Hostname: page-component-cb9f654ff-plnhv Total loading time: 0.001 Render date: 2025-08-27T13:06:41.220Z Has data issue: false hasContentIssue false
  • English
  • Français

On the Instability of Plane Poiseuille Flow of Two Immiscible Fluids Using the Energy Gradient Theory

Published online by Cambridge University Press:  13 March 2014

I. Farahbakhsh ,
S. S. Nourazar ,
H. Ghassemi ,
H.-S. Dou  and
A. Nazari-Golshan
I. Farahbakhsh*
Affiliation:
Ocean Engineering Department, Amirkabir University of Technology, Tehran, Iran
S. S. Nourazar
Affiliation:
Mechanical Engineering Department, Amirkabir University of Technology, Tehran, Iran
H. Ghassemi
Affiliation:
Ocean Engineering Department, Amirkabir University of Technology, Tehran, Iran
H.-S. Dou
Affiliation:
Faculty of Mechanical Engineering and Automation, Zhejiang Sci-Tech University, Hangzhou, China
A. Nazari-Golshan
Affiliation:
Department of Physics, Amirkabir University of Technology, Tehran, Iran
*
i.farahbakhsh@aut.ac.ir
Get access

Abstract

In the present study, the instability of laminar flow of two immiscible fluids is investigated. The theory of energy gradient is employed for the analysis. The distributions of energy gradient for various viscosity ratios, i.e., ratios of lower viscosity to higher one, are obtained and the results for the onset of instability are compared with the available experimental data. The comparison of the results shows excellent agreement with the existing experimental data. It will be also demonstrated that as the viscosity ratio decreases the flow becomes more stable even at high Reynolds numbers.

Keywords

Energy gradientInstabilityPlane Poiseuille flowViscosity ratio

Information

Type
Research Article
Information
Journal of Mechanics , Volume 30 , Issue 3 , June 2014 , pp. 299 - 305
Copyright
Copyright © The Society of Theoretical and Applied Mechanics, R.O.C. 2014 

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

Article purchase

Temporarily unavailable

References

REFERENCES

1.Drazin, P. G. and Reid, W. H., Hydrodynamic Stability, Cambridge University Press, Cambridge (1981).Google Scholar
2.Schmid, P. J. and Henningson, D. S., Stability and Transition in Shear Flows, Springer, New York (2001).CrossRefGoogle Scholar
3.Trefethen, L. N., Trefethen, A. E., Reddy, S. C. and Driscoll, T. A., “Hydrodynamic Stability Without Eigenvalues,” Science, 261, pp. 578–584 (1993).CrossRefGoogle ScholarPubMed
4.Grossmann, S., “The Onset of Shear Flow Turbulence,” Review Modeling Physics, 72, pp. 603–618 (2000).Google Scholar
5.Patel, V. C. and Head, M. R., “Some Observations on Skin Friction and Velocity Profiles in Full Developed Pipe and Channel Flows,” Journal of Fluid Mechanics, 38, pp. 181–201 (1969).CrossRefGoogle Scholar
6.Tillmark, N. and Alfredsson, P. H., “Experiments on Transition in Plane Couette Flow,” Journal of Fluid Mechanics, 235, pp. 89–102 (1992).Google Scholar
7.Daviaud, F., Hegseth, J. and Berg´e, P., “Subcritical Transition to Turbulence in Plane Couette Flow,” Physical Review Letters, 69, pp. 2511–2514 (1992).Google Scholar
8.Malerud, S., Molfy, K. J. and Goldburg, W. I., “Measurements of Turbulent Velocity Fluctuations in a Planar Couette Cell,” Physics of Fluids, 7, pp. 1949–1955 (1995).Google Scholar
9.Orszag, S. A., “Accurate Solution of the Orr-Sommerfeld Stability Equation,” Journal of Fluid Mechanics, 50, pp. 689–703 (1971).CrossRefGoogle Scholar
10.Dou, H. S., “Mechanism of Flow Instability and Transition to Turbulence,” International Journal of Non-Linear Mechanics, 41, pp. 512–517 (2006).Google Scholar
11.Dou, H. S., “Physics of Flow Instability and Turbulent Transition in Shear Flows,” International Journal of Physics Science, 6, pp. 1411–1425 (2011).Google Scholar
12.Dou, H. S., “Three Important Theorems for Flow Stability,” Proceedings of the Fifth International Conference on Fluid Mechanics, Shanghai, China (2007).Google Scholar
13.Dou, H. S., Khoo, B. C. and Yeo, K. S., “Instability of Taylor-Couette Flow between Concentric Rotating Cylinders,” International Journal of Thermal Sciences, 47, pp. 1422–1435 (2008).Google Scholar
14.Dou, H. S. and Khoo, B. C., “Criteria of Turbulent Transition in Parallel Flows,” Modeling Physics Letters B, 24, pp. 1437–1440 (2010).Google Scholar
15.Dou, H. S. and Khoo, B. C., “Mechanism of Wall Turbulence in Boundary Layer Flows,” Modeling Physics Letters B, 23, pp. 457–460 (2009).Google Scholar
16.Yan, B. H., “Analysis of Laminar to Turbulent Transition of Pulsating Flow in Ocean Environment with Energy Gradient Method,” Annales Nuclear Energy, 38, pp. 2779–2786 (2011).CrossRefGoogle Scholar
17.Joseph, D. D., Bai, R., Chen, K. P. and Renardy, Y. Y., “Core-Annular Flows,” Annual Review of Fluid Mechanics, 29, pp. 65–90 (1997).Google Scholar
18.Regner, M., Henningsson, M., Wiklund, J., Öster-gren, K. and Trägårdh, C., “Predicting the Displacement of Yoghurt by Water in a Pipe Using CFD,” Chemical Engineers Technology, 30, pp. 844–853 (2007).CrossRefGoogle Scholar
19.Yih, C. S., “Instability Due to Viscous Stratification,” Journal of Fluid Mechanics, 27, pp. 337–352 (1967).Google Scholar
20.Li, C. H., “Instability of Three-Layer Viscous Stratified Flow,” Physics of Fluids, 12, pp. 2473–2481 (1969).Google Scholar
21.Khomami, B., “Interfacial Stability and Deformation of Two Stratified Power Law Fluids in Plane Poiseuille Flow Part I — Stability Analysis,” Journal of Non-Newtonian Fluid, 36, pp. 289–303 (1990).Google Scholar
22.Khomami, B., “Interfacial Stability and Deformation of Two Stratified Power Law Fluids in Plane Poiseuille Flow Part II — Interface Deformation,” Journal of Non-Newtonian Fluid, 37, pp. 19–36 (1990).Google Scholar
23.Tilley, B. S., Davis, S. H. and Bankoff, S. G., “Linear Stability Theory of Two-Layer Fluid Flow in an Inclined Channel,” Physics of Fluids, 6, pp. 3906–3922 (1994).Google Scholar
24.Pouliquen, O., Chomaz, J. M. and Huerre, P., “Propagating Holmboe Waves at the Interface Between Two Immiscible Fluids,” Journal of Fluid Mechanics, 266, pp. 277–302 (1994).CrossRefGoogle Scholar
25.Pinarbasi, A. and Liakopoulosa, A., “The Effect of Variable Viscosity on the Interfacial Stability of Two-Layer Poiseuille Flow,” Physics of Fluids, 7, pp. 1318–1324 (1995).CrossRefGoogle Scholar
26.Boomkamp, P. A. M. and Miesen, R. H. M., “Classification of Instabilities in Parallel Two-Phase Flow,” International Journal of Multiphase Flow, 22, pp. 67–88 (1996).Google Scholar
27.Gondret, P. and Rabaud, M., “Shear Instability of Two-Fluid Parallel Flow in a Hele-Shaw Cell,” Physics of Fluids, 9, pp. 3267–3274 (1997).CrossRefGoogle Scholar
28.Cao, Q., Ventresca, A. L., Sreenivas, K. R. and Prasad, A. K., “Instability Due to Viscosity Stratification Downstream of a Centerline Injector,” The Canadian Journal of Chemical Engineering, 81, pp. 913–922 (2003).CrossRefGoogle Scholar
29.Shankar, V. and Kumar, L., “Stability of Two-Layer Newtonian Plane Couette Flow Past a Deformable Solid Layer,” Physics of Fluids, 16, pp. 4426–4442 (2004).Google Scholar
30.Vempati, B., Oztekin, A. and Neti, S., “Stability of Two-Layered Fluid Flows in an Inclined Channel,” Acta Mechanics, 209, pp. 187–199 (2010).Google Scholar
31.Cao, Q., Sarkar, K. and Prasad, A. K., “Direct Numerical Simulations of Two-Layer Viscosity-Stratified Flow,” International Journal of Multiphase Flow, 30, pp. 1485–1508 (2004).CrossRefGoogle Scholar
32.Govindarajan, R., “Effect of Miscibility on the Linear Instability of Two-Fluid Channel Flow,” International Journal of Multiphase Flow, 30, pp. 1177–1192 (2004).CrossRefGoogle Scholar
33.Nishioka, M., Iida, S. and Ichikawa, Y., “An Experimental Investigation of the Stability of Plane Poiseuille Flow,” Journal of Fluid Mechanics, 72, pp. 731–751 (1975).Google Scholar
34.Nishi, M., Unsal, B., Durst, F. and Biswas, G., “Laminar-to-Turbulent Transition of Pipe Flows Through Puffs and Slugs,” Journal of Fluid Mechanics, 614, pp. 425–446 (2008).Google Scholar
35.Dou, H. S. and Khoo, B. C., “Energy Gradient Method for Turbulent Transition with Consideration of Effect of Disturbance Frequency,” Journal of Hy-drodynamics, 22, pp. 23–28 (2010a).Google Scholar
36.Dou, H. S., Khoo, B. C. and Yeo, K. S., “Energy Loss Distribution in the Plane Couette Flow and the Taylor-Couette Flow between Concentric Rotating Cylinders,” International Journal of Thermal Sciences, 46, pp. 262–275 (2007).Google Scholar