The transverse force on a spinning sphere moving in a viscous fluid

Rubinow, S. I.; Keller, Joseph B.

doi:10.1017/s0022112061000640

Cited by 936 publications

(372 citation statements)

References 8 publications

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“…They are based on perturbing Stokes flow with inertia (e.g. Rubinow & Keller 1961, Saffman 1965, 1968, Bretherton 1962, Asmolov 1990, McLaughlin 1991, Krishnan & Leighton 1995 and reference therein) or on perturbing potential flow (e.g. Auton 1987, Drew & Passman 1999) with a little vorticity.…”

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confidence: 99%

Power law correlations for sediment transport in pressure driven channel flows

Patankar

Joseph

Wang

et al. 2002

International Journal of Multiphase Flow

115

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Lift forces acting on particles play a central role in many cases, such as sediment transport, proppant transport in fractured reservoirs, removal of drill cuttings in horizontal drill holes and cleaning of particles from surfaces. We study the problem of lift using 2D direct numerical simulations and experimental data. The lift-off of single particles and many particles in horizontal flows follow laws of similarity, power laws, which may be obtained by plotting simulation data on log-log plots. Data from slot experiments for fractured reservoirs is processed (for the first time) on log-log plots. Power laws with a parameter dependent power emerge as in the case of Richardson-Zaki correlations for bed expansion by drag.

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mentioning

confidence: 99%

Power law correlations for sediment transport in pressure driven channel flows

Patankar

Joseph

Wang

et al. 2002

International Journal of Multiphase Flow

115

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“…For C D , Henderson relations [7] were used. For calculating C ω , the exact solution obtained by Rubinow and Keller [8] was used as well as the formula suggested by Oesterl‚ e and Bui Dinh [9]. The expression for C L was taken in the form suggested by Dennis et al [10].…”

Section: Modeling Of Particle-phase Flowmentioning

confidence: 99%

Effects of particle mixing and scattering in the dusty gas flow through moving and stationary cascades of airfoils

Tsirkunov

Romanyuk

Panfilov

2011

Progress in Propulsion Physics

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Time-dependent two-dimensional (2D) §ow of dusty gas through a set of two cascades of airfoils (blades) has been studied numerically. The ¦rst cascade was assumed to move (rotor) and the second one to be immovable (stator). Such a §ow can be considered, in some sense, as a §ow in the inlet stage of a turbomachine, for example, in the inlet compressor of an aircraft turbojet engine. Dust particle concentration was assumed to be very low, so that the interparticle collisions and the e¨ect of the dispersed phase on the carrier gas were negligible. Flow of the carrier gas was described by full Navier Stokes equations. In calculations of particle motion, the particles were considered as solid spheres. The particle drag force, transverse Magnus force, and damping torque were taken into account in the model of gas particle interaction. The impact interaction of particles with blades was considered as frictional and partly elastic. The e¨ects of particle size distribution and particle scattering in the course of particle blade collisions were investigated. Flow ¦elds of the carrier gas and §ow patterns of the particle phase were obtained and discussed.

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“…These interactions include the inter-particle forces due to collision between particles (contact force and viscous contact damping force) [45][46][47] or other effects (van der Waals force and electrostatic force associated with fine particles, capillary and viscous forces associated with wet particles, and solidbonding forces). 48,49) Particle-fluid interactions include buoyancy, 22,50) drag force, 18,51) lift force, 52,53) virtual mass force [54][55][56] and Basset force. 54,55) These forces have been implemented in different particle systems by various investigators.…”

Section: Mathematical Modellingmentioning

confidence: 99%

Modelling of Multiphase Flow in a Blast Furnace: Recent Developments and Future Work

et al. 2007

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An ironmaking blast furnace is a complex multiphase flow reactor involving gas, powder, liquid and solid phases. Understanding the flow behaviour of these phases is of paramount importance to the control and optimization of the process. Mathematical modelling, often coupled with physical modelling, plays an important role in this development. Yagi 1) gave a comprehensive review of the early studies in this area in 1993. Significant progress has since been made, partially driven by the needs in research but mainly as a result of the rapid development of computer and computational technologies. This paper reviews these developments, covering the formulation, validation and application of mathematical models for gas-solid, gas-liquid, gas-powder and multiphase flows. The need for further developments is also discussed.KEY WORDS: ironmaking; blast furnace; multiphase flow; two fluid model; discrete element method. Review development. Mathematical ModellingGenerally speaking, the existing approaches to modelling the multiphase flow in a BF can be classified into two categories: continuum approach at a macroscopic level and discrete approach at a microscopic level. In the continuum approach, phases are generally considered as fully interpenetrating continuum media and described by separate conservation equations with appropriate constitutive relations and interaction terms representing the coupling between phases. The general governing equations are based on the so-called two fluid model (TFM), originally developed for gas-particle flow, [29][30][31] given by:Conservation The so-called Model A and Model B result from the treatment of the fluid pressure. For example, for gas-solid flow, Model A assumes the pressure is shared between the two phases, while in Model B, the pressure is attributed to gas phase only. 31) Model A formulation has been widely used in multiphase modelling, especially in process metallurgy. Model B formulation was recently used in the so called combined continuum and discrete method for coupled flow of continuum fluid and discrete particles. 32) The continuum approach is suitable for process modelling and applied research because of its computational convenience and efficiency. Indeed, most of the BF modelling is based on this approach. However, its effective use heavily depends on constitutive or closure relations and the momentum exchange between phases. For Newtonian fluids (gas and liquid here), these relations can be readily determined. For non-Newtonian fluids such as solids and powder, general theories are not yet available. In the past, various theories have been devised for different flow regimes (three flow regimes have been identified: quasi-static regime, rapid flow regime and a transitional regime that lies inbetween). For example, models have been proposed to derive the constitutive equations for the rate-independent deformation of granular materials based on either the plasticity theory or the double shearing theory; the rapid flow of granular materials has been described by extend...

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The transverse force on a spinning sphere moving in a viscous fluid

Cited by 936 publications

References 8 publications

Power law correlations for sediment transport in pressure driven channel flows

Power law correlations for sediment transport in pressure driven channel flows

Effects of particle mixing and scattering in the dusty gas flow through moving and stationary cascades of airfoils

Modelling of Multiphase Flow in a Blast Furnace: Recent Developments and Future Work

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