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 T_He = 11°C ±3°C and the air is at T_air = 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:
1. 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
2. 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
3. Movies of helium concentration and velocities
4. 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.

Figure 8 Boundary conditions for the O‘Hern et al. [4] experiments.

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.

Figure 9 Schematic of the Sandia FLAME facility showing the laser-light sheet that bisects the plume and two video cameras that record the PIV and PLIF images.

The Reynolds number based on the inlet diameter and velocity, and the helium mixture properties was $Re=DV_{0}/\nu =3200\pm 0.6\%$ and the Richardson number was $Ri=\left(\rho _{\infty }-\rho _{0}\right)gD/\left(\rho _{\infty }V_{0}^{2}\right)=76\pm 6.5\%$ , where $\rho _{\infty }$ is the air density and $\left.\rho _{0}\right.$ 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 $f=\left.0.8V_{0}{Ri}^{0.38}/D\right.$ from Cetegen & Kaspar [18] for helium-air plumes with Ri < 100, which gives a frequency of 1.35 Hz, and the empirical correlation of $f=\left.1.5D^{-1/2}\right.$ 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.

Figure 10 Four snapshots of the helium plume of O‘Hern et al. [4] taken 115 ms apart. The left-hand-side of each image shows the mass fraction field from the PLIF, the right-hand-side shows the corresponding PIV vector field overlaid with the general plume outline. The development and movement of a large toroidal vortex is indicated by circular arrows. The spike and bubble structures characteristic of Rayleigh-Taylor instability are indicated by straight arrows.

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:

${\frac {\partial \left(\rho U_{i}\right)}{\partial t}}+{\frac {\partial \left(\rho U_{i}U_{j}+p\delta _{\mathit {ij}}\right)}{\partial x_{j}}}={\frac {\partial }{\partial x_{j}}}\left[\mu \left({\frac {\partial U_{i}}{\partial x_{j}}}+{\frac {\partial U_{j}}{\partial x_{i}}}\right)-{\frac {2}{3}}\mu {\frac {\partial U_{k}}{\partial x_{k}}}\delta _{\mathit {ij}}\right]+{\frac {\partial \tau _{u_{i}u_{j}}}{\partial x_{j}}}+\rho g_{i}$

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 ( ${\overline {uu}}$ and ${\overline {ww}}$ ) by assuming that the horizontal component is the same in the out-of-plane direction ( ${\overline {vv}}={\overline {ww}}$ ), i.e. assuming that $k\approx \left({\overline {\mathit {uu}}}+2{\overline {\mathit {ww}}}\right)/2$ .
↑ Dr. Tieszen (srtiesz@sandia.gov) or Dr. O‘Hern (tjohern@sandia.gov)
↑ S. Tieszen, Private Communication, March 2010.