TRANSIENT LAMINAR SEPARATED FLOW AROUND AN IMPULSIVELY STARTED SPHERICAL PARTICLE AT 20≤RE≤1000
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Keywords

transient flow
hermitian compact
vortex length
drag
sphere

How to Cite

BENABBAS, F. ., & BRAHIMI , M. (2021). TRANSIENT LAMINAR SEPARATED FLOW AROUND AN IMPULSIVELY STARTED SPHERICAL PARTICLE AT 20≤RE≤1000. Journal of Sciences & Technology, 6(2), 21–28. Retrieved from http://revue.umc.edu.dz/index.php/st/article/view/3768

Abstract

Numerical simulations of the axisymmetric laminar flow characteristics past a rigid sphere impulsively started are presented for Reynolds numbers from 20 to 1000. The results are obtained by solving the complete time dependant Navier-Stokes equations in vorticity and stream function formulation. A fourth order compact method is used to discretize the Poisson equation of stream function while the vorticity transport equation is solved by an alternating direction implicit method. Time evolution of flow separation angle and length of the vortex behind the sphere are reported. Time variation of the axial velocity in the vortex and the wall vorticity around the sphere are also examined. Secondary vortices are seen to be initiated at Reynolds number of 610 and for dimensionless time t about 5. Comparisons with previously published simulations and experimental data for steady state conditions show very good agreement.

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References

Bagchi P., Kottam K., 2008. Effect of free stream isotropic turbulence on heat transfer from sphere. Phys. Fluids. 20, 073305.

Bontoux P., 1978. Contribution à l’étude des écoulements visqueux en milieu confiné. Analyse et Optimisation de méthodes numériques de haute précision. Thèse de Doctorat ès-sciences, Université d’Aix-Marseille II, France.

Benabbas F. ,1987. Etude numérique de l’écoulement autour d’une sphère aux grands nombres de Reynolds en régime stationnaire et instationnaire. Thèse de Doctorat de Troisième cycle. Université de Poitier, France.

Benabbas F., Brahimi M., Tighzert H. , 2003. Caractérisation du très proche sillage d’une sphere à des nombres de Reynolds modérés et spectres singuliers . “16ième Congrès Français de Mécanique.” , Nice, France, Sep. 1–5, pp. 1–7.

Benabbas F., Brahimi M., 2012. Transient mass transfer around an impulsively started spherical particle at low to high Peclet numbers. “The 9th EuroMech Fluid Mech. Conf.”, Rome, Italy, Sep. 9-13, accepted.

Bouard R., Coutanceau M., 1980. The early stage of development of the wake behind an impulsively started cylinder for 40≤Re≤104. J. Fluid Mech. 101, 583-607

Collins W. M., Dennis S .C. R., 1973. Flow past an impulsively started circular cylinder. J. Fluid. Mech., 60,105-127.

Dhole S. D., Chhabra R. P., Eswaran V., 2006. A numerical study on the forced convection heat transfer from an isothermal and isoflux sphere in the steady symmetric flow regime. Int. J. heat and mass transfer. 49, 984-994.

Dixon A. G., Taskin M. E., Nijemesisland M., Stitt E. H., 2011. Systematic mesh development for 3D CFD simulation of fixed beds: Single sphere study. Comp. Chem. Eng., 35, 1171-1185.

Fornberg B., 1988. Steady viscous flow past a sphere at high Reynolds numbers. J. Fluid Mech.190, 471-489.

Feng Z., Michaelides E. E., 2000. A numerical study on transient heat transfer from a sphere at high Reynolds and Peclet numbers. Int. J. Heat and Mass transfer. 43, 219-229.

Gushchin V. A., Matyushin R. V., 2006. Vortex formation mechanisms in the wake behind a sphere for 200≤Re≤380. Fluid Dyn. 41, N°5,795-809.

Johnson T. A., Patel V. C. (1999). Flow past a sphere up to a Reynolds number of 300. J. Fluid Mech. 378, 19-70.

Kechroud N., Brahimi M., Djati A. (2010a). Characterization of dynamic behavior of the continuous phase in liquid fluidized bed. Powder Tech., 200, issue 3, 149-157.

Kechroud N., Brahimi M., Djati A. (2010b). Spectral analysis of dynamic behavior of the continuous phase in liquid fluidized bed. “ Proc. of 7th Int. Conf. on Multiphase Flow .,” Tampa Fl, USA, May 30 –June 4, pp.1-7

Lee S., (2000). A numerical study of the unsteady wake behind a sphere in a uniform flow at moderate Reynolds numbers. Comp. Fluids, 29,639-667.

Lin C. L., Lee S. C., (1973). Transient state analysis of separated flow around a sphere. Comp. Fluids, 1,235-250.

Magnaudet J., Rivero M.,Fabre J., (1995). Flows past a rigid sphere or a spherical bubble.1. steady straining flow. J. Fluid Mech., 284, 97-135.

Masliyah J. H., (1972). Steady wakes behind oblate spheroids: flow visualization. Physics of fluids 16, 6-8.

Nakamura, I., (1976). Steady wake behind a sphere. Physics of fluids. 19, 5-8.

Reddy R. K., Joshi J. B., Nandakumar K., Minev P. D., (2010). Direct numerical simulations of a freely falling sphere using fictitious domain method: Breaking of axisymmetric wake. Chem. Eng. Sc.,65, 2159-2171

Richter A., Nikrityuk P. A., (2012). Drag forces and heat transfer coefficients for spherical, cuboidal and ellipsoidal particles in cross flow at sub-critical Reynolds numbers.Int. J. heat and mass transfer,55, 1343-1354

Rimon Y., Cheng J., (1969). Numerical solution of a uniform flow over a sphere at intermediate Reynolds numbers. Phys. Fluids 12, N°5, 949-959

Sekhar T. V. S., Hema Sundar Raju B., (2012). Higher-Order compact scheme for the incompressible Navier-Stokes equations in spherical geometry,Commun. Comput. Phys., 11, N°1, 99—113.

Smith P. A., Stansby P. K., (1988). Impulsively started flow around a circular cylinder by the vortex method. J. Fluid Mech., 194, 45-77.

Taneda S.,(1956). Experimental investigation of the wake behind a sphere at low Reynolds numbers. Journal of the physical society of Japan, 11, 1104-1108.

Ta Phuoc Loc, Bouard R., (1985). Numerical solution of the early stage of the unsteady viscous flow around a circular cylinder: a comparison with experimental visualization and measurements. J. Fluid Mech., 160, 93-117.

Ta Phuoc Loc, (1980). Numerical analysis of unsteady secondary vortices generated by an impulsively started circular cylinder. J. Fluid Mech., 100,111-128.

Thoman D. C., Szewczyk A. A., (1969). Time-dependant viscous flow over a circular cylinder. Phys. Fluids Suppl., 12, 76-87.

Turton R., Levenspiel O., (1986). A short note on the drag correlation for spheres. Powd. Tech.47, 83-86.

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