Comparison of Three Turbulence Models in Wear Prediction of Multi-Size Particulate Flow through Rotating Channel
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.
[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.
[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.
@article{"International Journal of Mechanical, Industrial and Aerospace Sciences:52662", author = "Pankaj K. Gupta and Krishnan V. Pagalthivarthi", title = "Comparison of Three Turbulence Models in Wear Prediction of Multi-Size Particulate Flow through Rotating Channel", 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.", volume = "5", number = "2", pages = "327-8", }
