A front-tracking method for the computations of multiphase flow

A distributed Lagrange multiplier/fictitious domain method for particulate flows

A fictitious domain approach to the direct numerical simulation of incompressible viscous flow past moving rigid bodies: application to particulate flow

Direct numerical simulations of bubbly flows are reviewed and recent progress is discussed. Simulations, of homogeneous bubble distribution in fully periodic domains at relatively low Reynolds numbers have already yielded considerable insight into the dynamics of such flows. Many aspects of the evolution converge rapidly with the size of the systems and results for the rise velocity, the velocity fluctuations, as well as the average relative orientation of bubble pairs have been obtained. The challenge now is to examine bubbles at higher Reynolds numbers, bubbles in channels and confined geometry, and bubble interactions with turbulent flows. We briefly review numerical methods used for direct numerical simulations of multiphase flows, with a particular emphasis on methods that use the so-called "one-field" formulation of the governing equations, and then discuss studies of bubbles in periodic domains, along with recent work on wobbly bubbles, bubbles in laminar and turbulent channel flows, and bubble formation in boiling.

https://assets.cambridge.org/97805217/82401/frontmatter/9780521782401_frontmatter.pdf

Direct Numerical Simulations of Gas-Liquid Multiphase Flows

This paper reports the result of direct simulations of fluid–particle motions in two dimensions. We solve the initial value problem for the sedimentation of circular and elliptical particles in a vertical channel. The fluid motion is computed from the Navier–Stokes equations for moderate Reynolds numbers in the hundreds. The particles are moved according to the equations of motion of a rigid body under the action of gravity and hydrodynamic forces arising from the motion of the fluid. The solutions are as exact as our finite-element calculations will allow. As the Reynolds number is increased to 600, a circular particle can be said to experience five different regimes of motion: steady motion with and without overshoot and weak, strong and irregular oscillations. An elliptic particle always turn its long axis perpendicular to the fall, and drifts to the centreline of the channel during sedimentation. Steady drift, damped oscillation and periodic oscillation of the particle are observed for different ranges of the Reynolds number. For two particles which interact while settling, a steady staggered structure, a periodic wake-action regime and an active drafting–kissing–tumbling scenario are realized at increasing Reynolds numbers. The non-linear effects of particle–fluid, particle–wall and interparticle interactions are analysed, and the mechanisms controlling the simulated flows are shown to be lubrication, turning couples on long bodies, steady and unsteady wakes and wake interactions. The results are compared to experimental and theoretical results previously published.

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Direct Simulation of Initial Value Problems for the Motion of Solid Bodies in a Newtonian Fluid Part 1. Sedimentation

Experiments on fluidization with water of spherical particles falling against gravity in columns of rectangular cross-section are described. All of them are dominated by inertial effects associated with wakes. Two local mechanisms are involved: drafting and kissing and tumbling into stable cross-stream arrays. Drafting, kissing and tumbling are rearrangement mechanisms in which one sphere is captured in the wake of the other. The kissing spheres are aligned with the stream. The streamwise alignment is massively unstable and the kissing spheres tumble into more stable cross-stream pairs of doublets which can aggregate into larger relatively stable horizontal arrays. Cross-stream arrays in beds of spheres constrained to move in two dimensions are remarkable. These arrays may even coalesce into aggregations of close-packed spheres separated by regions of clear water. A somewhat weaker form of cooperative motion of cross-stream arrays of rising spheres is found in beds of square cross-section where the spheres may move freely in three dimensions. Horizontal arrays rise where drafting spheres fall because of greater drag. Aggregation of spheres seems to be associated with relatively stable cooperative motions of horizontal arrays of spheres rising in their own wakes.

Nonlinear mechanics of fluidization of beds of spherical particles

Nonlinear Mechanics of Fluidization of Spheres, Cylinders, and Disks in Water

We treat the problem of the stability of an infinite horizontal array of cylinders, spaced periodically, by a direct numerical simulation of the Navier–Stokes equations for steady flow at Reynolds numbers less than or equal to 100. We find that the only stable configuration for the array is one with equal spacing between cylinders and all cylinders lying on a line perpendicular to the flow. The array is found to be stable under displacements of the cylinders perpendicular and parallel to the array. We say a perturbation is stable when it gives rise to a force which acts to restore the original stable configuration. Our results are consistent with experiments in which spheres were confined by the sidewalls of a fluidized bed to move in two dimensions. As a secondary issue we consider the variation with parameters of the length and width of wakes behind cylinders.

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A. F. Fortes

Papers

Nonlinear mechanics of fluidization of beds of spherical particles

Nonlinear Mechanics of Fluidization of Spheres, Cylinders, and Disks in Water

Stability of periodic arrays of cylinders across the stream by direct simulation