UFR 1-07 Test Case: Difference between revisions
| Line 180: | Line 180: | ||
species mass fraction and energy: | species mass fraction and energy: | ||
{| | |||
|- | |||
|width="750" align="center"| | |||
<math>\frac{\partial \left(\rho U_{i}\right)}{\partial t}+\frac{\partial | <math>\frac{\partial \left(\rho U_{i}\right)}{\partial t}+\frac{\partial | ||
\left(\rho U_{i}U_{j}+p\delta _{\mathit{ij}}\right)}{\partial | \left(\rho U_{i}U_{j}+p\delta _{\mathit{ij}}\right)}{\partial | ||
| Line 188: | Line 190: | ||
x_{k}}\delta _{\mathit{ij}}\right]+\frac{\partial \tau | x_{k}}\delta _{\mathit{ij}}\right]+\frac{\partial \tau | ||
_{u_{i}u_{j}}}{\partial x_{j}}+\rho g_{i}</math> | _{u_{i}u_{j}}}{\partial x_{j}}+\rho g_{i}</math> | ||
|} | |||
== Footnotes == | == Footnotes == | ||
Revision as of 09:40, 12 July 2010
Unsteady Near-Field Plumes
Underlying Flow Regime 1-07
Test Case Study
Brief Description of the Study Test Case
- A summary of the boundary conditions is shown in Figure 8.
- A gas mixture mainly composed of helium is discharged through a circular orifice into ambient air.
- The gas is composed of 96.4% helium, 1.7% acetone and 1.9% oxygen by volume.
- The molecular weight of the gas released is 5.45 g/mol ±2.7%.
- The mixture is discharged at a temperature of THe = 11°C ±3°C and the air is at Tair = 13°C ±3°C.
- The circular plume source has diameter, D = 1 metre.
- The helium is discharged at a Reynolds-averaged velocity V0 = 0.325 m/s ±1.3% and a Favre-averaged velocity of approximately 0.339 m/s.
- The flow through the orifice is laminar.
- The ambient pressure is 80.9 kPa ±0.4 kPa.
- The measurements include:
- Time-history of vertical velocity at a point 0.5 m from the centreline and 0.5 m above the inlet, used to estimate the puffing frequency
- Measurements on a vertical plane through the plume from the plume source to a distance of one orifice diameter of:
- Reynolds-averaged and Favre-averaged mean axial and radial velocities
- Reynolds-averaged and Favre-averaged shear stresses, normal stresses and turbulent kinetic energy[1]
- Favre-averaged helium concentrations
- Movies of helium concentration and velocities
- Profiles of the mean and RMS velocities, and mean and RMS helium concentrations at six measurement positions (0.1, 0.2, 0.3, 0.4, 0.5 and 0.6 m downstream of the plume source)
Item 1 is available in the O‘Hern et al. [4] paper, Items 2 and 3 can be obtained by contacting the authors of the study[2]. and Item 4 is presented by Chung & Devaud [39].
Test Case Experiments
The experiments selected for this UFR are those undertaken by O‘Hern et al. [4] at the Fire Laboratory for Accreditation of Models by Experimentation (FLAME) facility at Sandia National Laboratories, Albuquerque, New Mexico, in the late 1990s/early 2000s. The aim of these experiments was to examine the characteristics of turbulent buoyant plumes and provide data that could be used to help validate LES models suitable for modelling fires.
The experimental arrangement is shown in Figures 8 and 9. The main
chamber has dimensions 6.1 × 6.1 × 7.3 metres
and converges to a square chimney outlet at the top with nominal
dimensions of 2.4 m on each side. The plume source is located in the
centre of the chamber 2.45 m off the floor. Air is directed through a
series of diverters, screens and honeycombs to form an annular
low-velocity inlet flow surrounding the helium plume. A relatively
large plume source (diameter, D = 1 m) was chosen to ensure
that the plume would be fully turbulent. This is surrounded by a 0.51 m
wide sheet of steel which simulates the ground plane. Air is drawn into
the helium plume passing over this sheet flowing radially inwards. The
experiments were designed specifically to mimic an unconfined plume on
an infinite ground plane with negligible wind effects. Extensive CFD
simulations were performed to help design the facility and to ensure
that any separation bubble formed by the vertical flow of air around
the 0.51 m ground plane did not disturb the plume[3].
The helium flowed through a diffuser, a series of perforated plates and
three layers of honeycomb before being released through the orifice.
The honeycomb immediately upstream of the orifice suppressed turbulence
and flow visualization suggested that the inflow conditions were
laminar. A detailed study of the inlet flow characteristics also found
that the inlet velocity profile was uniform to within 6% [64].
Within just a few centimetres downstream of the inlet, observations suggested
that the plume had become fully-turbulent. To ensure that the flow
had reached a quasi-steady state, the helium was released for a
couple of minutes before recordings were taken. Particle Image
Velocimetry (PIV) was conducted using around 11,500 images spanning 70
puff cycles while Planar Laser-Induced Fluorescence (PLIF) analyses
were performed on approximately 2,300 images, covering 33 puffs. The
experiments were repeated 10 times and the inlet velocity was on
average 0.325 m/s ±1.3% [4].
The acetone and oxygen needed to
be added into the helium released in order for laser fluorescence. As a
consequence, the molecular weight of the mixture was 5.45 g/mol ±2.7%
compared to the pure helium value of 4.00 g/mol.
The Reynolds number based on the inlet diameter and velocity, and the
helium mixture properties was
and the Richardson number was , where
is the air
density and the plume fluid density.
The PIV and PLIF measurements produced simultaneous time-resolved
velocity and mass fraction data. The data was used to calculate
density-weighted Favre-averaged statistics in addition to the more
usual Reynolds or time-averaged statistics. Interestingly, the
difference between the Favre- and Reynolds-averaged quantities was
found to be less than the uncertainty in the data throughout the flow
field [4].
The puffing frequency of the plume was analysed from the time-history
of the vertical velocity at a point in space 0.5 m above the inlet and
0.5 m radially from the centreline. The recorded mean measured
frequency was 1.37 Hz which compares well with the empirical
correlation of
from Cetegen & Kaspar [18]
for helium-air plumes with Ri < 100,
which gives a frequency of 1.35 Hz, and the empirical correlation of
from
Cetegen & Ahmed [25] for fire plumes which gives
a frequency of 1.5 Hz.
O‘Hern et al. [4] discussed in some
detail the dynamics of the unsteady plume and the role of the
Rayleigh-Taylor instability in producing bubble and spike flow
structures. Figure 10, taken from their paper, shows four snapshots of
the plume where the spike and bubble structures are identified with
arrows and the location of the large coherent puffing vortex is
indicated with a circle.
Details of the uncertainties in the experiments are discussed at length
in their paper. These include measurement errors due to the effects of
out-of-plane motion and improper choice of peak correlation in the
cross-correlation analysis of the PIV measurements, and the influence
of film response, image registration and laser-sheet intensity
normalization in the PLIF measurements. Overall, the uncertainties are
estimated to be ±18% for the difference between the plume and
air density, ±5% for the air density, ±20% for
the velocities and ±30% for the turbulence statistics [2].
CFD Methods
DesJardin et al. [1]: Description of CFD Work
Governing Equations
Desjardin et al. [1] used the fully-compressible form of the Favre-averaged Navier Stokes equations. Transport equations were solved for the Favre-averaged momentum, species mass fraction and energy:
|
|
![{\displaystyle {\frac {\partial \left(\rho U_{i}\right)}{\partial t}}+{\frac {\partial \left(\rho U_{i}U_{j}+p\delta _{\mathit {ij}}\right)}{\partial x_{j}}}={\frac {\partial }{\partial x_{j}}}\left[\mu \left({\frac {\partial U_{i}}{\partial x_{j}}}+{\frac {\partial U_{j}}{\partial x_{i}}}\right)-{\frac {2}{3}}\mu {\frac {\partial U_{k}}{\partial x_{k}}}\delta _{\mathit {ij}}\right]+{\frac {\partial \tau _{u_{i}u_{j}}}{\partial x_{j}}}+\rho g_{i}}](https://en.wikipedia.org/api/rest_v1/media/math/render/svg/557d311dbe06e8d90b19df7e86a096fdd7cc91f6)
Footnotes
- ↑ Only velocities parallel to a two-dimensional plane were recorded. The turbulent kinetic energy, k, is calculated from the vertical and horizontal normal stresses ( and ) by assuming that the horizontal component is the same in the out-of-plane direction ( ), i.e. assuming that .
- ↑ Dr. Tieszen (srtiesz@sandia.gov) or Dr. O‘Hern (tjohern@sandia.gov)
- ↑ S. Tieszen, Private Communication, March 2010.
Contributed by: Simon Gant — UK Health & Safety Laboratory
© copyright ERCOFTAC 2010