Title: Statistical Properties of a Meandering Plume in Turbulent Boundary Layer
1Statistical Properties of a Meandering Plume in
Turbulent Boundary Layer
- Alex Skvortsov Ralph Gailis
- CSIRO Complex Systems Science Annual Workshop
- August 8-10, 2006
2Outline
- Very Brief Overview of the Fluctuating Plume
Model - Summary of Previous Work
- New Results
- 2D LIF/Theory
- Meander Fluctuation Theory
- Future Work Integration Plans
3Motivation
- A general model for dispersion, including
concentration fluctuations - shear boundary layers and canopies
- relatively fast calculations
- as many analytical components as possible
- integrate with/complement other models of
dispersion and wind flow - Use the fluctuating plume paradigm
4The Fluctuating Plume Model
Transverse plane distance x downstream
Transverse coords xT (y, z), so that x (x, xT)
Instantaneous plume centroid xT,c (yc, zc)
Moving ref. frame fixed to plume centroid with
coords xT,r (yr, zr)
It follows that xT xT,r xT,c
5Basic Concept of the Model
- The total concentration PDF is the average of the
conditional PDF of instantaneous concentration c
over the fluctuations in centroid motion xT,c - PDF of relative concentration
- relies on moments of relative concentration, Cr ,
ir - Take moments of PDFs many statistics can be
derived analytically
6Summary of Previous Work - The Coanda Water
Channel
- Coanda meteorological water channel (10 m long,
with cross-section 1.5 m wide and 1.0 m high)
with model canopy (flat plate array) installed on
the channel floor - Square bar array and saw-tooth fence at channel
inlet used in acceleration of development of deep
boundary layer over the model canopy - Dispersing dye dispersion measured using Laser
Induced Fluorescence (LIF)
7Obstacle Arrays
- Originally analysed No Obstacles Canopy and
Urban Arrays config. - These cases can be seen to be baseline and
extreme obstacle arrays - Analysis of 2D LIF is now well underway
8New Experiment - 2D Data Collection
- Fluctuating position of plume centroid against
fixed 1D LIF beam may cause data inconsistencies
in relative frame - More reliable way to collect data is to employ 2D
transverse scan
92D LIF Dataset
- All data has now been collected
- Canopy Array
- No obstacles _at_ 3 different heights
- Regular Cubic arrays
- Random height arrays
- Random placement arrays
- Data processing is in progress
10Array 004 Random obstacle heights (1H, 2H 3H)
11Statistics Images (example - Array 004)
12Centroid Statistics Array 001 (left) and Array
018 (right)
- Array 001 regular array of 1H obstacles
- Array 018 random placement of 1H obstacles
- Spread of centroid position in each
cross-section does not seem to be self-similar
and depends on particular obstacle configuration,
source and measurement points
13Centroid StatisticsHorizontal Meander Histograms
Array 018
Array 001
- Very self-similar - good fit for Gaussian
14Centroid StatisticsVertical Meander Histograms
Array 001
Array 018
- Lognormal fit (i.e. its Log fits Gaussian)
15Concentration Statistics Horizontal Relative
Concentration Profiles
Array 018
Array 001
- Horizontal linescan across mean centroid position
- Clear Gaussian fit up to 3s
16Theory Plume Meander Fluctuations
- Analytical self-similar solution for power-law
velocity profile and eddy viscosity
- Large Deviations Theory ltConcentrationgtParticle
PDF
17Theory Relative Fluctuation Intensities
- The relative PDF is given by the formula below,
and is dependent on the relative fluctuation
intensity (k i-1/2) - Up to now we have used a bulk fluctuation
intensity, assuming it remains constant over a
constant y-z plane - Gives analytical results, but is an over
simplification
18QQ-Plots to Validate Meander PDF
19Work with CSIRO Atmospheric Research -(Dr
M.Borgas)
Relative Dispersion Lagrangian framework pair
correlation concentration covariance
Cross section integral averaged over separation
vector angles
Analysis from COANDA 2D LIF (smooth wall)
20Relationship with separation PDF /internal
fluctuations
p from a modified Richardsons Diffusion Model
Sample fits using Richardsons Diffusion Model
21Velocity Field Characterisation
- In UrbanArray water channel experiments we used
an LDV (Laser Doppler Velocimeter) to
characterise flow field - The LDV only measures two components of the flow
at a time, so we considered the use of a Sontek
acoustic Doppler velocimeter (ADV) - The sampling volume of the Sontek is much larger
than for the LDV, so we expect some trade-off in
the detail we see for small-scale structure of
the flow
22ADV LDV Comparison
23Initial Analysis Results
- We expect that this data will provide a better
understanding of how the upstream obstacles
influence the flow field around the source - Also plan to use this detailed measured data as
flow input during testing of our initial
prototype urban fluctuating plume model - Preliminary analysis of this dataset shows
variations in the height and arrangement of
obstacles in both the near and far field has a
surprisingly small impact on the flow statistics
24Future Work
- Complete analysis of 2D dispersion data
- Analytical Model for plume internal fluctuations
- Analysis of Velocity data to aid theoretical
development of model and as a data input for
testing prototype concentration model - Interface with a Lagrangian particle model
- a higher level layer, interpreting stochastic
model output - gives higher order concentration moments or the
full concentration PDF - can then simulate concentration time series