DOCSLIB.ORG

Vortex-Lattice Utilization

Total Page：16

File Type：pdf, Size：1020Kb

Download full-text PDF Read full-text
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. MINIMUM TRIM DUG DESIGN FOR INTERFERING LIFTING SURFACES USING VORTEX-LATTICE METHODOLOGY ................. 89 John E. Lamar, NASA Langley Research Center 7. APPLICATIONS OF VORTEX-LATTICE THEORY TO PRELIMINARY AERObYNAMICDESIGN ........................ 113 John W. Paulson, Jr., NASA Langley Research Center C. PROPULSION AERODYNAMICS 8. UTILIZATION OF THE AEDC THREE-DIMENSIONAL POTENTIAL FLOW COMPUTER PROGRAM ......................... 127 Richard L. Palko, ARO, Inc. D . WALL EFFECTS 9. REPORT ON THE STATUS OF A SLOTTED WIND-TUNNEL WALL REPRESENTATION USING THE VORTEX-LATTICE TECHNIQUE ......... 145 Fred L. Heltsley, ARO, Inc. SESSION I1 - HIGH LIFT Chairman: Edward C, Polhamus, NASA Langley Research Center A. FLAPS 10. A QUADRILATERAL VORTEX METHOD APPLIED TO CONFIGURATIONS WITH HIGH CIRCULATION ......................... 163 Brian Maskew, Analytical Methods, Inc. B. WING-JET 11. UPPER-SURFACE-BLOWING JET-WING INTERACTION ............. 187 C. Edward Lan, The University of Kansas 12. CALCULATION OF THE LONGITUDINAL AERODYNAMIC CHARACTERISTICS OF WINGFLAP CONFIGURATIONS WITH EXTERNALLY BLOWN FLAPS ....... 199 Michael R. Meadenhall, Nielsen Engineering & Research, Inc. C. VORTEX LIFT 13. SOME RECENT APPLICATIONS OF THE SUCTION ANALOGY TO ASYMMETRIC ~OWSITUATIONS........................... 219 James M. Luckring, NASA Langley Research Center 14. APPLICATION OF THE VORTEX-LATTICE TECHNIQUE TO THE ANALYSIS OF THIN WINGS WITH VORTEX SEPARATION AM) THICK MULTI-ELEMENT WINGS............................... 237 Charles W. Smith and Ishwar C. Bhateley, Fort Worth Division of General Dynamics 15. COMPARISON OF VORTEX LATTICE PREDICTED FORCES WITH WIND TUNNEL EXPERIMENTS FOR THE F-4E(CCV) AIRPLANE WITH A CLOSELY COUPLED CANARD .......................... 261 Lloyd W. Gross, McDonnell Aircraft Company 16. NEW CONVERGENCE CRITERIA FOR THE VORTEX-LATTICE MODELS OF THE LEADINGEDGE SEPARATION ...................... 285 Osama A. Kandil, Dean 7'. Mook, and Ali H. Nayfeh, Virginia Polytechnic Institute and State University SESSION I11 - NEW PROCEDURES Chairman: Willia; B. Kemp, Jr. , NASA Langley Research Center A. LATTICE ARRANGEMENT 17. ARRANGEMENT OF VORTEX LATTICES ON SUBSONIC WINGS .......... 301 Fred R. DeJarnette, North Carolina State University 18. LATTICE ARRANGEMENTS FOR RAPID CONVERGENCE ............. 325 Gary R. Hough, Vought Corporation Advanced Technology Center 19. OPTIMUM LATTICE ARRANGEMENT DEVELOPED FROM A RIGOROUS ANALYTICAL BASIS.. ............................. 343 John DeYoung, Vought Corporation Hampton Technical Center 20. A SUBVORTEX TECHNIQUE FOR THE CLOSE APPROACH TO A DISCRETIZED VORTEXSHEET ........................... 369 Brian Maskew, Analytical Methods, Inc. B. OTHERS 21. SOME APPLICATldNS OF THE QUASI VORTEX-LATTICE METHOD IN STEADY AND UNSTEADY AERODYNAMICS ................. ... 385 C. Edward Lan, The University of Kansas 22. UNSTEADY now OVER WINGS HAVING SHARP-EDGE SEPARATION ........ 407 E. H. Atta, 0. A. Kandil, D. T. Mook, and A. H. Nayfeh, Virginia Polytechnic Institute and State University SESSION IV - OPEN DISCUSSION RELATED TO FUTURE WORK Chairman: John C. Houbolt, NASA Langley Research Center 23. SUMMARY OF OPEN DISCUSSION ON FUTURE VORTEX-LATTICE UTILIZATION ... 419 John C. Houbolt, NASA Langley Research Center 24. SAMPLEWINGSFORSTUDY ....................... 423 John E. Lamar, NASA Langley Research Center vii HISTORICAL EVOLUTION OF VORTEX-LATTICE METHODS John DeYoung Vought Corporation Hampton Technical Center Good morning. In this short talk I will give a review of the beginnings and some orientation of the vortex-latti ce method. The vortex-1 attice method is a discrete vortex colocation method for obtaining numerical solutions to the loading integral equation relating normal velocity an2 wing loading. It is . a branch of computer fluid dynamics which in turn is math~maticallydescended from finite-di fference concepts. Finite-difference concepts had been appl ied to the development of calculus which dates it a relatively long time ago. For our subject the beginning is much more current. Here for orientation we will follow the historical course of the vortex-lattice method in conjunction with its field of computational fluid dynamics. An outline of the concurrent development of computer fluid dynamics and vortex-lattice methods is as fol lows: L.F. RICHARDSON (1910) V.M. FALKNER (1943) FIRST USE OF NAME VORTEX-LATTI CE THEORY L. PRANDTL (1918, 1921) R. V. SOUTHWELL (1946) H. LIEPMANN (1918) C.M. TYLER, JR. (1949) R. COURANT, K. FRIEDRICHS, AND H. LEWY (1928) ELLIPTIC AND D. N. DeG. ALLEN, AND S.C.R. DENNIS HYPERBOLIC EQUATIONS (1951) A. THOM (1928) FIRST NUMEPICAL D. N. DeG. ALLEN, AND R.V. SOUTHWELL SOLUTION OF VISCOUS FLUID- (1955) DYNAMICS PROBLEM F. H. HARLOW, AND J. E. FROMFI (1965) 114 - 314 RULE CHORD CONCEPT (1 937) AERODYNAMIC ANALYSIS REQUIRING G. H. SHORTLEY, AND R. WELLER ADVANCED COMPUTERS, NASA SP347 (1975) (1938) LOS ALAMOS SCIENTIFIC LABORATORY (WORLD WAR II) Since many mathematical models of fluid dynamics can be expressed as partial differential equations then, historically, computer fluid dynamics can be said to start with L. F. Richardson's paper. Some consider this paper as the foundation of modern numerical analysis of partial differential equations. He applied his methods to the engineering problem of determining stresses in a masonry dam. In 1918 Prandtl formulated the 1 ifting-line theory. The chord loading is concentrated into a single load vortex, thus it is a one panel chord- wise vortex lattice with flow conditions satisfied at the load line, In 1938 Prandtl proposed an expl icit fini te-di fference method for solving boundary- layer equations. Liepmann showed how to improve the convergence rate of -- - a). r.lP-Y.r.--, 4-tr*- .,.--"..Us- 7 Richardson's procedure. In later years Liepmann's method was found very compatible with electronic computers and has been further developed. The i classic paper of Courant, Friedrichs, and Levy has become a guide for practical fluid flow computational solutions. AThomn did early computational work in fluid flow, two-dimensional and flow past circular cyl inders. The 114-314 rule has a fundamental role in vortex-lattice methods. This concept first appeared in a paper by E. Pistolesi in 1937. He in effect did a single panel vortex-lattice solution for a two-dimensional wing and found that with the load vortex at the 114 chord line and downwash or normal wash point (no-flow through condition) at 314 chord, the section lift and moment for con- stant angle of attack is exactly that of thin wing theory. And lift is predicted exactly for wing with parabolic camber. This rule was first applied to wings of finite aspect ratio by W. Mutterperl (1941) and J. Weissinger (1942) and very often since by others. P.A. Byrd (1ng.-Arch. 19, 321-323, 1951) expanded Pistolesi 's work for sections divided into more than one panel on the chord and with the 1/4-314 rule applied for each panel found that l ift and moment are predicted exactly. In later years this chordwise rule received further mathematical attention. Shortley and We1 1er developed block re1axation- a developed version of Liepmann's method. It was this work from Ohio State University I had used in a gradu,,te course at Washington State in 1943 to numerically solve the Laplace equation for determining the stress pattern in a twisted grooved rod. Work at the Los Alamos Scientific Laboratory has contributed much to the advancement of computer fl uid dynamics. This includes the work of J. von Neumann, J. Fromrn, and F. Harlow. From Los Alamos a graphics fluid dynamics motion picture was circulated in this country in the 1960's. It showed a computer fluid dynamics flow prediction of a dam bursting and the water cascading down a gorge. V. Fa1 kner covered the wing with a grid
Load more

Recommended publications
  • Variational Formulation of Fluid and Geophysical Fluid Dynamics
    Advances in Geophysical and Environmental Mechanics and Mathematics Gualtiero Badin Fulvio Crisciani Variational Formulation of Fluid and Geophysical Fluid Dynamics Mechanics, Symmetries and Conservation Laws Advances in Geophysical and Environmental Mechanics and Mathematics Series editor Holger Steeb, Institute of Applied Mechanics (CE), University of Stuttgart, Stuttgart, Germany More information about this series at http://www.springer.com/series/7540 Gualtiero Badin • Fulvio Crisciani Variational Formulation of Fluid and Geophysical Fluid Dynamics Mechanics, Symmetries and Conservation Laws 123 Gualtiero Badin Fulvio Crisciani Universität Hamburg University of Trieste Hamburg Trieste Germany Italy ISSN 1866-8348 ISSN 1866-8356 (electronic) Advances in Geophysical and Environmental Mechanics and Mathematics ISBN 978-3-319-59694-5 ISBN 978-3-319-59695-2 (eBook) DOI 10.1007/978-3-319-59695-2 Library of Congress Control Number: 2017949166 © Springer International Publishing AG 2018 This work is subject to copyright. All rights are reserved by the Publisher, whether the whole or part of the material is concerned, specifically the rights of translation, reprinting, reuse of illustrations, recitation, broadcasting, reproduction on microfilms or in any other physical way, and transmission or information storage and retrieval, electronic adaptation, computer software, or by similar or dissimilar methodology now known or hereafter developed. The use of general descriptive names, registered names, trademarks, service marks, etc. in this publication does not imply, even in the absence of a specific statement, that such names are exempt from the relevant protective laws and regulations and therefore free for general use. The publisher, the authors and the editors are safe to assume that the advice and information in this book are believed to be true and accurate at the date of publication.
    [Show full text]
  • The Vortex Lattice Method . for the Rotor-Vortex Interaction Problem
    NASA CONTRACTOR NASA CR-2421 REPORT - THE VORTEX LATTICE METHOD . FOR THE ROTOR-VORTEX INTERACTION PROBLEM by Raghuveera Padakannaya Prepared by THE PENNSYL VANIA ST ATE UNIVERSITY University Park, Pa. 16802 for Langley Research Center NATIONAL AERONAUTICS AND SPACE ADMINISTRATION • WASHINGTON, D. C. • JULY 1974 1. Report No. , I 2. Government Accession No. 3. Recipient's Catalog No. CR-Z4Z1 4. TItle and Subtitle 5. Report Date THE VORTEX LATTICE METHOD FOR THE ROTOR-VORTEX JULY 1974 INTERACTION PROBLEM 6. Performing Organization Code 7. Author(s) 8. Performing Organization Report No. Raghuveera Padakannaya 1-------------------------------1 10. Work Unit No. g. Performing Organization Name and Address The Pennsylvania State University 11. Contract or Grant No. University Park, PA 16802 NGR - 39 - 009 - 111 ~------------------------------I13. Type of Report and Period Covered 12. Sponsoring Agency Name and Address Contractor Report National Aeronautics and Space Administration 14. Sponsoring Agency Code Washington, D.C. 20546 15. Supplementary Notes Topical report 16. Abstract This study is concerned with the rotor blade-vortex interaction problem and the resulting impul sive airloads which generate undesirable noi se level s. A numerical 1ifting surface method to predict unsteady aerodynamic forces induced on a finite aspect ratio rectangular wing by a straight, free vortex placed at an arbitrary angle in a subsonic incompressible free stream is developed first. Using a rigid wake assumption, the wake vortices are assumed to move down­ steam with the free steam velocity. Unsteady load.distributions are obtained which compare favorably with the results of planar lifting surface theory. The vortex lattice method has been extended to a single bladed rotor operating at high advance 'ratios aodeocc)untering a ft:eevottex from afixed.wing upstream of the rotor.
    [Show full text]
  • Potential Flow Theory
    2.016 Hydrodynamics Reading #4 2.016 Hydrodynamics Prof. A.H. Techet Potential Flow Theory “When a flow is both frictionless and irrotational, pleasant things happen.” –F.M. White, Fluid Mechanics 4th ed. We can treat external flows around bodies as invicid (i.e. frictionless) and irrotational (i.e. the fluid particles are not rotating). This is because the viscous effects are limited to a thin layer next to the body called the boundary layer. In graduate classes like 2.25, you’ll learn how to solve for the invicid flow and then correct this within the boundary layer by considering viscosity. For now, let’s just learn how to solve for the invicid flow. We can define a potential function,!(x, z,t) , as a continuous function that satisfies the basic laws of fluid mechanics: conservation of mass and momentum, assuming incompressible, inviscid and irrotational flow. There is a vector identity (prove it for yourself!) that states for any scalar, ", " # "$ = 0 By definition, for irrotational flow, r ! " #V = 0 Therefore ! r V = "# ! where ! = !(x, y, z,t) is the velocity potential function. Such that the components of velocity in Cartesian coordinates, as functions of space and time, are ! "! "! "! u = , v = and w = (4.1) dx dy dz version 1.0 updated 9/22/2005 -1- ©2005 A. Techet 2.016 Hydrodynamics Reading #4 Laplace Equation The velocity must still satisfy the conservation of mass equation. We can substitute in the relationship between potential and velocity and arrive at the Laplace Equation, which we will revisit in our discussion on linear waves.
    [Show full text]
  • Far Field Velocity Potential Induced by a Rapidly Decaying Vorticity Distribution
    Journal of Applied Mathematics and Physics (ZAMP) 0044-2275/90/030395-24$ 1.50 + 0.20 Vol. 41, May 1990 1990 Birkh~iuser Verlag, Basel Far field velocity potential induced by a rapidly decaying vorticity distribution By Rupert Klein, Dept. of Mathematics, Princeton University, Princeton, NJ and Lu Ting, Courant Institute of Mathematical Sciences, New York University, New York, NY 10012, USA 1. Introduction The results to be obtained in this paper are applicable to a general problem regarding the far field behavior of the solution A(x) of the vector Poisson equation in space, zXA = -f~, (1.1) subjected to the boundary condition, IA]--*0 as r = Ixi- 00. (1.2) Here x denotes the position vector with Cartesian coordinates xi, i = 1, 2 and 3. In this paper, boldface symbols are used to denote vector quantities and the subscripts i = 1, 2 and 3 denote their components. Thus A; and coi denote the three components of A and 12 respectively. The inhomogeneous term, 12(x), is assumed to be divergence free, V.12 =0, (1.3) and to decay exponentially in r, that is 1121= o(r-"), for all n as r ~ 00. (1.4) Note that (1.4) is a realistic condition for vortical flows but is not necessary- for the results to be derived here. It suffices to require that (1.4) holds for n less than a sufficiently large integer instead of for all n. The above problem originated from our analysis of a three dimensional unsteady incompressible flow induced by a vorticity field 12.
    [Show full text]
  • Unsteady Lift Prediction with a Higher-Order Potential Flow Method
    aerospace Article Unsteady Lift Prediction with a Higher-Order Potential Flow Method Julia A. Cole 1,* , Mark D. Maughmer 2, Goetz Bramesfeld 3, Michael Melville 3 and Michael Kinzel 4 1 Mechanical Engineering, Bucknell University, 1 Dent Dr., Lewisburg, PA 17837, USA 2 Aerospace Engineering, The Pennsylvania State University, 229 Hammond Bldg, University Park, PA 16802, USA; [email protected] 3 Aerospace Engineering, Ryerson University, 350 Victoria St., Toronto, ON M5B 2K3, Canada; [email protected] (G.B.); [email protected] (M.M.) 4 Mechanical and Aerospace Engineering, University of Central Florida, P.O. Box 162450, Orlando, FL 32816, USA; [email protected] * Correspondence: [email protected] Received: 24 April 2020; Accepted: 18 May 2020; Published: 21 May 2020 Abstract: An unsteady formulation of the Kutta–Joukowski theorem has been used with a higher-order potential flow method for the prediction of three-dimensional unsteady lift. This study describes the implementation and verification of the approach in detail sufficient for reproduction by future developers. Verification was conducted using the classical responses to a two-dimensional airfoil entering a sharp-edged gust and a sinusoidal gust with errors of less than 1% for both. The method was then compared with the three-dimensional unsteady lift response of a wing as modeled in two unsteady vortex-lattice methods. Results showed agreement in peak lift coefficient prediction to within 1% and 7%, respectively, and mean agreement within 0.25% for the full response. Keywords: unsteady aerodynamics; potential flow; applied aerodynamics 1. Introduction 1.1. Motivation In previous work [1–4], the authors developed a time-stepping potential flow method that uses higher-order vorticity elements to represent lifting surfaces and wakes.
    [Show full text]
  • A Generalized Vortex Lattice Method for Subsonic and Supersonic Flow Applications
    https://ntrs.nasa.gov/search.jsp?R=19780008059 2020-03-22T05:30:34+00:00Z NASA Contractor Report 2865 A Generalized Vortex Lattice Method for Subsonic and Supersonic Flow Applications Luis R. Miranda, Robert D. Elliott, and William M. Baker ,8 J CONTRACT NAS 1-12972 DECEMBER 1977 N/ /X NASA Contractor Report 2865 A Generalized Vortex Lattice Method for Subsonic and Supersonic Flow Applications Luis R. Miranda, Robert D. Elliott, and William M. Baker Lockheed-California Company Burbank, California Prepared for Langley Research Center under Contract NAS1-12972 National Aeronautics and Space Administration Scientific end Technical Information Office 1977 TABLE OF CONTENTS Page LIST OF ILLUSTRATIONS ......................... iv SUMMARY ............................... i INTRODUCTION ............................. i THEOP_TICAL DISCUSSION ........................ 3 The Basic Equations ....................... 3 Extension to Supersonic Flow ................. 5 The Skewed-Horseshoe Vortex ................. 9 Modeling of Lifting Surfaces with Thickness .......... 14 Modeling of Fusiform Bodies ................... 15 Computation of Sideslip Effects ................. 17 THE GENERALIZED VORTEX LATTICE METHOD ................. 18 Description of Computational Method ............... 18 Numeric 8.1 Considerations .................... 2O COMPARISON WITH OTHER THEORIES AND EXPERIMENTAL RESULTS ........ 21 CONCLUDING REMARKS ......................... 22 APPENDIX A USER'S MANUAL FOR A GENERALIZED VORTEX LATTICE METHOD FOR SUBSONIC AND SUPERSONIC FLOW APPLICATIONS
    [Show full text]
  • Hydrodynamic Analysis of Ocean Current Turbines Using Vortex Lattice Method
    HYDRODYNAMIC ANALYSIS OF OCEAN CURRENT TURBINES USING VORTEX LATTICE METHOD by Aneesh Goly A Thesis Submitted to the Faculty of The College of Engineering and Computer Science in Partial Fulfillment of the Requirements for the Degree of Master of Science Florida Atlantic University Boca Raton, Florida August 2010 ACKNOWLEDGEMENTS I would like to express my gratitude to my advisor, Palaniswamy Ananthakrishnan, for his support, patience, and encouragement throughout my graduate studies. It is not often that one finds an advisor who always finds the time for listening to the little problems that unavoidably crop up in the course of performing research. His technical and editorial advice was essential to the completion of this master’s thesis and has taught me innumerable lessons and insights. I would like to sincerely thank my committee members Dr. Dhanak, Dr. Hanson and Dr. Xiros for their valuable comments, suggestions and input to the thesis. My special thanks go to Ranjith for his encouragement and numerous fruitful discussions related to the research. I feel privileged to have been able to work with Zaqie, Waazim, Lakitosh and Baishali who were encouraging me all through my thesis. My deepest gratitude goes to my family for their unflagging love and support throughout my life. In the first place to my parents, Srinivas and Rajani for giving me everything in my life. Second, to my grandparents and aunt, Jaishanker, Pushpavathy and Rekha for their unparalleled love and care. Next, to uncle Ravi for his motivation throughout my thesis. Last but not the least, to my uncle Kumar Allady, who directed me in choosing this field and together with aunt, Vishala, has given me unparalleled love, affection and guidance.
    [Show full text]
  • 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.
    [Show full text]
  • SNS COLLEGE of TECHNOLOGY (An Autonomous Institution
    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
    [Show full text]
  • 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.
    [Show full text]
  • An Introduction to Acoustics
    An Introduction to Acoustics S.W. Rienstra & A. Hirschberg Eindhoven University of Technology 2 Oct 2021 This is an extended and revised edition of IWDE 92-06. Comments and corrections are gratefully accepted. This file may be used and printed, but for personal or educational purposes only. © S.W. Rienstra & A. Hirschberg 2004. Contents Page Preface 1 Some fluid dynamics 1 1.1 Conservation laws and constitutive equations ..................... 1 1.2 Approximations and alternative forms of the conservation laws for ideal fluids ..... 4 2 Wave equation, speed of sound, and acoustic energy 9 2.1 Order of magnitude estimates ............................. 9 2.2 Wave equation for a uniform stagnant fluid and compactness ............. 13 2.2.1 Linearization and wave equation ........................ 13 2.2.2 Simple solutions ................................. 14 2.2.3 Compactness .................................. 16 2.3 Speed of sound ..................................... 17 2.3.1 Ideal gas ..................................... 17 2.3.2 Water ...................................... 19 2.3.3 Bubbly liquid at low frequencies ........................ 19 2.4 Influence of temperature gradient ........................... 20 2.5 Influence of mean flow ................................. 22 2.6 Sources of sound .................................... 22 2.6.1 Inverse problem and uniqueness of sources ................... 22 2.6.2 Mass and momentum injection ......................... 23 2.6.3 Lighthill’s analogy ............................... 24 2.6.4 Vortex sound .................................. 27 2.7 Acoustic energy .................................... 29 2.7.1 Introduction ................................... 29 2.7.2 Kirchhoff’s equation for quiescent fluids .................... 30 2.7.3 Acoustic energy in a non-uniform flow ..................... 33 2.7.4 Acoustic energy and vortex sound ........................ 35 ii Contents 3 Green’s functions, impedance, and evanescent waves 38 3.1 Green’s functions ...................................
    [Show full text]
  • A Comparison of Euler Finite Volume and Supersonic Vortex Lattice Methods Used During the Conceptual Design Phase of Supersonic Delta Wings
    A Comparison of Euler Finite Volume and Supersonic Vortex Lattice Methods used during the Conceptual Design Phase of Supersonic Delta Wings THESIS Presented in Partial Fulfillment of the Requirements for the Degree Master of Science in the Graduate School of The Ohio State University By Daniel Guillermo-Monedero, B.S. Graduate Program in Aeronautical and Astronautical Engineering The Ohio State University 2020 Master’s Examination Committee: Dr. Clifford A. Whitfield, Advisor Dr. Richard J. Freuler Dr. Matthew H. McCrink 1 Copyrighted by Daniel Guillermo-Monedero 2020 2 Abstract This thesis uses two different methods to analyze wings in supersonic flows with a focus on preliminary design. The primary goals of this study are to compare the Euler equations finite volume method and supersonic vortex lattice method in predicting surface pressure on wings, and to develop a low-order supersonic vortex lattice method as a baseline tool that can be extended for further wing design and analysis. The supersonic vortex lattice method uses vortical sources to model the flow on the boundary, which replicates the aerodynamic shape of interest, in an inviscid and irrotational flow field and obtain solutions. The Euler equations of flow can be discretized using finite volume methods and can be integrated over the volume of interest and solutions can be obtained over the surface. These mathematically similar methods have a lot of differences in their numerical formulations, which can be critical in the design and analysis of wings. Hence, it is important to understand the key differences of these in order to develop a reliable baseline low-order design tool.
    [Show full text]