This document summarizes research on noise generation mechanisms by an airfoil, specifically trailing-edge noise. Key findings include:
- Trailing-edge noise occurs due to turbulent flow interacting with the airfoil surface near the trailing edge.
- Spanwise-coherent turbulent structures that are elongated in the spanwise direction (kz = 0) always radiate sound, according to theoretical analysis of the Green's function.
- Isolating two-dimensional motions around the airfoil and correlating them to far-field sound yielded much higher correlations, consistent with theory showing these structures radiate sound.
This study examines the effect of rain on ASCAT observations of sea surface radar cross-section using simultaneous rain measurements from NEXRAD radars. Three rain events were analyzed over Gulf of Mexico in 2008-2009. Results show rain can cause substantial increases in backscatter, from 2-4 dB depending on incidence angle, leading to errors in estimated wind speed of around 60%. The change in backscatter was found to depend on incidence angle but consequences were similar across angles due to wind speed models. Substantial wind errors were identified for rain rates of 6-20 mm/hr. Extra care is needed when using ASCAT data in tropical rainy regions.
Probing the Hurricane Boundary Layer using NOAA's Research AircraftJun Zhang
Jun Zhang presented this work during his short visit at NCAR in June 2011. Below is the abstract of this talk:
The boundary layer is known to play an important role in the energy transport processes of a hurricane, regulating the radial and vertical distribution of momentum and enthalpy that are closely related to storm development and intensification. However, the hurricane boundary layer is the least observed part of a storm till now. In particular, there is a lack of turbulence observation due to instrumentation limitation and safety constraint. This talk will present aircraft observations of the atmospheric boundary layer structure in intense hurricanes. Turbulence data presented are related to topics of air-sea exchange of turbulent fluxes, turbulent kinetic energy budget, dissipative heating, and vertical mixing in the boundary layer. The question of how to define the top of the hurricane boundary layer is also discussed.
The document presents a new technique called C-2PO for retrieving wind speeds from cross-polarized synthetic aperture radar (SAR) data during hurricanes. C-2PO uses the cross-polarization ratio, which is insensitive to wind direction and incidence angle, making it easier to map to wind speed compared to existing techniques. Comparisons show C-2PO provides more accurate wind speed retrievals than existing methods for hurricanes, with lower biases and errors. Reasons include existing models becoming saturated at high winds and not accounting for rain and other factors that impact radar backscatter.
The document presents a new technique called C-2PO for retrieving wind speeds from cross-polarized synthetic aperture radar (SAR) data during hurricanes. C-2PO uses the cross-polarization ratio, which is insensitive to wind direction and incidence angle, making it easier to map to wind speed compared to existing techniques. Comparisons show C-2PO provides more accurate wind speed retrievals than existing methods for hurricanes, with lower biases and errors. Reasons C-2PO performs better include existing models saturating at high winds and not accounting for rain and other factors.
Towards the identification of the primary particle nature by the radiodetecti...Ahmed Ammar Rebai PhD
This document summarizes a study using the CODALEMA experiment to analyze radio signals from air showers and identify properties of primary cosmic ray particles. It describes:
1) Analyzing time delays of radio signals compared to a plane wavefront hypothesis and finding systematic deviations, indicating the wavefront is curved.
2) Developing a model to reconstruct the emission center position based on fitting time delays to a parabolic function dependent on curvature radius and antenna distances.
3) Applying the model to 450 selected CODALEMA events and comparing reconstructed shower core positions to results from other models, finding consistency.
The document discusses an airborne DInSAR study conducted over São Sebastião, Brazil to monitor terrain movements that could impact oil and gas pipelines. P-band and X-band data were acquired in 2009 and 2010 and processed to generate deformation maps. P-band results had sub-centimeter accuracy and detected movements in forested areas, while X-band detected millimeter movements in urban areas. Comparisons to in-situ sensors showed correlations. The study demonstrated airborne DInSAR is well-suited for monitoring complex terrain and vegetation areas for natural and potentially hazardous movements.
1) Conventional semblance analysis assumes no amplitude variation with offset (AVO), which can cause issues for events with strong AVO or polarity reversals. 2) The document proposes generalized semblance methods that incorporate AVO by modeling events with both hyperbolic moveout and amplitude variation. 3) It compares traditional, AB, and AK semblance on synthetic data, finding AK semblance maintains good velocity resolution while handling AVO better than traditional semblance.
This study examines the effect of rain on ASCAT observations of sea surface radar cross-section using simultaneous rain measurements from NEXRAD radars. Three rain events were analyzed over Gulf of Mexico in 2008-2009. Results show rain can cause substantial increases in backscatter, from 2-4 dB depending on incidence angle, leading to errors in estimated wind speed of around 60%. The change in backscatter was found to depend on incidence angle but consequences were similar across angles due to wind speed models. Substantial wind errors were identified for rain rates of 6-20 mm/hr. Extra care is needed when using ASCAT data in tropical rainy regions.
Probing the Hurricane Boundary Layer using NOAA's Research AircraftJun Zhang
Jun Zhang presented this work during his short visit at NCAR in June 2011. Below is the abstract of this talk:
The boundary layer is known to play an important role in the energy transport processes of a hurricane, regulating the radial and vertical distribution of momentum and enthalpy that are closely related to storm development and intensification. However, the hurricane boundary layer is the least observed part of a storm till now. In particular, there is a lack of turbulence observation due to instrumentation limitation and safety constraint. This talk will present aircraft observations of the atmospheric boundary layer structure in intense hurricanes. Turbulence data presented are related to topics of air-sea exchange of turbulent fluxes, turbulent kinetic energy budget, dissipative heating, and vertical mixing in the boundary layer. The question of how to define the top of the hurricane boundary layer is also discussed.
The document presents a new technique called C-2PO for retrieving wind speeds from cross-polarized synthetic aperture radar (SAR) data during hurricanes. C-2PO uses the cross-polarization ratio, which is insensitive to wind direction and incidence angle, making it easier to map to wind speed compared to existing techniques. Comparisons show C-2PO provides more accurate wind speed retrievals than existing methods for hurricanes, with lower biases and errors. Reasons include existing models becoming saturated at high winds and not accounting for rain and other factors that impact radar backscatter.
The document presents a new technique called C-2PO for retrieving wind speeds from cross-polarized synthetic aperture radar (SAR) data during hurricanes. C-2PO uses the cross-polarization ratio, which is insensitive to wind direction and incidence angle, making it easier to map to wind speed compared to existing techniques. Comparisons show C-2PO provides more accurate wind speed retrievals than existing methods for hurricanes, with lower biases and errors. Reasons C-2PO performs better include existing models saturating at high winds and not accounting for rain and other factors.
Towards the identification of the primary particle nature by the radiodetecti...Ahmed Ammar Rebai PhD
This document summarizes a study using the CODALEMA experiment to analyze radio signals from air showers and identify properties of primary cosmic ray particles. It describes:
1) Analyzing time delays of radio signals compared to a plane wavefront hypothesis and finding systematic deviations, indicating the wavefront is curved.
2) Developing a model to reconstruct the emission center position based on fitting time delays to a parabolic function dependent on curvature radius and antenna distances.
3) Applying the model to 450 selected CODALEMA events and comparing reconstructed shower core positions to results from other models, finding consistency.
The document discusses an airborne DInSAR study conducted over São Sebastião, Brazil to monitor terrain movements that could impact oil and gas pipelines. P-band and X-band data were acquired in 2009 and 2010 and processed to generate deformation maps. P-band results had sub-centimeter accuracy and detected movements in forested areas, while X-band detected millimeter movements in urban areas. Comparisons to in-situ sensors showed correlations. The study demonstrated airborne DInSAR is well-suited for monitoring complex terrain and vegetation areas for natural and potentially hazardous movements.
1) Conventional semblance analysis assumes no amplitude variation with offset (AVO), which can cause issues for events with strong AVO or polarity reversals. 2) The document proposes generalized semblance methods that incorporate AVO by modeling events with both hyperbolic moveout and amplitude variation. 3) It compares traditional, AB, and AK semblance on synthetic data, finding AK semblance maintains good velocity resolution while handling AVO better than traditional semblance.
1. AVO inversion and processing of seismic data from the Penguin Field was challenging due to noise in the data and lack of clear AVO trends.
2. Pre-stack diagnostics identified issues like residual moveout and multiples that were addressed through additional processing steps.
3. Post-stack diagnostics on near, mid, and far stacks helped assess whether the data obeyed expected AVO behavior needed for inversion.
4. Inversion results for properties like Vshale, porosity, and net-to-gross ratio showed improved detail compared to original reservoir models.
This document provides an introduction to seismic exploration and refraction, including:
1) A ray incident on a surface with two layers results in three reflected and refracted rays, which can be identified as P or S waves based on the velocities in each layer.
2) As the angle of incidence increases, the angle of refraction also increases.
3) At the critical angle, a critically refracted wave travels along the top of the lower layer and leaks energy back into the upper layer.
4) Seismic reflection occurs when the acoustic impedance differs between two layers, producing V-shaped ray paths on a reflection profile.
The document discusses seismic data acquisition and processing for the Shaybah Field. Over 120 million seismic traces were recorded over an area of 1,100 square kilometers using over 100,000 shot points. Processing of the data lasted about 18 months and was carried out in-house by Saudi Aramco. The document also discusses various seismic data processing techniques including normal moveout correction, velocity analysis, muting, and static corrections.
Seismic refraction is a method that uses seismic waves, specifically P-waves, to investigate geological structures below the Earth's surface. There are two main types of elastic body waves: P-waves and S-waves. P-waves travel faster and are studied in simple seismic methods. When seismic waves encounter an interface between geological layers, the waves are reflected, refracted, and converted between P and S-waves. Refraction occurs when the velocity increases with depth, causing head waves that travel parallel to interfaces and are recorded by geophones on the surface. Snell's law governs refraction and describes how the refraction angle changes based on the velocity in each layer.
The document discusses wind energy and wind turbines. It begins by explaining how wind is formed from pressure gradients and the Coriolis effect. It then discusses different types of winds and how wind speed and patterns vary over time. Methods for measuring wind are presented, including wind atlases. The basics of how wind power is captured by wind turbines are covered, including swept area, power output formulas, and optimal turbine spacing in wind farms. Environmental impacts and public acceptance issues are also summarized.
Seismic data Interpretation On Dhodak field PakistanJamal Ahmad
I (Jamal Ahmad) presented this on 21 Feb, 2009 to defend my M.Phil dissertation in Geophysics at QAU, Islamabad, Pakistan. For more information about this, you may contact me directly at jamal.qau@gmail.com.
ALMA will deliver exciting opportunities to advance our understanding of solar prominences and filaments, and constrain models of prominence fine structures.
1) Geophysics uses remote sensing to determine subsurface conditions by analyzing seismic and radar signals that travel through and reflect off underground materials.
2) There are four main modes of signal propagation: vertical reflection, wide angle reflection, critical refraction, and direct waves. Precisely measuring the travel times of these signals allows subsurface structures to be interpreted.
3) Reflection seismology analyzes reflected signals to determine depth to interfaces by relating travel time, distance between source and receiver, and velocity, while refraction seismology uses travel times of critically refracted signals to determine shallow subsurface velocity structure.
The document discusses advances in SAR interferometry over the past 20 years for measuring millimeter-scale land motion. Key points include:
1) Revisit times have decreased from 35 days with ERS-1 to 12 days with Sentinel-1 constellations, improving ground motion recovery.
2) Persistent scatterer interferometry techniques like SqueeSAR can now measure motions to the millimeter by using all available interferograms.
3) Atmospheric phase screens still limit accuracy but can be estimated and removed using numerical weather models, GPS, and other independent datasets.
4) Future opportunities include using wide Doppler bandwidths from satellites to achieve high-resolution azimuth measurements of ground motion.
This document discusses seismic reflection acquisition, processing, and waveform analysis. It introduces key concepts like reflection coefficients, convolution, and how the earth acts as a filter on seismic energy. Examples are provided to illustrate convolution and how it is used to model seismic reflections within the earth. Key wave properties like amplitude, wavelength, velocity and their relationships are also defined. Homework problems at the end ask about wave properties and applications of seismic reflection and refraction methods.
The document discusses seismic reflection acquisition, processing, and waveform analysis. It introduces key concepts in seismic reflection including common midpoint gathers, common depth point gathers, and normal moveout correction. The document also discusses equipment used in land and marine seismic reflection acquisition such as vibrator trucks, geophones, and receiver trucks. It notes that processing aims to enhance the quality of compressional waves and improve the signal-to-noise ratio through techniques like stacking traces.
This document provides an overview of seismic exploration fundamentals and concepts related to refracted and reflected seismic waves. It discusses topics like refracted ray and angle, total time of refraction travel, apparent versus true velocity, constructing time-distance plots from single-layer models, and exercises for determining arrival times using ray-tracing concepts. Homework problems are also presented relating to Nafe-Drake curves, seismic velocities in a two-layer model, and anomalous velocities for ice. Students are directed to online resources for more information on derivations and single-layer modeling equations.
The document discusses seismic reflection acquisition, processing, and waveform analysis. It provides examples of a large seismic data acquisition project in Saudi Arabia that collected over 120 million traces. It also defines key concepts in seismic processing like normal moveout correction, velocity analysis, muting, static corrections, average velocity, root mean square velocity, and interval velocity. It notes that the mid-term exam will be on May 3rd and that a field trip is scheduled for April 26th.
1) Strong ground motion refers to the strong earthquake shaking that occurs close to the causative fault (within about 50 km). It is recorded using accelerometers.
2) Starting in 1976, IIT Roorkee operated a network of over 200 analog strong motion accelerographs across northern India to record strong ground motion.
3) Key ground motion parameters used in structural design include peak ground acceleration (PGA), response spectra, and acceleration time histories. PGA measures the largest acceleration, while response spectra show maximum response of structures of varying frequencies.
Extended seismic data processing lec25, fk filteringAmin khalil
The document discusses seismic data processing techniques in the frequency-wavenumber (f-k) domain. It defines the f-k domain as a two-dimensional Fourier transform over time and space. Noise like groundroll and multiples can be more readily separated and filtered in the f-k domain before inverse transforming. Spatial aliasing is also discussed, and the Nyquist criterion and proper trace sampling are important to avoid aliasing. Filtering techniques like pie-slice filters in the f-k domain can be used to remove noise like groundroll.
Wide aperture reflection refraction profiling uses wide-angle reflected and diving wave energy to develop velocity models of seismic sections. It exploits long offset data to observe diving waves and wide-angle reflections that penetrate deeper than conventional methods. The technique involves first break tomography to obtain an initial velocity model, which is then refined through iterative forward modeling and matching of observed and calculated arrival times and amplitudes.
This document describes a new ocean vector wind retrieval technique for tropical cyclones called X-Winds. X-Winds uses a specialized geophysical model function trained on hurricane data to account for backscatter saturation with wind speed and rain effects. It estimates wind direction from the anisotropy in forward and aft radar measurements, then estimates wind speed using the estimated wind direction. Comparisons with H*Wind analysis and QuikSCAT data show X-Winds provides improved wind speed and direction estimates over standard products in hurricanes. A new SeaWinds tropical cyclone ocean vector winds dataset will be produced using this technique.
This document provides an introduction to refraction seismology. It discusses how refraction seismology can be used to indirectly observe the layers inside the Earth by interpreting the depths to subsurface interfaces and seismic wave velocities for each layer. It explains that refraction seismology works by analyzing the times of first arriving seismic energy versus distance recorded by receivers from a seismic source. The goal is to interpret depths to interfaces and wave velocities without later arriving seismic waves that could interfere with the analysis.
The document describes seismic interpretation workflows, including conventional and unconventional techniques. Conventional techniques involve horizon interpretations, fault picking, and tying seismic data to well logs to understand subsurface geology. Unconventional techniques analyze seismic attribute variations like amplitudes to identify hydrocarbon indicators. The workflow includes generating synthetics from well logs, interpreting horizons on seismic sections, identifying structures like faults and gas chimneys, and determining direct hydrocarbon indicators.
El documento describe los rasgos de una sociedad pasiva y cómo la falta de capacitación en tecnologías de la información y comunicación (TIC) puede conducir a dificultades en su operación, desconocimiento de su utilidad y falta de conocimiento en su aplicación. También señala que es necesario que la comunidad educativa esté actualizada en el uso y manejo de las TIC para proveer a los alumnos de las herramientas necesarias para el siglo actual.
An individual named Víctor Macón Arranz received a course certificate on August 2, 2016 from the Technical University of Denmark and Coursera for completing an online non-credit course called "Antimicrobial resistance - theory and methods". The certificate was verified by Lina Cavaco, a senior researcher at the National Food Institute of the Technical University of Denmark.
Existen varios tipos de ropa diseñados para diferentes propósitos y climas, incluyendo ropa casual, ropa formal, ropa deportiva, abrigos, trajes de baño y más. La ropa casual incluye jeans, camisetas y sudaderas y se usa para ocasiones informales. La ropa formal como trajes y vestidos se usa para ocasiones más formales como el trabajo y eventos especiales. La ropa deportiva como mallas y tenis se diseña para actividades físicas y ejercicio.
1. AVO inversion and processing of seismic data from the Penguin Field was challenging due to noise in the data and lack of clear AVO trends.
2. Pre-stack diagnostics identified issues like residual moveout and multiples that were addressed through additional processing steps.
3. Post-stack diagnostics on near, mid, and far stacks helped assess whether the data obeyed expected AVO behavior needed for inversion.
4. Inversion results for properties like Vshale, porosity, and net-to-gross ratio showed improved detail compared to original reservoir models.
This document provides an introduction to seismic exploration and refraction, including:
1) A ray incident on a surface with two layers results in three reflected and refracted rays, which can be identified as P or S waves based on the velocities in each layer.
2) As the angle of incidence increases, the angle of refraction also increases.
3) At the critical angle, a critically refracted wave travels along the top of the lower layer and leaks energy back into the upper layer.
4) Seismic reflection occurs when the acoustic impedance differs between two layers, producing V-shaped ray paths on a reflection profile.
The document discusses seismic data acquisition and processing for the Shaybah Field. Over 120 million seismic traces were recorded over an area of 1,100 square kilometers using over 100,000 shot points. Processing of the data lasted about 18 months and was carried out in-house by Saudi Aramco. The document also discusses various seismic data processing techniques including normal moveout correction, velocity analysis, muting, and static corrections.
Seismic refraction is a method that uses seismic waves, specifically P-waves, to investigate geological structures below the Earth's surface. There are two main types of elastic body waves: P-waves and S-waves. P-waves travel faster and are studied in simple seismic methods. When seismic waves encounter an interface between geological layers, the waves are reflected, refracted, and converted between P and S-waves. Refraction occurs when the velocity increases with depth, causing head waves that travel parallel to interfaces and are recorded by geophones on the surface. Snell's law governs refraction and describes how the refraction angle changes based on the velocity in each layer.
The document discusses wind energy and wind turbines. It begins by explaining how wind is formed from pressure gradients and the Coriolis effect. It then discusses different types of winds and how wind speed and patterns vary over time. Methods for measuring wind are presented, including wind atlases. The basics of how wind power is captured by wind turbines are covered, including swept area, power output formulas, and optimal turbine spacing in wind farms. Environmental impacts and public acceptance issues are also summarized.
Seismic data Interpretation On Dhodak field PakistanJamal Ahmad
I (Jamal Ahmad) presented this on 21 Feb, 2009 to defend my M.Phil dissertation in Geophysics at QAU, Islamabad, Pakistan. For more information about this, you may contact me directly at jamal.qau@gmail.com.
ALMA will deliver exciting opportunities to advance our understanding of solar prominences and filaments, and constrain models of prominence fine structures.
1) Geophysics uses remote sensing to determine subsurface conditions by analyzing seismic and radar signals that travel through and reflect off underground materials.
2) There are four main modes of signal propagation: vertical reflection, wide angle reflection, critical refraction, and direct waves. Precisely measuring the travel times of these signals allows subsurface structures to be interpreted.
3) Reflection seismology analyzes reflected signals to determine depth to interfaces by relating travel time, distance between source and receiver, and velocity, while refraction seismology uses travel times of critically refracted signals to determine shallow subsurface velocity structure.
The document discusses advances in SAR interferometry over the past 20 years for measuring millimeter-scale land motion. Key points include:
1) Revisit times have decreased from 35 days with ERS-1 to 12 days with Sentinel-1 constellations, improving ground motion recovery.
2) Persistent scatterer interferometry techniques like SqueeSAR can now measure motions to the millimeter by using all available interferograms.
3) Atmospheric phase screens still limit accuracy but can be estimated and removed using numerical weather models, GPS, and other independent datasets.
4) Future opportunities include using wide Doppler bandwidths from satellites to achieve high-resolution azimuth measurements of ground motion.
This document discusses seismic reflection acquisition, processing, and waveform analysis. It introduces key concepts like reflection coefficients, convolution, and how the earth acts as a filter on seismic energy. Examples are provided to illustrate convolution and how it is used to model seismic reflections within the earth. Key wave properties like amplitude, wavelength, velocity and their relationships are also defined. Homework problems at the end ask about wave properties and applications of seismic reflection and refraction methods.
The document discusses seismic reflection acquisition, processing, and waveform analysis. It introduces key concepts in seismic reflection including common midpoint gathers, common depth point gathers, and normal moveout correction. The document also discusses equipment used in land and marine seismic reflection acquisition such as vibrator trucks, geophones, and receiver trucks. It notes that processing aims to enhance the quality of compressional waves and improve the signal-to-noise ratio through techniques like stacking traces.
This document provides an overview of seismic exploration fundamentals and concepts related to refracted and reflected seismic waves. It discusses topics like refracted ray and angle, total time of refraction travel, apparent versus true velocity, constructing time-distance plots from single-layer models, and exercises for determining arrival times using ray-tracing concepts. Homework problems are also presented relating to Nafe-Drake curves, seismic velocities in a two-layer model, and anomalous velocities for ice. Students are directed to online resources for more information on derivations and single-layer modeling equations.
The document discusses seismic reflection acquisition, processing, and waveform analysis. It provides examples of a large seismic data acquisition project in Saudi Arabia that collected over 120 million traces. It also defines key concepts in seismic processing like normal moveout correction, velocity analysis, muting, static corrections, average velocity, root mean square velocity, and interval velocity. It notes that the mid-term exam will be on May 3rd and that a field trip is scheduled for April 26th.
1) Strong ground motion refers to the strong earthquake shaking that occurs close to the causative fault (within about 50 km). It is recorded using accelerometers.
2) Starting in 1976, IIT Roorkee operated a network of over 200 analog strong motion accelerographs across northern India to record strong ground motion.
3) Key ground motion parameters used in structural design include peak ground acceleration (PGA), response spectra, and acceleration time histories. PGA measures the largest acceleration, while response spectra show maximum response of structures of varying frequencies.
Extended seismic data processing lec25, fk filteringAmin khalil
The document discusses seismic data processing techniques in the frequency-wavenumber (f-k) domain. It defines the f-k domain as a two-dimensional Fourier transform over time and space. Noise like groundroll and multiples can be more readily separated and filtered in the f-k domain before inverse transforming. Spatial aliasing is also discussed, and the Nyquist criterion and proper trace sampling are important to avoid aliasing. Filtering techniques like pie-slice filters in the f-k domain can be used to remove noise like groundroll.
Wide aperture reflection refraction profiling uses wide-angle reflected and diving wave energy to develop velocity models of seismic sections. It exploits long offset data to observe diving waves and wide-angle reflections that penetrate deeper than conventional methods. The technique involves first break tomography to obtain an initial velocity model, which is then refined through iterative forward modeling and matching of observed and calculated arrival times and amplitudes.
This document describes a new ocean vector wind retrieval technique for tropical cyclones called X-Winds. X-Winds uses a specialized geophysical model function trained on hurricane data to account for backscatter saturation with wind speed and rain effects. It estimates wind direction from the anisotropy in forward and aft radar measurements, then estimates wind speed using the estimated wind direction. Comparisons with H*Wind analysis and QuikSCAT data show X-Winds provides improved wind speed and direction estimates over standard products in hurricanes. A new SeaWinds tropical cyclone ocean vector winds dataset will be produced using this technique.
This document provides an introduction to refraction seismology. It discusses how refraction seismology can be used to indirectly observe the layers inside the Earth by interpreting the depths to subsurface interfaces and seismic wave velocities for each layer. It explains that refraction seismology works by analyzing the times of first arriving seismic energy versus distance recorded by receivers from a seismic source. The goal is to interpret depths to interfaces and wave velocities without later arriving seismic waves that could interfere with the analysis.
The document describes seismic interpretation workflows, including conventional and unconventional techniques. Conventional techniques involve horizon interpretations, fault picking, and tying seismic data to well logs to understand subsurface geology. Unconventional techniques analyze seismic attribute variations like amplitudes to identify hydrocarbon indicators. The workflow includes generating synthetics from well logs, interpreting horizons on seismic sections, identifying structures like faults and gas chimneys, and determining direct hydrocarbon indicators.
El documento describe los rasgos de una sociedad pasiva y cómo la falta de capacitación en tecnologías de la información y comunicación (TIC) puede conducir a dificultades en su operación, desconocimiento de su utilidad y falta de conocimiento en su aplicación. También señala que es necesario que la comunidad educativa esté actualizada en el uso y manejo de las TIC para proveer a los alumnos de las herramientas necesarias para el siglo actual.
An individual named Víctor Macón Arranz received a course certificate on August 2, 2016 from the Technical University of Denmark and Coursera for completing an online non-credit course called "Antimicrobial resistance - theory and methods". The certificate was verified by Lina Cavaco, a senior researcher at the National Food Institute of the Technical University of Denmark.
Existen varios tipos de ropa diseñados para diferentes propósitos y climas, incluyendo ropa casual, ropa formal, ropa deportiva, abrigos, trajes de baño y más. La ropa casual incluye jeans, camisetas y sudaderas y se usa para ocasiones informales. La ropa formal como trajes y vestidos se usa para ocasiones más formales como el trabajo y eventos especiales. La ropa deportiva como mallas y tenis se diseña para actividades físicas y ejercicio.
Christopher Ndolo Mutunga is seeking a career in improving livelihoods and access to resources for small farmers through sustainable production and environmental conservation. He has 12 years of experience in forestry projects, conducting surveys, data collection and analysis. He holds a Master's degree in Environmental Science from Kenyatta University and a Bachelor's degree in Forestry from Moi University.
La comunicación científica implica transmitir conocimientos científicos de manera organizada y accesible para todos. Implica compartir los avances científicos con la sociedad a través de canales formales e informales. La comunicación científica es importante porque permite distinguir diferentes tipos de textos y su clasificación, así como la forma correcta de redactarlos y estructurarlos siguiendo los pasos del método científico para una mejor comprensión.
El documento presenta la información personal de Alejandro Mora García, quien trabaja en el Hotel Real Intercontinental. Sus pasatiempos favoritos son leer libros y armar aviones o carros de modelo. Su expectativa general del curso es aprender sobre herramientas computacionales que pueda aplicar a una futura empresa propia, entender completamente el curso, y poder aplicar los conocimientos en su vida diaria.
Materiales, herramientas y manode obra por santiago rojas y ronaldo henaoerhvdsrg
El documento detalla los materiales, herramientas y procesos necesarios para construir un producto. Lista las tablas de aglomerado, cilindro de madera, tornillos y ruedas que se usarán, junto con sus cantidades y precios. Identifica el taladro, lápiz, broca y pintura como las herramientas necesarias y el taller de mecánica como el lugar para obtenerlas. Explica los pasos del proceso de construcción, incluida la medición, trazado, división, colocación de tornillos, ensam
EN EL SIGUIENTE MAPA CONCEPTUAL ENCONTRARÁS CONCEPTOS Y GENERALIDADES DE LA GERENCIA DE PROYECTOS EN TECNOLOGÍA EDUCATIVA.
ESPERO LES SEA DE GRAN AYUDA Y PUEDAN ENCONTRAR INFORMACIÓN PERTINENTE A SUS NECESIDADES.
Managing Connections to Maximize Innovationguestaf4746
Developing "relationship capital" is something more than adding more connections to your network. This is an abridged deck for a talk I give on how to differentiate between connections and relationships to maximize innovation.
Webinar: PHP and MySQL - Server-side Scripting Language for Web Development Edureka!
The free webinar on PHP and MySQL titled "PHP and MySQL - Server-side Scripting Language for Web Development" was conducted by Edureka on 22nd November 2014
Buku ini membahas tentang fisika untuk SMA/MA kelas XII. Buku ini memuat 10 bab yang mencakup materi gejala gelombang, bunyi, cahaya, listrik statis, induksi magnet, imbas elektromagnetik, radiasi benda hitam, fisika atom, relativitas dan fisika inti.
This document is a certificate from the Board of Intermediate and Secondary Education in Dhaka, Bangladesh. It certifies that Razeeb Robert Rozario, son of Rafael Rozario and Ujjala Rozario, studying at Banani Bidyaniketon in Dhaka, passed the Secondary School Certificate Examination in 2002 in the Business Studies group with a GPA of 4.50 out of 5.00. His date of birth is recorded as the 10th of August 1987. The certificate is signed by the Controller of Examinations and dated the 3rd of July 2002, indicating the date the exam results were published.
Trailing edge noise prediction from NACA 0012 and NACA 6320 using empirical p...vasishta bhargava
Trailing edge of airfoil represents one of important sources in aerodynamic noise production. In this paper, the numerical computation of sound pressure using quasi empirical model and wall pressure spectrum models based on external pressure gradients was conducted for NACA 0012 and NACA 6320 airfoils. The development of boundary layer thickness and displacement thickness for different chord lengths and Mach numbers with varying angles of attack, are illustrated for NACA 0012. The sound pressure levels evaluated between 00 to 60angles of attack and at constant chord length of 1.2m using BPM model showed change of ~5dB in peak amplitude. The maximum test velocity and chord length used for analysis is 65 m/s and 1.5m. The relative velocities for airfoils have been computed using the boundary element and panel method. Boundary layer properties involving chord Reynolds number, 3.14 x106, 4.6 x106and Reynolds number based on wall shear, 7410, 6865 were assessed at 20 AOA for NACA 0012. Results have found higher values for thickness at increasing angle of attack but decayed along chord length. Comparison of wall pressure spectrum for favorable and adverse pressure gradients were done and validated with existing literature predictions
This document summarizes the research investigating the effect of longitudinal atmospheric turbulence on the dynamics of an airfoil with a structural nonlinearity in pitch. Three different regions of dynamic behavior are observed when the airfoil is excited by longitudinal turbulence, compared to two regions for the nonexcited case. A new region exists where the airfoil response is concentrated about the equilibrium position, attributed to the parametric nature of the turbulence excitation. Utter occurs at a lower velocity and limit cycle oscillations occur at a higher velocity for the excited case versus the nonexcited case. The airfoil and aerodynamic models used in the numerical simulations are described.
This document discusses investigating duct propagation and far field radiation of fan noise sources with acoustic wall treatment. It presents two codes - the Eversman radiation code and a modified version that includes compressibility effects. The modified code is used to study modal reflection and scattering inside the inlet and exit ducts due to wall treatment. Validation of the codes is performed by comparing predictions to experimental data for hard wall and treated configurations. Parameters like inlet lip thickness that affect far field directivity patterns are also investigated.
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1) Streamwise vortices play an important role in sustaining wall turbulence by regenerating streaks through the lift-up effect.
2) In turbulent plane Couette flow at low Reynolds numbers, streamwise vortices that span the entire gap between plates have been observed.
3) The document proposes a two-step Galerkin projection method to derive a low-order model that can illustrate the dynamics and generation mechanism of these streamwise vortices, in a way that is analogous to what is observed in turbulent boundary layers.
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Ocheltree & Frizzell (1989) Sound Field for Rectangular SourcesAlexander Cave
This document presents a method for calculating the sound field produced by a rectangular continuous wave acoustic source surrounded by a rigid plane baffle. The method involves dividing the radiating surface into rectangular elements and summing the pressure contributions from each element using approximations valid in the far field. Sound field calculations are shown for square sources ranging in size from 0.5 to 100 wavelengths on a side. The results are compared to published sound fields for similarly sized circular sources, showing similarities in beam width and locations of on-axis minima but a more uniform transverse pressure distribution for square sources in the near field. The effects of attenuation on the sound field of a square source are also examined.
Role of Coherent Structures in Supersonic Jet Noise and Its Controlaswiley1
This document summarizes a study examining the flow and acoustic characteristics of a supersonic jet impinging on a flat surface, with and without microjet-based active flow control. Measurements were taken at two nozzle-to-plate distances (h/d), one where microjet control was very effective in reducing noise and one where it was minimally effective. Results show that for the effective case, microjets significantly reduced the dominant impinging tone and broadband noise levels. For the ineffective case, microjets did not reduce the dominant tone but eliminated some other tones. Phase-locked PIV was used to understand the coherent flow structures and their role in noise generation and suppression.
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This document summarizes an experimental and numerical study on controlling noise from a deep cavity with slanted walls at low Mach numbers. The study tested a rectangular cavity with a depth-to-length ratio of 1.5 and width-to-length ratio of 3 in a wind tunnel. Passive control using slanted front and rear walls was evaluated. Results showed that a slanted rear wall effectively suppressed tones by reflecting unsteadiness back into the shear layer, breaking up vortices. However, a slanted front wall enhanced tones by enlarging and accelerating vortices in the shear layer, intensifying impingement on the rear wall. Computational fluid dynamics simulations revealed the mechanisms of noise reduction and enhancement by the
This document discusses a numerical study of the effect of thermal radiation on free convection boundary layer flow over a vertical wavy cone. The governing equations for steady, laminar, two-dimensional flow are presented and non-dimensionalized. These equations are then solved using the Mathematica technique. Graphs of the dimensionless temperature, velocity, skin friction coefficient, and Nusselt number are generated for various values of the Prandtl number, radiation parameter, surface wave amplitude, and cone half-angle. The results are discussed to analyze the impact of thermal radiation on the flow and heat transfer characteristics.
Effect of mainstream air velocity on velocity profile over a rough flat surfaceijceronline
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The document discusses the key characteristics of lightning and its phenomena based on historical studies. It covers Benjamin Franklin's contributions to understanding lightning in the 18th century. It also summarizes lightning characteristics such as incidence rates, flash polarity, number of strokes, peak currents, current shapes, and electric field measurements. The document analyzes lightning data to quantify parameters like flash duration, probability distributions of peak currents, and the spatial development of negative strikes to ground.
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This document describes a numerical study of the radiation patterns of resistively loaded dipole antennas. It computes the far field radiation patterns as a superposition of transient solutions for infinitesimal dipole elements. The current excitation for each dipole element is modeled as a half cycle of a sine squared waveform that propagates along the antenna at an adjustable speed. The radiation patterns are presented for different dielectric media to model antennas used in ground penetrating radar applications in various materials like water, ice, and soil. Comparisons are made to field observations.
EXPERIMENTAL AND NUMERICAL INVESTIGATIONS OF A TURBULENT BOUNDARY LAYER UNDER...Barhm Mohamad
In this article we present an experimental and numerical study of the behavior of the boundary layer type viscous flow in the presence of the thermal effect. The flow was held in a three-dimensional field with a uniform infinite velocity in the case of an adiabatic wall with heat input. The presented experimental work was performed in the Thermal Laboratory (LET) of the Prime Institute of Poitiers (France). It describes the analysis of a turbulent boundary layer created in a wind tunnel on the surface of a flat plate covered with epoxy resin. An HP 6012A power supply system was used to provide circulating heat flux to heat the flat plate to 80°C by the Joule effect. The numerical result shows a clear difference in the evolution of the thermal boundary layer between the three temperatures of the wall.
This document discusses atmospheric chemistry models and their use in quantifying atmospheric concentrations and fluxes. Global 3D models divide the atmosphere into grid boxes and use the continuity equation to track species concentrations over time, accounting for transport, chemistry, emissions and deposition. Transport is parameterized using turbulence and convection schemes. Chemistry is solved using operator splitting and implicit methods. Models are evaluated and improved using atmospheric observations from satellites, aircraft and surface sites through data assimilation techniques like inverse modeling. Examples are given of various applications of the GEOS-CHEM global model.
Noise and Flowfield Characteristics of Supersonic Jet Impinging on a Porous S...aswiley1
This document summarizes a study on using passive and active control methods to reduce noise and unsteadiness in supersonic impinging jets. Passive control involved using a porous surface under the jet, while active control used microjet injection. Results showed that passive control reduced broadband noise, while active control attenuated impinging tones. A hybrid control combining both methods reduced both broadband noise and tones more effectively than either method alone. Experiments were conducted in a supersonic jet facility on a Mach 1.5 jet impinging on surfaces at varying distances, measuring unsteady pressures, near-field acoustics, and flow velocities.
Obtaining three-dimensional velocity information directly from reflection sei...Arthur Weglein
This paper present a formalism for obtaining the subsurface
velocity configuration directly from reflection seismic data.
Our approach is to apply the results obtained for inverse
problems in quantum scattering theory to the reflection
seismic problem. In particular, we extend the results of
Moses (1956) for inverse quantum scattering and Razavy
(1975) for the one-dimensional (1-D) identification of the
acoustic wave equation to the problem of identifying the
velocity in the three-dimensional (3-D) acoustic wave equation
from boundary value measurements. No a priori knowledge
of the subsurface velocity is assumed and all refraction,
diffraction, and multiple reflection phenomena are
taken into account. In addition, we explain how the idea of
slant stack in processing seismic data is an important part
of the proposed 3-D inverse scattering formalism.
2. He Helmholtz number
Tij Lighthill tensor
M∞ Mach number
∆˜x Non-dimensional distance
n Surface normal vector
xi Observer position
vφ Phase velocity
Pr Prandtl number
p Pressure
˜p Fourier Transform of pressure
r Radius
γ Ratio of specific heats
Re Reynolds number
SG Lighthill’s tensor in the frequency domain
ao Sound speed
yi Source position
Pi Dipole strength
S Surface
T Temperature
E Total energy
t Time
˜t Non-dimensional time
u u-component of velocity in a Cartesian system
v v-component of velocity in a Cartesian system
w w-component of velocity in a Cartesian system
τij Viscous stress tensor
V Volume
λ Wavelength
k Wavenumber
I. Introduction
Noise emitted by airfoils and wings occurs due to the interaction of turbulence with the neighbouring
solid surfaces. This kind of problem is fundamental for aeroacoustics, and there are several applications
where this phenomenon is relevant, among which the design of low-noise aerodynamic profiles, rotor blades
and fans.
Brooks, Pope and Marcolini2
classify five different mechanisms of sound generation by an airfoil, namely:
turbulent boundary layer convected past the trailing edge noise; separation stall noise; laminar boundary
layer leading to vortex shedding noise; tip vortex formation noise; and trailing edge bluntness vortex shedding
noise. Most of the cases above correspond to the interaction between trailing edge and flow, which is a result
of the end of the profile inducing an abrupt change of boundary condition for pressure and/or velocity.
This was recognised early by Ffowcs Williams and Hall, who showed theoretically that a trailing edge
scatters the neighbouring turbulent fluctuations, leading to significant sound radiation. This phenomenon
has since been labelled trailing-edge noise. Unlike sound emission by compact surfaces, which tends to be
dominated by lift fluctuations as shown by Curle,6
trailing-edge noise approaches the non-compact limit,
modelled by Ffowcs Williams and Hall as a half plane with eddies on the vicinity of its edge. Follow-up
modelling work by Amiet1
considered that trailing-edge noise is due to induced dipoles in the vicinity of the
edge, due to advected turbulence, considered in statistical terms to remain stationary as it is advected.
The objective of the present work is to use flow simulation data to study in more detail the relevant
sound-production mechanisms in the flow around an airfoil, in particular with a view to extracting the
relevant turbulent scales to the trailing-edge noise problem. To do this we study the large-eddy simulation
(LES) of Wolf, Azevedo and Lele,13
of a NACA0012 airfoil at zero angle of attack, Mach number M∞ = 0.115
and Reynolds number based on the airfoil chord equal to Rec = 408000. We use the full simulation data
to calculate flow-acoustic correlations in order to examine the relevant fluid motions related to acoustic
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3. radiation.
Some previous work have also used numerical simulations to study trailing-edge noise. As shown by
Oberai, Roknaldin and Rughes9
using an LES, the source of acoustic noise in major part is concentrated on
trailing edge due the interaction of the turbulent flow and the end of the profile. Sandberg and Sadham10
have conducted a direct numerical simulation (DNS) to investigate the interaction of the turbulent flow past
a trailing edge and shown that two-dimensional theory for low frequencies predicts the far field acoustic
pressure due the significant spanwise coherence of pressure disturbances, showing that in this case the noise
generation is predominately two-dimensional.
A theoretical analysis, using the tailored Green’s function for a trailing edge derived by Ffowcs Williams
and Hall, guides our investigation. We show in section II that only spanwise-elongated structures radiate
to the far-field, and subsequently we examine in section III how two-dimensional motions around the airfoil
are related to the far-field sound. In addition, we study what the influence on flow-acoustic correlations
when the quantities are manipulated doing a delta between the upper and lower surface, in other words, the
difference of the properties between upper and lower surface of the airfoil.
II. Theory
A. Basic equations
We review here the fundamental theory of noise generation by an airfoil. Lighthill8
rearranged the equations
of motion of a fluid in a way to obtain an inhomogeneous wave equation, with a source term called Lighthill
tensor, Tij:
∂2
ρ
∂t2
− a2
o
2
ρ =
∂2
Tij
∂xi∂xj
(1)
Tij = ρvivj + pij − a2
oρδij (2)
The solution of equation 1 neglecting solid boundaries makes use of the free-field Green’s function to the
problem, defined as
∂2
G
∂t2
− a2
o
2
G = δ(x − y)δ(t − τ) (3)
where the Green’s function G should satisfy the Sommerfeld boundary condition and also a causality condi-
tion. Manipulation of eqs. (1) and (3) leads to
ρ − ρo =
1
4πa2
o
∂2
∂xi∂xj
V
Tij(y, t − |x−y|
ao
)
|x − y|
dV (4)
The previous equation does not account for solid boundaries to the problem, which are relevant for
trailing-edge noise. Extension to Lighthill’s analogy accounting for surface effects are presented by Curle6
and Ffowcs Williams and Hall.12
Curle’s theory employs a more general resolution to equation 1, as follows
ρ − ρo =
1
4πa2
o
v
∂2
Tij
∂xi∂xj
dt
|x − y|
+
1
4π
S
1
r
∂ρ
∂n
+
1
r2
r
n
ρ +
1
aor
∂r
∂n
∂ρ
∂t
dS(y) (5)
With further manipulation, Curle rewrote the solution as
ρ − ρo =
1
4πa2
o
∂2
∂xi∂xj
V
Tij(y, t − r
ao
)
r
dy −
1
4πa2
o
∂
∂xi
S
Pi(y, t − r
ao
)
r
dS(y) (6)
where
Pi = −njpij (7)
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4. The term Pi corresponds to a surface distribution of dipoles and nj is the direction outward over the airfoil
surface.
Without knowledge of the normal tension Pi on the surface (approximately equal to the pressure for high-
Re flows), eq. (6) is actually an integral equation, which should be solved numerically using a boundary
element method. However, a simplification is possible if instead of the free-field Green’s function G in eq.
(3) one manipulates the corresponding equations using a tailored Green’s function Gt that satisfies the same
boundary conditions as the pressure. For the trailing-edge noise problem, the Green’s function in a domain
bounded by a rigid, semi-infinite flat plate was derived by Ffowcs Williams and Hall12
in the frequency
domain as
Gt(x, y, ω) =
e
1
4 iπ
√
π
e−ikR
R
uR
−∞
e−iu2
du +
e−ikR
R
uR
−∞
e−iu2
du , (8)
where uR and uR are given by
uR = 2
krr0
D + R
1
2
cos
θ − θ0
2
, (9)
uR = 2
krr0
D + R
1
2
cos
θ + θ0
2
, (10)
R is the separation between source (r0, θ0, z0) and observer (r, θ, z) and R is the distance between the
source’s image (r0, −θ0, z0) and the observer in cylindrical coordinates (z and z0 are equivalent to x3 and
y3, respectively). The far-field assumption for the observers was taken into account and the relationship
between the two coordinate systems can be seen in Figure 1.
Trailing
Edge
∞
∞
∞
z0
θ0
r0
θ
r
Plate
z
x1
y1
x2
y2
x3
y3
Figure 1. Relationship between different coordinate systems of the problem
The distances R, R and D can be obtained in cylindrical coordinates as
R = r2
+ r2
0 − 2rr0 cos (θ − θ0) + (z − z0)2
1
2
, (11)
R = r2
+ r2
0 − 2rr0 cos (θ + θ0) + (z − z0)2
1
2
, (12)
D = (r + r0)2
+ (z − z0)2
1
2
. (13)
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5. Using the hypothesis of source near the plate (kr 1, i.e. the distance between trailing edge and source
is much smaller than the acoustic wavelength), the leading-order Taylor-series approximation of the Green’s
function (labelled here as Gs) is shown by Ffowcs-Williams and Hall to be
Gs(x, y, ω) =
2e
1
4 iπ
√
π
2krr0
r2 + (z − z0)2
1
2
cos
θ
2
cos
θ0
2
e−ikR
R
(14)
Using either form of the tailored Green’s function, Gt or Gs, the far-field sound at frequency ω can be
obtained as
ˆp(x, ω) =
1
4π y1 y2 y3
SG(y, ω)G(x, y, ω)dy3dy2dy1 (15)
with Lighthill’s tensor in the frequency domain,
SG(y, ω) =
ˆ∂2Tij
∂yi∂yj
(y, ω). (16)
The source can be defined throughout the domain, being defined as zero outside the turbulent region, so
that the integration limits eq. (15) go from −∞ to ∞
B. Radiating and non-radiating spanwise wavenumbers in the trailing-edge noise problem
Further insight on the dominant turbulent structures leading to trailing-edge noise can be obtained by
evaluating the contributions of different spanwise wavenumbers to the far-field sound. The source term can
be defined as a function of its Fourier transform in the spatial spanwise direction y3:
SG(y1, y2, y3, ω) =
1
2π
∞
kz=−∞
ˆSG(y1, y2, kz, ω)e−ikzy3
dkz (17)
Replacing in equation (15) we obtain
ˆp(x, ω) =
1
8π2
∞
y1=−∞
∞
y2=−∞
∞
kz=−∞
ˆSG(y1, y2, kz, ω)
∞
y3=−∞
G(x, y, ω)e−ikzy3
dy3 dkzdy2dy1 (18)
where the expression inside the brackets can be defined as:
∞
y3=−∞
G(x, y, ω)e−ikzy3
dy3 = ˆG(x, y1, y2, −kz, ω) (19)
Replacing this result in equation (18) we can obtain the final expression for the pressure field in terms
of the spanwise Fourier transform of both Green’s function and source, as
ˆp(x, ω) =
1
8π2
∞
y1=−∞
∞
y2=−∞
∞
kz=−∞
ˆSG(y1, y2, kz, ω) ˆG(x, y1, y2, −kz, ω)dkzdy2dy1 (20)
Equation (20) shows that each spanwise wavenumber kz in the source, ˆS(y1, y2, kz, ω), will have its
contribution to the far-field sound weighted by a corresponding wavenumber −kz in the Green’s function,
ˆG(x, y1, y2, −kz, ω). We will here evaluate analytically the Fourier transform in eq. (19) so as to determine
the said weighting factors, which will show us the dominant source wavenumbers for far-field radiation.
To apply the spatial Fourier transform along the z axis for the source, we need to evaluate the integral
ˆGs(x, y1, y1, kz, ω) =
∞
−∞
Gs(z0)eikzz0
dz0 (21)
considering that only z0 varies (the observers are fixed, as well as the other two components of the source).
Replacing equation 14 into 21, taking out of the integral the terms with no z0 dependency and reorganizing,
we obtain:
ˆGs(x, y1, y1, kz, ω) =
2e
1
4 iπ+ikzz
√
π
(2krr0)
1
2
cos
θ
2
cos
θ0
2
∞
−∞
1
R (r2 + (z − z0)2)
1
4
e−ikz(z−z0)−ikR
dz0 (22)
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6. With the integral in this form, we can apply the following transformation on z0:
z − z0 = q tan α, (23)
dz0 = −
q
cos2 α
dα, (24)
with q defined as
q = r2 + r2
0 − 2rr0 cos (θ − θ0) = (x1 − y1)2 + (x2 − y2)2. (25)
Since −∞ < z0 < ∞, α is a real number between −π/2 and π/2. If we apply the transform 23 on
equation 22 and make the necessary changes, we obtain:
ˆGs(x, y1, y1, kz, ω) = C
π/2
−π/2
F(α)eiqψ(α)
dα (26)
where
C =
2e
1
4 iπ+ikzz
√
π
(2krr0)
1
2
cos
θ
2
cos
θ0
2
(27)
F(α) =
1
r2 + q2 tan2
α
1
4
cos α
(28)
ψ(α) = −
k − kz sin α
cos α
(29)
It is easy to see that both F and ψ are continuous in the integration domain, as well as their first and
second derivatives. The far-field hypothesis corresponds to q → ∞; this allows an asymptotic solution to
the integral using the stationary phase method.5
The points αs leading to constant phase at eiqψ(α)
, which
have the leading-order contribution to the integral, must satisfy ψ (αs) = 0. The only root is given by
αs = arcsin
−kz
k
, (30)
and since α is a real number satisfying −π/2 < α < π/2, in order that the stationary phase point lie in the
integration path we must have
|kz| < k (31)
which means that the only wave numbers that radiate sound correspond to supersonic phase velocities along
the z axis, i.e. in the spanwise direction. This result is well known for the free-field Green’s function,4,11,7
and is here extended to the tailored Green’s function related to the edge scattering problem.
Using the far-field approximation (q → ∞) on integral 26, the stationary phase method gives an asymp-
totic approximation:
ˆGs(x, y1, y1, kz, ω) ≈ C
2π
q|ψ (α0)|
1
2
F(α0)eiqψ(α0)− 1
4 iπ
(32)
where
F(α0) =
1
r2 + q2 k2
z
k2−k2
z
1
4
√
k2−k2
z
k
(33)
ψ(α0) = − k2 − k2
z (34)
ψ (α0) = −
k2
k2 − k2
z
(35)
and C is defined by equation 27.
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7. From the results showed above we can deduce some features of the sound generation in this problem.
Firstly, from equation 31 we find that the only radiating turbulent disturbances are the ones with |kz| < k
(or the perturbations with supersonic phase velocity, since we can define kz = ω
vφ
, where vφ is the phase
velocity). In second place, the wavenumber kz for the source term is associated with the incidence angle of the
perturbations on the trailing edge of the plate: for waves normal to the trailing edge we have kz = 0 (there
is no component of the perturbation in z direction), with increasing wavenumber for increasing incidence
angles. If this incidence angle is related to a wavenumber outside the supersonic region, only evanescent
waves will be generated, with zero contribution to the far-field sound. It is important to notice that two-
dimensional disturbances, associated to kz = 0, are always radiating, whereas perturbations associated with
other wavenumber may not generate sound at a given frequency.
In the following section we will use this theoretical prediction to perform flow-acoustic correlations in
a different manner. Besides taking the usual two-point correlation, we will isolate the two-dimensional
component of the flow fluctuations, corresponding to kz = 0. This is always radiating, and by the evaluation
of the correlation between kz = 0 components in the turbulence and in the acoustic field we expect to
highlight the dominant mechanism of trailing edge noise.
III. Flow-acoustic correlations
A. Database
In this section we present the results of flow-acoustic correlations in order to discern the regions in the flow
most relevant for sound radiation. The large-eddy simulation (LES) of Wolf et al. of a NACA0012 airfoil at
zero angle of attack, M∞ = 0.115 and Rec = 4.08 · 105
was used for that matter. The simulation attempts
to represent an infinite-span airfoil by considering periodic boundary conditions at the spanwise extremities.
This spanwise periodicity leads to discrete values of the spanwise wavenumber kz, given as
kzc =
2πn
Lz
c, (36)
where n is an integer number. The simulation domain has Lz = 0.1c, which is large compared to the boundary
layer thickness, and was seen by Wolf et al. to be sufficient to obtain a decaying two-point coherence along
the span. With this computational domain, besides the two-dimensional mode kz = 0 the first non-zero
wavenumber corresponds to kzc = 20π, which is large in terms of the airfoil chord, but small in terms of the
boundary layer thickness. Table 1 shows the wavenumber in terms of boundary layer thickness.
x/c 0.8540 0.8980 0.9170 0.9520 0.9700 0.9830
δ∗
0.0039 0.0045 0.0048 0.0055 0.0059 0.0065
kzδ∗
0.2471 0.2806 0.2995 0.3477 0.3728 0.4063
Table 1. Calculation of the wavenumber in terms of the boundary layer thickness.
To determine flow-acoustic correlations we have taken flow fluctuations throughout a body-fitted O-
grid block (Figure 11, referenced as grid 1). Fluctuations at all these positions were with a representative
position in the acoustic field, aligned with the trailing edge, at x/c = 1 and y/c = 2. Details on the numerical
simulation can be found in the Appendix.
The use of numerical data has the advantage of allowing the study of correlations using different quantities,
taken at various positions in the flow. Moreover, it is possible to extract the expected dominant low spanwise
wavenumbers satisfying kz < k, which would be an ambitious task to perform experimentally. However, the
numerical simulation has a shorter duration (˜t = 15.98, ˜t = tao/L) compared to usual time series taken from
experiments, which impact the calculation of correlations. The clearest effect of this is an overall noise level
in the correlations, whose order is 60%. We will nonetheless see that for some positions the correlation peaks
greatly exceed the background noise, and are taken as significant despite the relative short time series.
B. Two-dimensionality of the acoustic field
A first observation on the radiated sound can be made with regard to the power spectral density (PSD) at
the point taken in the acoustic field. The PSD was calculated at this position in two ways: the first is the
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8. usual single-point PSD, and the second accounted solely for the kz = 0 component of the acoustic field; this
last approach amounts to taking a spanwise average prior to computing PSD. The results are shown in figure
2.
10
0
10
1
10
2
10
3
10
−20
10
−19
10
−18
10
−17
10
−16
10
−15
10
−14
10
−13
10
−12
10
−11
He
PSD[dB]
With spanwise averaged
Without spanwise averaged
He
n=0
He
n=1
He
n=2
He
n=3
Figure 2. Power spectral densities of pressure at x/c = 1 and y/c = 2
To help the analysis, the vertical lines in figure 2 show cut-on values of He for the successive spanwise
wavenumbers, according to the analysis of section II:
Hen = knc =
2πn
Lz
c (37)
Helmholtz numbers satisfying He > Hen (i.e. to the right of the corresponding vertical line) are such
that the nth spanwise wavenumber in the source is propagative. On the other hand, if He < Hen (left of the
corresponding line) the nth spanwise wavenumber leads solely to evanescent waves. The two-dimensional
mode kz = 0, or n = 0, is propagative for all He.
Note that there is virtually no difference between spectra with and without spanwise averaging up to He
corresponding to the cut-on condition for n = 1, which is consistent with the theoretical analysis. Above
that value some differences appear, but the energy-containing part of the acoustic spectrum is clearly two-
dimensional. It is interesting to notice that above the cut-on He for n = 2 a new peak also emerges in the
PSD.
These results are in line with the theory presented in section II, and suggest that the predominantly
two-dimensional acoustic field is generated by corresponding two-dimensional flow fluctuations. In a similar
manner to the approach of Cavalieri et al.,3
who have obtained more significant flow-acoustic correlation for
jets when the axisymmetric mode was isolated, we compare in what follows the usual two-point statistics
with correlations where the two-dimensional component was extracted by taking spanwise averages in the
turbulent and acoustic fields.
C. Correlations between pressure in the near and acoustic fields
We start the evaluation of correlation coefficients by looking solely at pressure fluctuations, with correlations
between near-field and acoustic pressure. The peak correlation, with acoustic pressure taken in the reference
point, is shown in Figure 3, where both quantities were spanwise averaged. To aid the analysis the boundary-
layer thickness and displacement thickness were plotted in the trailing edge region. Determination of the
boundary layer thickness close to the trailing edge becomes difficult due to the significant gradients of the
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9. outer velocity, and hence we show only values of δ up to x/c ≈ 0.94. There is a significant correlation
peak in outer portions of the figure, but this occurs outside the boundary layer, and is hence attributed to
correlations between acoustic waves.
Figure 3. Maximum correlation between near-field and acoustic pressure. Both quantities are spanwise
averaged.
A zoom of figure 3 in the trailing edge region is shown in figure 4 (a). We observe high correlation
peaks inside the boundary layer, extending all the way from the wall to the boundary layer thickness δ.
The correlation coefficients are roughly 40%. On the other hand, correlations without taking the spanwise
average of the pressure, shown by figure (b), do not display visible peaks above the noise level.
This result agrees with the theoretical considerations of section II, showing that higher correlations are
obtained when kz = 0 is isolated in the turbulence field. For the energy-containing part of the acoustic
spectrum only the two-dimensional mode is radiating. Furthermore we observe that the source of sound is
concentrated in the neighbourhood of the trailing edge (centred around x/c = 0.96), which is also predicted
by the theory12
.
Correlation coefficients were seen to be oscillatory, and besides presenting a positive peak they also present
negative peaks. In order to quantify these negative peaks, Figure 5 shows the minimum of flow-acoustic
correlation, again with a prior spanwise average of fluctuations. To facilitate the comparison with figures
of maximal correlation, the minimal were plotted using a reversed color scale. The results in Figure 5 also
show significant peaks (this time negative) of the correlation inside the boundary layer, in the vicinity of
the trailing edge. This negative peak occurs around x/c = 0.93, which is slightly upstream of the region of
positive peak. Furthermore, we also observe a region of significant correlation further downstream, in the
near-field of the wake.
We have seen that taking spanwise averages of flow fluctuations greatly enhances the correlation coeffi-
cients. If we now consider that trailing edge scattering occurs due to advected disturbances in both upper
and lower airfoil surfaces, it makes sense to extract the difference between upper- and lower-surface fluctu-
ations prior to the calculation of correlations. The underlying idea is that identical disturbances at both
sides of the trailing edge would lead to destructive interference and hence low acoustic scattering. This
idea is pursued in Figure 6, where we show the correlations of the pressure difference between upper and
lower surfaces of the airfoil to the acoustic pressure; spanwise-averaged quantities were taken. Similar to the
results previously presented, we observe high correlations inside the boundary-layer and close to the trailing
edge. This time, correlation coefficients are even higher, getting close to approximately 80%.
We have seen that correlation coefficients are greatly increased if spanwise averages and differences
between upper and lower surfaces are taken in the near-field, prior to the determination of correlations. This
suggests that the relevant sound-producing fluctuations are two-dimensional and in phase opposition in the
trailing edge region. This will be further pursued in the next section, where velocity-pressure correlations
are shown.
D. Velocity-pressure correlations
The results of the preceding section were of pressure-pressure correlations. Since velocity disturbances are
more often studied in analyses of the turbulent field, and are closely related to the source terms in acoustic
analogies, we present here similar correlations, this time taken between components of the velocity vector
with acoustic pressure.
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10. (a) With spanwise average
(b) Without spanwise average
Figure 4. Maximum correlation between grid 1 pressure and far-field pressure.
Figure 5. Minimum correlation between grid 1 pressure and far-field pressure, both quantities spanwise
averaged. We plot (−1) times the minimal correlation coefficient to allow direct comparison with the color
scales of Figure 4 and other similar plots.
Figure 7 shows the minimum velocity-pressure correlation, where the u component was taken. Fluctua-
tions were spanwise-averaged as in the analysis of the previous section. No significant positive correlation
peaks were observed, hence we focus on the minimum correlation (which displays the negative peaks); again,
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11. Figure 6. Maximum correlation between grid 1 pressure difference between the upper and lower surface of
the airfoil and far-field pressure; spanwise-averaged quantities.
an inversion of the color scale was done to allow direct comparison with the other plots. We observe a thin
region in the neighborhood of the trailing edge with high correlation with the radiated sound. This region
is inside the boundary layer, around the displacement thickness.
Figure 7. Minimum correlation between u-component and acoustic field pressure. Fluctuations were spanwise-
averaged. We plot (−1) times the minimal correlation coefficient to allow direct comparison with the color
scales of Figure 4 and other similar plots.
When the spanwise average is not taken, the correlation coefficients become negligible, as shown in Figure
8. This again shows that the two-dimensional part of the turbulent field is most relevant for sound radiation.
If the difference of the u-component between upper and lower surfaces is taken before correlation, we
obtain the results of Figure 9. As was observed with the pressure, the correlation coefficients become more
significant in the vicinity of the trailing edge.
The two-dimensional part of the acoustic field is the most correlated with the acoustic pressure, in spite
of its relative low kinetic energy. This is shown in Figure 10, which compares the root-mean-square (RMS)
of the u-component near the airfoil. We observe that downstream of the laminar-turbulent transition, in
a region with approximately 0.2 ≤ x/c ≤ 1.2, we have RMS(u2D) << RMS(u3D). The two-dimensional
part of the velocity field is thus a small fraction of the overall turbulence; however, these low-amplitude
two-dimensional structures are closely related with trailing-edge noise.
Correlations using v- and w-components are not presented here due to lack of expressive flow-acoustic
correlations.
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12. Figure 8. Minimum correlation between u-component and acoustic field pressure. Fluctuations were not
spanwise-averaged. We plot (−1) times the minimal correlation coefficient to allow direct comparison with the
color scales of Figure 4 and other similar plots.
Figure 9. Minimum correlation between grid 1 u-component, with difference between the upper and lower
surfaces of the airfoil, and acoustic field pressure. See comments in the caption of Figure 7.
IV. Conclusion
We have used flow-acoustic correlations to identify regions and mechanisms most effective to generate
sound in a turbulent flow around a NACA 0012 airfoil with zero angle of attack and M = 0.115.. Theoretical
results for the trailing-edge noise problem, modelled using the tailored Green’s function of Ffowcs Williams
and Hall12
show that only wavenumbers satisfying kz < k, where kz is the spanwise wavenumber of turbulent
disturbances and k is the acoustic wavenumber, radiate sound. In particular, two-dimensional disturbances
(kz = 0) are always radiating.
With this in mind we show, using flow-acoustic correlations obtained using data from a large eddy sim-
ulation, that when spanwise averages of flow fluctuations are taken, flow-acoustic correlations significantly
increase. We have obtained significant correlations in the trailing edge region for spanwise-averaged quanti-
ties: when pressure-pressure correlations were taken, a region extending from the wall to the boundary layer
thickness was found to present high correlation peaks; and for correlations between streamwise velocity and
acoustic pressure, an elongated region around the displacement thickness was found to have significant cor-
relation peaks as well, indicating that in this region there are coherent structures inside the boundary-layer
associated with far-field sound. If the two-dimensional mode is not isolated, correlation coefficients are lower,
and even negligible in some cases. Flow-acoustic correlations also increase when a difference of fluctuations
between the upper and lower surfaces is taken, which agrees with theory: convection of disturbances in phase
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13. (a) RMS of grid 1 u-component with spanwise-average
(b) RMS of grid 1 u-component with no spanwise-average
Figure 10. Comparison between the RMS of grid 1 u-component with spanwise-average and grid 1 u-component
with no spanwise-average
opposition across the trailing edge leads to maximal scattered sound.
Some features of the analysis are particular to the kind of numerical simulation used here, which is an
LES adopting periodic boundary conditions along the span. Similar simulations use the same approach
(e.g. Sandberg and Sandham10
), and, although validation of such simulations involve a demonstration of
coherence decay along the spanwise direction of the computational domain, an artefact persists: only discrete
values of spanwise wavenumbers are possible, and in some cases (such as in the simulation used in this work)
most of the sound radiation is two-dimensional, as kz = 0 is the only radiating wavenumber for most of the
acoustic spectrum. In experiments, we expect a much broader range of spanwise wavenumbers, and non-zero
kz would probably radiate sound. However, the |kz| < k condition implies that for most Helmholtz numbers
only spanwise-elongated structures, with characteristic dimension greater than the acoustic wavelength,
radiate sound to the far field. Further numerical and experimental work aiming at the characterization of
such structures is promising.
V. Acknowledgments
The authors acknowledge the financial support received from Conselho Nacional de Desenvolvimento
Cient´ıfico e Tecnol´ogico, CNPq, under grant No. 402233/2013-1 and 382381/2014-9. A. V. G. Cavalieri was
supported by Conselho Nacional de Desenvolvimento Cient´ıfico e Tecnol´ogico, CNPq, through a research
scholarship. The authors also acknowledge the financial support received from Funda¸c˜ao de Amparo `a
Pesquisa do Estado de S˜ao Paulo, FAPESP, under Grant No. 2013/03413-4 and from Conselho Nacional de
Desenvolvimento Cient´ıfico e Tecnol´ogico, CNPq, under Grant No. 470695/2013-7. We thank Peter Jordan
for helpful discussions regarding the present work.
References
1R. K. Amiet. Noise due to turbulent flow past a trailing edge. Journal of Sound and Vibration, 47(3):387–393, 1976.
2T. F. Brooks, D. S. Pope, and M. A. Marcolini. Airfoil self-noise and prediction, volume 1218. National Aeronautics and
Space Administration, Office of Management, Scientific and Technical Information Division, 1989.
3A. V. G. Cavalieri, D. Rodr´ıguez, P. Jordan, T. Colonius, and Y. Gervais. Wavepackets in the velocity field of turbulent
jets. Journal of Fluid Mechanics, 730:559–592, 2013.
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14. 4D. G. Crighton. Basic principles of aerodynamic noise generation. Progress in Aerospace Sciences, 16(1):31–96, 1975.
5D. G. Crighton, A. P. Dowling, J. E. Ffowcs-Williams, M. Heckl, and F. G. Leppington. Modern methods in analytical
acoustics: lecture notes. Springer, 1992.
6N. Curle. The influence of solid boundaries upon aerodynamic sound. Proceedings of the Royal Society of London. Series
A. Mathematical and Physical Sciences, 231(1187):505–514, 1955.
7P. Jordan and T. Colonius. Wave packets and turbulent jet noise. Annual Review of Fluid Mechanics, 45(1), 2013.
8M. J. Lighthill. On sound generated aerodynamically. i. general theory. Proceedings of the Royal Society of London.
Series A. Mathematical and Physical Sciences, 211(1107):564–587, 1952.
9Assad A. Oberai, Farzam Roknaldin, and Thomas J. R. Hughes. Computation of trailing-edge noise due to turbulent
flow over an airfoil. AIAA journal, 40(11):2206–2216, 2002.
10Richard D. Sandberg and Neil D. Sandham. Direct numerical simulation of turbulent flow past a trailing edge and the
associated noise generation. Journal of Fluid Mechanics, 596:353–385, 2008.
11Christopher K. W. Tam. Supersonic jet noise. Annual Review of Fluid Mechanics, 27(1):17–43, 1995.
12J. E. Williams and L. H. Hall. Aerodynamic sound generation by turbulent flow in the vicinity of a scattering half plane.
Journal of Fluid Mechanics, 40(04):657–670, 1970.
13W. R. Wolf, J. L. F. Azevedo, and S. K. Lele. Convective effects and the role of quadrupole sources for aerofoil
aeroacoustics. Journal of Fluid Mechanics, 708:502–538, 2012.
A. Numerical Simulation
The Large-Eddy Simulations (LES) in this work are the result of Wolf et al.13
for which time-resolved data
is available for all points in the grid. In what follows we summarize some of the simulation characteristics.
To perform the numerical simulation two different grids were used. The first allows accurate resolution of the
airfoil boundary layer. This grid is body-fitted O-grid block composed by 1536 x 125 x 128 nodes (Figure 11
(b)). The second grid is more appropriate for acoustic waves emanating from the airfoil. This grid is a
Cartesian background grid block and it is composed by 896 x 511 x 64 (Figure 11 (a)).
Wolf et al. performed the solution of general curvilinear form of the compressible Navier-Stokes equations,
given as
∂ρ
∂t
+
∂(ρui
)
∂t
= 0, (38)
∂(ρui
)
∂t
+
(ρui
uj
+ gij
p−τij)
∂xj
= 0, (39)
∂E
∂t
+
∂[(E + p)ui
− τijgikuk
+ qj]
∂xj
= 0, (40)
To close the set of equations we define the total energy equation, E, express the heat flux using Fourier’s
law and the viscous stress tensor using the expression for a Newtonian fluid. We obtain thus
E =
p
γ − 1
+
1
2
ρgikui
uk
, (41)
qj = −
µ
RePr
gij ∂T
∂xi
(42)
τij =
µ
Re
(gjk ∂ui
∂xk
+ gik ∂uj
∂xk
−
2
3
gij ∂uk
∂xk
) (43)
Finally, the gas is taken as calorically perfect, hence
p =
γ − 1
γ
ρT (44)
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15. (a) (b) (c)
Figure 11. Mesh details; (a)Full view of Cartesian grid with composed 896 x 511 x 64 nodes; (b)Body-fitted
O-grid block with composed 1536 x 125 x 128 nodes. (c)Detailed rounded trailing edge.
In Table 2 there is a summary of detailed properties used on current simulation. To force transition to
turbulence in the boundary layer, a boundary layer trip was simulated using artificial blowing and suction.
Figure 12 illustrates the region of boundary layer tripping.
Rec M∞ AoA[deg.] BL tripping ∆t NS NpS
408000 0.115 0 Top and bottom sides 0.0004 3 512
Table 2. Summary of flow configuration analyzed. Here, Rec is the Reynolds number based on the aerodynamic
profile chord, AoA is the angle of attack, δt is the dimensionless time step for time marching of the LES
equations, NS is the number of datasets for acoustic processing, and NpS is the number of samples in each
dataset.
Figure 12. Illustrative description of aerodynamic profile used on LES simulation and the region of boundary
layer tripping.
Figure 13 (a) shows a general view of the turbulent field around the airfoil by plotting the iso-surfaces of
λ2. Figure 13 (b) illustrates the boundary layer transition region and the noise generation due the airfoil.
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16. (a) (b)
Figure 13. LES of flow past a NACA0012 airfoil at AoA = 0 deg, M∞ = 0.115 and Rec = 408000; (a) iso-surfaces
of λ2 colored by vorticity magnitude; (b) iso-surfaces of vorticity magnitude colored by streamwise momentum
with contours of dilatation in the background
(a) (b)
Figure 14. (a) Points used to correlate with center at x/c = 0.5; (b) Points used to correlate with center at
x/c = 1.0
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