Finite Element Prediction of Multi-Size Particulate Flow through Two-Dimensional Pump Casing
Authors: K. V. Pagalthivarthi, R. J. Visintainer
Abstract:
Two-dimensional Eulerian (volume-averaged) continuity and momentum equations governing multi-size slurry flow through pump casings are solved by applying a penalty finite element formulation. The computational strategy validated for multi-phase flow through rectangular channels is adapted to the present study. The flow fields of the carrier, mixture and each solids species, and the concentration field of each species are determined sequentially in an iterative manner. The eddy viscosity field computed using Spalart-Allmaras model for the pure carrier phase is modified for the presence of particles. Streamline upwind Petrov-Galerkin formulation is used for all the momentum equations for the carrier, mixture and each solids species and the concentration field for each species. After ensuring mesh-independence of solutions, results of multi-size particulate flow simulation are presented to bring out the effect of bulk flow rate, average inlet concentration, and inlet particle size distribution. Mono-size computations using (1) the concentration-weighted mean diameter of the slurry and (2) the D50 size of the slurry are also presented for comparison with multi-size results.
Keywords: Eulerian-Eulerian model, Multi-size particulate flow, Penalty finite elements, Pump casing, Spalart-Allmaras.
Digital Object Identifier (DOI): doi.org/10.5281/zenodo.1336344
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[1] M.C. Roco and G. R. Addie "Analytical Model and Experimental Study on Slurry Flow and Erosion in Pump Casings,” Slurry Transportation, STA, vol. 8, pp. 263-271, 1983.
[2] M.C. Roco, and C. A. Shook, "Computational Model for Coal Slurry Pipelines with Heterogeneous Size Distribution,” Powder Technology, vol. 39, pp. 159-176, 1984.
[3] G.R. Addie, and K. V. Pagalthivarthi, "Prediction of Dredge Pump Shell Wear,” in: Proc. WODCON XII, 12th World Dredging Conference, World Organization of Dredging Associations, Arlington, VA, pp. 481-504, 1989.
[4] K.V. Pagalthivarthi, P.V. Desai, and G. R. Addie, "Particulate Motion and Concentration fields in Centrifugal Pumps,” Particulate Science and Technology, vol. 8, pp. 77-96, 1990.
[5] R.J. Visintainer, G. R. Addie, and K. V. Pagalthivarthi, "Prediction of Centrifugal Slurry Pump Wear,” International Conf. on Pump and system, Beijing, China, May 19-21, 1992.
[6] G.R. Addie, K. V. Pagalthivarthi, and J. R. Kadambi, "PIV and Finite Element Comparisons of Particles inside a Slurry Pump Casing,” in Proc. Int. Conf. on Hydrotransport 16, Santiago, Chile, pp. 547-559, 2004.
[7] J.S. Ravichandra, K. V. Pagalthivarthi, and S. Sanghi, "Finite Element Study of Multi-size Particulate Flow in Horizontal Pipe,” Progress in Computational Fluid Dynamics, vol. 4, no. 6, pp. 299-308, 2004.
[8] K.V. Pagalthivarthi, J. S. Ravichandra, and S. Sanghi, "Multi-size Particulate Flow in Horizontal Ducts – Modeling and Validation,” Progress in Computational Fluid Dynamics, vol. 5, no. 8, pp. 466-481, 2005.
[9] P.K. Gupta, and K.V. Pagalthivarthi, "Effect of Diffusive Stress, Lift and Virtual Mass Forces on Multi-size Particulate Flow through Rotating Channel,” in: Dwivedy, S. K. and Maity, D., ed(s), Proc. Int. Cong. Computational Mechanics and Simulation, IIT Guwahati, India, December 8-10, 2006.
[10] P.K. Gupta, and K. V. Pagalthivarthi, "Finite Element Modelling and Simulation of Multi-Size Particulate Flow through Rotating Channel,” Prog. Comp. Fluid Dynamics, vol. 7, pp. 247-260, 2007.
[11] K.V. Pagalthivarthi, and P. K. Gupta, "Prediction of Erosion Wear in Multi-size Particulate Flow through Rotating Channels,” Fluid Dynamics & Materials Processing, vol. 5, no. 1, pp. 93-122, 2009.
[12] P.R. Spalart, and S. R. Allmaras, "A One-Equation Turbulence Model for Aerodynamic Flows,” La Recherche Aerospatiale, vol. 1, pp. 5-21, 1994.
[13] M. L. Shur, M. K. Strelets, and A. K. Travin, "Turbulence Modeling in Rotating and Curved Channels: Assessing the Spalart-Shur Correction,” AIAA Journal, vol. 38, no. 5, pp. 784-792, 2000.
[14] T.J.R. Hughes, and A. Brooks, "A Theoretical Framework for Petrov-Galerkin Methods with Discontinuous Weighting Functions: Application to the Streamline Upwind Procedure,” Finite Elements in Fluids, Eds. R. H. Gallagher et. al., vol. 4, pp. 47-65, 1982.
[15] M.R. Davidson, "A Numerical Model of Liquid-Solid Flow in a Hydrocyclone with High Solids Fraction,” Numerical Methods in Multiphase Flows, ASME, vol. 185, pp. 29-38, 1994.
[16] M. C. Roco, and N. Balakrishnan, "Multidimensional Flow Analysis of Solid-Liquid Mixtures,” J. Rheology, vol. 29, pp. 431-456, 1985.
[17] S. L. Lee, "Particle drag in a dilute turbulent two-phase suspension flow,” International Journal of Multiphase flow, vol. 13, no. 2, pp. 247-256, 1987.
[18] F.M. White, Viscous Fluid Flow, 2nd Ed. McGraw-Hill, NY, 1991.
[19] J. N. Reddy, and D. K. Gartling, The finite element method, CRC Press, 1994.
[20] D. R. Kaushal, V. Seshadri, and S. N. Singh, "Prediction of Concentration and Particle Size Distribution in the Flow of Multisized Particulate Slurry through Rectangular Duct,” Appl. Math. Modeling, vol. 26, pp. 941-952, 2002.