Begell House Inc.
International Journal of Fluid Mechanics Research
FMR
2152-5102
27
1
2000
Effect of Electrostatic Field on Rupture of Thin Micropolar Liquid Film
1-12
Rama Subba Reddy
Gorla
Department of Mechanical Engineering, Cleveland State University, Cleveland, OH, 44115 USA; Department of Mechanical Engineering, University of Akron, Akron, Ohio 44325, USA; Department of Mechanical & Civil Engineering, Purdue University Northwest, Westville, IN 46391, USA
Earnest N.
Poulos
Department of Mechanical Engineering Cleveland State University Cleveland, Ohio 44115, USA
Larry W.
Byrd
Thermal Structures Branch, Air Vehicles Directorate, Air Force Research Laboratory, Wright Patterson Air Force Base, OH 45433, USA
Nonlinear thin micropolar liquid film rupture has been analyzed by investigating the stability under the influence of a non-uniform electrostatic field to finite amplitude disturbances. The dynamics of the liquid film is formulated using the balance equations including a body force term due to van der Waals attractions. The effect of the electric field is included in the analysis only in the boundary condition at the liquid vapor interface. The governing equation for the film thickness was solved by finite difference method as part of an initial value problem for spatial periodic boundary conditions. The electric field stabilizes the film and increases the time to rupture when a long wavelength perturbation is introduced. The influence of material properties of the micropolar fluid on rapture is discussed.
Natural Convection from Combined Thermal and Mass Diffusion Buoyancy Effects in Micropolar Fluids
13-32
M. A.
EL-Hakiem
Mathematics Department, Aswan Faculty of Science, South Valley University, Aswan, Egypt
Rama Subba Reddy
Gorla
Department of Mechanical Engineering, Cleveland State University, Cleveland, OH, 44115 USA; Department of Mechanical Engineering, University of Akron, Akron, Ohio 44325, USA; Department of Mechanical & Civil Engineering, Purdue University Northwest, Westville, IN 46391, USA
S.M.M.
EL-Kabeir
Department of Mathematics, Salman bin Abdulaziz University, College of Science and Humanity Studies, Al-Kharj, 11942, Saudi Arabia; Department of Mathematics, Aswan University, Faculty of Science, 81528, Egypt
A regular parameter perturbation analysis is presented to study the effect of combined thermal and diffusion buoyancy in the presence of both viscous dissipation and pressure stress in micropolar fluids on natural convection flows. The following natural convective flows are analyzed: those adjacent to an isothermal surface and uniform heat flux surface, a plane plume and flow generated from a horizontal line energy source on a vertical adiabatic surface. The velocity, microrotation distribution, temperature and concentration profiles are shown. Numerical results are obtained for the local Nusselt number as well as Sherwood number, wall shear stress and wall couple stress.
A Fluid Dynamic Model of Filtration in Removing Iron Oxides from Ground Waters
33-42
S. K.
Kiselev
Kiev State Technical University of Construction and Architecture, Ukraine
A. Ya.
Oleynnik
Fluid Mechanics Institute, Ukrainian Academy of Sciences, Kiev, Ukraine
A fluid dynamic model of filtration in the course of removing iron oxides from water, consisting of two inter-related units: the fluid dynamic (filtration) and of the dynamics of iron compounds in the porous filtrating medium is constructed. Certain cases of a general model at homogeneous and inhomogeneous oxidation stages are analyzed. The general model is implemented by numerical methods, analytic solutions are obtained for particular models. A technique for calculating the principal purification parameters is suggested.
Equations of Turbulent Gas/Solids Flow
43-55
S. I.
Kril'
Institute of Hydromechanics of National Academy of Sciences of Ukraine, Kyiv, Ukraine
V. P.
Berman
Institute of Hydromechanics of National Academy of Sciences of Ukraine, Kyiv, Ukraine
Probabilistically-averaged differential equations describing gas/solids suspensions as a turbulent thermodynamic medium are derived. The feasibility of employing the mathematical tools of the theory of generalized function for deriving this kind of equations is demonstrated. It is shown that the formula for differentiating an integral taken over a moving volume of the suspension is invariant under transition from ordinary to generalized derivatives.
Two-Dimensional Stokes Flow in a Semicircle
56-61
V. V.
Meleshko
Institute of Hydromechanics of National Academy of Sciences of Ukraine, Kyiv, Ukraine
A. M.
Gomilko
Institute of Hydromechanics of National Academy of Sciences of Ukraine, Kyiv, Ukraine
An exact analytic solution of the two-dimensional Stokes flow in a semicircle induced by uniform motion of a circular or rectilinear boundary is constructed. The contour streamline pattern and a typical velocity distribution are presented.
Asymptotic Space-Time Properties of Laminar Boundary Layers above Curved Surfaces
62-81
Ye. I.
Nikiforovich
Fluid Mechanics Institute Ukrainian Academy of Sciences, Kiev, Ukraine
The effect of centrifugal forces on transient processes in laminar boundary layers and the time-space parameters of their two- and three-dimensional vortex structures are investigated. Radius of curvature R of the flow-washed surface is taken to be constant for simplicity and it is assumed that the Reynolds number ReR is high. Two- and three-dimensional equations of the boundary layer are obtained and scenari of its development in terms of space-time scales of vortex structures are proposed using methods of matching asymptotic expansions with a small parameter equal to the reciprocal of the Reynolds number. In particular, the space-time properties of two- and three-dimensional boundary layers are investigated as a function of the problem's governing parameters. The concept of susceptibility for this class of problems is formalized and validated.
Spectrum of Turbulent Fluctuations of the Sea-Water Refraction Index
82-98
V. V.
Nikishov
Institute of Hydromechanics of National Academy of Sciences of Ukraine, Kyiv, Ukraine
V. I.
Nikishov
Institute of Hydromechanics of National Academy of Sciences of Ukraine, 8/4, Zhelyabov St.,
Kyiv, 03057, Ukraine
The behavior of the spectrum of fluctuations En of refraction index n in turbulent sea water when the fluctuations of n are controlled by fluctuations T' of the temperature and S' of the salinity is analyzed. The spectrum of En is found for homogeneous and isotropic turbulence as a function of the rate of dissipation (equalization) of temperature and salinity fluctuations which, together with the dissipation rate of the energy of turbulence, control the statistical behavior of fluctuations of n. These rates were parametrized by employing the gradient hypothesis. It was found that, depending on the contributions of temperature and salinity fluctuations to fluctuations of n, one may observe domains of anomal behavior which may include appearance of local extrema.
Unrestricted Influx of Nutrients to a Root Community
99-108
V. L.
Polyakov
Institute of Hydromechanics of National Academy of Sciences of Ukraine, Kyiv, Ukraine
An effective analytic solution of the problem of intermittent unrestricted influx of nutrients by way of dispersion, molecular diffusion and mass flux to communities of roots with allowance for the mutual competition of the latter is obtained. A transition from a micro-level structural model describing the dynamics of ion concentration in the soil solution to a model of a continuous biological medium is discussed.
Unsteady Supercavitated Motion of Bodies
109-137
Yu. N.
Savchenko
Institute of Hydromechanics of National Academy of Sciences of Ukraine, Kyiv, Ukraine
V. N.
Semenenko
Institute of Hydromechanics of National Academy of Sciences of Ukraine, Kyiv, Ukraine
S. I.
Putilin
Institute of Hydromechanics of National Academy of Sciences of Ukraine, Kyiv
Experimental and computer-simulation results on phenomena accompanying unsteady supercavitated motion of bodies in water are presented. The latter were obtained on the basis of a mathematical model based on the Logvinovich principle of independence of cavity expansion. The numerical results are compared with experimental data. A method of approximate calculation of forces and moments acting on a model due to interaction with the inner surface of the cavity is worked out. A theoretical analysis of the stability of motion of supercavitated models is presented.
The Helical Analog of Potential Flow over a Sphere
138-145
P. A.
Shestopal
Institute of Hydromechanics of National Academy of Sciences of Ukraine, Kyiv, Ukraine
N. V.
Saltanov
Institute of Hydromechanics of National Academy of Sciences of Ukraine, Kyiv, Ukraine
The generalized potential is employed for solving the problem of homogeneous helical flow over a sphere. It is shown that when the helicity factor of this flow tends to zero, this solution becomes identical to the traditional solution of the problem of potential flow over bodies. The effect of the helicity factor on the streamline pattern and pressure coefficient is analyzed.
Propagation of Unsteady Nonlinear Surface Gravity Waves above an Irregular Bottom
146-157
Igor T.
Selezov
Institute of Hydromechanics of National Academy of Sciences of Ukraine, Zhelyabov St., 8/4, Kyiv, 03680, MSP, Ukraine
Certain mathematical models of wave dynamics of the shelf zone are presented. Numerical solutions demonstrating new characteristic effects of the interaction between nonlinear water waves and the bottom topography are obtained. Nonlinear dispersive asymptotic approximations describing the propagation of waves above the bottom topography are obtained on the basis of an exact two-dimensional formulation that includes the Laplace equation for the velocity potential, nonlinear conditions on the free surface and conditions at the bottom surface. This is done on the assumption that dispersion parameter β and gradient γ of the bottom surface are small, whereas nonlinearity factor α is assumed to be arbitrary, unlike the extensively employed traditional approximate theories. A nonlinear model for investigating the motion of saline sea water and also the restructuring of an irregularly shaped bottom by means of waves propagating above it are also presented. The corresponding initial- and boundary-value problem is solved by the method of finite differences for specified semisinusoidal-type pulses repeatedly generated at the inlet. In addition, this problem is analyzed on the basis of the KdV equation with a specified inlet soliton. Numerical results are presented and analyzed.