Attenuation of a shock wave passing through a cloud of water droplets

The mitigation of a planar shock wave caused by a cloud of calibrated water droplets was studied both experimentally and numerically. Experiments were carried out, with different shock wave Mach numbers ranging from 1.1 to 1.8, in a vertical shock tube coupled with a droplet generator which produced a well-characterized cloud of droplets of 120, 250 and 500 μm in diameter. By exploiting such an experimental set-up, we successfully measured the attenuation of a normal shock wave when passing through the water droplet cloud. This series of experiments allowed to identify the main parameters of this investigation and a clear dependence between the attenuation of the shock wave and terms governing the regimes of droplet breakup has been found. On the other hand, to support this experimental approach, 1D unsteady calculations were performed in similar configurations. Although the mathematical model based on an Eulerian/Eulerian approach was actually incomplete, the first comparisons between the experiments and the simulations were rather interesting and pointed out the need to improve the physical model, by taking into account the fragmentation and the vaporization of the droplets submitted to the shock wave as well as the size distribution of the water spray.     

Shock wave induced evaporation of water droplets in a gas-droplet mixture

A model is presented for the droplet evaporation process induced by a shock wave propagating in a fog. The model is based on the existence of a quasi-steady wet bulb state of the droplets during evaporation. It is shown that for moderate shock strength, Ma = < 2, and droplet radii in the range of 1–5 the, the major part of the evaporation process is governed by a balance between heat conduction and vapour diffusion. The formation of a fog by means of an unsteady adiabatic expansion of humid nitrogen is described. Experimental results of shock induced evaporation are shown for shock Mach numbers from 1.2 to 2.1, droplet mass fraction of 5 · 10^-3, and initial droplet radii of 1–1.4 m. The expected linear relation between droplet radius squared and time during evaporation is observed. Characteristic evaporation times appear to be strongly dependent on shock strength. A variation of about two decades, predicted by theory, was experimentally observed for the Mach number range studied.     

平面激波冲击并排液滴的三维数值模拟研究

采用三维守恒清晰界面数值方法, 研究平面激波冲击并排液滴的动力学过程. 研究的焦点在于激波接触液滴后的复杂波系结构生成, 以及并排液滴相互耦合作用诱导的单个液滴非对称界面演化. 首先, 分析并排液滴之间界面通道内的波系结构发展, 发现在冲击初期由于反射激波相交而形成新的反射激波以及马赫杆; 这些流动现象与液滴另外一侧 (非通道侧) 由激波反射所形成的弯曲波阵面截然不同, 而且所导致的液滴横向两侧流场差异是中后期冲击过程液滴两侧界面非对称演化的主要原因. 其次, 研究冲击中期时, 特别是入射激波已运动至液滴下游并远离并排液滴, 界面形态的演化过程和规律, 揭示通道下游出口处由于气流膨胀导致的界面闭合、以及随后气流阻塞导致的界面破碎等新的流动现象. 最后, 研究液滴间距对并排液滴相互作用的影响规律, 发现液滴间距大小与通道内压力峰值具有明显的关联关系. 研究表明, 更小的液滴间距不仅带来更大的压力峰值, 而且使得峰值出现的时间更早.      

液滴对爆炸冲击波的衰减作用

为分析液滴对舰船舱内爆炸冲击波的耗散与衰减作用,通过有限元分析方法,建立冲击波作用于不同尺寸单个液滴和多排液滴的模型,分析冲击波与单个及多个液滴的作用过程及液滴形态变化,对冲击波衰减规律进行分析总结。得到结论如下:单个液滴模型中,小液滴破碎更迅速,破碎的规律性强;大液滴抛撒现象发生较早,抛撒出的小液滴数目多,但整体变化规律性偏差;不同尺寸单个液滴对冲击波有一定的衰减作用,衰减率随液滴尺寸增大而增大,线性规律较明显;成排液滴对冲击波有明显的衰减作用,相同液滴密度下衰减率随着液滴数量的增多而增大,呈现明显的线性特性。     

Shock wave structure in a mixture of gas,vapour and droplets

The structure of the relaxation zone behind a shock wave of moderate strength in a mixture of gas, vapour and droplets is analysed. A model is presented for shock induced evaporation, which is based on wet-bulb equilibrium and on the absence of relative motion between droplets and gas. Experimental and numerical data on heterogeneous condensation induced by an unsteady rarefaction wave and on re-evaporation due to shock wave passage are reported for a mixture of water vapour, nitrogen gas and condensation nuclei. Pressure, temperature, saturation ratio and droplet size are experimentally obtained and are very well predicted by a numerical simulation based on the non-linear quasisteady wet-bulb model for phase transition, as well for the expansion wave as for the shock wave. During expansion, droplet number density decays much faster than predicted, which is not yet satisfactorily explained. Shock induced droplet evaporation is studied for post-shock saturation ratios ranging from 5×10^–3 to 0.2, corresponding to shock Mach numbers of 1.2 to 1.9. The evaporation times are well predicted by the theoretical model. No evidence is found for droplet break-up for Weber numbers up to 13, and droplet radii of the order of 1m.On leave at Institute of Fluid Science, Shock Wave Research Center, Tohoku University, Sendai 980, JapanThis article was processed using Springer-Verlag T_EX Shock Waves macro package 1.0 and the AMS fonts, developed by the American Mathematical Society.     

Optical measurement of velocity and drag coefficient of droplets accelerated by shock waves

The drag coefficient of micron-sized droplets accelerated by a shock wave has been investigated. The motion of the droplets was studied by an optical measurement system, and an inertial relaxation in the mist flow is discussed in detail. An expansion-shock tube was employed in the present experiment, in which water droplets were produced by a homogeneous condensation when humid nitrogen gas expanded adiabatically in the test section. The local mean diameter and local number density of the droplet cloud were 1.0 m and on the order of 10¹² particles/m³, respectively, as estimated using a light scattering measurement in a preliminary experiment. The droplet cloud accelerated behind a shock wave was observed using a direct shadowgraph method with a spatial filter. Since the intensity of transmitted light through the mist flow is a function of the radius and number density of droplets, we can obtain the locally averaged number density distribution under an adequate approximation. The transmitted light intensity was related to the velocity distribution of droplets under the adequate assumption. So, the acceleration of droplets was estimated from the velocity ratio between the droplets and gas flow. Then, the drag coefficient was calculated for the particle Reynolds number. The experimental result was also compared to a numerical prediction.     

Numerical modelling of film cooling with and without mist injection

Two-phase CFD calculations, using a Lagrangian model and commercial code Fluent 6.2.16, were employed to calculate the gas and droplet flows and film cooling effectiveness with and without mist on a flat plate. Two different three dimensional geometries are generated and the effects of the geometrical shape, size of droplets, mist concentration in the coolant flow and temperature of mainstream flow for different blowing ratios are studied. A cylindrical and laterally diffused hole with a streamwise angle of 30° and spanwise angle of 0° are used. The diameter of film cooling (d) hole, and the hole length to diameter ratio (L/d) for both of geometries are 10 mm and 4, respectively. Also the blowing ratio ranges from 1.0 to 2.0, and the mainstream Reynolds number based on the mainstream velocity and hole diameter (Re _d) is 6,219. The results are shown for different droplets diameters (1–10 μm), concentrations (1–5%) and mainstream temperatures (350–500 K). The centreline effectiveness and distribution of effectiveness on the surface of cooling wall are presented.     

Application of maximum entropy method for droplet size distribution prediction using instability analysis of liquid sheet

This paper describes the implementation of the instability analysis of wave growth on liquid jet surface, and maximum entropy principle (MEP) for prediction of droplet diameter distribution in primary breakup region. The early stage of the primary breakup, which contains the growth of wave on liquid–gas interface, is deterministic; whereas the droplet formation stage at the end of primary breakup is random and stochastic. The stage of droplet formation after the liquid bulk breakup can be modeled by statistical means based on the maximum entropy principle. The MEP provides a formulation that predicts the atomization process while satisfying constraint equations based on conservations of mass, momentum and energy. The deterministic aspect considers the instability of wave motion on jet surface before the liquid bulk breakup using the linear instability analysis, which provides information of the maximum growth rate and corresponding wavelength of instabilities in breakup zone. The two sub-models are coupled together using momentum source term and mean diameter of droplets. This model is also capable of considering drag force on droplets through gas–liquid interaction. The predicted results compared favorably with the experimentally measured droplet size distributions for hollow-cone sprays.     

Numerical simulation of Mach reflections

In this paper, the “FLIC” difference method with triangular mesh is adopted to numerically simulate the regular and Mach reflections that occur when a shock wave pass around a wedge. The compuational result is compared with the shock tube experimental results of G. Ben-Dor and I. I. Glass. The comparison shows that the position, shape of shock wave and height of Mach stem all show a good agreement. Consequently, the “FLIC” difference method with triangular mesh is quite satisfactory in numerical simulation of the regular and Mach reflections.     

Mach number effects on shock-bubble interaction

An investigation of Mach number effects on the interaction of a shock wave with a cylindrical bubble, is presented. We have conducted simulations with the Euler equations for various incident shock Mach numbers () in the range of , using high-resolution Godunov-type methods and an implicit solver. Our results are found in a very good agreement with previous investigations and further reveal additional gasdynamic features with increasing the Mach number. At higher Mach numbers larger deformations of the bubble occur and a secondary-reflected shock wave arises upstream of the bubble. Negative vorticity forms at all Mach numbers, but the “c-shaped” vortical structure appeared at gives its place to a circular-shaped structure at higher Mach numbers. The computations reveal that the (instantaneous) displacements of the upstream, downstream and jet interfaces are not significantly affected by the incident Mach number for values (approximately) greater than . With increasing the incident Mach number, the speed of the jet (arising from the centre of the bubble during the interaction) also increases. Received 21 December 2000 / Accepted 23 April 2001     

Measurement of parameters of a gas suspension behind a shock wave in foam

A study has been made of the propagation of a shock wave in dry polyhedral foam with cell diameter 1 cm. The experiments were made in a shock tube in the range of Mach numbers M < 1.4 of the shock wave. The interaction of the shock wave with the foam was photographed. This established that the destruction of the foam by the shock wave leads to the formation of a gas-droplet flow behind the shock front. To determine the parameters of the suspension, the flow was probed by He-Ne lasers with different radiation wavelengths. The spectral-transparency method was used to find the modal diameter of the droplets of the gas suspension and the volume concentration of the droplets in the flow. The modal diameter of the droplets was 2m, and the volume concentration of the droplets decreased downstream.Translated from Izvestiya Rossiiskoi Akademii Nauk, Mekhanika Zhidkosti i Gaza, No. 3, pp. 134–141, May–June, 1993.     

Numerical investigation of unsteady shock waves in vapor-gas-droplet mixtures

The results of mathematical modeling of the evolution of unsteady shock waves in two-phase mixtures of inert gas, vapor and suspended liquid droplets with allowance for dynamic, thermal and mass phase interaction processes are presented. The influence of interphase mass transfer effects (droplet breakdown and evaporation, vapor condensation) on the structure of unsteady shock waves in vapor-gas-droplet mixtures is analyzed. The important influence of phase mass transfer and, in particular, droplet breakdown as a result of surface layer stripping by the gas flow on the distribution of the parameters of the carrier and dispersed components of the mixture behind the shock front is demonstrated. The effect of the principal governing parameters of the two-phase mixture on the unsteady shock wave propagation process is analyzed.Translated from Izvestiya Rossiiskoi Akademii Nauk, Mekhanika Zhidkosti i Gaza, No.4, pp. 67–75, July–August, 1992.     

煤油液滴直径对两相旋转爆轰发动机流场的影响

为探究煤油液滴不同初始直径对气液两相旋转爆轰发动机流场的影响,假设初始注入的煤油液滴具有均匀直径,考虑雾化破碎、蒸发等过程,建立了非定常两相爆轰的Eulerian-Lagrangian模型,进行了液态煤油/高温空气爆轰的非预混二维数值模拟。结果表明：在初始液滴直径为1～70μm的工况范围,燃烧室内均形成了单个稳定传播的旋转爆轰波;全局当量比为1时,爆轰波前的空气区域大于液滴煤油的蒸气区域,导致波前燃料空气混合不均匀,波前均存在富油区和贫油区,两相速度差导致分离出的空气形成低温条带;当煤油液滴的初始直径较小时,波前的反应物混合过程主要受蒸发的影响,爆轰波可稳定传播;当直径减小至1μm时,煤油液滴在入口处即蒸发,旋转爆轰波表现为气相传播的特性,爆轰波结构平整;当煤油液滴的初始直径较大时,波前的反应物混合过程主要受液滴破碎的影响;对于相同的燃料质量流量,在不同初始煤油液滴直径工况下,煤油液滴最大的停留时间均占爆轰波传播时间尺度的80%以上;爆轰波前燃料预蒸发为气相的占比越高,爆轰波的传播速度越高;初始液滴直径为10～70μm的工况范围内,爆轰波的速度随初始直径的增大先升高后降低。     

Flow visualization of shock/water column interactions

The breakup of a liquid droplet induced by a high speed gas stream is a typical multiphase flow problem. The shock/droplet interaction is the beginning stage of the droplet breakup. Therefore, investigation of the shock/droplet interactions would be a milestone for interpreting the mechanism of the droplet breakup. In this study, a compressible multiphase solver with a five-equation model is successfully developed to study shock/water column interactions. For code validation, interface-only, gas–gas shock tube, and gas–liquid shock tube problems are first computed. Subsequently, a planar shock wave interacting with a water column is simulated. The transmitted wave and the alternative appearances of local high- and low-pressure regions inside the water column are observed clearly. Finally, a planar shock wave interacting with two water columns is investigated. In this work, both horizontal and vertical arrangements of two water columns are studied. It is found that different arrangements can result in the diversity of the interacting process. The complex flow structures generated by shock/water column interactions are presented by flow-visualization techniques.      

The interaction between shock waves and solid spheres arrays in a shock tube

When a shock wave interacts with a group of solid spheres, non-linear aerodynamic behaviors come into effect. The complicated wave reflections such as the Mach reflection occur in the wave propagation process. The wave interactions with vortices behind each sphere‘s wake cause fluctuation in the pressure profiles of shock waves. This paper reports an experimental study for the aerodynamic processes involved in the interaction between shock waves and solid spheres. A schlieren photography was applied to visualize the various shock waves passing through solid spheres. Pressure measurements were performed along different downstream positions. The experiments were conducted in both rectangular and circular shock tubes. The data with respect to the effect of the sphere array, size, interval distance, incident Mach number, etc., on the shock wave attenuation were obtained.     

Nonlinear Strong Shock Interactions: A Shock-Fitted Approach

This paper addresses nonlinear effects which result from the interaction of shock waves with vortices. A series of experiments are carried out, which involve the interaction of a strong shock wave with a single plane vorticity wave and a randomly distributed wave system. These experiments are first conducted in the linear regime to obtain a mutual verification of theory and computation. They are subsequently extended into the nonlinear regime. A systematic study of the interaction of a plane shock wave and a single vortex is then conducted. Specifically, we investigate the conditions under which nonlinear effects become important, both as a function of shock Mach number, M ₁, and incident vortex strength (characterized by its circulation Γ). The shock Mach number is varied from 2 to 8, while the circulation of the vortex is varied from infinitesimally small values (linear theory) to unity. Budgets of vorticity, dilatation, and pressure are obtained. They indicate that nonlinear effects become more significant as both the shock Mach number and the circulation increase. For Mach numbers equal to 5 and above, the dilatation in the vortex core grows quadratically with circulation. An acoustic wave propagates radially outward from the vortex center. As circulation increases, its upstream-facing front steepens at low Mach numbers, and its downstream-facing front steepens at high Mach numbers. A high Mach number asymptotic expansion of the Rankine--Hugoniot conditions reveals that nonlinear effects dominate both the shock motion and the downstream flow for ΓM ₁ > 1. Received 28 June 1997 and accepted 25 November 1997     

Normal shock interaction with a yawed wedge moving at supersonic speed

In this article, the interaction of a normal shock with a yawed wedge moving at supersonic speed has been considered. The vorticity distribution of a particle over the diffracted shock wave for various combinations of yawed angles, Mach number of the shock wave and Mach number of the moving wedge have been obtained. Further triple point angle χ in Mach reflection has been calculated for the various parameters.      

高马赫数下激波液滴相互作用的数值模拟研究

本文采用守恒清晰界面多相流数值方法模拟了超声速和高超声速环境下三维液滴的推进、变形和破碎演化过程.数值模拟结果与实验数据的一致性表明了本文所用数值方法和计算程序的准确性, 而网格无关性研究验证了采用的网格分辨率可以捕捉流场和界面的主要特征. 模拟结果验证了高韦伯数下液滴变形破碎过程所遵循的剪切诱导剥离(SIE)破碎机制, 其包含液滴的扁平化和剪切剥离两个主要特征. 而最近发现的SIE破碎机制下的循环破碎机制也在本文得到了验证, 即主液滴从球形液滴破碎为小液滴会经历多个循环重复的破碎阶段, 高韦伯数下液滴的破碎并非一次性剪切剥离的结果, 而是会发生逐层的剪切剥离和破碎. 本文还研究了马赫数对激波冲击液滴加速变形过程的影响. 结果表明, 高韦伯数下不同马赫数的液滴破碎过程具有高度一致性, 并遵循统一的SIE破碎机制.通过对液滴质心位移、速度、加速度和拽力系数的量化统计揭示其运动过程中的统一加速规律. 在激波的驱动下, 液滴并非以一个恒定的加速度做加速运动.在扁平化不明显的前期, 液滴以一个恒定的加速度做加速运动.随着液滴扁平化的发生, 迎风面积的增加导致拽力系数的增大, 进而导致液滴加速度的不断增大.      

Type of reflection of a near-wall shock wave in the process of diffraction from a square channel

The results of an experimental and numerical investigation of the process of diffraction of shock waves from a square channel at a ninety-degree convex corner are presented for various incident shock wave Mach numbers M₀ (1.4<M₀<7). The type of reflection of the near-wall fragment of the diffracting shock wave from the wall and the wave velocity are determined as functions of M₀, direction, and time. Moscow. Translated from Izvestiya Rossiiskoi Akademii Nauk, Mekhanika Zhidkosti i Gaza, No. 1, pp. 145–151, January–February, 2000. The work was carried out with partial support from the Russian Foundation for Basic Research (project No. 96-02-16170a).