3D Numerical Model of the Spherical Particle Saltation in a Channel with a Rough Fixed Bed

Abstract

The paper describes a 3D numerical model of the spherical particle saltation. Two stages of particle saltation were distinguished -the particle free motion in water and the particle-bed collision. The particle motion consists of the translational and rotational particle motion. A stochastic method of calculation of the particle-bed collision was developed. The collision height and the contact point were defined as random variables. Impulse equations were used and the translational and angular velocity components of the moving particle immediately after the collision were expressed as functions of the velocity components just before the collision. The dimensionless coefficients of the drag force and drag torque were determined as functions of both translational and rotational Reynolds numbers. The model is in good agreement with known experimental data. Examples of calculation of the particles' lateral dispersion and the mean absolute values of the deviation angle of the particle trajectory are presented. Studie popisuje 3D numerický model saltačního pohybu kulovité částice, v němž jsou uvažována dvě fáze saltačního pohybu -volný pohyb částice v proudící vodě a kolise částice se dnem. Model počítá s translačním i rotačním pohybem částice. Byla vyvinuta stochastická metoda výpočtu kolise částice se dnem. Kolizní výška a kontaktní bod byly definovány jako náhodné proměnné. Byla použita soustava momentových rovnic a složky translační a rotační rychlosti pohybující se částice po kolizi byly vyjádřeny jako funkce složek rychlosti těsně před kolizí. Bezrozměrné koeficienty odporu částice a odporu rotující částice byly určeny jako funkce translačního i rotačního Reynoldsova čísla částice. Výsledky modelu jsou v dobré shodě se známými experimentálními daty. Studie presentuje příklady výpočtu příčné disperze částice a střední absolutní hodnoty deviačního úhlu trajektorie částice.KLÍČOVÁ SLOVA: 3D model saltace, pohyb splavenin, kolise částice-dno, rotace částic, příčná disperze částic.

Numerical model of spherical particle saltation in a channel with a transversely tilted rough bed

“…The numerical model of the particle-bed collision is described in detail by Lukerchenko et al (2004).…”

“…The system of equations describing the particle motion in the channel is solved numerically using a fourth-order Runge-Kutta scheme (Lukerchenko et al, 2004). The numerical model of the particle-bed collision is described in detail by Lukerchenko et al (2004).…”

“…Wiberg and Smith, 1985;Nino and Garcia, 1994;Lee et al, 2000;Lukerchenko et al, 2006). However, a description of the saltation process in the case of a transversely tilted bed can be realised properly only if the 3D pattern of particle saltation is used (Lukerchenko et al, 2009). Sekine and Kikkawa (1992) and Lee et al (2006) developed 3D saltation models which were deterministic for the particle motion in fluid but stochastic for the particle-bed collision stage.…”

“…Therefore, to describe the saltation process reliably the model of saltation must take into account not only the translational but also the rotational particle motion. The present paper uses as a basis the 3D numerical model of spherical particle saltation (Lukerchenko et al, 2003(Lukerchenko et al, , 2004(Lukerchenko et al, , 2009), in which the particle rotation is taken into account and the problem of a particle-bed collision is solved using the concept of a contact zone.…”

Lattice Boltzmann method used to simulate particle motion in a conduit

“…The conveyed particles generally pass through different stages of movement such as sliding, rolling, saltation, or free suspension in the liquid flow (e.g., Abbott and Francis, 1977). To study the modes of particle motion some theoretical and numerical approaches employing Lagrangian models were suggested, for example, Wiberg and Smith (1985), Niño and Garcia (1994), and Lukerchenko et al (2006Lukerchenko et al ( , 2009. More recent advances in Lagrangian transport modelling are represented by Bialik et al (2012).…”