Hydrodynamically interacting droplets at small Reynolds numbers

Hollander, W.Th.F. den; Zaripov, S. K.

doi:10.1016/j.ijmultiphaseflow.2004.09.003

Cited by 19 publications

(19 citation statements)

References 27 publications

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“…11,16 Equation ͑66͒ is in agreement with Fuchs' observation that the Basset force for the decelerating motion of particles leads to an increase in the stopping distance as mentioned in the review by Hollander and Zaripov. 11 The error in Eq. ͑66͒ is of order ⑀ 3 even though all terms in the second approach are included.…”

Section: ͑66͒supporting

confidence: 84%

“…These results are in qualitative agreement with the experimental data collected by Hollander and Zaripov. 11 They presented results for droplets emitted horizontally and vertically and obtained the droplet trajectory endpoints for a horizontal jet and the maximum height of the droplet trajectory for a vertical jet, and compared experimental data with theoretical results. They showed that for particle arrays, the maximum droplet height increases by including the Basset force for an isolated sphere.…”

Section: Two Equal Spheres Moving In a Gravitational Fieldmentioning

confidence: 99%

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Unsteady motion of two solid spheres in Stokes flow

Ardekani

Rangel

2006

Physics of Fluids

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This study is concerned with the unsteady motion of two solid spherical particles in an unbounded incompressible Newtonian flow. The background flow is uniform and can be time dependent. In addition, the particle Reynolds numbers 2aVa∕ν and 2bVb∕ν, based on characteristic particles velocities Va and Vb, are assumed to remain small throughout the motion. Here, a and b denote the particle radii and ν is the kinematic viscosity of the fluid. Two approximate methods are employed in order to calculate the unsteady force exerted on each particle. In the first approach, a simplified method of reflections in combination with the point-force method is employed. In the second approach, a simplified method of reflections combined with Burger’s unsteady flow solution is considered. The forces due to the background flow and the disturbed flow created by the presence of particles are treated separately. The equation of motion for each particle is derived and some special cases are presented in detail including the motion with constant acceleration and the motion in a gravitational field. The results indicate that using the Basset force corresponding to the motion of two spheres gives rise to a larger drag force as compared to the solution utilizing the solitary-particle Basset force.

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Section: ͑66͒supporting

confidence: 84%

Section: Two Equal Spheres Moving In a Gravitational Fieldmentioning

confidence: 99%

Unsteady motion of two solid spheres in Stokes flow

Ardekani

Rangel

2006

Physics of Fluids

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“…Droplets, on the other hand, can deform and there may be internal circulation of the droplet fluid (Helenbrook andEdwards (2002), Prahl et al (2006)). Furthermore, aerodynamic four-way interaction may be important in dense sprays (Prahl et al (2006), Holländer and Zaripov (2005)). These effects compromise the model accuracy for the estimation of the drag coefficient C d .…”

Section: Droplet Trajectoriesmentioning

confidence: 99%

“…Four-way interaction can be divided into direct (collision) and indirect (aerodynamic) interaction. For in-line droplets the aerodynamic inter-droplet coupling has noticeable impacts up to many droplet diameters in the wake of a preceding droplet (Holländer and Zaripov, 2005). The drag coefficient of the second of two in-line particles decreases by 30% for an inter-particle spacing L/D p ∼ 6 (Prahl et al, 2006).…”

Section: Introductionmentioning

confidence: 99%

Consistency issues of Lagrangian particle tracking applied to a spray jet in crossflow

Salewski

Fuchs

2007

International Journal of Multiphase Flow

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Numerical simulations are performed for multiphase jets in crossflow. The flow solver uses an Eulerian/Lagrangian approach. Turbulence in the gas phase is modeled in the framework of large eddy simulation. The dispersed phase is handled using Lagrangian particle tracking. The model assumptions of solvers for Lagrangian particle tracking are critically assessed for typical flow conditions of spray jets in crossflow. The droplets are assumed to be spherical and isolated. It is shown that several model assumptions are apparently inconsistent in larger portions of the flow field. Firstly, average Weber numbers can be so large that the model assumption to regard droplets as spherical is questionable, not only near the nozzle, but also in the far-field. Secondly, the average droplet spacing can be so low that droplets directly interact with each other, again also in the far-field. Thirdly, the average Stokes numbers in the jet region can be so large that the phase coupling between the dispersed and continuous phase is weak. Some remedies to these deficiencies are proposed.

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“…For example, the aligned tandem formation results in drag reductions of 30% on the particle in the wake for an inter-particle spacing L/D p ∼ 6 [22]. Also chains of particles [23] and three spheres in a straight line at various angles [18] and in L-formation and side-byside-by-side formation [24] have been found to show remote interaction effects. Flow around a pair of spheres of unequal size has also been computed [20].…”

Section: Introductionmentioning

confidence: 99%

Effects of aerodynamic particle interaction in turbulent non-dilute particle-laden flow

Salewski

Fuchs

2008

Journal of Turbulence

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Aerodynamic four-way coupling models are necessary to handle twophase flows with a dispersed phase in regimes in which the particles are not dilute enough to neglect particle interaction but not dense enough to bring the mixture to equilibrium. We include an aerodynamic particle interaction model within the framework of large-eddy simulation (LES) together with Lagrangian particle tracking (LPT). The particle drag coefficients are corrected depending on relative positions of the particles accounting for the strongest drag correction per particle but disregarding many-particle interactions. The approach is applied to simulate monodisperse, rigid, and spherical particles injected into crossflow as an idealization of a spray jet in crossflow. A domain decomposition technique reduces the computational cost of the aerodynamic particle interaction model. It is shown that the average drag on such particles decreases by more than 40% in the dense particle region in the near-field of the jet due to the introduction of aerodynamic four-way coupling. The jet of monodisperse particles therefore penetrates further into the crossflow in this case. The strength of the counter-rotating vortex pair (CVP) and turbulence levels in the flow then decrease. The impact of the stochastic particle description on the four-way coupling model is shown to be relatively small. If particles are also allowed to break up according to a wave breakup model, the particles become polydisperse. An ad hoc model for handling polydisperse particles under such conditions is suggested. In this idealized atomizing mixture, the effect of aerodynamic four-way coupling reverses: The aerodynamic particle interaction results in a stronger CVP and enhances turbulence levels.

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Hydrodynamically interacting droplets at small Reynolds numbers

Cited by 19 publications

References 27 publications

Unsteady motion of two solid spheres in Stokes flow

Unsteady motion of two solid spheres in Stokes flow

Consistency issues of Lagrangian particle tracking applied to a spray jet in crossflow

Effects of aerodynamic particle interaction in turbulent non-dilute particle-laden flow

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