scholarly journals Potential flow of a second-order fluid over a tri-axial ellipsoid

2005 ◽  
Vol 2005 (4) ◽  
pp. 341-364 ◽  
Author(s):  
F. Viana ◽  
T. Funada ◽  
D. D. Joseph ◽  
N. Tashiro ◽  
Y. Sonoda
Keyword(s):  
Potential Flow ◽  
Flow Fields ◽  
Second Order ◽  
Stress Fields ◽  
Harmonic Potential ◽  
Gas Bubble ◽  
Two Dimensional ◽  
Trailing Edge ◽  
Principal Axes

The problem of potential flow of a second-order fluid around an ellipsoid is solved, and the flow and stress fields are computed. The flow fields are determined by the harmonic potential but the stress fields depend on viscosity and the parameters of the second-order fluid. The stress fields on the surface of a tri-axial ellipsoid depend strongly on the ratios of principal axes and are such as to suggest the formation of gas bubble with a round flat nose and two-dimensional cusped trailing edge. A thin flat trailing edge gives rise to a large stress which makes the thin trailing edge thinner.

A Two-Dimensional Potential Flow Model of the Wave Field Generated by a Semisubmerged Body in Heaving Motion

1988 ◽  
Vol 32 (02) ◽  
pp. 83-91
Author(s):  
X. M. Wang ◽  
M. L. Spaulding
Keyword(s):  
Free Surface ◽  
Boundary Conditions ◽  
Potential Flow ◽  
Flow Model ◽  
Second Order ◽  
Two Dimensional ◽  
Third Order ◽  
The Third ◽  
Potential Flow Model ◽  
Good Agreement

A two-dimensional potential flow model is formulated to predict the wave field and forces generated by a sere!submerged body in forced heaving motion. The potential flow problem is solved on a boundary fitted coordinate system that deforms in response to the motion of the free surface and the heaving body. The full nonlinear kinematic and dynamic boundary conditions are used at the free surface. The governing equations and associated boundary conditions are solved by a second-order finite-difference technique based on the modified Euler method for the time domain and a successive overrelaxation (SOR) procedure for the spatial domain. A series of sensitivity studies of grid size and resolution, time step, free surface and body grid redistribution schemes, convergence criteria, and free surface body boundary condition specification was performed to investigate the computational characteristics of the model. The model was applied to predict the forces generated by the forced oscillation of a U-shaped cylinder. Numerical model predictions are generally in good agreement with the available second-order theories for the first-order pressure and force coefficients, but clearly show that the third-order terms are larger than the second-order terms when nonlinearity becomes important in the dimensionless frequency range 1≤ Fr≤ 2. The model results are in good agreement with the available experimental data and confirm the importance of the third order terms.

Contact Problems Involving the Flow Past an Inflated Aerofoil

1982 ◽  
Vol 49 (2) ◽  
pp. 263-265 ◽  
Author(s):  
J.-M. Vanden-Broeck
Keyword(s):  
Potential Flow ◽  
Weber Number ◽  
Angle Of Attack ◽  
Contact Problems ◽  
Critical Value ◽  
Cavitation Number ◽  
Two Dimensional ◽  
Trailing Edge ◽  
Trailing Edges ◽  
Steady Potential

Steady potential flow around a two-dimensional inflated airfoil is considered. The aerofoil consists of a flexible and inextensible membrane which is anchored at both leading and trailing edges. The flow and the aerofoil shape are determined as functions of the angle of attack α, the cavitation number γ, and the Weber number λ. When γ decreases to a critical value γ0 (α, λ), opposite sides of the membrane become tangent to each other at the trailing edge. For γ < γ0 the aerofoil is partially collapsed near the trailing edge. The length of the region of collapse increases as γ decreases and for γ = −∞, the aerofoil is completely collapsed. The shape of the aerofoil and the value of γ0 are determined analytically by a perturbation solution for λ small. Graphs of the results are presented.

Integrable two-dimensional dynamical systems and the characteristic Lie algebras

2007 ◽  
Vol 5 ◽  
pp. 195-200
Author(s):  
A.V. Zhiber ◽  
O.S. Kostrigina
Keyword(s):  
Dynamical System ◽  
Dynamical Systems ◽  
Lie Algebra ◽  
Lie Algebras ◽  
Second Order ◽  
System Of Equations ◽  
Two Dimensional ◽  
Finite Dimensional ◽  
Dimensional Dynamical System

In the paper it is shown that the two-dimensional dynamical system of equations is Darboux integrable if and only if its characteristic Lie algebra is finite-dimensional. The class of systems having a full set of fist and second order integrals is described.

Molecular Dynamics Simulations of Shock-Defect Interactions in Two-Dimensional Nonreactive Crystals

1992 ◽  
Vol 296 ◽  
Author(s):  
Robert S. Sinkovits ◽  
Lee Phillips ◽  
Elaine S. Oran ◽  
Jay P. Boris
Keyword(s):  
Molecular Dynamics ◽  
Hexagonal Lattice ◽  
Square Lattice ◽  
Two Dimensional ◽  
Connection Machine ◽  
Defect Sites ◽  
Principal Axes ◽  
Shock Motion ◽  
Defect Interactions ◽  
Dynamics Simulations

AbstractThe interactions of shocks with defects in two-dimensional square and hexagonal lattices of particles interacting through Lennard-Jones potentials are studied using molecular dynamics. In perfect lattices at zero temperature, shocks directed along one of the principal axes propagate through the crystal causing no permanent disruption. Vacancies, interstitials, and to a lesser degree, massive defects are all effective at converting directed shock motion into thermalized two-dimensional motion. Measures of lattice disruption quantitatively describe the effects of the different defects. The square lattice is unstable at nonzero temperatures, as shown by its tendency upon impact to reorganize into the lower-energy hexagonal state. This transition also occurs in the disordered region associated with the shock-defect interaction. The hexagonal lattice can be made arbitrarily stable even for shock-vacancy interactions through appropriate choice of potential parameters. In reactive crystals, these defect sites may be responsible for the onset of detonation. All calculations are performed using a program optimized for the massively parallel Connection Machine.

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