Simulación de la calidad del aire en la isla de Gran Canaria mediante el método de los elementos finitos y

su validación con datos experimentales

A. Oliver, R. Montenegro, A. Perez-Foguet,E. Rodríguez, J.M. Escobar, G. Montero

Laboratori de Càlcul Numèric (LaCàN)Departament de Matemàtica Aplicada IIIUniversitat Politècnica de Catalunya - Barcelonatech

Instituto Universitario SIANI Ingeniería ComputacionalUniversidad de Las Palmas de Gran Canaria

Motivation

Validation of the framework proposed by the authors (Oliver et al. 2013, Energy)

Gran Canaria island (Canary Islands)

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Motivation

One emission stack (Electric power plant) 4 imission stations 3 consecutive days of emission and imission data

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Algorithm

Adaptive Finite Element ModelConstruction of a tetrahedral mesh

• Mesh adapted to the terrain using Meccano method

Wind field modeling• Horizontal and vertical interpolation from HARMONIE

data • Mass consistent computation• Calibration

Pollutant dispersion modeling• Wind field plume rise perturbation• Transport and reaction pollutant simulation• Calibration

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Mesh creation

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Meccano Method

Mesh creation

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Meccano Method

Mesh creation

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Meccano Method

Mesh creation

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Gran Canaria Mesh

Mesh creation

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Gran Canaria Mesh

Mesh creation

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Gran Canaria Mesh

Wind field modeling

Experimental data from 1 station (10 m over terrain) Use Harmonie model

Harmonie is a non-hidrostatic model U10 and V10 data from Harmonie has been used as

measure stations data Geostrophic wind from Harmonie

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Wind field modeling

Horizontal interpolation

• Weighting inverse to the squared distance and inverse height differences

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Wind field modeling

Vertical interpolation• Log-linear wind profile

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Gesostrophic wind

Mixing layer

Wind field modeling

Mass-consistent model

Lagrange multiplier

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Wind field modeling

Calibration• ε (Horizontal interpolation weight)• Tv Th (Mass consistent factors)

Genetic algorithms• G. Montero, E. Rodriguez, R. Montenegro, J.M. Escobar, J.M.

Gonzalez-Yuste, Genetic algorithms for na improved parameter estimation with local refinement of tetrahedral meshes in a wind model, Advances in Engineering Software, Volume 36, Issue 1, January 2005, Pages 3-10, ISSN 0965-9978, [DOI:10.1016/j.advengsoft.2004.03.011]

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Wind field modeling

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20 m

Plume rise modeling

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Briggs formula

• Buoyant (wc < 4Vo)• Driving-force: gas

temperature difference• Curved trajectory

• Momentum (wc > 4Vo)• Driving-force: Gas velocity• Vertical straight trajectory

Air quality modeling

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Stack outflow

Inlet wind boundaries

Outlet wind boundaries

Initial condition

Air quality modeling

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RIVAD reactive model (4 species)

Air quality modeling

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Splitting (Strang Splitting)

Rosembrock 2

J = Jacobian s(c)

Air quality modeling

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Temporal discretization: Cranck-Nicolson

Spatial discretization: Least Squares FEM

System solver: Conjugate gradient preconditioned with an Incomplete Cholesky Factorization

Matrix storage: sparse MCS

Air quality modeling

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Concentration after 1000 seconds

Air quality modeling

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Concentration after 1000 seconds

Air quality modeling

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Air quality modeling

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Calibration Diffusion (K) Time step (artificial diffusion)

Concentration SO2 at station 1

Measured data at station 1:6.35 μg

Conclusions and future work

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Suitable approach for modeling air transport and reaction over complex terrains

• A. Oliver, G. Montero, R. Montenegro, E. Rodríguez, J.M. Escobar, A. Pérez-Foguet, Adaptive finite element simulation of stack pollutant emissions over complex terrains, Energy, Volume 49, 1 January 2013, Pages 47-60, ISSN 0360-5442, http://dx.doi.org/10.1016/j.energy.2012.10.051.

Genetic algorithms useful for wind field calibration

Automatic calibration of diffusion and artificial diffusion for the transport and reaction of pollutants