Numerical simulation for entrainment of forced turbulent fountains
Authors: Awin Layth Ali , Armfield Steven W , Williamson Nicholas , Kirkpatrick Michael P , Lin Wenxian 
Published: September 2019

Numerical simulations are used to investigate the entrainment for forced turbulent fountains over a range of Reynolds numbers and Froude numbers, with ranges based on the fountain source properties. Other fountain properties such as height and width are also examined to provide information on the general structure of the fountains. The results show that the fountains have minimal Reynolds number dependency, while they have a strong linear relation with the Froude number for the cases considered in this study. The entrainment coefficient is obtained as well as scaling constants for height and width in terms of the Froude number.

References G. Abraham. Jets with negative buoyancy in homogeneous fluid. J. Hydraul. Res., 5(4):235248, 1967. doi:10.1080/00221686709500209. W. D. Baines, J. S. Turner, and I. H. Campbell. Turbulent fountains in an open chamber. J. Fluid Mech., 212:557592, 1990. doi:10.1017/S0022112090002099. L. J. Bloomfield and R. C. Kerr. A theoretical model of a turbulent fountain. J. Fluid Mech., 424:197216, 2000. doi:10.1017/S0022112000001907. H. C. Burridge and G. R. Hunt. Entrainment by turbulent fountains. J. Fluid Mech., 790:407418, 2016. doi:10.1017/jfm.2016.16. I. H. Campbell and J. S. Turner. Fountains in magma chambers. J. Petrol., 30(4):885923, 1989. doi:10.1093/petrology/30.4.885. P. D. Friedman, V. D. Vadakoot, W. J. Meyer, and S. Carey. Instability threshold of a negatively buoyant fountain. Exp. Fluids, 42(5):751759, 2007. doi:10.1007/s00348-007-0283-5. D. D. Gray and A. Giorgini. The validity of the Boussinesq approximation for liquids and gases. Int. J. Heat Mass Tran., 19(5):545551, 1976. doi:10.1016/0017-9310(76)90168-X. N. B. Kaye and G. R. Hunt. Weak fountains. J. Fluid Mech., 558:319328, 2006. doi:10.1017/S0022112006000383. 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. Eng., 30(4):729766, 1990. doi:10.1002/nme.1620300412. T. J. McDougall. Negatively buoyant vertical jets. Tellus, 33(3):313320, 1981. doi:10.3402/tellusa.v33i3.10718. T. Mizushina, F. Ogino, H. Takeuchi, and H. Ikawa. An experimental study of vertical turbulent jet with negative buoyancy. Warme Stoffubertrag., 16(1): 1521, 1982. doi:10.1007/BF01322802. B. R. Morton. Forced plumes. J. Fluid Mech., 5(1):151163, 1959. doi:10.1017/S002211205900012X. S. E. Norris. A parallel NavierStokes solver for natural convection and free surface flow. PhD thesis, University of Sydney, 2000. J. S. Turner. Jets and plumes with negative or reversing buoyancy. J. Fluid Mech., 26(4):779792, 1966. doi:10.1017/S0022112066001526. N. Williamson, N. Srinarayana, S. W. Armfield, G. D. McBain, and W. Lin. Low-Reynolds-number fountain behaviour. J. Fluid Mech., 608:297317, 2008. doi:10.1017/S0022112008002310. N. Williamson, S. W. Armfield, and W. Lin. Forced turbulent fountain flow behaviour. J. Fluid Mech., 671:535558, 2011. doi:10.1017/S0022112010005872. H. Zhang and R. E. Baddour. Maximum penetration of vertical round dense jets at small and large Froude numbers. J. Hydraul. Eng., 124(5):550553, 1998. doi:10.1061/(ASCE)0733-9429(1998)124:5(550).