Correlation study in shock wave�Cturbulent boundary layer interaction

Shock wave–turbulent boundary layer interaction is a critical problem in aircraft design. Therefore, a thorough understanding of the processes occurring in such flows is necessary. The most important task is to study the unsteady phenomena, in particular, the low-frequency ones, for this interaction. An experimental study of separated flow has been performed in the zone of interaction of the incident oblique shock wave with a turbulent boundary layer at Mach 2. Two-point correlation data in the separation zone and the upstream flow were obtained and showed that low-frequency oscillations of the reflected shock waves are related to pulsations in the inflow turbulent boundary layer.     

Convective Roll Instabilities of Vertical Throughflow with Viscous Dissipation in a Horizontal Porous Layer

The vertical throughflow with viscous dissipation in a horizontal porous layer is studied. The horizontal plane boundaries are assumed to be isothermal with unequal temperatures and bottom heating. A basic stationary solution of the governing equations with a uniform vertical velocity field (throughflow) is determined. The temperature field in the basic solution depends only on the vertical coordinate. Departures from the linear heat conduction profile are displayed by the temperature distribution due to the forced convection effect and to the viscous dissipation effect. A linear stability analysis of the basic solution is carried out in order to determine the conditions for the onset of convective rolls. The critical values of the wave number and of the Darcy–Rayleigh number are determined numerically by the fourth-order Runge–Kutta method. It is shown that, although generally weak, the effect of viscous dissipation yields an increase of the critical value of the Darcy–Rayleigh number for downward throughflow and a decrease in the case of upward throughflow. Finally, the limiting case of a vanishing boundary temperature difference is discussed.     

Unsteady filtration of a gas

The unsteady filtering flow of a gas described by the equations of motion proposed by Khristianovich in [1] is investigated. It is shown that for the gas flow in the pores a critical regime can develop when the reduced velocity (an analog of the Mach number in gas dynamics) is less than unity. The reduced velocity is the ratio of the flow velocity to the velocity of propagation of small filtering perturbations at a given point of the flow. St Petersburg. Translated from Izvestiya Rossiiskoi Akademii Nauk, Mekhanika Zhidkosti i Gaza, No. 1, pp. 201–203, January–February, 1994.     

Structure of compression shock waves in porous elastoplastic materials

The shock-wave structure in a porous elastoplastic material is studied. In a certain range of parameters, the existence of a four-wave structure of a compression shock wave is possible. Regimes in which a reflected shock wave does not appear at all have been found in the problem of shock-wave reflection from a rigid wall. In this case, the entire energy of the incident shock wave transforms to thermal energy due to dissipation induced by the viscous collapse of the pores. Institute of Theoretical and Applied Mechanics, Siberian Division, Russian Academy of Sciences, Novosibirsk 630090. Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, Vol. 39, No. 6, pp. 27–32, November–December, 1998.     

Guderley reflection for higher Mach numbers in a standard shock tube

An experimental study shows that the Guderley reflection (GR) of shock waves can be produced in a standard shock tube. A new technique was utilised which comprises triple point of a developed weak Mach reflection undergoing a number of reflections off the ceiling and floor of the shock tube before arriving at the test section. Both simple perturbation sources and diverging ramps were used to generate a transverse wave in the tube which then becomes the weak reflected wave of the reflection pattern. Tests were conducted for three ramp angles (10°, 15°, and 20°) and two perturbation sources for a range of Mach numbers (1.10–1.40) and two shock tube expansion chamber lengths (2.0 and 4.0 m). It was found that the length of the Mach stem of the reflection pattern is the overall vertical distance traveled by the triple point. Images with equivalent Mach stem lengths in the order of 2.0 m were produced. All tests showed evidence of the fourth wave of the GR, namely the expansion wave behind the reflected shock wave. A shocklet terminating the expansion wave was also identified in a few cases mainly for incident wave Mach numbers of approximately 1.20.     

The interaction of a shock wave with the boundary layer in a reflected shock tunnel

The influence of a nontotal reflection on the interaction of a reflected shock wave with the boundary layer in a reflected shock tunnel has been investigated. The calculating method of the velocity, the temperature and the Mach number profiles in the boundary layer in reflected shock fixed coordinates has been obtained. To account for equilibrium real gas effects of nitrogen, the numerical results show that the minimum Mach number in the boundary layer has been moved from the wall into the boundary layer with the increasing of the incident shock Mach number. The minimum Mach number, the shock angle in the bifurcated foot and the jet velocity along the wall to the end plate are reduced owing to the increasing of the area of nozzle throat. The numerical results are in good agreement with measurements.     

Shock wave structure for a fully ionized plasma

We study planar shock wave structure in a two-temperature model of a fully ionized plasma that includes electron heat conduction and energy exchange between electrons and ions. For steady flow in a reference frame moving with the shock, the model reduces to an autonomous system of ordinary differential equations which can be numerically integrated. A phase space analysis of the differential equations provides an additional insight into the structure of the solutions. For example, below a threshold Mach number, the model produces continuous solutions, while above another threshold Mach number, the solutions contain embedded hydrodynamic shocks. Between the threshold values, the appearance of embedded shocks depends on the electron diffusivity and the electron–ion coupling term. We also find that the ion temperature may achieve a maximum value between the upstream and downstream states and away from the embedded shock. We summarize the methodology for solving for two-temperature shocks and show results for several values of shock strength and plasma parameters in order to quantify the shock structure and explore the range of possible solutions. Such solutions may be used to verify hydrodynamic codes that use similar plasma physics models.     

Decay of a centered prandtl-mayer compression wave in a steady gas flow

Discontinuity decay at a singular point of a centered compression wave is considered. Analytical solutions are given that allow one to determine the type of reflected discontinuity that issues from the point of decay and the boundaries of ranges of parameters within which a solution of the problem exists. Baltiisk State Technical University, St. Petersburg 198005. Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, Vol. 39, No. 3, pp. 59–68, May–June, 1998.     

HLLE++格式在高马赫数空腔流动模拟中的应用

空腔流动存在剪切层运动、涡脱落与破裂,以及激波与激波、激波与剪切层、激波与膨胀波和激波/涡/剪切层相互干扰等现象,流动非常复杂,特别是高马赫数(M>2)时,剪切层和激波更强,激波与激波干扰更严重,对数值格式的要求更高,既需要格式耗散小,对分离涡等有很高的模拟精度,又需要格式在激波附近具有较大的耗散,可以很好地捕捉激波,防止非物理解的出现。Roe和HLLC等近似Riemann解格式在高马赫数强激波处可能会出现红玉现象,而HLLE++格式大大改善了这种缺陷,在捕捉高超声速激波时避免了红玉现象的发生,同时还保持在光滑区域的低数值耗散特性。本文在结构网格下HLLE++格式的基础上,通过改进激波探测的求解,建立了基于非结构混合网格的HLLE++计算方法,通过无粘斜坡算例,验证了HLLE++格式模拟高马赫数流动的能力,并应用于高马赫数空腔流动的数值模拟,开展了网格和湍流模型影响研究,验证了方法模拟高马赫数空腔流动的可靠性和有效性。     

Effect of viscosity of the wave process in a nonuniform flow with a critical level

A continuous analytical representation of an acoustic-gravitational field in a medium with a nonuniform flow in the presence of a critical layer is constructed. It is shown that taking into account the effect of viscosity eliminates singular values of the field. St. Petersburg State University, St. Petersburg 198904. Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, Vol. 41, No. 2, pp. 97–101, March–April, 2000.     

Time-resolved stereo PIV measurements of shock–boundary layer interaction on a supercritical airfoil

Time-resolved stereo particle-image velocimetry (TR-SPIV) and unsteady pressure measurements are used to analyze the unsteady flow over a supercritical DRA-2303 airfoil in transonic flow. The dynamic shock wave–boundary layer interaction is one of the most essential features of this unsteady flow causing a distinct oscillation of the flow field. Results from wind-tunnel experiments with a variation of the freestream Mach number at Reynolds numbers ranging from 2.55 to 2.79 × 10⁶ are analyzed regarding the origin and nature of the unsteady shock–boundary layer interaction. Therefore, the TR-SPIV results are analyzed for three buffet flows. One flow exhibits a sinusoidal streamwise oscillation of the shock wave only due to an acoustic feedback loop formed by the shock wave and the trailing-edge noise. The other two buffet flows have been intentionally influenced by an artificial acoustic source installed downstream of the test section to investigate the behavior of the interaction to upstream-propagating disturbances generated by a defined source of noise. The results show that such upstream-propagating disturbances could be identified to be responsible for the upstream displacement of the shock wave and that the feedback loop is formed by a pulsating separation of the boundary layer dependent on the shock position and the sound pressure level at the shock position. Thereby, the pulsation of the separation could be determined to be a reaction to the shock motion and not vice versa.     

Gas combination for shock wave enhancement

It was recently demonstrated that shock wave enhancement could be achieved when a shock propagates in a constant cross-section duct through pairs of air–helium layers having a continually decreasing width (Igra and Igra in Shock Waves 16(3):199–207). A parametric study was conducted aimed at finding a two-layered, light–heavy gas arrangement that yields maximal shock enhancement; the heavy and the light gases used were air and helium, respectively. Effects associated with changes in following parameters were investigated: the number of alternating heavy/light gas layers, the applied reduction ratio between successive layers thickness, and the initial shock wave Mach number.      

Focusing of a shock wave in a rarefied gas A numerical study

The process of focusing of a shock wave in a rarefied noble gas is investigated by a numerical solution of the corresponding two dimensional initial–boundary value problem for the Boltzmann equation. The numerical method is based on the splitting algorithm in which the collision integral is computed by a Monte Carlo quadrature, and the free flow equation is solved by a finite volume method. We analyse the development of the shock wave which reflects from a suitably shaped reflector, and we study influence of various factors, involved in the mathematical model of the problem, on the process of focusing. In particular, we investigate the pressure amplification factor and its dependence on the strength of the shock and on the accommodation coefficient appearing in the Maxwell boundary condition modelling the gas-surface interaction. Moreover, we study the dependence of the shock focusing phenomenon on the shape of the reflector, and on the Mach number of the incoming shock. Received 25 May 1998 / Accepted 4 January 2000     

Optimum overtaking compression shocks with restrictions imposed on the total flow-deflection angle

The problem of optimization of gasdynamic variables behind a system of two steady oblique compression shocks with restrictions imposed on the flow-defection angle is considered. The intervals of input parameters, in which this system turns out to be more effective than one shock, are determined. On the basis of an analysis of the system optimal for the static pressure, the physical meaning of the transition from one type of the reflected discontinuity to another is explained for the problem of interaction of overtaking oblique compression shocks. Baltic State Technical University, St. Petersburg 198005. Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, Vol. 40, No. 4, pp. 99–108, July–August, 1999.     

Numerical investigation of ethylene flame bubble instability induced by shock waves

In this paper, the ethylene/oxygen/nitrogen premixed flame instabilities induced by incident and reflected shock wave were investigated numerically. The effects of grid resolutions and chemical mechanisms on the flame bubble deformation process are evaluated. In the computational frame, the 2D multi-component Navier–Stokes equations with second-order flux-difference splitting scheme were used; the stiff chemical source term was integrated using an implicit ordinary differential equations (ODEs) solver. The two ethylene/oxygen/nitrogen chemical mechanisms, namely 3-step reduced mechanism and 35-step elementary skeletal mechanism, were used to examine the reliability of chemistry. On the other hand, the different grid sizes, Δx × Δy = 0.25 × 0.5mm and Δx × Δy = 0.15 × 0.2mm, were implemented to examine the accuracy of the grid resolution. The computational results were qualitatively validated with experimental results of Thomas et al. (Combust Theory Model 5:573–594, 2001). Two chemical mechanisms and two grid resolutions used in present study can qualitatively reproduce the ethylene spherical flame instability process generated by an incident shock wave of Mach number 1.7. For the case of interaction between the flame and reflected shock waves, the 35-steps mechanism qualitatively predicts the physical process and is somewhat independent on the grid resolutions, while the 3-steps mechanism fails to reproduce the instability of ethylene flame for the two selected grid resolutions. It is concluded that the detailed chemical mechanism, which includes the chain elementary reactions of fuel combustion, describes the flame instability induced by shock wave, in spite of the fact that the flame thickness (reaction zone) is represented by 1–2 grids only.      

Gradients at a curved shock in reacting flow

The inviscid equations of motion for the flow at the downstream side of a curved shock are solved for the shock–normal derivatives. Combining them with the shock–parallel derivatives yields gradients and substantial derivatives. In general these consist of two terms, one proportional to the rate of removal of specific enthalpy by the reaction, and one proportional to the shock curvature. Results about the streamline curvature show that, for sufficiently fast exothermic reaction, no Crocco point exists. This leads to a stability argument for sinusoidally perturbed normal shocks that relates to the formation of the structure of a detonation wave. Application to the deflection–pressure map of a streamline emerging from a triple shock point leads to the conclusion that, for non–reacting flow, the curvature of the Mach stem and reflected shock must be zero at the triple point, if the incident shock is straight. The direction and magnitude of the gradient at the shock of any flow quantity may be written down using the results. The sonic line slope in reacting flow serves as an example. Extension of the results – derived in the first place for plane flow – to three dimensions is straightforward. Received 12 February 1997 / Accepted 10 June 1997     

Numerical simulation of shock wave propagation in microchannels using continuum and kinetic approaches

Numerical simulations of shock wave propagation in microchannels and microtubes (viscous shock tube problem) have been performed using three different approaches: the Navier–Stokes equations with the velocity slip and temperature jump boundary conditions, the statistical Direct Simulation Monte Carlo method for the Boltzmann equation, and the model kinetic Bhatnagar–Gross–Krook equation with the Shakhov equilibrium distribution function. Effects of flow rarefaction and dissipation are investigated and the results obtained with different approaches are compared. A parametric study of the problem for different Knudsen numbers and initial shock strengths is carried out using the Navier–Stokes computations.      

Gas content factor in the interaction of shock waves of different intensity in a two-phase gas-liquid medium

The transition from regular to Mach interaction is investigated in connection with the interaction of two plane weak or moderate shock waves of different intensity in a two-phase gas-liquid medium over the entire range of gas contents. A nonmonotonic dependence of the transition limit and the flow parameters on the gas content is detected. The investigation extends the results of [1] corresponding to the reflection of a shock wave from a wall. At intermediate gas contents in the case of opposing shock waves, analogous to the normal reflection of a shock wave from a solid wall, the results are in agreement with [2]. In the case of weak shock waves non-linear asymptotic expansions [3] are employed. In the extreme cases of single-phase media the results coincide with the findings of [3, 4]. Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 6, pp. 172–174, November–December, 1986.     

Re-initiation phenomenon of gaseous detonation induced by shock reflection

The two-dimensional, time-dependent, reactive Navier–Stokes equations including the effects of viscosity, thermal conduction and molecular diffusion were solved to reveal the wave evolution and chemical dynamics involved in the re-initiation process. The computation was performed for hydrogen–oxygen–argon mixtures at the low initial pressure (8.00 kPa), using detailed chemical reaction model. The results show that, the decoupled leading shock reflects on the right wall of the vertical branch. High temperature and pressure behind the reflected shock induce the generation of hot spots and local explosion. Therefore, the re-initiation of gaseous detonation occurs. In the re-initiation area, there exist very high OH concentration and no H ₂ concentration. However, in front of reflected shock, there exist relatively high H ₂ concentration and no OH radicals. Additionally, the shock–flame interaction induces RM instability. This results in the fast mixing between hot reacted gas mixture and the relatively cold unreacted gas mixture and accelerates the chemical reactions. However, the shock–flame interaction contributes much less to the re-initiation, in contrast with shock reflection. The transition of leading shock from regular reflection to Mach reflection happens during the re-initiation. The computed evolution of wave structures involved in the re-initiation is qualitatively agreeable with that from the experimental schlieren images.      

A numerical study of oblique shock wave reflections over wedges in an ideal quantum gas

The various oblique shock wave reflection patterns generated by a moving incident shock on a planar wedge using an ideal quantum gas model are numerically studied using a novel high resolution quantum kinetic flux splitting scheme. With different incident shock Mach numbers and wedge angles as flow parameters, four different types of reflection patterns, namely, the regular reflection, simple Mach reflection, complex Mach reflection and the double Mach reflection as in the classical gas can be classified and observed. Both Bose–Einstein and Fermi–Dirac gases are considered.