Nonstationary interaction of a short blunt body with a cavity in a compressible liquid

The shock-interaction problem for a rigid spherical body and a spherical cavity in a compressible liquid is formulated and solved. Three typical cases of typical dimensions of the body and cavity are examined. An asymptotic solution valid at the earliest stage of interaction is obtained. In the general case, the problem is reduced to an infinite system of integral equations of the second kind. It is numerically solved for the case of a nonsmall air gap __________ Translated from Prikladnaya Mekhanika, Vol. 42, No. 11, pp. 40–56, November 2006.     

考虑动水压力和流固耦合的库水-坝体-地基系统建模与动力分析

结合动水压力模型和罚函数耦合算法,考虑地基和坝体结构的接触以及边界效应,构建动水压力和流固耦合作用下的库水-坝体-地基地震响应分析模型和方法。通过与试验结果及解析解和实测数据对比,验证了本文模型和方法能准确反映系统地震荷载和分析整体耦合系统的动力响应,引入罚函数处理流固耦合界面能提高计算收敛速度。进一步以某重力坝工程实际为背景,验证本文构建的模型和方法适用于库水-坝体-地基耦合系统动力分析的可行性,并分析了地震作用下地基变形对系统动力响应的影响。     

Some Aspects of the Lift Force on a Spherical Bubble

Several situations in which a spherical bubble experiences a lift force are examined, especially through the use of computational results obtained by solving the full Navier–Stokes equations. The lift force is computed over a wide range of Reynolds number for the case of pure shear flow, pure strain and solid body rotation. Using these results, the validity of asymptotic solutions derived in the limit of low Reynolds number or inviscid flow is discussed. A general expression of the lift force valid for low to moderate shears is proposed. It is shown that for such shears, the lift force in a complex flow can be predicted by superposing the results obtained in pure strain flow and solid body rotation flow. Finally, the interaction force experienced by two bubbles rising side-by-side is studied. The computational results reveal that, at variance with the predictions of potential theory, the sign of this force changes when the Reynolds number or the separation distance between the bubbles decreases below a critical value. All these results are discussed in terms of vorticity. The respective role played by the vorticity generated at the bubble surface and by the one that is eventually present in the unperturbed flow is emphasized.     

Impact of a spherical rigid body on the surface of a cavity in a compressible liquid: An axisymmetric problem

The shock interaction of a spherical rigid body with a spherical cavity is studied. This nonstationary mixed boundary-value problem with an unknown boundary is reduced to an infinite system of linear Volterra equations of the second kind and the differential equation of motion of the body. The hydrodynamic and kinematic characteristics of the process are obtained __________ Translated from Prikladnaya Mekhanika, Vol. 44, No. 1, pp. 11–19, January 2008.     

Numerical simulation of time‐dependent hydrodynamic removal of a contaminated fluid from a cavity

The time‐dependent hydrodynamic removal of a contaminated fluid from a rectangular cavity on the floor of a duct is analysed numerically. Laminar duct flows are considered for Reynolds numbers of 50 and 1600 where the characteristic length is the duct height. Two cases are considered where: (1) the fluid density in the cavity is the same as that for the duct fluid and (2) the cavity fluid has a higher density than the duct fluid but the two fluids are miscible. The flow is solved by a numerical solution of the time‐dependent Navier–Stokes equations. Attention is focused on the convective transport of contaminated fluid out from the cavity and the effect of duct flow velocity profile on the cleaning process. Passive markers are used in the numerical simulation for the purpose of identifying the contaminated cavity fluid. The results show that the flow patterns in the cavity are influenced by the type of duct flow. From a cleaning perspective, the results suggest that it is easier for the duct flow to penetrate a cavity and to remove contaminated cavity fluid when the duct flow is of the Poiseuille type and the aspect ratio is large. Copyright © 2003 John Wiley & Sons, Ltd.     

Three-dimensional instability on the interaction between a vortex and a stationary sphere

We present direct numerical simulations of the interaction between a vortex ring and a stationary sphere for Re = 2,000. We analyze the vortex dynamics of the ring as it approaches the sphere surface, and the boundary layer formed on the surface of the sphere undergoes separation to form a secondary vortex ring. This secondary vortex ring can develop azimuthal instabilities, which grow rapidly as it interacts with the primary ring. The azimuthal instabilities on both rings are characterized by analysis of the azimuthal component decomposition of the axial vorticity.     

Effect of inertia on the hydrodynamic interaction between two liquid capsules in simple shear flow

Three-dimensional numerical simulations using front-tracking method are performed to study the hydrodynamic interaction between two liquid capsules suspended in simple shear flow in presence of inertia. Capsules are modeled as liquid drops surrounded by neo-Hookean elastic membranes. In the limit of zero inertia, it has been known from past research that the hydrodynamic interaction between two deformable particles (drops/capsules) suspended in shear flow results in an irreversible shift in the trajectories of the particles as one particle rolls over the other. In this article, we show that the presence of inertia can significantly alter the capsule trajectories. When inertia is small but finite, the capsules do undergo an irreversible displacement, but the lateral separation between them first decreases before they roll over each other, unlike in Re ? 1. For moderate to high inertia, the capsules reverse their directions of motion before coming close to each other. The reversal of motion occurs progressively earlier in time (that is, the capsules come less closer to each other) with increasing inertia. The long-time behavior of the capsule–capsule interaction at finite inertia showed that the capsules engage in spiraling motions. Based on our simulations, four different regimes of capsule–capsule interaction at finite inertia are identified: (i) a self-diffusive type interaction, (ii) an outwardly spiraling motion, (iii) a fixed-orbit spiraling motion, and (iv) an inwardly spiraling motion in which the capsules settle with zero relative velocity. The reversal of motion, and the spiraling trajectories at finite inertia have no analogy in the limit of zero inertia. Such motions are explained by analyzing the flow field around a deformed capsule which shows reverse flow regions and off-surface stagnation points, similar to those previously reported in case of rigid spheres and cylinders under torque-free condition.     

Numerical simulation of the hydrodynamic interaction between a sedimenting particle and a neutrally buoyant particle

A new method for the simulation of the translational and rotational motions of a system containing a sedimenting particle interacting with a neutrally buoyant particle has been developed. The method is based on coupling the quasi-static Stokes equations for the fluid with the rigid body equations of motion for the particles. The Stokes equations are solved at each time step with the boundary element method. The stresses are then integrated over the surface of each particle to determine the resultant forces and moments. These forces and moments are inserted into the rigid body equations of motion to determine the translational and rotational motions of the particles. Unlike many other simulation techniques, no restrictions are placed on the shape of the particles. Superparametric boundary elements are employed to achieve accurate geometric representations of the particles. The simulation method is able to predict the local fluid velocity, resolve the forces and moments exerted on the particles, and track the particle trajectories and orientations.     

非饱和土中弹性支承桩的扭转振动响应分析

基于已建立的非饱和土中的波动方程,对均质非饱和滞回阻尼土层中的弹性支承桩扭转振动特性进行了分析.首先利用拉普拉斯变换,在拉氏交换域中求得了土体振动位移形式解,依据桩土接触面处的衔接条件将该解耦合进桩身动力平衡方程,求解桩的动力平衡方程,得到了桩顶速度导纳的频域响应解析解和半正弦脉冲激励作用下桩顶时域响应的半解析解,并分析了主要参数对振动特性的影响.结果表明,桩底支承刚度因子影响较大,土滞回材料阻尼有一定的影响,而土底支承剐度因子基本没有影响.     

Effects of surface waves on hydrodynamic pressures on rigid dams with arbitrary upstream face

The effects of surface gravity waves on earthquake‐induced hydrodynamic pressures on rigid dams with nonvertical upstream face are examined, taking the compressibility and viscosity of water into account. A simple closed‐form solution is obtained by using the Trefftz numerical method. The boundary under study is reduced to the upstream face only and the degrees of freedom of the problem are restricted to the number of trial functions used for analysis. For harmonic base excitation, a number of numerical examples for various geometries of the upstream face are presented. The hydrodynamic pressure distribution, the resultant lateral force and its effective height of application are evaluated. The results are strongly influenced by the upstream shape and, in a lesser degree, by the consideration of surface waves. Copyright © 2009 John Wiley & Sons, Ltd.     

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…     

On the energy equation for a spatially developing instability wave in the theory of hydrodynamic stability

In this article, it is shown that the energy equation for a spatially developing disturbance used in all the literatures dealing with the problem of hydrodynamic stability suffers from a small, but crucial error.     

Dynamical formation of cavity in a composed hyper-elastic sphere

The dynamical formation of cavity in a hyper-elastic sphere composed of two materials with the incompressible strain energy function, subjected to a suddenly applied uniform radial tensile boundary dead-load, was studied following the theory of finite deformation dynamics. Besides a trivial solution corresponding to the homogeneous static state, a cavity forms at the center of the sphere when the tensile load is larger than its critical value. An exact differential relation between the cavity radius and the tensile land was obtained. It is proved that the evolution of cavity radius with time displays nonlinear periodic oscillations. The phase diagram for oscillation, the maximum amplitude, the approximate period and the critical load were all discussed.     

考虑桩土相互作用效应的桩顶纵向振动时域响应分析

在考虑桩土耦合作用以及土竖向波动效应条件下,对均质滞回材料阻尼土中弹性支承桩桩顶纵向振动时域响应进行了理论研究。首先建立了桩与滞回阻尼土在谐和振动情况下的定解问题,然后先对土层动力平衡方程进行求解并得到土体振动位移形式解,接着依据平衡条件将该形式解祸合进桩身动力平衡方程,并通过对桩动力平衡方程的求解,最终得到桩顶位移和速度频域响应解析解和半正弦脉冲激励作用下桩顶时域响应的半解析解。通过与其它相关理论解的对比验证了本文解的正确性和适用性,并基于所得解对桩顶时域响应特性进行了分析,最后将理论曲线与现场工程实测曲线进行了拟合对比,结果表明两者符合较好。     

The hydrodynamic force and torque on a bounded sphere in Poiseuille flow

The lattice Boltzmann (LB) method is used to study the hydrodynamic force and torque acting on a sphere held stationary between parallel plates in pressure‐driven flow. This and associated flow configurations are explored in this paper. LB results are in excellent agreement with existing theory and numerical results for simple pressure‐driven flow between parallel plates, for flow through a periodic medium of spheres [Zick AA, Homsy GM. Stokes flow through periodic arrays of spheres. Journal of Fluid Mechanics 1982; 115: 13], and for the force and torque acting on a sphere held fixed at the quarter vertical position in a pressure‐driven flow between parallel plates. In the latter case, LB calculations reveal a screening effect caused by neighboring periodic images of the test sphere. It is shown that the test sphere is hydrodynamically decoupled from its periodic images when separated by approximately 30 sphere radii. LB results for force and torque as a function of sphere height and flow cell height are also reported. Copyright © 2001 John Wiley & Sons, Ltd.     

压力相关的壁面滑移在滑动间隙流体动压力产生中的作用

近年来,壁面滑移在纳米流变学、微流体力学、薄模润滑和微机电系统(MEMS)等领域越来越引起关注。以前大部分研究集中于表面初始极限剪应力对薄模润滑的壁面滑移和流体动力学的影响。本文通过一个极限剪切应力比例系数主要研究了与压力相关的壁面滑移滑动间隙流体动压力产生中的作用,发现极限剪切应力比例系数以相反的两种方式影响着流体膜的流体动力学:在高初始剪应力区使流体动力增加,但在低初始剪应力区使流体动力减小,这意味着就极限剪切应力比例系数影响流体动压力而言,存在一个初始极限剪切应力的转换点。但是在界面滑移存在时,较小的极限剪切应力比例系数总是产生较小的摩擦阻力。     

Effect of hydrodynamic forces on the pressure-difference equation

Because of the influence of hydrodynamic forces, the difference in macroscopic pressure which exists, at static equilibrium, between two immiscible phases located in a porous medium may be different from that which pertains during flow. In this paper, the concept of relative pressure difference, together with a new pressure-difference equation, is used to investigate the impact that the hydrodynamic forces have on the difference in macroscopic pressure which pertains when two immiscible fluids flow simultaneously through a homogeneous, water-wet porous medium. This investigation reveals that, in general, the equation defining the difference in pressure between two flowing phases must include a term which takes proper account of the hydrodynamic effects. Moreover, it is pointed out that, while neglect of the hydrodynamic effects introduces only a small amount of error when the two fluids are flowing cocurrently, such neglect is not permissible during steady-state, countercurrent flow. This is because failure to include the impact of the hydrodynamic effects in the latter case makes it impossible to explain the pressure behaviour observed in steady-state, countercurrent flow. Finally, the results of this investigation are used as a basis for arguing that, during steady-state, countercurrent flow, saturation is uniform, as is the case of steady-state, cocurrent flow.Roman Letters a parameter in Equation (18) - k absolute permeability, m² - k _i effective permeability to phasei;i=1, 2, m² - k _ij generalized effective permeability for phasei;i, j=1, 2, m² - p _d p ₂–p ₁=difference in macroscopic pressure between two flowing phases, N/m² - p _i pressure for phasei;i=1, 2, N/m² - p _h hydrodynamic contribution to difference in macroscopic pressure which exists during flow, N/m² - P _c macroscopic static capillary pressure, N/m² - R ₁₂ function defined by Equation (18) - S _i saturation of phasei;i=1, 2 - S _n normalized saturation of phase 1 - t time, s - u _i flux of phasei;i=1, 2m³/m²/s - x distance in direction of flow, m Greek Letters _R relative pressure difference - _i k _i / _i =mobility of phasei;i=1, 2m²/Pa·s - _ij k _ij / _j =generalized mobility of phasei;i, j=1, 2m²/Pa·s - _i viscosity of phasei;i=1, 2, Pa·s - porosity     

On the theory of stability of a cylindrical hydrodynamic suspension

The stability of a cylindrical hydrodynamic suspension is investigated with complete account for the dependence of the fluid velocity distribution profile on the radial coordinate in the supporting layer without an a priori representation of the inertial terms in the fluid layer in terms of the velocity averaged over the clearance cross-section. It is shown that the central position of a light inner body in the cylindrical hydrodynamic suspension is asymptotically stable. The suspension remains asymptotically stable for a fairly long time as the light inner body is displaced from the central position along the dynamic equilibrium curve. The central position of a heavy inner body is unstable; however, as it is displaced from the central position under the action of a constant external decentering force a stability domain develops.