Axisymmetric buoyant far-field plume in a quiescent unstratified environment

Underlying Flow Regime 1-06

Test Case

Brief Description of the Study Test Case

The experiments used in this UFR are those of George et al. [3] which were conducted in 1974 at the Factory Mutual Research Corporation and were subsequently repeated by Shabbir & George [33] at the University of Buffalo.

Heated air is discharged through a circular orifice into ambient air that is at rest.
The plume source temperature is 300°C and the ambient air is 29°C.
The source has diameter, D = 6.35 cm.
The hot air is discharged at a velocity of U0 = 67 cm/s with a approximately a top-hat profile.
Temperature and velocity fluctuations at the inlet are less than 0.1%.
George et al. [3] present experimentally measured profiles

of both mean and fluctuating components of the temperature and axial velocity in the self-similar region at x/D = 8, 12 and 16 above the source.

Test Case Experiments

CFD Methods

${\frac {\partial }{\partial x_{j}}}\left({\overline {\rho }}U_{j}\varepsilon \right)={\frac {\partial }{\partial x_{j}}}\left[\left(\mu +{\frac {\mu }{\sigma _{\varepsilon }}}\right){\frac {\partial \varepsilon }{\partial x_{j}}}\right]+c_{\varepsilon 1}{\overline {\rho }}S{\frac {\varepsilon }{k}}-c_{\varepsilon 2}{\overline {\rho }}{\frac {\varepsilon ^{2}}{k+{\sqrt {\nu \varepsilon }}}}+S_{\varepsilon B}$