scholarly journals Energy Growth, Complexity and Efficiency

10.5772/9827 ◽  
2010 ◽  
Author(s):  
Riccardo Basosi ◽  
Franco Ruzzenenti
Keyword(s):  
Energy Growth

scholarly journals SCALING INVARIANCE IN A TIME-DEPENDENT ELLIPTICAL BILLIARD

2012 ◽  
Vol 22 (09) ◽  
pp. 1250207 ◽  
Author(s):  
DIEGO F. M. OLIVEIRA ◽  
MARKO ROBNIK
Keyword(s):  
Integrable System ◽  
Average Velocity ◽  
Moving Boundary ◽  
Time Dependent ◽  
Scaling Invariance ◽  
Energy Growth ◽  
Dynamical Properties ◽  
Scaling Arguments

We study some dynamical properties of a classical time-dependent elliptical billiard. We consider periodically moving boundary and collisions between the particle and the boundary are assumed to be elastic. Our results confirm that although the static elliptical billiard is an integrable system, after introducing time-dependent perturbation on the boundary the unlimited energy growth is observed. The behavior of the average velocity is described using scaling arguments.

Exponential energy growth in a Fermi accelerator

2010 ◽  
Vol 81 (5) ◽  
Author(s):  
Kushal Shah ◽  
Dmitry Turaev ◽  
Vered Rom-Kedar
Keyword(s):  
Energy Growth

RESONANCE OF NONMODAL PERTURBATIONS IN THE BATCHELOR VORTEX

2010 ◽  
Vol 24 (13) ◽  
pp. 1449-1452
Author(s):  
ZHI-WEI GUO ◽  
DE-JUN SUN
Keyword(s):  
Resonant Mode ◽  
Resonance Phenomenon ◽  
Mode Switch ◽  
Energy Growth ◽  
Optimal Energy ◽  
Maximum Value ◽  
Resonant Character ◽  
Swirl Parameter

The resonance phenomenon for nonmodal perturbation of Batchelor vortex is studied. For azimuthal wavenumber n = - 1, two resonant peaks appear and the left one is always dominant. For n = 1, the resonant character becomes very complicated. There is a resonant mode switch from right peak to left peak as swirl parameter q increases from 2 to infinity. The resonant wavenumber k is the largest when q approaches to infinity for n = - 1 while it is the smallest for n = 1. The maximum value of the optimal energy growth for n = 1 is at q approaches to infinity, whereas it decreases monotonically as q increases for n = - 1. The resonance for n = - 1 is the more important one.

Transient Flutter Stability Analysis of Structural Mistuned Blisk by Energy Growth Method

2021 ◽  
Author(s):  
Luohui Ouyang ◽  
Qingzhen Bi ◽  
Hua Chen ◽  
Hai Shang ◽  
Li-Min Zhu
Keyword(s):  
Stability Analysis ◽  
Finite Time ◽  
Transient Stability ◽  
Maximum Energy ◽  
Dynamic State ◽  
Infinite Time ◽  
Structural Dynamic ◽  
Energy Growth ◽  
Eigenvalue Method ◽  
Growth Method

Abstract Blisks suffer from flutter, a self-sustained vibration caused by aerodynamic coupled forces. This instability could cause serious damage to the blades and the machine. Flutter stability is usually analyzed based on the eigenvalue method in the aspect of the linear structural dynamic system, which transforms a dynamics stability analysis into a point of equilibrium in an infinite time scale. However, in reality, most of the blisk vibrations arise on a finite time horizon. The transient vibration amplification may cause serious damage. This paper proposes a transient flutter stability analysis method in a finite time for structural mistuned blisk based on the energy growth method. Firstly, two common blisk models coupled aerodynamic force with different complexity are built, and are all expressed in the state space representation. A novel energy growth method is then employed to analyze the transient stability and to find the maximum energy growth of the models. The optimal initial condition which leads to the maximum energy growth is obtained. A new flutter stability criterion is developed to consider the transient stability based on the energy growth method and the infinite time stability based on the eigenvalue method. The new transient stability method is verified by two numerical studies. It is found that the structural mistuned blisk model which is traditionally predicted stable still has a transient instability in a finite time due to the non-normal property of the dynamic state matrix.

House Committees Endorse Controlled Energy Growth

Science ◽  
1975 ◽  
Vol 187 (4172) ◽  
pp. 147-147
Author(s):  
Robert Gillette
Keyword(s):  
Energy Growth

Limits to solar and biomass energy growth

1985 ◽  
Vol 12 (1) ◽  
pp. 65-66
Author(s):  
Donald E. Shult
Keyword(s):  
Biomass Energy ◽  
Energy Growth

Self-limiting and regenerative dynamics of perturbation growth on a vortex column

2013 ◽  
Vol 718 ◽  
pp. 39-88 ◽  
Author(s):  
Fazle Hussain ◽  
Eric Stout
Keyword(s):  
Reynolds Stress ◽  
Stokes Equations ◽  
Initial Energy ◽  
Navier Stokes ◽  
Axisymmetric Mode ◽  
Energy Growth ◽  
Decay Behaviour ◽  
Peak Energy ◽  
Trailing Vortices ◽  
Instability Energy

AbstractWe study the mechanisms of centrifugal instability and its eventual self-limitation, as well as regenerative instability on a vortex column with a circulation overshoot (potentially unstable) via direct numerical simulations of the incompressible Navier–Stokes equations. The perturbation vorticity (${\boldsymbol{\omega} }^{\prime } $) dynamics are analysed in cylindrical ($r, \theta , z$) coordinates in the computationally accessible vortex Reynolds number, $\mathit{Re}({\equiv }\mathrm{circulation/viscosity} )$, range of 500–12 500, mostly for the axisymmetric mode (azimuthal wavenumber $m= 0$). Mean strain generates azimuthally oriented vorticity filaments (i.e. filaments with azimuthal vorticity, ${ \omega }_{\theta }^{\prime } $), producing positive Reynolds stress necessary for energy growth. This ${ \omega }_{\theta }^{\prime } $ in turn tilts negative mean axial vorticity, $- {\Omega }_{z} $ (associated with the overshoot), to amplify the filament, thus causing instability. (The initial energy growth rate (${\sigma }_{r} $), peak energy (${G}_{\mathit{max}} $) and time of peak energy (${T}_{p} $) are found to vary algebraically with $\mathit{Re}$.) Limitation of vorticity growth, also energy production, occurs as the filament moves the overshoot outward, hence lessening and shifting $\vert {- }{\Omega }_{z} \vert $, while also transporting the core $+ {\Omega }_{z} $, to the location of the filament. We discover that a basic change in overshoot decay behaviour from viscous to inviscid occurs at $Re\sim 5000$. We also find that the overshoot decay time has an asymptotic limit of 45 turnover times with increasing $\mathit{Re}$. After the limitation, the filament generates negative Reynolds stress, concomitant energy decay and hence self-limitation of growth; these inviscid effects are enhanced further by viscosity. In addition, the filament transports angular momentum radially inward, which can produce a new circulation overshoot and renewed instability. Energy decays at the $\mathit{Re}$ studied, but, at higher $\mathit{Re}$, regenerative growth of energy is likely due to the renewed mean shearing. New generation of overshoot and Reynolds stress is examined using a helical ($m= 1$) perturbation. Regenerative energy growth, possibly resulting in even vortex breakup, can be triggered by this new overshoot at practical $\mathit{Re}$ (${\sim }1{0}^{6} $ for trailing vortices), which are currently beyond the computational capability.

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