Flow induced by an asymmetrically placed disk rotating coaxially inside a cylindrical casing

In this paper, the flow due to a rotating disk non-symmetrically placed with respect to the height of the enclosing stationary cylinder is analyzed numerically. The full Navier-Stokes equations expressed in terms of stream function and vorticity are solved by successive over-relaxation for different disk radii, its distance from the bottom casing and rotational Reynolds numbers. It is observed that the flow pattern is strongly influenced by the size and the position of the disk. When the disk is very close to the top casing and small in radius, there are two regions of different scales and the vortices in the region of small scale are trapped between the disk and the top casing. Further, the variation of the moment coefficient is determined for different positions and sizes of the rotating disk. The calculations shows that the frictional torque increases rapidly, when the disk approaches the top casing. This finding is of importance for the design of vertical rotating disk reactors applied in chemical vapor deposition.

The effect of surface mass transfer on buoyancy induced flow in a variable porosity medium adjacent to a vertical heated plate

The effect of surface mass transfer on buoyancy induced flow in a variable porosity medium adjacent to a heated vertical plate is studied for high Rayleigh numbers. Similarity solutions are obtained within the frame work of boundary layer theory for a power law variation in surface temperature,T Wpropx lambda and surface injectionv Wpropx(lambda–1/2). The analysis incorporates the expression connecting porosity and permeability and also the expression connecting porosity and effective thermal diffusivity. The influence of thermal dispersion on the flow and heat transfer characteristics are also analysed in detail. The results of the present analysis document the fact that variable porosity enhances heat transfer rate and the magnitude of velocity near the wall. The governing equations are solved using an implicit finite difference scheme for both the Darcy flow model and Forchheimer flow model, the latter analysis being confined to an isothermal surface and an impermeable vertical plate. The influence of the intertial terms in the Forchheimer model is to decrease the heat transfer and flow rates and the influence of thermal dispersion is to increase the heat transfer rate.

Thermodynamics of flow and vaporization processes in long-chain liquids

The flow and vaporization behaviors of long-chain esters of varying molecular weights (300-900) ana branching (linear, Y-shaped, and +-shaped molecules) have been studied. The flow behavior is found to depend on the structure as well as the molecular weight. Below a molecular weight of 600, the molecules flow wholly but above this, segmental motion occurs, and the flow becomes independent of the molecular weight which is explained from the blob model. The blob concept demonstrates that the hole of a size of about 11 angstrom is needed for the flow to occur and it is much less than the size of the molecule. The blob size is observed to slightly decrease along the series linear and Y- and +-branched esters. The heat of vaporization is found to be independent of the molecular structure since the molecules acquire a coiled spherical shape during vaporization and hence depends only on the molecular weight. A significant structural effect is observed for the esters on their glass transition temperature (T(g)). The T(g) vs molecular weight plot displays contrasting trend for linear and +-branched esters, with Y esters showing an intermediate behavior. It is explained from their molecular packing and entanglement as visualized by the blob model.

Work fluctuations in an elastic dumbbell model of polymers in planar elongational flow

We use a path-integral approach to calculate the distribution P(w, t) of the fluctuations in the work W at time t of a polymer molecule (modeled as an elastic dumbbell in a viscous solvent) that is acted on by an elongational flow field having a flow rate (gamma) over dot. We find that P(w, t) is non-Gaussian and that, at long times, the ratio P(w, t)/ P (-w, t) is equal to expw/(k(B)T)], independent of (gamma) over dot. On the basis of this finding, we suggest that polymers in elongational flows satisfy a fluctuation theorem.

Stability of the viscous flow of a fluid through a flexible tube

The stability of the Hagen-Poiseuille flow of a Newtonian fluid in a tube of radius R surrounded by an incompressible viscoelastic medium of radius R < r < HR is analysed in the high Reynolds number regime. The dimensionless numbers that affect the fluid flow are the Reynolds number Re = (rho VR/eta), the ratio of the viscosities of the wall and fluid eta(r) = (eta(s)/eta), the ratio of radii H and the dimensionless velocity Gamma = (rho V-2/G)(1/2). Here rho is the density of the fluid, G is the coefficient of elasticity of the wall and V is the maximum fluid velocity at the centre of the tube. In the high Reynolds number regime, an asymptotic expansion in the small parameter epsilon = (1/Re) is employed. In the leading approximation, the viscous effects are neglected and there is a balance between the inertial stresses in the fluid and the elastic stresses in the medium. There are multiple solutions for the leading-order growth rate s((0)), all of which are imaginary, indicating that the fluctuations are neutrally stable, since there is no viscous dissipation of energy or transfer of energy from the mean flow to the fluctuations due to the Reynolds stress. There is an O(epsilon(1/2)) correction to the growth rate, s((1)), due to the presence of a wall layer of thickness epsilon(1/2)R where the viscous stresses are O(epsilon(1/2)) smaller than the inertial stresses. An energy balance analysis indicates that the transfer of energy from the mean flow to the fluctuations due to the Reynolds stress in the wall layer is exactly cancelled by an opposite transfer of equal magnitude due to the deformation work done at the interface, and there is no net transfer from the mean flow to the fluctuations. Consequently, the fluctuations are stabilized by the viscous dissipation in the wall layer, and the real part of s(1) is negative. However, there are certain values of Gamma and wavenumber k where s((1)) = 0. At these points, the wall layer amplitude becomes zero because the tangential velocity boundary condition is identically satisfied by the inviscid flow solution. The real part of the O(epsilon) correction to the growth rate s((2)) turns out to be negative at these points, indicating a small stabilizing effect due to the dissipation in the bulk of the fluid and the wall material. It is found that the minimum value of s((2)) increases proportional to (H-1)(-2) for (H-1) much less than 1 (thickness of wall much less than the tube radius), and decreases proportional to H-4 for H much greater than 1. The damping rate for the inviscid modes is smaller than that for the viscous wall and centre modes in a rigid tube, which have been determined previously using a singular perturbation analysis. Therefore, these are the most unstable modes in the flow through a flexible tube

Stability of the viscous flow of a fluid through a flexible tube

The stability of Hagen-Poiseuille flow of a Newtonian fluid of viscosity eta in a tube of radius R surrounded by a viscoelastic medium of elasticity G and viscosity eta(s) occupying the annulus R < r < HR is determined using a linear stability analysis. The inertia of the fluid and the medium are neglected, and the mass and momentum conservation equations for the fluid and wall are linear. The only coupling between the mean flow and fluctuations enters via an additional term in the boundary condition for the tangential velocity at the interface, due to the discontinuity in the strain rate in the mean flow at the surface. This additional term is responsible for destabilizing the surface when the mean velocity increases beyond a transition value, and the physical mechanism driving the instability is the transfer of energy from the mean flow to the fluctuations due to the work done by the mean flow at the interface. The transition velocity Gamma(t) for the presence of surface instabilities depends on the wavenumber k and three dimensionless parameters: the ratio of the solid and fluid viscosities eta(r) = (eta(s)/eta), the capillary number Lambda = (T/GR) and the ratio of radii H, where T is the surface tension of the interface. For eta(r) = 0 and Lambda = 0, the transition velocity Gamma(t) diverges in the limits k much less than 1 and k much greater than 1, and has a minimum for finite k. The qualitative behaviour of the transition velocity is the same for Lambda > 0 and eta(r) = 0, though there is an increase in Gamma(t) in the limit k much greater than 1. When the viscosity of the surface is non-zero (eta(r) > 0), however, there is a qualitative change in the Gamma(t) vs. k curves. For eta(r) < 1, the transition velocity Gamma(t) is finite only when k is greater than a minimum value k(min), while perturbations with wavenumber k < k(min) are stable even for Gamma--> infinity. For eta(r) > 1, Gamma(t) is finite only for k(min) < k < k(max), while perturbations with wavenumber k < k(min) or k > k(max) are stable in the limit Gamma--> infinity. As H decreases or eta(r) increases, the difference k(max)- k(min) decreases. At minimum value H = H-min, which is a function of eta(r), the difference k(max)-k(min) = 0, and for H < H-min, perturbations of all wavenumbers are stable even in the limit Gamma--> infinity. The calculations indicate that H-min shows a strong divergence proportional to exp (0.0832 eta(r)(2)) for eta(r) much greater than 1.

Unsteady laminar compressible swirling flow with massive blowing

THE study of swirling boundary layers is of considerable importance in many rotodynamic machines such as rockets, jet engines, swirl generators, swirl atomizers, arc heaters, etc. For example, the introduction of swirl in a flow acceleration device such as a nozzle in a rocket engine promises efficient mass flow control. In nuclear rockets, swirl is used to retain the uranium atoms in the rocket chamber. With these applications in mind, Back1 and Muthanna and Nath2 have obtained the similarity solutions for a low-speed three-dimensional steady laminar compressible boundary layer with swirl inside an axisymmetric surface of variable cross section. The aim of the present analysis is to study the effect of massive blowing rates on the unsteady laminar swirling compressible boundary-layer flow of an axisymmetric body of arbitrary cross section when the freestream velocity and blowing rate vary with time. The type of swirl considered here is that of a free vortex superimposed on the longitudinal flow of a compressible fluid with variable properties. The analysis is applicable to external flow over a body as well as internal flow along a surface. For the case of external flow, strong blowing can have significant use in cooling the surface of hypervelocity vehicles, particularly when ablation occurs under large aerodynamic or radiative heating, but there may not be such an important application of strong blowing in the case of internal flow. The governing partial differential equations have been solved numerically using an implicit finite difference scheme with a quasilinearization technique.3 High temperature gas effects, such as radiation, dissociation, and ionization, etc., are not investigated. The nomenclature is usually that of Ref. 4 and is listed in the full paper.

Nonsimilar mixed convection flow of a non-Newtonian fluid past a vertical wedge

The flow and heat transfer characteristics of a second-order fluid over a vertical wedge with buoyancy forces have been analysed. The coupled nonlinear partial differential equations governing the nonsimilar mixed convection flow have been solved numerically using Keller box method. The effects of the buoyancy parameter, viscoelastic parameter, mass transfer parameter, pressure gradient parameter, Prandtl number and viscous dissipation parameter on the skin friction and heat transfer have been examined in detail. Particular cases of the present results match exactly with those available in the literature.

Vesicle formation from dimeric surfactants through ion-pairing. Adjustment of polar headgroup separation leads to control over vesicular thermotropic properties

Eight new vesicle-forming dimeric surfactants are synthesized: the polar headgroup separation in such dimeric amphiphiles strongly influences their vesicular thermotropic phase-transition behaviour.

Power Flow Analysis in MTDC-AC System—A New Approach

This paper presents a new approach to the power flow analysis in steady state for multiterminal DC-AC systems. A flexible and practical choice of per unit system is used to formulate the DC network and converter equations. A converter is represented by Norton's equivalent of a current source in parallel with the commutation resistance. Unlike in previous literature, the DC network equations are used to derive the controller equations for the DC system using a subset of specifications. The specifications considered are current or power at all terminals except the slack terminal where the DC voltage is specified. The control equations are solved by Newton's method, using the current injections at the converter terminals as state variables. Further, a systematic approach to the handling of constraints is proposed by identifying the priorities in rescheduling of the specified variables. The methodology is illustrated by example of a 5 terminal DC system.

Flow of liquid/liquid dispersions in a Hele-Shaw cell

Flow of liquid/liquid dispersions have been investigated in a Hele-Shaw cell which contained a thin disk held between two parallel plates. This device offers a well defined flow field and also permits visual observation of the dispersed drop movement. The dispersed drops coalesce with the disk for the systems where the dispersed phase wets the disk surface. The dispersed phase accumulate at the downstream end of the disk and they detach from there as blobs. Through an accurate measurement of accumulated dispersed phase volume, the coalescence rate was determined. The coalescence efficiency in the Hele Shaw cell is determined by dividing the coalescence hate by the undisturbed flow rate of the dispersed phase through an area equal to the projected area of the disk on a plane normal to the flow direction. The coalescence efficiency first increases and then decreases with the flow rate of dispersion. The coalescence rate/disk dimensions increases with the decrease in the disk dimensions. The rate of coalescence increases with the increase in the dispersed drop diameter and it decreases with the increase in the continuous phase viscosity. The presence of surfactants reduces the coalescence rate. All these results are quantitatively explained through a model, which takes into account several important features like various mechanism of drainage, the roles of dispersion and continuous phase viscosities, and the drop deformation.

Prediction of separation factor in foam separation of proteins

A phenomenological model has been developed for predicting separation factors obtained in concentrating protein solutions using batch-foam columns. The model considers the adsorption of surface active proteins onto the air-water interface of bubbles, and drainage of liquid from the foam, which are the two predominant processes responsible for separation in foam columns. The model has been verified with data collected on casein and bovine serum albumin (BSA) solutions, for which adsorption isotherms are available in the literature. It has been found that an increase in liquid pool height above the gas distributor and the time allowed for drainage result in a better separation. Further, taller foam columns yield poorer separation at constant time of drainage. The model successfully predicts the observed results. (C) 1997 Elsevier Science Ltd.

Temperature dependence of the levitation effect - Implications for separation of multicomponent mixtures

Sufficiently long molecular dynamics simulations have been carried out on spherical monatomic sorbates in NaY zeolite, interacting via simple Lennard-Jones potentials, to investigate the dependence of the levitation effect on the temperature. Simulations carried out in the range 100-300 K suggest that the anomalous peak in the diffusion coefficient (observed when the levitation parameter, gamma, is near unity) decreases in intensity with increase in temperature. The rate of cage-to-cage migrations also exhibits a similar trend. The activation energy obtained from Arrhenius plots is found to exhibit a minimum when the diffusion coefficient is a maximum, corresponding to the gamma approximate to 1 sorbate diameter. In the linear or normal regime, the activation energy increases with increase in sorbate diameter until it shows a sharp decrease in the anomalous regime. Locations and energies of the adsorption sites and their dependence on the sorbate size gives interesting insight into the nature of the underlying potential-energy surface and further explain the observed trend in the activation energy with sorbate size. Cage residence times, tau(c), show little or no change with temperature for the sorbate with diameter corresponding to gamma approximate to 1, whereas there is a significant decrease in tau(c) with increase in temperature for sorbates in the linear regime. The implications of the present study for the separation of mixtures of sorbates are discussed.

Transformation of a laterally diverging boundary layer flow to a two-dimensional boundary layer flow

Laterally diverging boundary layer flow over a plate is shown to be reducible to a two-dimensional flow by modelling the diverging streamlines by a source flow.