Nonstationary motion of a shell on the surface of a heavy fluid

A three-dimensional nonstationary problem of vibrations of a flexible shell moving on the surface of an ideal heavy fluid. The forces due to surface tension are ignored. The problem is formulated in the space of the acceleration potential. The potential of the pulsating source is found by solving the Euler equation and the continuity equation taking into account the free-surface conditions (linear theory of small waves) and the conditions at infinity. The density distribution function of the dipole layer is determined from the boundary conditions on the surface of the shell. Formulas for determining the shape of gravity waves on the fluid surface and the natural frequencies of vibrations of the shell are obtained. __________ Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, Vol. 50, No. 4, pp. 66–75, July–August, 2009.     

Nanoscale Poiseuille flow and effects of modified Lennard–Jones potential function

Numerical simulation of Poiseuille flow of liquid Argon in a nanochannel using the non-equilibrium molecular dynamics simulation (NEMD) is performed. The nanochannel is a three-dimensional rectangular prism geometry where the concerned numbers of Argon atoms are 2,700, 2,550 and 2,400 at 102, 108 and 120 K. Poiseuille flow is simulated by embedding the fluid particles in a uniform force field. An external driving force, ranging from 1 to 11 PN (Pico Newton), is applied along the flow direction to inlet fluid particles during the simulation. To obtain a more uniform temperature distribution across the channel, local thermostating near the wall are used. Also, the effect of other mixing rules (Lorenthz–Berthelot and Waldman–Kugler rules) on the interface structure are examined by comparing the density profiles near the liquid/solid interfaces for wall temperatures 108 and 133 K for an external force of 7 PN. Using Kong and Waldman–Kugler rules, the molecules near the solid walls were more randomly distributed compared to Lorenthz–Berthelot rule. These mean that the attraction between solid–fluid atoms was weakened by using Kong rule and Waldman–Kugler rule rather than the Lorenthz–Berthelot rule. Also, results show that the mean axial velocity has symmetrical distribution near the channel centerline and an increase in external driving force can increase maximum and average velocity values of fluid. Furthermore, the slip length and slip velocity are functions of the driving forces and they show an arising trend with an increase in inlet driving force and no slip boundary condition is satisfied at very low external force (<1 PN).     

Filtration in a Porous Granular Medium: 1. Simulation of Pore-Scale Particle Deposition and Clogging

This paper presents a numerical model for simulating the pore-scale transport and infiltration of dilute suspensions of particles in a granular porous medium under the action of hydrodynamic and gravitational forces. The formulation solves the Stokes’ flow equations for an incompressible fluid using a fixed grid, multigrid finite difference method and an embedded boundary technique for modeling particle–fluid coupling. The analyses simulate a constant flux of the fluid suspension through a cylindrical model pore. Randomly generated particles are collected within the model pore, initially through contact and attachment at the grain surface (pore wall) and later through mounding close to the pore inlet. Simple correlations have been derived from extensive numerical simulations in order to estimate the volume of filtered particles that accumulate in the pore and the differential pressure needed to maintain a constant flux through the pore. The results show that particle collection efficiency is correlated with the Stokes’ settling velocity and indirectly through the attachment probability with the particle–grain surface roughness. The differential pressure is correlated directly with the maximum mound height and indirectly with particle size and settling velocity that affect mound packing density. Simple modification factors are introduced to account for pore length and dip angle. These parameters are used to characterize pore-scale infiltration processes within larger scale network models of particle transport in granular porous media in a companion paper. Articlenote: Currently at GZA GeoEnvironmental Inc., 1 Edgewater Drive, Norwood, MA 02062, U.S.A.     

Velocity profiles and interface instability in a two-phase fluid: investigations using ultrasonic velocity profiler

In the present study the velocity profiles and the instability at the interface of a two phase water-oil fluid were investigated. The main aim of the research project was to investigate the instability mechanisms that can cause the failure of an oil spill barrier. Such mechanisms have been studied before for a vast variety of conditions (Wicks in Fluid dynamics of floating oil containment by mechanical barriers in the presence of water currents. In: Conference on prevention and control of oil spills, pp 55–106, 1969; Fannelop in Appl Ocean Res 5(2):80–92, 1983; Lee and Kang in Spill Sci Technol Bull 4(4):257–266, 1997; Fang and Johnston in J Waterway Port Coast Ocean Eng ASCE 127(4):234–239, 2001; among others). Although the velocity field in the region behind the barrier can influence the failure significantly, it had not been measured and analyzed precisely. In the present study the velocity profiles in the vicinity of different barriers were studied. To undertake the experiments, an oil layer was contained over the surface of flowing water by means of a barrier in a laboratory flume. The ultrasonic velocity profiler method was used to measure velocity profiles in each phase and to detect the oil–water interface. The effect of the barrier geometry on velocity profiles was studied. It was determined that the contained oil slick, although similar to a gravity current, can not be considered as a gravity current. The oil–water interface, derived from ultrasonic echo, was used to find the velocity profile in each fluid. Finally it was shown that the fluctuations at the rearward side of the oil slick head are due to Kelvin–Helmholtz instabilities.     

Numerical analysis of the flutter of a shallow shell

The stability of vibrations of a shallow shell that is rectangular in plant in a gas flow is studied for an arbitrary vector of flow velocity. Mathematically, the problem is shown to reduce to an ill-conditioned computational problem. To solve this problem, we propose a numerical saturation-free algorithm that allows one to obtain a sufficiently accurate solution for a grid containing 169 (13×13) nodes. In calculations for cylindrical and spherical shallow shells, new mechanical effects concerning the vibration modes and the dependence of the critical flutter velocity on the direction of the flow-velocity vector were found. Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, Vol. 40, No. 6, pp. 97–102, November–December, 1999.     

Effects of Chemical Reaction and Double Dispersion on Non-Darcy Free Convection Heat and Mass Transfer

In this article, the effects of chemical reaction and double dispersion on non-Darcy free convection heat and mass transfer from semi-infinite, impermeable vertical wall in a fluid saturated porous medium are investigated. The Forchheimer extension (non-Darcy term) is considered in the flow equations, while the chemical reaction power–law term is considered in the concentration equation. The first order chemical reaction (n = 1) was used as an example of calculations. The Darcy and non-Darcy flow, temperature and concentration fields in this study are observed to be governed by complex interactions among dispersion and natural convection mechanisms. The governing set of partial differential equations were non-dimensionalized and reduced to a set of ordinary differential equations for which Runge–Kutta-based numerical technique were implemented. Numerical results for the detail of the velocity, temperature, and concentration profiles as well as heat transfer rates (Nusselt number) and mass transfer rates (Sherwood number) are presented in graphs.     

Front Tracking Using a Hybrid Analytical Finite Element Approach for Two-Phase Flow Applied to Supercritical CO<Subscript>2</Subscript> Replacing Brine in a Heterogeneous Reservoir and Caprock

Predicting fluid replacement by two-phase flow in heterogeneous porous media is of importance for issues such as supercritical CO₂ sequestration, the integrity of caprocks and the operation of oil water/brine systems. When considering coupled process modelling, the location of the interface is of importance as most of the significant interaction between processes will be happening there. Modelling two-phase flow using grid based techniques presents a problem as the fluid–fluid interface location is approximated across the scale of the discretisation. Adaptive grid methods allow the discretisation to follow the interface through the model, but are computationally expensive and make coupling to other processes (thermal, mechanical and chemical) complicated due to the constant alteration in grid size and effects thereof. Interface tracking methods have been developed that apply sophisticated reconstruction algorithms based on either the ratio of volumes of a fluid in an element (Volume of Fluid Methods) or the advective velocity of the interface throughout the modelling regime (Level set method). In this article, we present an “Analytical Front Tracking” method where a generic analytical solution for two-phase flow is used to “add information” to a finite element model. The location of the front within individual geometrical elements is predicted using the saturation values in the elements and the velocity field of the element. This removes the necessity for grid adaptation, and reduces the need for assumptions as to the shape of the interface as this is predicted by the analytical solution. The method is verified against a standard benchmark solution and then applied to the case of CO₂ pooling and forcing its way into a heterogeneous caprock, replacing hot brine and eventually breaking through. Finally the method is applied to simulate supercritical CO₂ injected into a brine saturated heterogeneous reservoir rock leading to significant viscous fingering and developement of preferential flow paths. The results are compared with to a finite volume simulation.     

PIV-based investigations of animal flight

An overview is presented of the principles of estimation of fluid forces exerted upon solid bodies, based upon whole-field velocity measurements such as provided by PIV. The focus will be on the range of length and velocity scales characterised by the flight of large insects, birds, bats and small unmanned air vehicles, so that while viscous terms in the Navier–Stokes equations can many times be ignored in the quantitative analysis, understanding and measuring boundary-layer flows, separation and instability will ultimately be critical to predicting and controlling the fluid motions. When properly applied, PIV methods can make accurate estimates of time-averaged and unsteady forces, although even ostensibly simple cases with uncomplicated geometries can prove challenging in detail. Most PIV-based force estimates are embedded in some analytical model of the fluid–structure interaction, and examples of these with varying degrees of complexity are given. In any event, the performance and accuracy of the PIV method in use must be well understood as part of both the overall uncertainty analysis and the initial experimental design.     

Analysis of nonstationary processes in cylindrical shells interacting with a fluid flow

The paper outlines a technique to analyze the nonstationary vibrations of cylindrical shells interacting with a fluid flow and subjected to external periodic pressure with slowly varying frequency. The dynamic processes occurring in the shell–fluid system as the resonance region is passed forth and back are analyzed     

Inertial motion of a body in an ideal fluid from the state at rest

The motion of a body in an ideal incompressible fluid flow without vortices in the absence of external forces is considered. It is demonstrated that the body can move inertially from the state at rest if its shape satisfies certain conditions. __________ Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, Vol. 49, No. 4, pp. 214–219, July–August, 2008.     

Motion of a gas inclusion in a capillary under the action of vibration

The motion of gas inclusions in a liquid-filled duct under the action of vibration for comparable cross-sectional dimensions of the inclusion and the duct is studied. Two limiting cases of inclusion motion differing with respect to the drag mechanism are considered. For low velocities, it is assumed that the drag is mainly determined by the capillary forces and the friction in the liquid film separating the gas inclusion from the duct wall. As the inclusion velocity increases, the main contribution to the drag is made by such mechanisms as flow separation, the formation of a low-pressure region in the wake, etc. It is demonstrated that due to the vibration a gas inclusion traveling in a capillary under the action of steady forces is halted at certain points of the capillary. The capillary behaves like a filter, impermeable for inclusions smaller than a certain threshold size. Moscow. Translated from Izvestiya Rossiiskoi Akademii Nauk, Mekhanika Zhidkosti i Gaza, No. 3, pp. 85–92, May–June, 1998. The work received financial support from the Russian Foundation for Basic Research (project No.96-01-01813).     

Quasi-cylindrical figures of equilibrium of a rotating fluid

The problem of the equilibrium shape of a steady rotating rectilinear infinite cord of ideal self-gravitating homogeneous fluid is considered. The question whether, apart from the obvious solution, namely, an infinite circular cylinder, noncylindrical equilibrium figures can exist is investigated. A search is carried out among axisymmetric figures with periodic surface structure (“wavy” cylinders). The period of the wave structure and, in the first approximation, the shape of the surface are found as functions of the angular velocity of rotation. Sankt-Peterburg. Translated from Izvestiya Rossiiskoi Akademii Nauk, Mekhanika Zhidkosti i Gaza, No. 3, pp. 22–30, May–June, 2000.     

Radial electroelastic nonstationary vibration of a hollow piezoceramic cylinder subject to electric excitation

The paper studies the radial nonstationary vibration of a piezoceramic cylinder polarized throughout the thickness and subjected to a dynamic electric load. A numerical algorithm for solving an initial–boundary-value problem using mesh-based approximations and difference schemes is developed. The dynamic electroelastic state of the cylinder subjected to a constant potential difference applied instantaneously is analyzed Translated from Prikladnaya Mekhanika, Vol. 45, No. 2, pp. 30–35, February 2009.     

Dynamics of a chain system of rigid bodies with gravity-friction seismic dampers: fixed supports

A design model for a chain system of N elastically linked rigid bodies with a spheroidal gravity-friction damper is proposed. The Lagrange–Painlevé equations of the first kind are used to construct nonlinear dynamical models of a mechanical system undergoing translational vibrations about the equilibrium position. The conditions under which the system moves in one plane are established. The double nonstationary phase–frequency resonance of a system with N = 2 is analyze. After the numerical integration of the systems of differential equations, the phase–frequency surfaces are plotted and examined for several combinations of system parameters under two-frequency loading     

Grip pressure distribution under static and dynamic loading

The dynamic response of a vibrating handarm system is strongly related to the grip force. While the relationship between total grip force and vibration characteristics of the hand-arm system has been extensively studied, no attempts have been made to investigate the distribution of grip pressure at the hand-handle interface. The local grip-pressure distribution may be more closely related to the finger blood flow, fatigue and loss of productivity than total grip force. In the present study, distribution of static and dynamic forces at a hand-handle interface is investigated using a grid of pressure sensors mounted on the handle. The pressure distribution is acquired for different values of static and dynamic grip forces in the range of 25–150 N. The dynamic measurements were conducted at various discrete frequencies in the 20–1000 Hz range with peak acceleration levels of 0.5 g, 1.0 g, 2.0 g and 3.0 g. The grip-pressure distribution under static loads revealed a concentration of high pressures near the tips of the index and middle fingers, and the base of the thumb. This concentration of high pressures shifted towards the middle of the fingers under dynamic loads, irrespective of grip force, excitation frequency and acceleration levels. These local pressure peaks may be related to impairment of blood flow to finger tips and the possible causation of vibration white finger. Paper was presented at the 1992 SEM Spring Conference on Experimental Mechanics held in Las Vegas, NV on June 8–11.     

Particle interaction in a flow with a parabolic velocity profile

The hydrodynamic interaction of two rigid spherical particles in a viscous incompressible fluid with the velocity at infinity represented by a second-degree polynomial in the coordinates is considered. An analytical solution of the problem is suggested. The forces and torques exerted on the particles and also the linear and angular particle velocities are calculated. The results are compared with previous theoretical and experimental data. Saransk. Translated from Izvestiya Rossiiskoi Akademii Nauk, Mekhanika Zhidkosti i Gaza, No. 1, pp. 84–91, January–February, 2000. The work received financial support from the Russian Foundation for Basic Research (project No. 98-01-03295).     

On the stability and extension of reduced-order Galerkin models in incompressible flows

Proper orthogonal decomposition (POD) has been used to develop a reduced-order model of the hydrodynamic forces acting on a circular cylinder. Direct numerical simulations of the incompressible Navier–Stokes equations have been performed using a parallel computational fluid dynamics (CFD) code to simulate the flow past a circular cylinder. Snapshots of the velocity and pressure fields are used to calculate the divergence-free velocity and pressure modes, respectively. We use the dominant of these velocity POD modes (a small number of eigenfunctions or modes) in a Galerkin procedure to project the Navier–Stokes equations onto a low-dimensional space, thereby reducing the distributed-parameter problem into a finite-dimensional nonlinear dynamical system in time. The solution of the reduced dynamical system is a limit cycle corresponding to vortex shedding. We investigate the stability of the limit cycle by using long-time integration and propose to use a shooting technique to home on the system limit cycle. We obtain the pressure-Poisson equation by taking the divergence of the Navier–Stokes equation and then projecting it onto the pressure POD modes. The pressure is then decomposed into lift and drag components and compared with the CFD results.     

The effect of particles on fluid turbulence in a turbulent boundary layer over a cylinder

The turbulent fluid and particle interaction in the turbulent boundary layer for cross flow over a cylinder has been experimentally studied. A phase-Doppler anemometer was used to measure the mean and fluctuating velocities of both phases. Two size ranges of particles (30μm–60μm and 80μm–150μm) at certain concentrations were used for considering the effects of particle sizes on the mean velocity profiles and on the turbulent intensity levels. The measurements clearly demonstrated that the larger particles damped fluid turbulence. For the smaller particles, this damping effect was less noticeable. The measurements further showed a delay in the separation point for two phase turbulent cross flow over a cylinder. The project supported by the National Natural Science Foundation of China     

FLUIDELASTIC ANALYSIS OF TUBE BUNDLE VIBRATION IN CROSS-FLOW

Tube bundles in cross-flow vibrate in response to motion-induced fluid-dynamic forces; hence, the resultant motions are considered to be a fluidelastic vibration. The characteristics of the vibration depend greatly on the features of the fluid-dynamic forces and the structure of the tube bundle. Therefore, in this study, the equations of motion of the tube bundle are derived. From the viewpoint of vibration, each tube is not independent of the surrounding tubes because its vibration is affected by fluid-dynamic coupling with the neighboring tubes. Thus, the equations are a set of coupled equations and the solution is obtained as an eigenvalue problem. The fluid-dynamic forces, which are indispensable in the calculation, have been obtained by experiments using a vibrating tube in the bundle; it was found that the forces depend strongly on the reduced velocity. Using these equations and the fluid forces, critical velocities of the tube bundle vibration are calculated, and it is found that the critical velocity is strongly dependent on the fluid-dynamic force characteristics, as they vary with the reduced velocity. Vibration tests of the tube bundle have also been conducted, and the critical velocities obtained in the tests are compared with the calculated values; agreement with the calculated values is good, demonstrating that the method of calculation is useful. The effects of mass ratio, frequency deviation and damping deviation of tubes in the bundle on the critical velocity are also examined theoretically. It is found that it is better to treat the mass ratio and the logarithmic decrement separately when the mass ratio is less than 10. Differences in natural frequencies make the critical velocity large. Similarly, differences in logarithmic decrement may distribute the vibration energy to other tubes and make the critical velocity large.     

Numerical study on a vertical plate with variable viscosity and thermal conductivity

Free convection over an isothermal vertical plate immersed in a fluid with variable viscosity and thermal conductivity is studied in this paper. We consider the two-dimensional, laminar and unsteady boundary layer equations. Using the appropriate variables, the basic governing equations are transformed to non-dimensional governing equations. These equations are then solved numerically using a very efficient implicit finite difference scheme known as Crank–Nicolson scheme. The fluid considered in this study is of viscous incompressible fluid of temperature dependent viscosity and thermal conductivity. The effect of varying viscosity and thermal conductivity on velocity, temperature, shear stress and heat transfer rate are discussed. The velocity and temperature profiles are compared with previously published works and are found to be in good agreement.