Influences of the wall thickness on the granular dispersion in a dense gas–solid coaxial jet

The granular dispersion for different wall thicknesses of the inner channel in a dense gas–solid coaxial jet is investigated by morphology. In the wave dispersion, the Kelvin–Helmholtz instability has a strong influence on the granular stream. However, increasing the wall thickness damps the K–H instability, namely weakens the wave dispersion. Consequently, the non-dimensional wavelength increases and the non-dimensional amplitude decreases as the wall thickness increases for the same annular gas velocity. The instability analysis combining with the modification of the vorticity thickness of the annular gas stream indicates that the non-dimensional wavelength increases linearly with the non-dimensional modified vorticity thickness. The relation between the amplitude of the granular dispersion and the non-dimensional modified vorticity thickness is reliable for the wave dispersion as well. In addition, the granular dispersion angle is proportional to the annular gas velocity, which slightly depends on the wall thickness.     

Composite steady waves in a gravity fluid stream of finite depth

The problem of plane steady gravitational waves of finite amplitude, caused by a periodically distributed pressure over the surface of an ideal incompressible gravity fluid stream of finite depth, is considered. It is assumed that these waves do not vanish as the pressure becomes constant, but become free waves, which exist at constant pressure and special values of the stream velocity. As in [1], where a stream of finite depth is considered, such waves will be designated composite as contrasted with forced waves which vanish together with the variable part of the pressure. A general method is given for computing the composite wave characteristics. The first three approximations are computed to the end. An approximate equation for the wave profile is found.     

Free surface waves in equilibrium with a vortex

Finite amplitude solitary waves of uniform depth which interact with a stationary point vortex are considered. Waves both with and without a submerged obstacle are computed. The method of solution is collocation of Bernoulli's equation at a finite number of points on the free surface coupled with equations for equilibrium of a point vortex. The stream function and vortex location are found by computing a conformal map of the flow domain to an infinite strip. For a given obstacle the solutions are parametrized with respect to Froude number and vortex circulation. When no obstacle is present there are two families of solutions, in one of which the amplitude of the wave increases by increasing the circulation, while in the other amplitude increases by decreasing the circulation. Beyond a certain critical Froude number the maximum amplitude wave has a sharp crest with an angle of 120 degrees. Similar behavior is observed for the flow past a submerged obstacle except that there is a critical Froude number below which there is no solution at all.     

Spectroscopic study of the properties of a supersonic plasma stream

A plasma diagnosis has been carried out by spectroscopic methods. The behavior of temperature and concentration of charged particles was measured along the stream as a function of polarity for a stream with a shock wave and a stream with periodic structure. An explanation of the observed phenomena is given. The physical processes occuring in a supersonic plasma stream are quite distinctive [1], Spectroscopic investigations are necessary since they provide more detailed information on the physical state of the plasma. It is also of interest to study wave processes taking place in the stream from the point of view of the additional plasma heating thus obtained.We take this opportunity to express our sincere thanks to M. A. El'yashevich for discussing the results.     

Disturbances to a rotating fluid with a sphere moving along the axis of rotation

I.IntroductionWhenabodyprojectedinthewaterisintranslationalmotionthroughwateritwillcertainlycausesdisturbances.Howtodetectthedisturbancesf'arawayfromthebodyandhowtodetermillebytheintbrlnationobtainedthepositionandvelocityofthebodyandthesiteofprojectionareimportant.Astheprojectedbodyisrotating,thefluidaroundisinauniformlyrotationrelativetothereferenceframerotatinginsynchronismwiththebody,andthisisaquestionofthemotionofabodyinarotatingfluid.SuchproblemswerefirststudiedbyProudman(1916)l']andTay…     

白云岩受压声学特性及其在裂缝研究中的应用

通过实验手段研究了白云岩在三轴和单轴加载过程中的声波波速、幅度、频谱特性的变化特征. 结果发现:(1)白云岩在受压变形过程中,声波波速的变化较好地反映了岩石内部裂缝的闭合、产生、扩展和贯穿等变化. 总体而言,横波波速比纵波能更好地预测裂缝的产生,而纵波对裂缝的非稳定发展或贯穿有较敏感的反映. (2)随着轴压的增大,纵、横波波形的末端都有散射波的出现,且横波波形末端的"鱼尾"状散射波信号更为明显(此时应力点为极限强度的60%左右),预示着岩石内部裂缝的产生和稳定扩展. (3)频谱曲线也很好地反映了岩石内部结构变形情况. 随着岩石受力的增大,频谱曲线上的振幅都呈现增大趋势,标志着岩石的压实阶段;当频谱曲线上低频段较高频段活跃时,标志着裂缝的产生;更有甚者,低频还会取代高频成为主频. (4)在岩石受压裂缝闭合阶段,首波振幅和频谱主振幅都呈现上升趋势;而在裂缝不稳定扩展阶段,主振幅表现出比首波振幅低的上升趋势;振幅曲线达到峰值后都存在一突降拐点,预示着岩石的贯通破坏. 研究对于地层岩石的动态长期监测和工程岩体的稳定性评价都具有重要的理论参考价值.      

Surface waves generated by a line load on a half-space with depth-dependent properties

The reciprocity theorem of elastodynamics is used in this paper to determine the surface waves that are radiated from a time-harmonic line load applied at the surface of a solid body, whose elastic moduli and mass density depend on the distance from the surface. In a high-frequency approximation, the surface wave velocity and expressions for the displacement and stresses of free surface waves are employed in the reciprocity theorem. The general expressions for the surface wave radiated by the oscillating line load, together with a virtual free surface wave, when employed in the reciprocity theorem, yield relatively simple expressions for the amplitude factor of the radiated surface wave. Results show the amplitude factor as a function of the wavenumber.     

Wave development on a thinning liquid film

Experimental results are presented for the growth of surface waves on a liquid film that thins as it flows under gravity over the surface of an upright circular cone. The characteristics of the mean film are calculated on the assumption of quasi-parallel flow, and the actual mean thickness found to relate very closely to that found on this basis. The development of the film was found to fall into three phases: the entry zone in which the velocity profile of the film becomes established where no waves are visible, a region of wave growth in which amplitude, wave speed, and wave length all grow, and a final region in which amplitude and wave speed decline as the film thins further although wave length continues to grow. An empirical relationship is presented which expresses the wave number at any point on the cone in terms of the flow rate and a parameter based on the local Reynolds and Weber numbers and cone angle. It was found that for a given flow rate the maximum wave amplitude was reached at a value of wave number of 0·048.     

Interaction of a tollmien-schlichting wave with a local flow inhomogeneity

The method of parabolic stability equations is used to study the laminar-turbulent transition in a boundary layer with a stationary velocity inhomogeneity concentrated in a narrow stream. The location of the transition is found as a function of the magnitude and sign of the velocity defect. It is shown that if the inhomogeneity amplitude is small, it affects only the final nonlinear stage of disturbance development. In this case, the location of the transition is independent of the sign of the velocity defect. Having a moderate amplitude, a lower-velocity inhomogeneity shifts the transition location significantly more strongly than a higher-velocity inhomogeneity of similar shape and amplitude. This is caused by amplification of unstable disturbances in the low-velocity region and, conversely, their attenuation in the high-velocity stream. The effect of disturbance amplification in the low-velocity region is shown not to be connected with inflection-type instability. Another explanation of this phenomenon is offered. Central Aerohydrodynamic Institute, Zhukovskii 140160. Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, Vol. 39, No. 1, pp. 75–83, January–February, 1998.     

Effect of incident shock wave strength on the decay of Richtmyer–Meshkov instability-introduced perturbations in the refracted shock wave

The effect of incident shock wave strength on the decay of interface introduced perturbations in the refracted shock wave was studied by performing 20 different simulations with varying incident shock wave Mach numbers (M ~ 1.1? 3.5). The analysis showed that the amplitude decay can be represented as a power law model shown in Eq.7, where A is the average amplitude of perturbations (cm), B is the base constant (cm^?(E?1), S is the distance travelled by the refracted shockwave (cm), and E is the power constant. The proposed model fits the data well for low incident Mach numbers, while at higher mach numbers the presence of large and irregular late time oscillations of the perturbation amplitude makes it hard for the power law to fit as effectively. When the coefficients from the power law decay model are plotted versus Mach number, a distinct transition region can be seen. This region is likely to result from the transition of the post-shock heavy gas velocity from subsonic to supersonic range in the lab frame. This region separates the data into a high and low Mach number region. Correlations for the power law coefficients to the incident shock Mach number are reported for the high and low Mach number regions. It is shown that perturbations in the refracted shock wave persist even at late times for high incident Mach numbers.     

Peristaltic transport of a Jeffrey fluid under the effect of magnetic field in an asymmetric channel

The peristaltic flow of a Jeffrey fluid in an asymmetric channel is studied under long wavelength and low Reynolds number assumptions. The fluid is electrically conducting by a transverse magnetic field. The channel asymmetry is produced by choosing the peristaltic wave train on the walls to have different amplitudes and phase. The flow is investigated in a wave frame of reference moving with the velocity of the wave. The expressions for stream function, axial velocity and axial pressure gradient have been obtained. The effects of various emerging parameters on the flow characteristics are shown and discussed with the help of graphs. The pumping characteristics, axial pressure gradient and trapping phenomenon have been studied. Comparison of various wave forms (namely sinusoidal, triangular, square and trapezoidal) on the flow is discussed.     

Dipole nature of sound radiation by free turbulence with shear

The theory of aerodynamic generation of sound, whose fundamental principles were expounded by Lighthill in [1, 2], is used most in studying stream noise. According to this theory, the process of sound generation by free turbulence reduces to a quadrupole radiation mechanism and the sound intensity (without taking account of the effects of refraction and convection) depends on the stream velocity to the eighth power. In later years the Lighthill theory received intensive development in various directions. In particular, a number of papers, for example [3–7], in which the radiation of sound by a free stream was represented as the superposition of “shear noise” and “intrinsic noise” of turbulent pulsations, are devoted to the questions considered here about the influence of the mean velocity shear. A deduction is made in these papers which rely on the Lighthill theory, about the identical order of the intrinsic and shear noises. At the same time, the results of a number of experiments [8, 9] on the noise of subsonic jets show that the noise intensity at low subsonic velocities is proportional to the sixth power of the stream velocity. A dependence of the noise intensity on the sixth power of the velocity has been obtained by computational means in [10, 11] without relying on the Lighthill scheme for the solution. The noise intensity of a subsonic jet for just the shear component of the radiation was computed in [10] on the basis of the general solution of the wave equation, and it has been clarified that for low Mach numbers Maxa [M≤0.5] the sixth-power law is valid. This same law has been obtained in [11] for an acoustic field produced by pairs of moving vortices by using the method of matched asymptotic expansions. An attempt to explain the sixth-power law for the noise intensity of free turbulent streams by starting from the quadrupole radiation scheme was tried in [6], where it was assumed that the velocity pulsations depend on the stream velocity to the 3/4 rather than the first power. Utilization of this argument is inadequate since a direct dimensional analysis of the Lighthill solution results in a 7.5 power-law for shear noise and a seventh power law for the intrinsic noise of turbulent pulsations. This paper is devoted to an analysis of the discrepancy between the Lighthill quadrupole character of the sound radiation and the sixth-power dependence of the sound intensity on the stream velocity obtained as a result of the mentioned calculations [10, 11] and a number of experiments.     

Particle image velocimetry investigation of a finite amplitude pressure wave

Particle image velocimetry is used to study the motion of gas within a duct subject to the passage of a finite amplitude pressure wave. The wave is representative of the pressure waves found in the exhaust systems of internal combustion engines. Gas particles are accelerated from stationary to 150 m/s and then back to stationary in 8 ms. It is demonstrated that gas particles at the head of the wave travel at the same velocity across the duct cross section at a given point in time. Towards the tail of the wave viscous effects are plainly evident causing the flow profile to tend towards parabolic. However, the instantaneous mean particle velocity across the section is shown to match well with the velocity calculated from a corresponding measured pressure history using 1D gas dynamic theory. The measured pressure history at a point in the duct was acquired using a high speed pressure transducer of the type typically used for engine research in intake and exhaust systems. It is demonstrated that these are unable to follow the rapid changes in pressure accurately and that they are prone to resonate under certain circumstances.     

波浪扰动下河口幂律异重流的动力场分布特性

河口底层浮泥异重流的运动特性对于河口维持以及港口航道泥沙淤积过程具有重要的作用, 是海岸学科研究的关键内容, 也是热点内容之一. 本文首先综述了河口泥沙异重流研究的重要意义, 分析并总结了各家异重流理论模型的不同点和适应条件; 其次, 根据本文研究问题的实际需要, 构建了波浪与底泥相互作用的双层流体理论分析模式, 将上层流体简化为常见的牛顿体, 而将下层流体的流变关系设置为幂律函数, 研究了波浪作用下河口底部幂律异重流的流场特性. 这些特性包括:波浪速度场、底泥运动的流速场、不同密度影响下的压力场以及异重流泥面波与表面 波的波幅比等, 分析了泥层密度、波动圆频率以及底泥幂律指数对流场及界面波的影响. 研究发现, 在波浪扰动下, 两层流体交界处速度分量连续, 压强出现突变. 在下部泥层中, 水平速度幅值曲线存在极大值. 随着波动圆频率增加以及泥层密度与流动指数的减小, 界面处上下压强差值呈现增大的趋势. 本模型与实测波幅比的数据进行对比结果证实了模型的合理性.      

Fluctuation characteristics of bubbly liquid flow in converging-diverging nozzle

The pressure fluctuation characteristics in bubbly liquid flow in a converging-diverging nozzle are interpreted on the basis of the previous theoretical results concerning the possible wave modes in bubbly liquid flow and their properties. The experiment is performed in a visual blowdown facility using water and nitrogen gas. The intensity and power spectrum density of the pressure fluctuations are measured, as well as the velocities of liquid and bubbles, the void fraction and the chord length of bubbles. All the fluctuation characteristics and their relation with the main stream condition are compatible with the theoretical predictions. The instability of the convection mode in the presence of the velocity slip and the cut off of the propagation modes in moderate frequency are demonstrated.     

Magnetohydrodynamic peristaltic flow of a hyperbolic tangent fluid in a vertical asymmetric channel with heat transfer

In the present paper we discuss the magnetohydrodynamic (MHD) peristaltic flow of a hyperbolic tangent fluid model in a vertical asymmetric channel under a zero Reynolds number and long wavelength approximation. Exact solution of the temperature equation in the absence of dissipation term has been computed and the analytical ex- pression for stream function and axial pressure gradient are established. The flow is analyzed in a wave frame of reference moving with the velocity of wave. The expression for pressure rise has been computed numerically. The physical features of pertinent parameters are analyzed by plotting graphs and discussed in detail.     

Nonlinearwaves in a liquid film-gas flow system

The instability and regular nonlinear waves in the film of a heavy viscous liquid flowing along the wall of a round tube and interacting with a gas flow are investigated. The solutions for the wave film flows are numerically obtained in the regimes from free flow-down in a counter-current gas stream to cocurrent upward flow of the film and the gas at fairly large gas velocities. Continuous transition from the counter-current to the cocurrent flow via the state with a maximum amplitude of nonlinear waves and zero values of the liquid flow rate and the phase velocity is investigated. The Kapitsa-Shkadov method is used to reduce a boundary value problem to a system of evolutionary equations for the local values of the layer thickness and the liquid flow rate.     

Propagation of pressure waves in two-phase flow

We deal with a pressure wave of finite amplitude propagating in a gas and liquid medium or in the fluid in an elastic tube. We study the effects of pipe elasticity on the propagation velocity of the pressure wave. Pressure waves of finite amplitude progressing in the two-phase flow are treated considering the void fraction change due to pressure rise. The propagation velocity of the two-phase shock wave is also investigated, and the behavior of the reflection of the pressure wave at the rigid wall is analyzed and compared to that in a pure gas or liquid. The results are compared to experimental data of a pressure wave propagating in the two-phase flow in a vertical shock tube.     

Generation of locked-on flow tones: Effect of damping

The overall objective of this investigation is to determine the effect of variable damping on the pressure response of a deep cavity. The pressure fluctuations arise from coupling between the unsteady shear layer along the cavity opening and a resonant mode of the cavity. The damping of the cavity is tuned to desired values without changes of geometry or other parameters.The amplitude of the cavity pressure fluctuation as a function of flow velocity is characterized for the first, second and third acoustic modes of the cavity. For each mode, variation of the value of damping over a relatively wide range yields corresponding attenuation of the pressure amplitude. For higher acoustic modes and sufficiently large damping, abrupt decreases of the pressure amplitude occur at threshold values of flow velocity.The variable damping of the deep cavity does not significantly alter the eigenfrequencies of the system. The peak response amplitude of the pressure fluctuation, however, occurs at a value of Strouhal number that increases with increasing values of damping. Moreover, this peak response amplitude, when normalized by the free stream dynamic head, generally shows a linear variation with the value of damping, for three acoustic modes of the cavity.The strength of lock-on of the pressure oscillation, as a function of the degree of damping, is evaluated in terms of the coherent and broadband pressure amplitudes. Both amplitudes are attenuated for increased damping; the difference between them, however, remains relatively large (40 dB minimum), thereby indicating well-defined lock-on, even when the amplitude of the spectral peak of the coherent component is substantially attenuated.