DOCSLIB.ORG

Development and Numerical Investigation of Magneto-Fluid-Dynamics Formulations

Total Page：16

File Type：pdf, Size：1020Kb

Download full-text PDF Read full-text
Development and Numerical Investigation of Magneto-Fluid-Dynamics Formulations DEVELOPMENT AND NUMERICAL INVESTIGATION OF MAGNETO-FLUID-DYNAMICS FORMULATIONS A Dissertation by Ovais U. Khan Master of Science, King Fahd University of Petroleum and Minerals, 2003 Bachelor of Engineering, NED University of Engineering and Technology, 2000 Submitted to the Department of Aerospace Engineering and the faculty of the Graduate School of Wichita State University in partial fulfillment of the requirements for the degree of Doctor of Philosophy December 2009 c Copyright by Ovais Khan 2009 ° All Rights Reserved DEVELOPMENT AND NUMERICAL INVESTIGATION OF MAGNETO-FLUID-DYNAMICS FORMULATIONS The following faculty have examined the final copy of this dissertation for form and content, and recommend that it be accepted in partial fulfillmentoftherequirementforthedegree of Doctor of Philosophy with a major in Aerospace Engineering . Klaus A. Hoffmann, Committee Chair Leonard S. Miller, Committee Member Roy Y. Myose, Committee Member Hussein H. Hamdeh, Committee Member Kamran Rokhsaz, Committee Member Accepted for the College of Engineering Zulma Toro-Ramos, Dean Accepted for the Graduate School J. David McDonald, Dean iii DEDICATED TO ALLAH subhanahu-wa-ta ala The most Merciful, The most Benevolent iv ACKNOWLEDGEMENTS Words cannot at all express my thankfulness to Almighty Allah, subhanahu-wa-ta ala,the most Merciful; the most Benevolent Who blessed me with the opportunity and courage to complete this task. My heartfelt gratitude and special thanks to my thesis advisor learned Professor Klaus A. Hoffmann. I am grateful to him for his consistent help, untiring guidance, constant encouragement and precious time that he has spent with me in completing this course of work. I do admire his exhorting style that has given me tremendous confidence and ability to do independent research. Working with him in a friendly and motivating environment was really a joyful and learning experience. I must appreciate and thank Dr. J. F Dietiker for his extraordinary attention and thought- provoking contribution in my research. His assistance and encouragement can never be forgotten, working with him was really a good experience. I am also thankful to all the committee members, Dr. Myose, Dr. Miller, Dr. Hamdeh and Dr. Rokhsaz for their comments and suggestions. I must appreciate and thank Professor Robert W. MacCormack from Stanford University for his constant guidance, constructive and positive criticism about my research. It was surely an honor and an exceptional learning experience to work with him. v I am thankful to Dr. Datta Gaitonde and Dr. Jonathan Poggie from Air Force Research Laboratory, Wright-Patterson Air Force Base, Ohio; for technical discussion and providing positive feed back about my research. I would also like to acknowledge the sponsorship of my research from the US Air Force Office of Scientific Research (AFOSR). Sincere friendship is the spice of life. I owe thanks to my graduate fellow students from Pakistan, India, France and the United States; most particularly, Arshed bhai, Hassan Khurshid, Ikram bhai and Raheel bhai. A special note of thanks to a person who contributed a lot in building up my academic skills and personality by precious advising, guidance, and encouragement. Family support plays a vital role in the success of an individual. I must appreciate the efforts of my brothers and sisters who supported me a lot during my education. I am thankful to my entire family for its love, support and prayers throughout my life especially my dearest mother and father who devoted their lives in the endeavor of getting me a quality education. I am grateful to my parents for all the hardships in supporting their family and making bright future for their children. May Allah help us in following Islam according to Quran and Sunnah ! (Aameen) vi ABSTRACT Magnetofluiddynamics(MFD)isthebranchoffluid dynamics that involves mutual interaction of electrically conducting non-magnetic fluids and magnetic fields. MFD offers promising advances in flow control and propulsion of future hypersonic vehicles. With the advent of computational fluid dynamics (CFD), the numerical study of inherently complicated fluid dynamics problems, such as flows at high velocities, high-temperature re-entry bodies, and mixed subsonic-supersonic flows, has become an interesting area of research. Further advancement in high-speed cluster machines and development of efficient algorithmshasmadeitpossibletoexploreMFDproblemsnumerically. In this work, development and validation of numerical algorithms for the simulation of MFD problems of supersonic and hypersonic flows have been conducted. Validity of low magnetic Reynolds number approximation has been checked with respect to the results obtained from full MFD equations. In addition to the two commonly used formulations for MFD, a third formulation based on the decomposition of a magnetic field for solving full MFD equations was explored. The governing equations were transformed to a generalized computational domain and discretized using a finite difference technique. A time-explicit multistage Runge-Kutta scheme augmented with total variation diminishing (TVD) limiters for time integration was implemented. The developed codes were validated with the existing closed form solution of the magnetic Rayleigh problem for both two- and three- dimensional cases. The results obtained from decomposed full MFD equations compare well with the results obtained by solving low magnetic Reynolds number approximation and classical full MFD equations for a wide range of magnetic Reynolds numbers. It is shown that the decomposed full MFD technique requires substantially less computation time compare to classical full MFD equations for the solution of flow fields with strong imposed magnetic fields. Finally, high-speed flows over a backward-facing step that is subject to an applied magnetic field were numerically simulated. The global domain of computation was vii decomposed into upstream and downstream domains from the step location. The low magnetic Reynolds number approximation under a multiblock grid approach was used for modeling the backstep flow. Pressure distribution for the Navier-Stokes analysis was found to be in good agreement with the experimental data. Different types of magnetic field distributions were investigated. Both uniform and variable electrical conductivity distributions were considered. It was observed that an increase in the separation zone and displacement of oblique shock wave towards the exit section occurs subsequent to application of the magnetic field. A comparison of results obtained with uniform and variable electrical conductivities showed a reduction in magnetic interaction for variable electrical conductivity. viii LIST OF FIGURES Figure Page 1.1Bowshockwaveinfrontofblunt-body..................... 4 1.2 Comparison of flow field obtained without and with the application of mag- netic field..................................... 7 2.1 Hypersonic flowoverblunt-body........................ 17 2.2 Illustration of supersonic flow fieldoverbackward-facingstep........ 39 3.1 Different types of boundary conditions for a typical external flow...... 75 5.1 Solution algorithm based on modifiedRunge-Kuttascheme......... 120 5.2Solutionalgorithmbasedonmultiblockapproach............... 131 6.1 Development of velocity profilesforMFDRayleighproblem......... 136 6.2 Comparison of numerical and analytical velocity distributions for different time intervals at Rm =2.5. ........................... 139 6.3 Comparison of numerical and analytical induced magnetic field distributions for different time intervals at Rm =2.5..................... 140 6.4 Comparison of velocities obtained by Full MFD and low magnetic Reynolds 3 number formulations at Rm =2.5 10− . ................... 141 6.5 Comparison of induced magnetic fi×eld distributions obtained from Full MFD formulation for differentvaluesofmagneticReynoldsnumber........ 142 6.6 Percentage average error in velocities obtained by Full MFD and low mag- netic Reynolds number formulations for different values of magnetic Reynolds number...................................... 143 6.7 Wall clock time for full MFD and low magnetic Reynolds number formulations.144 6.8 Comparison of velocities obtained from exact solution and DFMFD formu- lation at differenttimeintervals......................... 146 6.9 Comparison of induced magnetic fields obtained from exact solution and DFMFD formulation at differenttimeintervals................ 147 6.10 Comparison of velocities obtained by DFMFD, FMFD, and low magnetic 3 Reynolds number formulations at Rm =2.5 10− . ............. 148 6.11 Comparison of induced magnetic fields obtained× from FMFD and DFMFD formulations for different time intervals at Rm =2.5. ............ 149 6.12 Wall clock time for FMFD, DFMFD, and low magnetic Reynolds number formulations................................... 150 6.13 Comparison of wall clock times taken by FMFD and DFMFD formulations 3 for magnetic field strength of 1.422 10− TatRm =0.125. ........ 153 × xii 6.14 Comparison of wall clock times taken by FMFD and DFMFD formulations 2 for magnetic field strength of 1.3944 10− TatRm =0.125. ....... 154 6.15 Comparison of wall clock times taken× by FMFD and DFMFD approaches 3 2 for magnetic field strength of 1.422 10− TatRm =2.5 10− . ..... 155 6.16 Comparison of wall clock times taken× by FMFD and DFMFD× approaches 2 2 for magnetic field strength of 1.3944 10− TatRm =2.5 10− ...... 156 6.17 Wall clock time for FMFD, DFMFD,× and low magnetic Reynolds× number formulations................................... 158
Load more

Recommended publications
  • Diagnostic Techniques for MHD in Hypersonic Flows
    UNIVERSITA’ DEGLI STUDI DI BOLOGNA FACULTY OF ELECTRICAL ENGINEERING SCIENTIFIC FIELD ING‐IND/31 XXII CYCLE Diagnostic Techniques for MHD in Hypersonic Flows PhD Thesis Veronica Maria Granciu Advisor: Chiar.mo Prof. CARLO ANGELO BORGHI Second Advisor: Prof. ANDREA CRISTOFOLINI Ph.D. Coordinator: Chiar.mo Prof. FRANCESCO NEGRINI Bologna, March 2010 UNIVERSITA’ DEGLI STUDI DI BOLOGNA FACULTY OF ELECTRICAL ENGINEERING SCIENTIFIC FIELD ING‐IND/31 XXII CYCLE Diagnostic Techniques for MHD in Hypersonic Flows PhD Thesis Veronica Maria Granciu Advisor: Chiar.mo Prof. CARLO ANGELO BORGHI Second Advisor: Prof. ANDREA CRISTOFOLINI Ph.D. Coordinator: Chiar.mo Prof. FRANCESCO NEGRINI Bologna, March 2010 ACKNOWLEDGEMENTS I would like to express my heartfelt gratitude to my advisors Professor Carlo Borghi and Professor Andrea Cristofolini for excellent guidance and motivation. Their encouragement and understanding during the study has been a source of inspiration for me. My special thank belongs to my lab co‐worker Gabriele, who gave me the first live taste of the beauty plasma research. It was a very great experience to work with him. Thanks Hugo! I’m also grateful to my colleagues Chiara and Fabio, “i plasmatici”, for their suggestions and moral support. In conclusion, I wish to dedicate this work to my family and to Marco, who offer me courage, hope and a lot of patience. Without his love, I never would have made it. Thank you for believing in me. Index INTRODUCTION .............................................................................................................. 1 PART I Diagnostic procedures theory Chapter 1 Microwave Transmission System 1.1 Introduction ............................................................................................... 5 1.2 Electromagnetic waves in collisionless plasma .......................................... 5 1.3 Electromagnetic waves in collisional plasma ……………………......................
    [Show full text]
  • Surface Pressure Fluctuations Near an Axisymmetric Stagnation Point
    KM m Vk I •/•*.*.•* .^ >.,*.' . i • I H H '**<J2 MITED STATES \RTMENT OF 1MERCE NBS TECHNICAL NOTE 563 JUCATION If"' Surface Pressure Fluctuations Near an Axisymmetric Stagnation Point U.S. VRTMENT OF MMERCE National Bureau of -. ndards Lz UI — NATIONAL BUREAU OF STANDARDS 1 The National Bureau of Standards was established by an act of Congress March 3, 1901. The Bureau's overall goal is to strengthen and advance the Nation's science and technology and facilitate their effective application for public benefit. To this end, the Bureau conducts research and provides: (1) a basis for the Nation's physical measure- ment system, (2) scientific and technological services for industry and government, (3) a technical basis for equity in trade, and (4) technical services to promote public safety. The Bureau consists of the Institute for Basic Standards, the Institute for Materials Research, the Institute for Applied Technology, the Center for Computer Sciences and Technology, and the Office for Information Programs. THE INSTITUTE FOR BASIC STANDARDS provides the central basis within the United States of a complete and consistent system of physical measurement; coordinates that system with measurement systems of other nations; and furnishes essential services leading to accurate and uniform physical measurements throughout the Nation's scien- tific community, industry, and commerce. The Institute consists of a Center for Radia- tion Research, an Office of Measurement Services and the following divisions: Applied Mathematics—Electricity—Heat—Mechanics—Optical Physics—Linac Radiation2—Nuclear Radiation 2—Applied Radiation 2—Quantum Electronics 3— Electromagnetics 3—Time and Frequency 3—Laboratory Astrophysics 3—Cryo- 3 genics .
    [Show full text]
  • Unsteady Flows in a Single-Stage Transonic Axial-Flow Fan Stator Row Michael Dale Hathaway Iowa State University
    Iowa State University Capstones, Theses and Retrospective Theses and Dissertations Dissertations 1986 Unsteady flows in a single-stage transonic axial-flow fan stator row Michael Dale Hathaway Iowa State University Follow this and additional works at: https://lib.dr.iastate.edu/rtd Part of the Mechanical Engineering Commons Recommended Citation Hathaway, Michael Dale, "Unsteady flows in a single-stage transonic axial-flow fan stator row " (1986). Retrospective Theses and Dissertations. 8250. https://lib.dr.iastate.edu/rtd/8250 This Dissertation is brought to you for free and open access by the Iowa State University Capstones, Theses and Dissertations at Iowa State University Digital Repository. It has been accepted for inclusion in Retrospective Theses and Dissertations by an authorized administrator of Iowa State University Digital Repository. For more information, please contact [email protected]. INFORMATION TO USERS While the most advanced technology has been used to photograph and reproduce this manuscript, the quality of the reproduction is heavily dependent upon the quality of the material submitted. For example: • Manuscript pages may have indistinct print. In such cases, the best available copy has been filmed. • Manuscripts may not always be complete. In such cases, a note will indicate that it is not possible to obtain missing pages. • Copyrighted material may have been removed from the manuscript. In such cases, a note will indicate the deletion. Oversize materials (e.g., maps, drawings, and charts) are photographed by sectioning the original, beginning at the upper left-hand comer and continuing from left to right in equal sections with small overlaps. Each oversize page is also filmed as one exposure and is available, for an additional charge, as a standard 35mm slide or as a 17"x 23" black and white photographic print.
    [Show full text]
  • 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.
    [Show full text]
  • On the Circulation and the Position of the Forward Stagnation Point on Airfoils
    On the circulation and the position of the forward stagnation point on airfoils J. Meseguer (corresponding author), G. Alonso, A. Sanz-Andres and I. Perez-Grande IDR/UPM. EJ.S.I. Aeronauticos, Universidad Politecnica de Madrid, E-28040 Madrid, Spain E-mail: jmeseguer@idr. upm. es Abstract Lift and velocity circulation around airfoils are two aspects of the same phenomenon when airfoils are not stalled and the Kutta-Joukowski theorem applies. This theorem establishes a linear dependence between lift and circulation, which breaks when stalling occurs. As the angle of attack increases beyond this point, the circulation vanishes. Since the circulation determines to a great extent the position of the forward stagnation point on an airfoil, the measurement of this position is an easy and simple way to determine the circulation, which is of help in understanding the role of the latter in the generation of aerodynamic forces on airfoils. Keywords Kutta-Joukowski theorem; airfoil; stagnation point Introduction Wing profiles are aerodynamic devices which are designed to provide high values of the ratio lift/aerodynamic drag, lid. Airfoils are characterised by the camber line, the thickness distribution and the angle of attack. These streamlined two- dimensional bodies generally have a rounded leading edge and a wedged trailing edge, the latter being of paramount importance in generating lift. As is well known, due to the airfoil's shape, in normal operation the flow is accel­ erated on the airfoil's upper side and decelerated on its lower side. Hence, the pres­ sure decreases on the upper side and increases on the lower side, and thus a net force appears.
    [Show full text]
  • Ultra-Short Nacelles for Low Fan Pressure Ratio Propulsors
    Ultra-Short Nacelles for Low Fan Pressure Ratio Propulsors The MIT Faculty has made this article openly available. Please share how this access benefits you. Your story matters. Citation Peters, Andreas, Zoltán S. Spakovszky, Wesley K. Lord, and Becky Rose. “Ultra-Short Nacelles for Low Fan Pressure Ratio Propulsors.” Volume 1A: Aircraft Engine; Fans and Blowers (June 16, 2014). As Published http://dx.doi.org/10.1115/GT2014-26369 Publisher American Society of Mechanical Engineers Version Final published version Citable link http://hdl.handle.net/1721.1/116091 Terms of Use Article is made available in accordance with the publisher's policy and may be subject to US copyright law. Please refer to the publisher's site for terms of use. Proceedings of ASME Turbo Expo 2014: Turbine Technical Conference and Exposition GT2014 June 16 – 20, 2014, Düsseldorf, Germany GT2014-26369 ULTRA‐SHORT NACELLES FOR LOW FAN PRESSURE RATIO PROPULSORS Andreas Peters and Zoltán S. Spakovszky Wesley K. Lord and Becky Rose Gas Turbine Laboratory Pratt & Whitney Massachusetts Institute of Technology East Hartford, CT 06118 Cambridge, MA 02139 ABSTRACT NOMENCLATURE As the propulsor fan pressure ratio (FPR) is decreased for Afan face, AHL Fan face area, inlet highlight area improved fuel burn, reduced emissions and noise, the fan A0 Streamtube capture area diameter grows and innovative nacelle concepts with short AoA Engine angle-of-attack (relative to rotational axis) inlets are required to reduce their weight and drag. This paper a, b Semi-diameter of super-ellipse describing inlet LE addresses the uncharted inlet and nacelle design space for low- BPR Bypass ratio FPR propulsors where fan and nacelle are more closely coupled D, Dmax Fan rotor, maximum nacelle diameter than in current turbofan engines.
    [Show full text]
  • Modern Layout and Design Strategy for Axial Fans
    Maria Teodora Pascu Modern Layout and Design Strategy for Axial Fans Moderne Auslegungs- und Entwurfsstrategie für Axialventilatoren Back cover Front cover Modern Layout and Design Strategy for Axial Fans Moderne Auslegungs- und Entwurfsstrategie für Axialventilatoren Der Technischen Fakultät der Friedrich–Alexander–Universität Erlangen–Nürnberg zur Erlangung des Grades DOKTOR–INGENIEUR vorgelegt von Maria Teodora Pascu Erlangen, 2009 Als Disseration genehmigt von der Technischen Fakultät der Universität Erlangen-Nürnberg Tag der Einreichung: 11.12.2008 Tag der Promotion: 24.04.2009 Dekan: Prof. Dr. J. Huber Berichterstatter: Prof. Dr. Dr. h.c. F. Durst Prof. Dr. M. Wensing ii Acknowledgements This work received financial support from the Bavarian Science Foundation in the form of an individual grant, which is gratefully acknowledged. I would like especially to thank my supervisor, Prof. Dr. Dr. h.c. F. Durst, who from the first day we met, during the Summer Academy Kuşadasi 2004, captured my attention for fluid mechanics research, and by supporting my diploma thesis at the Institute of Fluid Mechanics LSTM Erlangen, brought me in close contact with the topic and stirred my interest in further academic education. He has enabled me to work in the field of turbomachines and constantly supported the present work. I would also like to thank Prof. Dr. M. Wensing for his kind acceptance to review the present work. Furthermore, I would like to thank Prof. Dr. A. Delgado, head of the Institute of Fluid Mechanics LSTM Erlangen, who supported and encouraged the present work, always taking a genuine interest in the outcome of the investigations. My deepest acknowledgements go to Dr.
    [Show full text]
  • Hypersonics: Laying the Road Ahead Aerospace Engineering
    Hypersonics: Laying the Road Ahead Pedro Miguel Rodrigues da Costa Simões Gonçalves Thesis to obtain the Master of Science Degree in Aerospace Engineering Supervisors: Prof. José Carlos Fernandes Pereira Prof. Mário António Prazeres Lino da Silva Examination Committee Chairperson: Prof. Fernando José Parracho Lau Supervisor: Prof. Mário António Prazeres Lino da Silva Member of the Committee: Prof. André Calado Marta July 2018 ii Acknowledgments A` minha fam´ılia, em particular os meus pais e irma˜ por todo o apoio incondicional que me deram ao longo de todos estes anos, permitindo que eu chegasse a esta etapa da minha vida. Um agradecimento especial a` minha tia Ilda Fernandes pelo seu apoio e pelos seus conselhos, apesar da distancia.ˆ Aos meus amigos e colegas que me acompanharam ao longo do curso e sem os quais tudo teria sido tao˜ mais dif´ıcil. Ao Professor Mario´ Lino da Silva pela sua contribuic¸ao˜ imprescind´ıvel para a qualidade deste tra- balho e pela sua disponibilidade, quer na revisao˜ e aconselhamento a proposito´ desta dissertac¸ao˜ como tambem´ das publicac¸oes˜ inerentes a este projecto. Ao Dr. Ricardo Reis pela extensa bibli- ografia proporcionada e pela sua constante exigenciaˆ por um trabalho cada vez mais ambicioso. Ao Dr. Carlos Ilario´ pelo sua presenc¸a nos Estados Unidos, que serviu de apoio para a minha primeira apresentac¸ao˜ de uma publicac¸ao.˜ Por ultimo,´ ao Professor Andre´ Marta por ter disponibilizado o mod- elo desta dissertac¸ao.˜ iii iv Resumo O desafio hipersonico´ comec¸ou ha´ quase um seculo´ atras;´ nao˜ obstante, apesar dos recentes pro- gressos tecnologicos,´ continua a nao˜ ser uma realidade nos dias de hoje.
    [Show full text]