Atwood Number Effects In Buoyancy
Driven Flows
Author(s)
M. J. Andrews & F. F. Jebrail
Abstract
Consideration is given to Atwood number (non-dimensional density difference)
effects in buoyancy driven flows. Buoyancy driven (natural convection) flows
may be treated as Boussinesq for small Atwood number, but as Atwood number
increases (>0.1, i.e. large temperature differences) the Boussinesq approximation
is no longer valid and the distinct \“bubble” and \“spike” geometry of Rayleigh–
Taylor buoyant plumes is formed. Aside from asymmetry in the flow the Atwood
number also affects key turbulent mix parameters such as the molecular mix, and
heat transfer coefficients. This paper will present recent experimental work being
performed in the buoyancy driven mix laboratory at Texas A&M University with
air/helium as mixing components. Corresponding numerical simulations
performed at Los Alamos are presented for the experiments, and future directions
for the research discussed.
Keywords: buoyancy, Boussinesq, Atwood number, natural convection.
1 Introduction
This paper describes experiments and corresponding simulations to investigate
non-Boussinesq effects at high Atwood (At) number (At ( ) ( ) 2 1 2 1 ρ ρ ρ ρ + − ≡ a
non-dimensional density ratio) in buoyancy driven turbulence (Rayleigh-Taylor
mixing). The Boussinesq assumption for buoyancy driven flows states that
density difference effects need only be accounted for in the gravitational terms,
and density may be taken as a constant elsewhere in the equations. At small
Atwood number (At<<1) the Boussinesq approximation is valid, however, at
large At (~1) it implies a symmetry to the flow that is contrary to the familiar
bubbles and spikes of water falling out of a glass. Here we explore the limits of
the Boussinesq approximation.
Keywords
buoyancy, Boussinesq, Atwood number, natural convection.
Related Book
Other papers in this volume
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