Direct numerical simulation of turbulent intermediate Froude number fountain flow

Abstract

Fountains are an important flow in many industrial and geophysical problems but the understanding of this flow at low Froude numbers is limited. In this study we use direct numerical simulation to examine two regimes of turbulent fountain flow, weak flow at Fr=2.2 and very weak flow at Fr=0.45. At Fr=0.45 buoyancy stabilises the flow and there is little entrainment of ambient fluid. Kelvin--Helmholtz instabilities are generated at the interface between the upwelling flow and the ambient fluid. At Fr= 2.2 the shear interaction between the rising and falling flow streams becomes important as it drives both large and small scale vortex structures. Large scale structures draw ambient fluid into the fountain while small scale structures exchange mass between the upflow and downflow. Periodic ejection of mass from the top of the fountain is shown to be an important dynamic in the flow. The results provided here can assist in analytical model development. References J. S. Turner. Jets and plumes with negative or reversing buoyancy. J. Fluid Mech., 26:779--792, 1966. doi:10.1017/S0022112066001526. T. Mizushina, F. Ogino, H. Takeuchi, and H. Ikawa. An experimental study of vertical turbulent jet with negative buoyancy. Warme-und Stoffubertragung, 16:15--21, 1982. doi:10.1007/BF01322802. R. W. Cresswell and R. T. Szczepura. Experimental investigation into a turbulent jet with negative buoyancy. Phys. Fluids A, 5:2865--2878, 1993. doi:10.1063/1.858749. N. B. Kaye and G. R. Hunt. Weak fountains. J. Fluid Mech., 558:319--328, 2006. doi:10.1017/S0022112006000383. N. Williamson, N. Srinarayana, S. W. Armfield, G. D. McBain, and W. Lin. Low-reynolds-number fountain behaviour. J. Fluid Mech., 608:297--317, 2008. doi:10.1017/S0022112008002310. W. Lin and S. W. Armfield. Very weak axisymmetric fountains in a homogeneous fluid. Numer. Heat Transfer A, 38:377--396, 2000. doi:10.1080/104077800750022520. P. D. Friedman, V. D. Vadokoot, W. J. Meyer, and S. Carey. Instability threshold of a negatively buoyant fountain. Exp. Fluids, 42:751--759, 2007. doi:10.1007/s00348-007-0283-5. H. Zhang and R. E. Baddour. Maximum penetration of vertical round dense jets at small and large {F}roude numbers. J. Hydraulic Eng., 124:550--553, 1998. doi:10.1061/(ASCE)0733-9429(1998)124:5(550). B. R. Morton, G. I. Taylor, and J. S. Turner. Turbulent gravitational convection from maintained and instantaneous sources. Proc. R. Soc. Lond., 234:1--23, 1956. http://www.jstor.org/stable/99936. B. P. Leonard and S. Mokhtari. Beyond first-order upwinding: the ultra-sharp alternative for non-oscillatory steady state simulation of convection. Int. J. Numer. Meth. Engng, 30:729--766, 1990. doi:10.1002/nme.1620300412. I. H. Campbell and J. S. Turner. Fountains in magma chambers. J. Petrol., 30:885--923, 1989. http://petrology.oxfordjournals.org/cgi/content/abstract/30/4/885 W. D. Baines, J. S. Turner, and I. H. Campbell. Turbulent fountains in an open chamber. J. Fluid Mech., 212:557--592, 1990. doi:10.1017/S0022112090002099. W. Lin and S. W. Armfield. Direct simulation of weak axisymmetric fountains in a homogeneous fluid. J. Fluid Mech., 403:67--88, 2000. doi:10.1017/S0022112099006953. E. Kaminski, S. Tait, and G. Carazzo. Turbulent entrainment in jets with arbitrary buoyancy. J. Fluid Mech., 526:361--376, 2005. doi:10.1017/S0022112004003209.