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A Study on the Flow Patterns of a Second Grade Viscoe-Lastic Fluid Past a Cavity in a Horizontal Channel

Published online by Cambridge University Press:  20 December 2012

C. H. Hsu ,
S. Y. Hu ,
K. Y. Kung ,
C. C. Kuo  and
C. C. Chang
C. H. Hsu
Affiliation:
Department of Mechanical Engineering, Chung-Yuan Christian University, Taoyuan, Taiwan 32023, R.O.C.
S. Y. Hu
Affiliation:
Department of Mechanical Engineering, Chung-Yuan Christian University, Taoyuan, Taiwan 32023, R.O.C.
K. Y. Kung
Affiliation:
Graduate School of Materials Applied Technology, Taoyuan Innovation of Institute Technology, Taoyuan, Taiwan 32091, R.O.C.
C. C. Kuo*
Affiliation:
Department of Mechanical Engineering, Taoyuan Innovation of Institute Technology, Chung Li, Taiwan 32091, R.O.C.
C. C. Chang
Affiliation:
Department of Mechanical Engineering, Army Academy R.O.C, Taoyuan, Taiwan 32093, R.O.C.
*
*Corresponding author (gckuo@tiit.edu.tw)
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Abstract

This paper studies the behavior of second grade viscoelastic fluid past a cavity in a horizontal channel. The effects of Reynolds number, fluid elasticity and the aspect ratio of the cavity on the flow field are simulated numerically. The equations are converted into the vorticity and stream function equations. The solution is obtained by the finite difference method.

The behavior of viscoelastic fluids is quite different from the Newtonian fluid, due to the effects of fluid elasticity. Only one flow pattern appears when the Newtonian fluid past the cavity. However, three kinds of flow patterns appear while the viscoelastic fluids past the cavity by increasing Reynolds number from 20 to 300. The flow field is affected by the fluid elasticity as well as the aspect ratio of the cavity. The transitional flow pattern appears at lower Reynolds number as the higher elasticity fluid past the cavity with larger aspect ratio.

Keywords

CavityElastic coefficientHorizontal channelReynolds numberViscoelastic fluid
Type
Articles
Information
Journal of Mechanics , Volume 29 , Issue 2 , June 2013 , pp. 207 - 215
Copyright
Copyright © The Society of Theoretical and Applied Mechanics, R.O.C. 2013

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References

REFERENCES

1.Grillet, A. M., Shaqfeh, E. S. G. and Khomamib, B., “ObservaTions of Elastic Instabilities in Lid-Driven Cavity Flow,” Journal of Non-Newtonian Fluid Mechanics, 94, pp. 15–35 (2000).Google Scholar
2.Hsu, C. H. and Chou, T. Y., “Unsteady Flow of a Second-Grade Fluid Past a Backward-facing Step,” International Journal of Non-Linear Mechanics, 32, pp. 947–960 (1997).Google Scholar
3.Cochrane, T., Walters, K. and Webster, M. F., “On Newtonian and Non-Newtonian Flow in Complex Geometries,” Philosophical Transactions of the Royal Society A: Physical, Mathematical and Engineering Sciences, 301, pp. 163–181 (1981).Google Scholar
4.Grillet, A. M., Yang, B. and Shaqfeh, E. S. G., “Modeling of Viscoelastic Lid Driven Cavity Flow Using Finite Element Simulations,” Journal of Non-Newtonian Fluid Mechanics, 88, pp. 99–131 (1999).CrossRefGoogle Scholar
5.Kim, J.-H., Öztekin, A. and Neti, S., “Instabilities in Viscoelastic Flow Past a Square Cavity,” Journal of Non-Newtonian Fluid Mechanics, 90, pp. 261–281 (2000).CrossRefGoogle Scholar
6.Takehiro, Y., “Three-Dimensional Viscoelastic Flows Through a Rectangular Channel with a Cavity,” Journal of Non-Newtonian Fluid Mechanics, 114, pp. 13–31 (2003).Google Scholar
7.Al-Amiri, A. M., Khanafer, K. M. and Pop, I., “Numerical Simulation of Combined Thermal and Mass Transport in a Square Lid-Driven Cavity,” International Journal of Thermal Sciences, 46, pp. 662–671 (2007).CrossRefGoogle Scholar
8.Hsu, C. H., Chang, Y.-P. and Chen, B.-C., “Transient Mixed Convection of a Second-Grade Fluid Past a Backward-Facing Step,” International Journal of Non-Linear Mechanics, 34, pp. 881–893 (1999).Google Scholar
9.Kung, K. Y., Hsu, C. H. and Chiang, H. L., “Transient Mixed Convection Flow of a Second Grade Viscoelastic Fluid Past an Inclined Backward Facing Step,” International Journal of Non-Linear Mechanics, 39, pp. 427–439 (2004).Google Scholar
10.Rivlin, R. S. and Ericksen, J. L., “Stress Deformation Relation for Isotropic Materials,” Journal of Rational Mechanics and Analysis, 4, pp. 323–425 (1955).Google Scholar
11.Rajagopal, K. R., Gupta, A. S. and Wineman, A. S., “On a Boundary Layer Theory for Non-Newtonian Fluids,” International Journal of Engineering Science, 18, pp. 875–883 (1980).Google Scholar
12.Fosdick, R. L. and Rajagopal, K. R., “Uniqueness and Drag for Fluids of Second Grade in Steady Motion,” International Journal of Non-Linear Mechanics, 13, pp. 131–137 (1978).CrossRefGoogle Scholar