Comparison of Three Turbulence Models in Wear Prediction of Multi-Size Particulate Flow through Rotating Channel

Authors: Pankaj K. Gupta, Krishnan V. Pagalthivarthi

Abstract:

The present work compares the performance of three turbulence modeling approach (based on the two-equation k -ε model) in predicting erosive wear in multi-size dense slurry flow through rotating channel. All three turbulence models include rotation modification to the production term in the turbulent kineticenergy equation. The two-phase flow field obtained numerically using Galerkin finite element methodology relates the local flow velocity and concentration to the wear rate via a suitable wear model. The wear models for both sliding wear and impact wear mechanisms account for the particle size dependence. Results of predicted wear rates using the three turbulence models are compared for a large number of cases spanning such operating parameters as rotation rate, solids concentration, flow rate, particle size distribution and so forth. The root-mean-square error between FE-generated data and the correlation between maximum wear rate and the operating parameters is found less than 2.5% for all the three models.

Keywords: Rotating channel, maximum wear rate, multi-sizeparticulate flow, k −ε turbulence models.

Digital Object Identifier (DOI): doi.org/10.5281/zenodo.1330525

References:

[1] K. V. Pagalthivarthi and G. R. Addie, "Prediction methodology for twophase flow and erosion wear in slurry impellers", 4th International Conference on Multiphase Flow, ICMF-2001, New Orleans, LA, May 27-June 1, 2001.
[2] G. R. Addie, A. Sellgren, J. Mudge, "SAG mill pumping cost considerations. SAG Conference", 3rd International Conference on Autogenous & Semiautogenous Grinding Technology, September 30 - October 3, 2001, Vancouver, B.C., Canada, 2001.
[3] G. R. Addie and A. Sellgren, "Effect of wear on the performance of centrifugal slurry pumps", ASME Fluids Engineering Summer Meeting, Washington, D.C., 1998.
[4] D.R. Kaushal, V. Seshadri, S.N. Singh, "Prediction of concentration and particle size distribution in the flow of multi-sized particulate slurry through rectangular duct", Appl. Math. Model., Vol. 26, No. 10, pp. 941-952, 2002.
[5] J.S. Ravichandra, K.V. Pagalthivarthi, S. Sanghi, "Finite Element Study of Multi-size Particulate Flow in Horizontal Pipe", Progress in Computational Fluid Dynamics, Vol. 4, Issue 6, pp. 299-308, 2004.
[6] J.S. Ravichandra, K.V. Pagalthivarthi, S. Sanghi, "Multi-size particulate flow in horizontal ducts - modeling and validation", Progress in Computational Fluid Dynamics, Vol. 5, Issue 8, pp. 466-481, 2005.
[7] P.K. Gupta and K.V. Pagalthivarthi, "Finite Element Modelling and Simulation of Multi-Size Particulate Flow through Rotating Channel", Progress in Computational Fluid Dynamics, Vol. 7, Issue 5, pp. 247- 260, 2007.
[8] P.K. Gupta and K.V. Pagalthivarthi, "Application of Multifrontal and GMRES Solvers for Multi-Size Particulate Flow in Rotating Channels", Progress in Computational Fluid Dynamics, Vol. 7, Issue 5, pp. 323- 336, 2007.
[9] P.K. Gupta and K.V. Pagalthivarthi, "Effect of inlet concentration on solid-liquid mixture flow through rotating channel" In Proceedings of International Congress on Computational Mechanics and Simulation - 2006, December 8-10, 2006, IIT Guwahati, India, 2006.
[10] P.K. Gupta and K.V. Pagalthivarthi, "Effect of particle size distribution on multi-size particulate flow through rotating channel" In Proceedings of NCFMFP 33rd National and 3rd International Conference on Fluid Mechanics and Fluid Power, December 7-9, 2006, IIT Bombay, India, 2006.
[11] 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), Proceedings of International Congress on Computational Mechanics and Simulation, December 8-10, 2006, IIT Guwahati, India, 2006.
[12] M.C. Roco and C.A. Shook, "Modeling of Slurry Flow: The Effect of Particle Size" Canadian Journal of Chemical Engineering, Vol. 61, pp. 494-503, 1983.
[13] 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.
[14] S.L. Soo, "Development of Theories on Liquid-Solid Flows," in: Roco, M.C., ed., ASME-FED, Vol. 13, 1984, pp. 1-6, 1984.
[15] K.V. Pagalthivarthi, P.V. Desai, G.R. Addie, "Particulate Motion and Concentration Fields in Centrifugal Slurry Pumps", Particulate Science and Technology, Vol. 8, pp. 77-96, 1990.
[16] M.C. Roco and E. Reinhardt, "Calculation of Solid Particle Concentration in Centrifugal Impellers using Finite Element Technique", in: Proc. Hydrotransport 7 Conf., 1980, BHRA, pp. 359-376, 1980.
[17] Y. Zhong Sen and Er. Lai Min, "Computation of Solid Particles Velocity and Concentration in Centrifugal Pump Impellers using Finite Element Method", International Conference on Pumps and Systems, Bejing, China, May 1992, paper number K4, pp. 513-526, 1992.
[18] K.V. Pagalthivarthi and V.R. Ramanathan, "Finite Element Study of Two-phase Free Surface Flow in Rotating Channel", in: Proc. Int. Conf. Multiphase Flows, May 27-June 1, 2004, Tokyo, Japan, Paper No. 294, 2004.
[19] K.V. Pagalthivarthi and P.K. Gupta, "Simulation of Developing Flow through Rotating Channel using Q1Q0 Finite Elements", Progress in Computational Fluid Dynamics, Vol. 4, Issue 6, pp. 285-298, 2004.
[20] P.K. Gupta and K.V. Pagalthivarthi, "Comparison of Zero-equation and Two-equation k-╬Á Model in Rotating Channel Flow", in: Proc. 2nd BSMEASME Int. Conf. Thermal Engg., 2-4 January, 2004, Dhaka, 2004.
[21] J.H.G. Howard, S.V. Patankar, R.M. Bordynuik, "Flow Prediction in Rotating Ducts using Coriolis-modified Turbulence Models", ASME J. Fluids Engineering, vol. 102, pp. 456-461, 1980.
[22] K.V. Pagalthivarthi and P.K. Gupta, "Prediction of erosion wear in multisize particulate flow through rotating channels" Fluid Dynamics & Materials Processing, vol. 5, issue 1, pp.93-122, 2009.
[23] P.K. Gupta and K.V. Pagalthivarthi, "Multi-size particulate flow in rotating channels - Modelling and validation using three turbulence models" Journal of Computational Multiphase Flows, vol. 1, No. 2, pp. 133-160, 2009.
[24] M. Manninen, V. Taivassalo, S. Kallio, "On the Mixture Model for Multiphase Flow", VTT Publications 288, Technical Research Centre of Finland, Espoo, pp. 1-67, 1996.
[25] S. Kallio, M. Manninen, V. Taivassalo, "Turbulence in Mixture Models", Report :98-1, Åbo Akademi, Department of Chemical Engineering, Åbo, 1-31, 1998.
[26] R. Visintainer, K.V. Pagalthivarthi, H.H. Tian, "Wear coefficient-s dependence on particle size" GIW Internal Report, 2005.
[27] H.H. Tian, G.R. Addie, K.V. Pagalthivarthi, "Determination of wear coefficients for prediction through Coriolis wear testing", WEAR, Vol. 259, pp. 160-170, 2005.
[28] K.V. Pagalthivarthi and R. Veeraraghavan, "Numerical insight into experimental results of particle size effect in Coriolis wear tester" Proc. of the First International FMFP Conference, 15-17 Dec., 1998, IIT Delhi, New Delhi, 1998.