International Scientific Journal

Authors of this Paper

External Links


In this paper, the numerical solution of non-Newtonian two-phase fluid-flow through a channel with a cavity was studied. Carreau-Yasuda non-Newtonian model which represents well the dependence of stress on shear rate was used and the effect of n index of the model and the effect of input Reynolds on the attribution of flow were considered. Governing equations were discretized using the finite volume method on staggered grid and the form of allocating flow parameters on staggered grid is based on marker and cell method. The QUICK scheme is employed for the convection terms in the momentum equations, also the convection term is discretized by using the hybrid upwind-central scheme. In order to increase the accuracy of making discrete, second order Van Leer accuracy method was used. For mixed solution of velocity-pressure field SIMPLEC algorithm was used and for pressure correction equation iteratively line-by-line TDMA solution procedure and the strongly implicit procedure was used. As the results show, by increasing Reynolds number, the time of sweeping the non-Newtonian fluid inside the cavity decreases, the velocity of Newtonian fluid increases and the pressure decreases. In the second section, by increasing n index, the velocity increases and the volume fraction of non-Newtonian fluid after cavity increases and by increasing velocity, the pressure decreases. Also changes in the velocity, pressure and volume fraction of fluids inside the channel and cavity are more sensible to changing the Reynolds number instead of changing n index.
PAPER REVISED: 2018-05-01
PAPER ACCEPTED: 2018-05-06
CITATION EXPORT: view in browser or download as text file
THERMAL SCIENCE YEAR 2020, VOLUME 24, ISSUE Issue 2, PAGES [1045 - 1054]
  1. Taotao, F., Lijuan, W., Chunying, Z., Youguang, M., Flow Patterns of Liquid-Liquid Two-Phase Flow in Non-Newtonian Fluids in Rectangular Microchannels, Chemichal Engineering and Processing: Process Intensification., 91 (2015), pp.114-120. (doi: 10.1016/j.cep.2015.03.020)
  2. Achab, L., Mahfoud, M., Benhadid, S, Numerical Study of the Non-Newtonian Blood Flow in a Stenosed Artery Using two Rheological Models, Thermal Science., 20 (2016), 2, pp .449-460. (doi: 10.2298/TSCI130227161A)
  3. Demin, W., Jiecheng, C., Qingyan, Y., Viscous-elastic polymer can Increase in cores, Society of Petroleum Engineers., (2000), pp. 2-8. (doi: 10.2118/63227-MS)
  4. Huifen, X., Demin, W., Junzheng, W., Elasticity of HPAM solutions increases displacement efficiency under mixed wettability conditions, Society of Petroleum Engineers., (2004), pp. 18-20. (doi: 10.2118/88456-MS)
  5. Huifen, X., Demin, W., Qingjie, G., Experiment of viscoelasticity of polymer solution, Journal of Daqing Petroleum Institute., 2 (2002), pp. 105-108.
  6. Carreau, PJ., Rheological equations from molecular network theories, Journal of Rheology., 16 (1972), pp. 99-127. (doi: 10.1122/1.549276)
  7. Puyang, G., Jie, O., Wen, Zh., Coupling of Finite Element Method and Discontinuous Galerkin Method to simulate viscoelastic flows, International Journal for Numerical Methods in Fluids., (2017), pp. 1-19. (doi: 10.1002/fld.4461)
  8. Bakhti, H., Azrar, L., Baleanu, D, Pulsatile Blood Flow in Constricted Tapered Artery Using a Variable-Order Fractional Oldroyd-B Model, Thermal Science., 21 (2016), 1A, pp .29-40. (doi: 10.2298/TSCI160421237B)
  9. Huang, C., Lei, J. M., Liu, M. B., Peng, X. Y., An improved KGF-SPH with a novel discrete scheme of Laplacian operator for viscous incompressible fluid flows, International Journal for Numerical Methods in Fluids., 81 (2016), pp. 377-396. (doi: 10.1002/fld.4191)
  10. Xu, Y., Wen, CH., Rui, X., Leevan, L., A Fractional Model for Time-Variant Non-Newtonian Flow, Thermal Science., 21 (2017), 1A, pp .61-68. (doi:10.2298/TSCI160426245Y)
  11. Freydier, P., Chambon, G., Naaim, M., Experimental characterization of velocity fields within the front of viscoplastic surges down an incline, Journal of Non-Newtonian Fluid Mechanics., (2017), pp. 56-69. (doi:10.1016/j.jnnfm.2017.01.002)
  12. Dimitri, G., Multiphase flow and fluidization, Academic Press, San Diego, 1994.
  13. Autee, A., Rao, S.S., Puli, R., Shrivastava, R, An Experimental Study on Two-Phase Pressure Drop in Small Diameter Horizontal, Downward Inclind, and Vertical Tubes, Thermal Science., 19 (2015), 5, pp .1791-1804. (doi: 10.2298/TSCI130118081A)
  14. Tsuji, Y., Kawaguchi, T., Tanaka, T., Discrete particle simulation of two-dimensional fluidized bed, Powder Technology., 77 (1993), pp. 79-87. (doi: 10.1016/0032-5910(93)85010-7)
  15. Zhou, L., Cai, Z. W., Zong, Z., Chen, Z., An SPH pressure correction algorithm for multiphase flows with large density ratio, International Journal for Numerical Methods in Fluids., 81 (2016), pp. 765-788. (doi: 10.1002/fld.4207)
  16. Boris, JP., New directions in computational fluid dynamics, Annual Review of Fluid Mechanics., 21 (1989), pp. 345-385. (doi: 10.1146/annurev.fl.21.010189.002021)
  17. Sahil, O. U., Gretar, T., A front-tracking method for viscous, incompressible, multi-fluid flows, Journal of Computational Physics., 100 (1992), pp. 25-37. (doi: 10.1016/0021-9991(92)90307-K)
  18. Mazza, R. A., Rosa, E. S., Yoshizawa, C. J., Analyses of liquid film models applied to horizontal and near horizontal gas-liquid slug flows, Chemical Engineering Science., 65 (2010), pp. 3876-3892. (doi: 10.1016/j.ces.2010.03.035)
  19. Jing-yu, X., Ying-xiang, W., Hua, L., Jun, G., Yin, C., Study of drag reduction by gas injection for power-law fluid flow in horizontal stratified and slug flow regimes, Chemical Engineering Journal., 147 (2009), pp. 235-244. (doi: 10.1016/j.cej.2008.07.006)
  20. Jia, N., Gourma, M., Thompson, C. P., Non-Newtonian multi-phase flows: on drag reduction, pressure drop and liquid wall friction factor, Chemical Engineering Science., 66 (2011), pp. 4742-4756. (doi: 10.1016/j.ces.2011.06.067)
  21. Arun, A., Srinivasa, R., Ravikumar. P., Ramakant, Sh., An experimental study on two-phase pressure drop in small diameter horizontal, downward inclined and vertical tubes, Thermal science., 19 (2015), 5, pp. 1791-1804. (doi: 10.2298/TSCI130118081A)
  22. Agus, S., Daiki, G., Tomoaki, T., Akimaro, K., Michio, S., Two-Phase Flow Characteristics across Sudden Contraction in Horizontal Rectangular Minichannel, Journal of Mechanical Engineering and Automation., 6 (2016), pp. 58-64. (doi: 10.5923/j.jmea.20160603.03)
  23. Patankar, S. V., Numerical Heat Transfer and Flow, McGraw-Hill, New York, 1980.
  24. Arakawa, C., Computational Fluid Dynamics for Engineering, University of Tokyo Press, Tokyo, 1994.
  25. Ferziger, J. H., Peric, M., Computational Methods for Fluid Dynamics, Springer-Verlag, Berlin, 1996.
  26. Bird, R. B., Armstrong, R. C., Hassager, O., Dynamics of polymeric liquids, Fluid Mechanics, John Wiley & Sons, Inc, 1977.
  27. Giesekus, H., Dynamische und thermodynamische Grundlagen, Phanomenologische Rheologie, 1994.
  28. Hirt, C. W., Nichols. B. D., Volume of fluid (VOF) method for the dynamics of free boundaries, Journal of Computational Physics., 39 (1981), pp. 201-225. (doi: 10.1016/0021-9991(81)90145-5)
  29. Ruben, S., Stephane, Z., Direct numerical simulation of free-surface and interfacial flow, Annu. Rev. Fluid Mech., 31 (1999), pp. 567-603. (doi: 10.1146/annurev.fluid.31.1.567)
  30. Min, S. K., Woo, I. L., A new VOF-based numerical scheme for the simulation of fluid flow with free surface. Part I: New free surface-tracking algorithm and its verification, International Journal for Numerical Methods in Fluids., (2003), pp. 765-790. (doi: 10.1002/fld.553)
  31. Friedrich, G., Kai, V., Frank, J. M., 3D CFD simulation of bottle emptying processes, Journal of Food Engineering., 109 (2012), pp. 609-618. (doi: 10.1016/j.jfoodeng.2011.10.008)
  32. Mustafa, T., Ferruh, E., Numerical simulation for heat transfer and velocity field characteristics of Two-phase flow systems in axially rotating horizontal cans, Journal of Food Engineering., 111 (2012), pp. 366-385. (doi: 10.1016/j.jfoodeng.2012.02.008)
  33. Jeffrey, Y., Kyle, F., Rodney, W. T., Matthew, J. M. K., Simulation of slag-skin formation in electroslag remelting using a volume-of-fluid method, Numerical Heat Transfer., 67 (2015), pp. 268-292. (doi: 10.1080/10407782.2014.937208)
  34. Saincher, S., Banerjee, J., A redistribution-based volume-preserving PLIC-VOF technique, Numerical Heat Transfer., 67 (2015), pp. 338-362. (doi: 10.1080/10407790.2014.950078)
  35. Takuya, Y., Yasunori, O., Sadik, D., Validation of the S-CLSVOF method with the density-scaled balanced continuum surface force model in multiphase systems coupled with thermocapillary flows, International Journal for Numerical Methods in Fluids., (2017), pp. 223-244. (doi: 10.1002/fld.4267)
  36. Tome, MF., Mangiavacchi, N., Cuminato, JA., Castelo, A., McKee, S., A finite difference technique for simulating unsteady viscoelastic free surface flows, J. Non-Newton. Fluid Mech., 106 (2002), pp. 61-106. (doi:10.1016/S0377-0257(02)00064-2)
  37. Darwish, M. S., Whiteman, J. R., Numerical modeling of viscoelastic liquids using a finite-volume method, Journal of Non-Newtonian Fluid Mechanics., 45 (1992), pp. 311-337. (doi: 10.1016/0377-0257(92)80066-7)
  38. Raanan, F., Raz, K., Time dependent simulation of viscoelastic flows at high Weissenberg number using the log-conformation representation, Journal of Non-Newtonian Fluid Mechanics., 126 (2005), pp. 23-37. (doi: 10.1016/j.jnnfm.2004.12.003)
  39. Ahmadi, M., Natural Convective Heat Transfer in a Porous Medium within a Two Dimension Enclosure, IIUM Engineer Journal., 18 (2017), 2, pp. 196-211.
  40. Bram, V. L., Towards the ultimate conservative difference scheme: Monotonicity and conservation combined in a second order scheme, Journal of Computational Physics., 14 (1974), pp. 361-370. (doi: 10.1016/0021-9991(74)90019-9)
  41. Doormal, J.P.V., Raithby, G.D., Enhancement of the Simple Method for Predicting incompressible Flows, Numerical Heat Transfer., 7(1984), pp.147-163. (doi: 10.1080/01495728408961817)
  42. Skelland, A.H.P., non-Newtonian Flow Heat transfer, Wiley., New York, 1967.

© 2024 Society of Thermal Engineers of Serbia. Published by the Vinča Institute of Nuclear Sciences, National Institute of the Republic of Serbia, Belgrade, Serbia. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution-NonCommercial-NoDerivs 4.0 International licence