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.      

Eduction of vortical structures by pressure measurements in noncircular jets

Vortical structures in the noncircular jets excited at the interaction mode were educed by measuring fluctuating static pressure, and their characteristics were discussed in relation to the mixing mechanism of the noncircular jets. The contours of phase-average fluctuating pressure show clearly the vortical structures of the noncircular jets, which compare reasonably with those observed by the flow visualization experiments. The evolution of the vortical structures is characterized by partial merging, stretching and splitting to smaller vortices. The effects of the noncircular vortical structures on mixing were also discussed based on the quantitative measurements of the velocity fields, the results suggesting that the interactions of vortical structures in the noncircular jets are very effective to enhance mixing.     

再冲击载荷作用下流动混合的数值模拟

基于多介质的流体体积分数VOF（volume of fluid）方法和PPM（piecewise parabolic method）方法,给出和发展了可用于多介质粘性流体动力学的数值计算方法和计算代码MVPPM（multi-viscosity-fluid piecewise parabolic method）。为了检验和验证此计算代码,对某激波管实验再冲击载荷作用下的流体动力学不稳定性及其导致的混合过程进行了数值模拟,计算结果与实验结果一致。同时还研究了激波反射冲击作用下流体混合区的演化情况,在反射激波和混合区相互作用的瞬间,混合区的宽度明显减小,之后又迅速增大;另外,混合增长率与初始扰动的频谱有很大关联。通过对有粘性（分子动力学粘性）和无粘性结果的对比,发现粘性对混合区的影响很小。     

Spanwise domain effects on the evolution of the plane turbulent mixing layer

Large Eddy Simulation is used to simulate a series of plane mixing layers. The influence of the spanwise domain on the development of the mixing layer, and the evolution of the coherent structures, are considered. The mixing layers originate from laminar conditions, and an idealised inflow condition is found to produce accurate flow predictions when the spanwise computational domain extent is sufficient to avoid confinement effects. Spanwise domain confinement of the flow occurs when the ratio of spanwise domain extent to local momentum thickness reaches a value of ten. Flow confinement results in changes to both the growth mechanism of the turbulent coherent structures, and the nature of the interactions that occur between them. The results demonstrate that simulations of the two-dimensional mixing layer flow requires a three-dimensional computational domain in order that the flow will evolve in a manner that is free from restraints imposed by the spanwise domain.     

Development of the Richtmyer-Meshkov instability during interaction of the diffusion mixing layer of two gases with transient and reflected shock waves

The evolution of the initially disturbed mixing layer of two gases of different densities under the action of an incident shock wave, shock waves reflected from the end face, compression and expansion waves is studied in a two-dimensional unsteady approximation on the basis of the previously formulated mathematical model of mechanics of a two-velocity two-temperature mixture of gases. Problems of wave interaction with a sinusoidally disturbed diffusion layer are solved numerically. It is shown that the calculated width of the mixing region is in good agreement with experimental data.     

稳定分层流动中湍流特性的研究综述

本文总结了近60 年来分层流动中湍流特性研究的成果. 主要从两个方面进行了综述:(1) 分层流动中湍流场的演变和混合. 在这方面主要分析稳定分层对湍流混合和湍流结构的影响, 以及混合层内湍流结构的特性和混合层的演化规律. (2) 分层流动中湍流的扩散和输运. 动量和标量的逆梯度输运特性是分层湍流研究的一个重要方向;分析分层对湍流扩散的影响. 并指出了一些值得今后进一步研究的方向.     

扩散型气柱界面R-M失稳中混合率的实验研究

Richtmyer-Meshkov(R-M)不稳定性普遍存在于众多工程问题中,激波管实验是研究R-M失稳问题的主要手段.高精度的平面激光诱导荧光(planar laser-induced fluorescence,PLIF)技术具有分子量级的示踪能力,可获得界面气体浓度(摩尔分数)分布,为研究界面失稳混合问题提供了有力工具.在弱激波(Ma=1.25)冲击扩散型气柱界面实验中,采用PLIF技术对R-M失稳引起的SF6-Air界面混合问题进行了研究.通过改变椭圆形初始界面的长短轴比,得到了3种扩散型初始界面失稳演化过程中气体摩尔分数,观察到了斜压机制下界面的简单拉伸、二次不稳定性、挤压射流等现象.利用浓度分布进一步得到了界面的瞬时混合率,通过瞬时混合率、界面整体平均混合率以及混合率的概率密度分布,分析了界面在不同演化阶段的界面混合特征,初步讨论了界面失稳混合的机制.演化初期,界面在斜压涡的作用下发生拉伸卷曲,通过增大浓度梯度来促进界面的混合.当演化进一步发展,二次不稳定性出现后,界面通过小尺度对流的方式达到湍流混合状态,而浓度梯度驱使的分子间混合逐渐减弱.由浓度梯度引起的扩散与由二次不稳定性引起的对流存在着"竞争"关系,二者共同主导了界面的混合.     

Acoustic sounding of perforated wellbores by short waves

The reflection and transmission of harmonic waves and waves of finite duration through the boundary of the perforated zone of a cased wellbore filled with a fluid are studied. A model of the plane fluid flow in the well (in a quasi-one-dimensional approximation) and filtration absorption of the fluid by the porous medium surrounding the well is proposed. The effect of the quality of the perforation (length of perforation tunnels) on the evolution of the waves reflected from the boundary of the perforated zone of the well is studied.     

On the evolution of large scale structures in three-dimensional mixing layers

In this paper, several mathematical models for the large scale structures in some special kinds of mixing layers, which might be practically useful for enhancing the mixing, are proposed. First, the linear growth rate of the large scale structures in the mixing layers was calculated. Then, using the much improved weakly non-linear theory, combined with the energy method, the non-linear evolution of large scale structures in two special mixing layer configurations is calculated. One of the mixing layers has equal magnitudes of the upstream velocity vectors, while the angles between the velocity vectors and the trailing edge were π/2-φ and π/2+φ, respectively. The other mixing layer was generated by a splitter-plate with a 45-degree-sweep trailing edge. The project supported by the National Natural Science Foundation of China (19642001) and Deutsche Forschungsgemeinschaft (DFG)     

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。     

Mixing dynamics of a vapor-condensate cloud with the ambient air

The mixing of a wet vapor with a gas is studied using analytical and numerical models. The one-dimensional problem of diffusion mixing accompanied by phase transitions is solved in a self-similar formulation. The versions of mixing of the vapor with a cold and warm gas and with a superheated vapor are analyzed. The atmospheric diffusion of immediate emissions containing water vapor and condensate is modeled numerically in a three-dimensional formulation. A study is made of the evolution of hydrodynamic, concentration, and temperature fields as a function of the initial emission parameters (temperature and humidity) and ambient air parameters. __________ Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, Vol. 49, No. 3, pp. 114–127, May–June, 2008.     

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].     

Study of the membrane effect on turbulent mixing measurements in shock tubes

The effect of the thin membrane on the time evolution of the shock wave induced turbulent mixing between the two gases initially separated by it is investigated using two different sets of experiments. In the first set, in which a single-mode large-amplitude initial perturbation was studied, two gas combinations (air/SF and air/air) and two membrane thicknesses were used. The main conclusion of these experiments was that the tested membrane has a negligible effect on the evolution of the mixing zone, which evolves as predicted theoretically. In the second set, in which similar gas combinations and membrane thicknesses were used, small amplitude random-mode initial perturbation, caused by the membrane rupture, rather than the large amplitude single-mode initial perturbation used in the first set, was studied. The conclusions of these experiments were: (1) The membrane has a significant effect on the mixing zone during the initial stages of its growth. This has also been observed in the air/air experiment where theoretically no growth should exist. (2) The membrane effect on the late time evolution, where the mixing zone width has reached a relatively large-amplitude, was relatively small and in good agreement with full numerical simulations. The main conclusion from the present experiments is that the effect of the membrane is important only during the initial stages of the evolution (before the re-shock), when the perturbations have very small amplitudes, and is negligible when the perturbations reach relatively large amplitudes. Received 29 August 1998 / Accepted 25 December 1998     

Development of the Rayleigh–Taylor instability due to interaction of a diffusion mixing layer of two gases with compression waves

A mathematical model of mechanics of a two-velocity and two-temperature mixture of gases is developed. Based on this model, the evolution of the mixing layer of two gases of different densities, which are accelerated by a compression wave, is considered by methods of numerical simulation. A solution of an initial-boundary problem is obtained in a one-dimensional approximation. This solution describes the formation of a diffusion layer between the two gases. The problem of interaction of this layer with the compression wave, the heavy medium being accelerated by the light medium, is solved numerically. Problems of instability development in a sine-perturbed mixing layer accelerated by a compression wave are solved numerically in a two-dimensional unsteady formulation. The calculated width of the mixing region is in reasonable agreement with experimental data.     

High-resolution measurements of two-dimensional instabilities and turbulence transition in plane mixing layers

 High-resolution two-dimensional (2D) measurements on a large plane mixing layer provide new quantitative information of its spatial and temporal evolution to turbulence. Periodic acoustic excitation with three frequencies was used to stabilize the fundamental instability of the mixing layer (roll-up) and its first and second subharmonics (vortex pairings). Phase-locked velocity measurements of the time evolution in 2D space (x, y, t) reveal accurate spatially resolved primary (2D) instabilities of the mixing layer and turbulence transition. The measurements unveil new quantitative details of the initial Kelvin–Helmholtz waves and their spatial and temporal evolution into vortex shedding and the effect of the second subharmonic on the first vortex pairing. The second-subharmonic effect hastens alternate first pairings of the rollers, with the result that pairing is completed at two downstream locations. The pairings that occur closer to the knife-edge are more organized (laminar) than those occurring farther downstream (transitional). This effect is corroborated using Taylor’s hypothesis to compute the vorticity distributions from the measured velocity field and a pseudo-spectral simulation of the temporal evolution of the mixing layer. Received: 26 March 1998/Accepted: 2 March 1999     

用格子Boltzmann方法数值模拟混合层中旋涡的合并过程

用格子Boltzmann方法计算混合层中的流动问题。在流场的入口处加不同频率、振幅和相位的小扰动,观察混合层中旋涡的演进机理,模拟二维混合层中旋涡合并现象。在基本扰动波的基础上,又加入频率为基本波频率一半的亚谐波,得到了两个涡合并的计算结果,当加入的亚谐波频率为基本波频率的三分之一时,得到了三个涡合并的计算结果。这些计算结果与已有文献的结果基本一致,显示用格子Boltzmann方法模拟混合层问题是可行的。     

Eulerian-Lagranigan simulation of aerosol evolution in turbulent mixing layer

The formation and evolution of aerosol in turbulent flows are ubiquitous in both industrial processes and nature. The intricate interaction of turbulent mixing and aerosol evolution in a canonical turbulent mixing layer was investigated by a direct numerical simulation (DNS) in a recent study (Zhou, K., Attili, A., Alshaarawi, A., and Bisetti, F. Simulation of aerosol nucleation and growth in a turbulent mixing layer. Physics of Fluids, 26, 065106 (2014)). In this work, Monte Carlo (MC) simulation of aerosol evolution is carried out along Lagrangian trajectories obtained in the previous simulation, in order to quantify the error of the moment method used in the previous simulation. Moreover, the particle size distribution (PSD), not available in the previous works, is also investigated. Along a fluid parcel moving through the turbulent flow, temperature and vapor concentration exhibit complex fluctuations, triggering complicate aerosol processes and rendering complex PSD. However, the mean PSD is found to be bi-modal in most of the mixing layer except that a tri-modal distribution is found in the turbulent transition region. The simulated PSDs agree with the experiment observations available in the literature. A different explanation on the formation of such PSDs is provided.     

Turbulent Dynamics of a Critically Reflecting Internal Gravity Wave

Results from computational fluid dynamics experiments of internal wave reflection from sloping boundaries are presented. In these experiments the incident wave lies in a plane normal to the slope. When the angle of wave energy propagation is close to the bottom slope the reflection causes wave breakdown into a quasi-periodic, turbulent boundary layer. Boundary layer energetics and vorticity dynamics are examined and indicate the importance of the three-dimensional turbulence. The boundary layer exhibits intermittent turbulence: approximately every 1.2 wave periods the boundary layer mixes energetically for a duration of about one-third of a wave period, and then it restratifies until the next mixing event. Throughout the wave cycle a strong thermal front is observed to move upslope at the phase speed of the incident waves. Simulations demonstrate that the net effects of turbulent mixing are not confined to the boundary layer, but are communicated to the interior stratified fluid by motions induced by buoyancy effects and by the wave field, resulting in progressive weakening of the background density gradient. Transition to turbulence is determined to occur at Reynolds numbers of approximately 1500, based upon the wavelength and maximum current velocity of the oncoming wave train. The boundary layer thickness depends on the Reynolds number for low Richardson numbers, with a characteristic depth of approximately one-half of the vertical wavelength of the oncoming wave. Received 21 May 1997 and accepted 14 October 1997     

Modeling transonic weakly underexpanded turbulent jets

The results of the calculations of model and actual turbulent jet flows with shock waves at low supersonic Mach numbers are presented. The gasdynamic flow features characterizing shock reflection from a mixing layer are analyzed. A possible version of the modified model for the turbulent viscosity is proposed; the model makes it possible to improve the prediction of the shock (rarefaction wave) intensity distribution along jet flows.     

A mixing layer in a homogeneous fluid

A mathematical model for the evolution of a mixing layer in shear flows is constructed. The problem of a mixing layer with pressure gradient is solved: in particular, the distributions of the velocity and basic characteristics of turbulent flow in the mixing layer are obtained. Lavrent'ev Institute of Hydrodynamics, Siberian Division, Russian Academy of Sciences, Novosibirsk 630090. Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, Vol. 41, No. 4, pp. 81–92, July–August, 2000.