UFR 1-07 Test Case: Difference between revisions
Line 368: | Line 368: | ||
assumed that the experimental conditions represented an unconfined | assumed that the experimental conditions represented an unconfined | ||
plume. The computational domain was then constructed as a cube with | plume. The computational domain was then constructed as a cube with | ||
sides of length 4 metres. DesJardin | sides of length 4 metres. | ||
DesJardin ''et al.'' [[UFR_1-07_References#1|[1]]] commented that | |||
this domain size was found necessary for the plume to be unaffected | |||
by the presence of the domain boundaries, due to the large quantity of | by the presence of the domain boundaries, due to the large quantity of | ||
air drawn into the plume in each puffing cycle. Note that in | air drawn into the plume in each puffing cycle. Note that in | ||
comparison, the central chamber of the FLAME facility, where the | comparison, the central chamber of the FLAME facility, where the | ||
experiments were conducted, comprised a cube of sides 6.1 m and the | experiments were conducted, comprised a cube of sides 6.1 m and the | ||
ground plane around the plume source extended 0.51 m radially outwards | ground plane around the plume source extended 0.51 m radially outwards | ||
from the perimeter of the source orifice (see Figure 9). Two grids were | from the perimeter of the source orifice (see Figure 9). Two grids were | ||
used comprising 80 {\texttimes} 80 {\texttimes} 80 (= 512k nodes) and | used comprising 80 {\texttimes} 80 {\texttimes} 80 (= 512k nodes) and |
Revision as of 10:44, 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:
|
|
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where ρ is the density,
Ui the velocity components, p the pressure, Y the species mass fraction,
e the total energy and h the enthalpy (N.B.
all of these parameters are Favre-averaged quantities). For the
diffusion of helium into air, the molecular Schmidt and Prandtl numbers
were set to values of Sc = 0.2 and Pr = 0.7.
Thermodynamic properties, such as cp, were evaluated based on
the mixture composition using the Chemkin libraries. The molecular
viscosity, μ, was determined from
Sutherland's law for pure air.
Turbulence Modelling
The Smagorinsky model was used for the SGS stresses in the momentum equation, , and a simple Boussinesq gradient-diffusion model was used for the SGS stress terms in the species mass fraction and energy equations, and :
|
|
|
where is the strain rate and
is
the strain-invariant. The filter width was taken as twice the
cube-root of the local computational cell volume, , where ,
, and , are the cell widths.
This is twice as large as the commonly used value and was chosen in an
effort to minimize numerical errors. The three modelling “constants”,
CR, CY and Ch
were calculated dynamically [65][66]
using a second explicit filter that was twice the size of the
first implicit filter. To ensure numerical stability, the constants
were locally smoothed using explicit filtering with a filter function
described by Fureby [67].
The magnitude of the effective viscosity or
diffusivity was also clipped to be always greater than or equal to zero
( and ).
DesJardin et al. [1]
noted that the advantage of this approach over
other approaches is that it allows for some backscatter that may be
important for laminar to turbulent transition. Triple correlations
appearing in the energy equation, , were
modelled using an approach proposed by
Ragab et al. [68][69],
for details see [1].
DesJardin et al. [1] also presented
results obtained without using the SGS model (i.e. a “no-model” approach).
Numerical Methods
DesJardin et al. [1] used a finite-volume treatment where the mass, momentum and energy equations equations were differenced in time using a fourth-order Runge-Kutta scheme. Convective terms were discretized using a blend of a fifth-order ENO scheme for the first two stages of the Runge-Kutta integration and ninth-order upwind-biased scheme for the final two stages. This combination of high-order schemes was chosen to prevent dispersive errors (undershoots and overshoots), minimize numerical dissipation and avoid odd-even decoupling errors (chequerboarding) in regions of the flow where the Mach number was small. Where the flow was aligned to the grid, their approach should have provided up to ninth-order accuracy for the momentum equations and fifth-order accuracy for mass, energy and species mass fraction. Diffusion terms were discretized using fourth-order central differences. Near the boundaries, the differencing schemes used for the convection and diffusion terms were of lower order accuracy.
To avoid having to use a time-step limited by the acoustic wave speed, DesJardin et al. [1] used the Pressure Gradient Scaling (PGS) method of O‘Rouke et al. [70][71]. This approach decomposes the pressure into two parts comprising thermodynamic and hydrostatic components. The thermodynamic component, which contains acoustic information, is pre-multiplied by a scaling factor which artificially reduces the acoustic wave speeds. Details of this technique are given in the Appendix of DesJardin et al.‘s paper [1].
Boundary Conditions
The vertical boundaries and top outlet planes were assumed to be open, allowing for flow to be entrained into or exit the domain. On the inlet plane, the inlet velocity for the helium was Up = 0.351 m/s, whereas the experimental Favre-averaged velocity was 0.339 m/s [4]. A small axial coflow velocity of 0.01 m/s was specified outside the plume whereas in the experiments there was a fixed ground plane. The cross-stream velocities were set to zero on the inlet plane. A considerable amount of detail on the treatment used to avoid acoustic waves reflecting back from open boundaries into the domain and contaminating the solution was provided in an Appendix to their paper [1]. The non-reflective pressure relation used at open boundaries was based on an approach developed by Rudy & Strikwerda [72][73]. In the simulations, the gas released was pure helium with a molecular weight of 4.0 g/mol, whilst in the experiments, the gas released had a molecular weight of 5.4 g/mol.
The inlet velocity, the co-flow and the gas density differed slightly
compared to the experiments since the simulations and the experiments
were undertaken concurrently, and the final measured conditions
differed from those originally planned[4].
It was not found necessary to superimpose turbulent fluctuations on the inlet velocity to obtain transition to turbulence. Tests found that using different prescribed inlet turbulence intensities did not affect the resulting flow behaviour[5].
Grid Used
Rather than model the same geometry as used in the experiments, it was assumed that the experimental conditions represented an unconfined plume. The computational domain was then constructed as a cube with sides of length 4 metres. DesJardin et al. [1] commented that this domain size was found necessary for the plume to be unaffected by the presence of the domain boundaries, due to the large quantity of air drawn into the plume in each puffing cycle. Note that in comparison, the central chamber of the FLAME facility, where the experiments were conducted, comprised a cube of sides 6.1 m and the ground plane around the plume source extended 0.51 m radially outwards from the perimeter of the source orifice (see Figure 9). Two grids were used comprising 80 {\texttimes} 80 {\texttimes} 80 (= 512k nodes) and 136 {\texttimes} 136 {\texttimes} 136 (${\approx}$ 2.5M nodes). The grids were refined near the centreline and the base of the plume resulting in minimum and maximum grid spacings of 2.8 cm and 13.1 cm for the coarse grid and 1.6 cm and 7.8 cm for the fine grid. A plot showing a cross{}-section through the mesh is given in their paper. It is not clear how the circular inlet orifice was modelled using the structured mesh although from their plot of the grid it would appear that a stair{}-stepped or sawtoothed approach was probably taken.
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.
- ↑ DesJardin, Personal Communication, 2010.
- ↑ DesJardin, Personal Communication, 2007.
Contributed by: Simon Gant — UK Health & Safety Laboratory
© copyright ERCOFTAC 2010