The Effect Of Wind And Turbulence On Sound Propagation In .
The effect of wind and turbulence on sound propagation inthe atmosphereAndré Filipe Garcia Peixoto de OliveiraDissertação para obtenção do Grau de Mestre emEngenharia AeroespacialJúriPresidente:Doutor Fernando José Parracho LauOrientador:Doutor João Manuel Gonçalves de Sousa OliveiraVogais:Doutor Pedro da Graça Tavares Alvares SerrãoMaio 2012
ACKNOWLEDGEMENTSI would like to begin by thanking my advisor Professor João Oliveira, for the opportunity of workingwith him and for his patience, understanding and availability while advising me in my work.I would also like to express my gratitude to my Family, whose support and love have carried methroughout my Masters degree and will, undoubtedly, continue to do so throughout the rest of my life.Finally, to my colleagues and friends, whose friendship was important to the conclusion of myMasters degree, I thank you all.i
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ABSTRACTIn the last years, societies growing environmental and health conscience, obliged the nationalauthorities to reinforce existing legislation concerning the maximum permissible noise levels. Thesenew demands lead to increasingly accurate tools to perform noise analysis, not only because theymust include a growing number of parameters that influence its propagation, thus with morecomplexity, but also with more flexibility, quick and easy use and less computational effort.This dissertation, after presenting the several existing numerical methods to evaluate the soundpropagation and its intrinsic limitations, describes the acoustic wave equation resolution method, usinga Green function. Since the focus of this work is to develop a numerical application, which allowsincorporating the wind and turbulence effects on sound propagation in the atmosphere, was created aC language numerical program. It includes input and output interfaces which ease the analysis of thereferred effects variations on sound propagation.The numerical program validation was achieved not only by comparing its results with exactnumerical methods, but also by using numerical approaches with known accuracy and with resultsfrom experimental measurements. The program was applied to an airport by using realisticparameters. The coherent results obtained confirmed that the program developed is numericallyaccurate and its user interface is suitable and can be, easily and effectively, used to evaluate theeffects of wind and turbulence on sound in the vicinity of an airport.Keywords: sound propagation, wind, turbulence, noise, sound refraction, shadow zone.iii
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RESUMONos últimos anos, crescentes preocupações ambientais e de saúde, obrigaram as autoridadesnacionais a reforçar a legislação existente referente aos níveis máximos de ruído admissíveis. Estasexigências conduzem à necessidade de dispor de ferramentas mais precisas de análise de ruído, porum lado mais complexas, por terem de incluir o maior número possível de parâmetros quecondicionam a sua propagação, por outro lado mais flexíveis, de rápida e fácil ultilização e com maiorrapidez de cálculo.A presente dissertação, após apresentar os vários métodos númericos existentes para aavaliação da propagação do som e as suas limitações intrínsecas, descreve o método de resoluçãoda equação geral do som por intermédio de uma função de Green. Sendo o objectivo deste trabalhodesenvolver uma aplicação numérica que permitisse incorporar o efeito do vento e da turbulência napropagação do som, foi desenvolvido um programa em linguagem C. Este dispõe de interfaces deentrada e saída de dados, que facilitam a análise da variação de ambos os efeitos.A validação numérica da aplicação foi efectuada, quer por comparação com métodos numéricosexactos, quer usando aproximações numéricas de precisão conhecida, quer ainda, por comparaçãocom resultados de medições experimentais. O programa foi aplicado à situação de um aeroportousando parâmetros realistas e a coerência dos resultados obtidos confirmou a sua precisão numéricae que a interface é adequada e pode ser, fácil e eficazmente, usada para avaliar o efeito do vento eda turbulência no som, nas proximidades de um aeroporto.Palavras Chave:propagação do som,vento, turbulência, ruído, refracção do som, região desombra.v
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CONTENTSAcknowledgements .iAbstract . iiiResumo .vContents . viiList of Figures . xiList of Tables . xvList of Acronyms and Symbols . xvii1Introduction . 11.1Background. 11.2Motivation . 11.3Outline . 22Background on sound propagation . 32.1Atmospheric Acoustics . 32.2Sound propagation in a homogeneous atmosphere . 42.2.1Geometrical spreading . 42.2.2Atmospheric absorption . 52.2.3Ground interaction . 62.3Sound propagation in an inhomogeneous atmosphere. 82.3.1Atmospheric refraction . 82.3.2Atmospheric turbulence . 102.4Numerical models . 112.4.1Fast Field Program (FFP) . 112.4.2Parabolic equation method . 122.4.3Ray Model . 153Theoretical Formulation . 173.1Inhomogeneous Helmholtz equation . 173.2Kirchhoff-Helmholtz integral equation. 183.3General Green's function method . 20vii
3.4Constant sound speed profile . 213.5Non-constant sound speed profile . 233.6Atmospheric Turbulence . 253.6.1Atmospheric model . 253.6.2Gaussian and von Kármán spectral density . 263.6.3Turbulent phase factor . 273.6.4Refractive-index fluctuations . 294Numerical implementation . 314.1Green's function parabolic equation method . 314.1.1Starting field . 314.1.2Discretization of the Fourier integrals . 324.1.3Fast Fourier Transform . 344.2GFPE method: additional functions . 344.2.1Artificial absorption layer . 344.2.2Window function . 364.2.3Alternate refraction factor . 384.2.4Pseudorandom number generator. 394.3Program description . 404.3.1User interface . 414.3.2Input files . 424.3.3Simulation calculation . 424.3.4Output files . 435Analysis and results . 475.1Benchmark test cases . 475.2GFPE method validation . 495.2.1Non-refracting atmosphere . 505.2.2Refracting atmosphere . 515.3Turbulence analysis and results . 555.3.1Turbulence numerical parameters . 555.3.2Experimental test cases . 575.3.3Comparison of theory and experiment . 59viii
6Program application to an airport . 636.1Wind and temperature profiles . 636.2Meteorological parameters . 656.3Simulation parameters . 686.4Effect of atmospheric turbulence on sound propagation . 696.5Effect of wind on sound propagation . 726.6Airport scenario simulation: case studies . 746.7Program application to an airport: conclusion notes . 777General conclusions and future developments . 798References . 81ix
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LIST OF FIGURESFigure 2.1 - Outdoor sound propagation basic geometry . 3Figure 2.2 - Schematic diagram for spherical spreading (left) and cylindrical spreading (right) [Piercy,et al., (1977)] . 5Figure 2.3Absorption coefficientin dB/100m as a function of frequency, calculated for aotemperature of 20 C, relative humidity of 70 % and a pressure of 1 atm [Piercy, et al.,1977]. . 6Figure 2.4 Reflection of a sound wave on a flat reacting ground surface . 7Figure 2.5 Variation of temperature with height; examples of lapse (solid line) and inversion (dashedline) conditions from [Munn, (1966)] . 8Figure 2.6 Top: illustration of downward refraction of sound. Bottom: illustration of upward refraction ofsound [Piercy, et al., (1977)]. . 9Figure 2.7 Top: Illustration of laminar flow. Bottom: Illustration of turbulent flow . 11Figure 2.8 - Representation of a stratified atmosphere for the FFP method, where each layer has itsown wave numberFigure 2.9 - Grid on the[Salomons, (2001)]. . 12plane used in the two dimensional PE models [Salomons, (2001)]. . 13Figure 2.10 - Representation of the angular limitation of the PE method. . 13Figure 3.1 - Example of a geometry for the Kirchhoff-Helmholtz integral . 18Figure 3.2 - Geometry for the two-dimensional Kirchhoff-Helmholtz integral . 20Figure 4.1 - Two-dimensional complete plots using the simulation parameters from test case B1 (Table5.6), with an absorption layer ofm. . 35Figure 4.2 - Summand of the inverse Fourier transform in relation to the wave number. 37Figure 4.3 - Summand of the inverse Fourier transform in relation to the wave numberwith thewindow function apllied. . 37Figure 4.4 - Cumulative sum of equation (4.15), the blue line has the window function active and in thered line the window function is not applied. . 38Figure 4.5 - Real and imaginary part of. The red line represents the window function active, while inthe blue line the window function is not applied. . 38Figure 4.6 - Flow chart illustration of the computational program . 40Figure 4.7 - Home screen interface . 41Figure 4.8 - Input file example. . 42Figure 4.9 - Schematic representation off the computational grid. 43Figure 4.10 - Left image represents one-dimensional graph. Right image represents two-dimensionalgraph. . 44Figure 4.11 - One-dimensional output file of the example test case displayed in Figure 4.8 . 45Figure 4.12 - A portion of the two-dimensional output file of the example test case with parametersfrom Figure 4.8 . 45xi
Figure 5.1- Plots of the sound speed profiles of Table 5.2. . 49Figure 5.2 - Relative sound pressure up tocase 2 (right figure), for akm with parameters from test case 1 (left figure) and testHz point source. . 50Figure 5.3 - Relative sound pressure up tokm, with parameters from test case 1 (left figure) andtest case 2 (right figure), with and without the window function, for aHz point source. 51Figure 5.4 - Comparison between the GFPE and the CNPE methods, with parameters from test case3. The respective range steps used are displayed in the bottom right table. . 52Figure 5.5 - Comparison between the GFPE and the CNPE methods, with parameters from test case4. The respective range steps used are displayed in the bottom right table. . 53Figure 5.6 - Comparison between the GFPE and the CNPE methods, with parameters from test case5. The respective range steps used are displayed in the bottom right table. . 54Figure 5.7 - Comparison between the GFPE (two refraction factors) and the CNPE methods, withparameters from test case 6. The respective range steps used are displayed in the bottomright table. . 54Figure 5.8 - Example of the refractive-index fluctuationsline in the, for a height ofm along a horizontaldirection (left figure) and its corresponding mode amplitudewith(right figure) for both von Kármán and Gauss spectra, using the parameters listed above.andare the wave number parameters [equation (3.63)] . 56Figure 5.9 - Graphical representation of the sound speed profiles for upwind (solid blue line) andcrosswind propagation (solid red line). . 58Figure 5.10 - Wind directions of the experimental measurement study by [Weiner, et al., (1959)]. . 58Figure 5.11 - Two trials of the relative sound pressure up to a range ofm for test case A1 . 60Figure 5.12 - Two trials of the relative sound pressure up to a range ofm using test case B1 . 60Figure 5.13 - Two trials of the relative sound pressure up to a range ofm using test case A2 . 61Figure 5.14 - Two trials of the relative sound pressure up to a range ofm using test case B2 . 61Figure 5.15 – Example of the step function for a turbulent upward refracting atmosphere. . 62Figure 6.1 - Temperature (left) and wind (right) profiles, for the meteorological conditions from Table6.5, up to a height ofm. . 66Figure 6.2 - Sound speeds obtained for two meteorological conditions from Table 6.5, including threedifferent wind directions. . 67Figure 6.3 - Schematic representation of the source and receivers position (m) and wind direction. . 68Figure 6.4 - Representation of scattering of sound into the shadow region . 70Figure 6.5 - One trial of the relative sound pressure up to a range ofm using test case up2 (leftplot) and test case down2 (right plot), with and without atmospheric turbulence. . 70Figure 6.6 - One trial of the relative sound pressure up to a range ofm using test case up100(left plot) and test case down100 (right plot), with and without atmospheric turbulence. . 71Figure 6.7 - Two-dimensional plots of the relative sound pressure leveltest case up2. The source height is(dB), with parameters fromm and the frequency isHz, with upwindpropagation. . 71xii
Figure 6.8 - Two-dimensional plots of the relative sound pressure leveltest case down2. The source height is(dB), with parameters fromm and the frequency isHz, with crosswindpropagation. . 72Figure 6.9 - Comparison of the relative sound pressure values, at a range ofdirections (three different receiver locations at a height ofm, for three windm) , each one for light wind(left plot) and moderate wind (right plot) atmospheric conditions and for a source height ofm. . 73Figure 6.10 - Comparison of the relative sound pressure values, at a range ofdirections (three different receiver locations at a height ofm, for three windm) , each one for light wind(left plot) and moderate wind (right plot) atmospheric conditions and for a source height ofm. . 73Figure 6.11 - Schematic representation of case study 1. All distances are displayed in meters. . 74Figure 6.12 - Schematic representation of case study 2. The aircraft travels from position 1 to position3 and all the distances are displayed in meters. . 75Figure 6.13 - Attenuation values for case study 1 (top left and top right plots) and case study 2 (bottomleft plot), for a source frequency ofHz. The horizontal axis represents the horizontaldistance traveled by the aircraft. . 76Figure 6.14 - Attenuation values for case study 1 (top left and top right plots) and case study 2 (bottomleft plot), for a source frequency ofHz. The horizontal axis represents the horizontaldistance traveled by the aircraft. . 77xiii
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LIST OF TABLESTable 4.1- Values of the attenuation factor for an octave band scale . 35Table 4.2 - Test case parameters . 36Table 4.3 - Home screen options explained in detail . 41Table 5.1- Acoustic and environment parameters for two test cases in a non-refracting atmosphere . 47Table 5.2 - Atmospheric refraction parameters of four test cases . 48Table 5.3 - Acoustic and environment parameters for test cases from Table 5.2. 48Table 5.4 - von Kármán spectrum parameters . 56Table 5.5 - Turbulence parameters used . 57Table 5.6 - Atmospheric and ground parameters from the experimental study . 59Table 5.7 - Simulation parameters for the experimental test cases . 59Table 6.1 - Pasquill meteorological stability classes . 63Table 6.2 - Definitions and values of the parameters used to describe the Monin-Obukhov profiles . 64Table 6.3 - Value of constantsandfor the six Pasquill classes . 65Table 6.4 - Some typical roughness lengths. 66Table 6.5 - Parameters used in the Monin-Obukhov profiles for two meteorological conditions . 66Table 6.6 - Gauss spectrum parameters at a height. 67Table 6.7 - Normalized impedance values for an octave band spectrum . 68Table 6.8 - Test cases and their respective parameters . 69xv
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LIST OF ACRONYMS AND SYMBOLSMathematical notationBoldfaced symbols are used for vectors, for example,A line above the symbol denotes a time average over turbulent fluctuations, for examplepartial derivate of function ,second derivate of function ,gradient of a scalar function .AcronymsABLAtmospheric Boundary LayerASLAtmospheric Surface LayerCC programming languageCLICommand Line type InterfaceCNPECrank-Nicolson Parabolic EquationDTFDiscrete Fourier TransformDUCDownward Upward Constant profileFFPFast Field ProgramFFTFast Fourier TransformFFTWFastest Fourier Transform in the WestGFPEGreen s Function Parabolic EquationPEParabolic EquationPRNGPseudorandom Number GeneratorTATotal AttenuationTLTransmission LossRoman symbolscorrelation length of turbulent refractive index fluctuationsattenuation factorparameter of logarithmic sound speed profileparameter in equation (6.6)parameter in equation (6.6)(adiabatic) sound speedsound speed at ground surfacexvii
effective sound speedcumulative of equation (4.16)structure parameter for the temperature fluctuationstructure parameter of the wind speed fluctuationconstant value in equation (5.2)frequencycenter frequency of an octave bandlowest frequency of an octave bandhighest frequency of an octave bandspectral density functiongrain shape factor of porous mediumtwo dimensional Green's functionthree dimensional Green's functionmode amplitude in equation (3.63)two dimensional Green's functionwave numberreference value of wave number at some average heightabsorption layer wave numbereffective wave numberhorizontal wave numbercomponents of wave number vectorvertical wave numberwave number corresponding toby Fourier transformationparameter of von Kármán turbulence spectrumsize of largest eddies, outer scale of turbulenceMonin-Obukhov lenghtsound pressure levelsound pressure level of free fieldsound power levelnumber of vertical pointsacoustic refractive indexdeterminist part of acoustic refractive indexunit normal vectorintegralPrandtl numbercomplex amplitude of acoustic pressurecomplex pressure of free fieldreference pressure levelxviii
complex pressure of acoustic pressuretortuosity of porous mediumquantity defined in equation (3.4)quantity defined in equation (3.4)operator defined in equation (3.33)operator defined in equation (3.39)horizontal distancedistance from source do receiverposition vectorplane wave reflection coefficientpore shape factor ratio of porous medium(integration) surfaceintegral number in equation (3.62)summand of equation (4.15)closed surfaceabsolute temperateconstant temperatureturbulent temperature fluctuationscaling temperaturewind vector of three componentshorizontal wind component (cylindrical coordinate)turbulent wind velocity fluctuationvertical wind component (cylindrical coordinate)angular wind component (cylindrical coordinate)friction velocity(integration) volumemaximum elevation anglecoordinate ofcoordinate systemroughness length of ground surfaceheight of bottom of absorption layer in PE gridnormalized acoustic impedance of (ground) surfacereceiver heightsource heightheight of PE gridGreek symbolsatmospheric absorption coefficientrandom angle for calculation of turbulent refractive index fieldquantity defined in equation (3.28)xix
specific heat ratio of airgamma functionAdiabatic correction factorDirac delta functionquantity defined in equation (4.20)quantity defined in equation (3.32)wave number spacingrelative sound pressure levelhorizontal grid spacingvertical grid spacingazimuthal anglevon Kármán constantwave lengthturbulent fluctuation of acoustic refractive indexaverage refractive indexfluctuation defined in equation (3.59)reflection anglerandom angle for calculation of turbulent refractive index fieldaverage turbulent phase fluctuation defined in equation (3.61)quantity defined in equation (4.8)(acoustic) density of atmosphereair density(effective) flow resistivity of groundstandard deviation of wind speed fluctuationsstandard deviation of temperature fluctuationsquantity defined in equation (3.65)angular frequencyporosity of porous mediumquantity defined in equation (3.40)Diabatic momentum profile correction functionDiabatic heat profile correction functionFourier transform defined in equation (3.41)(specific) acoustic impedance of propagation medium(specific) acoustic impedance of air(specific) acoustic impedance of (ground) su
The effect of wind and turbulence on sound propagation in the atmosphere André Filipe Garcia Peixoto de Oliveira Dissertação para obtenção do Grau de Mestre em Engenharia Aeroespacial Júri Presidente: Doutor Fernando José Parracho Lau Orientador: Doutor João Manuel Gonçalves de Sousa Oliveira
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