Begell House Inc.
International Journal of Fluid Mechanics Research
FMR
2152-5102
29
1
2002
Numerical Modelling of Darcy - Brinkman - Forchheimer Magnetohydrodynamic Mixed Convection Flow in a Porous Medium with Transpiration and Viscous Heating
26
Ali J.
Chamkha
Department of Mechanical Engineering, Prince Sultan Endowment for Energy and
Environment, Prince Mohammad Bin Fahd University, Al-Khobar 31952, Kingdom of Saudi
Arabia; RAK Research and Innovation Center, American University of Ras Al Khaimah, United Arab Emirates, 10021
Harmindar S.
Takhar
Engineering Department, Manchester Metropolitan University, Oxford Rd., Manchester, M15GD, UK
O. Anwar
Bég
Fluid Mechanics, Nanosystems and Propulsion, Aeronautical and Mechanical Engineering,
School of Computing, Science and Engineering, Newton Building, University of Salford,
Manchester M54WT, United Kingdom
A mathematical model is presented to investigate the combined effects of buoyancy, porous inertial drag, boundary vorticity diffusion (Brinkman friction), transverse magnetic field, viscous dissipation, wall transpiration, thermal conductivity and various other thermofluid parameters on the convection boundary layer flow of an electrically-conducting fluid past a vertical permeable semi-infinite plate in a saturated porous medium. The transformed boundary layer equations are solved numerically on a x-h domain using the robust Keller-box finite difference method and a powerful double-shooting Runge-Kutta method (DSRK). Results are presented graphically for the local skin-friction function (surface shear stress parameter) and the local Nusselt number function (local heat transfer parameter) for a wide range of the pertinent physical parameters. For the special case of x = 0 (at the leading edge), plots are given to compare the computations by both numerical methods and found to be in excellent agreement.
Laser Doppler Anemometry Study of Oscillating Bubbles
13
C. A.
Greated
The University of Edinburgh, Department of Physics and Astronomy, Edinburgh, EH9 3JN, Scotland, UK
S. H.
Douglas
The University of Edinburgh, Department of Physics and Astronomy, Edinburgh, EH9 3JN, Scotland, UK
R.
Royles
The University of Edinburgh, School of Engineering and Electronics, Institute for Infrastructure and Environment, Crew Building, The King's Buildings, West Mains Road, Edinburgh, EH9 3JN, Scotland, UK
The use of laser Doppler anemometry (LDA) to investigate the non-stationary signal from an oscillating bubble produced by an underwater spark is presented. The major benefit of using LDA to measure the flow over traditional techniques such as hydrophones is that the method is non-intrusive and therefore does not influence the flow. The non-stationary Doppler signal is analyzed in a novel way using wavelets to produce the instantaneous velocity of the flow at the measurement point and hence pressure. This can be used to obtain the bubble oscillation period, maximum radius and energy. The form of the energy transfer from the circuit to the bubble in terms of the spark gap width is found to be non-linear and an empirical relationship for the decay of the bubble peak pressure with distance from the bubble center is obtained.
On the Relationship between Fluid Velocity and de Broglie's Wave Function and the Implications to the Navier - Stokes Equation
13
V. V.
Kulish
School of Mechanical & Production Engineering, Nanyang Technological University, 50 Nanyang Ave., Singapore, 639798
Jose' L.
Lage
Southern Methodist University, Department of Mechanical Engineering,
POBox 750337, Dallas, TX 75275-0337, USA
By exploring the relationship between the group velocity of the de Broglie's waves and a particle velocity we can demonstrate the existence of a close relationship between the continuity equation and the Schrodinger's equation. This relationship leads to the proportionality between the fluid velocity v and the corresponding de Broglie's wave's phase at the same location. That is, the existence of a scalar function q proportional to the phase of the de Broglie's wave, such that v = Сq can be proven without reference to the flow being inviscid. We then proceed to show that the Navier-Stokes equation in the case of constant viscosity incompressible fluid is equivalent to a reaction-diffusion equation for the wave function of the de Broglie's wave associated to the moving fluid element. A general solution to this equation, written in terms of the Green's functions, and the criterion for the solution to be stable is presented. Finally, in order to provide an example, the procedure is applied to obtain the solution for the simplest case of the Burgers' equation.
Vortex Shedding from a Square Cylinder at Different Blockage Ratios and Locations
12
Necati
Mahir
Thermal Science and Technology Association
Vortex shedding from a square cylinder in a channel is investigated by the numerical solution of the unsteady two-dimensional Navier-Stokes equations. A high order finite difference scheme is employed to solve these equations. The effects of walls on the vortex structure and drag coefficient are studied at different blockage ratios for the Reynolds number of 250 where the flow is laminar. Blockage ratios, A/H, vary as 0.17, 0.25, 0.33 and 0.5. Gap ratio between the cylinder and wall, s/A, also changes as 2.5, 1.5, 1.0, and 0.5. H and s represents the channel height and the gap between the cylinder and the wall respectively. The results reveal that the increase in blockage ratio strengthens the vortex formation. Reducing of gap ratio destabilizes vortex formation. For s/A = 0.5, vortex formation is suppressed.
Modeling of Noise Generation by a Vascular Stenosis
24
A. O.
Borisyuk
Institute of Hydromechanics of the National Academy of Sciences of Ukraine, Zhelyabov Str., 8/4, 03680, Kyiv-180, MSP, Ukraine
An in-vitro experiment is carried out in order to study the properties of an acoustic field in the human chest produced by flow in a larger, blood vessel. The cases of intact and partially occluded vessels are considered, and abrupt rigid-wall hollow axisymmetric cylindrical plugs of varying inner diameters and lengths are used as stenoses. The analysis of the noise fields reveals the characteristic signs of the presence of a stenotic obstruction in the vessel. These are the general increase of the noise levels and production of the new frequency components in the power spectrum. The components are identified with the characteristic frequencies of vortex formation in the disturbed flow region behind a stenosis and the resonance frequencies of vibrations of the poststenotic segment of vessel. The stenosis generated acoustic power is found to be approximately proportional to the fourth power of the constriction severity and fourth power of the flow's Reynolds number.
Local Stretching Maps: an Application for an Advection Problem in an Arbitrary Velocity Field
22
Hassan
Peerhossaini
Thermofluids, complex flows and energy research group - Laboratoire de Thermocinétique, CNRS-UMR 6607, Ecole polytechnique de université de Nantes, Nantes, France
The local stirring properties of a passive fluid domain with arbitrary borders in known velocity field are discussed. Analytical solution for local stretching permits to single out an exponential coefficient that describes stretching of the domain studied and is analogous to the largest Lyapunov's exponent used in chaotic dynamics. This coefficient exists in all solutions; it does not depend on the shape of the contour, and is determined by the gradients of the velocity field components only. Another local mechanism of stirring is determined by integral characteristics of the flow and the shape of the contour under consideration. Construction of maps for local stretching values in fixed moments allows to analyze informatively an evolution of regions, in which an intensive stirring takes place. The stirring process is explored in a sample of an advection problem of a passive impurity in the velocity field induced by a system of point vortices moved periodically. This interaction regime generates a chaotic motion of passive fluid particles. Local stretching maps show that the regions of chaotic motion of fluid particles and of intensive stirring do not coincide. Chaotic region has a zone of weak stirring, in which contours are transported from one intensive stretching zone to another without any deformation.
A Method for Evaluation of an Unsteady Preassure Field in a Mixed Potential-Vortical Domain Adjacent to a Rotating Wing
13
A. V.
Shekhovtsov
Institute of Hydromechanics of National Academy of Sciences of Ukraine, Kyiv, Ukraine
It is shown in the paper that a pressure field in a vorticity domain surrounding a rotating wing can be evaluated using the improved method of discrete vortices along with the Cauchy-Lagrange integral. The computational formulae are obtained for the cases of wing motion in either bounded or unbounded medium, and in either presence or absence of an external flow. Application of the method to the problems of rotation of a thin wing (vorticity generator) in an unbounded medium or near a screen indicates that the method provides a quite efficient and accurate way of evaluating the fields possessing high gradients of the pressure coefficient.
Unsteady Oscillations of a Liquid-Saturated Poroelastic Soil Layer
10
A. N.
Trofimchuk
Institute of Hydromechanics of National Academy of Sciences of Ukraine, Kyiv, Ukraine
The paper is concerned with the problem of unsteady oscillations of a liquid-saturated poroelastic medium layer governed by the system of the Biot's differential equations. The finite-element method is used for numerical determination of dynamic displacements of the solid and liquid phases, pore pressure and effective stresses in the solid phase. The numerical analysis of the single-axis loading of a poroelastic liquid-saturated soil layer is performed, the effects of interaction between the phases in the layer are studied at various values of the permeability parameter. The numerical results presented in the paper suggest that the consolidation process slows down with decreasing the medium's permeability; in the case of a high permeability material, the appreciable oscillation damping is observed.