Effective drag coefficient investigation in the acceleration zone of an upward gas–solid flow

Abstract A new correlation has been developed for the purpose of evaluating the effective drag coefficient of gas–solid systems of ascending flow. In the proposed expression, the effects of particle acceleration in the acceleration zone and Basset force have been considered. The radioactive particle tracking measurement technique (RPT) was used to obtain a dynamic picture of particle trajectory in the system. The Cartesian coordinates ( x , y and z ) of the radiotracer were registered every 10 ms and other useful variables, such as particle velocity, particle velocity fluctuation and acceleration, were calculated. The effects of particle velocity, acceleration and Basset force on the measurement of the drag coefficient were investigated in the internal circulating fluidized bed (ICFB). The experiments were carried out using sand and alumina particles in an ICFB unit with a 1 m riser length and a 0.052 m riser diameter. The gas velocity range studied was between 2 and 12 m/s. The most common correlations for calculating the drag coefficient were reviewed and compared to the one developed in this work. Numerical analysis of the one-dimensional two-phase flow model demonstrates that the drag coefficient proposed here is in good agreement with experimental data and covers a variety of operating conditions ( G s = 29 , 50 and 240 kg / m 2 s ; U = 4.2 , 5.8 and 8.5 m/s; D = 0.05 , 0.2 and 0.4 m ID).

[1]  John D. Paccione,et al.  Modeling and measurement of the effective drag coefficient in decelerating and non-accelerating turbulent gas—solids dilute phase flow of large parti , 1993 .

[2]  P. N. Rowe,et al.  A Convenient Empirical Equation for Estimation of the Richardson-Zaki Exponent , 1987 .

[3]  Jason M. Reese,et al.  The drag force in two-fluid models of gas–solid flows , 2003 .

[4]  P. Thomas.  On the influence of the Basset history force on the motion of a particle through a fluid , 1992 .

[5]  Yassir Makkawi,et al.  The voidage function and effective drag force for fluidized beds , 2003 .

[6]  S. Ergun.  Fluid flow through packed columns , 1952 .

[7]  S. Stemerding,et al.  The pneumatic transport of cracking catalyst in vertical risers , 1962 .

[8]  John Happel,et al.  Viscous flow in multiparticle systems: Slow motion of fluids relative to beds of spherical particles , 1958 .

[9]  K. Nakamura,et al.  Vertical pneumatic conveying: An experimental study with particles in the intermediate and turbulent flow regimes , 1973 .

[10]  C. Wen.  Mechanics of Fluidization , 1966 .

[11]  J.A.M. Kuipers,et al.  Gas-particle interactions in dense gas-fluidised beds , 2003 .

[12]  P. Foscolo,et al.  Generalized friction factor and drag coefficient correlations for fluid-particle interactions , 1985 .

[13]  Udo Fritsching,et al.  Spray Simulation: Modeling and Numerical Simulation of Sprayforming metals , 2016 .

[14]  Walter H. Graf,et al.  Drag Coefficient of Cylinders in Turbulent Flow , 1972 .

[15]  Jonathan Seville,et al.  Processing of Particulate Solids , 1997 .

[16]  J. F. Richardson,et al.  Sedimentation and fluidisation: Part I , 1997 .

[17]  D. Gidaspow,et al.  A bubbling fluidization model using kinetic theory of granular flow , 1990 .

[18]  A. B. Basset,et al.  Treatise on Hydrodynamics , 1889, Nature.

[19]  Wallis S. Hamilton,et al.  Forces on a sphere accelerating in a viscous fluid , 1964, Journal of Fluid Mechanics.

[20]  W. Gauvin,et al.  The drag coefficients of single spheres moving in steady and accelerated motion in a turbulent fluid , 1961 .

[21]  R. Clift,et al.  Bubbles, Drops, and Particles , 1978 .

[22]  R. Clift,et al.  Motion of entrained particles in gas streams , 1971 .

[23]  K. Nakamura,et al.  Vertical pneumatic conveying: A theoretical study of uniform and annular particle flow models , 1973 .

[24]  D. Pei,et al.  Particle Dynamics in Solids-Gas Flows in Vertical Pipe , 1969 .

[25]  J. Chaouki,et al.  A γ-ray detection system for 3-D particle tracking in multiphase reactors , 1994 .

[26]  Željko Grbavčić,et al.  Hydrodynamic modeling of vertical accelerating gas-solids flow , 1997 .

[27]  Pertti Sarkomaa,et al.  Solids friction factors in upward, lean gas-solids flows , 1998 .

[28]  V. Armenio,et al.  The importance of the forces acting on particles in turbulent flows , 2001 .

[29]  R. Adrian,et al.  Unsteady drag on a sphere at finite Reynolds number with small fluctuations in the free-stream velocity , 1991, Journal of Fluid Mechanics.

[30]  R. D. Felice,et al.  The voidage function for fluid-particle interaction systems , 1994 .

[31]  Franco Berruti,et al.  A predictive hydrodynamic model for circulating fluidized bed risers , 1996 .

[32]  O. Levenspiel,et al.  Drag coefficient and terminal velocity of spherical and nonspherical particles , 1989 .

[33]  Efstathios E. Michaelides,et al.  Effect of the history term on the motion of rigid spheres in a viscous fluid , 1994 .

[34]  Lounes Tadrist,et al.  Numerical study of cluster formation in a gas–particle circulating fluidized bed , 2000 .

[35]  S. McKee,et al.  The dispersive effects of Basset history forces on particle motion in a turbulent flow , 1984 .

[36]  Efstathios E. Michaelides,et al.  Drag coefficients of irregularly shaped particles , 2004 .

[37]  J. Chaouki,et al.  3‐D mapping of solids flow fields in multiphase reactors with RPT , 1995 .