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: o.coceal@reading.ac.uk

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