Accelerated Flows Past a Rigid Sphere or a Spherical Bubble. Part 1. Steady Straining Flow

Journal of Fluid Mechanics

Volumn 284, Issue , 1995, Pages 97-135

  Magnaudet, Jacques ^a   Fabre, Jean ^a   Rivero, Mayela ^a  

^a CNRS   (France)

Author keywords

[No Author keywords available]

Indexed keywords

BODIES-SPHERICAL; BUBBLES; STEADY FLOW; STRAINING;

BOUNDARY CONDITIONS; BUBBLES (IN FLUIDS); DRAG; FINITE VOLUME METHOD; HYDRODYNAMICS; NAVIER STOKES EQUATIONS; REYNOLDS NUMBER; SPHERES; STRAIN; VISCOUS FLOW; VORTEX FLOW; WAKES;

KELVIN-HELMHOLTZ INSTABILITY; STEADY STRAINING FLOW; VORTICITY TRANSPORT PROPERTIES;

FLOW OF FLUIDS;

EID: 0029239948     PISSN: 00221120     EISSN: 14697645     Source Type: Journal    
DOI: 10.1017/S0022112095000280     Document Type: Article

References (56)

1. ACHENBACH, E. 1974 Vortex shedding from spheres. J. Fluid Mech. 62, 209.
2. AMSDEN, A. & HARLOW, F. 1972 The SMAC Method: A numerical technique for calculating incompressible fluid flow. Los Alamos Res. Lab. Rep. LA-4370.
3. AUTON, T. R., HUNT, J. C. R. & PRUD’HOMME, M. 1988 The force exerted on a body in inviscid unsteady non-uniform rotational flow. J. Fluid Mech. 197, 241.
4. BASSET, A. B. 1888 A treatise in Hydrodynamics, vol. 2. Cambridge: Deighton Bell.
5. BATAILLE, J., LANCE, M. & MARIE, J. L. 1990 Some aspect of the modeling of bubbly flows. In Phase-Interface Phenomena in Multiphase Flow (ed. G. F. Hewitt, F. Mayinger & J. R. Riznic). Hemisphere.
6. BATCHELOR, G. K. 1967 An introduction to Fluid Dynamics. Cambridge University Press.
7. BOUSSINESQ, J. 1885 Sur la resistance qu’oppose un fluide indefini au repos, sans pesanteur, au mouvement varie d’une sphere solide qu’il mouille sur toute sa surface, quand les vitesses restent bien continues et assez faibles pour que leurs carres et produits soient negligeables. C. R. Acad. Sci. Paris 100, 935.
8. BRABSTON, D. C. & keller, H. B. 1975 Viscous flows past spherical gas bubbles. J. Fluid Mech. 69, 179.
9. BRAILOVSKAYA, I. Y. 1965 A difference scheme for numerical solution of the two-dimensional nonstationary Navier-Stokes equations for a compressible gas. Sov. Phys. Dokl. 10, 107.
10. CLIFT, R., GRACE, J. R. & WEBER, M. E. 1978 Bubbles, Drops and Particles. Academic Press.
11. CONNER, J. M. & ELGOBASHI, S. E. 1987 Numerical solution of laminar flow past a sphere with surface mass transfer. Num. Heat Transfer 12, 57.
12. DARWIN, C. 1953 Note on hydrodynamics. Camb. Phil. Trans. 49, 342.
13. DENNIS, S. C. R. & WALKER, J. D. A. 1971 Calculation of the steady flow past a sphere at low and moderate Reynolds numbers. J. Fluid Mech. 48, 771.
14. DREW, D. A. & LAHEY, R. T. 1979 Application of general constitutive principles to the derivation of multidimensional two-phase flows equations. Intl J. Multiphase Flow 5, 243.
15. DREW, D. A. & WALLIS, G. B. 1992 Fundamentals of two-phase flow modeling. Symp. Two-Phase Flow Modelling, London (unpublished).
16. FORNBERG, B. 1988 Steady viscous flow past a sphere at high Reynolds number. J. Fluid Mech. 190, 471.
17. GALPIN, P. F. & RAITHBY, G. D. 1986 Treatment of non-linearities in the numerical solution of the incompressible Navier-Stokes equations. Inti J. Num. Meth. Fluids 6, 409.
18. GATIGNOL, R. 1983 The Faxen formulae for a rigid particle in an unsteady non-uniform Stokes flow. J. Mec. Theor. App. 1, 143.
19. HADAMARD, J. S. 1911 Mouvement permanent lent d’une sphere liquide et visqueuse dans un liquide visqueux. C.R. Acad. Set Paris 152, 1735.
20. HARLOW, F. H. & WELCH, J. E. 1965 Numerical calculation of time-dependent viscous incompressible flow of fluid with free surface. Phys. Fluids 8, 2182.
21. KANG, I. S. & LEAL, L. G. 1987 Numerical solution of axisymmetric, unsteady free-boundary problems at finite Reynolds number. I. Finite-difference scheme and its application to the deformation of a bubble in a uniaxial straining flow. Phys. Fluids 30, 1929.
22. KANG, I. S. & LEAL, L. G. 1988 The drag coefficient for a spherical bubble in a uniform streaming flow. Phys. Fluids 31, 233.
23. KANG, I. S. & LEAL, L. G. 1989 Numerical solution of axisymmetric, unsteady free-boundary problems at finite Reynolds number. II. Deformation of a bubble in biaxial straining flow. Phys. Fluids A 1, 644.
24. KIM, I. & PEARLSTEIN, A. J. 1990 Stability of the flow past a sphere. J. Fluid Mech. 211, 73.
25. LAMB, H. 1932 Hydrodynamics, 6th edn. Cambridge University Press.
26. LE CLAIR, B. P., HAMIELEC, A. E. & PRUPPACHER, H. E. 1970 A numerical study of the drag of a sphere at low and intermediate Reynolds numbers. J. Atmos. Sci. 27, 308.
27. LEAL, G. 1989 Vorticity transport and wake structure for bluff bodies at finite Reynolds number. Phys. Fluids A 1, 124.
28. LEVICH, V. G. 1949 Bubble motion at high Reynolds numbersZh. Eksp. Teoret. Fiz. 19, 18 (in Russian).
29. LEVICH, V. G. 1962 Physicochemical Hydrodynamics. Prentice Hall.
30. LHUILLIER, D. 1982 Forces d’inertie sur une bulle en expansion se deplaiant dans un fluide. C.R. Acad. Sci. Paris 295 (11), 95.
31. MAGNAUDET, J., RIVERO, M., LEGENDRE, D. & FABRE, J. 1995 Accelerated flows past a rigid sphere or a spherical bubble. Part 2. Uniform unsteady flows. J. Fluid Mech. (to be submitted).
32. MAXEY, M. R. & RILEY, J. J. 1983 Equation of motion for a small rigid sphere in a non-uniform flows. Phys. Fluids 26, 883.
33. MOIN, P. & KIM, J. 1985 Application of a fractional-step method to incompressible Navier-Stokes equations. J. Comput. Phys. 59, 308.
34. MOORE, D. W. 1963 The boundary layer on a spherical gas bubble. J. Fluid Mech. 16, 161.
35. NACIRI, A. 1992 Contribution a Tetude des forces exercees par un liquide sur une bulle de gaz: portance, masse ajoutee et interactions hydrodynamiques. These de Doctorat, Ec. Centrale de Lyon.
36. NATARAJAN, R. & ACRIVOS, A. 1993 The instability of the steady flow past spheres and disks. J. Fluid Mech. 254, 323.
37. OLIVER, D. L. R. & CHUNG, I. N. 1987 Flow about a sphere at low to moderate Reynolds numbers. J. Fluid Mech. 177, 1.
38. PEYRET, R. & TAYLOR, T. 1983 Computational Methods for Fluid Flow. Springer.
39. POPE, S. B. 1978 The calculation of turbulent recirculating flows in general orthogonal coordinates. J. Comput. Phys. 26, 197.
40. PROUDMAN, I. & PEARSON, J. R. A. 1957 Expansions at small Reynolds for the flow past a sphere and a circular cylinder. J. Fluid Mech. 2, 237.
41. PRUPPACHER, H. R., LE CLAIR, B. P. & HAMILIEC, A. E. 1970 Some relations between drag and flow pattern of viscous flow past a sphere and a cylinder at low and intermediate Reynolds numbers. J. Fluid Mech. 44, 781.
42. RALLISON, J. M. 1984 The deformation of small viscous drops and bubbles in shear flows. Ann. Rev. Fluid Mech. 16, 45.
43. RIBCZYNSKI, W. 1911 On the translatory motion of a fluid sphere in a viscous medium. Bull. Intl Acad. Pol. Sci. Lett. : Sci. Math. Nat. (A), 40 (in German).
44. RIMON, Y. & CHENG, I. 1969 Numerical solution of a uniform flow over a sphere at intermediate Reynolds numbers. Phys. Fluids 12, 949.
45. RIVERO, M. 1991 Etude par simulation numerique des forces exercees sur une inclusion spherique par un ecoulement accelere. These de Doctorat, Inst. Polytech, de Toulouse.
46. RYSKIN, G. & LEAL, L. G. 1984a Numerical solution of free boundary problems in fluid mechanics. Part 1. The finite difference technique. J. Fluid Mech. 148, 1.
47. RYSKIN, G. & LEAL, L. G. 1984b Numerical solution of free boundary problems in fluid mechanics. Part 3. Uniaxial straining flow. J. Fluid Mech. 148, 37.
48. RYVKIND, V. Y. & RYSKIN, G. 1976 Flow structure in motion of a spherical drop in a fluid medium at intermediate Reynolds number. Fluid Dyn. 11, 5.
49. SAKAMOTO, H. & HANIU, H. 1990 A study of vortex shedding from spheres in a uniform flow. Trans. ASME I: J. Fluids Engng 112, 386.
50. STOKES, G. G. 1851 On the effect of the internal friction of fluids on the motion of pendulums. Trans. Camb. Phil. Soc. 9, 8.
51. TANEDA, S. 1956 Studies on wake vortices (III). Experimental investigation of the wake behind a sphere at low Reynolds numbers. J. Phys. Soc. Japan 11, 1104.
52. TAYLOR, G. I. 1928 The forces on a body placed in a curved or converging stream of fluid. Proc. R. Soc. Lond. A 120, 260.
53. TAYLOR, T. D. & ACRIVOS, A. 1964 On the deformation and drag of a falling viscous drop at low Reynolds number. J. Fluid Mech. 18, 466.
54. TCHEN, C. M. 1947 Mean value and correlation problems connected with the motion of small particles suspended in a turbulent fluid. PhD dissertation, Technische Hogeschool Delft.
55. TOLLMIEN, W. 1938 Uber krafte und momente in schwach gekrummten oder konvergenten stromungen. Ing.-Arch. 9, 308.
56. VOINOV, V. V., VOINOV, O. V. & PETROV, A. G. 1973 Hydrodynamic interactions between bodies in a perfect incompressible fluid and their motion in non-uniform streams. Prikl. Math. Mekh. 37, 680.