Turbulent flow over groups of urban-like obstacles
O. Coceal1, T.G. Thomas2, I.P. Castro2 and S.E. Belcher1
1Department of Meteorology, University of Reading, U.K.
2School of Engineering Sciences, University of Southampton, U.K.
1Email: [email protected]
www.met.rdg.ac.uk/bl_met
Motivation and Aims
• Modelling flow and dispersion in urban areas
• Wider application, e.g. in engineering
Aims
• To perform high resolution simulations – no turbulence modelling, no tuning
• To validate simulations against a high quality dataset
• To compute 1-d momentum balance for canopy of cubical roughness, and compare with vegetation canopies
compare with rough walls in general
• To compare flow within canopy with that above & understand their coupling
• To investigate effect of layout of the obstacles
Spatial averaging
'~ uuUu Uuu ~
uUuu ~'
spatial fluctuation from mean
turbulent wind speed
Compute from LES/DNS data
Dwuz
wuzx
P
Dt
DU
~~''1
Spatial average of Reynolds-averaged momentum equation
uU
''wu is spatial average of Reynolds stress
is dispersive stress
is distributed drag term
wu ~~
S i dSnp
VD
1
is spatially averaged mean wind speed
See e.g. Raupach & Shaw (1982), Finnigan (2000)
Numerical method• Multiblock LES/DNS code developed by T.G. Thomas
• Resolutions:
DNS at 64 x 64 x 64 grid points per cube (256 x 256 x 256 grid points)
32 x 32 x 32 grid points per cube (128 x 128 x 128 grid points)
16 x 16 x 16 grid points per cube (64 x 64 x64 grid points)
•Boundary conditions:
free slip at top
no slip at bottom and cube surfaces
periodic in streamwise and lateral directions
• Reynolds number = 5000 (based on Utop and h)
• Flow driven by constant body force
Domain set-up
Repeating unit
Staggered Aligned Square
Obstacle density 0.25
Domain sizes: 4h x 4h x 4h, 8h x 8h x 4h, 4h x 4h x 6h
Grid resolution tests
Domain size tests (I)
Domain size tests (II)
Unsteady flow viz - windvectors
Unsteady flow viz - windvectors
Unsteady flow very different from mean flow
Streamwise vortex structures
Streamwise-vertical plane Lateral-vertical plane
Unsteady flow viz - vorticity
Unsteady flow viz - vorticity
Strong, continuous shear layer Interacting shear layers
Enhanced lateral mixing Decoupling of flow ?
Streamwise-vertical plane Horizontal plane
Time-mean flow - windvectorsRobust recirculation upstream of cube
Staggered array
Square array
No recirculation bubble behind cube
Divergence point near ground
Steady vortex in canyon
More two-dimensional in nature
Time-mean flow – pressure
Pressure on back face more uniform
Front face Back face
Side face Top face
Negative pressure on top face
Pressure drag profile
Compared with data from Cheng and Castro (2003)
Mean velocity profiles
Compared with data from Cheng and Castro (2003)
Spatially-averaged stress budget
Dispersive stress negligible above canopycf Finnigan (1985) Cheng and Castro (2003)
Dispersive stress significant within canopy
Spatially-averaged stress budget
Very large averaging times needed to average out effects of slow-evolving vortex structures (~ 400 T)
Characteristic timescale T = h / u*
50 T 400 T
Stress budget – effect of layout
Dispersive stress changes sign for aligned/square arrays
Due to recirculation (cf Poggi et al., 2004)
Reynolds and dispersive stresses
Dispersive stresses of order 1% of total stress above array
Stress measurements above array Cheng and Castro (2003)
Aligned array
Mean velocity and drag profiles
Spatially-averaged mean velocity profile
Well predicted with few sampling points
Sectional drag coefficient
Much lower for aligned/square arrays - sheltering
Much lower for staggered array
Mixing length profile
Velocity profile not exponential in canopy
Velocity profile logarithmic above canopy
Mixing length minimum at top of canopy
Blocking of eddies by shear layer
dzdU
wu
ml /
''
Conclusions• High resolution DNS of flow over cubes – excellent agreement with data
• Vortex structures both above and within array
unsteady flow very different from mean flow
• Strong shear layer at top of array
decouples flow within array from that within
• Time-mean flow structure depends on layout
vortex in canyon for aligned/square arrays
no recirculation bubble for staggered array
• Dispersive stress small above array, large within
• Log profile above arrays
• Mean flow and turbulence structure is different from plant canopies