Threshold velocities of particle-fluid flows in horizontal pipes and ducts: literature review

Abstract

Numerous industrial processes such as conveying, fl uidizing and handling involve two-phase (fl uid-solids) fl ows. Investigation of the two-phase fl ow mechanisms have importance in both industrial manufacturing processes and natural phenomenon such as dust storms, erosion, air pollution and soil deposition in rivers and ocean fl ows. One of the most signifi cant parameters for designing two-phase (fl uid-solids) fl ow conveying systems is the fl uid velocity magnitude. Inaccurate determination of the fl uid velocity can lead to high energy consumption, particle attrition, pipe erosion and in some cases pipe blockage. This work reviews numerous studies presented in the literature concerning various threshold velocities in horizontal two-phase (fl uid-solids) fl ow systems. The threshold velocities include: incipient motion, pickup from a layer of particles, pickup from hill-shape particle deposits, boundary saltation and minimum pressure velocity. Most of the studies were conducted in pneumatic and hydraulic conveying systems and large-scale wind tunnels systems. As each threshold velocity characterizes a transition between two or more fl ow regimes and mode of particle movement, all possible fl ow regimes of the particle-fl uid horizontal conveying systems are present fi rst. Then the threshold velocity models and correlations are analyzed and compared. The theoretical models are compared for the forces and torque vectors taken into account for various threshold conditions and particle package geometry. In addition, the main parameters infl uencing the pickup and saltation mechanisms and the dimensionless numbers are reviewed. Finally, four threshold velocities are used to characterize a generalized fl ow regime diagram for horizontal conveying systems. This diagram makes a signifi cant contribution to researching and designing twophase fl ow systems. For example, the diagram may assist in the transition conditions between dilute and stratifi ed fl ow regimes. However, more theoretical and empirical research is required to discover all the possible states of horizontal systems.

Constraints on the functional form of the critical deposition velocity in solid–liquid pipe flow at low solid volume fractions

“…Various definitions of the deposition d on a number of other studies (Gruesbeck et al, 1979(Gruesbeck et al, urian, 1980Kalman, 2009, 2011; h delineates the onset of settling and full suspension rticles initially having been at rest on the surface of a within the fluid"; the incipient motion velocity, at w the saltation velocity, which is the minimum flow velo the bottom of the pipe; and the equilibrium velocit ook (1991) example, Spells (1955) for a slurry and its e pressure gradientinimum -is invoked in ing and non-depositing uated with the critical a distinction has been sure velocity generally erature (Soepyan et al, s at low solids volume eposition velocity were , 1979; Hayden et al, ;Zenz, 1964): the uspension; the pick-up rface of a particle bed city, at which a single flow velocity at which velocity, at which the rate of settling onto the bottom of the pipe balances the rate of pick-up from it. In fact, in one review article, the incipient motion velocity has been categorised as a type of pick-up velocity, and the minimum-pressure velocity as a type of saltation velocity (Rabinovich and Kalman, 2011).…”

“…The functional form given in Equation [1] differs from that suggested by Rabinovich and Kalman (2011), which is as follows:…”

“…Soepyan et al (2014) only analysed the pick-up velocity, and not the critical deposition velocity, in hydraulic flows, but the functional form they proposed is adopted in this study, by analogy (Rabinovich and Kalman, 2011). Soepyan et al (2014) used only data in the range 0 < < 10 -4 for their optimisation procedure, so it is not surprising that the most successful functional forms contained little or no dependence on .…”

Determinación de la Velocidad de Transporte de Partículas por Saltos en Conductos Horizontales

“…La deposición de sólido puede formar un lecho en la parte inferior del conducto, reduciendo su sección transversal (Jo y Ray, 1999). Sin embargo, si la velocidad de diseño es excesiva puede producir la erosión de los conductos, el desgaste de las partículas y fundamentalmente el aumento del consumo energético del ventilador requerido (Rabinovich y Kalman, 2011). De esta forma, el diseño de las instalaciones de ventilación localizada, es importante no solamente desde el punto de vista de la higiene y seguridad industrial, sino también por el aspecto económico y energético, porque seleccionar una velocidad elevada en el conducto puede llevar a instalaciones sobredimensionadas, con el consecuente aumento de la energía consumida.…”

“…En los conductos horizontales pueden definirse además, otras velocidades relacionadas con la velocidad mínima como son las velocidades de transporte por saltos y la velocidad de arranque o pickup (Khan et al, 2016;Rabinovich y Kalman, 2011;Hubert y Kalman, 2003;Cabrejos y Klinzing, 1994). En los conductos verticales la sedimentación del sólido comienza cuando la velocidad del aire disminuye hasta igualar la velocidad terminal de sedimentación de las partículas sólidas.…”