Second moment modelling for the numerical simulation of passive scalar dispersion of air pollutants in urban environments [Elektronische Ressource] / vorgelegt von Rafael Izarra

Rafael Izarra

Informations

• Publié par: universitat_siegen
• Publié le: 01 janvier 2009
• Nombre de lectures: 21
• Langue: English
• Poids de l'ouvrage: 12 Mo

Extrait

Second Moment Modelling for the
Numerical Simulation of Passive
Scalar Dispersion of Air Pollutants
in Urban Environments



Dissertation
zur Erlangung des akademischen Grades
DOKTOR-INGENIEUR




vorgelegt von
MSc.-Ing. Rafael Izarra
aus Venezuela




eingereicht dem
Fachbereich Maschinenbau
der Universität Siegen




Referent: Dr.-Ing. J. Franke
Korreferent: Univ.- Prof. Dr. F. Dinkelacker



Tag der mündlichen Prüfung
18. Dezember 2009

Acknowledgments

The present work was done during my scientific fellowship in the Institut für
Fluid- und Thermodynamik of Universitaet Siegen (Germany) and financially
supported by the German Academic Exchange Service (DAAD).
I would like to express my gratitude to my two supervisors Prof. h.c. Univ.-
Prof. Dr.-Ing. habil. Wolfram Frank and Dr.-Ing. Joerg Franke. Thank you for giving
me the opportunity to work as a PhD candidate in the institute and for the support and
guidance received during my time there.
I would like to thank Prof. Dr.-Ing. Friderich Dinkelaker for his pertinent
advice and his willingness to be a co-referent of this work. Furthermore, I thank Prof.
Dr.-Ing. habil. Peter Betsch and Prof. Dr.-Ing Claus-Peter Fritzen for their assistance
during my doctoral examination.
Many thanks are due to all my colleagues and friends for the useful
discussions and suggestions as well as their technical and moral support during my
time in Siegen. They are Dr.-Ing. Thorsten Kray, Dipl.-Ing. Thomas Gora, Dipl.-Ing.
Mehdi Agami, Frau Reinhild Hoof, Dipl.-Ing Herman Geppert and others. I had a
wonderful time working together with all and every one of you.
I gratefully acknowledge DAAD for honouring me with the scholarly award
to pursue my PhD. Similarly, I would like to thank the team of COST Action 732 for
the useful material and the technical and friendly discussions.
I am also thankful to my family, especially to my parents Rafael and Yasmin,
sisters Tibisay and Tahiana, cousins, aunts and grandmothers. Their love, blessing
and stimulating words encourage me to achieve the best throughout my stay in
Germany.
This dissertation would not have been possible without the unconditional
support of my wife Elizabeth. Therefore, I dedicated this work to her and to our
daughter Victoria. Thank you for your love, constant support, patience and faith in
me. Both of you represent my main source of happiness, motivation and
achievements.
I wish God bless this book and every one of the persons who collaborate with
its realization and receive the double of successfulness.

Rafael Izarra

Summary
Since the Industrial Revolution mankind has needed to deal with increasing
air pollution problems as a result of manufacturing, mining, transportation, and power
production. Air pollution concerns the interaction of gases and particles emitted into
the atmosphere with the surrounding environment. This interaction can redirect
pollutants toward sensitive areas, concentrate different species above acceptable
levels, or even mitigate concentration levels by enhancing diffusion and dispersion.
The present EU environmental legislation has been implemented to control these high
pollutant concentrations and improve the air quality conditions in urban areas. The
numerical simulation of dispersion has shown to be a useful tool for both the
scientific description of pollution phenomena and for planning and decision making.
The numerical simulation of pollution dispersion in urban environments by
means of solution of the statistically steady Reynolds Averaged Navier Stokes
(RANS) equations is known to be strongly dependent on turbulence models. If
pollution dispersion is modelled, the turbulence models do not only have to be used
for the Reynolds stresses, but also for the turbulent scalar fluxes. While the influence
of several turbulence models for Reynolds stresses on pollution dispersion in urban
environments has already been examined several times, the turbulent scalar fluxes are
usually modelled by the simple gradient diffusion assumption. In the present work,
the influence of more advanced models for the turbulent scalar fluxes on the
dispersion of pollutants is examined. Two different wind tunnel experiments, a two-
dimensional (2D) street canyon and a three-dimensional (3D) urban area model, were
selected for the validation of the models’ performance. In total, five anisotropic
algebraic flux models and two second moment models were implemented in the
commercial software FLUENT 6.3. All these models together with the simple
gradient diffusion model (with different turbulent Schmidt numbers) are used and the
results are compared with measurements using statistical performance measures to
assess their predictive capability.
All evaluated models showed good general agreement in comparison to the
experiments. The anisotropic models provided better concentration predictions than
the isotropic models in 2D simulations. However, these improvements were very
small in 3D simulations and usually disappeared. In the end, modelling improvements
based on the sensitivity analysis of model coefficients, numerical and experimental
model limitations and other parameters and assumptions relevant for the simulation of
passive scalar pollution dispersion are presented and discussed.
Key words: Turbulent scalar fluxes, anisotropic modelling, RANS, CFD,
MUST, atmospheric dispersion, model improvement.

CONTENTS
1 INTRODUCTION ..................................................................................1
1.1 Pollution in the Environment...................................................................... 1
1.2 The Engineering Problem ........................................................................... 3
1.3 State of the Art............................................................................................. 5
1.4 Structure of the Dissertation..................................................................... 10
2 SIMULATION OF POLLUTION DISPERSION USING CFD ..............11
2.1 Governing Equations and Computer Approach ...................................... 11
2.2 Reynolds Averaged Navier-Stokes Equations .......................................... 15
2.3 Passive Contaminant Transport ............................................................... 17
2.4 Active Contaminant Transport................................................................. 18
3 CLOSURE OF FUNDAMENTAL EQUATIONS..................................21
3.1 Reynolds Stress Modelling ........................................................................ 21
3.1.1 One Equations Spalart-Allmaras model........................................ 24
3.1.2 Two Equations Models................................................................. 25
3.1.2.1 k-ε Turbulence Models ................................................................. 26
3.1.2.2 k-ω Turbulence Model ................................................................. 29
3.1.3 Differential Stress Models............................................................ 30
3.2 Passive Scalar Flux Modelling .................................................................. 34
3.2.1 Algebraic Scalar Flux Models ...................................................... 35
3.2.1.1 Isotropic Algebraic Scalar Flux Models........................................ 36
3.2.1.2 Anisotropic Algebraic Scalar Flux Models ................................... 39
3.2.2 Second Moment Models for Passive Scalars................................. 41
3.2.2.1 Pressure-Scalar Term ................................................................... 42
3.2.2.2 Turbulent Diffusion Term ............................................................ 44
3.3 Near Wall Modelling Approach................................................................ 44
3.3.1 Near-Wall Functions .................................................................... 45
3.3.2 Enhanced Wall Treatment ............................................................ 48
3.3.3 Derivation of Second Moment Boundary-Layer Flow Modelling . 51
4 NUMERICAL PROCEDURE...............................................................55
4.1 General Convection-Diffusion Transport Equation: Discretization and
Solution.................................................................................................................. 55

4.1.1 Approximation of Diffusion Terms .............................................. 57
4.1.2 Approximation of Convective Term ............................................. 58
4.1.3 Approximation of Source Terms .................................................. 61
4.2 General Solution Procedure. ..................................................................... 61
4.3 Discretization of Continuity and Momentum Equation........................... 63
4.3.1 Discretization of the Momentum Equation ................................... 64
4.3.2 Discretization of the Continuity Equation..................................... 66
4.3.3 Pressure-Velocity Coupling...................................................