可压缩流体中封闭薄球壳的自由振动

通过引入位移函数，成功地研究了薄球壳在可压缩流体中的自由振动。发现存在两类自由振动：第一类与外界流体无关；第二类则受到流体性质的影响．证明了第二类振动的频率方程具有多项式形式并只存在复频率（除ｎ＝１时有Ω＝０）．求解ｎ＝０，１和２时的频率方程，并讨论参数的影响及给出根轨迹图。最后就小阻尼系数法作了对比分析。     

Interaction of a heavy fluid flow in a channel with a transverse jet barrier

An experimental and numerical analysis of the interaction between a plane horizontal water flow in a rectangular channel (free water current) and a plane thin water jet (water jet curtain) is presented; the jet flows out vertically from either a slot nozzle in the bottom of the channel or the crest of a rigid spillway at a velocity appreciably (several times) greater than the water velocity in the channel. Numerical calculations were carried out using the STAR-CD software package preliminarily tested against the experimental data obtained. The dependence of the water level in the channel at a certain distance ahead of the jet barrier on the main jet parameters and the water flow rate in the horizontal channel is studied. It is found that in the region of the interface between the flows both steady and unsteady (self-oscillatory) flow patterns can be realized. Steady stream/jet interaction patterns of the “ejection” and “ejection-spillway” types are distinguished and a criterion separating these regimes is obtained. The notion of a rigid spillway equivalent to a jet curtain is introduced and an approximate dependence of its height on the relevant parameters of the problem is derived. The possibility of effectively controlling the water level ahead of a rigid spillway with a sharp edge by means of a plane water jet flowing from its crest is investigated. The boundary of transition to self-oscillation interaction patterns in the region of the flow interface is determined. The structure of these flows and a possible mechanism of their generation are described. Within the framework of the inviscid incompressible fluid model in the approximate formulation for a “thin” jet, an analytical dependence of the greatest possible depth of a reservoir filled with a heavy fluid at rest and screened by a vertical jet barrier on the jet parameters is obtained.     

Motion of a system of seismic sources over ice on a body of water under the action of a pulse

The vertical motion of a system of two identical seismic sources and a spring truck tractor on ice under the action of a shock pulse from the seismic sources is studied to estimate the strength of ice. It is shown that during the pulse time, the interaction of the masses of the seismic sources and the tractor is small and the compressibility effect of the liquid can be ignored. Calculations show that for the seismic sources, the dynamic load far exceeds the static load and for the tractor, the static load is maximal. __________ Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, Vol. 48, No. 2, pp. 147–155, March–April, 2007.     

Theoretical analysis of non-uniform extensional flows in relation to processing rheology and predictions of some constitutive equations

In this paper, a characteristic equation involving the stream function, already given by one of the authors in a previous work for classifying axisymmetric incompressible flows, is re-considered. Non-uniform nearly extensional flows are derived as particular solutions from this equation. Using experimental data in the literature for polymer solutions and melts, it is proved that particular solutions of the characteristic equation lead to kinematics very close to those encountered in the fiber-spinning process. The kinematic equations satisfactorily correlating the fiber-spinning data are used in order to determine the ability of constitutive equations to predict realistic stresses in the flow domain. The rheological parameters of the fluids, obtained from experiments, are used for computation of differential and integral constitutive equations in the spinning conditions. Comparisons with the stress response of adequate constitutive equations are given and discussed.Also affiliated to: Université Joseph Fourier Grenoble I and Institut National Polytechnique de Grenoble, Associé au CNRS (URA 1510)     

Coriolis Effect on the Linear Stability of Convection in a Porous Layer Placed Far Away from the Axis of Rotation

The linear stability theory is used to investigate analytically the Coriolis effect on centrifugally driven convection in a rotating porous layer. The problem corresponding to a layer placed far away from the axis of rotation was identified as a distinct case and therefore justifying special attention. The stability of the basic centrifugally driven convection is analysed. The marginal stability criterion is established as a characteristic centrifugal Rayleigh number in terms of the wavenumber and the Taylor number.     

Vortex structure generation on the frontal surface of a cylinder set transversely in a hypersonic flow

The problem of formation of spatially periodic structures on the frontal surface of a cylindrically blunted body set transversely in a hypersonic flow is studied. Within the framework of the model adopted, a possible mechanism of vortex structure generation on the frontal surface of the blunt body is proposed and confirmed by calculations; in this mechanism, the curved bow shock produces a vortex flow, while in its turn the vortex, which persists under weak dissipation, acts on the shock thus maintaining its curved shape. It is shown that the spatially periodic mode of hypersonic flow past a cylinder can exist in the case of a uniform incident flow and under homogeneous boundary conditions on the body surface.     

Series solutions of unsteady MHD flows above a rotating disk

The series solutions of unsteady flows of a viscous incompressible electrically conducting fluid caused by an impulsively rotating infinite disk are given by means of an analytic technique, namely the homotopy analysis method. Using a set of new similarity transformations, we transfer the Navier–Stokes equations into a pair of nonlinear partial differential equations. The convergent series solutions are obtained, which are uniformly valid for all dimensionless time 0 ≤ τ < ∞ in the whole spatial region 0 ≤ η < ∞. To the best of our knowledge, such kind of series solutions have never been reported. The effect of magnetic number on the velocity is investigated.     

Vibrational Convection in the Hele-Shaw Cell. Theory and Experiment

The influence of high-frequency horizontal vibrations on convection in the Hele-Shaw cell located in a uniform gravity field is considered experimentally and theoretically. Nonlinear regimes of vibrational convection in the supercritical region are examined. It is shown that horizontal vibrations (directed toward the wide sides of the cell) decrease the threshold of quasi-equilibrium stability. Regions of existence of one- and two-vortex steady flows are found, and unsteady regular and random regimes of thermal vibrational convection are considered. New random regimes in the Hele-Shaw cell are found, which result from nonlinear interaction of the “lower” modes responsible for the formation of regular supercritical convective regimes. __________ Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, Vol. 47, No. 2, pp. 40–48, March–April, 2006.     

A note on the extensional viscosity of elastic liquids under strong flows

In this article a parametric study based on a balance between viscous drag and restoring Brownian forces is used in order to construct a nonlinear dumbbell model with a finite spring and a drag correction for a dilute polymer solution. The constitutive equations used are reasonable approximation for describing flows of very dilute polymer solutions such as those used in turbulent drag reduction. We investigate the response of an elastic liquid under extensional flows in order to explore the roles of a stress anisotropy and of elasticity in strong flows. It is found that for low Reynolds numbers, the extensional viscosity of a dilute polymer solution is governed by two parameters: a Deborah number representing the importance of the elasticity on the flow and the macromolecule extensibility that accounts for the viscous anisotropic effects caused by the macromolecule orientation. Two different asymptotic regimes are described.The first corresponds to an elastic limit in which the extensional viscosity is a function of the Deborah number and the particle volume fraction. The second is an anisotropic regime with the extensional viscosity independent of Deborah number but strongly dependent on macromolecule aspect ratio. The analysis may explain from a phenomenological point of view why few ppms of macromolecules of high molecule weight or a small volume fraction of long fibres produce important attenuation of the pressure drop in turbulent flows. On the basis of our analysis it is seen that the anisotropic limit of the extensional viscosity caused by extended polymers under strong flows should play a key role in the attenuation of flow instability and in the mechanism of drag reduction by polymer additives.