Iranian Journal of Mechanical Engineering Transactions of ISME

Iranian Journal of Mechanical Engineering Transactions of ISME

Analysis of Non-Newtonian Fluid Flow through a Conical Duct Based on Bingham Model

Authors
Peyman Shoobi
Hossein Mahbadi
Armen Adamian
Department of Mechanical Engineering, Central Tehran Branch, Islamic Azad University, Tehran, Iran
Abstract
In this paper the laminar Bingham fluid flow through a converging conical duct is analyzed. The constitutive law of Bingham fluids is applied to model the yield dependent properties behavior of the fluid. An analytical solution is obtained for the pressure gradient assuming small conical angle of the duct. According to the yield dependent properties of the fluid, a region is developed in the fluid wherein the rate of deformation tensor is zero. This region is called plug region. According to obtained pressure gradient, the plug region is determined. Then, assuming the cylindrical symmetry, the governing equations are solved in cylindrical coordinate system and velocity field is obtained across the duct section. The results obtained in the paper is compared with the experimental data given in the literature search and Fluent numerical solution. The comparison of these two methods shows that the result of current paper is well compared with those given in the literature search. Finally, the effect of parameters such as yield strength and conical angle on velocity field and plug region is investigated.
 
Keywords
Non-Newtonian fluid
Flow analysis
Conical Duct
Bingham Model
Plug region
[1]
Fusi, L., Farina, A., and Rosso, F., "Flow of a Bingham-like Fluid in a Finite Channel of Varying Width: A Two-scale Approach", Journal of Non-newtonian Fluid Mechanics, Vols. 177-178, pp. 76-88, (2012).
[2]
Frigaarda, I., and Ryanb, D., "Flow of a Visco-plastic Fluid in a Channel of Slowly Varying Width, Journal of Non-newtonian Fluid Mechanics", Vol. 123, pp. 67-83, (2004).
[3]
Gupta, R. C., "Developing Bingham Fluid Flow in Channel", Mathematical Computer Modelling, Vol. 21, pp. 21-28, (1995).
 
[4]
Chemloul, N. S., "Analytical Study of Bingham Fluid Flow Through a Conical Tube, Mechanika", Vol. 19, pp. 665-670, (2013).
[5]
Avinash, K., Rao, J., Kumar, Y., and Sreenadh, Bingham S., "Fluid Flow through a Tapered Tube with Permeable Wall", Journal of Applied Fluid Mechanics, Vol. 6, pp. 143-148, (2013).
[6]
Kemblowski, Z., and Kiljanski, T., "Flow of Stokesian Fluids Through Conical Ducts", Chemical Engineering Journal, Vol. 9, pp. 141-151, (1975).
 
[7]
Walicki, E., and Walicka, A., "Pressure Drops in Conical Flow", Solidification of Metals and Alloys, Vol. 24, pp. 147-154, (1995).
[8]
Lipscomb, G., and Denn, M., "Flow of Bingham Fluids in Complex Geometries", Journal of Non-newtonian Fluid Mechanics, Vol. 14, pp. 337-346, (1984).
[9]
How, T., Black, R., and Annis, D., "Comparison of Pressure Losses in Steady Non-Newtonian Flow through Experimental Tapered and Cylindrical Arterial Prostheses", J. Biomed. Eng., Vol. 10, pp. 225-230, (1987).
[10]
Dorier, C., and Tichy, J., "Behavior of a Bingham-like Viscous Fluid, Journal of Non-Newtonian Fluid Mechanics", Vol. 45, pp. 291-310, (1992).
­[11]
Oliveira, G., Rocha, L., Franco, A., and Negrao, C., "Numerical Simulation of the Start-up of Bingham Fluid Flows in Pipelines", Journal of Non-newtonian Fluid Mechanics, Vol. 165, pp. 1114-1128, (2010).
[12]
Huilgol, R., and You, Z., "Application of the Augmented Lagrangian Method to Steady Pipe Flows", Journal of Non-newtonian Fluid Mechanics, Vol. 128, pp. 126-143, (2005).
[13]
Ponalagusamyn, R., Selvi, R., and Banerjee, A.K., "Mathematical Model of Pulsatile Flow of Non-newtonian Fluid in Tubes of Varying Cross-sections and its Implications to Blood Flow", Journal of Franklin Institute, Vol. 349, pp. 1681-1698, (2012).
Iranian Journal of Mechanical Engineering Transactions of ISME
Volume 19, Issue 4 - Serial Number 49
Fluid Mechanics and Heat Transfer
Winter 2017
Pages 6-17

  • Receive Date 10 April 2018