Mathematical Methods For Vortex Identification With Application On Shock Wave Vortex Ring Interaction
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| Author | : Yinlin Dong |
| Publisher | : |
| Total Pages | : 69 |
| Release | : 2017 |
| Genre | : Boundary layer |
| ISBN | : |
Vortices are seen everywhere in nature, from smoke rings to tornadoes. Vortical structures play an essential role in the turbulence dynamics such as turbulence generation, kinetic energy production and dissipation, enhancement of transport of mass, heat and momentum and so on. In this dissertation, we present several vortex identification methods and compare them by the visualization of the examples studied by direct numerical simulation for flows with different speeds. The comparisons show the Omega method is much close to give vortex a mathematical definition and better visualization for vortical structures. We apply our method on the Micro Vortex Generator (MVG) data to reveal the significant role of the transport of vortices in the shock wave boundary layer interaction. A wedge-shaped MVG is placed on a flat plate over which a turbulent boundary layer at Mach number 2.5 is developed. We investigate the interaction between an oblique shock and high-speed vortex rings in the MVG controlled ramp flow by using a high order implicit large eddy simulation with the fifth order bandwidth optimized WENO scheme. By tracking several typical vortex rings before, when and after they pass through the shock front, the quantitative changes of flow properties are studied in detail. The vortex ring propagation is found to be responsible for the shock motion, and thus cause the pulsation of the separation bubble. The shock ring interaction will provide an insight for the study of flow control.
| Author | : Christopher Radcliff Anderson |
| Publisher | : American Mathematical Soc. |
| Total Pages | : 776 |
| Release | : 1991-12-23 |
| Genre | : Science |
| ISBN | : 9780821896969 |
Understanding vortex dynamics is the key to understanding much of fluid dynamics. For this reason, many researchers, using a great variety of different approaches--analytical, computational, and experimental--have studied the dynamics of vorticity. The AMS-SIAM Summer Seminar on Vortex Dynamics and Vortex Methods, held in June 1990 at the University of Washington in Seattle, brought together experts with a broad range of viewpoints and areas of specialization. This volume contains the proceedings from that seminar. The focus here is on the numerical computation of high Reynolds number incompressible flows. Also included is a smaller selection of important experimental results and analytic treatments. Many of the articles contain valuable introductory and survey material as well as open problems. Readers will appreciate this volume for its coverage of a wide variety of numerical, analytical, and experimental tools and for its treatment of interesting important discoveries made with these tools.
| Author | : Kyoji Kamemoto |
| Publisher | : World Scientific |
| Total Pages | : 228 |
| Release | : 2000-05-11 |
| Genre | : Technology & Engineering |
| ISBN | : 9814493287 |
Vortex methods have been developed and applied to many kinds of flows related to various problems in wide engineering and scientific fields. The purpose of the First International conference on Vortex methods was to provide an opportunity for engineers and scientists to present their achievements, exchange ideas and discuss new developments in mathematical and physical modeling techniques and engineering applications of vortex methods.
| Author | : Christopher R. Anderson |
| Publisher | : Springer |
| Total Pages | : 150 |
| Release | : 2006-11-14 |
| Genre | : Mathematics |
| ISBN | : 3540460349 |
| Author | : Chaoqun Liu |
| Publisher | : Springer Nature |
| Total Pages | : 479 |
| Release | : 2021-07-26 |
| Genre | : Science |
| ISBN | : 3030702170 |
This book collects papers presented in the Invited Workshop, “Liutex and Third Generation of Vortex Definition and Identification for Turbulence,” from CHAOS2020, June 9-12, 2020, which was held online as a virtual conference. Liutex is a new physical quantity introduced by Prof. Chaoqun Liu of the University of Texas at Arlington. It is a vector and could give a unique and accurate mathematical definition for fluid rotation or vortex. The papers in this volume include some Liutex theories and many applications in hydrodynamics, aerodynamics and thermal dynamics including turbine machinery. As vortex exists everywhere in the universe, a mathematical definition of vortex or Liutex will play a critical role in scientific research. There is almost no place without vortex in fluid dynamics. As a projection, the Liutex theory will play an important role on the investigations of the vortex dynamics in hydrodynamics, aerodynamics, thermodynamics, oceanography, meteorology, metallurgy, civil engineering, astronomy, biology, etc. and to the researches of the generation, sustenance, modelling and controlling of turbulence.
| Author | : Chaoqun Liu |
| Publisher | : Academic Press |
| Total Pages | : 458 |
| Release | : 2020-10-29 |
| Genre | : Science |
| ISBN | : 0128190248 |
Liutex and Its Applications in Turbulence Research reviews the history of vortex definition, provides an accurate mathematical definition of vortices, and explains their applications in flow transition, turbulent flow, flow control, and turbulent flow experiments. The book explains the term "Rortex" as a mathematically defined rigid rotation of fluids or vortex, which could help solve many longstanding problems in turbulence research. The accurate mathematical definition of the vortex is important in a range of industrial contexts, including aerospace, turbine machinery, combustion, and electronic cooling systems, so there are many areas of research that can benefit from the innovations described here. This book provides a thorough survey of the latest research in generalized and flow-thermal, unified, law-of-the-wall for wall-bounded turbulence. Important theory and methodologies used for developing these laws are described in detail, including: the classification of the conventional turbulent boundary layer concept based on proper velocity scaling; the methodology for identification of the scales of velocity, temperature, and length needed to establish the law; and the discovery, proof, and strict validations of the laws, with both Reynolds and Prandtl number independency properties using DNS data. The establishment of these statistical laws is important to modern fluid mechanics and heat transfer research, and greatly expands our understanding of wall-bounded turbulence. Provides an accurate mathematical definition of vortices Provides a thorough survey of the latest research in generalized and flow-thermal, unified, law-of-the-wall for wall-bounded turbulence Explains the term “Rortex as a mathematically defined rigid rotation of fluids or vortex Covers the statistical laws important to modern fluid mechanics and heat transfer research, and greatly expands our understanding of wall-bounded turbulence
| Author | : Karl E. Gustafson |
| Publisher | : SIAM |
| Total Pages | : 226 |
| Release | : 1991-01-01 |
| Genre | : Science |
| ISBN | : 0898712580 |
Vortex methods have emerged as a new class of powerful numerical techniques to analyze and compute vortex motion. This book addresses the theoretical, numerical, computational, and physical aspects of vortex methods and vortex motion.
| Author | : Chaoqun Liu |
| Publisher | : BoD – Books on Demand |
| Total Pages | : 126 |
| Release | : 2024-01-24 |
| Genre | : Science |
| ISBN | : 1837686408 |
This book includes six chapters covering new vortex theories, vortex identification methods, and vortex simulation and applications. Vortices are ubiquitous in the universe and include tornados, hurricanes, airplane tip vortices, polar vortices, and even star vortices in the galaxy. Vortices are also building blocks, muscles, and sinews of turbulent flows. This book is useful for researchers in hydrodynamics, aerodynamics, thermodynamics, oceanography, meteorology, metallurgy, civil engineering, astronomy, biology, and more. It is also useful for research on the generation, sustenance, modeling, and controlling of turbulence.
| Author | : Ionut Danaila |
| Publisher | : Springer Nature |
| Total Pages | : 206 |
| Release | : 2021-04-16 |
| Genre | : Technology & Engineering |
| ISBN | : 3030681505 |
This book offers a guide to understanding models of vortex rings, starting from classical ones (circular vortex filament, Hill and Norbury-Fraenkel inviscid models) to very recent models incorporating viscous effects and realistic shapes of the vortex core. Unconfined and confined viscous vortex rings are described by closed formulae for vorticity, stream function, translational velocity, energy, impulse and circulation. Models are applied to predict the formation number of optimal vortex rings and to describe two-phase vortex ring-like structures generated in internal combustion engines. The book provides a detailed presentation of analytical developments of models, backed up by illustrations and systematic comparisons with results of direct numerical simulations. The book is useful for graduate students in applied mathematics, engineering and physical sciences. It is a useful reference for researchers and practising engineers interested in modelling flows with vortex rings.
| Author | : Chaoqun Liu |
| Publisher | : Bentham Science Publishers |
| Total Pages | : 321 |
| Release | : 2017-12-08 |
| Genre | : Technology & Engineering |
| ISBN | : 1681085976 |
This volume presents an implicitly implemented large eddy simulation (ILES) by using the fifth order bandwidth-optimized WENO scheme. The chosen method is applied to make comprehensive studies on ramp flows with and without control at Mach 2.5 and Re=5760. Flow control in the form of microramp vortex generators (MVG) is applied. The results show that a MVG can distinctly reduce the separation zone at the ramp corner and lower the boundary layer shape factor under simulated conditions. A series of new findings about the MVG-ramp flow are obtained, including structures relevant to surface pressure, three-dimensional structures of the re-compression shock waves, a complete surface separation pattern, momentum deficit and a new secondary vortex system. A new mechanism of shock-boundary layer interaction control by MVG associated with a series of vortex rings is also presented. Vortex rings strongly interact with air flow and play an important role in the separation zone reduction. Additionally, readers will learn about the governing equation, boundary condition, high quality grid generation, high order shock capturing scheme and DNS inflow condition in detail. This volume will, therefore, serve as a useful reference for aerospace researchers using LES methods to study shock boundary layer interaction and supersonic flow control.
