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George Haller - One of the best experts on this subject based on the ideXlab platform.
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Exact Theory of material spike formation in flow separation
Journal of Fluid Mechanics, 2018Co-Authors: Mattia Serra, Jérôme Vétel, George HallerAbstract:We develop a frame-invariant Theory of material spike formation during flow separation over a no-slip boundary in two-dimensional flows with arbitrary time dependence. Based on the Exact curvature evolution of near-wall material lines, our Theory identifies both fixed and moving flow separation, is effective also over short time intervals, and admits a rigorous instantaneous limit. As a byproduct, we derive explicit formulae for the evolution of material line curvature and the curvature rate for general compressible flows. The material backbone that we identify acts first as the precursor and later as the centrepiece of unsteady Lagrangian flow separation. We also discover a previously undetected spiking point where the backbone of separation connects to the boundary, and derive wall-based analytical formulae for its location. Finally, our Theory explains the perception of off-wall separation in unsteady flows and provides conditions under which such a perception is justified. We illustrate our results on several analytical and experimental flows.
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An Exact Theory of three-dimensional fixed separation in unsteady flows
Physics of Fluids, 2008Co-Authors: Amit Surana, O. Grunberg, Gustaaf Jacobs, George HallerAbstract:We develop a nonlinear Theory for separation and attachment on no-slip boundaries of three-dimensional unsteady flows that have a steady mean component. In such flows, separation and attachment surfaces turn out to originate from fixed lines on the boundary, even though the surfaces themselves deform in time. The Exact separation geometry is not captured by instantaneous Eulerian fields associated with the velocity field, but can be determined from a weighted average of the wall-shear and wall-density fields. To illustrate our results, we locate separation surfaces and attachment surfaces in an unsteady model flow and in direct numerical simulations of a time-periodic lid-driven cavity.
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Exact Theory of three-dimensional flow separation. Part 1. Steady separation
Journal of Fluid Mechanics, 2006Co-Authors: Amit Surana, O. Grunberg, George HallerAbstract:We derive an Exact Theory of three-dimensional steady separation and reattachment using nonlinear dynamical systems methods. Specifically, we obtain criteria for separation points and separation lines on fixed no-slip boundaries in compressible flows. These criteria imply that there are only four basic separation patterns with well-defined separation surfaces. We also derive a first-order prediction for the separation surface using wall-based quantities; we verify this prediction using flow models obtained from local expansions of the Navier-Stokes equations.
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Exact Theory of unsteady separation for two-dimensional flows
Journal of Fluid Mechanics, 2004Co-Authors: George HallerAbstract:We use a dynamical systems approach to extend Prandtl's steady separation criterion to two-dimensional unsteady flows with no-slip boundaries. Viewing separation profiles as non-hyperbolic unstable manifolds in the Lagrangian frame, we obtain explicit Eulerian formulae for the location of flow separation and reattachment on fixed and moving boundaries. We also derive high-order approximations for the unsteady separation profile in the vicinity of the boundary. Our criteria and formulae only use the derivatives of the velocity field along the boundary, and hence are of use in monitoring and controlling separation. In particular, we predict unsteady flow separation points and separation angles from distributed pressure and skin-friction measurements along the wall. As an example, we predict and verify separation points and separation profiles in variants of a two-dimensional oscillating separation-bubble flow.
Amit Surana - One of the best experts on this subject based on the ideXlab platform.
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An Exact Theory of three-dimensional fixed separation in unsteady flows
Physics of Fluids, 2008Co-Authors: Amit Surana, O. Grunberg, Gustaaf Jacobs, George HallerAbstract:We develop a nonlinear Theory for separation and attachment on no-slip boundaries of three-dimensional unsteady flows that have a steady mean component. In such flows, separation and attachment surfaces turn out to originate from fixed lines on the boundary, even though the surfaces themselves deform in time. The Exact separation geometry is not captured by instantaneous Eulerian fields associated with the velocity field, but can be determined from a weighted average of the wall-shear and wall-density fields. To illustrate our results, we locate separation surfaces and attachment surfaces in an unsteady model flow and in direct numerical simulations of a time-periodic lid-driven cavity.
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Exact Theory of three-dimensional flow separation. Part 1. Steady separation
Journal of Fluid Mechanics, 2006Co-Authors: Amit Surana, O. Grunberg, George HallerAbstract:We derive an Exact Theory of three-dimensional steady separation and reattachment using nonlinear dynamical systems methods. Specifically, we obtain criteria for separation points and separation lines on fixed no-slip boundaries in compressible flows. These criteria imply that there are only four basic separation patterns with well-defined separation surfaces. We also derive a first-order prediction for the separation surface using wall-based quantities; we verify this prediction using flow models obtained from local expansions of the Navier-Stokes equations.
O. Grunberg - One of the best experts on this subject based on the ideXlab platform.
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An Exact Theory of three-dimensional fixed separation in unsteady flows
Physics of Fluids, 2008Co-Authors: Amit Surana, O. Grunberg, Gustaaf Jacobs, George HallerAbstract:We develop a nonlinear Theory for separation and attachment on no-slip boundaries of three-dimensional unsteady flows that have a steady mean component. In such flows, separation and attachment surfaces turn out to originate from fixed lines on the boundary, even though the surfaces themselves deform in time. The Exact separation geometry is not captured by instantaneous Eulerian fields associated with the velocity field, but can be determined from a weighted average of the wall-shear and wall-density fields. To illustrate our results, we locate separation surfaces and attachment surfaces in an unsteady model flow and in direct numerical simulations of a time-periodic lid-driven cavity.
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Exact Theory of three-dimensional flow separation. Part 1. Steady separation
Journal of Fluid Mechanics, 2006Co-Authors: Amit Surana, O. Grunberg, George HallerAbstract:We derive an Exact Theory of three-dimensional steady separation and reattachment using nonlinear dynamical systems methods. Specifically, we obtain criteria for separation points and separation lines on fixed no-slip boundaries in compressible flows. These criteria imply that there are only four basic separation patterns with well-defined separation surfaces. We also derive a first-order prediction for the separation surface using wall-based quantities; we verify this prediction using flow models obtained from local expansions of the Navier-Stokes equations.
P. Ladevèze - One of the best experts on this subject based on the ideXlab platform.
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The Exact Theory of Plate Bending
Journal of Elasticity, 2002Co-Authors: P. LadevèzeAbstract:A new approach is introduced for the analysis and calculation of homogeneous, isotropic elastic plates of constant thickness under arbitrary bending loads. This Theory can be called “Exact” because it leads to Exact values of the generalized 2D quantities. Moreover, contrary to classical plate theories, it is not limited to relatively thin plates.
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An Exact Theory for Circular, End-Loaded, Anisotropic Beams of Narrow Rectangular Cross Section
Journal of elasticity and the physical science of solids, 2001Co-Authors: P. Ladevèze, J.g. SimmondsAbstract:The Exact Theory of linearly elastic beams developed by Ladevèze and Ladevèze and Simmonds is limited to prismatic beams. Herein, the Theory is extended to circular beams of narrow rectangular cross section, using the equations of plane stress for an anisotropic elastic body. Explicit formulas are given for the cross-sectional material operators that appear in the overall beamlike stress–strain relations between forces and a moment (the generalized stress) and derivatives of certain one-dimensional displacements and a rotation (the generalized strain). The extension to circular beams is non-trivial, especially for full anisotropy, because the analogues of the Saint-Venant solutions, that are key in the Exact Theory of straight beams, are more complicated.
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An Exact Theory for Circular, End-Loaded, Anisotropic Beams of Narrow Rectangular Cross Section
Journal of elasticity and the physical science of solids, 2001Co-Authors: P. Ladevèze, J.g. SimmondsAbstract:The Exact Theory of linearly elastic beams developed by Ladevèze and Ladevèze and Simmonds is limited to prismatic beams. Herein, the Theory is extended to circular beams of narrow rectangular cross section, using the equations of plane stress for an anisotropic elastic body. Explicit formulas are given for the cross-sectional material operators that appear in the overall beamlike stress–strain relations between forces and a moment (the generalized stress) and derivatives of certain one-dimensional displacements and a rotation (the generalized strain). The extension to circular beams is non-trivial, especially for full anisotropy, because the analogues of the Saint-Venant solutions, that are key in the Exact Theory of straight beams, are more complicated.
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An Exact Theory for Circular, End-Loaded, Anisotropic Beams of Narrow Rectangular Cross Section
Journal of Elasticity, 2001Co-Authors: P. Ladevèze, J.g. SimmondsAbstract:The Exact Theory of linearly elastic beams developed by Ladeveze and Ladeveze and Simmonds is limited to prismaticbeams. Herein, the Theory is extended to circular beams of narrow rectangular cross section, using the equations of plane stress for an anisotropic elastic body. Explicit formulas are given for the cross-sectional material operators that appear in the overall beamlike stress–strain relations between forces and a moment (the generalized stress) and derivatives of certain one-dimensional displacements and a rotation (the generalized strain). The extension to circular beams is non-trivial, especially for full anisotropy, because the analogues of the Saint-Venant solutions, that are key in the Exact Theory of straight beams, are more complicated.
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On Application of the Exact Theory of Elastic Beams
Advances in the Mechanics of Plates and Shells, 1Co-Authors: P. Ladevèze, P. Sanchez, J.g. SimmondsAbstract:A new approach is developed for the analysis and calculation of straight prismatic beams of piecewise constant cross-section under arbitrary loads. The material can be anisotropic and composite; it is only supposed that the beam is x-homogeneous, x being the abscissa. This Theory can be called “Exact” because it determines Exact static and kinematic generalized quantities. Contrary to classical theories, it is not limited to high aspect ratio (i.e. relatively slender beams). The paper is focused on how to use the Exact Theory of elastic beam for computing 3D stresses. It is shown in particular how to compute the basic operators which depend on the cross-section geometry, the material and the loading which are the basic building blocks of the Theory. An example is of an elastic tube with a small thickness submitted to nearly concentrated extremity loads.
B. R. Johnson - One of the best experts on this subject based on the ideXlab platform.
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Exact Theory of electromagnetic scattering by a heterogeneous multilayer sphere in the infinite-layer limit: effective-media approach
Journal of the Optical Society of America A, 1999Co-Authors: B. R. JohnsonAbstract:An Exact Theory is presented for calculating electromagnetic scattering by a model heterogeneous particle. The model is a multilayer sphere composed of alternating layers of different dielectric constants in the limit where the number of layers approaches infinity and the layer thickness approaches zero. The scattering analysis for this limiting case is based on a formulation of scattering Theory known as the variable-phase method (VPM). A derivation of the VPM formulation is presented. Analytic formulas are derived for the scattering coefficients of the heterogeneous sphere that are generalizations of similar Mie Theory formulas for scattering by a homogeneous sphere. The optical properties of the layered heterogeneous mixture are Exactly described in this Theory by the two effective-media parameters. The solution in the long-wavelength limit is used to derive a new formula for the effective dielectric constant for heterogeneous mixtures.
