Multifield computational fluid dynamics model of particulate flow in curved circular tubes

Limitations of mass transfer resulting from non-optimized fluid mechanics can severely affect the performance of synthetic membrane filtration systems. To improve membrane efficiency, modern applications of this technology have extensively used curved membrane ducts that take advantage of Dean vortices (i.e., curvature-induced secondary flows) to minimize membrane fouling. This paper is concerned with a complete three-dimensional analysis of single-phase and two-phase particle/liquid flows around a curved membrane tube. The proposed multidimensional model was implemented in an advanced (next-generation) multiphase computational fluid dynamics (CFD) solver, NPHASE. The results of simulations have been validated against experimental data and compared against other findings available in the literature. The consistency and accuracy of the present approach have been demonstrated. The novel aspects of this work include: the demonstration that azimuthal vortices may bifurcate at Dean numbers lower than previously anticipated, the use of vorticity magnitude as a measure of vortex strength, and the explanation of the role that Dean vortices play to mitigate the effect of gravity on particle settling. The overall results have direct relevance to synthetic membrane fouling during filtration of particle suspensions.     

Steady-State MHD Flows in Nozzles with an External Longitudinal Magnetic Field

Steady-state MHD flows in channels of the nozzle type in the presence of an external longitudinal magnetic field can be divided into two significantly different classes. Subcritical flows, in which the Alfvén velocity calculated from the longitudinal magnetic field is less than the plasma velocity, have mainly the same properties as flows in a transverse magnetic self-field and their quantitative characteristics depend only slightly on the longitudinal magnetic field strength. Supercritical flows with the opposite inequality for the velocities correspond to strong longitudinal magnetic field. The main difference is the transitions between different forms of energy (kinetic, thermal, and electromagnetic). The present study contains a classification of possible flows, namely, sub- and supercritical and sub-, super-, and transonic flows with respect to the fast and slow magnetosonic and Alfvén velocities. Examples of these flows are given. The effect of the problem parameters on the flow properties is investigated.     

Modelling Shock/Boundary-Layer Interaction with Nonlinear Eddy-Viscosity Closures

An investigation is reported of several nonlinear eddy-viscosity models, both from a fundamental point of view and as a basis for resolving turbulence transport in transonic flows, with particular emphasis placed on shock-induced separation. The models are first analyzed by reference to a homogeneous shear flow and a plane channel flow, after which they are applied to two transonic flows with strong shock-wave/boundary-layer interaction including separation. The computational results demonstrate that nonlinear models with coefficients appropriately sensitized to strain and vorticity invariants, yield results which are superior to a standard linear low-Re k– model often claimed to give the best predictive performance among low-Re k– models which do not contain ad-hoc corrections. While this superior performance is partly associated with the functional dependence of the linear coefficient on strain and vorticity, this cannot be separated from the role of at least some nonlinear terms which interact with that coefficient, especially in complex strain fields featuring large streamline curvature and irrotational straining.     

A turbulence model for inclined, bubbly flows

A new turbulence model for the flow of a two phase (liquid-liquid) flow in an inclined pipe is presented. An eddy viscosity is used to model the effects of shear induced turbulence and bubble induced turbulence. The cross-pipe momentum transport arising from the buoyant rise of bubbles across the axial flow is also modelled. Numerical simulations have been carried out in both one and two dimensions. One and two dimensional numerical simulations are presented.On leave from the University of Leeds, Leeds LS2 9JT, U.K.     

Unsteady flows of Oldroyd-B fluids in a channel of rectangular cross-section

The aim of this note is to present the exact solutions corresponding to two types of unsteady flows of an Oldroyd-B fluid in a channel of rectangular cross-section. The solutions that have been obtained satisfy both the associate partial differential equations and all imposed initial and boundary conditions. For λ_r or λ→0 they tend toward similar solutions for a Maxwell or second-grade fluid. If both λ_r and λ→0, the solutions for Navier-Stokes fluids are recovered.     

On the cross-effects of coupled macroscopic transport equations in porous media

In this paper, the derivation of macroscopic transport equations for this cases of simultaneous heat and water, chemical and water or electrical and water fluxes in porous media is presented. Based on themicro-macro passage using the method of homogenization of periodic structures, it is shown that the resulting macroscopic equations reveal zero-valued cross-coupling effects for the case of heat and water transport as well as chemical and water transport. In the case of electrical and water transport, a nonsymmetrical coupling was found.Notations b mobility - c concentration of a chemical - D rate of deformation tensor - D molecular diffusion coefficient - D _ij ^eff macroscopic (or effective) diffusion tensor - electric field - E ₀ initial electric field - k _ij molecular tensor - j, j ^*, current densities - K _ij macroscopic permeability tensor - l characteristic length of the ERV or the periodic cell - L characteristic macroscopic length - L _ijkl coupled flows coefficients - n _i unit outward vector normal to - p pressure - q _t ,q _t ⁺ , heat fluxes - q _c ,q _c ⁺ , chemical fluxes - s specific entropy or the entropy density - S entropy per unit volume - t time variable - t _ij local tensor - T absolute temperature - v _i velocity - V ₀ initial electric potential - V electric potential - x macroscopic (or slow) space variable - y microscopic (or fast) space variable - _i local vectorial field - _i local vectorial field - electric charge density on the solid surface - , bulk and shear viscosities of the fluid - _ij local tensor - _ij local tensor - _i local vector - _ij molecular conductivity tensor - _ij ^eff effective conductivity tensor - homogenization parameter - fluid density - ₀ ion-conductivity of fluid - _ij dielectric tensor - _i ¹ , _i ² , _i ³ local vectors - ⁴ local scalar - _S solid volume in the periodic cell - _L volume of pores in the periodic cell - boundary between _S and _L - ^s rate of entropy production per unit volume - total volume of the periodic cell - _l volume of pores in the cell On leave from the Politechnika Gdanska; ul. Majakowskiego 11/12, 80-952, Gdask, Poland.     

Approximate nonreflecting inflow-outflow boundary conditions for the calculation of navier-stokes equations in internal flows

In this paper, the nonreflecting boundary conditions based upon fundamental ideas of the linear analysis are developed for gas dynamic equations, and the modified boundary conditions for Navier-Stokes equations are proposed as a substitute of the nonreflecting boundary conditions inside boundary layers near rigid walls. These derived boundary conditions are then applied to calculations both for the Euler equations and the Navier-Stokes equations to determine if they can produce acceptable results for the subsonic flows in channels. The numerical results obtained by an implicit second-order upwind difference scheme show the effectiveness and generality of the boundary conditions. Furthermore, the formulae and the analysis performed here may be extended to three dimensional problems. recommended by Prof. Cui Erjie     

On Plane-Parallel Separated Flows of an Incompressible Fluid near Flat Boundaries

On the basis of Stokes separated flows, examples of separated flows described by the Navier-Stokes equations of a viscous incompressible fluid are constructed. These flows are represented by series convergent in a certain non-zero neighborhood of a flat contour immersed in the flow. In this neighborhood, the series have the same structure as those for the basic Stokes flows. Examples of the regions in which the series segments chosen give only a slight deviation from the numerical solutions of the Navier-Stokes equations are presented. The comparison between inviscid separated flows (without the no-slip condition on the contour) and viscous flows of the same structure (with the no-slip condition) shows that the viscosity does not play a decisive role in the formation of separation or the type of streamline approach to or departure from the contour.     

Anomalous steady flows in a tube

Tube flow of a viscoelastic liquid of the multiple integral type driven by periodic forcing is investigated. It is shown that mean longitudinal and secondary flows exist, independently of the explicit form of the constitutive functions, due to frequency cancellation when the forcing oscillates around a zero mean. Closed form expressions are given for these non-trivial flows at the lowest order of the algorithm where nonlinear effects appear.Presented at the Third European Rheology Conference, Edinburgh, UK, Sept. 3–7, 1990.