Shock waves in three-dimensional transonic flow with weak spatial heat release

The presence or absence of shock waves in the case of weak 3D heat release to homogeneous uniform transonic gas flow is analyzed. It is well known that shock waves can exist in a steady-state flow in the 2D case for a small transonic similarity number. It is shown that in the main approximation, shock waves are absent in the axisymmetric and 3D versions. In the next approximation, in which the logarithm factor of a small parameter is absent, shock waves can exist.     

化学激光器用文氏咀流场特性的数值模拟

 基于现有的文氏咀流量供给管道,提取出轴对称2维计算模型,计算了不同背压下文氏咀及下游管道的流场特性。计算结果显示,随着背压的升高,激波在管道内经历了3种状态,在直管道内为斜激波,到转接段时为拟正激波,进入文氏咀后则为正激波。在进行文氏咀流量计的设计时,应尽量将正激波控制在文氏咀喉道或向下游延伸的一小段距离内,此时是文氏咀的最佳工作状态。另外,采用壁面开孔法在文氏咀下游选取测压点时,为了准确测量截面上的静压,应将测压点选取在距离直管道入口数倍管径处,一般不低于8倍管径。     

Disappearance of holographic and interference fringes accompanies optical diagnostics of a supersonic bow shock flow

Preliminary results of optical diagnostics of bow shocks in a supersonic wind tunnel by applying dual-hologram shear interferometry technique are discussed. A strong refraction effect of the probing beam penetrating a region in the vicinity of a bow shock over a blunt nose cone model has been discovered. On a signal hologram the effect leads to the disappearance of holographic fringes in a narrow region attached to the shock wave front. A reconstructed interferogram in this region manifests the absence of an interference pattern.Computer simulations were performed for a part of the probing beam penetrating the area of high-density steep gradients of compressed air attached to the central part of the shock front of a bow shock. The compressed area was modeled as a hyperbolic cap. The bow shock was assumed axisymmetric. The simulations made it possible to evaluate angles of deflections and found conformity with reconstructed interferograms (shadowgraphs).It is concluded that in the above-indicated region of bow shocks probing light is deviated refractively into some angles, which could be large enough for light rays to be blocked out and never arrive at the detector (photo film). In the case when interferometric fringes disappear, the effect of strong refraction makes it impossible to measure air density gradients in some critical region.     

Shock-stable flux scheme for predicting aerodynamic heating load of hypersonic airliners

In the design of a hypersonic airliner that can considerably shorten the flight time, how to accurately predict the vehicle's aerodynamic heating loads is of great significance. In this study, a new shock-stable flux scheme called the simple low dissipation advection upwind splitting method(SLAU)-M1 is proposed for the prediction of hypersonic aerodynamic heating load. Based on the construction of the SLAU scheme for low-speed simulations, SLAU-M1 improves the robustness of the mass flux against shock instability. After validating the code employed, several numerical test cases are conducted. The onedimensional(1D) sod shock tube case and the two-dimensional(2D) inviscid NACA0012 airfoil case show that SLAU-M1 features a high level of accuracy at both low and high speeds. To simulate the hypersonic viscous flow over a blunt cone, we adopt different aspect ratios(ARs) of cells near the shock. The results suggest that SLAU-M1 is much less sensitive to the AR of cells near the shock in predicting hypersonic aerodynamic heating loads. Moreover, the findings show that the theoretical value is considerably better than that of the other schemes. The hypersonic viscous flow over a 2D double ellipsoid case and that over the Hypersonic Flight Experiment vehicle case also indicate that SLAU-M1 exhibits a considerably high level of accuracy in hypersonic heating predictions. These properties suggest that SLAU-M1 promises to be widely used in the accurate prediction of the aerodynamic heating loads of hypersonic airliners.     

Coherent vortices in strongly coupled liquids

Strongly coupled liquids are ubiquitous in both nature and laboratory plasma experiments. They are unique in the sense that their average potential energy per particle dominates over the average kinetic energy. Using "first principles" molecular dynamics (MD) simulations, we report for the first time the emergence of isolated coherent tripolar vortices from the evolution of axisymmetric flows in a prototype two-dimensional (2D) strongly coupled liquid, namely, the Yukawa liquid. Linear growth rates directly obtained from MD simulations are compared with a generalized hydrodynamic model. Our MD simulations reveal that the tripolar vortices persist over several turn over times and hence may be observed in strongly coupled liquids such as complex plasma, liquid metals and astrophysical systems such as white dwarfs and giant planetary interiors, thereby making the phenomenon universal.     

Effect of nose shape on the shock standoff distance at nearsonic flows

This paper describes a numerical solution of the bow shock shape ahead of some blunt and sharp axisymmetric noses containing sphere, blunt cone, and sharp cone at steady transonic flow in the Mach number range of 1.01 to 1.2. For validating the results, one sphere and three blunt cones are modeled, and their shock standoff distance is compared with other experimental and numerical studies. The flow over other noses with similar geometric parameters is then solved and compared with each other. In this study, the Reynolds-averaged Navier—Stokes equations are solved using the Spalart—Allmaras turbulence model. The purpose of this study is to determine the shock standoff distance for some blunt and sharp noses at low supersonic free flight speed. The shock standoff distance is determined from the Mach number curve on the symmetry line. The present numerical simulations reach down to M8=1.01 a range where it is almost very difficult to set in experimental studies. The shock wave locations were found to agree well with previous numerical and experimental studies. Our results are closer to the experimental results compared to other numerical studies. In addition, the results for shock standoff distances over paraboloids in these speed ranges have not been previously published as far as we know.     

Dynamic compaction of copper powder: 2D numerical simulation and experimental results

Abstract

A method for plate-impact dynamic compaction of copper powder has been developped. The optimization of the experimental set-up (impedance adjustments, tensile wave traps, relative thickness of impactor and target,…) is presented.

2D axisymetrical numerical simulations have been performed with a Lagrangian finite element code. Geometrical characteristics of the experimental set-up as well as the dynamic response of the powder (Reaugh equation of state) and of the material of the set-up have been taken into account. These simulations show that, due to the difference in shock velocities in the container and in the powder, the powder is submitted to 2D loading waves. As a matter of fact the powder may be loaded by a non-planar shock wave propagating in the as-expected direction, as well as by a sweeping wave initiated at the bottom of the powder container, and propagating obliquely from the bottom-up. This second wave loads the bottom of the powder first. The influence of the impactor thickness as well as its material on the shock front shape and on the shock density-pressure history of the material has been studied. 1D simulations are shown not to evaluate properly the stress history and the energy deposition in the powder sample.

Metallographic observations as well as X-ray tomography experiments have been performed on consolidated samples. A very good agreement has been found between results of 2D numerical simulations and the observed final shape and density maps of the samples. The shape of deformed powder particles are also in agreement with the expected shock history.     

纳米多晶铜中冲击波阵面的分子动力学研究

冲击波阵面反映材料在冲击压缩下的弹塑性变形行为以及屈服强度、应变率条件等宏观量, 还与冲击压缩后的强度变化联系. 本文使用分子动力学方法, 模拟研究了冲击压缩下纳米多晶铜中的动态塑性变形过程, 考察了冲击波阵面和弹塑性机理对晶界存在的依赖, 并与纳米多晶铝的冲击压缩进行了比较. 研究发现: 相比晶界对纳米多晶铝的贡献而言, 纳米多晶铜中晶界对冲击波阵面宽度的影响较小; 并且其塑性变形机理主要以不全位错的发射和传播为主, 很少观察到全位错和形变孪晶的出现. 模拟还发现纳米多晶铜的冲击波阵面宽度随着冲击应力的增加而减小, 并得到了冲击波阵面宽度与冲击应力之间的定量反比关系, 该定量关系与他人纳米多晶铜模拟结果相近, 而与粗晶铜的冲击压缩实验结果相差较大.     

Matter Effects on Neutrino Oscillations in Different Supernova Models

In recent years,with the development of simulations about supernova explosion,we have a better understanding about the density profiles and the shock waves in supernovae than before.There might be a reverse shock wave,another sudden change of density except the forward shock wave,or even no shock wave,emerging in the supernova.Instead of using the expression of the crossing probability at the high resonance,PH,we have studied the matter effects on neutrino oscillations in different supernova models.In detail,we have calculated the survival probability of νe(P_s)and the conversion probability of ν_x(P_c) in the Schrodinger equation within a simplified two-flavor framework for a certain case,in which the neutrino transfers through the supernova matter from an initial flavor eigenstate located at the core of the supernova.Our calculations was based on the data of density in three different supernova models obtained from simulations.In our work,we do not steepen the density gradient around the border of the shock wave,which differs to what was done in most of the other simulations.It is found that the mass and the density distribution of the supernova do make a difference on the behavior of P_s and P_c.With the results of P_s and P_c,we can estimate the number of νe(and ν_x) remained in the beam after they go through the matter in the supernova.     

Three-dimensional reactive shock bifurcations

We model interactions of a premixed flame with incident and reflected shocks in a rectangular shock tube using three-dimensional (3D) reactive Navier–Stokes numerical simulations. Shock-flame interactions occur in the presence of boundary layers that cause the reflected shock to bifurcate and form a reactive shock bifurcation (RSB), which contains a flame in the recirculation zone behind the oblique shock. The recirculation zone acts as a flame holder thus attaching the flame to the shock in the vicinity of the wall, and providing a mechanism for a detonationless supersonic flame spread. The accelerated burning induced by an RSB, and Mach stems that may result from RSB–RSB interactions, promote hot-spot formation, and eventually accelerate deflagration-to-detonation transition. Schlieren-type images generated from the simulation results show that the 3D structure of an RSB may not always be easily recognized in experiments if the RSB is attached to the surface of the observation window. The main 3D effect observed in the simulations is caused by the presence of the second no-slip wall in a 3D rectangular channel. Two RSBs that form at adjacent walls interact with each other and produce an oblique Mach stem between two oblique shocks. The oblique Mach stems then interacts with a central Mach stem that forms near symmetry plane, and this interaction creates a hot-spot that leads to a detonation initiation.     

斜激波与轴对称边界层干扰的数值模拟

使用两方程Menter-SST模型, 对来流Mach数为3时的斜激波与轴对称边界层的相互干扰现象进行了数值模拟与定性、定量分析。研究了斜楔激波发生器楔角和来流单位Reynolds数变化对干扰区流动的影响, 总结了参数变化引起的流动分离变化规律; 此外, 还计算了与三维计算中心对称面上的入射激波等效的二维情形, 并将三维结果与二维情形进行对比, 对比结果显示中心对称面上的壁面压力系数、分离涡尺寸、涡量分布等与相应的二维情形存在明显差异。      

A numerical method for simulating the dynamics of 3D axisymmetric vesicles suspended in viscous flows

We extend [Shravan K. Veerapaneni, Denis Gueyffier, Denis Zorin, George Biros, A boundary integral method for simulating the dynamics of inextensible vesicles suspended in a viscous fluid in 2D, Journal of Computational Physics 228(7) (2009) 2334–2353] to the case of three-dimensional axisymmetric vesicles of spherical or toroidal topology immersed in viscous flows. Although the main components of the algorithm are similar in spirit to the 2D case—spectral approximation in space, semi-implicit time-stepping scheme—the main differences are that the bending and viscous force require new analysis, the linearization for the semi-implicit schemes must be rederived, a fully implicit scheme must be used for the toroidal topology to eliminate a CFL-type restriction and a novel numerical scheme for the evaluation of the 3D Stokes single layer potential on an axisymmetric surface is necessary to speed up the calculations. By introducing these novel components, we obtain a time-scheme that experimentally is unconditionally stable, has low cost per time step, and is third-order accurate in time. We present numerical results to analyze the cost and convergence rates of the scheme. To verify the solver, we compare it to a constrained variational approach to compute equilibrium shapes that does not involve interactions with a viscous fluid. To illustrate the applicability of method, we consider a few vesicle-flow interaction problems: the sedimentation of a vesicle, interactions of one and three vesicles with a background Poiseuille flow.     

Shock waves in capillary collapse of colloids: a model system for two-dimensional screened Newtonian gravity

Using Brownian dynamics simulations, density functional theory, and analytical perturbation theory we study the collapse of a patch of interfacially trapped, micrometer-sized colloidal particles, driven by long-ranged capillary attraction. This attraction is formally analogous to two-dimensional (2D) screened Newtonian gravity with the capillary length λ as the screening length. Whereas the limit λ→∞ corresponds to the global collapse of a self-gravitating fluid, for finite λ[over ^] we predict theoretically and observe in simulations a ringlike density peak at the outer rim of a disclike patch, moving as an inbound shock wave. Possible experimental realizations are discussed.     

Vortex stretching and reconnection in a compressible fluid

Vortex stretching in a compressible fluid is considered. Two-dimensional (2D) and axisymmetric cases are considered separately. The flows associated with the vortices are perpendicular to the plane of the uniform straining flows. Externally-imposed density build-up near the axis leads to enhanced compactness of the vortices — “dressed" vortices (in analogy to “dressed" charged particles in a dielectric system). The compressible vortex flow solutions in the 2D as well as axisymmetric cases identify a length scale relevant for the compressible case which leads to the Kadomtsev-Petviashvili spectrum for compressible turbulence. Vortex reconnection process in a compressible fluid is shown to be possible even in the inviscid case — compressibility leads to defreezing of vortex lines in the fluid.     

氧碘化学激光器中相位扰动的模拟研究

 建立了含相位扰动的1维流场3维物理光学负载光腔模型。选用折叠非稳腔，模拟计算了斜激波中心距光轴不同距离时以及不同强度的斜激波对腔内光场相位分布和输出功率的影响。研究表明激光输出光束质量与腔内激波的分布位置和激波的强度有密切关系，应该避免激波中心近光轴时的强扰动效应引起的光束质量退变。实验装置的计算结果再现了实验现象。     

On the penetration depth of a porous striker moving with a hypersonic velocity

By means of numerical simulation in the framework of the 2D axisymmetric problem of continuum mechanics, the penetration of elongated porous strikers into a steel obstacle under hydrodynamic conditions (the velocity of the striker at collision is several kilometers per second) is studied. It is found that the penetration depth of these strikers exceeds the value predicted from the hydrodynamic theory in the approximation of incompressible fluid. This increase is thought of as being associated with a change in the striker penetration mechanism because of formation of an attached shock. A simple model allowing prediction of the piercing power of elongated porous strikers is suggested.     

Shocks in non-loaded bead chains with impurities

We numerically investigate the problem of the propagation of a shock in an horizontal non-loaded granular chain with a bead interaction force exponent varying from unity to large values. When is close to unity we observed a cross-over between a nonlinearity-dominated regime and a solitonic one, the latest being the final steady state of the propagating wave. In the case of large values of the deformation field given by the numerical simulations is completely different from the one obtained by analytical calculation. In the following we studied the interaction of these shock waves with a mass impurity placed in the bead chain. Two different physical pictures emerge whether we consider a light or a heavy impurity mass. The scatter of the shock wave with a light impurity yields damped oscillations of the impurity which then behave as a solitary wave source. Differently an heavy impurity is just shifted by the shock and the transmitted wave loses its solitonic character being fragmented into waves of decreasing amplitudes. Received 23 June 1999     

Fluctuations of spherical waves in a turbulent atmosphere: effect of the axisymmetric approximation in computational methods

The validity of the axisymmetric parabolic-equation (PE) method for line-of-sight sound propagation in a turbulent atmosphere is investigated. The axisymmetric PE method is a finite-difference method for solving a 2D parabolic wave equation, which follows from the 3D wave equation by the assumption of axial symmetry around the vertical axis through the source. It is found that this axisymmetric approximation has a considerable spurious effect on the fluctuations of the sound field. This is concluded from analytical expressions for the log-amplitude and phase variances, derived both for isotropic turbulence and for axisymmetric turbulence. The expressions for axisymmetric turbulence are compared with the results of numerical computations with the PE method.     

Effect of the incident shock wave interacting with transversal jet flow on the mixing and combustion

The interaction between an incident shock wave and a transverse jet flow for mixing and combustion in a supersonic airstream was investigated experimentally and numerically. NO planar laser induced fluorescence (NO-PLIF) and particle imaging velocimetry (PIV) for non-reactive flows and three-dimensional reactive/non-reactive numerical simulations were conducted to examine the effect of the incident shock wave on the three-dimensional flow structure and mixing mechanism between the airstream and the injected gas downstream of the injection slot. Results of NO-PLIF measurement and numerical simulation showed that, in the case without the incident shock wave, injected gas is seldom seen in the recirculation zone just downstream of the injection slot, while the injected gas with higher concentration is almost uniformly distributed in the recirculation zone when the incident shock wave is introduced downstream of the injection slot. Moreover, it was shown by the numerical simulations that the profiles of the local equivalence ratio is in the combustible range due to the enhanced entrainment of the airstream when the incident shock wave is introduced downstream of the injection slot. A large-scale recirculation in the direction parallel to the wall is generated by the three-dimensional flow effects, which enhances the mixing and extends the residence time in the recirculation zone in the case with incident shock wave downstream of the injection slot, the recirculation flow being confirmed successfully by PIV measurements as well. The results of three-dimensional reactive numerical simulations were in good agreement with the experimental flame-holding characteristics at a lower total temperature, which showed that flame-holding can be attained only when the incident shock wave was introduced downstream of the injection slot, confirming that the formation of three-dimensional and large-scale recirculation flow downstream of the injection slot enlarges the recirculation zone and enhances the mixing to produce the conditions for robust flame-holding.     

A Roe Scheme for Ideal MHD Equations on 2D Adaptively Refined Triangular Grids

In this paper we present a second order finite volume method for the resolution of the bidimensional ideal MHD equations on adaptively refined triangular meshes. Our numerical flux function is based on a multidimensional extension of the Roe scheme proposed by Cargo and Gallice for the 1D MHD system. If the mesh is only composed of triangles, our scheme is proved to be weakly consistent with the condition …B=0. This property fails on a cartesian grid. The efficiency of our refinement procedure is shown on 2D MHD shock capturing simulations. Numerical results are compared in case of the interaction of a supersonic plasma with a cylinder on the adapted grid and several non-refined grids. We also present a mass loading simulation which corresponds to a 2D version of the interaction between the solar wind and a comet.