UFR 1-06 Test Case
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 [34] 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
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 [34] at the University of Buffalo.
The general arrangement is shown in Figure 4.
Compressed air is passed through a set of heaters and porous mesh screens before exiting through a nozzle into
the enclosure. The nozzle is stated as a 15:1 contraction in [3],
a 12:1 contraction in [sg92]
and appears to be different again in a drawing of the arrangement in [3]
(see Figure 5). It resulted in a velocity
profile through the exit which was uniform to within 2% outside the wall boundary layer. The velocity and
temperature fluctuations at the exit were measured to be very low, less than 0.1%
in [3]
and 0.5% in [34].
The temperature of the source was 300°C and the ambient environment
29°C. Both were controlled to an accuracy of within 1°C. The discharge velocity was 67 cm/s, as
calculated from the measured heat flux. These source conditions corresponded to Reynolds number, Re0 = 870, and densimetric Froude number, Fr0 = 1.23
[#sdfootnote1sym 1].
There was no evidence of laminar flow behaviour at a position two inlet
diameters downstream from the source. The effective origin of the plume, x0, was
found to be at the same location as the exit
(see [3] for details of how this was determined).
The screen enclosure around the plume exit was 2.44 × 2.44 metres in cross-section and 2.44 metres high
(there is, presumably, an error in [3]
which suggests that the enclosure is 2.44 × 2.44 × 2.44 mm).
In the later Shabbir & George experiments, a 2 × 2 × 5 metre enclosure was used. The purpose
of the screens was to minimize the effect of cross-draughts and other disturbances affecting the flow.
Two-wire probes were used by George et al. [3]
to record velocities and temperature.
[#sdfootnote1anc 1]The densimetric Froude number is calculated here from the source and ambient temperatures, the exit velocity and source diameter given by George et al. [gat77], using Equation (1). However, George et al. [gat77] stated that the densimetric Froude number was 1.4. It is unclear how they determined this value. Using the approach taken by Chen & Rodi [cr80] in which the source density instead of the ambient density is used to make the density difference dimensionless, and Froude number is defined using the square of the expression given in Equation (1), this gives a Froude number of 0.80.
George et al. [3] reported that measurement errors, stemming from
directional ambiguity of the hot wire and its thermal inertia, were around 3% for the velocity and lower for
other mean and RMS values. The frequency response of the hot wires was estimated to be around 300 Hz compared
to the frequency of the energy-containing eddies at around 50 Hz and the Kolmogorov microscale at 1 Khz.
It was noted that measurement errors were likely to be higher on the outer edge of the plume where
the velocity fluctuations were higher.
In their review of plume experiments, Chen & Rodi [1]
noted that the data from George et al. differed significantly from earlier measurements by
Rouse et al. [64].
However, they considered it to be more reliable due to its use of more
sophisticated instrumentation.
George [40], describes an experimental program at the University of
Buffalo that was set up following publication of the original
George et al. [3] paper to investigate
possible causes of differences in experimental plume results. Possible sources of errors discussed
included:
- ambient thermal stratification
- the size of the enclosure
- the use of porous screens used to minimise disturbances from the far-field affected the plume source.
- hot wire measurement errors
The most significant concern was ambient thermal stratification.
One of the features of buoyant plumes in neutral environments is that the integral of the
buoyancy across the whole cross-section of the plume, F, should remain constant and equal to the
buoyancy added at the source, F0.
George [40] discussed how thermal stratification involving
small temperature differences of the order of 1°C across a 3 metre vertical span would be sufficient
to cause F to decrease to only 50% of the source value.
This would be likely to cause differences in measured temperature and velocity plume profiles.
In the initial experiments of George et al. [3],
the thermal stratification was not strictly controlled.
However, results from later experiments published in the PhD thesis of
Shabbir [32]
(reproduced in [34] and [40]),
which conserved buoyancy to within 10%, are in good agreement with the earlier results from
George et al. [3].
This suggests that, perhaps fortunately, ambient thermal stratification did not contaminate the
George et al. [3] results significantly.
A summary of the original results from George et al. [3]
and those reproduced later by Shabbir & George [11]
is presented in Table 3.
Also shown are the recommended values from
Chen & Rodi's review [1] and other studies.
The parameters given in Table 3 relate to the following empirical formulae for the mean vertical velocity:
and effective buoyancy acceleration:
CFD Methods
Contributed by: Simon Gant — Lea Associates
© copyright ERCOFTAC 2010