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 Hsieh 1 , Hua Ji 1 , Fue-Sang Lien 2 and Eugene Yee 3 1 Waterloo CFD Engineering Consulting Inc., Waterloo, Ontario, Canada 2 Department of Mechanical and Mechatronics Engineering, University of Waterloo, Waterloo, Ontario, Canada 3 Defence 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 Mass consistency Initial flow field Final flow field enforcement Empirical parameterizations

Fast-Response Wind Model z W Rockle’s empirical y parameterizations x d H (rule-based schema) L F S L R L Displacement Street Cavity Wake zone canyon zone zone 3L R Flow Field Parameterizations L L W H W H 2 2 = + = F F Displacement Displacement H W H 1 0.8 zone u = 0 x z (0 ≤ x ≤ L F , 2 2 0 + = 1 ( ) 0 ≤ y ≤ 0.6 H )   W − 2 L y H 2 2 1 0.6   F < S S * − u d S d Skimming flow: = − 0 ( ) u H S S 0.5 0.5 + <  W H W H 0 S * 1.25 0.15 2 Street canyon =  − v  d   S d  1 1 ≥ = − − − H W H 0      1.55 2 1 ( ) u H  S   S  2 0.5 0.5 0 L W H 1.8 = R 2   u x ( ) ( ) H = − 0.3 + L H W H 0   Cavity zone 1 1 0.24 ( ) u H d   (0 ≤ x ≤ L R , N 0 x z 2 2 + = 0 ≤ y ≤ H ) ( ) ( ) 1     = − 2 − 2 − d L y H z W L  ( )  W 1 1 0.5 2 − 2     L y H 2 N R 1   R Wake zone x z 2 2 1.5 u  d  + = 1 ( L R ≤ x ≤ 3 L R , = − N 0  1  ( )  ( )  W ( ) 2 L 2 − y H 2 u y  x  3 1   0 ≤ y ≤ H ) R 0

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:   ∂ λ ∂ λ ∂ λ ∂ ∂ ∂ u v w 2 2 2 1 1 1 + + = − + + 0 0 0 u 0 , v 0 , w 0   α ∂ α ∂ α ∂ ∂ ∂ ∂ x y z x y z 2 2 2 2 2 2   2 2 2 1 1 2 2. 2. Update initial flow field: Update initial flow field: λ ∂ λ ∂ λ ∂ λ 1 1 1 = + = + = + u u v v w w , , α ∂ α ∂ α ∂ 0 x 0 y 0 z 2 2 2 2 2 2 1 1 2 u , v , w λ : Lagrange multiplier α 1 , α 2 : weighting factors u 0 , v 0 , w 0 : initial flow field, does not satisfy continuity u , v , w : final flow field, satisfies continuity ( ∂ u i / ∂ x i = 0)

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 Example: obstacle shapes “known” to the rule-based schema

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) Mass consistency Initial flow field Final flow field enforcement Turbulence field Partially converged ( e.g., k and ε ) CFD flow solution 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 or u i , k , ε c urbanEU urbanFAST

Application: Regular Array of Cubes • 3-D array of model buildings (Brown et al., 2001) • Array of 11 by 7 cubes H = L = W = 150 mm Model domain and computational mesh • k- ε model with wall functions (linear eddy viscosity) • 130 by 22 by 40 grid nodes y/H (streamwise: spanwise: wall- normal)

Comparison: urbanSTREAM vs urbanFAST Z – based on 30 iterations of urbanSTREAM urbanFAST Y X Y/H=0.29 Row 1 Row 2 Rows 1 and 2 -1 0 1 2 3 4 Z urbanSTREAM Y X Y/H=0.29 Adjustment region Row 1 Row 2 Horizontal cross-section -1 0 1 2 3 4

Comparison of urbanSTREAM vs urbanFAST Adjustment region: Y Y Z X Z X Row 1 Row 2 Row 1 Row 2 -1 0 1 2 3 4 -1 0 1 2 3 4 urbanFAST urbanSTREAM Vertical cross-section through centerline of array

Comparison of urbanSTREAM vs urbanFAST – based on 30 iterations of urbanSTREAM Z urbanFAST Y X Y/H=0.29 Rows 4 and 5 Row 4 Row 5 5 6 7 8 9 10 Z urbanSTREAM Y X Equilibrium region Y/H=0.29 X Row 4 Row 5 Horizontal cross-section 5 6 7 8 9 10

Comparison of urbanSTREAM vs urbanFAST Equilibrium region: Y Y Z X Z X Row 4 Row 5 Row 4 Row 5 5 6 7 8 9 10 5 6 7 8 9 10 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) U b z y x • The predicted results from urbanFAST are compared to urbanSTREAM and to experimental data

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 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 15

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 97.6 L × 8.3 L × 21 L (where L is the obstacle length) with 203 × 43 × 45 control volumes (in the obstacle 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 source 3.5 row 9.5 row Flow 3.5 row 9.5 row 250 250 Expt urbanSTREAM urbanSTREAM 200 200 200 200 urbanFAST-80 urbanFAST-40 150 150 Z (mm) Z (mm) 100 100 50 50 0 0 -0.1 0 0.1 0.2 0.3 0.4 -0.1 0 0.1 0.2 0.3 0.4 U (m/s) U (m/s)

Streamwise Root-Mean-Square Velocity • All flow solvers under-predict the streamwise rms velocity source 3.5 row 9.5 row Flow 3.5 row 9.5 row 250 250 Expt urbanSTREAM urbanSTREAM 200 200 200 200 urbanFAST-80 urbanFAST-40 150 150 Z (mm) Z (mm) 100 100 50 50 0 0 0 0.025 0.05 0.075 0.1 0 0.025 0.05 0.075 0.1 u' rms (m/s) u' rms (m/s)

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 source 3.5 row 9.5 row Flow Expt 0.0008 0.0008 urbanSTREAM 3.5 row 3.5 row 9.5 row 9.5 row urbanFAST-80 urbanFAST-80 Z=1.5H Z=1.5H urbanFAST-40 0.0006 0.0006 c/c s c/c s 0.0004 0.0004 0.0002 0.0002 0 0 -150 -100 -50 0 50 100 150 -200 -150 -100 -50 0 50 100 150 200 y (mm) y (mm)

Application to Real Cityscape (Vancouver) • resolve all buildings in downtown Vancouver in 10.4 km 2 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