Development of a Fast Physically-Based Urban Wind Flow and - - PowerPoint PPT Presentation

Development of a Fast Physically-Based Urban Wind Flow and Dispersion Model for Emergency Response Applications

Kun-Jung Hsieh1, Hua Ji1, Fue-Sang Lien2 and Eugene Yee3

1Waterloo CFD Engineering Consulting Inc., Waterloo, Ontario, Canada 2Department of Mechanical and Mechatronics Engineering, University of

Waterloo, Waterloo, Ontario, Canada

3Defence R&D Canada – Suffield, Medicine Hat, Alberta, Canada

13th International Conference on Harmonisation within Atmospheric Dispersion Modelling for Regulatory Purposes Paris, France June, 2010

Introduction

• Challenges for Prediction of Urban Dispersion

─ Difficult to predict urban dispersion due to the presence of buildings ─ Buildings result in a highly disturbed flow field that can lead to ─ Buildings result in a highly disturbed flow field that can lead to complex three-dimensional dispersion patterns of airborne contaminants in urban area ─ For many applications (e.g., emergency response) where quick turn-around time is required, predictions based on CFD building-aware modeling is too computationally expensive ─ Development of fast-response building-aware models for urban flow and dispersion is needed

Fast-Response Wind Model

• Rockle’s approach (Rockle, 1990)

─ Empirical parameterizations are used to generate an initial flow field around a group of buildings ─ Initial flow field is subsequently adjusted to satisfy mass consistency using Sherman’s method (Sherman, 1978) ─ Final mass consistent flow field (generated quickly) can be used in conjunction with turbulence parameterizations to drive urban dispersion model Initial flow field Mass consistency enforcement Empirical parameterizations Final flow field

Fast-Response Wind Model

W LF L S LR H d x y z Displacement zone Street canyon Cavity zone Wake zone 3LR Flow Field Parameterizations Displacement 2

F

L W H =

Rockle’s empirical parameterizations (rule-based schema)

Displacement zone (0 ≤ x ≤ LF, 0 ≤ y ≤ 0.6H) 2 1 0.8

F

L W H H W H = +

( )

2 2 2 2 2

1 1 0.6

F

x z W L y H + =   −   u = Street canyon Skimming flow:

*

S S <

*

1.25 0.15 2 1.55 2 W H W H S W H H + <  =  ≥ 

( )

0.5 0.5 u d S d u H S S − = −

( )

1 1 1 2 0.5 0.5 v d S d u H S S −     = − − −         Cavity zone (0 ≤ x ≤ LR, 0 ≤ y ≤ H)

( ) ( )

0.3

1.8 1 0.24

R

L W H H L H W H = +

( )

2 2 2 2 2

1 1

R

x z W L y H + =   −  

( )

2

1

N

u x u H d   = −    

( ) ( )

2 2

1 1 0.5

N R

d L y H z W L     = − − −     Wake zone (LR ≤ x ≤ 3LR, 0 ≤ y ≤ H)

( ) ( )

2 2 2 2 2

1 3 1

R

x z W L y H + =   −  

( )

1.5

1

N

u d u y x   = −    

Fast-Response Wind Model – continued

• Sherman’s method (Sherman, 1978) to enforce mass

consistency of flow field

1. Solve the Euler-Lagrange equation based on initial flow field: 2. Update initial flow field:

2 2 2 2 2 2 2 2 2 1 1 2

1 1 1 2 2 2 u v w x y z x y z λ λ λ α α α   ∂ ∂ ∂ ∂ ∂ ∂ + + = − + +   ∂ ∂ ∂ ∂ ∂ ∂  

u0, v0, w0 2. Update initial flow field:

2 2 2 1 1 2

1 1 1 , , 2 2 2 u u v v w w x y z λ λ λ α α α ∂ ∂ ∂ = + = + = + ∂ ∂ ∂

λ : Lagrange multiplier α1, α2 : weighting factors u0, v0, w0: initial flow field, does not satisfy continuity u , v , w : final flow field, satisfies continuity (∂ui/∂xi = 0) λ u, v, w

Fast-Response Wind Model - problems

• Final mass-consistent flow field has sensitive

dependence on initial flow field (and on the empirical parameterizations used for their specification)

• No proof exists of the self-consistency of the Rockle

rule-based schema for specification of initial field

T-shaped building constructed using basic

• bstacle shapes “known” to the rule-based

schema

Example:

Fast-Response Dispersion Modeling Approach

• Our proposed approach

─ A partially converged CFD flow solution (instead of empirical flow parameterizations) is used as the initial wind field ─ The mass-consistent final flow field is used as input to drive the transport equations for turbulence (e.g., turbulence kinetic energy and viscous dissipation) ─ The flow and turbulence fields are used to drive the dispersion model (Eulerian or Lagrangian) Initial flow field Mass consistency enforcement

Partially converged CFD flow solution

Final flow field

Turbulence field

(e.g., k and ε) Concentration field

Numerical Framework

• The numerical simulations were performed with

several in-house computer codes:

─ The flow codes urbanSTREAM and urbanFAST, and the (Eulerian) dispersion code urbanEU ─ The wind and turbulence fields obtained from urbanSTREAM and urbanFAST are used to drive urbanEU urbanSTREAM

• r

urbanFAST ui, k, ε urbanEU c

Application: Regular Array of Cubes

• Array of 11 by 7 cubes

H = L = W = 150 mm

• 3-D array of model buildings (Brown et al., 2001)

Model domain and computational mesh

• k-ε model with wall functions

(linear eddy viscosity)

• 130 by 22 by 40 grid nodes

(streamwise: spanwise: wall- normal)

y/H

Rows 1 and 2

Y X Z

Y/H=0.29 Row 1 Row 2

Comparison: urbanSTREAM vs urbanFAST

urbanFAST

– based on 30 iterations of urbanSTREAM

Adjustment region

• 1

1 2 3 4

Y X Z

Y/H=0.29 Row 1 Row 2

• 1

1 2 3 4

urbanSTREAM

Horizontal cross-section

X Y Z X Y Z

Comparison of urbanSTREAM vs urbanFAST

Adjustment region:

• 1

1 2 3 4

Row 1 Row 2

• 1

1 2 3 4

Row 1 Row 2

urbanFAST urbanSTREAM

Vertical cross-section through centerline of array

Y X Z

Y/H=0.29 Row 4 Row 5

Comparison of urbanSTREAM vs urbanFAST

Rows 4 and 5

urbanFAST

– based on 30 iterations of urbanSTREAM 5 6 7 8 9 10

Y X Z

Y/H=0.29 Row 4 Row 5

X

5 6 7 8 9 10

Equilibrium region

urbanSTREAM

Horizontal cross-section

X Y Z X Y Z

Comparison of urbanSTREAM vs urbanFAST

Equilibrium region:

5 6 7 8 9 10

Row 4 Row 5

5 6 7 8 9 10

Row 4 Row 5

urbanFAST urbanSTREAM

Vertical cross-section through centerline of array

Application: Mock Urban Setting Trial

• Test case:

─ Mock Urban Setting Trial (MUST) water channel experiment (Hilderman and Chong, 2004)

Ub

• The predicted results from urbanFAST are compared to

urbanSTREAM and to experimental data

y x z

Simulation Approaches

• urbanSTREAM

─ Full CFD model

• urbanFAST-40

─ urbanFAST with the initial flow field obtained from urbanSTREAM after it has been run for 40 iterations from

15

urbanSTREAM after it has been run for 40 iterations from scratch

• urbanFAST-80

─ urbanFAST with the initial flow field obtained from urbanSTREAM after it has been run for 80 iterations from scratch

Computational Efficiency

• Table summarizes the CPU time required for urbanSTREAM,

urbanFAST-40(80) to obtain final solutions, where these CPU times are normalized by the CPU time of urbanSTREAM

• CPU times are based on the flow solutions obtained in a

computational domain of 97.6L × 8.3L × 21L (where L is the

• bstacle length) with 203 × 43 × 45 control volumes (in the
• bstacle length) with 203 × 43 × 45 control volumes (in the

streamwise, spanwise, and wall-normal directions, respectively) Normalized CPU Time

urbanSTREAM 1 urbanFAST-80 0.3 urbanFAST-40 0.18

Streamwise Mean Velocity

• The difference between three flow solvers is relatively small

200 250 Expt urbanSTREAM

3.5 row

200 250

9.5 row

source 3.5 row 9.5 row Flow

U (m/s) Z (mm)

• 0.1

0.1 0.2 0.3 0.4 50 100 150 200 urbanSTREAM urbanFAST-80 urbanFAST-40

U (m/s) Z (mm)

• 0.1

0.1 0.2 0.3 0.4 50 100 150 200

Streamwise Root-Mean-Square Velocity

• All flow solvers under-predict the streamwise rms velocity

200 250 Expt urbanSTREAM

3.5 row

200 250

9.5 row

source 3.5 row 9.5 row Flow

u'rms (m/s) Z (mm)

0.025 0.05 0.075 0.1 50 100 150 200 urbanSTREAM urbanFAST-80 urbanFAST-40

u'rms (m/s) Z (mm)

0.025 0.05 0.075 0.1 50 100 150 200

Urban Dispersion (urbanFAST-40/urbanEU)

Adapted from: Macdonald and Ejim, “Hydraulic Modeling of Flow and Dispersion in the MUST Array” (6th GMU Modeling Workshop, July 2002)

Horizontal Mean Concentration at z = 1.50H

• The solvers tend to over-estimate the peak mean concentration

value and under-predict the lateral plume spread

0.0008

9.5 row

0.0008

Expt urbanSTREAM urbanFAST-80

3.5 row

source 3.5 row 9.5 row Flow

y (mm) c/cs

• 200 -150 -100 -50

50 100 150 200 0.0002 0.0004 0.0006

9.5 row Z=1.5H

y (mm) c/cs

• 150
• 100
• 50

50 100 150 0.0002 0.0004 0.0006

urbanFAST-80 urbanFAST-40

3.5 row Z=1.5H

Application to Real Cityscape (Vancouver)

• resolve all buildings in downtown Vancouver in 10.4 km2 area
• 10.1 million grid nodes with horizontal resolution of 9 m
• parallel computational platform using 16 processors
• computational time for urbanSTREAM (12.4 h) vs urbanFAST (13.5 min)

Application to Real Cityscape (Vancouver)

Mean Streamline Flow Patterns around BC Place Stadium urbanSTREAM urbanFAST-40

Conclusions

• Alternative methodology for fast-response urban flow

and dispersion modeling has been investigated

• Predictive performance of approach, in terms of the

predictions of the mean flow, turbulence and mean predictions of the mean flow, turbulence and mean concentrations, is comparable to conventional CFD model

• Approach requires considerably less computational

time than that of conventional CFD model