Direct simulation of transitional plane fountains in a homogeneous fluid

Abstract

The fluid dynamics of transitional plane fountains with the Froude and Reynolds numbers in the ranges 1≤Fr≤6 and 100≤Re≤800 is investigated to examine the entrainment associated with the onset of turbulence. The direct numerical simulation results show that negligible entrainment occurs at the upflow-downflow interface for small Fr (<2) fountains, and only small entrainment on the downflow-ambient interface. However, entrainment occurs at both the upflow-downflow and the downflow-ambient interfaces for large Fr (>2) fountains, even at Re=100, with the extent of the entrainment increasing almost linearly with Re. The upflow and fountain widths show strong Re dependence and increase linearly with Fr, demonstrating that the onset of entrainment and instability occurs at relatively high Re (>1000) in small Fr (≤2) fountains, but at small Re (<100) in large Fr (>2) fountains. References W. Lin and S. W. Armfield. Direct simulation of weak axisymmetric fountains in a homogeneous fluid. J. Fluid Mech., 403, 2000, 67--88. doi:10.1017/S0022112099006953 W. Lin and S. W. Armfield. Weak fountains in a stratified fluid. Phys. Rev. E, 66, 2002, 066308. doi:10.1103/PhysRevE.66.066308 W. Lin and S. W. Armfield. The Reynolds and Prandtl number dependence of weak fountains. Computational Mechanics, 31, 2003, 379--389. doi:10.1007/s00466-003-0440-5 P. Philippe, C. Raufaste, P. Kurowski and P. Petitjeans. Penetratioon of negatively buoyant jet in a miscible liquid. Phys. Fluids, 17, 2005, 053601. doi:10.1063/1.1907735 P. F. Linden. The fluid mechanics of natural ventilation. Annu. Rev. Fluid Mech., 31, 1999, 201--238. doi:10.1146/annurev.fluid.31.1.201 P. Bhattacharjee and E. Loth. Entrainment by a refrigerated air curtain down a wall. ASME J. Fluids Eng., 126: 871--879, 2004. doi:10.1115/1.1792263 B. R. Morton. Forced plumes. J. Fluid Mech., 5, 1959, 151--163. doi:10.1017/S002211205900012X J. S. Turner. Jets and plumes with negative or reversing buoyancy. J. Fluid Mech., 26, 1966, 779--792. doi:10.1017/S0022112066001526 W. D. Baines, J. S. Turner and I. H. Campbell. Turbulent fountains in an open chamber. J. Fluid Mech., 212, 1990, 557--592. doi:10.1017/S0022112090002099 L. J. Bloomfield and R. C. Kerr. A theoretical model of a turbulent fountain. J. Fluid Mech., 424, 2000, 97--216. doi:10.1017/S0022112000001907