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-1 1001 6, INDIA FEBRUARY, 1995
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-110016, INDIA
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]
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.
CONTENTS Certificate Acknowledgements Abstract List of Figures Chapter 1 GENERAL INTRODUCTION 1.1 Introduction 1 1.2 Dispersion Modelling 2 1.3 General Governing Equations 5 1.4 Types of Emission Sources and Source Geometries 8 1.5 Turbulent Eddy Diffusivities 9 1.6 Puff and Plume Diffusion 10 1.6.1 Puff Approach 11 1.6.2 Plume Approach 13 1.7 Dispersion Parameters 14 1.8 Plume Rise 17 1.9 Low Wind Dispersion 17 1.9.1 General Characteristics 18 1.9.2 Plume Meandering 20 1.9.3 Turbulent Energy Spectra 22 1.9.4 Turbulence and Diffusion 23 1.9.5 Estimation of Dispersion Parameters 24 1.9.6 Dispersion Modelling Approaches 25 1.10 Present Work 29 Chapter 2 TURBULENCE AND SPECTRAL CHARACTERISTICS OF SURFACE LAYER DURING LOW WIND CONDITIONS 2.1 Introduction 31 2.2 Elements of Spectral Analysis of Atmospheric Motions 32 2.2.1 Scales of Atmospheric Motions 33 2.2.2 General Characteristics of Turbulent Energy Spectrum 34 2.2.3 Integral Scales of Atmospheric Turbulent Flows 35 2.2.4 Fourier Transform and Energy Spectrum 36 2.3 Spectral Analysis of Low Wind Near-Surface Data 38 2.3.1 Description of Data 39 2.3.2 Spectra Normalized by Friction Velocity 41 2.3.3 Spectra Normalized by Variance 46 2.3.4 Estimation of Length Scales 47
2.4 2.3.5 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 55 3.2 Model Formulation 56 3.3 Boundary Conditions 57 3.4 Method of Solution 57 3.5 Slender Plume Approximation 60 3.6 Comparison with the Traditional Approach 61 3.7 Parameterization of Eddy Diffusivities 63 3.8 Experimental Setup for Validation 64 3.9 Model Parameters 65 3.10 Results and Discussion 66 3.10.1 Validation 66 3.10.2 Concentration Distribution 69 3.11 Limitations and Possible Improvements 71 3.12 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 74 4.2 Input Data Description 76 4.3 Governing Equations and Solution 77 4.4 Description of Sigma Schemes 80 4.5 Qualitative Analysis 84 4.6 Quantitative Analysis 88 4.6.1 Description of Statistical Measures 88 4.6.2 Methodology 91 4.6.3 Performance for Peak Concentration 93 4.6.4 Performance for Overall Concentration Distribution 97 4.7 Summary and Conclusions 100
Chapter 5 A VARIABLE K-THEORY BASED MATHEMATICAL MODEL FOR NEAR-SOURCE DISPERSION IN LOW WIND CONDITIONS 5.1 Introduction 103 5.2 Model Formulation 104 5.3 Method of Solution 106 5.4 Slender Plume Approximation 109 5.5 Parameterization 111 5.6 Results and Discussion 112 5.6.1 Stable Conditions 113 5.6.2 Convective Conditions 121 5.7 Summary and Conclusions 126 Chapter 6 A TIME-DEPENDENT MATHEMATICAL MODEL BASED ON COUPLED PLUME SEGMENT AND GAUSSIAN PUFF APPROACHES 6.1 Introduction 129 6.2 Setting the Objective 130 6.3 Diffusion Model 132 6.4 Methodology 135 6.5 Results and Discussion 136 6.5.1 Qualitative Analysis 136 6.5.2 Statistical Evaluation 138 6.6 Conclusions 140 REFERENCES 141 Bio-data List of Publications