Exact analytical solutions for axial flow of a fractional second grade fluid between two coaxial cylinders

The velocity field and the adequate shear stress corresponding to the longitudinal flow of a fractional second grade fluid,between two infinite coaxial circular cylinders,are determined by applying the Laplace and finite Hankel transforms.Initially the fluid is at rest,and at time t=0^+, the inner cylinder suddenly begins to translate along the common axis with constant acceleration. The solutions that have been obtained are presented in terms of generalized G functions.Moreover, these solutions satisfy both the governing differential equations and all imposed initial and boundary conditions.The corresponding solutions for ordinary second grade and Newtonian fluids are obtained as limiting cases of the general solutions.Finally,some characteristics of the motion,as well as the influences of the material and fractional parameters on the fluid motion and a comparison between models,are underlined by graphical illustrations.

Shear Flow Dispersion Under Wave and Current

The longitudinal dispersion of solute in open channel flow with short period progressive waves is investigated. The waves induce second order drift velocity in the direction of propagation and enhance the mixing process in concurrent direction. The 1-D wave-period-averaged dispersion equation is derived and an expression for the wave-current induced longitudinal dispersion coefficient （WCLDC） is propased based on Fiscber＇ s expression （1979） for dispersion in unidirectional flow. The result shows that the effect of waves on dispersion is mainly due to the cross-sectional variation of the drift velocity. Furthermore, to obtain a more practical expression of the WCLDC, the longitudinal dispersion coefficient due to Seo and Cheong （1998） is modified to incluee the effect of drift velocity. Laboratory experiments have been conducted to verify the propased expression. The experimental results, together with dimensional analysis, show that tbe wave effect can be reflected by the ratio between the wave amplitude and wave period. A comparative study between the cases with and without waves demonstrates that the magnitude of the longitudinal dispersion coefficient is increased nnder the presence of waves.

NUMERICAL STUDY OF FLOW IN CONICAL DIFFUSER WITH VORTEX GENERATOR JETS

To develop vortex generator jet （VGJ） method for flow control, the turbulence flow in a 14° conical diffuser with and without vortex generator jets are simulated by solving Navier-Stokes equations with k-ε turbulence model. The diffuser performance, based on different velocity ratio （ratio of the jet speed to the mainstream velocity）, is investigated and compared with the experimental study. On the basis of the flow characteristics using computation fluid dynamics （CFD） method observed in the conical diffuser and the downstream development of the longitudinal vortices, attempt is made to correlate the pressure recovery coefficient with the behavior of vortices produced by vortex generator jets.

ANALYSIS OF OSCILLATORY FLOW IN CONSIDERATION OF A PLASMA LAYER IN ARTERIAL STENOSES

This paper presents the influences of plasma layer on the oscillatory flow inarterial stenosis. The analysis demonstrates that the existence of the plasma layer mayobviously change the characteristics of flow such as velocity-profiles, longitudinalimpedance and pressure gradient, but hardly change the phase of longitudinalimpedance and pressure gradient. Besides. such influences vary with a and degree ofstenosis. These analyses have Special physiological significance in blood circulationsystem.

Exact solutions for the flow of second grade fluid in annulus between torsionally oscillating cylinders

The velocity field and the associated shear stress corresponding to the torsional oscillatory flow of a second grade fluid, between two infinite coaxial circular cylinders, are determined by means of the Laplace and Hankel transforms. At time t = 0, the fluid and both the cylinders are at rest and at t = 0 ＋ , cylinders suddenly begin to oscillate around their common axis in a simple harmonic way having angular frequencies ω 1 and ω 2 . The obtained solutions satisfy the governing differential equation and all imposed initial and boundary conditions. The solutions for the motion between the cylinders, when one of them is at rest, can be obtained from our general solutions. Furthermore, the corresponding solutions for Newtonian fluid are also obtained as limiting cases of our general solutions.

Some exact solutions of the oscillatory motion of a generalized second grade fluid in an annular region of two cylinders

The velocity field and the associated shear stress corresponding to the longitudinal oscillatory flow of a generalized second grade fluid, between two infinite coaxial circular cylinders, are determined by means of the Laplace and Hankel transforms. Initially, the fluid and cylinders are at rest and at t = 0＋ both cylinders suddenly begin to oscillate along their common axis with simple harmonic motions having angular frequencies Ω1 and Ω2. The solutions that have been obtained are presented under integral and series forms in terms of the generalized G and R functions and satisfy the governing differential equation and all imposed initial and boundary conditions. The respective solutions for the motion between the cylinders, when one of them is at rest, can be obtained from our general solutions. Furthermore, the corresponding solutions for the similar flow of ordinary second grade fluid and Newtonian fluid are also obtained as limiting cases of our general solutions. At the end, the effect of different parameters on the flow of ordinary second grade and generalized second grade fluid are investigated graphically by plotting velocity profiles.

Effect of vegetation on flow structure and dispersion in strongly curved channels

The effect of vegetation on the flow structure and the dispersion in a 180 o curved open channel is studied. The Micro ADV is used to measure the flow velocities both in the vegetation cases and the non-vegetation case. It is shown that the velocities in the vegetation area are much smaller than those in the non-vegetation area and a large velocity gradient is generated between the vegetation area and the non-vegetation area. The transverse and longitudinal dispersion coefficients are analyzed based on the experimental data by using the modified N- zone models. It is shown that the effect of the vegetation on the transverse dispersion coefficient is small, involving only changes of a small magnitude, however, since the primary velocities become much more inhomogeneous with the presence of the vegetation, the longitudinal dispersion coefficients are much larger than those in the non-vegetation case.