Begell House Inc.
International Journal of Fluid Mechanics Research
FMR
2152-5102
31
4
2004
Mathematical Modelling of Gradually Varied Flow in Open Channels: Corrections to the Chow and Bresse Integration Derivations
6
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
We present a re-examination of the gradually varied flow problem for open channels. A close study of the classical study by Bresse (1860) [1] and Bakhmeteff (1912) [2] and later Chow (1955) [4] has shown that their standard computations contain some errors. The objective is to clarify this error in open channel hydrodynamics and thereby assist engineers and modelers engaged in this area of research.
Conjugate Effect of Heat and Mass Transfer in Natural Convection Flow from an Isothermal Sphere with Chemical Reaction
13
Anwar
Hossain
Department of Mathematics, University of Dhaka, Dhaka-1000, Bangladesh
Md. Mamun
Molla
School of Engineering & Applied Science, Dept. of Electrical & Computer Engineering, North South University Dhaka-1229, Bangladesh
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
Natural convection flow from an isothermal sphere immersed in a viscous incompressible fluid in the presence of species concentration and chemical reaction has been investigated. The governing boundary layer equations are transformed into a non-dimensional form and the resulting nonlinear system of partial differential equations are reduced to local non-similarity boundary layer equations, which are solved numerically by very efficient implicit finite difference method together with Keller box scheme. Numerical results are presented by velocity, temperature and species concentration profiles of the fluid as well as the local skin-friction coefficients, local heat transfer rate and the local species concentration transfer rate for a wide range of chemical reaction parameter γ (= 0.0; 0.5; 1.0; 2.0; 4.0), buoyancy parameter w (= 0.0; 0.2; 0.6; 1.0), Schmidt number Sc (= 0.7; 10.0; 50.0; 100.0) and Prandtl number Pr (= 0.7; 7.0).
Sound Radiation by Circular Bimorphic Piezoceramic Plate
11
A. I.
Bogatiryov
Institute of Hydromechanics of National Academy of Sciences of Ukraine, Kyiv, Ukraine
I. V.
Vovk
Institute of Hydromechanics of National Academy of Sciences of Ukraine, Kyiv, Ukraine
Valery
Oliynik
Institute of Hydromechanics of National Academy of Sciences of Ukraine
A problem of sound radiation by a bimorphic piezoceramic disk submerged in fluid and being excited by a harmonic in time electric voltage is solved within the scope of the theory of thin bimorphic piezoplates and using the method of partial domains. The cases are considered when the bimorphic disk is placed inside an infinite baffle (acoustically soft or hard). The disk's contour is implied to be free or simply supported. A numerical analysis of radiated power and directivity pattern for acoustical system under consideration is conducted. As a result, it is shown that, contrary to a widespread opinion, the free disk in the soft baffle is an efficient sound source.
Chaotic Advection by Two-Dimensional Stokes Flow in a Semicircle
15
T. A.
Dunaeva
Kyiv National Technical University "KPI", Kyiv, Ukraine
A. A.
Gourjii
Institute of Hydromechanics of National Academy of Sciences of Ukraine, Kyiv, Ukraine
V. V.
Meleshko
Institute of Hydromechanics of National Academy of Sciences of Ukraine, Kyiv, Ukraine
A two-dimensional Stokes flow due to a periodic motion of a circular and rectilinear boundary in a semicircle is considered. An exact analytical solution for a description of a velocity field is given. Peculiarities of the velocity field and their influence on the motion of a surrounding passive fluid in the semicircle are also studied. Poincare section, trajectories of motion of passive fluid particles, the largest Lyapunov exponent are calculated and analyzed for various regimes and values of boundary velocities, that allow determining the zones of both intensive (chaotic) and weak (regular) mixing of the above regions of fluid flow in the semicircle.
The Regime Hysteresis of Viscous Flow with Free Surface in Rotating Horizontal Cylinder
11
Yu. V.
Naumenko
Rivne State Humanitarian University, Ukraine
The regime hysteresis of steady flow of liquid, which fills partially a steady-state rotating, horizontal cylinder is considered. The effect consists in exceeding the value of angular velocity of the cylinder in transition from circulating flow to wall layer flow, under the cylinder speed up over a value of its velocity in its reverse transition during deceleration. The hysteresis shows up when the Reynolds numbers are large, it is not observed when the numbers are small and it gains in strength when the degree of cylinder's filling with liquid increases. It is shown that the obtained analytical steady-state conditions of the wall layer are in agreement with experimental data for the case of large values of the Reynolds numbers, when disturbance of free surface arises, and they are not in agreement for the case of small values of the numbers, when circulating secondary flow springs up as a roller. On the basis of experimental data with allowance for accepted similarity criteria the universal diagrams are plotted which can be used in more exact calculations of the change boundary of regimes, are plotted.
Analysis of Acoustic Signal Generated by Axisymmetyic Localized Area of Cavitation Origin
14
A. A.
Nazarenko
I. I. Mechnikov Odessa National University, Odessa, Ukraine
The paper present results of an analysis of acoustic signals generated by immersed axisymmetric fluid jets that create local toroidal cavitation regions tending to collapse periodically. A transcendental dispersion equation has been derived, which describes this process, and an analytical relationship has been established which shows how the frequency of the generated vibrations depends on parameters of an emitting system. Coefficients have been introduced and evaluated that define a fraction of the fluid's flow rate spent for developing the cavitation region, a pressure change rate inside it, and a ratio of its volume to the volume cut off by the jet. Plots of experimental and theoretical relationships are presented, that describe the frequency of vibrations vs. parameters of the system in question.
Violation of the Solution Superposition Principle for the Initial-Boundary Problem with Mobile Boundaries for Wave Equation
7
V. A.
Pozdeev
Institute of Hydromechanics of National Academy of Sciences of Ukraine, Kyiv; and Institute of Pulse Processes and Technologies of National Academy of Sciences of Ukraine, Mykolayiv, Ukraine
Violation of the superposition principle when allowing for moving boundaries, even in the case of a linear wave equation, is shown on an example of analytical solution of the initial-boundary problem on acoustic wave radiation by a moving plane piston. The developed solution for the piston motion, represented as a superposition of low-amplitude oscillations upon the constant velocity, describes the well-known Doppler effect. All results are obtained on the basis of the non-linear time transformation technique.
Motion of a Fluid in a Capillary at Various Regimes of the Ultrasound Action
11
E. Yu.
Rozina
Odessa State Academy of Cold, Ukraine
Peculiarities of a sonocapillary effect in precavitational regime are investigated. It is shown that in this regime the small meniscus shift deep into the capillary is caused by the strong attenuation of ultrasonic field on the capillary inlet. The attenuation coefficient value has been determined experimentally. It is shown that a pulsating bubble, forming on the capillary end, can concentrate the ultrasonic wave energy and direct it into the capillary canal. In this case the capillary filling depth increases more than by one-two orders. It is shown that the stable liquid lifting in the capillary is possible in the absence of cavitation.
Evolutional Properties of Discontinuous Fluid Flows with Turbulent Viscosity
15
O. N.
Shablovskiy
P. O. Sukhoy Gomel State Engineering University, Byelarus
A new class of two-dimensional non-stationary flows has been developed for a viscous fluid with strong discontinuities. Approximate Bubnov-Galerkin method reduces the problem to the analysis of evolutional properties of a nonlinear dynamic system with two essential degrees of freedom. A qualitative research has been performed for viscous Newtonian fluid and both for positive and for alternating turbulent viscosities.