Unsteady oblique shock waves

A spatially and temporally local analysis is provided for unsteady, oblique shock waves, in which the flow is assumed to be two-dimensional or axisymmetric. Three unsteady parameters, in a laboratory frame, are viewed as the known independent variables. These are the upstream Mach number, the shock Mach number, and the angle of the shock relative to the instantaneous upstream velocity. Other steady and unsteady parameters, such as the velocity turn angles and downstream Mach numbers, are evaluated in closed form, in terms of these three quantities. Trends are assessed, and a sensitivity analysis is provided. It is suggested that the theory may find application in converting a shock capturing algorithm, at an early time during the computational process, into a shock fitting algorithm. Received 30 April 1999 / Accepted 29 November 1999     

One-dimensional steady magnetogasdynamic flow in oblique fields and the structure of shock waves

Summary An exact solution in closed form, in terms of elliptic functions, is obtained for the one-dimensional steady flow of a polytropic gas with finite constant electrical conductivity which is influenced by an oblique magnetic field and a transverse electric field in the absence of viscosity, thermal conductivity and all other non-electrical dissipative mechanisms. The solution is presented in terms of elementary functions and the many possible flow patterns are discussed in detail in the case when, at some position, the transverse momentum equals the transverse Maxwell stress; a case which is appropriate to the structure of switch-on and switch-off shock waves.The research reported in this paper was supported in part by the United States Air Force under Grant No. AF-EOAR-65-58 and monitored by the European Office, Office of Aerospace Research.     

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.     

Interaction between oblique shock waves in metal powders

In the paper, interaction between oblique shock waves in metal powders is numerically simulated. The boundaries between regular- and irregular-interaction regimes are established. A hysteresis that takes place during a transition from one regime to the other is revealed. Received 17 August 2001 / Accepted 6 December 2001     

Interference of stationary and non-stationary shock waves

The mathematical model of a gasdynamic discontinuity is used in the area of study concerning gas flows with large gradients of gasdynamic functions. Gasdynamic functions before and after the discontinuity meet non-linear algebraic equations called the dynamic compatibility conditions on the discontinuities. Different modes of shock wave structures forming as a result of regular or irregular interference of the incoming discontinuities of different types are described. Ranges of the initial flow parameters definition such that either shock wave structures of different modes take place or interference equations have no solutions are determined. Most attention is given to arbitrary triple shock-wave configurations. Their classification is proposed. Differential characteristics of the steady flow are studied. The notion “differential characteristics” includes first derivatives of the fundamental gasdynamic parameters with respect to natural coordinates and curvatures of the discontinuities surfaces. Effect of unsteadiness on the triple-shock configuration is examined. Some problems arising at creation of complete local theory of steady and propagating gasdynamic discontinuities interference are formulated.     

Magnetoacoustic shock waves in a nonuniform plasma flow

Translated from Zhurnal Prikladnoi Mekhaniki i Tekhnicheskoi Fiziki, No. 4, pp. 13–19, July–August, 1991.     

Supersonic H2-air combustions behind oblique shock waves

In order to study the mechanisms of initiation and stabilization of H₂-Air combustions (stoechiometric mixture initially atT ₀=293 K andp ₀=0.5 bar) in supersonic flow conditions behind an oblique shock wave (OSW), an original technique is used where OSW is generated in this mixture by the lateral expansion of the burnt gas behind a normal CJ gaseous detonation propagating into a bounding reactive mixture. Four Mach numberM of propagation of OSW are considered in the study, namelyM=7.7-6.1-4.4 and 3. Depending on the Mach numberM and inclinaison angle of OSW different regimes of combustion may occur in the driven mixture. For high values ofM (6.1 and 7.7) delayed steady overdriven oblique detonation waves (SODW) were obtained with a near CJ detonation wave as the critical regime. It was found that SODW obtained correspond quite well to prediction of the polar method. When thermal conditions behind the OSW are lower, either for high Mach number 6.1 and 7.7 for smaller angle than the previous case, or for lower Mach number, 4.4 and 3, the flame initiated at the apex is stabilized as a turbulent oblique flame behind the OSW. With much lower conditions, no combustion appears in the H₂-Air mixture.     

Heat transfer in the shock impingement zone around a cylinder in a hypersonic flow

Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 3, pp. 117–123, May–June, 1991.     

Behavior of shock trains in a hypersonic inlet/isolator model with complex background waves

The background flow field of a scramjet isolator that accommodates a shock train contains complex compression and expansion waves, referred as ??background waves,?? causing large streamwise and transverse parameter gradients upstream of the shock train. Therefore, the available results of shock train research obtained by direct-connect methods might be not applicable for real scramjet isolators. Special tests are therefore performed for an inlet/isolator model. Close coupling is found between the shock train and the background shocks. The pointing direction of the leading shock switches upwards and downwards repeatedly during the upstream propagation of the shock train. Three unstable stages with substantial oscillations are also observed, interlaced with four stable stages. In addition, the interference of the background shock waves increases the sustainable back-pressure ratio and decreases the length of the shock train. However, this does not mean that the background waves in the isolator should be intensified intentionally.     

Interference of steady shock waves traveling in the same direction

A classification of the possible types of shock-wave structures formed as a result of the interference between overtaking shocks in a homogeneous flow is developed on the basis of a previous study [1]. A series of analytic and numerical interaction type criteria is obtained, which makes it possible to justify and supplement the analysis, carried out in [2], of the regions of the governing flow parameters in which steady-state solutions for shock-wave structures of different types exist. The calculations are found to be consistent with the known experimental data.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 4, pp. 143–152, July–August, 1987.     

Nonstationary gas flow with shock waves in a supersonic compressor

Shock waves are formed in the channels between blades in a compressor working in the transsonic state, and the positions of these vary periodically and produce strong vibrations in the blades. The effect is extremely complex and is dependent on a large number of parameters. Here we present a simplified model for the effect, which can be examined theoretically. It is assumed that the nonstationary pulsations in the flow and the amplitudes in the oscillations of the shock waves are small, and therefore one can employ a steady-state flow whose characteristics may be taken as given, including the mean position of the shock waves.Translated from Zhurnal Prikladnoi Mekhaniki i Tekhnicheskoi Fiziki, No. 5, pp. 41–47, September–October, 1973.     

Rheology of rarefied gas flow in hypersonic shock and boundary layers

Using the Maxwell method, transfer equations describing molecular gas flows in viscous shock and hypersonic boundary layers are obtained. It is shown that, in contrast to the Navier-Stokes approximation, the kinetic model proposed makes it possible correctly to describe hypersonic flow around bodies under conditions of strong nonequilibrium of the internal and translational degrees of freedom of the gas particles.     

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.     

Radiation of a shock layer during hypersonic flow of air about a spherical segment

The problem on the flow of radiating air about a spherical segment is solved. A comparison of results obtained with investigations of the flow of a radiating gas about a sphere and the flow of gas about a spherical segment, with radiation left out of account, is made. The influence of radiation in the neighborhood of the rim of the segment on the flow in the shock layer is considered, and it is shown that it does not exert a significant influence on the fields of the gas-dynamical parameters because the latter are determined by processes occurring near the axis of symmetry, due to the phenomenon of radiation freezing.Moscow. Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 1, pp. 101–106, January–February, 1972.     

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.     

铅飞层中斜冲击波对碰马赫反射行为实验研究

采用线阵多普勒光纤探针测速技术(Doppler pins system,DPS)和高速光电分幅相机照相两种精密诊断技术,对铅飞层中斜冲击波对碰后的反射行为进行了观测。获得了飞层对碰部位速度-时间历史曲线和凸起形貌演化图像,给出了凸起轮廓发展演化过程、压力分布等实验数据和信息。结合冲击波反射理论,对铅飞层对碰区动力学现象进行了分析和解释,证实铅飞层中斜冲击波对碰后发生了马赫反射。     

Shock waves and turbulence in a hypersonic inlet

A numerical investigation for an axisymmetric hypersonic turbulent inlet flow field of a perfect gas is presented for a three-shock configuration consisting of a biconic and a cowl. An upwind parabolized Navier-Stokes solver based on Roe's scheme is used to compute an oncoming flow Mach numberM =8, temperatureT =216 K, and pressureP =5.5293×10³ N/m². In order to assess the flow quantities, the interaction between shock and turbulence, and the inlet efficiency, three different flow calculations — laminar, turbulent with incompressible and compressible two-equationk- turbulence models — have been performed in this work.Computational results show that turbulence is markedly enhanced across an oblique shock with step-like increases in turbulence kinetic energy and dissipation rate. This enhancement is at the expense of the mean kinetic energy of the flow. Therefore, the velocity behind the shock is smaller in turbulent flow and hence the shock becomes stronger. The entropy increase through a shock is caused not only by the amplification of random molecular motion, but also by the enhancement of the chaotic turbulent flow motion. However, only the compressiblek- turbulence model can properly predict a decrease in turbulence length scale across a shock. Our numerical simulation reveals that the incompressiblek- turbulence model exaggerates the interaction between shock and turbulence with turbulence kinetic energy and dissipation rate remaining high and almost undissipated far beyond the shock region. It is shown that proper modeling of turbulence is essential for a realistic prediction of hypersonic inlet flowfield. The performed study shows that the viscous effect is not restricted in the boundary layer but extends into the main flow behind a shock wave. The loss of the available energy in the inlet performance therefore needs to be determined from the shock-turbulence interaction. The present study predicts that the inlet efficiency becomes relatively lower when turbulence is taken into account.