Dynamical Mechanism and Energy Conversion of the Couette–Taylor Flow

2019 ◽  
Vol 29 (08) ◽  
pp. 1950100
Author(s):  
Heyuan Wang
Keyword(s):  
Reynolds Number ◽  
Energy Conversion ◽  
Physical Interpretation ◽  
Type System ◽  
Casimir Function ◽  
Key Factors ◽  
Kolmogorov Type ◽  
Dynamical Mechanism ◽  
Taylor Flow ◽  
Kinetic And Potential Energies

In this paper, we study the dynamical mechanism and energy conversion of the Couette–Taylor flow. The Couette–Taylor flow chaotic system is transformed into the Kolmogorov type system, which is decomposed into four types of torques. Combining different torques, the key factors of chaos generation and the physical interpretation of the Couette–Taylor flow are studied. We further investigate the conversion among Hamiltonian, kinetic and potential energies, as well as the correlation between the energies and the Reynolds number. It is concluded that the combination of the four torques is necessary to produce chaos, and the system can produce chaos only when the dissipative torques match the driving (external) torques. Any combination of three types of torques cannot produce chaos. Moreover, we introduce the Casimir function to analyze the system dynamics, and choose its derivation to formulate the energy conversion. The bound of chaotic attractor is obtained by the Casimir function and Lagrange multiplier. It is found that the Casimir function reflects the energy conversion and the distance between the orbit and the equilibria.

Mechanism and Energy Cycling of the Qi Four-Wing Chaotic System

2017 ◽  
Vol 27 (12) ◽  
pp. 1750180 ◽  
Author(s):  
Guoyuan Qi ◽  
Xiyin Liang
Keyword(s):  
Angular Momentum ◽  
Chaotic System ◽  
Common Ground ◽  
Type System ◽  
Casimir Function ◽  
State Variables ◽  
Key Factors ◽  
External Energy ◽  
Kolmogorov Type ◽  
Extremal Points

The Qi four-wing chaotic system is transformed into a Kolmogorov-type system, thereby building a bridge between a numerical chaotic system and a physical chaotic system that is convenient for analysis when finding common ground between the two. The vector field is decomposed into four types of torques: inertial, internal, dissipative and external. The angular momentum representing the physical analogue of the state variables of the chaotic system is identified. The cycling of energy among potential energy, kinetic energy, dissipation, and external energy is analyzed. The Casimir function is employed to identify the key factors producing chaos and other dynamical modes. The system is non-Rayleigh dissipative, which determines the extremal points of Casimir function to form a hyperboloid instead of ellipsoid.

Mechanics Analysis and Hardware Implementation of a New 3D Chaotic System

2018 ◽  
Vol 28 (13) ◽  
pp. 1850161 ◽  
Author(s):  
Hongyan Jia ◽  
Zhiqiang Guo ◽  
Shanfeng Wang ◽  
Zengqiang Chen
Keyword(s):  
Chaotic System ◽  
Analog Circuit ◽  
Type System ◽  
Type Systems ◽  
Physical Models ◽  
Key Factors ◽  
Kolmogorov Type ◽  
Inertial Torque ◽  
Field Programmable ◽  
Physical Background

In this study, a new 3D chaotic system was first transformed into a Kolmogorov-type system to describe the vector field from the viewpoint of torque. In this Kolmogorov-type system, only inertial torque and non-Rayleigh dissipation exist. Thus, this is different from previously reported Kolmogorov-type systems that are generally decomposed into inertial torque, internal torque, dissipation, and external torque. Moreover, by analyzing these two torques, the physical background of the system and the key factors of chaos generation were also determined. That is, the inertial torque and non-Rayleigh dissipation are responsible for chaos generation in the new 3D chaotic system. Then, the Casimir function and Hamiltonian energy function were also analyzed to investigate the cycling of energy in the chaotic system. Finally, both an analog circuit and a Field Programmable Gate Array (FPGA) circuit were designed to implement the chaotic system. All of the experimentally obtained results are consistent with the results of numerical analysis, which did not only indicate the chaotic characteristics of the 3D chaotic system physically, but also provided physical models for engineering applications.

Influence of Liquid Properties on Energy Conversion During Crown Evolution Following Drop Impact Upon Films

2019 ◽  
Vol 142 (1) ◽  
Author(s):  
Yujia Zhang ◽  
Peiqing Liu ◽  
Qiulin Qu ◽  
Fanglin Liu ◽  
Ramesh K. Agarwal
Keyword(s):  
Reynolds Number ◽  
Energy Conversion ◽  
Weber Number ◽  
Stokes Equations ◽  
Drop Impact ◽  
Navier Stokes ◽  
Impact Process ◽  
Vof Model ◽  
The Moment ◽  
The Impact

Abstract The energy conversion is proposed to analyze the effects of liquid properties on the formation of an ejecta sheet, prompt splashing, and crown evolution. The incompressible laminar Navier–Stokes equations coupled with the volume-of-fluid (VOF) model are solved numerically in an axisymmetric frame to simulate the impact process. Based on the energy conversion curves and liquid–gas interface shapes, the Weber number is shown to be the main dimensionless quantity controlling the impact process, especially with regard to crown evolution. However, the Reynolds number does have some influence on the drop impact process, especially during the stage of ejecta sheet formation and prompt splashing. By studying energy conversion during the impact process, the crown evolution is shown to be accelerated significantly with decreasing Weber number, but is hardly affected by the Reynolds number. A linear relation is found between the time to the moment of crown stabilization (when the crown height reaches its maximum value) and the square root of the Weber number. The relationship between the Weber number and the energy distribution at the moment of crown stabilization is also studied.

Oscillating Flow Past a Rigid Circular Cylinder: A Finite-Difference Calculation

1991 ◽  
Vol 113 (3) ◽  
pp. 377-383 ◽  
Author(s):  
Xuegeng Wang ◽  
Charles Dalton
Keyword(s):  
Reynolds Number ◽  
Finite Difference ◽  
Circular Cylinder ◽  
Physical Interpretation ◽  
Oscillating Flow ◽  
Flow Past ◽  
Dependent Variables ◽  
Good Comparison ◽  
Vortex Patterns ◽  
Difference Calculation

A finite-difference study of the sinusoidally oscillating flow past a fixed circular cylinder is made using vorticity and stream function as the dependent variables. Calculations are performed for conditions which lead to both a symmetric wake and an unsymmetric wake. The Reynolds number ranges from 100 to 3000 and the Keulegan-Carpenter number ranges from 1 to 12. A hybrid differencing scheme is introduced to provide a stable for large values of the parameters. Good comparison to flow visualization results and calculated force coefficients is found. The results are given a physical interpretation for the various vortex patterns observed.

Force Analysis of Qi Chaotic System

2016 ◽  
Vol 26 (14) ◽  
pp. 1650237 ◽  
Author(s):  
Guoyuan Qi ◽  
Xiyin Liang
Keyword(s):  
Chaotic System ◽  
Chaotic Attractor ◽  
Casimir Energy ◽  
State Variables ◽  
Force Analysis ◽  
Key Factors ◽  
Kolmogorov Type ◽  
Different Types ◽  
Inertial Torque ◽  
Energy Law

The Qi chaotic system is transformed into Kolmogorov type of system. The vector field of the Qi chaotic system is decomposed into four types of torques: inertial torque, internal torque, dissipation and external torque. Angular momentum representing the physical analogue of the state variables of the chaotic system is identified. The Casimir energy law relating to the orbital behavior is identified and the bound of Qi chaotic attractor is given. Five cases of study have been conducted to discover the insights and functions of different types of torques of the chaotic attractor and also the key factors of producing different types of modes of dynamics.

scholarly journals The Effects of Reynolds Number on Energy Harvesting from FIV by a Square Cylinder

2020 ◽  
Vol 38 (5) ◽  
pp. 928-936
Author(s):  
Peng Han ◽  
Guang Pan ◽  
Qiaogao Huang ◽  
Yao SHI
Keyword(s):  
Reynolds Number ◽  
Energy Harvesting ◽  
Energy Conversion ◽  
Reynolds Numbers ◽  
Energy Conversion Efficiency ◽  
Published Data ◽  
Square Cylinder ◽  
A Value ◽  
Vibration Responses ◽  
Intense Vibration

Under the action of incoming flow, the square cylinder can generate more intense vibration responses than the circular cylinder, which is beneficial for energy harvesting. Numerical simulations for FIV of the square-cylinder energy conversion system are carried out. URANS equations are used in conjunction with the shear stress transport k-ω turbulence model to predict the flow, and the equations for vibrations are solved by the Newmark-β algorithm. The present numerical method is validated against the published data with good consistency. The Reduced velocity Ur is varied from 1-20, with corresponding Reynolds numbers of 24 000-160 000. The numerical results indicate that the Reynolds number significantly affects the frequency response, amplitude response, vortex shedding mode, and energy conversion efficiency. The highest efficiency point locates at Re=88 000, with a value of 7.156%. When Re>120 000, the system transits from vortex-induced vibration into galloping, and its vibration responses as well as energy harvesting characteristics change sharply. Fully developed galloping motion occurs when Re>144 000.

Pressure Drop of Liquid-Liquid Taylor Flow in Mini-Scale Coiled and Curved Tubing

2019 ◽  
Author(s):  
W. Adrugi ◽  
Y. S. Muzychka ◽  
K. Pope
Keyword(s):  
Experimental Study ◽  
Reynolds Number ◽  
Pressure Drop ◽  
Slug Flow ◽  
Silicone Oil ◽  
Radius Of Curvature ◽  
Asymptotic Model ◽  
Dean Number ◽  
Taylor Flow ◽  
Low Viscosity

Abstract This paper presents an experimental study on pressure drop using non-boiling liquid-liquid Taylor flow in mini scale coiled and curved tubing. Experiments were carried out to measure the pressure drop characteristics by varying the numbers of turns in coiled tubes and the lengths of curved tubes of less than one turn, such that Dean number, Reynolds number, radius of curvature, and coil pitch were considered. A set of narrow coiled tubes (ID = 1.59 mm, 1.27 mm, 1.016 mm) was used as test sections with different radii of curvature and overall lengths, and thus a different quantity of turns. Water and 1 cSt low viscosity silicone oil were used to create a segmented slug flow. An asymptotic model is developed based on the experimental results and previous models to predict the pressure drop, based on Dean number and dimensionless slug length. The effects of varying tube curvature and tube diameter are also studied. The results provide new insights into the effect of coiling and secondary flow on pressure drop for a liquid-liquid Taylor flow in mini scale systems.

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