MATHEMATICAL MODELLING OF DISPERSION OF AIR POLLUTANTS IN LOW WIND CONDITIONS

Transcription

1 MATHEMATICAL MODELLING OF DISPERSION OF AIR POLLUTANTS IN LOW WIND CONDITIONS by ANIL KUMAR YADAV Thesis submitted to the Indian Institute of Technology, Delhi for the award of the degree of DOCTOR OF PHILOSOPHY Centre for Atmospheric Sciences INDIAN INSTITUTE OF TECHNOLOGY, DELHI NEW DELHI , INDIA FEBRUARY, 1995

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3 CERTIFICATE This is to certify that the thesis entitled "MATHEMATICAL MODELLING OF DISPERSION OF AIR POLLUTANTS IN LOW WIND CONDITIONS" being submitted by Mr. Anil Kumar Yadav to the Indian Institute of Technology, Delhi for the award of the degree of DOCTOR OF PHILOSOPHY, is a record of the original bonafide research work carried out by him. Mr. Yadav has worked under my guidance and supervision and has fulfilled the requirements for the submission of this thesis. The results contained in this thesis have not been submitted in part or full to any other University or Institute for the award of any degree or diploma. MAITHILI SHARAN) Centre for Atmospheric Sciences, Indian Institute of Technology, Delhi, New Delhi , INDIA

4 ACKNOWLEDGEMENTS I would like to express my deep sense of gratitude to Dr. Maithili Sharan for his invaluable guidance and whole-hearted supervision through out the tenure of this work. His painstaking efforts and immense care in. going through the manuscript are gratefully acknowledged. It is a matter of great pride to express my profound reverence and warmest regards to Prof. M.P. Singh for his noble guidance, enormous encouragement and kind insipiration. His probing insight was of crucial importance during the course of this study. I wish to express my deepest gratitude to Prof. Sethu Raman, North Carolina State University, USA for his encouragement and motivation. His help in the turbulence and spectral analysis is gratefully acknowledged. I am highly thankful to Dr. P.C. Sinha, Head, Centre.for Atmospheric Sciences for providing the nece.ssary,facilities.fbr early* out the present research work. Thanks are also due to faculty and stuff of the Centre pr Atmospheric Sciences for their help and encouragement. I am deeply obliged to Dr. (Mrs.) P. Goyallbr her whole-hearted encouragement and cooperation. at eve)), stage. My sincere thanks are due to all members of the Air Pollution Group, in particular, Dr. (Mrs.) Manju Mohan, Dr. (Ma.) P. Agarwal, Dr. (Mrs.) S. Nigam and Dr.T.S. Panwar. I would like to express my sincere thanks to Dr. 0. P. Sharma, Dr. G. Jayaraman and Dr. Jagpal Singh pr the moral support and genuine advice they provided at various stages. I owe my special thanks to Amita who gladly offered eve))) help throughout this work. It is my pleasure to acknowledge Sangeeta's true motivation which was immensely useful, especially when I needed it most. I wish to express my hearty thanks to my friends Dr. R.S. Adhikari, Subhash Gaur, Rajiv Joshi, Dr. R. K. Srivastav, Mr. D.P. Sharma (coach-cum-friend), Prabhakar Rao and Beer Singh with whom I shared my joys and sorrows and their warm company which made my stay at 1.1. T. pleasant and memorable. I extend my sincere appreciation to Gopalakrislmart, Rajesh Prakash, Ranjan and Promila for their nice company and active cooperation.. Last but not the least, I am highly indebted to my sister, brothers, bhabhi and other family members for their everlasting love, encouragement and assistance through out. [Anil Kumar Yadav]

5 ABSTRACT The importance of dispersion modelling in low wind conditions lies in the fact that these conditions occur frequently and are crucial for air pollution episodes. The first chapter of the thesis provides the general introduction including some basic concepts of dispersion modelling with special reference to low wind conditions. The understanding of turbulence structure which is quite important for dispersion modelling is inadequate for weak wind situations. Therefore, the spectral characteristics including the eddy dissipation rate of surface-layer turbulence have been studied in the second chapter using the turbulence data collected at IIT Delhi micrometeorological tower. In low wind conditions, the downwind diffusion which is neglected in most of the dispersion models may be comparable with the advection. Therefore, a steady-state mathematical model accounting for downwind, crosswind and vertical diffusion besides the advection has been described in the third chapter. It is validated with the tracer data collected at the IIT Delhi sports ground. The use of conventional methods for estimating dispersion parameters in low wind conditions becomes questionable because of their limited applicability. Thus, various sigma schemes for dispersion parameters have been studied through intercomparison in the fourth chapter using the data collected by the U.S. NOAA in low wind stable conditions. A steady-state mathematical model has been formulated in the fifth chapter by taking linear variation of diffusivities with downwind distance, following Taylor's statistical theory for near-source diffusion. Analytical solution for the resulting advection-diffusion equation with the physically relevant boundary conditions has been obtained using Integral transforms. The model has been validated with the data tor stable as well as convective conditions. The dispersion conditions in weak winds (particularly stable atmosphere) are generally non-stationary and non-homogeneous and thus can not be treated suitably by the models described in the earlier chapters. Therefore, a time-dependent mathematical model based on coupled plume segment and Gaussian puff approaches has been described in the sixth chapter to treat non-stationary and non-homogeneous dispersion from a point source. The model involves representation of a plume by a series of contiguous puffs.

6 CONTENTS Certificate Acknowledgements Abstract List of Figures Chapter 1 GENERAL INTRODUCTION 1.1 Introduction Dispersion Modelling General Governing Equations Types of Emission Sources and Source Geometries Turbulent Eddy Diffusivities Puff and Plume Diffusion Puff Approach Plume Approach Dispersion Parameters Plume Rise Low Wind Dispersion General Characteristics Plume Meandering Turbulent Energy Spectra Turbulence and Diffusion Estimation of Dispersion Parameters Dispersion Modelling Approaches Present Work 29 Chapter 2 TURBULENCE AND SPECTRAL CHARACTERISTICS OF SURFACE LAYER DURING LOW WIND CONDITIONS 2.1 Introduction Elements of Spectral Analysis of Atmospheric Motions Scales of Atmospheric Motions General Characteristics of Turbulent Energy Spectrum Integral Scales of Atmospheric Turbulent Flows Fourier Transform and Energy Spectrum Spectral Analysis of Low Wind Near-Surface Data Description of Data Spectra Normalized by Friction Velocity Spectra Normalized by Variance Estimation of Length Scales 47

7 Turbulent Kinetic Energy and Eddy Dissipation 50 Summary and Conclusions 53 Chapter 3 A MATHEMATICAL MODEL FOR THE DISPERSION OF AIR POLLUTANTS IN LOW WIND CONDITIONS 3.1 Introduction Model Formulation Boundary Conditions Method of Solution Slender Plume Approximation Comparison with the Traditional Approach Parameterization of Eddy Diffusivities Experimental Setup for Validation Model Parameters Results and Discussion Validation Concentration Distribution Limitations and Possible Improvements Conclusions 72 Chapter 4 A MATHEMATICAL MODEL FOR AN ELEVATED SOURCE: COMPARISON OF VARIOUS SIGMA SCHEMES FOR ESTIMATING DISPERSION PARAMETERS IN LOW WINDS 4.1 Introduction Input Data Description Governing Equations and Solution Description of Sigma Schemes Qualitative Analysis Quantitative Analysis Description of Statistical Measures Methodology Performance for Peak Concentration Performance for Overall Concentration Distribution Summary and Conclusions 100

8 Chapter 5 A VARIABLE K-THEORY BASED MATHEMATICAL MODEL FOR NEAR-SOURCE DISPERSION IN LOW WIND CONDITIONS 5.1 Introduction Model Formulation Method of Solution Slender Plume Approximation Parameterization Results and Discussion Stable Conditions Convective Conditions Summary and Conclusions 126 Chapter 6 A TIME-DEPENDENT MATHEMATICAL MODEL BASED ON COUPLED PLUME SEGMENT AND GAUSSIAN PUFF APPROACHES 6.1 Introduction Setting the Objective Diffusion Model Methodology Results and Discussion Qualitative Analysis Statistical Evaluation Conclusions 140 REFERENCES 141 Bio-data List of Publications