Cold model study of metal droplet descent through fluids including a treatment of the non-Newtonian behaviour as exhibited by molten slag system

Abstract

In the context of several high temperature metallurgical processes including blast furnaces, a cold model study simulating a metal droplet descent through the surrounding fluid system is presented. The study comprises an experimental programme employing wide range of fluids exhibiting both Newtonian and non-Newtonian behaviour. Such fluid systems are encountered in slag-metal droplet systems where viscosity of the slag system has a significant effect on the kinetics of refining reactions. Slag systems generally possess random network structures comprising internal regions of weak ordering and the presence of these regions may result in non-Newtonian behaviour of the slag. As the viscosity of the slag is very sensitive to structure, a treatment of non-Newtonian behaviour as exhibited by some molten slag systems is therefore required. Two parameters have been identified and estimated that help to determine the rheological characteristics of fluids in relation to their network structure. The underlying principle of the model development has been that the external pressure exerts a driving force that affects the motion of the fluid to a degree dependent on the rheological behaviour and the network structure of the fluid. The paper also describes some results of a cold model study of the momentum transfer to the fluid system by correlating the drag Reynolds number with the modified drag coefficient for non-Newtonian fluids List of symbolsA empirical parameter for network forming liquids A p projected area, m 2 Bi* basicity index C D drag coefficient C Dm modified drag coefficient C D /X avg D diameter of the fluid span, m D c dia of capillary, m D p particle diameter, m D v settling column diameter, m E empirical parameter for network forming fluids F B buoyancy force, N F D drag force, N F E external force, N F R force of resistance exerted on the solid body by the fluid, N g acceleration due to gravity, m s -2 g c conversion factor k9 consistency index, N s n' m -2 L length of fluid column, m L c length of capillary, m n9 flow behaviour index U fluid velocity through capillary, m s -1 V m terminal velocity, m s -1 V m * drag velocity, m s -1 X drag coefficient factor N Rem modified Reynolds number N Rem * drag Reynolds number N Rep particle Reynolds number t yx shear stress, N m -2 dv x dy rate of deformation, s 21DUr m a form of Reynolds number based on fluid span N and N9 unknown parameters DP pressure gradient, N m -2 r s , r f density of solid, fluid, kg m -3 n kinematic viscosity (m/r), m 2 s -1 t w wall stress, N m -2 m viscosity, N s m -2 m ap apparent viscosity, k'(8U/D c ) n'21 , N s m -2 m 0 viscosity of non-network forming melts defined by Iida et al., 28 N s m -2 y network structure defining parameter 28 w and w9 unknown parameters P invariant of rate deformation tensor, s -1 P* dimensionless form of P

Cold Simulation of momentum transfer of a metal droplet falling through slag systems possessing net-work structured fluids

“…Prakash (2000) also conducted a study on cold modeling of slag rheology. Bird et al (1960), Prakash (2004) and Prakash et al (2005) studied the settling velocity of a spherical particle through the fluid, described by the Ostwald-De-Waele model (Eq. (3)).…”