Hostname: page-component-8448b6f56d-42gr6 Total loading time: 0 Render date: 2024-04-23T22:49:25.926Z Has data issue: false hasContentIssue false
  • English
  • Français

Prandtl number dependence and instability mechanism of the near-field flow in a planar thermal plume

Published online by Cambridge University Press:  30 August 2013

Tae Hattori ,
S. E. Norris ,
M. P. Kirkpatrick  and
S. W. Armfield
Tae Hattori*
Affiliation:
School of Aerospace, Mechanical and Mechatronic Engineering, The University of Sydney, Sydney, NSW 2006, Australia
S. E. Norris
Affiliation:
Department of Mechanical Engineering, The University of Auckland, Auckland, New Zealand
M. P. Kirkpatrick
Affiliation:
School of Aerospace, Mechanical and Mechatronic Engineering, The University of Sydney, Sydney, NSW 2006, Australia
S. W. Armfield
Affiliation:
School of Aerospace, Mechanical and Mechatronic Engineering, The University of Sydney, Sydney, NSW 2006, Australia
*
†Email address for correspondence: tae.hattori@sydney.edu.au
Get access Rights & Permissions [Opens in a new window]

Abstract

This study considers the convective-type instability of the near-field flow of a planar, pure thermal plume with a finite area source. Previous studies revealed the existence of an off-axis thermal boundary-layer instability, driving a puffing instability in the central ascending column, and qualitatively showed correlations between instabilities in these two flow regions. This paper extends the analysis to examine the effect of Prandtl number on transitional near-field behaviours and reports on the stability characteristics of a near-field, pure thermal plume based on a direct stability analysis. The variations in flow behaviours in response to symmetric and asymmetric disturbances suggest the existence of coupled instability mechanisms in the off-axis thermal boundary layer and the central ascending column.

JFM classification

Instability: Absolute/convective instability Convection: Buoyancy-driven instability Convection: Plumes/thermals
Type
Papers
Information
Journal of Fluid Mechanics , Volume 732 , 10 October 2013 , pp. 105 - 127
Copyright
©2013 Cambridge University Press 

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

Aberra, T., Armfield, S. W., Behnia, M. & McBain, G. D. 2012 Boundary layer instability of the natural convection flow on a uniformly heated vertical plate. Intl J. Heat Mass Transfer 55 (21–22), 6097–6108.CrossRefGoogle Scholar
Armfield, S. W. 1994 Ellipticity, accuracy, and convergence of the discrete Navier–Stokes equations. J. Comput. Phys. 114 (2), 176–184.CrossRefGoogle Scholar
Armfield, S. W. & Janssen, R. 1996 A direct boundary-layer stability analysis of steady-state cavity convection flow. Intl J. Heat Fluid Flow 17 (6), 539–546.CrossRefGoogle Scholar
Armfield, S. W. & Street, R. 2002 An analysis and comparison of the time accuracy of fractional-step methods for the Navier–Stokes equations on staggered grids. Intl J. Numer. Meth. Fluids 38 (3), 255–282.CrossRefGoogle Scholar
Cetegen, B. M. 1997 Behavior of naturally unstable and periodically forced axisymmetric buoyant plumes of helium and helium–air mixtures. Phys. Fluids 9 (12), 3742–3752.CrossRefGoogle Scholar
Cetegen, B. M., Dong, Y. & Soteriou, M. C. 1998 Experiments on stability and oscillatory behaviour of planar buoyant plumes. Phys. Fluids 10 (7), 1658–1665.CrossRefGoogle Scholar
Cetegen, B. M. & Kasper, K. D. 1996 Experiments on the oscillatory behaviour of buoyant plumes of helium and helium–air mixtures. Phys. Fluids 8, 2974–2984.CrossRefGoogle Scholar
Gebhart, B. 1973 Instability, transition, and turbulence in buoyancy-induced flows. Annu. Rev. Fluid Mech. 5, 213–246.CrossRefGoogle Scholar
Gebhart, B. 1988 Buoyancy-Induced Flows and Transport. Hemisphere.Google Scholar
Gebhart, B., Pera, L. & Schorr, A. W. 1970 Steady laminar natural convection plumes above a horizontal line heat source. Intl J. Heat Mass Transfer 13 (1), 161–171.CrossRefGoogle Scholar
Ghoniem, A. F., Lakkis, I. & Soteriou, M. 1996 Numerical simulation of the dynamics of large fire plumes and the phenomenon of puffing. In 26th International Symposium on Combustion, Napoli, Italy, 1, pp. 1531–1539 Combustion Institute.Google Scholar
Hattori, T., Bartos, N., Norris, S. E., Kirkpatrick, M. P. & Armfield, S. W. 2013a Experimental and numerical investigation of unsteady behaviour for the near-field pure plume flow. Exp. Therm. Fluid Sci. 46, 139–150.CrossRefGoogle Scholar
Hattori, T., Norris, S. E., Kirkpatrick, M. P. & Armfield, S. W. 2013b Simulation and analysis of puffing instability in the near field of pure thermal planar plumes. Intl J. Therm. Sci. 89, 1–13.CrossRefGoogle Scholar
Jiang, X. & Luo, K. H. 2000 Direct numerical simulation of the puffing phenomenon of an axisymmetric thermal plume. Theor. Comput. Fluid Dyn. 14, 55–74.CrossRefGoogle Scholar
Lakkaraju, R. & Alam, M. 2007 Effects of Prandtl number and a new instability mode in a plane thermal plume. J. Fluid Mech. 592, 221–231.CrossRefGoogle Scholar
Lei, C. & Patterson, J. C. 2003 A direct stability analysis of a radiation-induced natural convection boundary layer in a shallow wedge. J. Fluid Mech. 480, 161–184.CrossRefGoogle Scholar
Leonard, B. P. & Mokhtari, S. 1990 Beyond first-order upwinding: the ultra-sharp alternative for non-oscillatory steady-state simulation of convection. Intl J. Numer. Meth. Engng 30 (4), 729–766.CrossRefGoogle Scholar
Pera, L. & Gebhart, B. 1971 On the stability of laminar plumes: some numerical solutions and experiments. Intl J. Heat Mass Transfer 14, 975–984.CrossRefGoogle Scholar
Plourde, F., Pham, M. V., Kim, S. D. & Balachandar, S. 2008 Direct numerical simulations of a rapidly expanding thermal plume: structure and entrainment interaction. J. Fluid Mech. 604, 99–123.CrossRefGoogle Scholar
Soteriou, M. C., Dong, Y. & Cetegen, B. M. 2002 Lagrangian simulation of the unsteady near field dynamics of planar buoyant plumes. Phys. Fluids 14 (9), 3118–3140.CrossRefGoogle Scholar
Stone, H. L. 1968 Iterative solution of implicit approximations of multidimensional partial differential equations. SIAM J. Numer. Anal. 5 (3), 530–558.CrossRefGoogle Scholar
van der Vorst, H. A. 1981 Iterative solution methods for certain sparse linear systems with a non-symmetric matrix arising from PDE-problems. J. Comput. Phys. 44, 1–19.CrossRefGoogle Scholar
Wakitani, S. 1985 Non-parallel-flow stability of a two-dimensional buoyant plume. J. Fluid Mech. 159, 241–258.CrossRefGoogle Scholar