Dynamic stability analysis for capillary channel flow: One-dimensional and three-dimensional computations and the equivalent steady state technique

2010 ◽  
Vol 22 (1) ◽  
pp. 014101 ◽  
Author(s):  
Aleksander Grah ◽  
Michael E. Dreyer
Keyword(s):  
Steady State ◽  
Stability Analysis ◽  
Dynamic Stability ◽  
Channel Flow ◽  
Three Dimensional ◽  
Capillary Channel ◽  
One Dimensional ◽  
State Technique

SPATIAL DISORDER OF CNN — WITH ASYMMETRIC OUTPUT FUNCTION

2001 ◽  
Vol 11 (08) ◽  
pp. 2085-2095 ◽  
Author(s):  
JUNG-CHAO BAN ◽  
KAI-PING CHIEN ◽  
SONG-SUN LIN ◽  
CHENG-HSIUNG HSU
Keyword(s):  
Neural Networks ◽  
Steady State ◽  
Three Dimensional ◽  
Cellular Neural Networks ◽  
Output Function ◽  
One Dimensional ◽  
Spatial Entropy ◽  
The One ◽  
Steady State Solutions

This investigation will describe the spatial disorder of one-dimensional Cellular Neural Networks (CNN). The steady state solutions of the one-dimensional CNN can be replaced as an iteration map which is one dimensional under certain parameters. Then, the maps are chaotic and the spatial entropy of the steady state solutions is a three-dimensional devil-staircase like function.

Three dimensional simulations and stability analysis for convection induced by absorption of radiation

2015 ◽  
Vol 25 (4) ◽  
pp. 810-824 ◽  
Author(s):  
Akil Jassim Harfash
Keyword(s):  
Steady State ◽  
Stability Analysis ◽  
Fluid Layer ◽  
Three Dimensional ◽  
Linear Instability ◽  
Selective Absorption ◽  
Content Type ◽  
Linear Threshold ◽  
Divergence Equation ◽  
Three Dimensional Simulations

Purpose – The purpose of this paper is to investigate a model for convection induced by the selective absorption of radiation in a fluid layer. The concentration based internal heat source is modelled quadratically. Both linear instability and global nonlinear energy stability analyses are tested using three dimensional simulations. The results show that the linear threshold accurately predicts on the onset of instability in the basic steady state. However, the required time to arrive at the steady state increases significantly as the Rayleigh number tends to the linear threshold. Design/methodology/approach – The author introduce the stability analysis of the problem of convection induced by absorption of radiation in fluid layer, then the author select a situations which have very big subcritical region. Then, the author develop a three dimensions simulation for the problem. To do this, first, the author transform the problem to velocity – vorticity formulation, then the author use a second order finite difference schemes. The author use implicit and explicit schemes to enforce the free divergence equation. The size of the Box is evaluated according to the normal modes representation. Moreover, the author adopt the periodic boundary conditions for velocity and temperature in the $x, y$ dimensions. Findings – This paper explores a model for convection induced by the selective absorption of radiation in a fluid layer. The results demonstrate that the linear instability thresholds accurately predict the onset of instability. A three-dimensional numerical approach is adopted. Originality/value – As the author believe, this paper is one of the first studies which deal with study of stability of convection using a three dimensional simulation. When the difference between the linear and nonlinear thresholds is very large, the comparison between these thresholds is very interesting and useful.

Efficient Numerical Analysis for Dynamic Stability of Pipes Conveying Fluids

1989 ◽  
Vol 111 (3) ◽  
pp. 300-303 ◽  
Author(s):  
X. Q. Dang ◽  
W. M. Liu ◽  
T. S. Zheng
Keyword(s):  
Stability Analysis ◽  
Numerical Analysis ◽  
Dynamic Stability ◽  
Pulsatile Flow ◽  
Instability Region ◽  
Numerical Results ◽  
Numerical Analyses ◽  
One Dimensional ◽  
Search Approach

Based on the Floquet-Liapunov theory, this paper proposes an efficient one-dimensional search approach for stability analysis of pipes conveying pulsatile flow. The instability boundaries of a clamped-clamped pipe analyzed in this paper. The numerical results are satisfactory compared with existing results. Moreover, an instability region which failed to appear in ordinary numerical analyses is detected by our computations.

Bifurcation and Stability Analysis of a One-Dimensional Diffusion-Autocatalytic Reaction System

1987 ◽  
Vol 42 (9) ◽  
pp. 994-1004 ◽  
Author(s):  
B. De Dier ◽  
F. Walraven ◽  
R. Janssen ◽  
P. Van Rompay ◽  
V. Hlavacek
Keyword(s):  
Steady State ◽  
Stability Analysis ◽  
Reaction System ◽  
Reaction Diffusion ◽  
Reaction Diffusion Equations ◽  
One Dimensional ◽  
Asymmetric Structures ◽  
Flux Boundary Conditions ◽  
Model Scheme ◽  
Steady State Problem

Results of a numerical analysis of a set of one-dimensional reaction -diffusion equations are presented. The basis of these equations is a model scheme of chemical reactions, involving auto-and cross-catalytic steps (“Brusselator”). The steady state problem is solved numerically, fully exploiting the properties of recently developed continuation codes. Bifurcation diagrams are constructed for zero flux boundary conditions. For a relatively large diffusivity of initial species the Brusselator displays a huge number of dissipative steady state structures. At low system lengths a mechanism of perturbed bifurcation may be percieved. Bifurcations coincide with turning points of asymmetric solution branches. Completely isolated solutions prove to exist as well. For the problem without limited diffusion of the initial species, a careful bifurcation analysis show s the existence of a number of higher order bifurcations. At some of these points asymmetric profiles emanate from other asymmetric structures. Bifurcation points and limit points do not necessarily coincide. Stability analysis shows that relatively few steady states are stable. Especially symmetric solutions are found to be stable.

scholarly journals CASE STUDY ON PERFORMANCE MONITORING AND STABILITY ANALYSIS OF BAISHIHU SUSPENSION BRIDGE AND SIDE SLOPE

2022 ◽  
Vol 28 (2) ◽  
pp. 81-92
Author(s):  
Chihcheng Chen ◽  
Ban-Jwu Shih ◽  
Ching-Jiang Jeng
Keyword(s):  
Steady State ◽  
Stability Analysis ◽  
Slope Stability ◽  
Performance Monitoring ◽  
Three Dimensional ◽  
Suspension Bridge ◽  
Steel Beams ◽  
Steel Cable ◽  
Final Steady State ◽  
Steel Cables

The main structure of the Baishihu suspension bridge was connected to the anchor foundations by three main steel cables. The wooden pedestrian deck was fixed to the main steel cables using steel beams and was stabilized by two stabilizing cables. The stabilizing cables and bridge body were joined by 44 steel connecting rods. Therefore, the slope stability at the anchorage foundations of the main steel cables, as well as the performance monitoring and analysis of the main steel cables and stabilizing cables, are critical to the overall performance of the suspension bridge. This paper discusses the performance monitoring and analysis of the steel cable deflection and cable strength for this bridge, as well as the main considerations and results of the stability analysis of the bridge abutments and side slopes of the two banks. Water-level observation wells, inclinometers, and tiltmeters monitoring were used to record reference data for the analysis of the slope stability performance. Additionally, the three-dimensional dynamic analysis program VFIFE was used to analyze the deformation and motion of the bridge. The final steady-state results were used to compare the static design value and monitoring data. The dynamic response before the final steady state was also observed.

Numerical Analysis and Validation of the Rotor Blade Vibration Response Induced by High Pressure Compressor Deep Surge

2014 ◽  
Author(s):  
Thomas Giersch ◽  
Felix Figaschewsky ◽  
Peter Hönisch ◽  
Arnold Kühhorn ◽  
Sven Schrape
Keyword(s):  
Steady State ◽  
Numerical Analysis ◽  
Finite Volume ◽  
Rotor Blade ◽  
Compressible Flows ◽  
Rapid Change ◽  
Three Dimensional ◽  
Reversed Flow ◽  
Blade Vibration ◽  
One Dimensional

The following paper presents a numerical analysis of a deep surge cycle of a 4.5 stage research compressor. The resulting unsteady loads are used to determine the response of two particular rotor blade rows that are then compared to strain gauge data from measurements. Within a deep surge cycle the compressor experiences a rapid change of the flow field from forward to reversed flow. This rapid breakdown is linked to a new mean blade load. Hence, the rapid change in blade loads are able to excite fundamental blade modes similar to an impulse load. The resulting vibration magnitudes might reach critical levels. This paper demonstrates two different approaches to evaluate the unsteady flow during a surge cycle. The first uses a three dimensional, time accurate finite volume solver for viscid compressible flows to calculate the transient surge cycle of the compressor. The compressor itself is represented by a multi-blade-row sector model. The second approach makes use of the same solver and compressor domain to determine steady state characteristics of the HPC in forward, stalled and reversed flow. Based on these characteristics an one dimensional finite volume solver for inviscid compressible flows was developed to determine the transient compressor behavior. The one dimensional solver represents the compressor by source terms that are linked to the previously determined steady state characteristics.

scholarly journals Visco-Elastoplastic Constitutive Fatigue Model for Rocks

2020 ◽  
Vol 2020 ◽  
pp. 1-11
Author(s):  
Jianhao Liu ◽  
Shaoyun Pu ◽  
Junying Rao
Keyword(s):  
Steady State ◽  
Cyclic Loading ◽  
Yield Criterion ◽  
Three Dimensional ◽  
Fatigue Properties ◽  
Test Results ◽  
One Dimensional ◽  
Fatigue Model ◽  
Flow Criterion ◽  
Important Significance

The study on the constitutive fatigue model for rocks under cyclic loading has an important significance in rock engineering. In order to study the fatigue properties of rocks under cyclic loading, according to the theory of rheological mechanics and the existing three basic one-dimensional fatigue elements, i.e., elastic, viscous, and plastic fatigue elements, the three-dimensional elastic, viscous, and plastic fatigue elements were constructed. Meanwhile, a fatigue yield criterion for rocks under cyclic loading was proposed, and a three-dimensional nonlinear visco-elastoplastic fatigue constitutive model (NVPFM) for rocks was established by using the flow criterion related to the proposed fatigue yield criterion. Compared with the test results of rocks under cyclic loading, the three-dimensional NVPFM could be used to describe the transient, steady-state, and tertiary creep phases of rocks under cyclic loading.

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