Numerical Study On the Pneumatic Conveying of Gas-Solid Two-Phase In Vertical-to-Horizontal Bends

Pneumatic conveying is extensively used for the transportation of different types of dry and free-flowing powdered and granular materials. Owing to its wide application in chemical, cement, food, pharmaceutical, mining and power industries, the proper design of pneumatic conveying systems is of great importance. Bends and elbows often used in the pneumatic conveying systems offer flexible routing and distribution but at the cost of various problems such as high pressure loss, particle segregation and degrading, particle roping, and pipe wall erosion. In the past, several efforts have been made to understand the internal flow in such geometries and minimize the above stated problems by employing different bend designs such as T-bend, ankle-bend, ribbed bends and bends with flow mixers.

The important factors which influence the design of such systems are properties of gas and particles, conveying gas velocity and solid mass flow rate. It is of economical interest to convey solids at lowest possible gas velocity so as to reduce the power consumption, pipe erosion and particle attrition. However, below certain gas velocity the particles cannot remain in suspension leading to the particle deposition and pipe blockages thereby affecting the operating efficiency and safety of the conveying system. Hence, objective of the present work is to numerically investigate the gas-solid flow in a 90^o vertical-to-horizontal bend for low conveying gas velocities. The knowledge about the effects of gas flow velocity, gas to solids mass flow rate ratio and bend radius to pipe diameter ratio on particle concentration, velocity profiles and particle roping characteristics would further aid in design purposes.

The numerical investigation was conducted using the commercial Computational Fluid Dynamic (CFD) software Ansys-Fluent 12.1, employing the Euler-Lagrangian approach. The computational model was consisted of a circular elbow geometry with 5D long vertical straight duct, a circular 90^o elbow with R/D = 1.5, 3.0 and 5.0 and a 20D long horizontal straight duct, where R is the bend radius and D is the diameter of the pipe. The predictions were taken at y = 3D, 5D and x = 1D, 5D, 10D, 15D, 20D upstream of the bend exit in the horizontal duct. The gas and particle data were collected at six different angular locations (0^o, 30^o, 45^o, 60^o, 75^o and 90^o), where x and y are the transverse distances in pipe cross-section. All calculations were performed on structured hexagonal grids created in Ansys-Workench 12.1. The grid was sufficiently refined at the wall and was found to produce a grid-independent solution. Pulverized coal particles, having an average particle diameter of 50 mm and particle density of 1680 kg/m³, was used as the solid material. The solid particles were released into the duct at the same velocity as the gas phase, i.e., zero slip, and from random locations on the inlet plane.

Euler-Discrete phase methodology (DPM) along with renormalization group (RNG) k-ε model was employed to perform numerical calculations of the particle-laden gas flow in 90^o elbow with different bend ratios. This approach computes the Navier-Stokes equation for the gas phase and the motion of individual particles by the Newtonian equations of motion. Computations were performed for the gas phase followed by the solution of the solid phase. Hence, various hydrodynamics forces acting on the particles were determined based on the prior knowledge of predicted gas flow. The renormalization group (RNG) k-ε model was used to simulate the gas phase turbulence (Yin et al., 1996). DPM treats the interaction between the gas and solid phases using the particle-source-in-cell method (Crowe et al., 1977). The conservation equations include appropriate source terms resulting from the dispersed phase (i.e. two-way coupling). Stochastic method was used to account for the influence of gas turbulence on the solid phase (Gosman and Ioannides, 1981). The interaction between particles and the wall was modeled using a coefficient of restitution. The effect of particulate phase on the gas flow, turbulent dispersion, lift forces and particle-wall collisions were incorporated in the model. Fully developed turbulent flow was assumed at the inlet. A ‘no-slip’ boundary condition was employed for the gas velocity at the wall.

The pressure based segregated solver was used, with the SIMPLE scheme for pressure-velocity coupling. All the diffusion terms used second-order discretization. The second-order upwind interpolation was used for the convection terms. Under-relaxation factors were usually left at the Fluent default settings. To handle the nonlinearity of the equations, the treatment of all transported variables involved two nested levels of iterations referred to as inner and outer iterations. Outer iterations were repeated until the problem satisfied a convergence criterion. A converged solution of the coupled two-phase flow system is obtained by successive solution of the Eulerian and discrete phase, respectively. For the simulations performed in this study, the convergence of outer iteration was judged by how accurately the continuity equation was satisfied by the current values of the dependent variables. The solution procedure was considered converged when the ratio of the summation of absolute mass source residuals to the total rate of mass inflow fell below a prescribed tolerance (1x 10^-6).Thereafter, a large number of particles were tracked through the flow field (typically 100000 or more). Each case was simulated for 2 to 5 s.

For the purpose of the model validation, the parameters used in the simulation are mainly taken from the experiments of Akilli et al. (2005). The solid particles and the gas segregate in the bend due to centrifugal forces. It was observed that most of the particles aggregate towards the outer wall of the duct, referred to as ropes. This can as well observed from the particle concentration profiles. As the particle ropes flows along the horizontal duct, they falls from the top-outer wall towards the bottom-inner wall of the duct due to gravity. Similar observations were also made by McCluskey et al. (1989) and Akilli et al. (2001, 2005). They reported that particle deposition was a consequence of rope formation in bends. Further, parametric investigations were performed to study the effect of operating variables on particle roping and the results henceforth can offer improved insight and initial design modelling capability for gas-solid pneumatic conveying systems. The comparison of the mean streamwise velocity profiles for both air and pulverized coal particles and pressure drop for with the experimental data set of Akilli et al. (2005). The fundamental features like particle roping phenomena, particle segregation, secondary flow and recirculation, gas-particle interaction were reasonably captured and compared for different circular bends. The results show secondary flows disperse the particle rope by carrying particles around the pipe circumference while turbulence disperses the rope by localized mixing of particles. The results presented in this work are directly applied to engineering applications such as development of coal gasification plants, fluidized pneumatic conveying.

REFERENCES

Akilli, H., Sahin, B. and Levy, E.K., (2001), “Gas–solid flow behavior in a pipe after a 90◦ vertical-to-horizontal elbow”, Powder Technol., 116, 43–52.

Akilli, H., Sahin, B. and Levy, E.K., (2005), “Investigation of gas–solid flow structure after a 90◦ vertical-to-horizontal elbow for low conveying gas velocities, Advanced Powder Technol., 16(3), 261-274.

Crowe, G. T., Sharma, M. P. and Stock, D. E.: 1977, ‘The particle-source-in-cell model for gas droplet flows, J. Fluid Eng. 99, 325−332.

Gosman,A., E. Ionnides, Aspects of computer simulation of liquid fuelled combustors, AIAA paper. No. 81-0323, 1981.

McCluskey, D. R., Easson, W. J., Greated, G.A. and Glass, D. H., (1989), “The use of particle image velocimetry to study roping in pneumatic conveyance”, Particle Particle Syst. Character. J. 6, 129–132.

Yin,M., F. Shi, Z. Xu, Renormalization group based C turbulence model for flows in a duct with strong curvature, Int. J. Eng. Sci. 34, 1996. 243–248.