DOCSLIB.ORG

Vorticity Confinement Applied to Induced Drag Prediction And

Total Page：16

File Type：pdf, Size：1020Kb

Download full-text PDF Read full-text
Vorticity Confinement Applied to Induced Drag Prediction And VORTICITY CONFINEMENT APPLIED TO INDUCED DRAG PREDICTION AND THE SIMULATION OF TURBULENT WINGTIP VORTICES FROM FIXED AND ROTATING WINGS A Thesis Presented to The Graduate Faculty of The University of Akron In Partial Fulfillment of the Requirements for the Degree Master of Science Kristopher C Pierson May, 2014 VORTICITY CONFINEMENT APPLIED TO INDUCED DRAG PREDICTION AND THE SIMULATION OF TURBULENT WINGTIP VORTICES FROM FIXED AND ROTATING WINGS Kristopher Pierson Thesis Approved: Accepted: _______________________________ _______________________________ Advisor Dean of the College Dr. Alex Povitsky Dr. George K. Haritos _______________________________ _______________________________ Faculty Reader Dean of the Graduate School Dr. Scott Sawyer Dr. George R. Newkome _______________________________ _______________________________ Faculty Reader Date Dr. Minel Braun _______________________________ Department Chair Dr. Sergio Felicelli ii ABSTRACT To improve accuracy of CFD simulations by combating numerical viscosity, the vorticity confinement (VC) approach was applied to tip vortices shed by stationary wings for the prediction of induced drag by far-field integration in Trefftz plane as well as the simulation of tip vortex evolution. Vorticity confinement schemes are first evaluated and compared using 2D Euler simulation of a Taylor vortex. The effect of numerical dissipation is shown to cause the vortex to spread and decay without the presence of physical dissipative terms; VC counteracts this effect and maintains the vortex strength. For 3D simulations, the coefficient of confinement was determined for various flight parameters. Dependence of vorticity confinement parameter on the flight Mach number and the angle of attack was evaluated. The aerodynamic drag results with VC are much closer to analytic lifting line theory compared to integration over surface of wing. To apply VC to viscous and turbulent flows, it is shown that in many cases VC does not affect the physical rate of dissipation of line vortices for temporal and viscous scales relevant to wingtip vortex simulations. VC was applied to the simulation turbulent wingtip vortices originating from fixed and rotating wings. The six Reynolds stress turbulence model combined with VC most accurately matched experimental results of tip vortex evolution. iii ACKNOWLEDGEMENTS I would like acknowledge the financial support and guidance from DAGSI/AFRL Ohio Student-Faculty Research Fellowship in 2011-2013 sponsored by Drs. J. Camberos and L. Downie, Army Research Office in 2012-2013 by ARO program director Dr. F Ferguson, and ASEE/AFRL summer faculty grant (AFRL/WPAFB, Dayton, OH) in 2012. Also, DAGSI/AFRL was the sponsor of previous work at the University of Akron from 2009-2011 that was built upon in the present research. Finally, I would like to thank Dr. Povitsky for his guidance and support that made this research possible. iv TABLE OF CONTENTS Page LIST OF TABLES ............................................................................................................ vii LIST OF FIGURES ......................................................................................................... viii NOMENCLATURE ........................................................................................................... x CHAPTER I. INTRODUCTION .......................................................................................................... 1 1.1 Background ................................................................................................... 1 1.2 Finite Volume Method .................................................................................. 4 1.3 Upwind Schemes and TVD .......................................................................... 5 1.4 Vorticity Confinement .................................................................................. 8 1.5 Wake-Integral Method ................................................................................ 12 1.6 Turbulence Modeling .................................................................................. 13 1.7 Research Goals............................................................................................ 15 II. SIMULATION OF 2-D VORTICES USING VORTICITY CONFINEMENT AND TVD ................................................................................................................................ 17 2.1 2D Code Description................................................................................... 17 2.2 Vorticity Confinement implementation and Formulations ......................... 20 2.3 Results of Second Order Euler Simulations without TVD ......................... 21 2.4 Comparison of TVD Schemes .................................................................... 26 2.5 Decay of Line Vortex, Viscous Test Case .................................................. 29 v III. INDUCED DRAG PREDICTION SIMULATIONS USING WAKE- INTEGRAL COMBINED WITH VORTICITY CONFINEMENT.................................................... 33 3.1 Implementation of VC in ANSYS FLUENT .............................................. 33 3.2 Lifting Line Theory..................................................................................... 34 3.3 Problem Description ................................................................................... 35 3.4 Results ......................................................................................................... 37 3.5 Differentiable Limiter ................................................................................. 42 IV. TURBULENT SIMULATIONS OF FIXED WINGTIP VORTICES USING VORTICITY CONFINEMENT ..................................................................................... 46 4.1 Evaluation of Viscous Drag ...................................................................... 46 4.2 Results of Turbulent 3D Fixed Wing Simulations .................................... 48 4.3 Comparison to Experiements .................................................................... 51 V. TURBULENT SIMULATIONS OF WINGTIP VORTEX COMBINED WITH VORTICITY CONFINEMENT ..................................................................................... 57 5.1 Grid and Setup .......................................................................................... 57 5.2 Inviscid Results ......................................................................................... 59 5.3 Turbulence Model Results ........................................................................ 61 5.4 Winglet Modeling and Results.................................................................. 63 VI. CONCLUSIONS AND RECOMMENDATIONS FOR FUTURE WORK ............. 66 BIBLIOGRAPHY ............................................................................................................. 69 APPENDICES .................................................................................................................. 72 APPENDIX A. FLUX SPLITING FOR STEGER WARMING SCHEME ....... 73 APPENDIX B. 2D MATLAB CODE ................................................................. 75 APPENDIX C. ANSYS FLUENT UDF .............................................................. 82 vi LIST OF TABLES Table Page 3.1 Solver settings, model settings and solution methods for inviscid simulations .. 37 3.2 Drag coefficients by surface integration and wake-integral method compared to lifting line theory ................................................................................................. 39 3.3 Tuned confinement parameters ........................................................................... 39 4.1 Flow characteristics for boundary layer in flat plate .......................................... 47 4.2 Results for near-field and far-field integration for viscous flow about flat plate, error is determined by comparison to Blasius solution for shear stress .............. 48 4.3 Shear force and induced drag results for turbulent simulations ......................... 51 5.1 Physical problem specifications for rotating wing simulations .......................... 58 5.2 Computational parameters for rotating wing simulations ................................... 58 vii LIST OF FIGURES Figure Page 2.1 Positive flux extrapolation used in second order scheme .................................. 19 2.2 First order simulation of Taylor vortex .............................................................. 23 2.3 Upwind second-order simulation of Taylor vortex with and without VC .......... 24 2.4 Results of second order calculations using VCF2 with c=4.5 ............................ 26 2.5 Comparison of TVD Schemes, c=4.0 ................................................................. 28 2.6 Comparison of TVD Schemes, c=5.0 ................................................................. 29 2.7 Decay of line vortex, second-order minmod TVD simulation comparison of epsilon values; Δx=Δy=0.1 ................................................................................. 32 2.8 Decay of line vortex, second-order minmod TVD simulations comparison of epsilon values; Δx=Δy=0.016 ............................................................................ 32 3.1 Computational domain for 3D fixed wing .......................................................... 35 3.2 Residual convergence for AoA = 4 Degrees and Mach = 0.3 ............................ 37 3.3 Induced drag coefficient for various Trefftz plane locations for inviscid simulations .........................................................................................................
Load more

Recommended publications
  • LD5655.V856 1996.P483.Pdf (6.211Mb)
    NEW EFFICIENT CONTACT DISCONTINUITY CAPTURING TECHNIQUES IN SUPERSONIC FLOW SIMULATIONS By Sergei V. Pevchin A DISSERTATION SUBMITTED TO THE FACULTY OF VIRGINIA POLYTECHNIC INSTITUTE AND STATE UNIVERSITY IN PARTIAL FULFILLMENT OF THE REQUIREMENTS FOR THE DEGREE OF DOCTOR OF PHILOSOPHY IN AEROSPACE ENGINEERING Rr ernard Grossman, Chairman fel CL Ah Le John SteiAVoff Robert W. Walters Seek hy SHED é Joseph A. Schetz jes FIM. Lfff September 1996 Blacksburg, Virginia Keywords: CFD, supersonic flow, discontinuities, confinement, capturing Abstract NEW EFFICIENT CONTACT DISCONTINUITY CAPTURING TECHNIQUES IN SUPERSONIC FLOW SIMULATIONS by Sergei V. Pevchin Committee Chairman: Bernard Grossman Aerospace Engineering (ABSTRACT) Accurate numerical algorithms for solving systems of nonlinear hyperbolic equations are considered. The issues of the capturing and the non-diffusive resolution of contact discontinuities were investigated using two different approaches: a kinetic fluctuation splitting scheme and a discontinuity confinement scheme based on an antidiffusion approach. In both approaches cell-vertex fluctuation-splitting methods are used in order to generate a multi-dimensional procedure. The kinetic fluctuation-splitting scheme presented here is a Boltzmann type scheme based on an LDA-scheme discretization on a triangulated Cartesian mesh that uses di- agonal adaptive strategy. The LDA scheme developed by Struijs, Deconinck and Roe has the property of being second-order accurate and linear for a scalar advection equa- tion. It is implemented for the Boltzmann equation following the work of Eppard and Grossman and completes the series of multi-dimensional Euler solvers with upwinding applied at the kinetic level. The MKFS-LDA scheme is a cell-vertex scheme. It was obtained by taking the moments of the fluctuation in the distribution function that are calculated according to the LDA fluctuation splitting procedure on a kinetic level.
    [Show full text]
  • Arxiv:1612.09558V1 [Math.NA] 30 Dec 2016
    Semi-implicit discontinuous Galerkin methods for the incompressible Navier-Stokes equations on staggered adaptive Cartesian grids a, a Francesco Fambri ∗, Michael Dumbser aLaboratory of Applied Mathematics, Department of Civil, Environmental and Mechanical Engineering, University of Trento, Via Mesiano 77, I-38123 Trento, Italy Abstract In this paper a new high order semi-implicit discontinuous Galerkin method (SI-DG) is presented for the solution of the incompressible Navier-Stokes equations on staggered space-time adaptive Cartesian grids (AMR) in two and three space-dimensions. The pressure is written in the form of piecewise polynomials on the main grid, which is dynamically adapted within a cell-by-cell AMR framework. According to the time dependent main grid, different face-based spatially staggered dual grids are defined for the piece-wise polynomials of the respective velocity components. Although the resulting adaptive staggered grids are more complex than classical uniform Cartesian meshes, the numerical scheme can still be written in a rather compact form. Thanks to the use of a tensor-product formulation for the definition of the nodal basis in the d-dimensional space (d = 2; 3), all the discrete operators can be efficiently written as a combination of linear one-dimensional operators acting in the d space directions separately. Arbitrary high order of accuracy is achieved in space, while a very simple semi-implicit time discretiza- tion is obtained via an explicit discretization of the nonlinear convective terms, and an implicit discretization of the pressure gradient in the momentum equation and of the divergence of the velocity field in the con- tinuity equation.
    [Show full text]
  • Development and Verification of a Navier-Stokes Solver with Vorticity Confinement Using Openfoam
    University of Tennessee, Knoxville TRACE: Tennessee Research and Creative Exchange Masters Theses Graduate School 5-2012 Development and Verification of a Navier-Stokes Solver with Vorticity Confinement Using OpenFOAM Austin Barrett Kimbrell University of Tennessee, [email protected] Follow this and additional works at: https://trace.tennessee.edu/utk_gradthes Part of the Aerodynamics and Fluid Mechanics Commons, Computational Engineering Commons, and the Computer-Aided Engineering and Design Commons Recommended Citation Kimbrell, Austin Barrett, "Development and Verification of a Navier-Stokes Solver with Vorticity Confinement Using OpenFOAM. " Master's Thesis, University of Tennessee, 2012. https://trace.tennessee.edu/utk_gradthes/1173 This Thesis is brought to you for free and open access by the Graduate School at TRACE: Tennessee Research and Creative Exchange. It has been accepted for inclusion in Masters Theses by an authorized administrator of TRACE: Tennessee Research and Creative Exchange. For more information, please contact [email protected]. To the Graduate Council: I am submitting herewith a thesis written by Austin Barrett Kimbrell entitled "Development and Verification of a Navier-Stokes Solver with Vorticity Confinement Using OpenFOAM." I have examined the final electronic copy of this thesis for form and content and recommend that it be accepted in partial fulfillment of the equirr ements for the degree of Master of Science, with a major in Mechanical Engineering. John S. Steinhoff, Major Professor We have read this thesis and recommend its acceptance: K. C. Reddy, Joseph C. Yen Accepted for the Council: Carolyn R. Hodges Vice Provost and Dean of the Graduate School (Original signatures are on file with official studentecor r ds.) Development and Verification of a Navier-Stokes Solver with Vorticity Confinement Using OpenFOAM A Thesis Presented for the Master of Science Degree The University of Tennessee, Knoxville Austin Barrett Kimbrell May 2012 Copyright © 2012 by Austin B.
    [Show full text]
  • Nbutsunt-Thesis.Pdf
    TIME SPECTRAL METHOD FOR ROTORCRAFT FLOW WITH VORTICITY CONFINEMENT A DISSERTATION SUBMITTED TO THE DEPARTMENT OF MECHANICAL ENGINEERING AND THE COMMITTEE ON GRADUATE STUDIES OF STANFORD UNIVERSITY IN PARTIAL FULFILLMENT OF THE REQUIREMENTS FOR THE DEGREE OF DOCTOR OF PHILOSOPHY Nawee Butsuntorn June 2008 c Copyright by Nawee Butsuntorn 2008 All Rights Reserved ii I certify that I have read this dissertation and that, in my opinion, it is fully adequate in scope and quality as a dissertation for the degree of Doctor of Philosophy. (G. Antony Jameson) Principal Advisor I certify that I have read this dissertation and that, in my opinion, it is fully adequate in scope and quality as a dissertation for the degree of Doctor of Philosophy. (Sanjiva K. Lele) I certify that I have read this dissertation and that, in my opinion, it is fully adequate in scope and quality as a dissertation for the degree of Doctor of Philosophy. (Robert W. MacCormack) Approved for the University Committee on Graduate Studies. iii Preface This thesis shows that simulation of helicopter flows can adhere to engineering accu- racy without the need of massive computing resources or long turnaround time by choosing an alternative framework for rotorcraft simulation. The method works in both hovering and forward flight regimes. The new method has shown to be more computationally efficient and sufficiently accurate. By utilizing the periodic nature of the rotorcraft flow field, the Fourier based Time Spectral method lends itself to the problem and significantly increases the rate of convergence compared to tradi- tional implicit time integration schemes such as the second order backward difference formula (BDF).
    [Show full text]
  • Final Programme
    From 08:00 REGISTRATION 08:30 – 09:10 OPENING SESSION (Room A1) 09:10 – 09:50 PLENARY LECTURE: Isogeometric and Variational Multiscale Methods in Computational Fluid Dynamics. Thomas J. R. Hughes, University of Texas, USA. 09:50 – 10:30 PLENARY LECTURE: Higher Order Discontinuous Galerkin methods with emphasis on Aeronautical applications. Francesco Bassi, University of Bergamo. 10:30 – 10:50 Coffee Break Room Room A1 Room A2 Room A3 Room A4 Room B5 4.1 MS18 Reliable Numerical Methods 1.1 Numerical Methods for High Speed 3.1 MS12 Numerical Modelling of Waves 2.1 Computational Electromagnetics I for Atmosphere and Ocean Models: Part 5.1 Gas-Liquid Interfaces Flows I Interacting with Coastal Structures I Organizers: A. Mahalov, P. Organizers: E. Didier, M. G. Neves Neittaanmaki, S. Repin 10:50 – 11:20 A 3D Finite Element Method for the A Lagrangian Smoothed Particle New Limiter and Gradient Reconstruction Coupled Numerical Simulation of Hydrodynamics – SPH – Method for An Optimal Approach for Velocity Method for HLLC-Finite Volume Scheme Wind Power Energy Activity in Finland ? 11:00 – 11:20 Electrochemical Systems and Fluid Flow: Modelling Waves-Coastal Structure Interpolation in Multilevel VOF Method to Solve Navier-Stokes Equations AUTHORS: Pekka J. Neittaanmäki Ion Transport in Electrodeposition Interaction AUTHORS: Antonio Cervone; Sandro AUTHORS: Lakhdar Remaki; OuBay SPEAKER: Pekka J. Neittaanmäki AUTHORS: Georg Bauer; Volker AUTHORS: Eric Didier; Maria G. Neves Manservisi; R. Scardovelli Hassan; Kenneth Morgan Gravemeier; Wolfgang A. Wall SPEAKER: Eric Didier SPEAKER: Antonio Cervone SPEAKER: Lakhdar Remaki SPEAKER: Georg Bauer Spectral Volume Method : Application to HyBridization of Numerical Schemes in Comparisons of Wave Overtopping at Indeterminant Data in ProBlems of Segment Patching of the Higher Order Euler Equations and Performance Time Domain to Solve the Vlasov-Maxwell Coastal Structures Calculated with Continuum Mechanics Interface Reconstruction for the Volume of Appraisal Equations AMAZON, COBRAS-UC and SPHYSICS 11:20 – 11:40 AUTHORS: Olli J.
    [Show full text]
  • Investigation of Vorticity Confinement As a High Reynolds Number Turbulence Model
    University of Tennessee, Knoxville TRACE: Tennessee Research and Creative Exchange Doctoral Dissertations Graduate School 12-2007 Investigation of Vorticity Confinement as a High Reynolds Number Turbulence Model Nicholas F. Lynn University of Tennessee - Knoxville Follow this and additional works at: https://trace.tennessee.edu/utk_graddiss Part of the Mechanical Engineering Commons Recommended Citation Lynn, Nicholas F., "Investigation of Vorticity Confinement as a High Reynolds Number Turbulence Model. " PhD diss., University of Tennessee, 2007. https://trace.tennessee.edu/utk_graddiss/235 This Dissertation is brought to you for free and open access by the Graduate School at TRACE: Tennessee Research and Creative Exchange. It has been accepted for inclusion in Doctoral Dissertations by an authorized administrator of TRACE: Tennessee Research and Creative Exchange. For more information, please contact [email protected]. To the Graduate Council: I am submitting herewith a dissertation written by Nicholas F. Lynn entitled "Investigation of Vorticity Confinement as a High Reynolds Number Turbulence Model." I have examined the final electronic copy of this dissertation for form and content and recommend that it be accepted in partial fulfillment of the equirr ements for the degree of Doctor of Philosophy, with a major in Mechanical Engineering. John Steinhoff, Major Professor We have read this dissertation and recommend its acceptance: Gary A. Flandro, K. C. Reddy, Lloyd M. Davis Accepted for the Council: Carolyn R. Hodges Vice Provost and Dean of the Graduate School (Original signatures are on file with official studentecor r ds.) To the Graduate Council: I am submitting herewith a dissertation written by Nicholas F. Lynn entitled “Investigation of Vorticity Confinement as a High Reynolds Number Turbulence Model”.
    [Show full text]
  • Efficient Deformations Using Custom Coordinate Systems
    University of California Santa Barbara Efficient Deformations Using Custom Coordinate Systems A Dissertation submitted in partial satisfaction of the requirements for the degree Doctor of Philosophy in Computer Science by Yun Teng Committee in charge: Professor Theodore Kim, Co-Chair Professor Tobias H¨ollerer,Co-Chair Professor Linda Petzold September 2016 The Dissertation of Yun Teng is approved. Professor Linda Petzold Professor Tobias H¨ollerer,Committee Co-Chair Professor Theodore Kim, Committee Co-Chair July 2016 Efficient Deformations Using Custom Coordinate Systems Copyright c 2016 by Yun Teng iii Acknowledgements I owe gratitude to a great many people for making this dissertation possible and for making my graduate school years such an amazing journey. My deepest gratitude is to my advisor, Professor Theodore Kim. Your inspiring classes on various aspects of Computer Graphics has made me fall in love with this field. You have been guiding me through various stages of research, while allowing me the freedom to explore on my own. Your encouragement and support helped me overcome numerous difficulties over the years and led to this dissertation. I am sincerely grateful to my co-advisor, Professor Tobias H¨ollerer. Your insightful comments and constructive suggestions greatly improved the quality of my research work as well as my understanding of the research field. I am very thankful to you for the fruitful discussions that helped me build up my research road map, clarify technical details, and refine presentation quality. My sincere appreciation to Professor Linda Petzold for serving on my committee. Your class on numerical simulation prepared a sound theoretical foundation for all my later work and ignited my research interest in this area.
    [Show full text]
  • Development and Analysis of High-Order Vorticity Confinement Schemes I
    Development and Analysis of High-Order Vorticity Confinement Schemes I. Petropoulos, M. Costes, P. Cinnella To cite this version: I. Petropoulos, M. Costes, P. Cinnella. Development and Analysis of High-Order Vorticity Confine- ment Schemes. ICCFD9, Jul 2016, ISTANBUL, Turkey. hal-01371794v1 HAL Id: hal-01371794 https://hal.archives-ouvertes.fr/hal-01371794v1 Submitted on 26 Sep 2016 (v1), last revised 23 Mar 2018 (v2) HAL is a multi-disciplinary open access L’archive ouverte pluridisciplinaire HAL, est archive for the deposit and dissemination of sci- destinée au dépôt et à la diffusion de documents entific research documents, whether they are pub- scientifiques de niveau recherche, publiés ou non, lished or not. The documents may come from émanant des établissements d’enseignement et de teaching and research institutions in France or recherche français ou étrangers, des laboratoires abroad, or from public or private research centers. publics ou privés. COMMUNICATION A CONGRES Development and Analysis of High-Order Vorticity Confinement Schemes I. Petropoulos (ONERA), M. Costes (ONERA), P. Cinnella (DynFluid Laboratory) ICCFD9 ISTANBUL, TURQUIE 11-15 juillet 2016 TP 2016-513 Powered by TCPDF (www.tcpdf.org) Ninth International Conference on ICCFD9-2016-0136 Computational Fluid Dynamics (ICCFD9), Istanbul, Turkey, July 11-15, 2016 Development and Analysis of High-Order Vorticity Confinement Schemes Ilias Petropoulos1, Michel Costes1 and Paola Cinnella2 1 ONERA, The French Aerospace Lab, 8 rue des Vertugadins, 92190 Meudon, France 2 DynFluid Laboratory, Arts et Métiers ParisTech, 151 Bd. de l’Hôpital, 75013 Paris, France Corresponding author: [email protected] Abstract: High-order extensions of the Vorticity Confinement (VC) method are developed for the accurate computation of vortical flows, following the VC2 conservative formulation of Steinhoff.
    [Show full text]