On some analytic and computational aspects of two dimensional vortex sheet evolution

1990 ◽  
pp. 143-154
Author(s):  
O. F. Orellana
Keyword(s):  
Vortex Sheet ◽  
Two Dimensional ◽  
Computational Aspects

Computational aspects of the two-dimensional propagation of R-matrices on MPPs

1998 ◽  
Vol 114 (1-3) ◽  
pp. 195-209 ◽  
Author(s):  
J.W. Heggarty ◽  
M.P. Scott ◽  
N.S. Scott ◽  
P.G. Burke
Keyword(s):  
Two Dimensional ◽  
Computational Aspects

Long Time Computation of Two-Dimensional Vortex Sheet by Point Vortex Method

2003 ◽  
Vol 72 (8) ◽  
pp. 1968-1976 ◽  
Author(s):  
Sun-Chul Kim ◽  
June-Yub Lee ◽  
Sung-Ik Sohn
Keyword(s):  
Point Vortex ◽  
Vortex Method ◽  
Vortex Sheet ◽  
Two Dimensional ◽  
Long Time

Vortex Sheet Analysis of the Giromill

1978 ◽  
Vol 100 (3) ◽  
pp. 340-342 ◽  
Author(s):  
R. E. Wilson
Keyword(s):  
Wind Turbine ◽  
Vertical Axis ◽  
Vortex Sheet ◽  
Maximum Energy ◽  
Power Coefficient ◽  
Two Dimensional ◽  
Vertical Axis Wind Turbine ◽  
Wind Force ◽  
Force Coefficient ◽  
Horizontal Axis Wind Turbine

A two-dimensional analysis of the performance and flowfield of the Giromill is presented. The Giromill is a vertical-axis wind turbine with straight blades that are articulated to produce maximum energy extraction from the wind. It is found that the power coefficient and windwise force coefficient for the Giromill have the same limit as obtained for the horizontal-axis wind turbine. A cross-wind force is also obtained with this type of wind turbine. The cross-wind force is of second order and decreases with tip speed. Streamlines and velocity profiles are illustrated for several loading conditions.

A Two-Dimensional Multibody Integral Approach for Forces in Inviscid Flow With Free Vortices and Vortex Production

2014 ◽  
Vol 137 (2) ◽  
Author(s):  
Juan Li ◽  
Chen-Yuan Bai ◽  
Zi-Niu Wu
Keyword(s):  
Flat Plate ◽  
Lift Force ◽  
Vortex Sheet ◽  
Inviscid Flow ◽  
The Body ◽  
Integral Approach ◽  
Two Dimensional ◽  
Middle Point ◽  
Dependent Behavior ◽  
The Individual

In this paper, we propose an integral force approach for potential flow around two-dimensional bodies with external free vortices and with vortex production. The method can be considered as an extension of the generalized Lagally theorem to the case with continuous distributed vortices inside and outside of the body and is capable of giving the individual force of each body in the case of multiple bodies. The lift force formulas are validated against two examples. One is the Wagner problem with vortex production and with moving vortices in the form of a vortex sheet. The other is the lift of a flat plate when there is a standing vortex over its middle point. As a first application, the integral approach is applied to study the lift force of a flat plate induced by a bounded vortex above the plate. This bounded vortex may represent a second small airfoil at incidence. For this illustrative example, the lift force is found to display an interesting distance-dependent behavior: for a clockwise circulation, the lift force acting on the main airfoil is attractive for small distance and repulsive for large distance.

The starting mechanism of wave-induced flow through a sharp-edged orifice

1977 ◽  
Vol 82 (1) ◽  
pp. 115-128 ◽  
Author(s):  
R. A. Evans ◽  
M. I. G. Bloor
Keyword(s):  
Pressure Distribution ◽  
Growth Rates ◽  
Vortex Sheet ◽  
Plane Shock ◽  
Initial Growth ◽  
Two Dimensional ◽  
Flow Through ◽  
Weak Plane ◽  
Christoffel Transformation ◽  
Wave Induced

Following weak plane shock diffraction at a knife-edge situated in a duct, a two-dimensional vortex sheet springs from the salient edge. The method of ‘vortex discretization’ is used, in conjunction with a Schwarz-Christoffel transformation, to develop a two-dimensional potential model for this constrained form of vortex generation. The analysis is independent of empirical parameters and describes, qualitatively, the pattern of streamlines through the orifice.Flow-visualization photographs are presented which illustrate the spiral shape of the starting vortex. Although of a limited nature, quantitative experimental vortex growth rates have been obtained and are compared with initial growth rates predicted theoretically. The results are discussed together with other aspects of the problem, including the limitations of the theory.An extension of vortex discretization is developed whereby the pressure distribution remote from the vortex sheet can be calculated. The combination of flow separation and the associated static wall pressure distribution gives theoretical insight into the mechanism of flow through an orifice.

The flow field near the centre of a rolled-up vortex sheet

1967 ◽  
Vol 30 (1) ◽  
pp. 177-196 ◽  
Author(s):  
K. W. Mangler ◽  
J. Weber
Keyword(s):  
Delta Wing ◽  
Present Report ◽  
Vortex Sheet ◽  
Slender Body ◽  
Two Dimensional ◽  
Slender Body Theory ◽  
Vortex Sheets ◽  
Dimensional Flow ◽  
Two Dimensional Flow ◽  
Body Theory

Most of the existing methods for calculating the inviscid flow past a delta wing with leading-edge vortices are based on slender-body theory. When these vortices are represented by rolled-up vortex sheets in an otherwise irrotational flow, some of the assumptions of slender-body theory are violated near the centres of the spirals. The aim of the present report is to describe for the vortex core an alternative method in which only the assumption of a conical velocity field is made. An asymptotic solution valid near the centre of a rolled-up vortex sheet is derived for incompressible flow. Further asymptotic solutions are determined for two-dimensional flow fields with vortex sheets which vary with time in such a manner that the sheets remain similar in shape. A particular two-dimensional flow corresponds to the slender theory approximation for conical sheets.

Unsteady Hydrofoils: Theoretical and Computational Analysis

2013 ◽  
Author(s):  
Daniel T. Valentine
Keyword(s):  
Flat Plate ◽  
Computational Analysis ◽  
Vortex Sheet ◽  
Vortex Wake ◽  
Two Dimensional ◽  
Fixed Angle ◽  
Induced Drag ◽  
Wake Model ◽  
Theoretical Results ◽  
Computational Predictions

In this paper the computational problem examined is the impulsive start of a two-dimensional flat-plate hydrofoil at a fixed angle of attack. The method applied is an equally-spaced lumped-vortex panel method. The results from a lumped-vortex wake model and a shed-vortex sheet wake model are reported. Comparisons with the linear theory of Wagner (1925), the theoretical results associated with the single lumped-vortex wake model and the full wake model are presented. In addition, it is shown that the computational predictions are consistent with results reported by Katz and Plotkin (2001); they applied a distribution of vortices to model the wake. In the present paper the importance of resolving the chordwise pressure distribution in unsteady hydrofoil problems is elucidated. New predictions of both the evolution of lift and induced drag are reported for the instantaneously started flat plate. The computational predictions are compared with theorecticalpredictions also discussed in this paper.

scholarly journals Well-posedness of two-dimensional hydroelastic waves

2017 ◽  
Vol 147 (3) ◽  
pp. 529-570 ◽  
Author(s):  
David M. Ambrose ◽  
Michael Siegel
Keyword(s):  
A Priori ◽  
Vortex Sheet ◽  
Energy Estimates ◽  
Elastic Membrane ◽  
Well Posedness ◽  
Two Dimensional ◽  
Main Challenge ◽  
Spatial Dimensions ◽  
Bending Stresses ◽  
Definition Of

A well-posedness theory for the initial-value problem for hydroelastic waves in two spatial dimensions is presented. This problem, which arises in numerous applications, describes the evolution of a thin elastic membrane in a two-dimensional (2D) potential flow. We use a model for the elastic sheet that accounts for bending stresses and membrane tension, but which neglects the mass of the membrane. The analysis is based on a vortex sheet formulation and, following earlier analyses and numerical computations in 2D interfacial flow with surface tension, we use an angle–arclength representation of the problem. We prove short-time well-posedness in Sobolev spaces. The proof is based on energy estimates, and the main challenge is to find a definition of the energy and estimates on high-order non-local terms so that an a priori bound can be obtained.

Vorticity generation and conservation for two-dimensional interfaces and boundaries

2014 ◽  
Vol 758 ◽  
pp. 63-93 ◽  
Author(s):  
M. Brøns ◽  
M. C. Thompson ◽  
T. Leweke ◽  
K. Hourigan
Keyword(s):  
Free Surface ◽  
Circular Cylinder ◽  
Couette Flow ◽  
Poiseuille Flow ◽  
Vortex Sheet ◽  
Newtonian Fluids ◽  
Two Dimensional ◽  
Two Fluids ◽  
Vorticity Generation ◽  
Planar Couette Flow

AbstractThe generation, redistribution and, importantly, conservation of vorticity and circulation is studied for incompressible Newtonian fluids in planar and axisymmetric geometries. A generalised formulation of the vorticity at the interface between two fluids for both no-slip and stress-free conditions is presented. Illustrative examples are provided for planar Couette flow, Poiseuille flow, the spin-up of a circular cylinder, and a cylinder below a free surface. For the last example, it is shown that, although large imbalances between positive and negative vorticity appear in the wake, the balance is found in the vortex sheet representing the stress-free surface.

Shear layer instability of an inviscid compressible fluid. Part 2

1975 ◽  
Vol 71 (2) ◽  
pp. 305-316 ◽  
Author(s):  
W. Blumen ◽  
P. G. Drazin ◽  
D. F. Billings
Keyword(s):  
Shear Layer ◽  
Compressible Fluid ◽  
Unstable Mode ◽  
Vortex Sheet ◽  
Two Dimensional ◽  
Shear Layer Instability ◽  
Hyperbolic Tangent ◽  
Asymptotic Results ◽  
The Difference ◽  
Inviscid Compressible Fluid

The linear stability of a shear layer of an inviscid compressible fluid is considered. It is shown that there is instability of two-dimensional disturbances at all values of the Mach number, contrary to previous results for a vortex sheet. The difference arises from the discovery of a second unstable mode. This mode is supersonic, decays weakly with distance from the shear layer, and is not governed by the principle of exchange of stabilities. Detailed numerical and asymptotic results are given for the hyperbolic-tangent shear layer.

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