Planar laser-induced fluorescence imaging in shock tube flows

The planar laser-induced fluorescence (PLIF) imaging method was used to perform flow visualization and quantitative planar thermometry in shock tube flow fields using toluene as a fluorescence tracer in nitrogen. Fluorescence quantum yield values needed to quantify PLIF images were measured in a static cell at low pressures (<1 bar) for various toluene partial pressures in nitrogen bath gas. Images behind incident and reflected shocks were taken in the core flow away from regions affected by boundary layers. Temperature measurements from these images were successfully compared with predicted values using ideal shock equations. Measured temperatures ranged between 296 and 800 K and pressures between 0.15 and 1.5 atm. The average temperature discrepancies between measurements and the predicted values behind the incident and reflected shocks were 1.6 and 3.6%, respectively. Statistical analyses were also conducted to calculate the temperature measurement uncertainty as a function of image resolution. The technique was also applied to the study of more complex supersonic flows, specifically the interaction of a moving shock with a wedge. Measured temperatures agreed well with the results of numerical simulations in all inviscid regions, and all pertinent features of the single Mach reflection were resolved.     

Shear layer behavior resulting from shock wave diffraction

All previous studies on shock wave diffraction in shock tubes have spatial and temporal limitations due to the size of the test sections. These limitations result from either the reflection of the expansion wave, generated at the corner, from the top wall and/or of the reflection of the incident diffracted shock from the bottom wall of the test section passing back through the region of interest. This has limited the study of the evolution of the shear layer and its associated vortex, which forms a relatively small region of the flow behind the shock with an extent of only a few centimeters, and yet is a region of significant interest. A special shock tube is used in the current tests which allow evolution of the flow to be examined at a scale about an order of magnitude larger than in previously published results, with shear layer lengths of up to 250 mm being achieved without interference from adjacent walls. Tests are presented for incident shock wave Mach numbers of nominally 1.3–1.5. Studies have been undertaken with wall angles of 10, 20, 30 and 90°. Significant changes are noted as the spatial and temporal scale of the experiment increases. For a given wall angle, the flow behind the incident shock is not self-similar as is usually assumed. Both shear layer instability and the development of turbulent patches become evident, neither of which have been noted in previous tests.     

Application of unsteady mixing equations to some aerodynamic problems

Tangential discontinuities [1] are introduced in solving several transient and steady-state problems of gas dynamics. These discontinuities are unstable [2] as a result of the effects of viscosity and thermal conductivity. Therefore it is advisable to replace the tangential discontinuity by a mixing region and account for its interaction with the inviscid flows, establishing on the boundaries of this region the conditions of vanishing friction stress and equality of the velocity and temperature components to the corresponding velocity and temperature components of the inviscid flows. This formulation improves the accuracy of the solution of such problems by posing them as problems with irregular reflection and intersection of shock waves [1].The consideration of the interaction of unsteady turbulent mixing regions with the inviscid flow also permits the formulation of several problems in which the effects of viscosity lead to complete rearrangement of the flow pattern (the lambda-configuration) with the interaction of the reflected shock wave with the boundary layer in the shock tube [3,4], the formation of zones of developed separation ahead of obstacles, etc.).In this connection, §1 presents an analysis of the self-similar solutions of the unsteady turbulent mixing equations (a corresponding analysis of the laminar mixing equations which coincide with the boundary layer equations is presented in [1]). It is shown that these self-similar solutions describe, along with the several problems noted above, the problems of the formation of steady jets and mixing zones in the base wake.As an example, §2 presents, within the framework of the proposed schematization, an approximate solution of the problem of the interaction of a shock wave reflected from a semi-infinite wall with the boundary layer on a horizontal plate behind the incident shock wave. The results obtained are applied to the analysis of reflection in a shock tube. Computational results are presented which are in qualitative agreement with experiment [3, 4].     

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.     

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.     

气相爆轰波反应区结构的平面激光诱导荧光测量

基于平面激光诱导荧光(PLIF)技术对2H2 O2 10Ar的预混气体爆轰波反应区结构进行实验研究.采用高浓度的氩稀释有利于减小爆轰化学反应自发辐射光对OH荧光的影响.合理设置PLIF系统、爆轰波和ICCD之间的同步控制触发延时,得到爆轰波阵面附近的OH荧光分布图像.结果表明:诱导激波后反应阵面不是平面且不稳定.荧光图像上能清晰地看到类似拱顶石的结构,它位于两马赫杆之间,以入射激波、剪切层和反应阵面为边界.无论是在马赫杆后还是在入射激波后,OH浓度分布在诱导区末端急剧增加至最大值.随着离开反应阵面的距离增加,OH浓度快速减小.由于爆轰模式和激光片光方向的影响,从PLIF图像上测得的横波间距值较离散,均小于胞格宽度.     

Reflection of shock waves from a solid boundary in a mixture of condensed materials. 1. Equilibrium approximation

The process of reflection of shock waves (SW) from a solid wall in a two-component mixture of condensed materials is studied within the framework of mechanics of heterogeneous media. The velocity of a reflected SW and the values of the parameters behind its front are analytically determined as functions of the velocity of the incident wave and the initial parameters of the mixture. It is shown that the absolute value of the velocity of the reflected SW can be greater than the velocity of the incident SW in mixtures with a small content of the light component and at low velocities of the incident shock wave. The nonmonotonic character of the dependence of pressure in the final equilibrium state behind the incident SW on the initial volume concentration of particles is demonstrated. The velocity of the incident SW is estimated for the case where a similar effect is also observed behind a reflected SW. It is established that, for weak shock waves, the dependence of the amplification factor of the reflected SW on the initial volume concentration of the light component is nonmonotonic and has a local maximum. It is noted that, as the velocity of the incident SW increases, the effect of compacting of the mixture (increase in concentration of the heavy component) behind the reflected SW becomes much less pronounced than in a passing SW. Institute of Theoretical and Applied Mechanics, Siberian Division, Russian Academy of Sciences. Novosibirsk 630090. Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, Vol. 40, No. 5, pp. 73–78, September–October, 1999.     

Attenuation of weak shock waves along pseudo-perforated walls

In order to attenuate weak shock waves in ducts, effects of pseudo-perforated walls were investigated. Pseudo-perforated walls are defined as wall perforations having a closed cavity behind it. Shock wave diffraction and reflection created by these perforations were visualized in a shock tube by using holographic interferometer, and also by numerical simulation. Along the pseudo-perforated wall, an incident shock wave attenuates and eventually turns into a sound wave. Due to complex interactions of the incident shock wave with the perforations, the overpressure behind it becomes non-uniform and its peak value can locally exceed that behind the undisturbed incident shock wave. However, its pressure gradient monotonically decreases with the shock wave propagation. Effects of these pseudo-perforated walls on the attenuation of weak shock waves generated in high speed train tunnels were studied in a 1/250-scaled train tunnel simulator. It is concluded that in order to achieve a practically effective suppression of the tunnel sonic boom the length of the pseudo-perforation section should be sufficiently long. Received 23 June 1997 / Accepted 16 September 1997     

Formation and evolution of vortex rings induced by interactions between shock waves and a low-density bubble

The deformation and instability of a low-density spherical bubble induced by an incident and its reflected shock waves are studied by using the large eddy simulation method. The computational model is firstly validated by experimental results from the literature and is further used to examine the effect of incident shock wave strength on the formations and three-dimensional evolutions of the vortex rings. For the weak shock wave case (Ma?=?1.24), the baroclinic effect induced by the reflected shock wave is the key mechanism for the formation of new vortex rings. The vortex rings not only move due to the self-induced effect and the flow field velocity, but also generate azimuthal instability due to the pressure disturbance. For the strong shock wave case (Ma?=?2.2), a boundary layer is formed adjacent to the end wall owing to the approach of vortex ring, and unsteady separation of the boundary layer near the wall results in the ejection and formation of new vortex rings. These vortex rings interact in the vicinity of the end wall and finally collapse to a complicated vortex structure via azimuthal instability. For both shock wave strength cases, the evolutions of vortex rings due to the instability lead to the formation of the complicated structure dominated by the small-scale streamwise vortices.     

抽吸激波管的性能分析与计算

为了减小由于反射激波和透射激波分叉引起的反射型激波风洞试验气体提前受到污染的现象,本文研究了一种新的具有抽吸的激波管流动,分析了抽吸缝的作用,给出了这种抽吸激波管性能参数的计算方法,同时还给出了反射激波与边界层相互作用引起的激波分叉的形状随抽吸量变化的计算公式。实验证实了边界层抽吸可以有效地减小激波与壁面边界层相互作用所产生的分离现象。计算与测量结果是一致的。     

Radiative cooling of plasma behind a reflected shock front

Calculation of gas flow in a shock tube on the basis of ideal theory [1] leads to results that differ from the real picture. In particular, the calculated velocity of the reflected shock wave exceeds the experimentally measured velocity [2] by about 20%. The calculated parameters of shock-heated gas agree well with the experimental results only directly behind the shock front [3]. The present paper reports a theoretical and experimental investigation of the variation of the plasma parameters behind the front of a reflected shock wave in argon. A picture of the gas-dynamic processes taking place after reflection of the incident shock wave by the end of the shock tube is determined. A method is developed for approximate analytic calculation, this making it possible to determine not only the parameters of the gas directly behind the front of the reflected shock wave for different positions of the wave relative to the end of the shock tube but also the variation of these parameters in other regions behind the reflected shock wave. The calculation takes into account the influence of the boundary layer and radiative cooling in the approximation of a low degree of ionization of the plasma and persistence of equilibrium conditions in the entire region behind the reflected shock wave. The experimental and theoretical profiles of the radiation behind the reflected shock wave are compared.     

Comparative study of amorphous and crystalline Zr-based alloys in response to nanosecond pulse laser ablation

In shock tube experiments, the interaction between the reflected shock and boundary layer can induce shock bifurcation and weak ignition. The weak ignition can greatly affect the ignition delay time measurement in a shock tube experiment. In this work, two-dimensional simulations considering detailed chemistry and transport are conducted to investigate the shock bifurcation and non-uniform ignition behind a reflected shock. The objectives are to interpret the formation of shock bifurcation induced by the reflected shock and boundary layer interaction and to investigate the weak ignition and its transition to strong ignition for both hydrogen and dimethyl ether. It is found that the non-uniform reflection of the incident shock at the end wall produces a wedge-shaped oblique shock foot at the wall. The wedge-shaped structure results in strong interactions between reflected shock and boundary layer, which induces the shock bifurcation. It is demonstrated that the local high-temperature spots at the foot of the bifurcated shock is caused by viscous dissipation and pressure work. As the post-reflected shock temperature increases, the transition from weak ignition to strong ignition in a stoichiometric hydrogen/oxygen mixture is observed. The relative sensitivity of ignition delay time to the post-reflected shock temperature is introduced to characterize the appearance of weak ignition behind the reflected shock. Unlike in the hydrogen/oxygen mixture, weak ignition is not observed in the stoichiometric dimethylether/oxygen mixture since it has a relatively longer ignition delay time and smaller relative sensitivity.

     

On flows behind shock waves reflected from a solid wall

The flow fields associated with the interaction of a normal shock wave with a plane wall kept at a constant temperature were studied based on kinetic theory which can describe appropriately the shock structure and its reflection process. With the use of a difference scheme, the time developments of the distributions of the fluid dynamic quantities (velocity, temperature, pressure and number density of the gas) were obtained numerically from the BGK model of the Boltzmann equation subject to the condition of diffusive-reflection at the wall for several cases of incident Mach number:M ₁=1.2, 1.5, 2.0, 3.0, 4.0, 5.0 and 6.0. The reflection process of the shocks is shown explicitly together with the resulting formation of the flow fields as time goes on. The nonzero uniform velocity toward the wall occurring between the viscous boundary layer and the reflected shock wave is found to be fairly large, the magnitude of which is of the order of several percent of the velocity induced behind the incident shock, decreasing as the incident Mach number increases. It is also seen that a region of positive velocity (away from the wall) within the viscous boundary layer manifests itself in the immediate vicinity of the wall, which is distinct for larger incident Mach numbers. Some of the calculated density profiles are compared with available experimental data and also with numerical results based on the Navier-Stokes equations. The agreement between the three results is fairly good except in the region close to the wall, where the difference in the conditions of these studies and the inappropriateness of the Navier-Stokes equations manifest themselves greatly in the gas behavior.This article was processed using Springer-Verlag TEX Shock Waves macro package 1990.     

Reflection of a plane shock wave from a rigid concave wall

We present the results of an experimental study of the reflection of a plane stationary shock wave with Mach number in the range 1.21–1.35 from a rigid cylindrical concave wall. The experiments were carried out in a shock tube. In experimental shock tube technology the reflection of a shock wave from a rigid wall is often used for obtaining high temperatures [1]. This circumstance is associated with the fact that the temperature behind the reflected wave is significantly higher than that behind the incident wave.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 4, pp. 33–39, July–August, 1970.     

A turbulent boundary layer over a two-dimensional rough wall

Particle image velocimetry (PIV) measurements and planar laser induced fluorescence (PLIF) visualizations have been made in a turbulent boundary layer over a rough wall. The wall roughness consisted of square bars placed transversely to the flow at a pitch to height ratio of λ/k = 11 for the PLIF experiments and λ/k = 8 and 16 for the PIV measurements. The ratio between the boundary layer thickness and the roughness height k/δ was about 20 for the PLIF and 38 for the PIV. Both the PLIF and PIV data showed that the near-wall region of the flow was populated by unstable quasi-coherent structures which could be associated to shear layers originating at the trailing edge of the roughness elements. The streamwise mean velocity profile presented a downward shift which varied marginally between the two cases of λ/k, in agreement with previous measurements and DNS results. The data indicated that the Reynolds stresses normalized by the wall units are higher for the case λ/k = 16 than those for λ/k = 8 in the outer region of the flow, suggesting that the roughness density effects could be felt well beyond the near-wall region of the flow. As expected the roughness disturbed dramatically the sublayer which in turn altered the turbulence production mechanism. The turbulence production is maximum at a distance of about 0.5k above the roughness elements. When normalized by the wall units, the turbulence production is found to be smaller than that of a smooth wall. It is argued that the production of turbulence is correlated with the form drag.     

Boundary layer flows behind constant speed shock waves moving into a dusty gas

Laminar boundary layer flows behind constant speed shock waves moving into a dusty gas are analyzed numerically. The basic equations of two-phase flows are derived in shock fixed coordinates and solved by an implicit finite-difference method for the side wall boundary layer in a dusty gas shock tube. The development of the boundary layer and resulting velocity and temperature profiles, respectively, for the gas and particles are given from the shock front to far downstream. The effects of diaphragm pressure ratio, mass loading ratio of particles and particle size upon the flow properties are discussed in detail.This article was processed using Springer-Verlag T_EX Shock Waves macro package 1990.     

“Non-free” interaction of plane shock waves and the boundary layer in the neighborhood of the leading edge of a plate with slip

The interaction between a normally impinging shock wave and the boundary layer on a plate with slip is studied in the neighborhood of the leading edge using various experimental methods, including special laser technology, to visualize the supersonic conical gas flows. It is found that in the “non-free” interaction, when the leading edge impedes the propagation of the boundary layer separation line upstream, the structure of the disturbed flow is largely identical to that in the developed “free” interaction, but with higher parameter values and gradients in the leading part of the separation zone. The fundamental property of developed separation flows, namely, coincidence of the values of the pressure “plateau” in the separation zone and the pressure behind the oblique shock above the separation zone of the turbulent boundary layer, is conserved. Moscow. e-mail: ostap@inmech.msu.su. Translated from Izvestiya Rossiiskoi Akademii Nauk, Mekhanika Zhidkosti i Gaza, No. 3, pp. 57–69, May–June, 2000. The work was carried out with financial support from the Russian Foundation for Basic Research (project No. 97-01-00099).     

The interaction between shock waves and foam in a shock tube

An experimental study and a numerical simulation were conducted to investigate the mechanical and thermodynamic processes involved in the interaction between shock waves and low density foam. The experiment was done in a stainless shock tube (80 mm in inner diameter, 10 mm in wall thickness and 5 360 mm in length). The velocities of the incident and reflected compression waves in the foam were measured by using piezo-ceramic pressure sensors. The end-wall peak pressure behind the reflected wave in the foam was measured by using a crystal piezoelectric sensor. It is suggested that the high end-wall pressure may be caused by a rapid contact between the foam and the end-wall surface. Both open-cell and closed-cell foams with different length and density were tested. Through comparing the numerical and experimental end-wall pressure, the permeability coefficients α and β are quantitatively determined.     

Regular reflection of a shock wave from a solid wall in a stream of fuel mixture

The two-dimensional stationary problem of regular reflection of a shock wave from a plane solid wall in a fuel gas mixture is examined in the case when the mixture is ignited at the intersection of the incident wave with the wall and a flame front is formed behind the reflected shock wave. The shock waves and the flame front are considered plane surfaces of discontinuity. The fuel mixture and the reaction products are considered perfect, inviscid, and non-heat-conducting gases.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 4, pp. 161–163, July–August, 1978.     

Formation of one-dimensional flows of viscous heat-conducting gas for small parameter perturbations

The formation of unsteady one-dimensional flows is studied, using the solution of the problem of reflection of a normally incident plane shock wave from a heat-conducting wall as an example. The process is considered for low intensities of the incident wave, behind which the gas temperature hardly differs from the initial wall temperature. The flows with complicated internal structures that arise are investigated on the basis of Navier-Stokes equations linearized near the initial state. An analytic solution of the problem describing the discontinuous structure of the reflected flow is constructed, which can serve as a test in the numerical solution of the original nonlinearized Navier-Stokes equations. The influence of the Prandtl numbers, the specific heat ratio, and dissipative and other factors is considered. The features of the effects of viscosity, thermal conductivity, and accommodation on the formation of flows and ideal (inviscid, nonheat-conducting) and dissipative zones are traced. It is shown that the solution of the linearized system agrees with the solution for asymptotic flow regimes.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 5, pp. 105–111, September–October, 1986.