on the basis of the numerical solution of the Navier-Stokes equations. The mean flow distortion by disturbances and the nonlinear self-interaction between spectral modes is investigated by varying the initial amplitudes of the acoustic waves introduced. The appearance of combination frequencies, both summarized and subtracted, and their interaction with each other is shown to exist.     

Experimental investigation of the influence of the flow structure on the aerodynamic coefficients of the IXV vehicle

In the framework of the ESA Future Launchers Preparatory Program (FLPP) an experimental study on the aerodynamic behavior during the re-entry phase of the Intermediate eXperimental Vehicle (IXV) configuration was conducted in the DLR hypersonic wind tunnel H2K in Cologne. Tests were carried out at Mach 6.0 and 8.7 with different flap deflection angles and the angle of attack varied continuously between 20° and 55° to investigate the flow topology as well as the aerodynamic forces and moments and the surface pressure distribution. The experimental data show that depending on the combination of the flap deflection angle (δ _L/R) and angle of attack (α) the complex flow structure in the vicinity of the flaps significantly influences the vehicle’s aerodynamic coefficients. An analysis of this shock/shock and shock/boundary layer interaction causing flow separation with reattachment is performed.     

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.     

Controlling the disturbances in a hypersonic flat-plate shock layer by unsteady action from the surface

The results of a wind-tunnel experiment on the joint action of periodic acoustic fast-mode disturbances of the outer flow and disturbances generated at the leading edge of a plate on the hypersonic (M_∞ = 21) viscous shock layer on the plate are presented. The possibility of positively controlling the intensity of density fluctuations in the plate shock layer by means of disturbances introduced from the leading edge is shown. Direct numerical simulation of the suppression (enhancement) of disturbances under the simultaneous action on the shock layer of the two-dimensional fast-mode acoustic waves in the outer flow and the source of two-dimensional suction/injection disturbances near the leading edge of the plate is performed under the experimental conditions. The experimental and calculated results are shown to be in good agreement.     

Experimental study of density fluctuations in a hypersonic laminar wake behind a cone

The characteristics of natural fluctuations of density in a laminar near wake behind a sharp cone in a hypersonic flow of nitrogen at zero incidence are studied by the method of electronbeam fluorescence at Mach numberM=21 and unit Reynolds numberRe ₁=6·10⁵ m⁻¹. The distributions of the mean density, integral fluctuations, and spectra of density fluctuations are obtained, the longitudinal and azimuthal phase velocities of perturbations are determined, and the growth rates of perturbations in the wake are found. The results are compared with the measurement data in the shock layer on a flat plate. Institute of Theoretical and Applied Mechanics, Siberian Division, Russian Academy of Sciences, Novosibirsk 630090. Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, Vol. 41, No. 3, pp. 111–117, May–June, 2000     

Numerical modeling of the receptivity of a supersonic boundary layer to acoustic disturbances

The receptivity of a supersonic (M_∞ = 6) boundary layer on a flat plate to acoustic disturbances is investigated on the basis of a numerical solution of the 2D Navier-Stokes equations. Numerical results obtained for fast and slow acoustic waves impinging on the plate at zero angle agree qualitatively with asymptotic theory. Calculations carried out for other angles of incidence of the acoustic waves reveal new features of the perturbation field in the neighborhood of the leading edge of the plate. It is shown that, due to visco-inviscid interaction, the shock formed near the leading edge may significantly affect the acoustic field and the receptivity.     

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.     

Three-dimensional receptivity of boundary layers

The paper presents a review of results of some recent (mainly experimental) studies devoted to a quantitative investigation of the problem of receptivity of the 2D and 3D boundary layers with respect to various 3D (in general) external perturbations. The paper concentrates on the mechanisms of excitation and development of stationary and travelling instability modes in a 3D boundary layer on a swept wing, as well as in 2D boundary layers including the Blasius flow and a self-similar boundary layer with an adverse pressure gradient. In particular, the following problems of the boundary-layer receptivity are discussed: (i) receptivity to localized 3D surface roughness, (ii) receptivity to localized 3D surface vibrations, (iii) acoustic receptivity in presence of 3D surface roughness, and (iv) acoustic receptivity in the presence of 3D surface vibrations. All experiments described in the paper were conducted using controlled disturbance conditions with the help of simulation of the stationary and non-stationary perturbations by means of several disturbance generators. This approach gives us the possibility to obtain quantitative results which are independent of any uncontrolled background perturbations of the flow and the experimental model. In contrast to the data obtained at “natural” environmental conditions these results can be directly compared with calculations without any significant assumptions about the physical nature of the disturbances under investigation. The complex (amplitude and phase) coefficients of the boundary-layer receptivity to external perturbations, obtained as functions of the disturbance frequency and the spanwise wavenumber (or the wave propagation angle), represent the main results of the experiments described. These results can be used for the evaluation of the initial amplitudes and phases of the instability modes generated by various external perturbations, as well as for quantitative verification of linear receptivity theories. Several examples of the comparison of experimental results with calculations are also presented in this paper. A brief analysis of the state-of-art in the field is performed and some general properties of different receptivity mechanisms are discussed.     

Reynolds-number-dependence of the maximum in the streamwise velocity fluctuations in wall turbulence

A survey is made of the standard deviation of the streamwise velocity fluctuations in near-wall turbulence and in particular of the Reynolds-number-dependency of its peak value. The following canonical flow geometries are considered: an incompressible turbulent boundary layer under zero pressure gradient, a fully developed two-dimensional channel and a cylindrical pipe flow. Data were collected from 47 independent experimental and numerical studies, which cover a Reynolds number range of R _θ=U _∞ θ/v=300−20,920 for the boundary layer with θ the momentum thickness and R ⁺=u _*R/v=100-4,300 for the internal flows with R the pipe radius or the channel half-width. It is found that the peak value of the rms-value normalised by the friction velocity, u _*, is within statistical errors independent of the Reynolds number. The most probable value for this parameter was found to be 2.71±0.14 and 2.70±0.09 for the case of a boundary layer and an internal flow, respectively. The present survey also includes some data of the streamwise velocity fluctuations measured over a riblet surface. We find no significant difference in magnitude of the normalised peak value between the riblet and smooth surfaces and this property of the normalised peak value may for instance be exploited to estimate the wall shear stress from the streamwise velocity fluctuations. We also consider the skewness of the streamwise velocity fluctuations and find its value to be close to zero at the position where the variance has its peak value. This is explained with help of the equations of the third-order moment of velocity fluctuations. These results for the peak value of the rms of the streamwise velocity fluctuations and also the coincidence of this peak with the zero value of the third moment can be interpreted as confirmation of local equilibrium in the near-wall layer, which is the basis of inner-layer scaling. Furthermore, these results can be also used as a requirement which turbulence models for the second and triple velocity correlations should satisfy. The authors are indebted to Prof. P. Bradshaw for making available his list of references on this topic and for his remarks on “active” and “inactive” motions. We also gratefully acknowledge discussions with Prof. I. Castro regarding the value of σ _u ⁺ above rough walls.     

Numerical prediction of turbulent boundary layer noise from a sharp-edged flat plate

An efficient hybrid uncorrelated wall plane waves–boundary element method (UWPW-BEM) technique is proposed to predict the flow-induced noise from a structure in low Mach number turbulent flow. Reynolds-averaged Navier-Stokes equations are used to estimate the turbulent boundary layer parameters such as convective velocity, boundary layer thickness, and wall shear stress over the surface of the structure. The spectrum of the wall pressure fluctuations is evaluated from the turbulent boundary layer parameters and by using semi-empirical models from literature. The wall pressure field underneath the turbulent boundary layer is synthesized by realizations of uncorrelated wall plane waves (UWPW). An acoustic BEM solver is then employed to compute the acoustic pressure scattered by the structure from the synthesized wall pressure field. Finally, the acoustic response of the structure in turbulent flow is obtained as an ensemble average of the acoustic pressures due to all realizations of uncorrelated plane waves. To demonstrate the hybrid UWPW-BEM approach, the self-noise generated by a flat plate in turbulent flow with Reynolds number based on chord Re_c = 4.9 × 10⁵ is predicted. The results are compared with those obtained from a large eddy simulation (LES)-BEM technique as well as with experimental data from literature.     

Heating characteristics of blunt swept fin-induced shock wave turbulent boundary layer interaction

An experimental study was conducted on shock wave turbulent boundary layer interactions caused by a blunt swept fin-plate configuration at Mach numbers of 5.0, 7.8, 9.9 for a Reynolds number range of (1.0∼4.7)×10⁷/m. Detailed heat transfer and pressure distributions were measured at fin deflection angles of up to 30° for a sweepback angle of 67.6°. Surface oil flow patterns and liquid crystal thermograms as well as schlieren pictures of fin shock shape were taken. The study shows that the flow was separated at deflection of 10° and secondary separation were detected at deflection of ϑ≥20°. The heat transfer and pressure distributions on flat plate showed an extensive plateau region followed by a distinct dip and local peak close to the fin foot. Measurements of the plateau pressure and heat transfer were in good agreement with existing prediction methods, but pressure and heating peak measurements atM≥6 were significantly lower than predicted by the simple prediction techniques at lower Mach numbers. The project supported by China Academy of Launch Vehicle Technology     

Experimental and numerical analysis of the structure of pseudo-shock systems in laval nozzles with parallel side walls

Detailed numerical and experimental investigations of pseudo-shock systems in a Laval nozzle with parallel side walls are carried out. The location of the pseudo-shock system is defined in this system of two choked Laval nozzles by the ratio of the critical cross sections A₂^*/A₁^*{{A}_{2}^*/{A}_{1}^*} , the stagnation pressure loss across the shock system and viscous losses. The wall pressure distributions and high-speed schlieren videos recorded in the experiments are compared to the results of a steady and an unsteady numerical simulation. For the steady case, good agreement is found between the calculated and measured shock structure and pressure distribution along the primary nozzle wall, except for a remaining slight deviation in the shock position. For the unsteady case, in which asymmetric shock configurations are observed, deviations of the results with respect to the stochastic wall attachment of the shock system are given which indicate the necessity of further investigations on that topic.     

Numerical investigation of the hypersonic viscous shock layer on wings of infinite span at angles of attack and slip

In the framework of the theory of a hypersonic viscous shock layer [1] with modified Rankine-Hugoniot relations [2] at the shock wave a study is made of flow past wings of infinite span with a rounded leading edge. A numerical solution to the problem has been obtained in a wide range of variation of the Reynolds number (5–10⁶), the blowing-suction parameter, the angle of attack (0–45 °), and the angle of slip (0–70 °). Data are given on the influence of the angle of slip on the profiles of the temperature and the velocity across the shock layer. A study is made of the dependence of the distributions of the pressure, the heat flux, and the friction coefficients along the surface of the body on the blowing-suction parameter and the angles of attack and slip.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 2, pp. 104–108, March–April, 1984.     

Mach reflection of a plane shock wave passing a mountain of 45° inclination

The transition from regular reflection (RR) to Mach reflection (MR) as a plane shock wave diffracts around a triangular mountain of 45° inclination is analysed in this paper, both by optical measurement in a shock tube and by numerical simulation the numerical method developed by Li Yingfan^[1] is of the FLIC type with triangular mesh. The dependence of the critical transition point Lk ofRR→MR on shock Mach numberM _i is analyzed and the variations of the incidence angle ω _i of the impinging shock and the reflection angle ω _r with the distanceL ^* are investigated. Our experimental and numerical results agree well with the theoretical results of Iton and Italya.