Plane problem of the impact of several shock pulses on a viscoelastic plate floating on a fluid surface

The impact of a series of sequential and simultaneous pulse loads on the deflection and stress of ice covering a body of water is considered. The effects of the water-body depth, plate thickness, pulse loading conditions, and interpulse interval on the height of the flexural-gravity wave and plate bending stress are analyzed.     

Transversal oscillations of a fluid in a long cylindrical container with membrane or elastic plate on the free surface

We propose approximate solutions of two-dimensional hydroelastic problems that describe free oscillations of an ideal fluid in a horizontal long cylindrical container with arbitrary symmetric cross section. The free surface of the fluid is covered by a plane membrane or an elastic plate. Using specific examples, we analyze the obtained solutions and the results of computation of frequencies and forms of oscillations of the mechanical system under consideration.     

Impact of thermal radiation on MHD slip flow over a flat plate with variable fluid properties

The influence of partial slip, thermal radiation and temperature dependent fluid properties on the hydro-magnetic fluid flow and heat transfer over a flat plate with convective surface heat flux at the boundary and non-uniform heat source/sink is studied. The transverse magnetic field is assumed as a function of the distance from the origin. Also it is assumed that the fluid viscosity and the thermal conductivity vary as an inverse function and linear function of temperature respectively. Using the similarity transformation, the governing system of non-linear partial differential equations are transformed into similarity non-linear ordinary differential equations and are solved numerically using symbolic software MATHEMATICA 7.0. The numerical values obtained within the boundary layer for the dimensionless velocity, temperature, skin friction coefficient and the Nusselt number are presented through graphs and tables for several sets of values of the parameters. The effects of various physical parameters on the flow and heat transfer characteristics are discussed from the physical point of view.     

Two-dimensional problem concerning the impact of a rigid body onto a thin elastic plate lying on the surface of a compressible fluid

Institute of Mechanics, Academy of Sciences of the UkrSSR, Kiev. Kiev Autorail Institute. Translated from Prikladnaya Mekhanika, Vol. 27, No. 9, pp. 59–66, September, 1991.     

Vortex on the surface of a viscous fluid

The system of Navier-Stokes equations is solved for boundary conditions corresponding to the case when an axisymmetric tangential transversal load acts at the surface of a gravity viscous incompressible fluid of infinite depth. An integral representation is obtained for the shape of the free surface under the prolonged effect of a stationary vortex load. The example of a tangential load, similar to a concentrated vortex, is examined. In this case a column is squeezed out of the fluid, the height of the column being directly proportional to the square of the moment of the transverse tangential forces and inversely proportional to the square of the product of the dynamic fluid viscosity and the area of the tangential stress distribution. The depth of the annular funnel being formed in front of the column is determined.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 4, pp. 127–132, July–August, 1978.     

Impact of a rectangular plate on a liquid half-space

The potential flow of an ideal incompressible fluid occupying a half-space resulting from the impact of a rectangular plate on its surface is considered. Outside the plate the surface of the fluid is free. An integral equation of the first kind is obtained for the impulsive pressure beneath a flexible plate. It is solved on a computer by the power series method for the particular case of a rigid nondeformable plate. The accuracy of the method is estimated. The theoretical dependence of the virtual mass and virtual moment of inertia coefficients of a rigid nondeformable plate on the plate geometry is constructed and compared with the experimental data and with empirical formulas [1-3] not directly related with the solution of the Laplace equation.Translated from Izvestiya Rossiiskoi Akademii Nauk, Mekhanika Zhidkosti i Gaza, No.5, pp. 120–126, September–October, 1992.     

Rotating flow of a second-order fluid on a porous plate

A study is made of the unsteady flow engendered in a second-order incompressible, rotating fluid by an infinite porous plate exhibiting non-torsional oscillation of a given frequency. The porous character of the plate and the non-Newtonian effect of the fluid increase the order of the partial differential equation (it increases up to third order). The solution of the initial value problem is obtained by the method of Laplace transform. The effect of material parameters on the flow is given explicitly and several limiting cases are deduced. It is found that a non-Newtonian effect is present in the velocity field for both the unsteady and steady-state cases. Once again for a second-order fluid, it is also found that except for the resonant case the asymptotic steady solution exists for blowing. Furthermore, the structure of the associated boundary layers is determined.     

Impact on the boundary of a compressible two-layer fluid

Within the framework of the acoustic approximation a solution of the plane nonstationary problem of impact on a fluid boundary is found. The fluid occupies the lower half-plane and consists of two layers with given speeds of sound and densities. The upper layer has a constant depth and is bounded above by a plate with a given normal velocity. The solution is constructed using the Fourier and Laplace integral transforms. Numerical calculations are performed for piston impact across a rigid screen and the impact of a jet with an aerated head on a rigid wall. It is shown that the presence of an interlayer with reduced speed of sound and/or density considerably changes the evolution of the hydrodynamic pressure distribution over the impacting surface: the absolute pressure maximum decreases but pressures of significant amplitude are maintained for a longer time than for a homogeneous fluid.     

Impact on the surface of a compressible liquid

The evolution of a weak, nearly plane shock wave produced by the impact on the plane boundary of a compressible liquid is considered. At the initial moment the liquid is at rest and occupies the lower half-plane. Then the points of its boundary get instantly velocities directed into the liquid domain. This leads to the formation of a shock wave the intensity of which is non-uniform due to a non-uniform distribution of the impact velocities. Initially the shock wave is plane but then it bends due to the non-linear effects and can later be focused. To analyze the liquid flow, the method of matched asymptotic expansions is used. For finite times the flow and the evolution of the shock wave are described within the framework of the acoustic approximation. For large times the flow becomes non-linear, and the form of the shock front depends essentially on the characteristics of the liquid flow behind it. If the non-uniformity of the impact velocity distribution is slight then the focusing of the shock wave is shown not to occur. The influence of viscosity of the liquid on the structure of its motion is discussed.     

Three-dimensional waves on the surface of a viscous fluid

The study of the effect of viscosity on the propagation of surface waves has traditionally been confined to the consideration of plane (two-dimensional) waves [1, 2]. So far the effect associated with taking the transverse modulation of the wave profile into account have not been studied. In what follows, a solution is constructed and analyzed for linear three-dimensional periodic waves in an infinitely deep fluid. Their distinguishing property is the presence of a vorticity in the direction of propagation. An expression for the average (over the wavelength) velocity of horizontal particle drift is found in the quadratic approximation in the small wave steepness.     

Moving load on a pre-stressed plate resting on a fluid half-space

Summary An analysis is made of the problem of vibrations of a plate with an axial force resting on compressible fluid half-space, when the plate is uniform and of infinite length and is subjected to a load which moves with constant velocity along the plate. An example is provided where the bending moment and the fluid pressure are calculated. From the results of theoretical analysis, it becomes evident that the axial force in the plate has considerable effect upon the dynamical behaviour of the system.

---

Übersicht Die Schwingungen einer auf kompressibler Flüssigkeit liegenden Platte, die durch eine Axialkraft beansprucht ist, werden für den Fall analysiert, daß die Platte gleichförmig und unendlich ausgedehnt ist, und daß eine Last an der Platte angreift, die sich mit konstanter Geschwindigkeit entlang der Platte verschiebt. In einem Beispiel werden das Biegemoment und der Flüssigkeitsdruck ermittelt. Die Ergebnisse zeigen, daß die Axialkraft auf das dynamische Verhalten des Systems erheblichen Einfluß hat.

---

---

The author would like to acknowledge the consistent guidance and encouragement of Professor H. Saito of Tohoku University. The research in this paper was conducted under a Scientific Research Grant from the Ministry of Education of the Government of Japan.     

Stability of a steady-state discontinuity of a fluid layer on the surface of an immiscible fluid

A new stable structure of the three-phase system formed by a gas, a horizontal liquid layer with a free upper surface and an underlying immiscible liquid substrate is investigated experimentally and theoretically. When the upper layer has a greater surface tension than the lower layer and its thickness is fairly small, a local deformation of its surface can lead to the development of a steady-state concentric discontinuity within whose limits the lower layer os in contact with the gas. The conditions of stability of such a phase system with a steady-state discontinuity are studied and the dependences of the discontinuity parameters on the vessel diameter, the upper layer thickness, and the liquid surface tensions are obtained for various pairs of liquids. The formulation of the analytic problem of the layer discontinuity is discussed. The experimental data are compared with the results of calculations carried out for a model of a discontinuity in an infinite layer.     

Impact of a drop on a solid surface

A numerical solution is obtained to the unsteady-state problem of a direct collision between a liquid drop of cylindrical form and a rigid surface. It is shown that unsteady-state interaction between shock waves inside the drop leads to the development of broad zones of cavitation, promoting the dispersion of the drop.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 5, pp. 151–155, September–October, 1977.The authors thank L. F. Shaikhatarova for making the calculations.     

Nonlinear standing waves on the surface of a viscous fluid

Standing surface waves in a viscous infinite-depth fluid are studied. The solution of the problem is obtained in the linear and quadratic approximations. The case of long, as compared with the boundary layer thickness, waves is analyzed in detail. The trajectories of fluid particles are determined and an expression for the vorticity is derived.     

Waves on the surface of a falling power-law fluid film

Waves that occur at the surface of a falling film of thin power-law fluid on a vertical plane are investigated. Using the method of integral relations an evolution equation is derived for two types of waves equation which are possible under long wave approximation. This equation reveals the presence of both kinematic and dynamic wave processes which may either act together or singularly dominate the wave field depending on the order of different parameters. It is shown that, at a small flow rate, kinematic waves dominate the flow field and the energy is acquired from the mean flow during the interaction of the waves, while, for high flow rate, inertial waves dominate and the energy comes from the kinematic waves. It is also found that this exchange of energy between kinematic and inertial waves strongly depends on the power-law index n. Linear stability analysis predicts the contribution of different terms in the wave mechanism. Further, it is found that the surface tension plays a double role: for a kinematic wave process, it exerts dissipative effects so that a finite amplitude case may be established, but for a dynamic wave process it yields dispersion. Further, it is shown that the non-Newtonian character n plays a vital role in controlling the role of the term that contains surface tension in the above processes.     

Viscous dissipative fluid flow past a semi‐infinite vertical plate with variable surface temperature

An analysis of the effect of viscous dissipative heat on two‐dimensional viscous incompressible fluid flow past a semi‐infinite vertical plate with variable surface temperature is carried out. The dimensionless governing equations are unsteady, two‐dimensional, coupled, and non‐linear governing equations. A most accurate, unconditionally stable and fast converging implicit finite‐difference scheme is used to solve the non‐dimensional governing equations. Velocity and temperature of the flow have been presented graphically for various parameters occurring in the problem. The local and average skin friction and Nusselt number are also shown graphically. It is observed that greater viscous dissipative heat causes a rise in the temperature. Copyright © 2007 John Wiley & Sons, Ltd.