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SNS COLLEGE OF TECHNOLOGY (An Autonomous Institution) COIMBATORE–35 DEPARTMENT OF AERONAUTICAL ENGINEERING BOUND VORTEX AND HORSESHOE VORTEX 02-04-2020 PREPARED BY MS.X.BERNADETTE EVANGELINE AP/AERO 1 Bound Vortex a vortex that is considered to be tightly associated with the body around which a liquid or gas flows, and equivalent with respect to the magnitude of speed circulation to the real vorticity that forms in the boundary layer owing to viscosity. In calculations of the lift of a wing of infinite span, the wing can be replaced by a bound vortex that has a rectilinear axis and generates in the surrounding medium the same circulation as that generated by the real wing. In the case of a wing of finite span, the bound vortex continues into the surrounding medium in the form of free vortices. Knowledge of the vortex system of a wing permits calculation of the aerodynamic forces acting upon the wing. In particular, the interaction between bound and free vortices gives rise to the induced drag of the wing. The idea of the bound vortex was made use of by N. E. Zhukovskii in the theory of the wing and the screw propeller. 02-04-2020 PREPARED BY MS.X.BERNADETTE EVANGELINE AP/AERO 2 02-04-2020 PREPARED BY MS.X.BERNADETTE EVANGELINE AP/AERO 3 WHAT IS HORSE SHOE VORTEX? The horseshoe vortex model is a simplified representation of the vortex system of a wing. In this model the wing vorticity is modelled by a bound vortex of constant circulation, travelling with the wing, and two trailing wingtip vortices, therefore having a shape vaguely reminiscent of a horseshoe 02-04-2020 PREPARED BY MS.X.BERNADETTE EVANGELINE AP/AERO 4 STARTING VORTEX • A starting vortex is shed as the wing begins to move through the fluid, which dissipates under the action of viscosity, as do the trailing vortices far behind the aircraft 02-04-2020 PREPARED BY MS.X.BERNADETTE EVANGELINE AP/AERO 5 WING TIP VORTEX •The trailing wingtip vortices are responsible for the component of the downwash which creates induced drag 02-04-2020 PREPARED BY MS.X.BERNADETTE EVANGELINE AP/AERO 6 HORSE SHOE VORTEX MODEL • The horseshoe vortex model is unrealistic in that it implies uniform circulation (and hence, according to the Kutta–Joukowski theorem, uniform lift) at all sections on the wingspan. 02-04-2020 PREPARED BY MS.X.BERNADETTE EVANGELINE AP/AERO 7 HORSE SHOE VORTEX MODEL Aviation Lighting 02-04-2020 PREPARED BY MS.X.BERNADETTE EVANGELINE AP/AERO 8 HORSE SHOE VORTEX MODEL PREPARED BY MS.X.BERNADETTE EVANGELINE 02-04-2020 9 AP/AERO HORSE SHOE VORTEX MODEL 02-04-2020 PREPARED BY MS.X.BERNADETTE EVANGELINE AP/AERO 10 HORSE SHOE VORTEX-REALISTIC MODEL • In a more realistic model, the lifting-line theory, the vortex strength varies along the wingspan, and the loss in vortex strength is shed as a vortex sheet all along the trailing edge, rather than as a single trail at the wing-tips. Nevertheless, the simpler horseshoe vortex model used with a reduced effective wingspan but same mid-plane circulation provides an adequate model for the flows induced far from the aircraft PREPARED BY MS.X.BERNADETTE EVANGELINE 02-04-2020 11 AP/AERO HS-VORTEX FLOW VISUALISATION PREPARED BY MS.X.BERNADETTE EVANGELINE 02-04-2020 12 AP/AERO .

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Clearing Certain Misconception in the Common Explanations of the Aerodynamic Lift

Clearing certain misconception in the common explanations of the aerodynamic lift Clearing certain misconception in the common explanations of the aerodynamic lift Navinder Singh,∗ K. Sasikumar Raja, P. Janardhan Physical Research Laboratory, Ahmedabad, India. [email protected] October 30, 2018 Abstract Air travel has become one of the most common means of transportation. The most common question which is generally asked is: How does an airplane gain lift? And the most common answer is via the Bernoulli principle. It turns out that it is wrongly applied in common explanations, and there are certain misconceptions. In an alternative explanation the push of air from below the wing is argued to be the lift generating force via Newton’s law. There are problems with this explanation too. In this paper we try to clear these misconceptions, and the correct explanation, using the Lancaster-Prandtl circulation theory, is discussed. We argue that even the Lancaster-Prandtl theory at the zero angle of attack needs further insights. To this end, we put forward a theory which is applicable at zero angle of attack. A new length scale perpendicular to the lower surface of the wing is introduced and it turns out that the ratio of this length scale to the cord length of a wing is roughly 0.4930 ± 0.09498 for typical NACA airfoils that we analyzed. This invariance points to something fundamental. The idea of our theory is simple. The "squeezing" effect of the ﬂow above the wing due to camber leads to an effective Venturi tube formation and leads to higher velocity over the upper surface of the wing and thereby reducing pressure according the Bernoulli theorem and generating lift.
Joukowski Theorem for Multi-Vortex and Multi-Airfoil Flow (A

CORE Metadata, citation and similar papers at core.ac.uk Provided by Elsevier - Publisher Connector Chinese Journal of Aeronautics, (2014),27(1): 34–39 Chinese Society of Aeronautics and Astronautics & Beihang University Chinese Journal of Aeronautics [email protected] www.sciencedirect.com Generalized Kutta–Joukowski theorem for multi-vortex and multi-airfoil flow (a lumped vortex model) Bai Chenyuan, Wu Ziniu * School of Aerospace, Tsinghua University, Beijing 100084, China Received 5 January 2013; revised 20 February 2013; accepted 25 February 2013 Available online 31 July 2013 KEYWORDS Abstract For purpose of easy identification of the role of free vortices on the lift and drag and for Incompressible flow; purpose of fast or engineering evaluation of forces for each individual body, we will extend in this Induced drag; paper the Kutta–Joukowski (KJ) theorem to the case of inviscid flow with multiple free vortices and Induced lift; multiple airfoils. The major simplification used in this paper is that each airfoil is represented by a Multi-airfoils; lumped vortex, which may hold true when the distances between vortices and bodies are large Vortex enough. It is found that the Kutta–Joukowski theorem still holds provided that the local freestream velocity and the circulation of the bound vortex are modified by the induced velocity due to the out- side vortices and airfoils. We will demonstrate how to use the present result to identify the role of vortices on the forces according to their position, strength and rotation direction. Moreover, we will apply the present results to a two-cylinder example of Crowdy and the Wagner example to demon- strate how to perform fast force approximation for multi-body and multi-vortex problems.
Kutta Condition

SNS COLLEGE OF TECHNOLOGY (An Autonomous Institution) COIMBATORE–35 DEPARTMENT OF AERONAUTICAL ENGINEERING KUTTA CONDITION: The Kutta condition is a principle in steady-flow fluid dynamics, especially aerodynamics, that is applicable to solid bodies with sharp corners, such as the trailing edges of airfoils. A body with a sharp trailing edge which is moving through a fluid will create about itself a circulation of sufficient strength to hold the rear stagnation point at the trailing edge. In fluid flow around a body with a sharp corner, the Kutta condition refers to the flow pattern in which fluid approaches the corner from both directions, meets at the corner, and then flows away from the body. None of the fluid flows around the sharp corner. Prepared by Ms.X.Bernadette Evangeline AP/AERO 16AE208 AERODYNAMICS-I SNS COLLEGE OF TECHNOLOGY (An Autonomous Institution) COIMBATORE–35 DEPARTMENT OF AERONAUTICAL ENGINEERING The Kutta condition is significant when using the Kutta–Joukowski theorem to calculate the lift created by an airfoil with a sharp trailing edge. The value of circulation of the flow around the airfoil must be that value which would cause the Kutta condition to exist. In 2-D potential flow, if an airfoil with a sharp trailing edge begins to move with an angle of attack through air, the two stagnation points are initially located on the underside near the leading edge and on the topside near the trailing edge, just as with the cylinder. As the air passing the underside of the airfoil reaches the trailing edge it must flow around the trailing edge and along the topside of the airfoil toward the stagnation point on the topside of the airfoil.
Vortex-Lattice Utilization

NASA SP-405 VORTEX-LATTICE UTILIZATION (NRSA-5P-405) V3BTZX- LATTIZZ UTILIZF.TION N76-28163 (?iASA) 409 p HC 611.Ci0 CSCL 31A THRU N76-28186 rn Unclas .- H1/02 47615 A workshop held at LANGLEY RESEARCH CENTER Hampton, Virginia May 17-18, 1976 I NATIONAL AERONAUTICS AND SPAC ERRATA NASA SP-405 VORTEX-LATTICE UTILIZATION Page 231: Figure 6 is in error. Replace figure 6 with the following corrected version. Figure 6.- Span load and section suction distributions on a swept and skewed wing. h = 45O; A = 1; M = 0. NASA SP-405 VORTEX-LATTICE UTILIZATION A workshop held at Langley Research Center, Hampton, Virginia, on May 17-18, 1976 Prepared by Lungley Research Center Srietrlifir and Terhnirnl lrlformdtion Ofice !9'h u 5. b. NATIONAL AERONAUTICS AND SPACE ADMINISTRATION Washington, D.C. CONTENTS PREFACE ..................................iii o)tl/7- . 1. HISTORICAL EVOLUTION OF VORTEX-LATTICE METHODS ............ 1 j. John DeYoung, Vought Corporation Hampton Technical Center - SESSION I - CONFIGURATION DESIGN AND ANALYSIS AND WALL EFFECTS Chairman: Percy J. Bobbitt, NASA Langley Research Center A. WING-BODY COMBINATIONS 2. SUBSONIC FINITC ELEMENTS FOR WING-BODY COMBINATIONS ......... 11 James L. Thomas, NASA Langley Research Center 3. EXTENDED APPLICATIONS OF THE VORTEX LATTICE METHOD ......... 27 Luis R. Miranda, Lockheed-California Company B. NONPLANAR CONFIGURATIONS 4. WMERICAL METHOD TO CALCULATE THE INDUCED DRAG OR OPTIMUM LOADING FOR ARBITRARY NON-PLANAR AIRCRAFT ................. 49 James A. Blackwell, Jr., Lockheed-Georgia Company 5. OPTIMIZATION AND DESIGN OF THREE-DIMEKSIONAL AERODYNAMIC CONFIGURATIONS OF ARBITRARY SHAPE BY A VORTEX LATTICE METHOD .............................. 71 Wlnfried M. Feifel, The Boeing Company 6.
Simulation of Starting/Stopping Vortices for a Lifting Aerofoil

19th Australasian Fluid Mechanics Conference Melbourne, Australia 8-11 December 2014 Simulation of starting/stopping vortices for a lifting aerofoil M. Vincent and H. M. Blackburn Department of Mechanical and Aerospace Engineering Monash University, Victoria 3800, Australia Abstract More recently, Lei, Feng and Can (2013) found that at a low Reynolds number, laminar separation occurred in the flow field In order to recreate Prandtl’s flow visualisation films dealing around a symmetrical aerofoil and when the angle of attack with starting and stopping vortices produced by a lifting aerofoil reached a certain level, primary and secondary vortices were and expand on that research, direct numerical simulation was produced.[4] Jones and Babinsky (2011) found that leading edge used to perform numerical experiments on the starting and vortices were shed from the flat plates at Re=10000-60000.[5] stopping of lifting aerofoil by solving the two-dimensional Sun and Daichin (2011) looked at wing tip vortices and found incompressible Navier–Stokes equations. The simulation used a that the vorticity decreased with decreasing ground height.[6] NACA 0012 aerofoil at angle of attack , the chord Reynolds number based on peak translation speed was In the present work, Prandtl’s experiment was numerically , and was conducted using a spectral element simulation recreated by solving the two-dimensional incompressible Navier- code. Trailing edge starting and stopping vortices and also a Stokes equations in an accelerating reference frame stopping leading edge vortex pair were produced. Net circulation was calculated and was found to have a small positive value, which fell as domain size was increased.
Vortex Methods for Separated Flows Philippe R

a. - NASA Technical Meiorandlrn 100068 Vortex Methods for Separated Flows Philippe R. Spalart [WASA-TH-100068) VORTEX METADDS Pol? ma- 263 42 SE€?83ATED FLOWS (NASA) 66 p CSCL 318 Unclas G3/02 0 154827 June 1988 . National Aeronautics and Space Administration NASA Technical Memorandum 100068 Vortex Methods for Separated Flows Philippe R. Spalart, Ames Research Center, Moffett Field, California June 1988 National Aeronautics and Space Administration Ames Research Center Moffett Field, California 94035 TABLE OF CONTENTS SUMMARY 1. INTRODUCTION 3 1.1. Example: Flow Past a Multi- Element Airfoil 1.2. Governing Equations 1.3. Invariants of the Motion 1.4. Constraints on Vector Fields' 2. POINT-VORTEX METHODS 9 2.1. Basics 2.2. Dificulties with Vortex Sheets* 2.3. Application to Smooth Euler Solutions' 3. VORTEX-BLOB METHODS 13 3.1. Motivation and Basics 3.2. Convergence in Theory 3.3. Convergence in Practice 4. THREE-DIMENSIONAL FLOWS* 17 4.1. Essential Diflereiices with Two-Dimensional Flows' 4.2. Filament Methods* 4.3. Scgment Methods* 4.4. Monopole Met hods* 5. EXTENSION TO VISCOUS AND COMPRESSIBLE FLOWS 21 5.1. Viscous Flows 5.2. Compressible Flows* 6. INVISCID BOUNDARIES 25 6.1. Use of Boundary Elements 6.2. Remark on the Choice of Two Numerical Parameters" 6.3. Example: A Curved Mixing Layer 7. VISCOUS BOUNDARIES 31 7.1. Application of the Biot-Savart Law Inside a Solid Body 7.2. Creation of Vorticity 7.3. Choice of Numerical Parameters’ 7.4. h’utfa Condition 7.5. Eramylr: Starting Vortex on an Airfoil 7.6. Pressure and Force Eztraction’ 8.
Fluid Flow Lecture 1: Information and Introduction

Chapter 2: Vorticity Circulation and vorticity v C C v Aerodynamics 2 Chapter 2: Vorticity Circulation and vorticity Aerodynamics 3 Chapter 2: Vorticity Circulation and vorticity Stokes’ theorem v v C i.e. if = 0 = 0 Flows for which = 0 are irrotational. Aerodynamics 4 Chapter 2: Vorticity Stream tubes and vortex tubes v v Aerodynamics 5 Chapter 2: Vorticity Stream filament and vortex filament If A1 0 we have, respectively, a stream filament and a vortex filament. Biot Savart law Aerodynamics 6 Chapter 2: Vorticity Kinematics of vortex lines Since the divergence of the curl of a vector is zero (by definition, show it!) it is: This means that there are no sources or sinks of vorticity in the fluid the vortex lines must either form closed loops or terminate on the boundaries (solid surface or free surface) of the fluid. Aerodynamics 7 Chapter 2: Vorticity Correspondence velocity-vorticity v v Aerodynamics 8 Chapter 2: Vorticity Correspondence velocity-vorticity Incompressible flow: v Let’s integrate over the total volumeV of a stream tube (whose total outer surface is s): v v Gauss theorem ሶ v v 푉1ሶ = 푉2ሶ Aerodynamics 9 Chapter 2: Vorticity Correspondence velocity-vorticity Vorticity is divergence-free: Let’s integrate over the total volumeV of a vortex tube (including the ends): Gauss theorem 1 = 2 Aerodynamics 10 Chapter 2: Vorticity Helmholtz’s theorems (1858) The circulation at each cross-section of a vortex tube (or filament) is the same; alternatively, the average vorticity increases as the cross-section of the vortex tube decreases: Helmholtz’s first theorem the strength of a vortex filament is constant along its length, i.e.
AA200 Ch 11 Two-Dimensional Airfoil Theory Cantwell.Pdf

CHAPTER 11 TWO-DIMENSIONAL AIRFOIL THEORY ___________________________________________________________________________________________________________ 11.1 THE CREATION OF CIRCULATION OVER AN AIRFOIL In Chapter 10 we worked out the force that acts on a solid body moving in an inviscid fluid. In two dimensions the force is F d = Φndlˆ − U (t) × Γ(t)kˆ (11.1) ρ oneunitofspan dt ∫ ∞ ( ) Aw where Γ(t) = !∫ UicˆdC is the circulation about the body integrated counter-clockwise Cw about a path that encloses the body. It should be stated at the outset that the creation of circulation about a body is fundamentally a viscous process. The figure below from Van Dyke’s Album of Fluid Motion depicts what happens when a viscous fluid is moved impulsively past a wedge. Figure 11.1 Starting vortex formation about a corner in an impulsively started incompressible fluid. 1 A purely potential flow solution would negotiate the corner giving rise to an infinite velocity at the corner. In a viscous fluid the no slip condition prevails at the wall and viscous dissipation of kinetic energy prevents the singularity from occurring. Instead two layers of fluid with oppositely signed vorticity separate from the two faces of the corner to form a starting vortex. The vorticity from the upstream facing side is considerably stronger than that from the downstream side and this determines the net sense of rotation of the rolled up vortex sheet. During the vortex formation process, there is a large difference in flow velocity across the sheet as indicated by the arrows in Figure 11.1. Vortex formation is complete when the velocity difference becomes small and the starting vortex drifts away carried by the free stream.
Wing Trailing Vortex Paths in Formation Flight

WING TRAILING VORTEX PATHS IN FORMATION FLIGHT William P. Tipping-Woods Supervisor: Prof. C. Redelinghuys A dissertation submitted to the Department of Mechanical Engineering at the University of Cape Town, in partial fulfilment of the requirements for the degree of Master of Science in Mechanical Engineering. University of Cape Town September 2014 The copyright of this thesis vests in the author. No quotation from it or information derived from it is to be published without full acknowledgement of the source. The thesis is to be used for private study or non- commercial research purposes only. Published by the University of Cape Town (UCT) in terms of the non-exclusive license granted to UCT by the author. University of Cape Town Declaration 1. I know that plagiarism is wrong. Plagiarism is to use another’s work and pretend that it is one’s own. 2. I have used the ISO/690 NumericalReference convention for cita- − tion and referencing. Each significant contribution to, and quotation in, this dissertation from the work(s) of other people has been at- tributed, and has been cited and referenced. 3. This dissertation is my own work. 4. I have not allowed, and will not allow anyone to copy my work with the intention of passing it off as their own work. Signature: ............ Abstract Formation flight has been shown to reduce the induced drag for a formation of aircraft. The mechanism by which this is achieved is caused by the wake velocity field of the aircraft. This field is dominated by wing-tip trailing vortices. The paths of these vortices become too complex for rigid wake models downstream of the second aircraft in the formation.
1.3.5 the Kutta Condition ...17

Deift UniVersity ofTechnology Ship HydromechafliCS laboratory Library Mekelweg 2 26282 CD Deift Phone: +31 (0)15 2786873 E-mail: p.w.deheertUdelft.flI 13.04 LECTURE NOTES HYDROFOILS AND PROPELLERS* Justin E. Kerwin January 2OOl Contents i TWO DIMENSIONAL FOIL THEORY - i 1.1 Introduction 2 1.2Foil Geometry 3 1.3Conformal Mapping 9 1.3.1History 9 1.3.2Potential Flow Around A Circle 9 1.3.3Conformal Mapping for Dummies 13 1.3.4The Karman-Trefftz Mapping Function 15 1.3.5The Kutta Condition ....................17 1.3.6Pressure Distributions 19 1.3.7Lift and Drag 24 1.4Linearized Theory for a 2Dimensional Foil Section 26 *©Justjfl E. Kerwin 2001 t Web document updated March 9 i 1.41Problem Formulation 26 27 1.4.2Vortex and Source Distributions 1.4.3Glauert's Theory 31 1.4.4Example-The Flat Plate 35 1.45 Example-The Parabolic Mean Line 36 37 1.4.6The Design of Mean Lines-The NACA a-Series ......... 1.4.7Linearized Pressure Coefficient 40 1.4.8Comparison of Pressure Distributions 41 42 1.4.9Solution of the Linearized Thickness Problem 1.4.10 The Elliptical Thickness Form 43 1.4.11 The Parabolic Thickness Form 44 1.4.12 Superposition 45 47 1.4.13 Lighthill's Rule . 52 1.52-D Vortex Lattice Theory 53 1.5.1 Constant Spacing 53 1.5.2Cosine Spacing . 55 1.5.3Converting from ['to -y(x) 56 1.5.4Drag and Leading Edge Suction 62 1.5.5Adding Foil Thickness to VLM 66 1.5.6The Cavitation Bucket Diagram 74 2LIFTING SURFACES 75 2.1Introductory Concepts 78 2.2The Strength of the Free VortexSheet in the Wake 11 C, 81 2.3The velocity induced by a three-dimensionalvortex line.
Kinematics of Vorticity

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A Discrete Vortex Method Application to Low Reynolds Number Aerodynamic

A DISCRETE VORTEX METHOD APPLICATION TO LOW REYNOLDS NUMBER AERODYNAMIC FLOWS Thesis Submitted to The School of Engineering of the UNIVERSITY OF DAYTON In Partial Fulfillment of the Requirements for The Degree of Master of Science in Aerospace Engineering By Patrick R. Hammer University of Dayton Dayton, OH August 2011 i A DISCRETE VORTEX METHOD APPLICATION TO LOW REYNOLDS NUMBER AERODYNAMIC FLOWS Name: Hammer, Patrick Richard APPROVED BY: ____________________________ __________________________ Aaron Altman, PhD Greg Reich, PhD Advisory Committee Chairperson Committee Member Associate Professor Adaptive Structures Team Lead Department of Mechanical and Aerospace Eng. Air Vehicles Directorate ____________________________ Frank Eastep, PhD Advisory Committee Chairperson Professor Emeritus Department of Mechanical and Aerospace Eng. ____________________________ __________________________ John G. Weber, PhD Tony E. Saliba, PhD Associate Dean Dean, School of Engineering School of Engineering & Wilke Distinguished Professor ii ABSTRACT A DISCRETE VORTEX METHOD APPLICATION TO LOW REYNOLDS NUMBER AERODYNAMIC FLOWS Name: Hammer, Patrick R. University of Dayton Advisor: Dr. Aaron Altman Although experiments and CFD are very powerful tools in analyzing a niche of fluid dynamics problems relevant to developing Micro Aerial Vehicles (MAVs), reduced order methods have shown to be very capable in helping researchers achieve a basic understanding of flow physics with application to highly iterative design processes due to the less computationally expensive nature of the low order models. The current study used one low order method, the Discrete Vortex Method, to model the aerodynamic flow fields and forces around a thin airfoil undergoing a variety of flows, as well as parametric studies to determine the important factors that had to be adjusted to make the results more representative of the physical phenomenon being modeled.