Abstracts - KTH Mechanics

192
Measurements of buoyancy driven turbulence in a vertical pipe
Murali R. Cholemari ∗ , Jaywant H. Arakeri ∗
We present measurements of a buoyancy driven turbulent flow in long (length-todiameter
ratio = 9) vertical pipes. The flow is created by the density difference across
the ends of the vertical tube. We use brine and fresh water for creating the density
difference. The flow represents an ‘overturning process’ of the two fluids through the
pipe. Since the pipes are long, an axially homogeneous region of turbulence exists
away from the ends. In this region the flow is driven by a linear unstable density
gradient. The ratio of the diffusivities of momentum and salt, given by the Schmidt
number, Sc = ν/α, is about 670. The Rayleigh number based on the diameter d of
the pipe and the density gradient, Rag = g(∆ρ/ρL)d 4 /να, which gives the relative
importance of the buoyancy and diffusive effects, is of the order of 10 8 . The experimental
data consisted of measurements of salt concentration using a conductivity
probe and velocity measurements using planar particle image velocimetry (PIV).
Velocity measurements show that there is no mean flow. Flow visualization and
spatial velocity correlations show that large scales are of the order of the pipe diameter.
One dominant motion seems to be heavier particles going down accompanied by lighter
particles rising up on the sides. Another motion inferred from the data is the collision
of falling and rising fluid particles. The flow is anisotropic, both at large scales as
well as at the smallest scales measured 1 .
The turbulence in the fully developed region involves the dominance of a single
length scale, comparable to the diameter of the pipe. A mixing length model incorporating
this feature is shown to agree very well with the experimental measurements of
the scalar (salt concentration) flux and velocity measurements. The Nusselt number
scales as ∼ Ra 1/2
g Sc 1/2 suggesting that the molecular effects are negligible. This may
be compared to the ∼ Ra 1/3
g scaling obtained in turbulent Rayleigh-Bénard convection2
.
The unique feature about the present flow is that it is a axially homogeneous
purely buoyancy driven turbulent flow.
∗ Department of Mechanical Engineering, Indian Institute of Science, Bangalore 560012 INDIA.
1 Cholemari, PhD thesis, Indian Inst. Sci., (2004).
2 Cholemari and Arakeri, Int. J. Heat Mass Transfer. 48, 4467 (2005).