CFD | Joseph Mouallem

Targeted Particle Delivery via Vortex Ring Reconnection

Fri, 01 Oct 2021 00:00:00 +0000

Motivation

Precise particle targeting is important in manufacturing, propulsion, and medical applications. This work shows how vortex ring dynamics can coherently transport particles to specific wall locations, with design parameters (ring size, Stokes number) controlling delivery accuracy.

Concept

A conceptual model for targeted particle delivery is proposed using controlled vortex ring reconnection. Particles entrained in the core of a vortex ring are efficiently transported as the ring advects by self-induction.

Left: initial particle seeding within the cores of the two vortex rings. Right: the reconnection sequence — first reconnection, second reconnection, and pinch off — that redirects the particles toward the sidewalls.

Mechanism

A pair of these particle-transporting vortex rings traveling in the streamwise direction along parallel trajectories will mutually interact, resulting in a pair of vortex reconnection events. The reconnection causes a topological change to the ring, accompanied by a rapid repulsion in the plane perpendicular to the direction of travel. This effectively transports the particles toward the desired location on the sidewalls of a ducted flow.

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Simulation of the two particle-laden vortex rings advecting, interacting, and reconnecting inside the duct.

In addition to proposing this conceptual model, we identify the dominant physics of the process and the design considerations required to achieve targeted delivery.

Particle inertia sets the delivery

Whether the particles actually follow the rings is governed by the Stokes number. Low-inertia particles stay locked to the ring cores and are carried coherently through both reconnections, while high-inertia particles decouple from the vortex and disperse before reaching the wall.

Mean streamwise particle position (left) and mean wall-normal particle position (right) for St = 0.1, 1 and 10. Shaded bands show one standard deviation and the dashed lines mark the two reconnection events. At St = 0.1 and St = 1 the particles track the rings and are delivered together; at St = 10 they lag and spread widely.

Design considerations

The ring radius, relative to the channel width, controls how strongly the rings repel after reconnection and therefore where on the sidewall the particles arrive. This makes ring size the primary design parameter for aiming the delivery.

Spreading angle θ after reconnection for three ring sizes, with R set by the channel width W: R = 0.15W (blue), R = 0.125W (green) and R = 0.1W (red). Larger rings separate more aggressively, moving the impact point further upstream.

Reference

Mouallem, J., Daryan, H., Wawryk, J., Pan, Z., and Hickey, J.-P.: Targeted particle delivery via vortex ring reconnection, Physics of Fluids, 33(10), 2021. https://doi.org/10.1063/5.0066443

Macro-Scale Effects on Sub-Grid Closures in Gas-Solid Riser Flows

Fri, 01 Jun 2018 00:00:00 +0000

Motivation

Sub-grid closures for two-fluid models are traditionally derived at a single scale, but this work demonstrates that flow topology at the system scale strongly affects closure accuracy. Accounting for these effects is essential for predictive industrial riser flow simulations.

Background

Filtered two-fluid formulations of gas-solid fluidized flows require closure models to deal with sub-grid filtered parameters. These closures are derived by filtering the results of meso-scale highly resolved simulations (HRS) with two-fluid modeling, and then applying them on the coarse large-scale simulation (LSS) grid.

Closure strategy: a highly resolved simulation with the two-fluid model and microscopic closures is filtered to provide sub-grid closures for the coarse, large-scale filtered two-fluid model.

The question

Trusting in scale separation, the correlation of filtered parameters has traditionally been performed against meso-scale filtered data only, disregarding any macro-scale effects. In this work, the correctness of that practice is tested — and it fails.

Approach

Two macro-scale parameters associated with flow topology are considered for their effects on the relevant filtered parameters: the average solid volume fraction and the average gas Reynolds number. Highly resolved simulations are filtered while holding each of these macro-scale parameters constant at various levels. The interest is directed toward the dilute conditions typical of riser flows.

Instantaneous solid volume fraction for increasing solids loading (left to right) and increasing gas Reynolds number (top to bottom). The cluster structure — and therefore the sub-grid closure — depends strongly on both macro-scale parameters.

The drag closure is not scale separated

The drag coefficient correction H, the single most influential sub-grid term, is the clearest evidence of the failure of scale separation. Correlating H against the meso-scale filtered variables alone leaves a systematic spread that is set entirely by the macro-scale state of the flow.

Drag coefficient correction H against the filtered solid volume fraction. (a) Effect of the domain average gas Reynolds number at fixed solids loading; (b) effect of the domain average solid volume fraction at fixed Reynolds number. Curves that should collapse if scale separation held instead fan out by a factor of two or more.

The same holds for the stress closures

The effect is not limited to drag. The filtered solid pressure, which closes the solid-phase momentum equation, shifts by roughly an order of magnitude across the range of macro-scale conditions at an otherwise identical filtered state.

Dimensionless filtered solid pressure against the filtered solid volume fraction. (a) Varying the domain average gas Reynolds number; (b) varying the domain average solid volume fraction. The vertical spread at fixed filtered state is the macro-scale signature that traditional closures ignore.

Conclusion

Results show that both macro-scale parameters should be accounted for in sub-grid correlations if higher accuracy is to be achieved.

Reference

Mouallem, J., Chavez-Cussy, N., Niaki, S. R. A., Milioli, C. C., and Milioli, F. E.: On the effects of the flow macro-scale over meso-scale filtered parameters in gas-solid riser flows, Chemical Engineering Science, 182, 200-211, 2018. https://doi.org/10.1016/j.ces.2018.02.039

Targeted particle delivery via vortex ring reconnection

Fri, 01 Oct 2021 00:00:00 +0000

Macro-scale effects over filtered and residual stresses in gas-solid riser flows

Sat, 23 Feb 2019 00:00:00 +0000

On the effects of the flow macro-scale over meso-scale filtered parameters in gas-solid riser flows

Fri, 01 Jun 2018 00:00:00 +0000