Transitions of flow past a row of square bars

2000 ◽  
Vol 405 ◽  
pp. 305-323 ◽  
Author(s):  
J. MIZUSHIMA ◽  
Y. KAWAGUCHI
Keyword(s):  
Numerical Simulations ◽  
Flow Pattern ◽  
Bifurcation Analysis ◽  
Pitchfork Bifurcation ◽  
Side Length ◽  
Length Ratio ◽  
Two Dimensional ◽  
Bifurcation Diagrams ◽  
Flow Past ◽  
Flow Visualizations

Transitions of flow past a row of square bars placed across a uniform flow are investigated by numerical simulations and the bifurcation analysis of the numerical results. The flow is assumed two-dimensional and incompressible. It is already known that jets coming through gaps between square bars are independent of each other when the pitch-to-side-length ratio of the row is large, whereas the confluence of two or three jets occurs due to a first pitchfork bifurcation from the flow with independent jets when the pitch-to-side-length ratio is small. It is found that confluence of four jets occurs in consequence of the second pitchfork bifurcation from the flow with pairs of jets joined to each other. Bifurcation diagrams of the flow are obtained, which include confluences of double, triple and quadruple jets. Lengths of the twin vortices are evaluated for each flow pattern. The confluences of two, three and four jets are qualitatively confirmed experimentally by flow visualizations.

Flow past a rotationally oscillating cylinder

2013 ◽  
Vol 735 ◽  
pp. 307-346 ◽  
Author(s):  
S. Kumar ◽  
C. Lopez ◽  
O. Probst ◽  
G. Francisco ◽  
D. Askari ◽  
...  
Keyword(s):  
Reynolds Number ◽  
Vortex Shedding ◽  
Three Dimensional ◽  
Far Field ◽  
Two Dimensional ◽  
Flow Past ◽  
Vortex Shedding Frequency ◽  
Shedding Frequency ◽  
Flow Visualizations ◽  
Hydrogen Bubble Technique

AbstractFlow past a circular cylinder executing sinusoidal rotary oscillations about its own axis is studied experimentally. The experiments are carried out at a Reynolds number of 185, oscillation amplitudes varying from $\mathrm{\pi} / 8$ to $\mathrm{\pi} $, and at non-dimensional forcing frequencies (ratio of the cylinder oscillation frequency to the vortex-shedding frequency from a stationary cylinder) varying from 0 to 5. The diagnostic is performed by extensive flow visualization using the hydrogen bubble technique, hot-wire anemometry and particle-image velocimetry. The wake structures are related to the velocity spectra at various forcing parameters and downstream distances. It is found that the phenomenon of lock-on occurs in a forcing frequency range which depends not only on the amplitude of oscillation but also the downstream location from the cylinder. The experimentally measured lock-on diagram in the forcing amplitude and frequency plane at various downstream locations ranging from 2 to 23 diameters is presented. The far-field wake decouples, after the lock-on at higher forcing frequencies and behaves more like a regular Bénard–von Kármán vortex street from a stationary cylinder with vortex-shedding frequency mostly lower than that from a stationary cylinder. The dependence of circulation values of the shed vortices on the forcing frequency reveals a decay character independent of forcing amplitude beyond forcing frequency of ${\sim }1. 0$ and a scaling behaviour with forcing amplitude at forcing frequencies ${\leq }1. 0$. The flow visualizations reveal that the far-field wake becomes two-dimensional (planar) near the forcing frequencies where the circulation of the shed vortices becomes maximum and strong three-dimensional flow is generated as mode shape changes in certain forcing parameter conditions. It is also found from flow visualizations that even at higher Reynolds number of 400, forcing the cylinder at forcing amplitudes of $\mathrm{\pi} / 4$ and $\mathrm{\pi} / 2$ can make the flow field two-dimensional at forcing frequencies greater than ${\sim }2. 5$.

TWO-DIMENSIONAL BIFURCATION DIAGRAMS OF A CHAOTIC CIRCUIT BASED ON HYSTERESIS

2002 ◽  
Vol 12 (01) ◽  
pp. 43-69 ◽  
Author(s):  
FEDERICO BIZZARRI ◽  
MARCO STORACE
Keyword(s):  
Bifurcation Analysis ◽  
Piecewise Linear ◽  
Point Of View ◽  
Chaotic Oscillator ◽  
Circuit Parameter ◽  
Two Dimensional ◽  
Bifurcation Diagrams ◽  
Chaotic Circuit ◽  
Analysis Point

This paper deals with the bifurcation analysis of a chaotic oscillator based on hysteresis. The analysis is carried out using two different models of the nonlinear resistive elements of the oscillator. The first model (more convenient from an analysis point of view) is piecewise linear (PWL), whereas the second (more realistic from a synthesis point of view) is smooth. For both models, the main results presented in this paper are two-dimensional bifurcation diagrams obtained for several values of a third circuit parameter.

Bifurcation Analysis of Piezoelectric Bi-Stable Plates

2014 ◽  
Author(s):  
Lihua Chen ◽  
Ma Yepeng ◽  
Wei Zhang
Keyword(s):  
Numerical Simulations ◽  
Phase Portrait ◽  
Bifurcation Analysis ◽  
Nonlinear Dynamic ◽  
Piezoelectric Effect ◽  
Kutta Method ◽  
Bifurcation Diagrams ◽  
Nonlinear Dynamic Model ◽  
Piezoelectric Patch ◽  
Runge Kutta Method

The complex nonlinear dynamic behaviors of the composite bi-stable plates with piezoelectric patch are analyzed. Based on the Vo n Karman hypothesis and Hamilton’s principle, the nonlinear dynamic model is derived. Temperature and piezoelectric effect are also considered in the model. Numerical simulations are performed to study the nonlinear vibration response of the composite bi-stable plate using the Runge-Kutta method. The analysis of the phase portrait, waveforms and bifurcation diagrams of numerical simulations shows that the period, multi-period and chaotic responses can be observed with the variation of the excitation in frequency and amplitude.

BIFURCATION ANALYSIS IN A PWM CURRENT-CONTROLLED H-BRIDGE INVERTER

2011 ◽  
Vol 21 (03) ◽  
pp. 985-996 ◽  
Author(s):  
HIROYUKI ASAHARA ◽  
TAKUJI KOUSAKA
Keyword(s):  
Dynamical System ◽  
Parameter Space ◽  
Bifurcation Analysis ◽  
Specific Property ◽  
Two Dimensional ◽  
Bifurcation Diagrams ◽  
Rigorous Analysis ◽  
Bifurcation Phenomena ◽  
The One ◽  
Switched Dynamical System

This paper introduces the complete bifurcation analysis in a PWM current-controlled H-Bridge inverter in a wide parameter space. First, we briefly explain the behavior of the waveform in the circuit in terms of the switched dynamical system. Then, the consecutive waveform during the duration of the clock interval is exactly discretized, and the return map is defined for the rigorous analysis. Using the map, we derive the one- and two-dimensional bifurcation diagrams, and discuss the specific property of each bifurcation phenomena in the circuit.

scholarly journals Towards explicit regulating-ion-transport: nanochannels with only function-elements at outer-surface

2021 ◽  
Vol 12 (1) ◽  
Author(s):  
Qun Ma ◽  
Yu Li ◽  
Rongsheng Wang ◽  
Hongquan Xu ◽  
Qiujiao Du ◽  
...  
Keyword(s):  
Ion Transport ◽  
Numerical Simulations ◽  
Power Density ◽  
Outer Surface ◽  
Internal Resistance ◽  
Porous Membranes ◽  
Two Dimensional ◽  
Ionic Selectivity ◽  
Key Features ◽  
Energy Conversion Devices

AbstractFunction elements (FE) are vital components of nanochannel-systems for artificially regulating ion transport. Conventionally, the FE at inner wall (FEIW) of nanochannel−systems are of concern owing to their recognized effect on the compression of ionic passageways. However, their properties are inexplicit or generally presumed from the properties of the FE at outer surface (FEOS), which will bring potential errors. Here, we show that the FEOS independently regulate ion transport in a nanochannel−system without FEIW. The numerical simulations, assigned the measured parameters of FEOS to the Poisson and Nernst-Planck (PNP) equations, are well fitted with the experiments, indicating the generally explicit regulating-ion-transport accomplished by FEOS without FEIW. Meanwhile, the FEOS fulfill the key features of the pervious nanochannel systems on regulating-ion-transport in osmotic energy conversion devices and biosensors, and show advantages to (1) promote power density through concentrating FE at outer surface, bringing increase of ionic selectivity but no obvious change in internal resistance; (2) accommodate probes or targets with size beyond the diameter of nanochannels. Nanochannel-systems with only FEOS of explicit properties provide a quantitative platform for studying substrate transport phenomena through nanoconfined space, including nanopores, nanochannels, nanopipettes, porous membranes and two-dimensional channels.

scholarly journals Spatiotemporal Patterns Formed by a Discrete Nutrient-Phytoplankton Model with Time Delay

Complexity ◽  
2020 ◽  
Vol 2020 ◽  
pp. 1-18
Author(s):  
Feifan Zhang ◽  
Wenjiao Zhou ◽  
Lei Yao ◽  
Xuanwen Wu ◽  
Huayong Zhang
Keyword(s):  
Steady State ◽  
Time Delay ◽  
Numerical Simulations ◽  
Functional Response ◽  
Bifurcation Analysis ◽  
Discrete Model ◽  
Continuous Model ◽  
Spatiotemporal Patterns ◽  
Homogeneous Steady State ◽  
Simulation Results

In this research, a continuous nutrient-phytoplankton model with time delay and Michaelis–Menten functional response is discretized to a spatiotemporal discrete model. Around the homogeneous steady state of the discrete model, Neimark–Sacker bifurcation and Turing bifurcation analysis are investigated. Based on the bifurcation analysis, numerical simulations are carried out on the formation of spatiotemporal patterns. Simulation results show that the diffusion of phytoplankton and nutrients can induce the formation of Turing-like patterns, while time delay can also induce the formation of cloud-like pattern by Neimark–Sacker bifurcation. Compared with the results generated by the continuous model, more types of patterns are obtained and are compared with real observed patterns.

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