Quantum mechanics of highly excited states of the H+3 molecular ion: A numerical study of the two degree of freedom C2v subspace

1990 ◽  
Vol 92 (5) ◽  
pp. 3005-3017 ◽  
Author(s):  
Jonathan Tennyson ◽  
Otto Brass ◽  
Eli Pollak
Keyword(s):  
Quantum Mechanics ◽  
Excited States ◽  
Numerical Study ◽  
Degree Of Freedom ◽  
Molecular Ion ◽  
Two Degree Of Freedom

Hydrodynamics Loads on Two Degree-of-Freedom Cylinder With Uncertain Natural Frequencies Subject to VIV

2009 ◽  
Author(s):  
Didier Lucor
Keyword(s):  
Natural Frequencies ◽  
Numerical Study ◽  
Spectral Element ◽  
Numerical Approach ◽  
Response Surfaces ◽  
Degree Of Freedom ◽  
Two Dimensional ◽  
Wide Range ◽  
Two Dimensional Flow ◽  
Two Degree Of Freedom

In this numerical study, we build response surfaces of two degree-of-freedom vortex-induced vibrations (VIV) of flexibly mounted cylinders for a wide range of transverse and in-line natural frequencies. We consider both the structure and the flow to be two-dimensional and the structure has a low mass damping. The emphasis is put on the representation of the hydrodynamic loads acting on the cylinder in response to the change in the natural frequencies of the structure. The system is sampled for a wide range of natural frequencies within the synchronization region, totaling 149 two-dimensional flow-structure simulations. The parametric range of the in-line frequency is chosen to be larger than the one of the transverse frequency in order to favor multi-modal responses. No preferred frequencies are emphasized within the intervals of study. The fully spectral numerical approach relies on a stochastic collocation method coupled to a spectral element-based deterministic solver.

Numerical Study of the Influence of Initial Condition in Vortex Induced Vibration of a Circular Cylinder With Two Degree of Freedom

2011 ◽  
Author(s):  
Bruno C. Ferreira ◽  
Marcelo A. Vitola ◽  
Juan B. V. Wanderley ◽  
Sergio H. Sphaier
Keyword(s):  
Circular Cylinder ◽  
Stokes Equations ◽  
Numerical Study ◽  
Cross Flow ◽  
Degree Of Freedom ◽  
Curvilinear Coordinates ◽  
Initial Condition ◽  
Ocean Engineering ◽  
Vortex Induced Vibration ◽  
Two Degree Of Freedom

The vortex-induced vibration (VIV) is a classical problem in ocean engineering. Intensive research on this field for flow around a circular cylinder has been observed, due to practical application, mainly the design of risers, cables and pipelines with free span. The relevance of this phenomenon is related to the structure failure, consequence of large displacement or fatigue. In the present study the influence of initial condition on the vortex induced vibration (VIV) of a circular cylinder with two degree of freedom is investigated by the numerical solution of the slightly compressible formulation of Reynolds Average Navier-Stokes equations. An upwind and Total Variation Diminishing (TVD) conservative scheme is used to solve the governing equations written in curvilinear coordinates. The k–ε turbulence model is used to simulate the turbulent flow in the wake of the cylinder. Two different initial conditions have been tested, free-stream and continuous reduced velocity increase (using the previous reduced velocity as initial condition for the next value). Results for the phase angle, amplitude, frequency, and lift coefficient are presented. The numerical results have been compared with experimental data of Jauvtis and Williamson [1]. The results indicate that the history of cylinder movement has a important impact in the amplitude oscillation observed in-line and cross-flow, principally in the reduced velocity range associated with the upper branch. Results obtained for the initial and lower branch seems to be independent of the initial condition. Further investigation are necessary to understand the difference observed such as the absence of the jump in the cross-flow oscillation between the initial and upper branch and the absence of in-line oscillation for reduced velocity in the range of 1–4 and the peak of in-line oscillation at reduced velocity 6.0.

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