Simulated X-ray spectra from ionized wind-blown nebulae around massive stars

Using an ionization gas dynamics code, we simulate a model of the wind-blown bubble around a 40 M_⊙ star. We use this to compute the X-ray spectra from the bubble, which can be directly compared to observations. We outline our methods and techniques for these computations, and contrast them with previous calculations. Our simulated X-ray spectra compare reasonably well with observed spectra of Wolf–Rayet bubbles. They suggest that X-ray nebulae around massive stars may not be easily detectable, consistent with observations.     

Feasibility study of the standing accretion shock instability experiment at the National Ignition Facility

The primary hydrodynamic flow feature of early explosion phases of a core-collapse supernova is a spherical shock. This shock is born deep in the central regions of the collapsing stellar core, stalls shortly afterward, and in case of a successful explosion is revived and becomes the supernova shock. The revival process involves a standing accretion shock instability, SASI. This shock instability is considered the key processes aiding the core-collapse supernova (ccSN) explosion.The aim of our study is to identify feasible conditions and parameters for an experimental system that is able to capture the essential characteristics of SASI. We use semi-analytic methods and high-resolution hydrodynamic simulations in multidimensions to investigate a possible experimental design on the National Ignition Facility. The experimental configuration involves a steady, spherical shock. We explore a viable region of parameters and obtain limits on the shocked flow geometry. We study the stability properties of the shock and its post-shock region.We compare properties of the experimental design and the ccSN environment. The obtained model experimental flow field closely resembles converging nozzle flow. The post-shock region, in contrast to the supernova setting, is found to be stably stratified and stable against to perturbations upstream of the shock. We conclude that it is not possible to capture the characteristics of the ccSN SASI for the converging shocked flow configuration considered here. However, such configuration offers a very stable setting for precision studies of dense, high-temperature plasmas requiring finely-controlled conditions and long lifetimes.     

Jet formation in shock-heavy gas bubble interaction

The influences of the acoustic impedance and shock strength on the jet formation in shock-heavy gas bubble interaction are numerically studied in this work. The process of a shock interacting with a krypton or a SF 6 bubble is studied by the numerical method VAS2D. As a validation, the experiments of a SF 6 bubble accelerated by a planar shock were performed. The results indicate that, due to the mismatch of acoustic impedance, the way of jet formation in heavy gas bubble with different species is diversified under the same initial condition. With respect to the same bubble, the manner of jet formation is also distinctly different under different shock strengths. The disparities of the acoustic impedance result in different effects of shock focusing in the bubble, and different behaviors of shock wave inside and outside the bubble. The analyses of the wave pattern and the pressure variation indicate that the jet formation is closely associated with the pressure perturbation. Moreover, the analysis of the vorticity deposition, and comparisons of circulation and baroclinic torque show that the baroclinic vorticity also contributes to the jet formation. It is concluded that the pressure perturbation and baroclinic vorticity deposition are the two dominant factors for the jet formation in shock-heavy gas bubble interaction.     

Dependence between the shock and the separation bubble in a shock wave boundary layer interaction

We present experimental results obtained in a turbulent boundary layer at a Mach number of 2.3 impinged by an oblique shock wave. Strong unsteadiness is developed in the interaction, involving several frequency ranges which can extend over two orders of magnitude. In this paper, attention is focused on the links between the low-frequency shock motions and the separation bubble, in particular phase relationships are evaluated. An interpretation based on a simple scheme of the streamwise evolution of the instantaneous pressure is proposed. As it is mainly based on the pressure signal properties inside the region of the shock oscillation, it may be expected that it will still be relevant for different configurations of shock-induced separation as compression ramp, blunt bodies, or over expanded nozzles.     

Shock-unsteadiness model applied to oblique shock wave/turbulent boundary-layer interaction

Reynolds-averaged Navier–Stokes prediction of shock wave/turbulent boundary layer interactions can yield significant error in terms of the size of the separation bubble. In many applications, this can alter the shock structure and the resulting surface properties. Shock-unsteadiness modification of Sinha et al. (Physics of Fluids, Vol.15, No.8, 2003) has shown potential in improving separation bubble prediction in compression corner flows. In this article, the modification is applied to oblique shock wave interacting with a turbulent boundary layer. The challenges involved in the implementation of the shock-unsteadiness correction in the presence of multiple shock waves and expansion fans are addressed in detail. The results show that a robust implementation of the model yields appreciable improvement over standard k–ω turbulence model predictions.     

Radiation hydrodynamics of supernova shock breakouts

The first powerful burst of photon radiation in a supernova appears when the shock front is a few photon mean-free paths below the star photosphere. This is called “shock breakout” and it is the first observable event after the neutrino and gravitational wave bursts in core-collapsing supernovae. Any early information about collapse is vitally important for understanding the physics of explosion, constraining speed of neutrino propagation etc. Direct observations of shock breakouts have been carried out in a few supernovae. We discuss some puzzles related to those objects. Finally, we describe our current understanding of the most luminous (hyper-)supernovae. Their long living radiative shocks pause many interesting problems in numerical and laboratory astrophysics and may have important applications in cosmology.     

Amplification of shock waves in a bubble-filled liquid with gas concentration gradient

The properties are studied of the propagation of unsteady shock waves in a gas-liquid system of bubble structure in the case when the volume concentration of the gas changes in the direction of motion of the shock wave. It is established that when there is a sufficiently rapid drop in the gas content, an effect of amplification of the shock wave is observed which is due to the deceleration of the medium behind the shock wave. A study is made of the laws of the evolution of long- and short-wave pulsed perturbations in such systems. The authors consider processes of reflection of waves from obstacles and their passage from a gas into a bubble liquid, from a two-phase mixture into a pure liquid. The contribution is determined of nonequilibrium effects to the process of amplification of a wave.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 1, pp. 49–54, January–February, 1988.The authors wish to express gratitude to R. I. Nigmatulin for his interest in the study and for useful discussions.     

Formation and Amplification of Shock Waves in a Bubble “Cord”

The structure and dynamics of the wave field generated by a bubble system in the form of an axial bubble cylinder (cord) excited by a plane shock wave propagating along the axis in an axisymmetric shock tube are numerically examined. It is shown that consecutive excitation of oscillations of the bubble zone results in formation of a quasi-steady shock wave in the cord and in the ambient liquid. Results of the numerical analysis of the maximum amplitude of the resulting wave as a function of problems parameters are described.__________Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, Vol. 46, No. 5, pp. 46–52, September–October, 2005.     

自由场中液氮单空泡动力学特性的实验研究

本文专门设计搭建了低温介质空泡演化实验测试平台, 对液氮单空泡非定常演化过程和动力学特性开展了实验研究. 实验中利用电火花瞬态放电激发液氮汽化形成单空泡, 通过高速摄影系统对单空泡的瞬态特征进行了精细化捕捉. 为了进一步揭示低温介质独特的物理性质以及强热力学效应对单空泡演化过程的影响机制, 对比分析了在相同环境压力下, 77.41 K液氮和298.36 K水单空泡的演化过程和动力学特性. 基于实验得到空泡半径与界面速度等定量数据, 阐明了液氮单空泡球形与非球形演化阶段的非定常特性. 研究结果表明: (1) 在相同输入电压下, 液氮单空泡的整体尺寸比常温水更小, 当输入电压为400 V时, 液氮空泡的最大半径约为常温水空泡的0.69倍; 同时, 液氮单空泡经历了膨胀阶段?收缩阶段?振荡阶段以及上升阶段的演化过程. (2)液氮空泡的收缩过程主要由相界面的热传导主导, 没有明显的塌陷现象, 收缩阶段液氮空泡的最小收缩半径约为常温水的5.5倍. (3)在液氮空泡振荡初期, 空泡相界面传热增强, Rayleigh-Taylor不稳定与热力学效应共同引起了空泡界面的表面粗化效应; 在整个振荡阶段, 空泡界面附近存在破碎的小泡. 当输入电压较高时, 空泡底部的小泡数量显著增多. (4)由于液氮空泡浮力系数较大, 液氮空泡在演化后期空泡整体向上迁移显著, 液氮空泡底部收缩更快产生凹陷, 促使空泡变为环状.      

柱形汇聚激波冲击球形重气体界面的实验研究

采用高速纹影法实验研究了柱形汇聚激波与球形重气体界面相互作用的 Richtmyer-Meshkov不稳定性问题. 激波管实验段基于激波动力学理论设计, 将马赫数为1.2 的平面激波转化为柱形汇聚激波, 气体界面由肥皂膜分隔六氟化硫(内)和空气(外)得到. 采用高速摄影机在单次实验中拍摄激波运动的全过程, 对柱形激波的形成进行了实验验证, 并进一步观测了汇聚激波与球形气体界面相互作用过程中的波系发展和气体界面变形以及反射激波同已变形界面二次作用的流场演化. 结果表明: 当柱形汇聚激波穿过气泡界面以后, 气泡左侧界面极点沿激波传播方向保持匀速运动, 气泡右侧界面发展成为射流结构, 气泡主体发展成为涡环结构; 在反射激波的二次作用下, 流场中无序运动显著增强并很快进入湍流混合阶段.     

Cavitation phenomena in extracorporeal microexplosion lithotripsy

An experimental investigation was made of cavitation phenomena induced by underwater shock wave focusing applied to the extracorporeal microexplosion lithotripsy (microexplosion ESWL). Firstly an underwater microexplosion generated by detonation of a 10 mg silver azide pellet was studied and secondly underwater shock focusing and its induced cavitation phenomena were investgated. Underwater shock wave was focused by using a semi-ellipsoidal reflector in which a shock wave generated at the first focal point of the reflector was reflected and focused at the second focal point. It is found that an explosion product gas bubble did not produce any distinct rebound shocks. Meantime cavitation appeared after shock focusing at the second focal point where expansion waves originated at the exit of the reflector were simultaneously collected. A shock/bubble interaction is found to contribute not only to urinary tract stone disintegration but also tissue damage. The cavitation effect associated with the microexplosion ESWL was weaker in comparison with a spark discharge ESWL. The microexplosion ESWL is an effective method which can minimize the number of shock exposures hence decreasing tissue damage by conducting precise positioning of urinary tract stones.This article was processed using Springer-Verlag T_EX Shock Waves macro package 1.0 and the AMS fonts, developed by the American Mathematical Society.     

Level set method for numerical simulation of a cavitation bubble,its growth,collapse and rebound near a rigid wall

A level set method of non-uniform grids is used to simulate the whole evolution of a cavitation bubble, including its growth, collapse and rebound near a rigid wall. Single-phase Navier–Stokes equation in the liquid region is solved by MAC projection algorithm combined with second-order ENO scheme for the advection terms. The moving interface is captured by the level set function, and the interface velocity is resolved by “one-side” velocity extension from the liquid region to the bubble region, complementing the second-order weighted least squares method across the interface and projection inside bubble. The use of non-uniform grid overcomes the difficulty caused by the large computational domain and very small bubble size. The computation is very stable without suffering from large flow-field gradients, and the results are in good agreements with other studies. The bubble interface kinematics, dynamics and its effect on the wall are highlighted, which shows that the code can effectively capture the “shock wave”-like pressure and velocity at jet impact, toroidal bubble, and complicated pressure structure with peak, plateau and valley in the later stage of bubble oscillating. The project supported by the National Natural Science Foundation of China (10272032 and 10672043). The English text was polished by Keren Wang.     

Dynamics and radiation of a single bubble under conditions of abnormal compressibility of a bubbly liquid

An equation is proposed for the pulsation of a single cavity in an abnormally compressible bubbly liquid which is in pressure equilibrium and whose state is described by the Lyakhov equation. In the equilibrium case, this equation is significantly simplified. Numerical analysis is performed of the bubble dynamics and acoustic losses (the profile and amplitude of the radiation wave generated on the bubble wall from the side of the liquid). It is shown that as the volumetric gas concentration k₀ in the equilibrium bubbly medium increases, the degree of compression of the cavity by stationary shock wave decreases and its pulsations decrease considerably and disappear already at k₀ = 3%. In the compression process, the cavity asymptotically reaches an equilibrium state that does not depend on the value of k₀ and is determined only by the shock-wave amplitude. The radiation wave takes the shape of a soliton whose amplitude is much smaller and whose width is considerably greater than the corresponding parameters in a single-phase liquid. __________ Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, Vol. 48, No. 3, pp. 51–57, May–June, 2007.     

The problem of a gas bubble in plane ideal fluid flow

We study the problem of two-dimensional fluid flow past a gas bubble adjacent to an infinite rectilinear solid wall.Two-dimensional ideal fluid flow past a gas bubble on whose boundary surface-tension forces act (or a gas bubble bounded by an elastic film) has been studied by several authors. Zhukovskii, who first studied jet flows with consideration of the capillary forces, constructed an exact solution of the problem of symmetric flow past a gas bubble in a rectilinear channel [1]. However, Zhukovskii's solution is not the general solution of the problem; in particular, we cannot obtain the flow past an isolated bubble from his solution. Slezkin [2] reduced the problem of symmetric flow of an infinite fluid stream past a bubble to the study of a nonlinear integral equation. The numerical solution of this problem has recently been found by Petrova [3]. McLeod [4] obtained an exact solution under the assumption that the gas pressure p₁ in the bubble equals the flow stagnation pressure p₀. Beyer [5] proved the existence of a solution to the problem of flow of a stream having a given velocity circulation provided p₁p₀.We examine the problem of two-dimensional ideal fluid flow past a gas bubble adjacent to an infinite rectilinear solid wall. The solution depends on the value of the contact angle . The existence of a solution is proved in some range of variation of the parameters, and a technique for finding this solution is given. The situation in which =1/2 is studied in detail.     

自由场空泡溃灭过程能量转化机制研究

综合应用实验与数值模拟方法, 深入讨论了自由场空泡溃灭过程中的能量转化机制. 在实验研究中, 应用纹影法记录了空泡溃灭的演变过程, 提取了空泡在溃灭过程中的半径, 溃灭速度等数据, 结合空泡势能和动能方程, 描述了空泡能量的转化过程. 在开展数值模拟分析时, 运用弱可压缩流体质量守恒方程和动量方程, 建立了三维数值模型用以模拟空泡在自由场中的溃灭过程, 并且由结果中获取了空泡溃灭过程中的压力及速度变化规律, 揭示了空泡在溃灭过程中能量转化机制. 研究结果表明: (1) 自由场空泡在溃灭过程中, 空泡势能与空泡半径具有相同的演化趋势, 空泡动能与势能变化趋势相反; 当空泡达到最大半径处时, 空泡势能最大, 流场动能为零. (2) 溃灭后期在空泡周围会形成高压区域, 该区域的压力梯度与速度梯度较高, 随着空泡收缩, 高压区域面积逐渐减小. (3) 空泡在自由场中发生溃灭时, 空泡势能不断转化为流场动能, 在溃灭时刻可以明显观察到冲击波现象, 空泡的大部分能量会在此时转化为冲击波的波能.      

A design of a two-dimensional,multimode RM experiment on OMEGA-EP

An experiment, meant to investigate the evolution of Richtmyer–Meshkov (RM) instability in the bubble merger regime and at low Atwood number (A～0.3), is proposed and theoretically analyzed. This experiment is intended to provide a direct measurement of the two-dimensional bubble-front shape and spectrum evolution in time, along with the power-law coefficient for bubble-front growth (θ_b). It is unique in its use of a well-characterized two-dimensional initial perturbation, allowing controlled initiation and growth of the instability. The proposed design assures a significant time scale of steady RM conditions, taking advantage of the long drive (～30 ns) available on the OMEGA-EP laser facility, along with neither a Rayleigh–Taylor (RT) component nor shock-proximity effects, due to the use of a light to heavy configuration. Multimode RM growth for the proposed configuration has been analyzed using two-dimensional, direct numerical simulations, showing significant mode coupling and convergence to power-law growth of the bubble front. The effects of two-dimensional rarefactions were also investigated, and it was found that they introduce no major uncertainties or hazards to the physics. An experiment of this kind has not yet been performed, and therefore would serve to validate numerical results and analytical models presented in literature.     

Dynamics of soluble gas bubbles

The problem of the mass, thermal and dynamic interaction between a bubble containing a soluble gas and a liquid is considered. It is shown that this problem can be reduced to the problem of the behavior of a vapor bubble with phase transitions investigated in detail in [1–3]. Expressions are obtained for the rate of decay of the radially symmetric oscillations of the bubbles due to the solubility of the gas in the liquid. The effective coefficients of mass transfer between the radially pulsating bubbles and the liquid are determined. A numerical solution is obtained for the problem of the radial motion of a bubble created by a sudden change of pressure in the liquid which, in particular, corresponds to the behavior of the bubbles behind the shock front when a shock wave enters a bubble screen.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 6, pp. 52–59, November–December, 1985.     

Effect of Bubble Injection Pattern on the Bubble Size Distribution in a Gas-Solid Fluidized Bed

Three different bubble injection patterns including uniform, center oriented and corner oriented injection patterns over the gas distributor have been studied using a discrete bubble model in a 2-D gas solid fluidized bed. The results show that the bubble size and size distribution evolution through the bed are almost the same for uniform and corner oriented bubble injection patterns, but for the case of center oriented injection pattern, the area weighted average bubble diameter (d _b,21) is greater than the others. The results show that in the center oriented injection pattern, many of the small bubbles leave the bed without coalescence and this leads to smaller d _b,10 than two other cases. Moreover, in this work the size distribution evolution through the bed height is investigated in detail.     

Effect of thermal diffusion and electrostatic force on evolution of wind-blown sand flow

A theoretical model is suggested to mathematically describe the effect of thermal diffusion from a sand-bed on evolution of a wind-blown sand flow.An upward wind field is engendered by the thermal diffusion and the coupling interaction among the horizontal and upward wind flow,saltating grains,and a kind of electrostatic force exerted on the grains are considered in this theoretical model.The numerical results show that the effect of the thermal diffusion on the evolution process of wind-blown grain flow is quite obvious and very similar to the effect of the electrostatic force on the evolution.Not only the time for the entire system to reach a steady state(called the duration time),the transport rate of grains,the mass-flux profiles and the trajectory of saltating grains are affected by the thermal diffusion and the electrostatic force exerted on saltating grains, but also the wind profiles and the temperature profiles at the steady state are affected by the wind-blown sand flow.