Showing papers on "Second-order fluid published in 2004"

Rotating flow of a second-order fluid on a porous plate

Abstract: A study is made of the unsteady flow engendered in a second-order incompressible, rotating fluid by an infinite porous plate exhibiting non-torsional oscillation of a given frequency. The porous character of the plate and the non-Newtonian effect of the fluid increase the order of the partial differential equation (it increases up to third order). The solution of the initial value problem is obtained by the method of Laplace transform. The effect of material parameters on the flow is given explicitly and several limiting cases are deduced. It is found that a non-Newtonian effect is present in the velocity field for both the unsteady and steady-state cases. Once again for a second-order fluid, it is also found that except for the resonant case the asymptotic steady solution exists for blowing. Furthermore, the structure of the associated boundary layers is determined.

Potential flow of a second-order fluid over a sphere or an ellipse

Abstract: We study the potential flow of a second-order fluid over a sphere or an ellipse. The normal stress at the surface of the body is calculated and has contributions from the inertia, viscous and viscoelastic effects. We investigate the effects of Reynolds number and body size on the normal stress; for the ellipse, various angles of attack and aspect ratios are also studied. The effect of the viscoelastic terms is opposite to that of inertia; the normal stress at a point of stagnation can change from compression to tension. This causes long bodies to turn into the stream and causes spherical bodies to chain. For a rising gas bubble, the effect of the viscoelastic and viscous terms in the normal stress is to extend the rear end so that it tends to the cusped trailing edge observed in experiments.

Some steady MHD flows of the second order fluid

Abstract: The exact analytic solutions of two problems of a second order fluid in presence of a uniform transverse magnetic field are investigated. The governing equation is of fourth order ordinary differential equation and is solved using perturbation method. In the first problem we discuss the flow of a second order fluid due to non-coaxial rotations of a porous disk and a fluid at infinity. In second problem the flow of a second order conducting fluid between two infinite plates rotating about the same axis is investigated, with suction or blowing along the axial direction. For second order conducting fluid it is observed that asymptotic solution exists for the velocity both in the case of suction and blowing.

Diffusion of a line vortex in a second-order fluid

Abstract: In this paper, the diffusion of a line vortex in a second-order fluid is considered. The Hankel transform is used to solve this problem and an exact solution for the velocity distribution is found in terms of a definite integral. The integrand is an oscillatory function and the integration is performed by a numerical technique. It is found that there are pronounced effects of viscoelastic properties on the velocity distribution with respect to that of the Newtonian fluid.

Steady fall of bodies of arbitrary shape in a second-order fluid at zero reynolds number

Abstract: We study the slow motion of rigid bodies of arbitrary shape sedimenting in a quiescent viscoelastic liquid under the action of gravity. The liquid is modeled by the second-order fluid equations. We show existence of steady state solutions for small Weissenberg numbers. The case of pure translational motions is analyzed for specific geometric symmetries of the body and this allows us to show that the sedimentation behavior can be dramatically different between Newtonian and viscoelastic liquids.

Squeeze flow of a second-order fluid between two parallel disks or two spheres

Abstract: The normal viscous force of squeeze flow between two arbitrary rigid spheres with an interstitial second-order fluid was studied for modeling wet granular materials using the discrete element method. Based on the Reynolds' lubrication theory, the small parameter method was introduced to approximately analyze velocity field and stress distribution between the two disks. Then a similar procedure was carried out for analyzing the normal interaction between two nearly touching, arbitrary rigid spheres to obtain the pressure distribution and the resulting squeeze force. It has been proved that the solutions can be reduced to the case of a Newtonian fluid when the non-Newtonian terms are neglected.

Numerical solution of the flow of a second-order fluid under an enclosed rotating disc

Abstract: The solution of a non-linear boundary value problem arising due to the steady flow of an incompressible second-order fluid (flowing with a small mass rate of symmetrical radial outflow m, taken negative for a net radial inflow) under finite rotating disc (enclosed within a co-axial cylindrical casing) has been obtained numerically using finite difference method. The resulting equations are converted into a set of difference equations. Starting from the known values of flow functions for small values of the Reynolds number, the solution is extended for larger Reynolds number by making use of Newton-Raphson iterative method and Gauss elimination method. Effects of second order forces in the flow on the velocity field have been investigated in detail in the regions of recirculation and no-recirculation for the cases of radial outflow and inflow and illustrated graphically. Such flows are useful in mechanical and chemical industries.

Orientation of Rigid Bodies Freefalling in Newtonian and Non-Newtonian Fluids

Abstract: This thesis deals with the subject of terminal orientations of rigid bodies, sedimenting in Newtonian and non-Newtonian liquids. It is a well established fact that homogeneous bodies of revolution around an axis ('a') with fore-aft symmetry will orient themselves with respect to the direction of gravity ('g') depending upon their shape and upon the nature of the fluid in which they are immersed. If, for instance, we are considering an ellipsoidal object falling in a Newtonian fluid such as water, then the body falls with 'a' eventually becoming perpendicular to the direction of 'g'. However, if the same body falls in a viscoelastic fluid where the inertial effects can be disregarded, then 'a' will eventually become parallel to 'g'. It has also been noted that long bodies falling in fluids with certain polymeric concentrations can take on angles between the horizontal and vertical orientations. These intermediate angles are referred to as tilt angles. The objective of this thesis is the explanation of this orientation phenomenon in different liquids.Our approach to the problem has been three-fold, experimental, mathematical and also numerical. We perform several experiments on sedimentation of particles in a variety of viscoelastic and Newtonian liquids to verify and fill gaps in the previous observations. A second set of experiments that we perform involves a modified flow chamber setup where the particle is fixed at the center of the chamber while water flows past it. We are able able to replicate previous experiments at low and intermediate Re, with both these experiments. The equations to describe the problem of freefall of a rigid body of arbitrary shape, in a liquid, are obtained from a frame attached to the body and is formulated for any general fluid model. In addition, we also obtain the equations for the body, since the problem we are dealing with is one of fluid-structure interaction. We establish well-posedness of the equations by showing the exitence and uniqueness of steady solutions to the problem of sedimentation in a Second order fluid, with Re=0 and arbitrary material parameters using the Banach fixed point theorem. In order to explain the terminal orientation assumed by the body, we consider the effect of torques imposed by different components of the liquid such as inertia, viscoelasticiy and shear-thinning. The equilibrium resulting from the competition of the different torques should reveal the terminal angle. Guided by the fact that the orientation phnomenon is observed at very small Re and We, we formulate the torque equations at first order in these material parameters. The calculation is performed for four different liquid models, Newtownian, Power-law, Second order fluid and a modified Second order model which we introduce here for the first time. The different orientation observations seen in experiments is well explained by these models. Finally, a simple quasi-steady stability argument is used to establish stability of the equilibrium states. For this final argument, we numerically evaluate the torque imposed by the individual components of the liquid upon a sedimenting prolate ellipsoid in an unbounded three dimensional fluid domain surrounding the body.