On the Lagrangian Description of Unsteady Boundary Layer Separation. Part 1: General Theory

On the Lagrangian Description of Unsteady Boundary Layer Separation. Part 1: General Theory
Author: National Aeronautics and Space Adm Nasa
Publisher: Independently Published
Total Pages: 52
Release: 2018-10-25
Genre: Science
ISBN: 9781729219256

Although unsteady, high-Reynolds number, laminar boundary layers have conventionally been studied in terms of Eulerian coordinates, a Lagrangian approach may have significant analytical and computational advantages. In Lagrangian coordinates the classical boundary layer equations decouple into a momentum equation for the motion parallel to the boundary, and a hyperbolic continuity equation (essentially a conserved Jacobian) for the motion normal to the boundary. The momentum equations, plus the energy equation if the flow is compressible, can be solved independently of the continuity equation. Unsteady separation occurs when the continuity equation becomes singular as a result of touching characteristics, the condition for which can be expressed in terms of the solution of the momentum equations. The solutions to the momentum and energy equations remain regular. Asymptotic structures for a number of unsteady 3-D separating flows follow and depend on the symmetry properties of the flow. In the absence of any symmetry, the singularity structure just prior to separation is found to be quasi 2-D with a displacement thickness in the form of a crescent shaped ridge. Physically the singularities can be understood in terms of the behavior of a fluid element inside the boundary layer which contracts in a direction parallel to the boundary and expands normal to it, thus forcing the fluid above it to be ejected from the boundary layer. Vandommelen, Leon L. and Cowley, Stephen J. Glenn Research Center NASA-SAA-C-99066-G; RTOP 505-62-21...

On the Lagrangian Description of Unsteady Boundary Layer Separation. Part 2

On the Lagrangian Description of Unsteady Boundary Layer Separation. Part 2
Author: National Aeronautics and Space Administration (NASA)
Publisher: Createspace Independent Publishing Platform
Total Pages: 26
Release: 2018-07-09
Genre:
ISBN: 9781722455163

A theory to explain the initial stages of unsteady separation was proposed by Van Dommelen and Cowley (1989). This theory is verified for the separation process that occurs at the equatorial plane of a sphere or a spheroid which is impulsively spun around an axis of symmetry. A Lagrangian numerical scheme is developed which gives results in good agreement with Eulerian computations, but which is significantly more accurate. This increased accuracy, and a simpler structure to the solution, also allows verification of the Eulerian structure, including the presence of logarithmic terms. Further, while the Eulerian computations broke down at the first occurrence of separation, it is found that the Lagrangian computation can be continued. It is argued that this separated solution does provide useful insight into the further evolution of the separated flow. A remarkable conclusion is that an unseparated vorticity layer at the wall, a familiar feature in unsteady separation processes, disappears in finite time. Vandommelen, Leon L. Glenn Research Center ...

Vorticity and Vortex Dynamics

Vorticity and Vortex Dynamics
Author: Jie-Zhi Wu
Publisher: Springer Science & Business Media
Total Pages: 776
Release: 2007-04-20
Genre: Technology & Engineering
ISBN: 3540290281

This book is a comprehensive and intensive monograph for scientists, engineers and applied mathematicians, as well as graduate students in fluid dynamics. It starts with a brief review of fundamentals of fluid dynamics, with an innovative emphasis on the intrinsic orthogonal decomposition of fluid dynamic process, by which one naturally identifies the content and scope of vorticity and vortex dynamics. This is followed by a detailed presentation of vorticity dynamics as the basis of later development. In vortex dynamics part the book deals with the formation, motion, interaction, stability, and breakdown of various vortices. Typical vortex structures are analyzed in laminar, transitional, and turbulent flows, including stratified and rotational fluids. Physical understanding of vertical flow phenomena and mechanisms is the first priority throughout the book. To make the book self-contained, some mathematical background is briefly presented in the main text, but major prerequisites are systematically given in appendices. Material usually not seen in books on vortex dynamics is included, such as geophysical vortex dynamics, aerodynamic vortical flow diagnostics and management.

Boundary-Layer Separation

Boundary-Layer Separation
Author: Frank T. Smith
Publisher: Springer Science & Business Media
Total Pages: 403
Release: 2012-12-06
Genre: Science
ISBN: 3642830005

The IUTAM Symposium on Boundary-Layer Separation, suggested by the UK National Committee of Theoretical and Applied Mechanics and supported by the International Union of Theoretical and Applied Mechanics, was held at University College London on August 26-28, 1986. The proposed theme and scope of the Symposium were designed to help to bring about the necessary interaction between experimentalists, computationalists and theoreticians for the furthering of understanding in this challenging subject. The talks and discussions were aimed at representing the very wide range and application of separating-flow phenomena, which often substantially affect the whole of fluid dynamics at medium to large Reynolds numbers, covering in particular both laminar and turbulent flow, steady or unsteady, two- or three-dimensional, small or large-scale, incompressible or compressible, external or internal, from the experimental, computational and theoretical standpoints. It was intended that about 80 scientists would participate in the Symposium, with about 25 talks being delivered, to which poster sessions with 8 contributions were added subsequently. All the speakers and poster presenters were selected by the scientific committee, although two late replacements of speakers were required. Fruitful discussions, well led by the session chairmen, took place formally after each talk and after the poster sessions and informally on other occasions including the social events. The present proceedings of the Symposium appear to reflect much of the current state of experimental, computational and theoretical work and progress in boundary-layer separation. We hope that they provide also ideas, questions and stimulation, in addition to major recent developments.

Vortex Dynamics and Vortex Methods

Vortex Dynamics and Vortex Methods
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.

Aerodynamics And Aeroacoustics - Proceedings Of The Symposium

Aerodynamics And Aeroacoustics - Proceedings Of The Symposium
Author: Fung K Y
Publisher: World Scientific
Total Pages: 384
Release: 1994-04-19
Genre:
ISBN: 9814551570

The aim of the symposium was to gather fellow researchers, colleagues and friends of Professor William R Sears, a member of the National Academy of Science and the Academy of Engineering, on the occasion of his 80th birthday. Professor Sears is a leader in Aerospace Science and Aerodynamics research and the symposium was held in honour of his work in these areas.The symposium focussed on four areas in aeronautical science in which Professor Sears has made major contributions. These are wing design, unsteady aerodynamics and separation, aeroacoustics and self-correcting wind tunnels.

Advances in Applied Mechanics

Advances in Applied Mechanics
Author:
Publisher: Academic Press
Total Pages: 363
Release: 1979-03-07
Genre: Technology & Engineering
ISBN: 0080563961

Advances in Applied Mechanics