Powder Technology, Vol.77, No.3, 267-283, 1993
Modeling and Measurement of the Effective Drag Coefficient in Decelerating and Non-Accelerating Turbulent Gas-Solids Dilute Phase Flow of Large Particles in a Vertical Transport Pipe
The one-dimensional modeling of decelerating and non-accelerating turbulent dilute phase flow has been studied by transporting 1 mm glass spheres with air in a 28.45 mm electrically grounded stainless steel pipe. The two-fluid model used to analyze the data employs the continuity and individual phase momentum balances from the model of Nakamura and Capes, Canadian Journal of Chemical Engineering, 51 (1973) 39. Slip Reynolds numbers for the particles ranged from 471 to 986 and the pipe Reynolds number was of the order of 20 000. The loading ratio varied from 5.6 to 17.1. Evidence is presented to support the existence of a particle-free region near the wall making it possible to neglect particle-wall friction effects in the modeling. Fluid-wall friction effects were then modeled assuming turbulent flow in a pipe without particles. The non-acceleration drag coefficient, Cd-dn, correlates as 9.56x104/Re-p(1.96) or (4/3)epsilon Ar/Re-p(2). It decreases from values essentially the same as those on the standard drag curve to values significantly below that curve. C-dn is 0.13 when Re-p equals 986, a result attributed to freestream turbulence. The slip velocity decreases with distance from the pipe inlet so that relative to the gas phase the particle phase is decelerating. The deceleration drag coefficient was correlated by the equation cdd = {c(dn) + (4/3)K epsilon(NA)[(rho(p)/rho f) - 1][d(p)( - dU(R)/dt)/U(R)2]}[(1 - epsilon(NA))/(l - epsilon)] where K = 1.021 - 0.0188 (rho(p)c(2)/rho(f)c(1)). The effect of electrostatic forces on the drag coefficient and particle-wall friction factor are also discussed.