Chaotic mixing and heat transfer between confocal ellipses: Experimental and numerical results

Physics of Fluids

Volumn 8, Issue 3, 1996, Pages 677-691

  Saatdjian, E ^a   Midoux, N ^a   Gastou Chassaing, M I ^b   Leprevost, J C ^b   Andre J C ^b  

^a UNIVERSITÉ DE LORRAINE   (France)

^b DCPR CNRS   (France)

Author keywords

[No Author keywords available]

Indexed keywords

CHAOS; HEAT TRANSFER; MIXING;

EID: 0029671704     PISSN: 10706631     EISSN: None     Source Type: Journal    
DOI: 10.1063/1.868853     Document Type: Article

References (19)

1. As mentioned in Ch. 7 of J. M. Ottino, The Kinematics of Mixing: Stretching, Chaos and Transport (Cambridge University Press, Cambridge, 1989), most work is concerned with inviscid flows because a detailed analytical treatment is possible. Examples are H. Aref, "Stirring by chaotic advection," J. Fluid Mech. 143, 1 (1984); V. Rom-Kedar, A. Leonard, and S. Wiggins, "An analytical study of transport, mixing and chaos in an unsteady vortical flow," ibid. 214, 347 (1990). The inviscid flow considered in the latter study possesses some similar characteristics to the one considered here.
2. As mentioned in Ch. 7 of J. M. Ottino, The Kinematics of Mixing: Stretching, Chaos and Transport (Cambridge University Press, Cambridge, 1989), most work is concerned with inviscid flows because a detailed analytical treatment is possible. Examples are H. Aref, "Stirring by chaotic advection," J. Fluid Mech. 143, 1 (1984); V. Rom-Kedar, A. Leonard, and S. Wiggins, "An analytical study of transport, mixing and chaos in an unsteady vortical flow," ibid. 214, 347 (1990). The inviscid flow considered in the latter study possesses some similar characteristics to the one considered here.
3. As mentioned in Ch. 7 of J. M. Ottino, The Kinematics of Mixing: Stretching, Chaos and Transport (Cambridge University Press, Cambridge, 1989), most work is concerned with inviscid flows because a detailed analytical treatment is possible. Examples are H. Aref, "Stirring by chaotic advection," J. Fluid Mech. 143, 1 (1984); V. Rom-Kedar, A. Leonard, and S. Wiggins, "An analytical study of transport, mixing and chaos in an unsteady vortical flow," ibid. 214, 347 (1990). The inviscid flow considered in the latter study possesses some similar characteristics to the one considered here.
4. Another new two-dimensional flow for the study of chaotic mixing is S. Jana, G. Metcalfe, and J. M. Ottino, "Experimental and computational studies of mixing in complex Stokes flows: The vortex mixing flow and multicellular cavity flows," J. Fluid Mech. 269, 199 (1994). Unfortunately, an analytical solution is not available for the vortex mixing flow (VMF).
5. E. Saatdjian, N. Midoux, and J. C. André, "On the solution of Stokes equations between confocal ellipses," Phys. Fluids 6, 3833 (1994).
6. The analytical solution of the journal bearing flow is available in a mixed Cartesian-polar orthogonal system: G. H. Wannier, "A contribution to the hydrodynamics of lubrication," Q. J. Appl. Math. 8, 1 (1950), in bipolar coordinates (orthogonal); B. Y. Ballal and R. S. Rivlin, "Flow of a Newtonian fluid between eccentric rotating cylinders," Arch. Rat. Mech. Anal. 62, 237 (1977), or in modified bipolar coordinates; R. C. Di Prima and J. T. Stuart, "Flow between eccentric rotating cylinders," J. Lub. Technol., Trans. ASME 94, 266 (1972).
7. The analytical solution of the journal bearing flow is available in a mixed Cartesian-polar orthogonal system: G. H. Wannier, "A contribution to the hydrodynamics of lubrication," Q. J. Appl. Math. 8, 1 (1950), in bipolar coordinates (orthogonal); B. Y. Ballal and R. S. Rivlin, "Flow of a Newtonian fluid between eccentric rotating cylinders," Arch. Rat. Mech. Anal. 62, 237 (1977), or in modified bipolar coordinates; R. C. Di Prima and J. T. Stuart, "Flow between eccentric rotating cylinders," J. Lub. Technol., Trans. ASME 94, 266 (1972).
8. The analytical solution of the journal bearing flow is available in a mixed Cartesian-polar orthogonal system: G. H. Wannier, "A contribution to the hydrodynamics of lubrication," Q. J. Appl. Math. 8, 1 (1950), in bipolar coordinates (orthogonal); B. Y. Ballal and R. S. Rivlin, "Flow of a Newtonian fluid between eccentric rotating cylinders," Arch. Rat. Mech. Anal. 62, 237 (1977), or in modified bipolar coordinates; R. C. Di Prima and J. T. Stuart, "Flow between eccentric rotating cylinders," J. Lub. Technol., Trans. ASME 94, 266 (1972).
9. H. Aref and S. Balachandar, "Chaotic advection in a Stokes flow," Phys. Fluids 29, 3515 (1986).
10. J. Chaiken, C. K. Chu, M. Tabor, and Q. M. Tan, "Lagrangian turbulence and spatial complexity in a Stokes flow," Phys. Fluids 30, 687 (1987); J. Chaiken, R. Chevray, M. Tabor, and Q. M. Tan, "Experimental study of Lagrangian turbulence in Stokes flow," Proc. R. Soc. London Ser. A 408, 165 (1986).
11. J. Chaiken, C. K. Chu, M. Tabor, and Q. M. Tan, "Lagrangian turbulence and spatial complexity in a Stokes flow," Phys. Fluids 30, 687 (1987); J. Chaiken, R. Chevray, M. Tabor, and Q. M. Tan, "Experimental study of Lagrangian turbulence in Stokes flow," Proc. R. Soc. London Ser. A 408, 165 (1986).
12. P. D. Swanson and J. M. Ottino, "A comparative computational and experimental study of chaotic mixing of viscous fluids," J. Fluid Mech. 213, 227 (1990).
13. M. M. Peixoto, "Structural stability on two-dimensional manifolds," Topology 2, 101 (1962).
14. E. Saatdjian, M. I. Chassaing, N. Midoux, and J. C. André, "Sur le chaos Lagrangien dans une cuve elliptique," J. Phys. III France 5, 175-196 (1995); M. I. Gastou-Chassaing, "Chaos Lagrangien entre ellipses confocales," Thèse Institut National Polytechnique de Lorraine, Nancy, France, soutenue le 14 Septembre, 1995.
15. E. Saatdjian, M. I. Chassaing, N. Midoux, and J. C. André, "Sur le chaos Lagrangien dans une cuve elliptique," J. Phys. III France 5, 175-196 (1995); M. I. Gastou-Chassaing, "Chaos Lagrangien entre ellipses confocales," Thèse Institut National Polytechnique de Lorraine, Nancy, France, soutenue le 14 Septembre, 1995.
16. S. Ghosh, H. C. Chang, and M. Sen, "Heat-transfer enhancement due to slender recirculation and chaotic transport between counter-rotating eccentric cylinders," J. Fluid Mech. 238, 119 (1992).
17. H. Peerhossaini, C. Castelain, and Y. Le Guer, "Heat exchanger design based on chaotic advection," Exp. Thermal Fluid Sci. 7, 333 (1993).
18. T. Kaper and S. Wiggins, "An analytical study of transport in Stokes flows exhibiting large-scale chaos in the eccentric journal bearing," J. Fluid Mech. 4253, 211 (1993).
19. H. H. Bau, "Thermal convection in a horizontal, eccentric annulus containing a saturated porous medium - An extended perturbation expansion," Int. J. Heat Mass Transfer 27, 12,2277 (1984).