Unsteady axisymmetric stagnation-point flow of a viscous fluid on a cylinder

The unsteady viscous flow in the vicinity of an axisymmetric stagnation point of an infinite circular cylinder is investigated when both the free stream velocity and the velocity of the cylinder vary arbitrarily with time. The cylinder moves either in the same direction as that of the free stream or in the opposite direction. The flow is initially (t = 0) steady and then at t > 0 it becomes unsteady. The semi-similar solution of the unsteady Navier-Stokes equations has been obtained numerically using an implicit finite-difference scheme. Also the self-similar solution of the Navier-Stokes equations is obtained when the velocity of the cylinder and the free stream velocity vary inversely as a linear function of time. For small Reynolds number, a closed form solution is obtained. When the Reynolds number tends to infinity, the Navier-Stokes equations reduce to those of the two-dimensional stagnation-point flow. The shear stresses corresponding to stationary and the moving cylinder increase with the Reynolds number. The shear stresses increase with time for the accelerating flow but decrease with increasing time for the decelerating flow. For the decelerating case flow reversal occurs in the velocity profiles after a certain instant of time. (C) 1999 Elsevier Science Ltd. All rights reserved.

Investigation on average void fraction for air/non-Newtonian power-law fluids two-phase flow in downward inclined pipes

The present work has been carried out to investigate on the average void fraction of gas/non-Newtonian fluids flow in downward inclined pipes. The influences of pipe inclination angle on the average void fraction were studied experimentally. A simple correlation, which incorporated the method of Vlachos et al. for gas/Newtonain fluid horizontal flow, the correction factor of Farooqi and Richardson and the pipe inclination angle, was proposed to predict the average void fraction of gas/non-Newtonian power-law stratified flow in downward inclined pipes. The correlation was based on 470 data points covering a wide range of flow rates for different systems at diverse angles. A good agreement was obtained between theory and data and the fitting results could describe the majority of the experimental data within ±20%.

I. Stokes flow past a thin screen. II. Viscous flows past porous bodies of finite size

Part I

The slow, viscous flow past a thin screen is analyzed based on Stokes equations. The problem is reduced to an associated electric potential problem as introduced by Roscoe. Alternatively, the problem is formulated in terms of a Stokeslet distribution, which turns out to be equivalent to the first approach.

Special interest is directed towards the solution of the Stokes flow past a circular annulus. A "Stokeslet" formulation is used in this analysis. The problem is finally reduced to solving a Fredholm integral equation of the second kind. Numerical data for the drag coefficient and the mean velocity through the hole of the annulus are obtained.

Stokes flow past a circular screen with numerous holes is also attempted by assuming a set of approximate boundary conditions. An "electric potential" formulation is used, and the problem is also reduced to solving a Fredholm integral equation of the second kind. Drag coefficient and mean velocity through the screen are computed.

Part II

The purpose of this investigation is to formulate correctly a set of boundary conditions to be prescribed at the interface between a viscous flow region and a porous medium so that the problem of a viscous flow past a porous body can be solved.

General macroscopic equations of motion for flow through porous media are first derived by averaging Stokes equations over a volume element of the medium. These equations, including viscous stresses for the description, are more general than Darcy's law. They reduce to Darcy's law when the Darcy number becomes extremely small.

The interface boundary conditions of the first kind are then formulated with respect to the general macroscopic equations applied within the porous region. An application of such equations and boundary conditions to a Poiseuille shear flow problem demonstrates that there usually exists a thin interface layer immediately inside the porous medium in which the tangential velocity varies exponentially and Darcy's law does not apply.

With Darcy's law assumed within the porous region, interface boundary conditions of the second kind are established which relate the flow variables across the interface layer. The primary feature is a jump condition on the tangential velocity, which is found to be directly proportional to the normal gradient of the tangential velocity immediately outside the porous medium. This is in agreement with the experimental results of Beavers, et al.

The derived boundary conditions are applied in the solutions of two other problems: (1) Viscous flow between a rotating solid cylinder and a stationary porous cylinder, and (2) Stokes flow past a porous sphere.

Flow of wet powder in a conical centrifugal filter-an analytical model

A one-dimensional analytical model is developed for the steady state, axisymmetric, slender flow of saturated powder in a rotating perforated cone. Both the powder and the fluid spin with the cone with negligible slip in the hoop direction. They migrate up the wall of the cone along a generator under centrifugal force, which also forces the fluid out of the cone through the powder layer and the porous wall. The flow thus evolves from an over-saturated paste at inlet into a nearly dry powder at outlet. The powder is treated as a Mohr-Coulomb granular solid of constant void fraction and permeability. The shear traction at the wall is assumed to be velocity and pressure dependent. The fluid is treated as Newtonian viscous. The model provides the position of the colour line (the transition from over- to under-saturation) and the flow velocity and thickness profiles over the cone. Surface tension effects are assumed negligible compared to the centrifugal acceleration. Two alternative conditions are considered for the flow structure at inlet: fully settled powder at inlet, and progressive settling of an initially homogeneous slurry. The position of the colour line is found to be similar for these two cases over a wide range of operating conditions. Dominant dimensionless groups are identified which control the position of the colour line in a continuous conical centrifuge. Experimental observations of centrifuges used in the sugar industry provide preliminary validation of the model. © 2011 Elsevier Ltd.

HEATING IN VASCULAR TISSUE AND FLOW-THROUGH TISSUE PHANTOMS INDUCED BY FOCUSED ULTRASOUND

High intensity focused ultrasound (HIFU) can be used to control bleeding, both from individual blood vessels as well as from gross damage to the capillary bed. This process, called acoustic hemostasis, is being studied in the hope that such a method would ultimately provide a lifesaving treatment during the so-called "golden hour", a brief grace period after a severe trauma in which prompt therapy can save the life of an injured person. Thermal effects play a major role in occlusion of small vessels and also appear to contribute to the sealing of punctures in major blood vessels. However, aggressive ultrasound-induced tissue heating can also impact healthy tissue and can lead to deleterious mechanical bioeffects. Moreover, the presence of vascularity can limit one’s ability to elevate the temperature of blood vessel walls owing to convective heat transport. In an effort to better understand the heating process in tissues with vascular structure we have developed a numerical simulation that couples models for ultrasound propagation, acoustic streaming, ultrasound heating and blood cooling in Newtonian viscous media. The 3-D simulation allows for the study of complicated biological structures and insonation geometries. We have also undertaken a series of in vitro experiments, in non-uniform flow-through tissue phantoms, designed to provide a ground truth verification of the model predictions. The calculated and measured results were compared over a range of values for insonation pressure, insonation time, and flow rate; we show good agreement between predictions and measurements. We then conducted a series of simulations that address two limiting problems of interest: hemostasis in small and large vessels. We employed realistic human tissue properties and considered more complex geometries. Results show that the heating pattern in and around a blood vessel is different for different vessel sizes, flow rates and for varying beam orientations relative to the flow axis. Complete occlusion and wall- puncture sealing are both possible depending on the exposure conditions. These results concur with prior clinical observations and may prove useful for planning of a more effective procedure in HIFU treatments.

Numerical simulation of viscous three-dimensional flow over aerospace vehicles using Euler/boundary-layer zonal approach

This paper presents a viscous three-dimensional simulations coupling Euler and boundary layer codes for calculating flows over arbitrary surfaces. The governing equations are written in a general non orthogonal coordinate system. The Levy-Lees transformation generalized to three-dimensional flows is utilized. The inviscid properties are obtained from the Euler equations using the Beam and Warming implicit approximate factorization scheme. The resulting equations are discretized and approximated by a two-point fmitedifference numerical scheme. The code developed is validated and applied to the simulation of the flowfield over aerospace vehicle configurations. The results present good correlation with the available data.

Bubble extinction in Hele-Shaw flow with surface tension and kinetic undercooling regularisation

We perform an analytic and numerical study of an inviscid contracting bubble in a two-dimensional Hele-Shaw cell, where the effects of both surface tension and kinetic undercooling on the moving bubble boundary are not neglected. In contrast to expanding bubbles, in which both boundary effects regularise the ill-posedness arising from the viscous (Saffman-Taylor) instability, we show that in contracting bubbles the two boundary effects are in competition, with surface tension stabilising the boundary, and kinetic undercooling destabilising it. This competition leads to interesting bifurcation behaviour in the asymptotic shape of the bubble in the limit it approaches extinction. In this limit, the boundary may tend to become either circular, or approach a line or "slit" of zero thickness, depending on the initial condition and the value of a nondimensional surface tension parameter. We show that over a critical range of surface tension values, both these asymptotic shapes are stable. In this regime there exists a third, unstable branch of limiting self-similar bubble shapes, with an asymptotic aspect ratio (dependent on the surface tension) between zero and one. We support our asymptotic analysis with a numerical scheme that utilises the applicability of complex variable theory to Hele-Shaw flow.

Two-temperature accretion around rotating black holes: a description of the general advective flow paradigm in the presence of various cooling processes to explain low to high luminous sources

We investigate viscous two-temperature accretion disc flows around rotating black holes. We describe the global solution of accretion flows with a sub-Keplerian angular momentum profile, by solving the underlying conservation equations including explicit cooling processes self-consistently. Bremsstrahlung, synchrotron and inverse Comptonization of soft photons are considered as possible cooling mechanisms. We focus on the set of solutions for sub-Eddington, Eddington and super-Eddington mass accretion rates around Schwarzschild and Kerr black holes with a Kerr parameter of 0.998. It is found that the flow, during its infall from the Keplerian to sub-Kepleria transition region to the black hole event horizon, passes through various phases of advection: the general advective paradigm to the radiatively inefficient phase, and vice versa. Hence, the flow governs a much lower electron temperature similar to 10(8)-10(9.5) K, in the range of accretion rate in Eddington units 0.01 less than or similar to (M) over dot less than or similar to 100, compared to the hot protons of temperature similar to 10(10.2)-10(11.8) K. Therefore, the solution may potentially explain the hard X-rays and gamma-rays emitted from active galactic nuclei (AGNs) and X-ray binaries. We then compare the solutions for two different regimes of viscosity. We conclude that a weakly viscous flow is expected to be cooling dominated, particularly at the inner region of the disc, compared to its highly viscous counterpart, which is radiatively inefficient. With all the solutions in hand, we finally reproduce the observed luminosities of the underfed AGNs and quasars (e. g. Sgr A*) to ultraluminous X-ray sources (e. g. SS433), at different combinations of input parameters, such as the mass accretion rate and the ratio of specific heats. The set of solutions also predicts appropriately the luminosity observed in highly luminous AGNs and ultraluminous quasars (e. g. PKS 0743-67).

Critical serrated flow features during nanoindentation in La-based bulk metallic glasses

La57.6Al17.5(Cu,Ni)(24.9) and La64Al14(Cu,Ni)(22) bulk metallic glasses (BMGs) were prepared by copper-mould casting method. Plastic deformation behavior of the two BMGs at various loading rates was studied by nanoindentation. The results showed that the La57.6Al17.5(Cu,Ni)(24.9) BMG with a glass transition temperature of 423 K exhibited prominent serrated flow at low loading rates, whereas less pronounced serrated flow at high rates during nanoindentation. In contrast, the La64Al14(Cu,Ni)(22) BMG with a glass transition temperature of 401 K exhibited prominent serrated flow at high loading rates. The different rate dependency of serrated flow in the two La-based BMGs is related to the different glass transition temperature, and consequently the degree of viscous flow during indentation at room temperature. A smoother flow occurs in the alloy with relatively lower glass transition temperature, due to the relaxation of stress concentration.

Attractor crisis and bursting in a fluid flow with two no-slip directions

Characteristic burtsing behavior is observed in a driven, two-dimensional viscous flow, confined to a square domain and subject to no-slip boundaries. Passing a critical parameter value, an existing chaotic attractor undergoes a crisis, after which the flow initially enters a transient bursting regime. Bursting is caused by ejections from and return to a limited subdomain of the phase space, whereas the precrisis chaotic set forms the asymptotic attractor of the flow. For increasing values of the control parameter the length of the bursting regime increases progressively. Passing another critical parameter value, a second crisis leads to the appearance of a secondary type of bursting, of very large dynamical range. Within the bursting regime the flow then switches in irregular intervals from the primary to the secondary type of bursting. Peak enstrophy levels for both types of bursting are associated to the collapse of a primary vortex into a quadrupolar state.

Character of simplified Navier-Stokes (SNS) equations near separation point for two-dimensional laminar flow over a flat plate

It is proved that the simplified Navier-Stokes (SNS) equations presented by Gao Zhi[1], Davis and Golowachof-Kuzbmin-Popof (GKP)[3] are respectively regular and singular near a separation point for a two-dimensional laminar flow over a flat plate. The order of the algebraic singularity of Davis and GKP equation[2,3] near the separation point is indicated. A comparison among the classical boundary layer (CBL) equations, Davis and GKP equations, Gao Zhi equations and the complete Navier-Stokes (NS) equations near the separation point is given.

Chemical Nonequilibrium Effects on Flow Field for Reusable Launch Vehicles

High temperature chemical non-equilibrium phenomena have a great effect on the flow field around a reentry vehicle. A set of three dimensional Navier-Stokes equations have been solved by implicit finite volume NND scheme. Both ideal gas viscous flow and chemical non-equilibrium flow are calculated for a spherical-cone at a small angle of attack. The results of the two flows have been compared and the effect of chemical non-equilibrium has been analyzed. The effect of wall material's properties, such as catalysis and radiation were studied. The results are in good agreement with the referenced paper.

A Simple Model For Predicting The Void Fraction Of Gas/Non-Newtonian Fluid Intermittent Flows In Upward Inclined Pipes

In this work, a simple correlation, which incorporates the mixture velocity, drift velocity, and the correction factor of Farooqi and Richardson, was proposed to predict the void fraction of gas/non-Newtonian intermittent flow in upward inclined pipes. The correlation was based on 352 data points covering a wide range of flow rates for different CMC solutions at diverse angles. A good agreement was obtained between the predicted and experimental results. These results substantiated the general validity of the model presented for gas/non-Newtonian two-phase intermittent flows.

Numerical simulation of a bubble rising in shear-thinning fluids

The motion of a single bubble rising freely in quiescent non-Newtonian viscous fluids was investigated experimentally and computationally. The non-Newtonian effects in the flow of viscous inelastic fluids are modeled by the Carreau theological model. An improved level set approach for computing the incompressible two-phase flow with deformable free interface is used. The control volume formulation with the SIMPLEC algorithm incorporated is used to solve the governing equations on a staggered Eulerian grid. The simulation results demonstrate that the algorithm is robust for shear-thinning liquids with large density (rho(1)/rho(g) up to 10(3)) and high viscosity (eta(1)/eta(g) up to 10(4)). The comparison of the experimental measurements of terminal bubble shape and velocity with the computational results is satisfactory. It is shown that the local change in viscosity around a bubble greatly depends on the bubble shape and the zero-shear viscosity of non-Newtonian shear-thinning liquids. The shear-rate distribution and velocity fields are used to elucidate the formation of a region of large viscosity at the rear of a bubble as a result of the rather stagnant flow behind the bubble. The numerical results provide the basis for further investigations, such as the numerical simulation of viscoelastic fluids. (C) 2010 Elsevier B.V. All rights reserved.