Abstract
The USM-ϑ model of Bingham fluid for dense two-phase turbulent flow was developed, which combines the second-order moment model for two-phase turbulence with the particle kinetic theory for the inter-particle collision. In this model, phases interaction and the extra term of Bingham fluid yield stress are taken into account. An algorithm for USM-ϑ model in dense two-phase flow was proposed, in which the influence of particle volume fraction is accounted for. This model was used to simulate turbulent flow of Bingham fluid single-phase and dense liquid-particle two-phase in pipe. It is shown USM-ϑ model has better prediction result than the five-equation model, in which the particle-particle collision is modeled by the particle kinetic theory, while the turbulence of both phase is simulated by the two-equation turbulence model. The USM-ϑ model was then used to simulate the dense two-phase turbulent up flow of Bingham fluid with particles. With the increasing of the yield stress, the velocities of Bingham and particle decrease near the pipe centre. Comparing the two-phase flow of Bingham-particle with that of liquid-particle, it is found the source term of yield stress has significant effect on flow.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
Tchen C M. Mean value and correlation problems connected with the motion of small particles in a turbulent field[D]. Ph D Dissertation, Martinus Nijhoff, Delft University, Hague, 1947.
Hinze J O. Turbulence[M]. McGraw Hill, New York, 1975.
Zhou L X, Huang X Q. Prediction of confined gas-particle jets by an energy equation model of particle turbulence[J]. Science in China, 1990, 33:53–59.
Gidaspow D. Multiphase Flow and Fluidization: Continuum and Kinetic Theory Descriptions[M]. Academic Press, New York, 1994.
Cheng Y, Guo Y C, Wei F, et al. Modeling the hydrodynamics of downer reactors based on kinetic theory[J]. Chem Eng Sci, 1999, 54(13/14):2019–2027.
Zheng Y, Wan X T, Qian Z, et al. Numerical simulation of the gas-particle turbulent flow in riser reactor based on k f-ε f-k p-ε p-ϑ two-fluid model[J]. Chem Eng Sci, 2001, 56(24):6813–6822.
Yu Y, Zhou L X, Zheng C G, et al. Simulation of swirling gas-particle flows using different time scales for the closure of two-phase velocity correlation in the second-order moment two-phase turbulence model[J]. Transactions of ASME, Journal of Fluids Engineering, 2003, 125(2):247–250.
Yu Yong. Studies on gas turbulence modification in gas-particle flows and a dense two-phase turbulence model[D]. Ph D Dissertation, Tsinghu University, Beijing, 2004 (in Chinese).
Hu Chunbo, Shang Lianyin, Cai Timin. Governing equations of Bingham-fluid turbulent flow[J]. Journal of Northwestern Polytechnical University, 1998, 16(4):589–593 (in Chinese).
Hu Chunbo, Wei Jinjia, Jiang Peizheng, et al. A numerical study of Bingham turbulent flow in sudden-expansion straight circular pipe[J]. Applied Mathematics and Mechanics (English Edition), 1998, 19(11):1095–1101.
Hu Chunbo, Jiang Peizheng, Wei Jinjia. Numerical study of turbulent flow on Bingham fluid in pump impeller[J]. Journal of Applied Mechanics, 1999, 16(2):104–107 (in Chinese).
Salvi R. On the existence of two phase problem for Bingham fluids[J]. Nonlinear Analysis, 2001, 47(6):4205–4216.
Dziubinski M, Fidos H, Sosno M. The flow pattern map of a two-phase non-Newtonian liquid-gas flow in the vertical pipe[J]. Internat J Multiphase Flow, 2004, 30(6):551–563.
Fidos H. Flow hydrodynamics of multiphase mixtures of non-Newtonian liquid-gas-solid particles in vertical pipes[D]. Ph D Dissertation, Lodz Technical University, Poland, 2001.
Kang Liqiang, Zeng Zhuoxiong, Jiang Peizheng. Study on dense two-phase turbulent flow of Bingham fluid and particle[J]. Journal of Xi’an Jiaotong University, 2002, 36(7):693–696 (in Chinese).
Kang Liqiang. Theoretical analysis and numerical computation of dense two-phase turbulent flow of non-Newtonian fluid and particle[D]. M Sc Dissertation, Xi’an Jiaotong University, Xi’an, 2000 (in Chinese).
Zeng Z X, Xie Y B, Jiang Sh T. Numerical simulation on dense two-phase turbulent flow of Bingham fluid with particle[M]. In: Zhou L X (ed). The Second International Symposium on Multiphase, Non-Newtonian and Reacting Flows’04. International Academic Publishers/Beijing World Publishing Corporation, China, 2004, 427–429.
Zhou Lixing. Dynamics of Multiphase Turbulent Reacting Fluid Flows[M]. National Defence Industry Press, Beijing, 2002 (in Chinese).
Zhou L X, Xu Y, Fan L S, Li Y. Simulation of swirling gas-particle flows using an improved second-order moment two-phase turbulence model[J]. Powder Tech, 2001, 116(3):178–189.
Jiang Peizheng, Wei Jinjia, Wang Chang’an. Numerical research and theoretical analysis for dense liquid-solid two-phase flow[J]. Journal of Xi’an Jiaotong University, 1998, 32(4):84–88 (in Chinese).
Chen Li. The distribution of high sediment-laden pipe flow[J]. Journal of Hydrodynamics, 1993, 8(12):526–533 (in Chinese).
Van Doormaal J P, Raithby G D. Enhancements of the SIMPLE method for predicting incompressible fluid flows[J]. Numerical Heat Transfer, 1984, 7:147–163.
Alajbegovic A, Assad A, Benetto F. Phase distribution and turbulence structure for solid/fluid upflow in a pipe[J]. Internat J Multiphase Flow, 1994, 20(3):453–479.
Author information
Authors and Affiliations
Corresponding author
Additional information
Communicated by LI Jia-chun
Project supported by the National Key Basic Research and Development Program of China (No.G1999-0222-08)
Rights and permissions
About this article
Cite this article
Zeng, Zx., Zhou, Lx. & Liu, Zh. Second-order moment model for dense two-phase turbulent flow of Bingham fluid with particles. Appl Math Mech 27, 1373–1381 (2006). https://doi.org/10.1007/s10483-006-1009-z
Received:
Revised:
Issue Date:
DOI: https://doi.org/10.1007/s10483-006-1009-z