AN ABSTRACT OF THE DISSERTATION OF Trevor Kent Howard for the degree of Doctor of Philosophy in Nuclear Engineering presented on May 29, 2018. Title: On Primary Vortex Shedding Regimes between Long Tandem Plates Abstract approved: Wade R. Marcum Vortex shedding is a phenomenon relevant to any industry dealing with fluid flow. The shed vortices often produce oscillatory forces, which have been suspect in the catastrophic failure of airplanes and bridges alike. To prevent further engineering failures a better understanding of the underlying physics is needed. It has been well established that tandem plates exhibit different flow phenomena than cylinders, yet the study of the flow field around tandem plates is insufficient in providing a reasonable prediction of the Strouhal numbers for given geometry. This study fills the void in knowledge in three ways. First, it provides a review of the relevant literature related to vortex shedding for plates as well as that for cylinders, which have been well studied. Second, it develops the theory behind vortex shedding for plates through leveraging previous studies and applying a scaling analysis to the data. Third, it verifies the theory through a PIV analysis of various plate geometries. The results from the analysis are compared directly to the results of cylinders. The general plate has an l:b ratio of 20. Reynolds numbers (Reb) range from 150 (below which vortex shedding does not occur) to 1100 (the “constant” Strouhal limit of cylinders). Gap spacing ratios are taken from a value of zero to infinity. The results of the study provide a means of more accurately determining the Strouhal number for both single and tandem long plates. ©Copyright by Trevor Kent Howard May 29, 2018 All Rights Reserved On Primary Vortex Shedding Regimes between Long Tandem Plates by Trevor Kent Howard A DISSERTATION submitted to Oregon State University in partial fulfillment of the requirements for the degree of Doctor of Philosophy Presented May 29, 2018 Commencement June 2019 Doctor of Philosophy dissertation of Trevor Kent Howard presented on May 29, 2018 APPROVED: Major Professor, representing Nuclear Engineering Head of the School of Nuclear Science and Engineering Dean of the Graduate School I understand that my dissertation will become part of the permanent collection of Oregon State University libraries. My signature below authorizes release of my dissertation to any reader upon request. Trevor Kent Howard, Author ACKNOWLEDGEMENTS First and foremost, I would like to sincerely thank my advisor, Dr. Marcum. He provided me with countless hours of support. He always went above and beyond what was required. Without his mentorship I would not have been nearly as successful as I was in this program. I would like to thank the ARCS foundation, specifically my ARCS donors, Steve and Lynn Pratt who provided me additional funding to ensure my success as a Ph.D. student and beyond. It was such a wonderful pleasure being your ARCS scholar. I would like to thank my friends, and specifically those in my research group who were extremely supportive of my research endeavors. In particular, I would like to thank Laura Oliveira, Tommy Holschuh, Aaron Weiss, Chad Nixon, Griffen Latimer all of whom at one point or another, despite bearing the brunt of my harebrained ideas, half- finished sentences, and severe algebraic mistakes, were willing to listen to me and help steer me in the right direction. I would also like to express additional gratitude to Sam Goodrich who mentored me on the PIV system and Emory Brown who allowed me to use his 3d printer. Both of whom saved me countless hours that may have otherwise been wasted. Finally, I cannot express enough thanks to my parents, Victoria and Tracy, who have always been there to support my pursuit of science throughout my life, and my brother Trenton who was always there and willing to provide support both emotionally and academically. I could not wish for more wonderful family. A final thanks to all my friends, peers, professors, and coworkers who have made my stay at Oregon State University such a wonderful experience. TABLE OF CONTENTS Chapter Page 1 Introduction ........................................................................................................... 1 1.1 Vortex shedding ............................................................................................. 1 1.2 Vortex shedding in the Context of Engineering ............................................. 3 1.3 Motivation ...................................................................................................... 7 1.4 Objectives and Outcomes ............................................................................... 8 1.5 Overview of Proceeding Sections .................................................................. 9 2 Survey of Literature ............................................................................................. 10 2.1 Vortex shedding Theory and a Universal Strouhal Number ........................ 12 2.2 Vortex shedding for Cylinders ..................................................................... 21 2.2.1 Single Cylinders .................................................................................... 21 2.2.2 Tandem Cylinders ................................................................................. 29 2.3 Vortex shedding for Plates Parallel to the Flow ........................................... 35 2.3.1 Vortex shedding over Short Plates ........................................................ 36 2.3.2 Vortex shedding over Long Plates ........................................................ 39 2.3.3 Tandem Plates ....................................................................................... 40 2.4 Additional Vortex Shedding Observations .................................................. 42 2.4.1 Experimental Studies ............................................................................ 43 2.4.2 Numerical Studies ................................................................................. 45 2.5 Study Justification ........................................................................................ 47 3 Theory.................................................................................................................. 48 3.1 Fluid Dynamics ............................................................................................ 48 TABLE OF CONTENTS (CONTINUED) Chapter Page 3.1.1 Inviscid Flow Equations ....................................................................... 48 3.1.2 Navier Stokes Equations ....................................................................... 50 3.1.3 Considerations for Turbulence .............................................................. 53 3.2 Characteristics of Flow Over a Plate ............................................................ 56 3.2.1 Interaction with the Leading Edge ........................................................ 56 3.2.2 Boundary Layer Development along the Mid-Span ............................. 57 3.2.3 Separation and Vortex Shedding at the Tailing Edge ........................... 62 3.2.4 The Wake .............................................................................................. 65 3.3 Derivations of the Scale of Vortex Shedding ............................................... 67 3.3.1 Scaling Analysis of Vortex Shedding from a Bluff Body .................... 68 3.3.2 Scaling Analysis of Vortex Shedding from a Plate .............................. 72 3.3.3 Dimension of the Vortex Street ............................................................ 73 3.3.4 Derivation of Vortex Shedding from Long Tandem Plates .................. 78 4 Methodology........................................................................................................ 81 4.1 Wind Tunnel ................................................................................................. 81 4.1.1 Seed Region .......................................................................................... 83 4.1.2 Flow Conditioner .................................................................................. 85 4.1.3 Inlet Section .......................................................................................... 86 4.1.4 Working Test Section ........................................................................... 88 4.1.5 Outlet Section........................................................................................ 90 4.2 Measurement Instrumentation ...................................................................... 92 4.2.1 Non-PIV measurements. ....................................................................... 93 4.2.2 Particle Image Velocimetry Equipment ................................................ 95 TABLE OF CONTENTS (CONTINUED) Chapter Page 4.3 Conduct ........................................................................................................ 96 4.4 Test Matrix ................................................................................................... 97 4.4.1 Length Scale Reference ........................................................................ 97 4.4.2 Reynolds Numbers ................................................................................ 98 4.4.3 Gap Spacing Ratios ............................................................................... 99 4.4.4 Plate Sizing ......................................................................................... 100 5 Results ..............................................................................................................