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
Diffusers are extensively used in centrifugal
compressors, axial flow compressors, ram jets, combustion
chambers, inlet portions of jet engines and etc. A small change in
pressure recovery can increases the efficiency significantly.
Therefore diffusers are absolutely essential for good turbo
machinery performance. The geometric limitations in aircraft
applications where the diffusers need to be specially designed so
as to achieve maximum pressure recovery and avoiding flow
separation.
The study behind the investigation of flow separation in a planar
diffuser by varying the diffuser taper angle for axisymmetric
expansion. Numerical solution of 2D axisymmetric diffuser model
is validated for skin friction coefficient and pressure coefficient
along upper and bottom wall surfaces with the experimental
results of planar diffuser predicted by Vance Dippold and
Nicholas J. Georgiadis in NASA research center [2]
.
Further the diffuser taper angle is varied for other different
angles and results shows the effect of flow separation were it is
reduces i.e., for what angle and at which angle it is just avoided.
Estimation of Damping Derivative in Pitch of a Supersonic Delta Wing with Cur...iosrjce
In the Present paper effect of angle of incidence on Damping derivative of a delta wing with Curved
leading edges for attached shock case in Supersonic Flow has been studied. A Strip theory is used in which
strips at different span wise location are independent of each other. This combines with similitude to give a
piston theory which gives closed form solutions for damping derivatives at low to high supersonic Mach
numbers. From the results it is seen that with the increase in the Mach number, there is a progressive decrease
in the magnitude of damping derivatives for all the Mach numbers of the present studies; however, the decrease
in the magnitude is variable at different inertia level. It is seen that with the increase in the angle of attack the
damping derivative increases linearly, nevertheless, this linear behavior limit themselves for different Mach
numbers. For Mach number M = 2, this limiting value of validity is fifteen degrees, for Mach 2.5 & 3, it is
twenty five degrees, whereas, for Mach 3.5 & 4 it becomes thirty five degrees, when these stability derivatives
were considered at various pivot positions; namely at h = 0.0, 0.4, 0.6, and 1.0. After scanning the results it is
observed that with the shift of the pivot position from the leading edge to the trailing edge, the magnitude of the
damping derivatives continue to decrease throughout. Results have been obtained for supersonic flow of perfect
gases over a wide range of angle of attack and Mach number. The effect of real gas, leading edge bluntness of
the wing, shock motion, and secondary wave reflections are neglected.
IJERA (International journal of Engineering Research and Applications) is International online, ... peer reviewed journal. For more detail or submit your article, please visit www.ijera.com
Diffusers are extensively used in centrifugal
compressors, axial flow compressors, ram jets, combustion
chambers, inlet portions of jet engines and etc. A small change in
pressure recovery can increases the efficiency significantly.
Therefore diffusers are absolutely essential for good turbo
machinery performance. The geometric limitations in aircraft
applications where the diffusers need to be specially designed so
as to achieve maximum pressure recovery and avoiding flow
separation.
The study behind the investigation of flow separation in a planar
diffuser by varying the diffuser taper angle for axisymmetric
expansion. Numerical solution of 2D axisymmetric diffuser model
is validated for skin friction coefficient and pressure coefficient
along upper and bottom wall surfaces with the experimental
results of planar diffuser predicted by Vance Dippold and
Nicholas J. Georgiadis in NASA research center [2]
.
Further the diffuser taper angle is varied for other different
angles and results shows the effect of flow separation were it is
reduces i.e., for what angle and at which angle it is just avoided.
Estimation of Damping Derivative in Pitch of a Supersonic Delta Wing with Cur...iosrjce
In the Present paper effect of angle of incidence on Damping derivative of a delta wing with Curved
leading edges for attached shock case in Supersonic Flow has been studied. A Strip theory is used in which
strips at different span wise location are independent of each other. This combines with similitude to give a
piston theory which gives closed form solutions for damping derivatives at low to high supersonic Mach
numbers. From the results it is seen that with the increase in the Mach number, there is a progressive decrease
in the magnitude of damping derivatives for all the Mach numbers of the present studies; however, the decrease
in the magnitude is variable at different inertia level. It is seen that with the increase in the angle of attack the
damping derivative increases linearly, nevertheless, this linear behavior limit themselves for different Mach
numbers. For Mach number M = 2, this limiting value of validity is fifteen degrees, for Mach 2.5 & 3, it is
twenty five degrees, whereas, for Mach 3.5 & 4 it becomes thirty five degrees, when these stability derivatives
were considered at various pivot positions; namely at h = 0.0, 0.4, 0.6, and 1.0. After scanning the results it is
observed that with the shift of the pivot position from the leading edge to the trailing edge, the magnitude of the
damping derivatives continue to decrease throughout. Results have been obtained for supersonic flow of perfect
gases over a wide range of angle of attack and Mach number. The effect of real gas, leading edge bluntness of
the wing, shock motion, and secondary wave reflections are neglected.
IJERA (International journal of Engineering Research and Applications) is International online, ... peer reviewed journal. For more detail or submit your article, please visit www.ijera.com
International Journal of Computational Engineering Research(IJCER)ijceronline
International Journal of Computational Engineering Research(IJCER) is an intentional online Journal in English monthly publishing journal. This Journal publish original research work that contributes significantly to further the scientific knowledge in engineering and Technology
Numerical simulation and optimization of high performance supersonic nozzle a...eSAT Journals
Abstract The Principle purpose of a nozzle is to accelerate the flow to higher exit velocities. The fluid acceleration is based on the design criteria and characteristics. To achieve good performance characteristics with minimum energy losses a nozzle must satisfy all the design requirements at all operating conditions. This is possible only when the nozzle theory is assumed to be isentropic irrespective of the changes in pressure, temperature and density which is generally caused due to formation of a Shock Wave. The thesis focuses on the design, development and optimization of a Supersonic Convergent-Divergent Nozzle where the analytical results are validated using theory calculations. The simulation work is carried out for CD Nozzles with different angles of divergence keeping the other inputs fixed. The objective of the proposed thesis is to show the best Expansion ratio, Nozzle Pressure ratio (NPR) and Nozzle Area Ratio(NAR) where the thrust obtained by the supersonic nozzle is maximum. The simulation is then repeated for expansion gas the results of which are later compared with standard air to show which possesses better performance characteristics. The Nozzle design chosen is based upon existing literature studies. Key Words: CD Nozzle, Expansion Ratio, Nozzle Pressure Ratio (NPR), Nozzle Area Ratio(NAR),Divergence Angle etc…
Analysis of dual bell rocket nozzle using computational fluid dynamicseSAT Journals
Abstract Concept of Altitude adaptive rocket nozzles recently received greater importance and interest in the space explorations and other such applications in space and rocket technology. The operations reliability of rocket launcher and the earth to orbit rocket launch are the crucial for the space transportation in the future. The performance of the engine components such as the power plant and the thrust delivery of the engine such as nozzles are in renovation for the greater performance and applicability for complex space applications. In the recent progress of the combustion expansion system the rocket nozzles are greatly revised from both application and design perspectives. One of such development is the dual bell nozzle. The publications indicate that the research on the concept of dual bell nozzle is tardy and there is no much progress from the inception of the idea. The specific application purpose designs are tested experimentally and implemented but the large scale development can only be possible if the generalized design parameters can be suggested. In the present paper one of such nozzle is selected and studied using computational fluid dynamics (CFD) and the results are synthesized for bench marking the general approach to study the Dual Bell nozzles. The result shows the variation in the Mach number, pressure, temperature distribution and turbulence intensity. Keywords: Altitude adaptation, Dual bell nozzle, Nozzle pressure ratio, Over-expansion factor.
Brimmed diffuser is collection�acceleration device which shrouds a wind turbine.For a given turbine di ameter,the power augmentation can be achieved by brimmed diffuser,p opularly known as wind lens. The present numerical investigation deals with the effect of low pressure region created by wind l ens and hence to analyze the strong vortices formed by a brim attached to the shroud diffuser at exit. Also in this analysis,a c omparative numerical prediction of mass flow rates through the wind turbine has been carried out with various types of wind lens wh ich in turn helps to optimize the torque augmentati on. It has been numerically proved that there is significant increase in the wa ke formation & vortex strength when brimming effect is added to a diffuser
Analysis of Ground Effect on a Symmetrical AirfoilIJERA Editor
A Detailed Study and Computational Fluid Dynamics investigation was conducted to ascertain and highlight the
different ways in which ground effect phenomena are present around a symmetrical aerofoil-NACA 0015- when
in close proximity to the ground. The trends in force and flow field behaviour were observed at various ground
clearances, for different angle of attack. The analysis was carried out by varying the angle of attack from 00 to
100 and ground clearance of the trailing edge from minimum possible value to one chord length. It was found
that high values of pressure coefficient are obtained on the lower surface when the airfoil is close to the ground.
This region of high pressure extended almost over the entire lower surface for higher angles of attack. As a
result, higher values of lift coefficient are obtained when the airfoil is close to the ground. The flow accelerates
over the airfoil due to flow diversion from the lower side and higher mean velocity is observed near the suction
peak location. The pressure distribution on the upper surface did not change significantly with ground clearance
for higher angles of attack. The lift was found to drop at lower angles of attack at some values of ground
clearance due to suction effect on the lower surface as the result of formation of a convergent–divergent passage
between the airfoil and the ground plate. The values of drag coefficient were also noted for different ground
clearance, which is found to be decreasing as the airfoil is approaching to a closer ground clearance. This ground
effect is analyzed using FLUENT 5/6 code.
Prediction of aerodynamic characteristics for slender bluff bodies with nose ...vasishta bhargava
the numerical approach is used to verify the aero/hydrodynamic performance of different
geometries of nose cones. Computational methods predict the flow characteristics fairly accurately in order to validate
the data obtained from experiments. The simulation involves muzzle velocity that range from 5m/s to 25 m/s i.e. 1.69 to
8.4 x 105
and calculated for the different angle of attack, -10 to 20 degrees, to demonstrate the flow behavior around the
shells. Nosecone is the most forward section of any slender moving bodies which are used in rockets, guided missiles,
submarines, aircraft drop tanks and aircraft fuselage to reduce the aerodynamic or hydrodynamic drag. The basic
geometry of bluff body is cylinder with variant nosecone shapes such as flat and tapered head, with moderate to low
taper ratios and conical head.
Calculation of Fluid Dynamic for Wind Flow around Reinforced Concrete WallsIJERA Editor
A study on the flow phenomena around free-standing walls is important in practical building construction. In the present paper a numerical study is conducted for two- dimensional incompressible steady flow around freestanding walls using low-Re k-co turbulence model. The separation regions downstream the wall and on the roof of the leeward were predicted. Finally, results of numerical simulation are presented in the form of velocity vectors, velocity contour, pressure contours and streamlines
Naiver strokes equations :- These balance equations arise from applying Issac Newton’s second law to fluid motion , together with assumption that the stress in the fluid is the sum of a diffusing viscous and a pressure term- hence describing viscous flow.
Effect o f boundary layer and rotor speed on broadband noise from horizontal ...vasishta bhargava
In this paper, the effect of rotor speed and boundary layer on the broadband noise from wind turbines are discussed. The results from the computations have been validated using the far field acoustic measurements from a similar sized turbine
International Journal of Engineering Research and Applications (IJERA) is an open access online peer reviewed international journal that publishes research and review articles in the fields of Computer Science, Neural Networks, Electrical Engineering, Software Engineering, Information Technology, Mechanical Engineering, Chemical Engineering, Plastic Engineering, Food Technology, Textile Engineering, Nano Technology & science, Power Electronics, Electronics & Communication Engineering, Computational mathematics, Image processing, Civil Engineering, Structural Engineering, Environmental Engineering, VLSI Testing & Low Power VLSI Design etc.
International Journal of Computational Engineering Research(IJCER)ijceronline
International Journal of Computational Engineering Research(IJCER) is an intentional online Journal in English monthly publishing journal. This Journal publish original research work that contributes significantly to further the scientific knowledge in engineering and Technology
Numerical simulation and optimization of high performance supersonic nozzle a...eSAT Journals
Abstract The Principle purpose of a nozzle is to accelerate the flow to higher exit velocities. The fluid acceleration is based on the design criteria and characteristics. To achieve good performance characteristics with minimum energy losses a nozzle must satisfy all the design requirements at all operating conditions. This is possible only when the nozzle theory is assumed to be isentropic irrespective of the changes in pressure, temperature and density which is generally caused due to formation of a Shock Wave. The thesis focuses on the design, development and optimization of a Supersonic Convergent-Divergent Nozzle where the analytical results are validated using theory calculations. The simulation work is carried out for CD Nozzles with different angles of divergence keeping the other inputs fixed. The objective of the proposed thesis is to show the best Expansion ratio, Nozzle Pressure ratio (NPR) and Nozzle Area Ratio(NAR) where the thrust obtained by the supersonic nozzle is maximum. The simulation is then repeated for expansion gas the results of which are later compared with standard air to show which possesses better performance characteristics. The Nozzle design chosen is based upon existing literature studies. Key Words: CD Nozzle, Expansion Ratio, Nozzle Pressure Ratio (NPR), Nozzle Area Ratio(NAR),Divergence Angle etc…
Analysis of dual bell rocket nozzle using computational fluid dynamicseSAT Journals
Abstract Concept of Altitude adaptive rocket nozzles recently received greater importance and interest in the space explorations and other such applications in space and rocket technology. The operations reliability of rocket launcher and the earth to orbit rocket launch are the crucial for the space transportation in the future. The performance of the engine components such as the power plant and the thrust delivery of the engine such as nozzles are in renovation for the greater performance and applicability for complex space applications. In the recent progress of the combustion expansion system the rocket nozzles are greatly revised from both application and design perspectives. One of such development is the dual bell nozzle. The publications indicate that the research on the concept of dual bell nozzle is tardy and there is no much progress from the inception of the idea. The specific application purpose designs are tested experimentally and implemented but the large scale development can only be possible if the generalized design parameters can be suggested. In the present paper one of such nozzle is selected and studied using computational fluid dynamics (CFD) and the results are synthesized for bench marking the general approach to study the Dual Bell nozzles. The result shows the variation in the Mach number, pressure, temperature distribution and turbulence intensity. Keywords: Altitude adaptation, Dual bell nozzle, Nozzle pressure ratio, Over-expansion factor.
Brimmed diffuser is collection�acceleration device which shrouds a wind turbine.For a given turbine di ameter,the power augmentation can be achieved by brimmed diffuser,p opularly known as wind lens. The present numerical investigation deals with the effect of low pressure region created by wind l ens and hence to analyze the strong vortices formed by a brim attached to the shroud diffuser at exit. Also in this analysis,a c omparative numerical prediction of mass flow rates through the wind turbine has been carried out with various types of wind lens wh ich in turn helps to optimize the torque augmentati on. It has been numerically proved that there is significant increase in the wa ke formation & vortex strength when brimming effect is added to a diffuser
Analysis of Ground Effect on a Symmetrical AirfoilIJERA Editor
A Detailed Study and Computational Fluid Dynamics investigation was conducted to ascertain and highlight the
different ways in which ground effect phenomena are present around a symmetrical aerofoil-NACA 0015- when
in close proximity to the ground. The trends in force and flow field behaviour were observed at various ground
clearances, for different angle of attack. The analysis was carried out by varying the angle of attack from 00 to
100 and ground clearance of the trailing edge from minimum possible value to one chord length. It was found
that high values of pressure coefficient are obtained on the lower surface when the airfoil is close to the ground.
This region of high pressure extended almost over the entire lower surface for higher angles of attack. As a
result, higher values of lift coefficient are obtained when the airfoil is close to the ground. The flow accelerates
over the airfoil due to flow diversion from the lower side and higher mean velocity is observed near the suction
peak location. The pressure distribution on the upper surface did not change significantly with ground clearance
for higher angles of attack. The lift was found to drop at lower angles of attack at some values of ground
clearance due to suction effect on the lower surface as the result of formation of a convergent–divergent passage
between the airfoil and the ground plate. The values of drag coefficient were also noted for different ground
clearance, which is found to be decreasing as the airfoil is approaching to a closer ground clearance. This ground
effect is analyzed using FLUENT 5/6 code.
Prediction of aerodynamic characteristics for slender bluff bodies with nose ...vasishta bhargava
the numerical approach is used to verify the aero/hydrodynamic performance of different
geometries of nose cones. Computational methods predict the flow characteristics fairly accurately in order to validate
the data obtained from experiments. The simulation involves muzzle velocity that range from 5m/s to 25 m/s i.e. 1.69 to
8.4 x 105
and calculated for the different angle of attack, -10 to 20 degrees, to demonstrate the flow behavior around the
shells. Nosecone is the most forward section of any slender moving bodies which are used in rockets, guided missiles,
submarines, aircraft drop tanks and aircraft fuselage to reduce the aerodynamic or hydrodynamic drag. The basic
geometry of bluff body is cylinder with variant nosecone shapes such as flat and tapered head, with moderate to low
taper ratios and conical head.
Calculation of Fluid Dynamic for Wind Flow around Reinforced Concrete WallsIJERA Editor
A study on the flow phenomena around free-standing walls is important in practical building construction. In the present paper a numerical study is conducted for two- dimensional incompressible steady flow around freestanding walls using low-Re k-co turbulence model. The separation regions downstream the wall and on the roof of the leeward were predicted. Finally, results of numerical simulation are presented in the form of velocity vectors, velocity contour, pressure contours and streamlines
Naiver strokes equations :- These balance equations arise from applying Issac Newton’s second law to fluid motion , together with assumption that the stress in the fluid is the sum of a diffusing viscous and a pressure term- hence describing viscous flow.
Effect o f boundary layer and rotor speed on broadband noise from horizontal ...vasishta bhargava
In this paper, the effect of rotor speed and boundary layer on the broadband noise from wind turbines are discussed. The results from the computations have been validated using the far field acoustic measurements from a similar sized turbine
International Journal of Engineering Research and Applications (IJERA) is an open access online peer reviewed international journal that publishes research and review articles in the fields of Computer Science, Neural Networks, Electrical Engineering, Software Engineering, Information Technology, Mechanical Engineering, Chemical Engineering, Plastic Engineering, Food Technology, Textile Engineering, Nano Technology & science, Power Electronics, Electronics & Communication Engineering, Computational mathematics, Image processing, Civil Engineering, Structural Engineering, Environmental Engineering, VLSI Testing & Low Power VLSI Design etc.
APPLICATION OF TAGUCHI METHOD FOR PARAMETRIC STUDIES OF A FUNNEL SHAPED STRUC...ijmech
In this paper, attempt has been made to minimize sound reflection from the wall by using Taguchi’s method and to find optimal structure for the suggested test-section inside the cavitation tunnel. The suggested structure which was added to the test-section is funnel-shaped with a performance like a check valve. In order to obtain approximate values of five independent parameters, three levels were taken into account for each parameter. By combining parameters of different levels, 27 tests were designed using Taguchi’s method and Minitab Software. Different acoustic analyses were conducted in COMSOL Multiphysics software, and defined parameter of general reflection coefficient was obtained for 21 observer points. Applying the general reflection coefficients to Minitab Software and drawing the SNR graph, approximate values of the parameters were obtained. However, these values did not produce enough accuracy to design the optimal structure. For this reason, five levels around optimal values, obtained from the previous analysis, were considered for each parameter. Same steps were repeated again for the parameters at five
levels and optimal values were obtained. Optimal structure was modelled and analyzed. Consequently, appropriate defined parameters of general and local reflection coefficients were extracted which represented an optimal structure for the intended test section.
Investigation of Perforated Tube Configuration Effect on the Performance of E...Barhm Mohamad
Using perforated tube in exhaust mufflers is known to improve transmission loss (TL) by improving their sound pressure level (SPL) at the orifice. The perforated tube should affect the muffler performance analogous to a shell-and-tube heat exchanger. To the authors’ knowledge, there are few previous assessments reported in literature of the effects that the perforated tube configuration has on acoustic response and pressure drop predicted. The effects of (i) the perforated tube length, (ii) the diameter of tube holes, and (iii) flow through perforated tube were investigated. To assess the perforated tube effect on flow, the SOLIDWORKS 2017 based on Computational Fluid Dynamics (CFD) tool was utilized using real walls approach model with a surface roughness of 0.5 micrometres (AISI 316 cold rolled stainless steel sheet (ss) Ra = 0:5 μm). Perforated tube was found to cause back pressure which may increase SPL about 10%.
A full experimental and numerical modelling of the practicability of thin foa...Mehran Naghizadeh
This paper presents the performance of geofoam-filled trenches in mitigating of ground vibration transmissions by the means of a full experimental study. The results are interpreted in the frequency domain. Fully automated 2D and 3D numerical models are applied to evaluate the screening effectiveness of geofoam-filled trenches in the active and passive schemes. Experimental results are in good agreement with the prediction of numerical modelling. The validated model is used to investigate the influence of geometrical and dimensional features on the trench. In addition, three different systems including single, double and triangle wall obstacles are selected for analysis, and the results are compared for various situations. The parametric study is based on complete automation of the model through coupling finite element analysis software (Plaxis) and Python programming language to control input, change the parameters, as well as to produce output and calculate the efficiency of the barrier. The results show that the depth and the width of approximately 1λr and 0.2λr, respectively are enough to reach the acceptable amount of efficiency for the active isolation for all three systems. For the passive scheme, the role of depth can be ignored for the single and double wall barriers, while depth plays a significant role for the triangle wall system.
IJRET : International Journal of Research in Engineering and Technology is an international peer reviewed, online journal published by eSAT Publishing House for the enhancement of research in various disciplines of Engineering and Technology. The aim and scope of the journal is to provide an academic medium and an important reference for the advancement and dissemination of research results that support high-level learning, teaching and research in the fields of Engineering and Technology. We bring together Scientists, Academician, Field Engineers, Scholars and Students of related fields of Engineering and Technology
Open channel flow velocity profiles for different reynolds numbers and roughn...eSAT Journals
Abstract A series of laboratory tests were carried out to understand the extent of effect of roughness and Reynolds number on mean velocity in both outer and inner scaling. To this end, four different types of bed surface conditions (impermeable smooth bed, impermeable rough bed, permeable sand bed and impermeable distributed roughness) and two different Reynolds number (Reh = 47,500 and 31,000) were adopted in the study. Sand particles of median diameter of 2.46 mm were used to create the roughness. The results show that the mean velocities collapsed well for different Reynolds number and for all different bed surfaces. The maximum velocity for all flow conditions were observed below some distances from the free surface. The location of maximum velocity is seen to be dependent on both of roughness and Reynolds number. The smooth bed test data agrees well with the standard log law and collapses well in viscous sub layer and overlap region. The extent of collapses is found to be dependent on Reynolds number. Friction coefficient is noted to be dependent on both the Reynolds number and roughness. Key Words: Open channel flow, Reynolds number, Roughness, mean velocity, friction coefficient, log law
An Experimental Study on Vehicular Emission Dispersion through Single Storied...inventionjournals
International Journal of Engineering and Science Invention (IJESI) is an international journal intended for professionals and researchers in all fields of computer science and electronics. IJESI publishes research articles and reviews within the whole field Engineering Science and Technology, new teaching methods, assessment, validation and the impact of new technologies and it will continue to provide information on the latest trends and developments in this ever-expanding subject. The publications of papers are selected through double peer reviewed to ensure originality, relevance, and readability. The articles published in our journal can be accessed online.
Automotive silencer plays an important role in dyna mic performance of the exhaust system. As silencer is located at the tail end of the exhau st system with minimum support,it is subjected to intense vibrations. These vibrations c ause localized stresses in silencer. The vibrations and stresses are analyzed by finite elem ent method. Modal analysis is performed to evaluate dynamic characteristics of the silencer. I t is observed that natural frequencies are away from excitation frequency. Further,dynamic fr equency response analysis is performed with 3G acceleration in all directions varying with frequency. It is noticed that the stresses are concentrated at a joint between inlet pipe and flan ge and these stresses are above the material yield stress limit in X and Y directions. Hence,in order to reduce the induced stresses,the structural modification in silencer is proposed and subsequent analysis is carried out. The obtained stresses are below the yield stress limit in X as well as Y direction. The FEM results are verified by experimental results.
Financial accounting is described in with respect to information & operation involved in business, aspects of recording, classifying, summarizing. concepts applied for financial accounting
Enterprise product management in business environmentvasishta bhargava
Enterprise product management, factors & influence on the product flow in market segments. Product configurations & competencies in business environment.
Organization behavior & relationship in business environmentvasishta bhargava
Organization & relationship in business environment is comprehended as the interaction among the different states in development, levels of organization, its culture ...
Financial regulation & capital investment processvasishta bhargava
Financial regulation & capital investment process is presented with respect to the banking & non banking financial institutions. The primary & secondary capital market regulator along with intermediaries are depicted
Inventory management & supply chain management is indicated using standard measures of materials requirements, product demand, consistent use of the type of technology, utilization of inventory at different levels.
Financial instruments & marketability of securitiesvasishta bhargava
Financial instruments & factors affecting marketability of securities in corporate finance is shown,. The influence on the investor wealth quality is shown subjected to various risk factors involved in the process.
Development process of supply chain in business organizationvasishta bhargava
The development process of supply chain in business organization context is shown briefly. The key aspects involved in supply chain process is depicted in order to determine the development.
Organization Culture & change management in development process vasishta bhargava
Organization development & change management is discussed with its interrelationships. The process of change management is shown with the importance of management style & leadership skills prevalent in organization.
Final project report on grocery store management system..pdfKamal Acharya
In today’s fast-changing business environment, it’s extremely important to be able to respond to client needs in the most effective and timely manner. If your customers wish to see your business online and have instant access to your products or services.
Online Grocery Store is an e-commerce website, which retails various grocery products. This project allows viewing various products available enables registered users to purchase desired products instantly using Paytm, UPI payment processor (Instant Pay) and also can place order by using Cash on Delivery (Pay Later) option. This project provides an easy access to Administrators and Managers to view orders placed using Pay Later and Instant Pay options.
In order to develop an e-commerce website, a number of Technologies must be studied and understood. These include multi-tiered architecture, server and client-side scripting techniques, implementation technologies, programming language (such as PHP, HTML, CSS, JavaScript) and MySQL relational databases. This is a project with the objective to develop a basic website where a consumer is provided with a shopping cart website and also to know about the technologies used to develop such a website.
This document will discuss each of the underlying technologies to create and implement an e- commerce website.
Using recycled concrete aggregates (RCA) for pavements is crucial to achieving sustainability. Implementing RCA for new pavement can minimize carbon footprint, conserve natural resources, reduce harmful emissions, and lower life cycle costs. Compared to natural aggregate (NA), RCA pavement has fewer comprehensive studies and sustainability assessments.
The Internet of Things (IoT) is a revolutionary concept that connects everyday objects and devices to the internet, enabling them to communicate, collect, and exchange data. Imagine a world where your refrigerator notifies you when you’re running low on groceries, or streetlights adjust their brightness based on traffic patterns – that’s the power of IoT. In essence, IoT transforms ordinary objects into smart, interconnected devices, creating a network of endless possibilities.
Here is a blog on the role of electrical and electronics engineers in IOT. Let's dig in!!!!
For more such content visit: https://nttftrg.com/
Hierarchical Digital Twin of a Naval Power SystemKerry Sado
A hierarchical digital twin of a Naval DC power system has been developed and experimentally verified. Similar to other state-of-the-art digital twins, this technology creates a digital replica of the physical system executed in real-time or faster, which can modify hardware controls. However, its advantage stems from distributing computational efforts by utilizing a hierarchical structure composed of lower-level digital twin blocks and a higher-level system digital twin. Each digital twin block is associated with a physical subsystem of the hardware and communicates with a singular system digital twin, which creates a system-level response. By extracting information from each level of the hierarchy, power system controls of the hardware were reconfigured autonomously. This hierarchical digital twin development offers several advantages over other digital twins, particularly in the field of naval power systems. The hierarchical structure allows for greater computational efficiency and scalability while the ability to autonomously reconfigure hardware controls offers increased flexibility and responsiveness. The hierarchical decomposition and models utilized were well aligned with the physical twin, as indicated by the maximum deviations between the developed digital twin hierarchy and the hardware.
Sachpazis:Terzaghi Bearing Capacity Estimation in simple terms with Calculati...Dr.Costas Sachpazis
Terzaghi's soil bearing capacity theory, developed by Karl Terzaghi, is a fundamental principle in geotechnical engineering used to determine the bearing capacity of shallow foundations. This theory provides a method to calculate the ultimate bearing capacity of soil, which is the maximum load per unit area that the soil can support without undergoing shear failure. The Calculation HTML Code included.
Water billing management system project report.pdfKamal Acharya
Our project entitled “Water Billing Management System” aims is to generate Water bill with all the charges and penalty. Manual system that is employed is extremely laborious and quite inadequate. It only makes the process more difficult and hard.
The aim of our project is to develop a system that is meant to partially computerize the work performed in the Water Board like generating monthly Water bill, record of consuming unit of water, store record of the customer and previous unpaid record.
We used HTML/PHP as front end and MYSQL as back end for developing our project. HTML is primarily a visual design environment. We can create a android application by designing the form and that make up the user interface. Adding android application code to the form and the objects such as buttons and text boxes on them and adding any required support code in additional modular.
MySQL is free open source database that facilitates the effective management of the databases by connecting them to the software. It is a stable ,reliable and the powerful solution with the advanced features and advantages which are as follows: Data Security.MySQL is free open source database that facilitates the effective management of the databases by connecting them to the software.
Cosmetic shop management system project report.pdfKamal Acharya
Buying new cosmetic products is difficult. It can even be scary for those who have sensitive skin and are prone to skin trouble. The information needed to alleviate this problem is on the back of each product, but it's thought to interpret those ingredient lists unless you have a background in chemistry.
Instead of buying and hoping for the best, we can use data science to help us predict which products may be good fits for us. It includes various function programs to do the above mentioned tasks.
Data file handling has been effectively used in the program.
The automated cosmetic shop management system should deal with the automation of general workflow and administration process of the shop. The main processes of the system focus on customer's request where the system is able to search the most appropriate products and deliver it to the customers. It should help the employees to quickly identify the list of cosmetic product that have reached the minimum quantity and also keep a track of expired date for each cosmetic product. It should help the employees to find the rack number in which the product is placed.It is also Faster and more efficient way.
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NUMERICAL SIMULATIONS OF HEAT AND MASS TRANSFER IN CONDENSING HEAT EXCHANGERS...ssuser7dcef0
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6th International Conference on Machine Learning & Applications (CMLA 2024)ClaraZara1
6th International Conference on Machine Learning & Applications (CMLA 2024) will provide an excellent international forum for sharing knowledge and results in theory, methodology and applications of on Machine Learning & Applications.
Trailing edge noise prediction from NACA 0012 and NACA 6320 using empirical pressure spectrum models
1. IOSR Journal of Applied Physics (IOSR-JAP)
e-ISSN: 2278-4861.Volume 10, Issue 2 Ver. I (Mar. – Apr. 2018), PP 33-46
www.iosrjournals.org
DOI: 10.9790/4861-1002013346 www.iosrjournals.org 33 | Page
Trailing Edge Noise Prediction from NACA 0012 & NACA 6320
using Empirical Pressure Spectrum Models
Vasishta bhargava1
, S. Rahul2
, Dr. HimaBinduVenigalla3
1
Sreyas Institute of Engineering & Technology, Hyderabad
2
Indian Institute of Technology, Chennai
3
GITAM University, Hyderabad
Corresponding Author: Vasishta Bhargava
Abstract: 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 60
angles 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 x106
and 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.
Keywords: Airfoil, Noise, Sound Pressure Level, Trailing edge, Boundary layer.
---------------------------------------------------------------------------------------------------------------------------------------
Date of Submission: 26-02-2018 Date of acceptance: 17-03-2018
---------------------------------------------------------------------------------------------------------------------------------------
I. Introduction
Noise is unwanted sound waves produced due to pressure fluctuations in atmosphere which are
propagated and perceived by receiver. The thresholds of hearing and pain for a human are 0dB and 140dB and
limits for the sound perceived by observer at different frequency bands. Many engineering structures produce
noise when they interact with atmospheric air during operation and cause annoyance to inhabitants in
environment. Broadband aerodynamic noise contributes significantly to the overall sound pressure levels as
result of rotating components such as blades from wind turbine, fan, compressor etc. Airborne and structural
borne noise are two different noise sources that depend upon the aerodynamic and structural properties of
material. One of the contributions to sound radiation is unsteady fluid motion and shear stress within flow that
act as weak source of sound [16]. Velocity fluctuations within turbulence boundary layer flow induce acoustic
pressure fluctuations due to its interaction with the rigid flat surfaces and wall pressure fluctuations contribute to
noise in applications such as aircraft cabin noise, during transportation [7],[8]It has been observed that
aerodynamic and aero-acoustic problems posed with such structures require detail design taking account of the
acoustic source properties. Source characterization is done on the basis of the acoustic pressure fluctuations in
the atmosphere which are result of the fluid density or velocity component changes. This can be also be
attributed to the characteristic dimension of the source such as chord length, being greater or lesser with respect
to the acoustic wavelength and treated as either non compact or compact forms. Traditional acoustic analogy is
based on compressible Navier Stokes equation rearranged to form wave equation. However, Lighthill (1952)
had established the first theoretical background of the source characterization in free field by deriving the
inhomogeneous wave equation and rearranging unsteady compressible viscous Navier –Stokes equations, i.e. by
taking the difference between time derivative of continuity equation and divergence of momentum equation,
involving momentum transport containing three source terms[2], [3], [10]. They are fluctuating density and
pressure term, “Reynolds stress tensor”, and viscous stress tensor. However, the prediction of incident pressure
field was entirely described by the spatial distribution of non- linear volume quad poles not accounting for the
reflections from moving or rigid surfaces encountered in flow field. The acoustic pressure field was scaled with
Mach number, U8
of free stream velocity. Later Curle(1955) extended this analogy and made new formulations
that acoustic field is subjected to narrow angle reflections from flat surfaces enclosing all noise sources. The
1
Corresponding author: Email – vasishtab@gmail.com
2. Trailing Edge Noise Prediction from NACA 0012 & NACA 6320using Empirical Pressure Spectrum ..
DOI: 10.9790/4861-1002013346 www.iosrjournals.org 34 | Page
source is characterized into surface terms comprising acoustic monopoles and dipoles near the edge. Further, the
acoustic field behavior is governed by definition of control surface located inflow field, such as in Kirchoff
method, which assumes nonlinear sources enclosed within near and mid field and linear sources outside the
control surface in far field region and obeys linear wave equation. The acoustic pressure field is obtained in
terms of surface integral of pressure and its normal and time derivatives and including nonlinear quad pole noise
sources in far field [23]. FW-H (1970) proposed analogy for solid and moving source involving spatial
distribution of surface (thickness and loading noise) and volume terms emphasizing relationship between the
nonlinear aerodynamic near field and linear acoustic far field. Since calculating volume quad poles involves
significant computation effort using LES or DNS (Direct Numerical Simulations), it is not suitable for iterative
engineering design calculations. The acoustic pressure was scaled with Mach number, U4
and U6
of free stream
velocity that included effect of reflections from surfaces. For a given problem, the flow field can be described
by the viscous incompressible while the acoustic field as assumed inviscid which can be solved separately,
however they can be coupled to predict sound pressure level with less effort. The integral formulations for
acoustic field as proposed by Kirchoff and its extension by FW-H for porous surfaces can be extended using
RANS based statistical modeling (Doolan, 2010) to predict noise from turbulent boundary layer trailing edge
source [1] [2], [11]. The RANS based approach considers the mean values of velocity, turbulent kinetic energy
and dissipation terms ignoring time varying properties of turbulence to model the turbulent field with less
computational effort[24].
The earliest empirical models for predicting sound spectrum were based upon the wind tunnel
experimentation conducted by Paterson (1982), Brookes (1989), Blake (1986) who used NACA 0012 and
NACA 0018 airfoils for measuring the surface pressure fluctuations, boundary layer properties, and far field
noise spectra for low to moderate Reynolds number using chord lengths up to 1.2m. The measured data enabled
to understand the mechanism responsible for broadband and tonal noise caused due to pressure fluctuations
within the turbulent boundary layer and external pressure gradients that induced vortex shedding near the
trailing edge of airfoil [1],[9]. It was concluded that flow separation on airfoil trailing edge due to adverse
pressure gradient contributes to the acoustic field and found varying with angles of attack. Experiment studies
Paterson (1982) provided necessary background to derive the curve fitting expressions for boundary layer
thickness, displacement thickness and momentum thickness as function of tunnel wall corrected angles of attack
and chord Reynolds number in the BPM model (Brookes, Pope and Marcolini) (1989).The turbulence
phenomenon observed in canonical flows such as in pipes, duct or closed conduit and on airfoils is due to
existence of external pressure gradient within the boundary layer. In this paper, the effect of empirical pressure
gradient models on acoustic emissions from the airfoil is computed numerically using the wall pressure
spectrum and BPM model. The results obtained are compared with predictions from Tian, Kotte
(2016),Rozenberg (2012), Hu (2017) and experimental data from Keith et al (2005).It was found experimentally
in the past that adverse pressure gradient in the boundary layer interacts with surfaces like airfoil trailing edge as
found blades of wind turbine contribute to noise for incompressible flows [1],[2] [6]. The results of the wall
pressure spectrum are shown for the external pressure gradient models proposed initially by Chase (1980),
Howe (1998) and Amiet(1976) and modified by Goody who included the Reynolds number effect. A brief
review of Rosenberg model for the adverse pressure gradient flows is presented. Further, the airfoil self-noise
predictions from the BPM model for symmetric and cambered airfoils, NACA 0012, NACA 6320, 12 % and 20
% thick are illustrated at different airfoil chord length and Mach numbers.
II. WPS Models
Modeling the wall pressure fluctuations is based on interaction of convective velocity that varies
linearly within viscous sub-layer, with its mean value and nonlinear turbulent –turbulent velocity component
fluctuations within outer boundary layer. The velocity profile within the boundary layer varies due to effects of
pressure, temperature at wall or boundary. These effects can cause external pressure gradients within the
boundary layer leading to flow separations such as suction side of airfoil[1], [2] [14].Scaling laws available to
describe the velocity fluctuations within the turbulent boundary layer are insufficient to predict the behavior of
turbulent eddies which convect past the wall at different timescales [9],[10]. Hence, the determination of wall
pressure spectrum often involves analyzing spectral variables or through numerical simulations involving the
wave number or angular frequency represented by pressure and length scales. Broadband noise from turbulent
boundary layer is due to turbulent energy present in form of eddies which are defined by length and time scales
observed at low and high frequencies regions of spectrum. Accurate predictions are possible using DNS or LES
which is able to resolve such large energy containing scales of turbulence in flow but computationally intensive
compared to empirical models.
a) Amiet model
3. Trailing Edge Noise Prediction from NACA 0012 & NACA 6320using Empirical Pressure Spectrum ..
DOI: 10.9790/4861-1002013346 www.iosrjournals.org 35 | Page
Turbulent boundary layer can be characterized using integral length scales, and time scales. Trailing edge
represents one of the dominant acoustic sources in the form of cusped surface or bump where the strong adverse
pressure gradient exists. The wall pressure fluctuations near the trailing edge of a surface can be correlated with
the turbulent boundary layer length scales to determine the pressure amplitude. Close to wall, there exists a
laminar sub-layer in which velocity profile varies linear or parabolic [22]. The pressure spectra properties in
high or low frequency regions depend upon the wall shear stress, τw represented by “pressure scale” and ϑ/u2
for
“timescale” [8]. For the pressure spectra, boundary layer scaling is related to the inner and outer layers which
can be correlated with root mean square velocity fluctuations and wall shear stress. Experimental studies from
Willmarth and Roos, provided data which led to development of empirical model by Amiet[1],for the wall
pressure fluctuations inside the turbulent boundary layer region, [4] [6], [11] [13].By knowing the wall pressure
spectrum near the proximity of the trailing edge of airfoil surface, it is possible to predict whether the flow
remains attached or separated from boundary depending on when pressure gradient is negative or strong
positive. The sound convected past the trailing edge of an airfoil can therefore be predicted using the empirical
model formulated by Amiet for wall pressure spectrum, φpp (ω), which can be expressed by Eq (1) and Eq (2)
̅
(1)
̅̅̅̅
̅ ̅ ̅
(2)
Where ̅ - ωδ*/Ue and lie within the range 1 to20. Ue is the convective velocity, m/s, δ* is the boundary layer
displacement thickness.
b) Chase-Howe model
Chase (1980) derived generalized empirical wall spectrum combining the effect of mean shear and turbulent
shear for turbulent flows based on the experiments conducted by Ffwocs Williams, (1982) Kraichnan, (1956)
and compared them with the predictions from Corcos (1964) model. Howe (1998) further determined the
spectral characteristics of wall pressure fluctuations considering the mixed variables which use the boundary
layer thickness in outer and inner layers. In the experimental studies, the data from Keith (1992) used different
combinations of scaling variables at low frequencies in which pressure spectra collapsed for convective domain
[21]. The Chase- Howe spectrum is observed to vary with 2
at low frequencies. The wall pressure spectra are
found to be upward sloping near low frequencies, while negative in the transition region and steeply low in high
frequency regions. [2].
̅
[̅ ]
(3)
Where δ* is the boundary layer displacement thickness, Ue is the convective velocity, m/s. τwis the wall shear
stress within the boundary layer. Chase (1987) further developed the model by considering sub convective
region contribution from viscous sub layer and far field radiation domains in the acoustic spectrum applicable
for rigid flat surfaces [21].
c) Goody ZPG model
In this model, the wall pressure fluctuations are expressed in terms of wave number –frequency domain similar
to Chase –Howe (1980) model to predict the external pressure gradients. However, experimental studies from
Schloemer et al, have confirmed that this model does not predict APG flows accurately since it underestimates
the pressure amplitudes at low frequency regions of spectrum. According to Goody, Reynolds number
dependent on outer layer variable convective velocity, Ue and inner layer variable wall shear, τw influences the
acoustic pressure fluctuations and wall spectrum amplitudes, as result of turbulent velocity fluctuations within
the boundary layer. It can be expressed using Eq (4)
* + * +
(4)
Where C1, C2 and C3 are empirical constants with values 0.5, 0.3 and 1.1 and RT is the Reynolds number
dependence on wall shear stress, τw or outer to inner boundary layer time scale, .
d) Rosenberg APG model
In this model, modified form of Goody model which accounts for adverse pressure gradient effects,
within the boundary layer is formulated. Correction factors are obtained by taking boundary layer history which
adequately characterizes the mean adverse pressure gradient. It also uses local pressure gradient, βc known as
Clauser parameter that expresses the pressure forces within turbulent boundary layer involving wall shear stress,
τw, momentum thickness, θ, wake strength parameter, П, as postulated by Coles (1956) to describe the size of
4. Trailing Edge Noise Prediction from NACA 0012 & NACA 6320using Empirical Pressure Spectrum ..
DOI: 10.9790/4861-1002013346 www.iosrjournals.org 36 | Page
eddies in outer layer of turbulent boundary layer [2].Δ, is the ratio of thickness to displacement thickness and
use as measure of mean velocity defect, according to Zagarola-Smits law within the outer boundary layer as
well as to predict the mean pressure gradient [2]. However, from many experimental studies conducted by Na
and Moin, Schloemer, the wake strength parameter, П was also significant variable which affects the mean
pressure gradient. The velocity defects within the turbulent boundary layer take account of boundary layer
thickness, δ and displacement thickness, δ*. The final model developed by Rozenberg et al, using combined
parameters for mean adverse pressure gradient flow is given by Eq (5)
[ ]* +
[ ] [ ]
(5)
.Where F1 is expressed in terms of boundary layer thickness ratio and Clauser parameter,βc The effects of
changing Δ and β on the wall pressure spectrum can be found in figure 16 (a) and figure 16(b) [2]. A1, A2give
the empirical relationship between the Clauser parameter, βc, and ratio of outer to inner boundary layer time
scales.
III. Simulation details
The simulation is based on the incompressible flow over the airfoils NACA 0012 and NACA 6320
respectively. The program for BPM model for predicting the source region sound pressure spectrum and wall
pressure spectrum models was developed in MATLAB environment Analytical turbulence models coupled with
LES or DNS simulations produce turbulence by cross or auto correlation of fluctuating velocities and turbulence
constants. However, in the present study the assumption for turbulence in boundary layer flows is produced by
friction velocity dependent on surface roughness height at wall and corresponding to a range 0.01-0.2 m/s.
Linear and logarithmic law approximations are used for velocity profiles within boundary layer as well as model
parameters to represent the pressure gradients. The simulation parameters are outlined as, free stream velocities
of 65m/s and 40m/s resulted in chord Reynolds number, of 3.134 x106
, 4.612 x106
and free stream Mach number
corresponding to 0.1912 and 0.1176 respectively. The moderate angle of attack range was chosen to be within -2
to 60
and chord lengths for 1.2m, 0.5m and 0.8m. To study the effect of AOA on the development of boundary
layer thickness, displacement thickness ratios, two different chord lengths of 1.5m and 0.8m were assumed at
constant Ma-0.1912. The thicknesses are also evaluated at two different Mach numbers, Ma-0.1176 & 0.1912,
assuming a constant chord length of 1.5m. Three different aspect ratios were considered in simulation of sound
spectrum for NACA 0012 airfoil viz. 1, 3 and 4, with constant chord length of 0.5m.
IV. Results and Discussion
a) BPM Model &Effect of AOA, chord & Mach number on SPL
Figure 1 Turbulent boundary layer trailing edge, Sound pressure level (dB), 1/3rd
octave, for NACA 0012
airfoil, at different chord lengths, span - 2m, observer distance – 2m and free stream velocity – 65 m/s, 40
AOA. (a) Pressure side (b) Suction side (c) Stall separation (d) Total Turbulent Boundary Layer Trailing
5. Trailing Edge Noise Prediction from NACA 0012 & NACA 6320using Empirical Pressure Spectrum ..
DOI: 10.9790/4861-1002013346 www.iosrjournals.org 37 | Page
0
10
20
30
40
50
60
70
10 1000 100000
Soundpreessurelevel
[dB]
Frequency [Hz]
Pressure side
Ma 0.1912
Ma 0.1176
0
10
20
30
40
50
60
70
80
10 1000 100000
Soundpressurelevel[dB]
Frequency [Hz]
Suction side
Ma 0.1912
Ma 0.1176
0
20
40
60
80
10 100 1000 10000
Soundpressurelevel
[dB]
Frequency [Hz]
Stall seperation
Ma 0.1912
Ma 0.1176
Edge noise, Sound Power Level, dB, for three different receiver positions, 00
, 600
and 900
from trailing
edge
The BPM model characterizes the acoustic field using the scaling laws which are correlated with
boundary layer thickness, displacement and momentum thicknesses and function of chord length and angle of
attack. The scaling law helps to transform data from relatively small model to valuable design information for
large prototype model [22]. The model considers six noise mechanisms which include the effects of turbulent
boundary layer interaction with the trailing edge of airfoil and vortex shedding due to trailing edge thickness,
the tip noise, turbulent inflow noise [19], [20]. The airfoil is modeled as semi-infinite flat plate of finite
thickness on which incident pressure field undergoes diffraction at trailing edge as result of interaction of
turbulent boundary layer with airfoil surface to produce noise. The overall amplitude of the sound spectrum is
governed by amplitude and peak adjustment functions determined using chord Reynolds number and Strouhal
number based on boundary layer thickness on suction and pressure side of airfoils. The regions of sound
spectrum amplitude where the distinct peaks are observed were attributed to boundary layer instabilities or
amplification of acoustic pressure fluctuations caused due to diffraction at the trailing edge and its propagation
downstream. Figure 1shows the amplitude of SPL for turbulent boundary layer trailing edge on suction, pressure
and stall separation cases for NACA 0012 airfoil for three different chord lengths, 1.2m, 0.8m and 0.5m. It can
be noted that the amplitude is found to vary in low and high frequency regions of the spectrum, With increasing
chord length, the SPL, dB was found to increase between 100-1000 Hz while, decreasing in the very high
frequency regions, f>104
Hz. The present results showed similar trends to those from Brooks et al, for
symmetric airfoils for subsonic Mach number flows at different angles of attack for estimating the trailing edge
noise which were used to validate the BPM model[9], [11].
(a) (b)
(c) (d)
Figure 2Turbulent boundary layer trailing edge, SPL (dB) 1/3rd
Octave, for NACA 0012 airfoil at Mach
numbers, 0.1912 and 0.1176, for chord length –1.2m, free stream velocity, 65 m/s, 40
AOA. Receiver
position ~2m from trailing edge (a) Pressure side (b) Suction side (c) Stall separation (d) Total TBL-TE,
sound pressure level, dB variation with Strouhal number, St (fδs/U), for Ma – 0.1912, and at 2, 40
AOA.
Strouhal number scaled with displacement thickness, δ* of suction and pressure side, and peak at St~
0.07& 0.02
From figure 2, it can noted that the Mach number influence on the SPL, dB, by ~ 10dB in the 500-
1200Hz region of spectrum for pressure, suction sides of airfoil. For low Mach number flows, the
compressibility effect on the magnitude of SPL, dB is ignored, however, found to vary with angle of attack
negligibly. The dependence on angle of attack on the relative amplitude of SPL, dB for NACA 0012 is shown in
6. Trailing Edge Noise Prediction from NACA 0012 & NACA 6320using Empirical Pressure Spectrum ..
DOI: 10.9790/4861-1002013346 www.iosrjournals.org 38 | Page
0
10
20
30
40
50
60
70
10 100 1000 10000 100000
Soundpressurelevel
[dB]
Frequency [Hz]
AOA 0 deg
suction
pressure
seperation
0
10
20
30
40
50
60
70
80
10 100 1000 10000 100000
Soundpressurelevel[dB]
Frequency [Hz]
AOA 4 deg
suction
pressure
seperation
0
10
20
30
40
50
60
70
80
10 100 1000 10000 100000
AOA 6 deg
suction
pressure
seperation
figure 3. It can be seen that at 00
AOA, the suction and pressure side SPL coincide which indicates that for
symmetric airfoils the amplitude of SPL, dB remain same over whole spectrum. Further, it can be observed from
figure 3 (d) the separation noise becomes dominant at moderate angles of attack caused due to mean or strong
adverse pressure gradient leading to flow separation or backflow on the suction side of airfoil [9]. The influence
of external pressure gradients (see section d) in the flow over the stationary hard surfaces, indicate the velocity
profiles within the boundary layer region and radiated acoustic pressure field affect wall pressure fluctuations.
(a) (b)
(c) (d)
Figure 3 Turbulent boundary layer trailing edge, SPL(dB), for NACA 0012 airfoil, for chord length –
1.2m, free stream velocity, 65 m/s, Receiver position ~1.24m from source (a) AOA 00
(b) AOA 20
(c) AOA
40
(d) AOA 60
The analytical equations of the model for evaluating the sound pressure level from the contributing pressure,
suction, separation stall noise and the total TBLTE noise are
[
̅̅̅̅
] * + [ ] (6)
*
̅̅̅̅
+ * + [ ] (7)
*
̅̅̅̅
+ * + (8)
[ ] (9)
The Strouhal number and Reynolds number definitions are given by
* + * + [ ] * + (10)
* + * + (11)
The spectral shape functions for the model are denoted by A & B while amplitude correction and
adjustment functions are given by K1, K2 and dK1 Fink (1979) [9].The scaling laws relate the Strouhal
numbers, chord Reynolds number and Reynolds number based upon the displacement thickness, δ*
obtained
empirically, L- span length of airfoil,̅̅̅̅ is high frequency directivity functionexpressed in terms of directivity
0
20
40
60
80
10 100 1000 10000 100000
AOA 2 deg
suction
pressure
seperation
7. Trailing Edge Noise Prediction from NACA 0012 & NACA 6320using Empirical Pressure Spectrum ..
DOI: 10.9790/4861-1002013346 www.iosrjournals.org 39 | Page
angles and convective Mach number. Detailed equations for interpolation factors required to model sound
pressure levels are provided in BPM model. [1][9] [11] [15]. The boundary layer equations expressed in terms
of chord length, c, and AOA, are obtained empirically and combined to form analytical expressions as given by
Eq (6) – Eq (8) [9]. In practical case during microphone measurements for recording acoustic pressure use of A-
weighting filter dampens the pressure amplitudes in overall spectrum and does not truly represent the sound
pressure levels at receiver. Hence a comparison was therefore not made using A-weighted filter, for sensitivity
reasons.
Figure 4 BPM Model –Overall turbulent boundary layer trailing edge displacement thickness, δ* (cm)
thickness, δ (cm)of NACA 0012 airfoil, for angle of attack range [00
- 260
], U = 65 m/s, receiver distance
2m from source (a) Displacement thickness, δ*, at Ma = 0.1912, Ma = 0.1176 (b) Thickness, δ, at Ma =
0.1912, Ma = 0.1176 (c) Displacement thickness ratio (δ*/δ0
) at chord length 1.5 and 0.8m (d) Thickness
ratio (δ/δ0
) chord length 1.5m and 0.8m. Markers - indicate suction side, , - indicate pressure
side.
(a) (b)
Figure 5 Turbulent Boundary layer - thickness, δ, displacement thickness, δ*, momentum thickness, θ,
computed for NACA 0012 for (a) Ma - 0.1176 (b) Ma - 0.1912, between angle of attack, [0-200
] on suction
and pressure side of airfoil at x/c – 15, 50,75 and 90 % chord length.
8. Trailing Edge Noise Prediction from NACA 0012 & NACA 6320using Empirical Pressure Spectrum ..
DOI: 10.9790/4861-1002013346 www.iosrjournals.org 40 | Page
b) Comparison of SPL, dB, for NACA 0012 & NACA 6320
(a) (b)
Figure 7(a) Comparison of total turbulent boundary layer trailing edge, (TBLTE) sound power level (dB)
for NACA 6320 and NACA 0012 airfoil, chord length of 1.2m and span 2m.at Ma = 0.1912 and 0.1176 at
AOA = 40
(b) Illustration of Sound Power Level (SPL) dB for NACA 0012 airfoil at three different aspect
ratios, AR – 1, 3, 4 at 40
AOA and Free stream velocity, U – 65 m/s.
From figure 4 (a) and 4(b) numerical results obtained using BPM model for NACA 0012 airfoil
revealed that the thicknesses and displacement thickness on pressure side is decreasing steadily with AOA while
on suction side it increases steadily up to 100
AOA and large step increase was found after 100
. Similar trends
were observed for ratios of δ and δ* and found in figure 4(c) and 4(d). This is attributed to influence of external
pressure gradient, at which the onset of stall or flow separation begins to occur. Likewise, from figure 5 (a) and
5(b), figure 6(a) and 6(b) same trends are observed for δ and δ*, as well as momentum thickness, θ has been
computed, for NACA 0012 and NACA 63212 airfoil for two Mach numbers, Ma- 0.1912, 0.1176 and shown for
locations close to leading edge, mid span and trailing edge of airfoil, i.e. 15, 50, 75 and 90% of chord length.
The thickness, δ, was observed to be ~1.1cm very near leading edge on suction side while for pressure side it is
8mm between 12- 140
AOA. Further, it can also be noted that with increase in Reynolds number, the boundary
layer thickness, δ, and δ*are found to decrease at lower AOA however, increases steadily with increasing AOA
at given, Re.δ0 is the boundary layer thickness at zero AOA. The velocity field for both airfoils has been
Figure 6Turbulent Boundary layer – thickness, δ, displacement thickness, δ*, momentum thickness, θ,
computed for NACA 63212for (a) Ma - 0.1176 (b) Ma - 0.1912 between angle of attack, [0-200
] on suction
and pressure side of airfoil at x/c-15, 50, 75, 80 and 90 % chord length
9. Trailing Edge Noise Prediction from NACA 0012 & NACA 6320using Empirical Pressure Spectrum ..
DOI: 10.9790/4861-1002013346 www.iosrjournals.org 41 | Page
computed using panel method which is described in next section [17] [18]. From figure 7 (a) the SPL, dB are
compared for NACA 0012 and NACA 63212 for two different Mach numbers. It was found that a difference of
2dB between symmetric and cambered profiles in the low frequency part of spectrum, 100- 1000Hz however,
between 103
and 104
Hz, the spectral amplitude changed very negligibly. Figure 7(b) illustrates the effect of
aspect ratio on the SPL, dB, or noise emission from airfoil trailing edge at free stream velocity of 65m/s and at
40
AOA. With increase in aspect ratio (AR) of airfoil, from AR-1 to AR-3 for constant chord length of 0.5m,
the amplitude of SPL was found to increase by ~ 7dB for entire frequency spectrum; however, any further
change caused negligible amplitude fluctuation. This can be attributed to increased effective span length of
airfoil causing the turbulent boundary layer at trailing edge to radiate higher noise [1]. Further numerical studies
conducted from Howe et al confirmed that reducing the effective span length using trailing edge serrations
reduced pressure amplitudes by 10dB or more which when determined experimentally was found to be lower
reduction in amplitudes. In this work, no attempt was made to investigate the influence of serration structures
on the airfoils or controlling the boundary layer transitions by introducing grit, tripping, suction or blowing
methods for noise reduction.
c) Pressure distribution, Lift and Drag coefficients for NACA 0012 using Panel method
(a) (b)
Figure 8(a) Comparison of pressure distribution for NACA 0012 airfoil, at different angles of attack, Re-3
million. (b) Lift and Drag coefficients for NACA0012 airfoil between AOA [0 -200
] Markers
indicate the experiments [5]
Knowing pressure distribution on airfoil helps in structural design since it influences the boundary
layer flow on airfoil. Therefore, the geometry of airfoil is essential to determine the airfoil characteristics. Figure
9(a) shows the comparison of two NACA profiles used in study, figure 9(b) shows thickness distribution. Panel
methods are more suitable for modeling potential flows on thin airfoils. It involves the superposition of a
doublet, vortex strengths on a surface present in a uniform flow to predict the pressure coefficient and
aerodynamic characteristics such as lift and drag coefficients[17][18]19].Simple 2D lifting flows [18] can be
described using the velocity potential and stream line functions as Eq. (13) & Eq. (12)
(12)
(13)
Basic airfoil geometry is discretized into finite number of panels representing the surface. The panels
are shown by series of straight line segments to construct 2D airfoil surface [18]. Numbering of end points or
nodes of the panels is done from 1 to N. The center point of each panel is chosen as collocation points. The
periodic boundary condition of zero flow orthogonal to surface also known as impermeability condition is
applied to every panel. Panels are defined with unit normal and tangential vectors with source and sink
representing the nodes of each panel, and midpoint as control point. Velocity field over the entire surface is
predicted by calculating the tangential velocity on each panel obtained by solving the unknown source and
vortex strengths distributed on every panel relative to the flow field. By using matrix inversion procedure the
algebraic system of equations are solved involving the tangential and normal influence coefficients vector [19].
This method also utilizes the trailing edge condition known as “Kutta condition” and uses circulation strength to
10. Trailing Edge Noise Prediction from NACA 0012 & NACA 6320using Empirical Pressure Spectrum ..
DOI: 10.9790/4861-1002013346 www.iosrjournals.org 42 | Page
determine the position of stagnation point near the trailing edge. The pressure acting at any collocation point i
on panel surface can be expressed in non-dimensional form as in Eq. (14)
* + [ ]
Where the tangential velocity vector is determined using the influence coefficients, obtained using known
values of source and circulation strengths, U is the free stream velocity in m/s over the airfoil. The
impermeability boundary condition is given by Eq. (15) and applied on every panel of airfoil surface.
N
1j
i1Ni,ijj 0nˆUγNNσ
(15)
The pressure distribution of NACA 0012 and NACA 63212 computed using 2D panel method are
shown for different AOA in figure 8(a) and figure 9 (c), while the lift and drag coefficient characteristics of
NACA 0012 are compared with experimental data in figure 8 (b). Since the acoustic field can be suitably
described using invsicid flow assumption this method was chosen to determine the velocity field necessary for
the boundary layer parameters that influence wall pressure fluctuations. The turbulent boundary layer is
approximated using the boundary layer thickness along the chord length of airfoil and chord Reynolds number.
Von Karman (1921) momentum integral equations for laminar flow over flat plate are applicable for airfoil
analysis at low Reynolds number [22]. Similarly Blasius (1908) solution for dimensionless velocity profile
representing the laminar flow over the flat plate is also relevant in boundary layer analysis. Prandtl (1904) also
suggested an approximation for turbulent velocity profiles, using 1/7th
power law and valid for wide range of
Reynolds number [18], [22]. In the present study, the thickness for turbulent boundary layer for NACA 0012 is
approximated using Eq (16). Figure 12 (b) shows the comparison of laminar and turbulent boundary thickness
for NACA 0012 at Re- 2.19 x 106
and its shape along the chord length of airfoil. The displacement thickness, δ*
and momentum thickness, θ are approximated to give results close to those obtained from representative
turbulent flow over flat plate.
( ) , ; ; (16)
For laminar flow over the NACA 0012 airfoil, the boundary layer thickness, displacement thickness are
approximated using Von Karman integral momentum theory [18], [22] and given by Eq (17)
√
,
√
(17)
(a) (b)
11. Trailing Edge Noise Prediction from NACA 0012 & NACA 6320using Empirical Pressure Spectrum ..
DOI: 10.9790/4861-1002013346 www.iosrjournals.org 43 | Page
(c) (d)
Figure 9(a ) Airfoil profiles of NACA 0012 and NACA 63212 of same thickness, 12 % t/c (b) Thickness
distribution (c) Pressure coefficient of NACA 63212 and(d) surface velocity, m/s along chord, for NACA
0012 airfoil at U = 65 m/s between AOA [-20
to 120
]
(a) (b)
Figure 10 (a) Illustration of classical velocity defect law, for outer boundary layer of NACA 0012at Ma –
0.1912, 0.1176 on suction and pressure sides at AOA 40
and 120
and for u* - 0.2m/s (b) and NACA 63212
profile.
12. Trailing Edge Noise Prediction from NACA 0012 & NACA 6320using Empirical Pressure Spectrum ..
DOI: 10.9790/4861-1002013346 www.iosrjournals.org 44 | Page
d) Wall pressure spectrum models
(a) (b)
Figure 11(a) Wall pressure spectrums by Amiet compared with data from Keith et al [12], comparison of
normalized APG wall spectrum model with its present calculation for NACA 0012 and Wave number
spectrum proposed from Chase-Howe (1980) (b) Comparison of classical and Sagarola –Smits mean
velocity defect law (Urel – U)/[Urel(δ*/δ)] for NACA 0012 and NACA 63212 profiles for Mach number,
0.1912 and 0.1176 and at 40
AOA where Urel is relative velocity on the airfoil.
(a) (b)
Figure 12(a) Comparison of inner sub layer law relating to velocity profiles for NACA 0012, NACA 63-
212 along the chord length, Friction velocity, u* - 0.2, 0.34 and 0.49 m/s (b) Illustration of laminar and
turbulent boundary layer thickness, δ,along chord length of NACA 63212 airfoil at U = 40 m/s, Ma –
0.1176 at 40
AOA.
In figure 11, Numerical computation of APG models, analytical prediction model from Amiet (1981),
wave number spectrum from Chase-Howe, was done and compared with experimental data from Keith [9]. It
showed better agreement for low frequencies however, it collapses in the high frequency region. This was due to
outer layer scaling variables, convective velocity, Ue within the boundary layer, thickness, δ, and δ* in the low
frequency and inner layer scaling parameters, wall shear stress, τw and friction velocity, u*, for high frequency
region [2]. From figure 10 (a) and 10 (b) compares the velocity defect law for turbulent shear as given by Eq
(6.27) [22] is used for NACA 0012 and NACA 63212 at two different Mach numbers, 0.1912 and 0.1176
considering the friction velocity, u* - 0.2 m/s . It can be observed that velocity defect continues to grow with
increasing angle of attack, at constant surface roughness, and the defect in the velocity profile within the
boundary layer is decreasing on suction and pressure side for both profiles. Figure 12 (a) compares the pattern of
velocity profile within logarithmic overlap boundary layer, for three profiles, NACA 0012, NACA 63212 and
flat plate for different friction velocities and expressed in wall units, y+ and u+. Figure 12 (b) compares the
boundary layer thickness for laminar and turbulent boundary layers evaluated at 40
AOA for NACA 0012
profile. It can be noted that reduction of laminar boundary layer thickness along chord length, varies
13. Trailing Edge Noise Prediction from NACA 0012 & NACA 6320using Empirical Pressure Spectrum ..
DOI: 10.9790/4861-1002013346 www.iosrjournals.org 45 | Page
logarithmically, while steady increase in turbulent boundary layer thickness towards trailing edge. However, this
trend can change with flow configuration, i.e. varying AOA or Reynolds number, in which the effect of flow
separation plays critical role in the determination of boundary layer thickness over airfoil. The maximum
thickness, δ was found to be ~10 cm at x/c <10 %. Table 1 shows the results of laminar and turbulent boundary
layer parameters, evaluated for NACA 0012 at 20
AOA in MATLAB, which includes Reynolds number based
on chord, wall shear, uτ , corresponding thickness, δ & shape factor, H. The shape factor indicates the pressure
gradient which is responsible for the flow separation over the airfoil encountered in various flow conditions. The
average thickness of boundary layer was found to be 16.8mm and reduced to 13.6mm with increase in the Mach
number. The Reynolds number based on wall shear was found to be ~311 and ~ 269 while the equivalent
Reynolds number based on thickness was found to be 7410 and 6869 respectively. The Reynolds number based
on wall shear is equivalent to the corresponding thickness δ for the given AOA is shown in table 1, column 8.
Also from table 1, the shape factor H indicate the pressure fluctuations in the flow and turbulent energy within
the boundary layer which are driven by wall shear, where the no slip boundary condition exists, the outer region
of boundary layer thickness, δ and the free stream velocity for which free stream turbulence is expected to be
high for low Mach number flows and vice versa.
Table 1 Boundary layer parameters for NACA 0012 at 20
AOA
Ma „δ (mm) „δ*(mm) „θ (mm) H
Ϯ
(δ*/θ) Rex Reδ Reτ
0.1176 16.8 & 10.1 11.6& 2.5 4.7& 2 1.285
ɛ
, 2.5
×
3.134 x 106
7410 267
0.1912 13.6 & 8 8.7& 2.34 3.5& 1.8 1.28
ɛ
, 2.51
×
4.612 x 106
6869 243
Ϯ Shape factor for laminar and turbulent boundary layer flow indicates pressure gradient, ɛ- turbulent, ×
- laminar
Figure 13Comparison of results for APG, ZPG wall spectrum models from (Tian, Cotte -2016) for NACA
0012 airfoil for local pressure gradient parameter, β =0. RT – 24.7 with present results for 2, 4 and 60
AOA. Receiver position is 1.224m, from the trailing edge, chord length 1.2m. Mach number, Ma - 0.1912.
Reynolds number, Re –4.8 x 106
V. Conclusions
The BPM model for predicting the sound pressure level, from trailing edge of NACA 0012 and NACA
6320 showed that for increase in chord length of airfoil the change in the magnitude of SPL for constant span
increased by 10dB on the pressure side, ~ 8dB on the suction side and ~2dB for flow separation noise in low
frequency region of spectrum. Increase in Mach number also resulted in increase in SPL by ~10dB for both
pressure and suction side of airfoils. A difference of ~2 -5dB in SPL was found between the NACA 6320 and
NACA 0012 airfoils for increasing Mach number and in low frequency (100<f<400Hz) , region of spectrum,
however the peak amplitude of spectrum varied negligibly with angle of attack. Flow separation caused due to
mean APG influences acoustic pressure spectrum by 2-3dB in low frequency region. The results of APG models
were found in close agreement between current and previous predictions. For incompressible flows empirical
wall pressure spectrum models are more suitable to predict the acoustic pressure fluctuations due to its low
computational requirement. External pressure gradient models rely on turbulent boundary layer thickness
history, displacement thickness and wall shear. They are found to vary with angular frequency or wave number
in different regions of wall pressure spectrum.
-100
-90
-80
-70
-60
-50
-40
-30
-20
-10
0
0.01 0.1 1 10 100
10log10(φ(ω)U/τ2δ*)
ωδ*/U
AOA 4 deg
AOA 2 deg
AOA 6 deg
ZPG (Tian, Cotte - 2016)
APG (Tian, Cotte- 2016)
14. Trailing Edge Noise Prediction from NACA 0012 & NACA 6320using Empirical Pressure Spectrum ..
DOI: 10.9790/4861-1002013346 www.iosrjournals.org 46 | Page
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Vasishta Bhargava " Trailing Edge Noise Prediction from Naca 0012 & Naca 6320using
Empirical Pressure Spectrum Models.” IOSR Journal of Applied Physics (IOSR-JAP) , vol.
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