Begell House Inc.
International Journal of Fluid Mechanics Research
FMR
2152-5102
32
4
2005
Modelling Convection Heat Transfer in a Rotating Fluid in a Thermally-Stratified High-Porosity Medium: Numerical Finite Difference Solutions
383-401
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
Harmindar S.
Takhar
Engineering Department, Manchester Metropolitan University, Oxford Rd., Manchester, M15GD, UK
Tasveer A.
Beg
Engineering Mechanics Associates, Manchester, M16, England, United Kingdom
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
Girishwar
Nath
Professor S. K. Sinha, KNIT Campus, IV/17, KNIT, Sultanpur 228118, India
Rui
Majeed
Biomedical Scientist, Kashmir Gardens, Darnall, Sheffield, UK
The convective heat transfer flow in a rotating fluid over a vertical plate in a non-Darcian thermally-stratified high-porosity medium is studied. The governing partial differential equations for momentum and energy are solved numerically using Blottner's finite-difference method. The effects of Rossby number and various thermal parameters on velocities, temperature, skin friction and Nusselt number are presented graphically and discussed at length. The flow and temperature fields are strongly influenced by the thermal stratification, porosity, inertia and Rossby number, whereas they demonstrate a weak dependence on the permeability parameter. Beyond a critical value of the Rossby number (Ro ≥ 0.5) flow reversal occurs in the X-component of the velocity. Other flow phenomena including primary and secondary flows are discussed. The problem finds applications in rotating industrial and geophysical systems.
Oscillatory Flow in a Tube with Multiple Constrictions
402-419
Gorachand C.
Layek
Department of Mathematics, University of Burdwan Burdwan, West Bengal, India
Swati
Mukhopadhyay
Department of Mathematics, The University of Burdwan, India
Sk. A.
Samad
Department of Mathematics, The University of Burdwan, Burdwan - 713104, W.B., India
The unsteady incompressible Navier-Stokes equations are solved numerically in primitive variables (pressure and velocity) for calculating the flow variables in a tube with multiple constrictions under the axi-symmetric approximations. The computation is carried over by taking a suitable transformation for multiple constrictions. The effects of multiple constrictions on a viscous flow field are investigated. The disturbances created by the constrictions are mainly concentrated in the exit of the last constriction. It is found that over the entire Reynolds number ranges studied here, the flow in the downstream of the constrictions is dominated by the strong recirculating flow associated with a shear layer. Oscillatory flow has been noted at the Reynolds number 175 for 75 % area reduction in four consecutive constrictions in a tube. The streamwise velocity components at different points in the downstream of the constrictions oscillate with frequency 1.1. The computed wall shear stress, pressure, and stream lines are also noted fluctuating in the downstream of the constrictions. The flow characteristics (such as central line velocity, pressure distribution, wall shear stress, and stream lines at different Reynolds numbers) are shown graphically, and their consequences in the human cardiovascular system are discussed at length.
General Solution for Two-Dimensional Corner Flows Under Darcy's
420-438
Yu. A.
Semenov
Institute of Hydromechanics of NAS of Ukraine, 8/4 Zhelyabov Street, Kyiv-180, MSP, 03680, Ukraine
L. J.
Cummings
School of Mathematical Sciences, University of Nottingham, Nottingham NG7 2RD, UK
We consider two-dimensional Darcy flow of a viscous incompressible fluid with a free boundary in a corner between two non-parallel walls. The complex potential of the flow constructed in an auxiliary parameter domain admits a general form for the flow generated by a source/sink at the corner vertex or at infinity. We present a method used to construct the flow potential, and obtain an integral equation for the velocity modulus on the free boundary. We discuss a possible numerical procedure to solve this integral equation, and present sample numerical results concerning the initial shape of the free boundary and its time evolution.
Mathematical Modeling of Geophysical Vortex Flow
439-453
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 developed of the geophysical vortex flow using an order-of-magnitude analysis based on a laminar, steady axisymmetric vortex motion in a cylindrical frame of reference. A similarity method is adopted. The classical solution of Long (J. Fluid. Mech., 11, p. 611, 1961; Rossby number > 1) is reexamined. It is shown that true similarity solutions for the intermediate case of the Rossby number ∼ 1 do not exist, since this implies the physically impossible vortex flow wherein the fluxes of radial momentum and angular momentum are simultaneously zero. Numerical solutions are presented for our model using a shooting method with graphs depicting the variation of pressure and also axial, azimuthal, and radial velocities with non-dimensional radius parameter. The results are discussed with applications to tornado swirl and compared to the earlier studies by Long and Herbert.
Planimetry of Vibrocapillary Equilibria at Small Wave Numbers
454-487
A. N.
Timokha
National Academy of Sciences of Ukraine, Institute of Mathematics, Tereschenkivska 3, 01601 Kiev, Ukraine
Time-averaged geometrical shapes (vibroequilibria) of a limited volume of ideal liquid in a rectangular vessel which performs high-frequency reciprocating vibrations have been analyzed for a two-dimensional potential flow. A concept of quasi-potential energy and an assumption of smallness of the wave numbers is used in the research. Particular exact analytical solutions are presented. The general case study is based on straight numerical minimization of a quasi-potential energy functional. An auxiliary boundary-value problem for the wave function, being a constraint, is solved by the modified Nystrom- Kress method. A theoretical description is given for the experimental phenomena of “flattening” and vibrostabilization of the free liquid surface, “overturn” ( “reorientation” of the liquid, its localization near one of the vertical walls), and “dip” (an even spreading of the liquid between the walls with a “cavity” appearing in the center) which occur under horizontal vibrations of the vessel. Numerical results for the vibroequilibria in the conditions of the Earth gravitation (large Bond's numbers) and zero gravity (lack of mass forces) are discussed. The solution ambiguity and vibroequilibrium dependence on transitional processes are pointed out. It has been confirmed theoretically that an “overturn” is more probable with a small depth, while a “dip” is typical of non-small depths of the liquid. Preliminary theoretical results describing the “flattening” and vibrostabilization of a drop hanging on a vibrating plate have been obtained, including the case of a negligibly small surface-tension (large Bond's numbers).
Pseudo-Sound Behind an Obstacle on a Cylinder in Axial Flow
488-510
V. A.
Voskoboinick
Institute of Hydromechanics of National Academy of Sciences of Ukraine, Kyiv
A. P.
Makarenkov
Institute of Hydromechanics of National Academy of Sciences of Ukraine, Kyiv
Pseudo-sonic fluctuations of the wall pressure behind a ring-shaped obstacle on a flexible extended cylinder in longitudinal flow of fluid have been experimentally investigated. Integral and spectral statistical characteristics of pressure fluctuation field behind the obstacle have been obtained and its influence on the structure of the turbulent boundary layer has been investigated. Putting the obstacle in the interior of the boundary layer changes the structure of the whole boundary layer. As the obstacle diameter increases, the intensity of the near-wall pressure fluctuations grows. The maximum intensity is observed in the near wake of the obstacle. At the distances exceeding 100 diameters of the obstacle, the turbulent boundary layer recovers. An increase of the obstacle diameter and flow velocity results in a growth of the low-frequency spectral components of pressure fluctuations and in a decay of the high-frequency components, compared to a boundary layer on hydraulically smooth cylinder. The turbulent boundary layer behind the obstacle is saturated with large-scale vortical structures. The biggest contribution to the energy of the pseudo-sonic pressure fluctuation field is made by the vortices shedded from an obstacle transverse to the flow, the frequencies of those conforming to the Strouhal number Sh ≈ 0.1. In the subcritical regime of the separation flow on the ring obstacle, the Strouhal number is inversely proportional to the Reynolds number.