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Uncertainty quantification of inflow on passive scalar dispersion in an urban environment

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Abstract

Risk assessment, city planning, and emergency response are a few examples of potential applications of numerical simulations of scalar dispersion in urban environments. The complex flow fields and scalar dispersion are determined by the building layout and prevailing meteorological conditions that are highly uncertain. While the fidelity of a numerical model is important in providing an accurate prediction of flow and scalar fields, propagating the uncertain input through numerical models is imperative in those applications. However, it is uncommon to quantify input uncertainties due to expensive computational cost of high fidelity simulations such as large eddy simulations (LES) and Reynolds-averaged Navier–Stokes (RANS). In this work, the uncertain meteorological quantities viz., wind speed and its direction from field measurements are taken as inputs to RANS simulations that use realizable \(k-\varepsilon\) turbulence model, to investigate their effects on passive scalar dispersion in central London. The mean wind and scalar quantities from RANS are initially validated with wind-tunnel data and compared to large eddy simulations (LES). For comparison with field measurements, the deduced probability density function (pdf) for wind speed and direction from the field are used as inputs for RANS simulations. For a 3-min averaged concentration at a specific receiver location, LES with unsteady wind inputs showed better performance than LES with mean wind input and RANS whereas for 30-min averaged concentration at various receiver locations, performance measures indicated that RANS is better than LES. The latter certainly suggests the importance of considering such uncertainties. The flow variability in every street is quantified using RANS simulations. This demonstrated that approximations used in a fast, low-order street network model may not be necessarily valid for every street of heterogeneous urban canopies, which in turn affects scalar prediction.

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Ddata availability

The data will be provided upon request.

Code availability

The code used is opensource software.

Abbreviations

C :

Concentration of scalar

\(C^*\) :

Normalised scalar concentration

h :

Building height

\(h_m\) :

Mean building height

k :

Turbulent kinetic energy

\(k_m\) :

Molecular diffusivity

\(k_t\) :

Turbulent diffusivity

\(M_\ell\) :

Reference mesh where \(\ell =0,1,2\) in increasing order of mesh resolution

\(\mathcal {N}\) :

Sample size

p :

Pressure

\(Q_S\) :

Volumetric source

\(R_n\) :

Receiver locations

s :

Street index

\(S_m\) :

Source locations

\(Sc_m\) :

Molecular Schmidt number

\(Sc_t\) :

Turbulent Schmidt number

t :

Time

\(\textbf{u}\) :

Velocity magnitude

\(u_*\) :

Surface friction velocity

\(u_d\) :

Bulk exchange mass velocity

\(\textbf{u}_{BT}\) :

\(\textbf{u}\) at BT tower height

\(\textbf{u}_{hm}\) :

\(\textbf{u}\) at mean building height

\(\textbf{u}_{ref}\) :

\(\textbf{u}\) at reference height

\(\textbf{u}_{s}\) :

Street channel velocity

\(\textbf{u}_{zmax}\) :

\(\textbf{u}\) at free stream height

\(\mathcal {V}_s\) :

Volume of street canyon, s

z :

Vertical coordinate or height from ground

\(z_0\) :

Aerodynamic roughness length

\(\epsilon\) :

Mesh convergence error

\(\varepsilon\) :

Turbulence dissipation rate

\(\kappa\) :

Von Karman constant

\(\nu\) :

Kinematic viscosity

\(\nu _t\) :

Turbulent viscosity

\(\rho\) :

Density

\(\sigma _w\) :

Standard deviation of the vertical velocity at roof level

\(\sigma _{\phi _{s}}\) :

Standard deviation of \(\langle \phi \rangle _{s}\) from \(\overline{\phi }_{s}\)

\(\varsigma _{s}\) :

Standard deviation of velocity magnitude in street s

\(\phi _{s}\) :

Velocity component of street, s where \(\phi = u,v,w\)

\(\overline{\varsigma }_{s}\) :

Ensemble average of \(\varsigma _{s}\)

\(\langle \phi \rangle _{s}\) :

Volume average of \(\phi_{s}\)

\(\overline{\phi }_{s}\) :

Ensemble average of \(\phi _{s}\)

\(\omega\) :

Specific dissipation rate

ANOVA:

Analysis of variance

BT:

British Telecom

CFD:

Computational fluid dynamics

CI:

Confidence interval

ClearfLo:

Clean Air for London

DNS:

Direct numerical simulations

LBM:

Lattice Boltzmann method

LES:

Large eddy simulations

LiDAR:

Light Detection and Ranging

MRI:

Magnetic resonance imaging

NAD:

Normalised absolute difference

NMSE:

Normalised mean square error

pdf:

Probablity density function

POD:

Proper orthogonal decomposition

QoI:

Quantities of interest

RANS:

Reynolds-Averaged Navier–Stokes

SDG:

Sustainable Development Goals

UQ:

Uncertainty quantification

VLES:

Very large eddy simulations

WCC:

Westminster City Council

AERMOD:

American Meteorological Society/Environmental Protection Agency Regulatory Model

CALPUFF:

California puff model

Dakota:

Design Analysis Kit for Optimization and Terascale Applications

DAPPLE:

Dispersion of air pollution and its penetration into the local environment

EPSRC:

Engineering and physical sciences research council

QUIC:

Quick Urban and Industrial Complex

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Acknowledgements

The authors would like to thank Dr. Zheng-Tong Xie of University of Southampton, U.K. and Prof. Alan G Robins of University of Surrey, U.K. for sharing DAPPLE geometry information.

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Author notes

  1. Vinh-Tan Nguyen, Daniel J. Wise and Jason Yu Chuan Leong have equally contributed to this work.

Authors and Affiliations

  1. Institute of High Performance Computing (IHPC), Agency for Science, Technology and Research (A*STAR), 1 Fusionopolis Way, #16-16 Connexis, 138632, Singapore, Republic of Singapore

    Bharathi Boppana, Vinh-Tan Nguyen, Daniel J. Wise & Jason Yu Chuan Leong

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  1. Bharathi Boppana
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Contributions

BB: Conceptualization, Simulation, Data analysis, Methodology, Writing—draft, review & editing. VTN: Conceptualization, Methodology, Data analysis discussions, Writing—review & editing. DW: Geometry creation, Data analysis discussions, Writing—review. JL: Dakota testing, Data analysis discussion, Writing—review & editing.

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Correspondence to Bharathi Boppana.

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Appendix A Coordinates of source and receiver locations

Appendix A Coordinates of source and receiver locations

Table 3 The coordinates of the source and receiver locations shown in Fig. 2
Full size table

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Boppana, B., Nguyen, VT., Wise, D.J. et al. Uncertainty quantification of inflow on passive scalar dispersion in an urban environment. Environ Fluid Mech 23, 661–687 (2023). https://doi.org/10.1007/s10652-023-09927-z

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