Three-Dimensional Chaotic Mixing of Fluids in a Cylindrical Cavity

1995 ◽  
Vol 117 (4) ◽  
pp. 582-588 ◽  
Author(s):  
K. C. Miles ◽  
B. Nagarajan ◽  
D. A. Zumbrunen
Keyword(s):  
Cylindrical Cavity ◽  
Chaotic Behavior ◽  
Fluid Motion ◽  
Three Dimensional ◽  
Creeping Flow ◽  
Chaotic Mixing ◽  
Mixing Processes ◽  
Video Images ◽  
Return Maps ◽  
Neutrally Buoyant

Three-dimensional chaotic mixing of Newtonian fluids in a previously uninvestigated cylindrical cavity was studied both experimentally and numerically for creeping flow conditions. Such mixing processes have practical application to the blending of viscous fluids, biological suspensions, or can be used as test beds to study waterborne pollutant formation. A mixing chamber was fabricated which consisted of a cylindrical glass cavity with independently rotating upper and lower circular disks. Fluid motion was revealed by digitizing successive video images of a small neutrally buoyant sphere placed into the mixing cavity and also by photographing dyed blobs. Experimental particle tracking studies were supplemented by numerical simulations. Phase-space trajectories, return maps, and Lyapunov exponents were used to characterize the mixing process and to confirm chaotic behavior.

Numerical Integration of the Navier-Stokes Equations for a Disk Rotating in a Housing

1985 ◽  
Vol 40 (8) ◽  
pp. 789-799 ◽  
Author(s):  
A. F. Borghesani
Keyword(s):  
Boundary Layer ◽  
Cylindrical Cavity ◽  
Boundary Layer Thickness ◽  
Stokes Equations ◽  
Fluid Motion ◽  
Rotating Disk ◽  
Infinite Medium ◽  
Navier Stokes ◽  
Navier Stokes Equations ◽  
Viscous Torque

The Navier-Stokes equations for the fluid motion induced by a disk rotating inside a cylindrical cavity have been integrated for several values of the boundary layer thickness d. The equivalence of such a device to a rotating disk immersed in an infinite medium has been shown in the limit as d → 0. From that solution and taking into account edge effect corrections an equation for the viscous torque acting on the disk has been derived, which depends only on d. Moreover, these results justify the use of a rotating disk to perform accurate viscosity measurements.

BIFURCATION SCENARIO OF A THREE-DIMENSIONAL VAN DER POL OSCILLATOR

1993 ◽  
Vol 03 (02) ◽  
pp. 399-404 ◽  
Author(s):  
T. SÜNNER ◽  
H. SAUERMANN
Keyword(s):  
Bifurcation Diagram ◽  
Bifurcation Analysis ◽  
Chaotic Behavior ◽  
Three Dimensional ◽  
Global Bifurcation ◽  
Dynamical Behaviour ◽  
Van Der Pol Oscillator ◽  
Two Dimensional ◽  
Van Der Pol ◽  
Dimensional Models

Nonlinear self-excited oscillations are usually investigated for two-dimensional models. We extend the simplest and best known of these models, the van der Pol oscillator, to a three-dimensional one and study its dynamical behaviour by methods of bifurcation analysis. We find cusps and other local codimension 2 bifurcations. A homoclinic (i.e. global) bifurcation plays an important role in the bifurcation diagram. Finally it is demonstrated that chaos sets in. Thus the system belongs to the few three-dimensional autonomous ones modelling physical situations which lead to chaotic behavior.

A Correction Method for Non-Vertical View Angle Three-Dimensional Display

2014 ◽  
Vol 513-517 ◽  
pp. 3882-3885
Author(s):  
Tian Qi Zhao ◽  
Xun Bo Yu ◽  
Xin Zhu Sang ◽  
Chong Xiu Yu ◽  
Da Xiong Xu ◽  
...  
Keyword(s):  
Virtual Reality ◽  
Three Dimensional ◽  
Correction Method ◽  
Display System ◽  
Video Images ◽  
Three Dimensional Display

An non-vertical stereoscopic 3-D display method by changing the parallax value of the parallax images is proposed. This method is capable of displaying virtual reality with high-immersion sense because the observing depth only depends on the parallax value. An experimental 3-D display system capable of producing high-immersion and virtual reality video images at 45 degree is developed. Furthermore, the effectiveness of the method is demonstrated by using this system.

Diesel Droplet Diffusion in Isotropic Turbulence With Digital Holographic Cinematography

2005 ◽  
Author(s):  
Balaji Gopalan ◽  
Edwin Malkiel ◽  
Jian Sheng ◽  
Joseph Katz
Keyword(s):  
Time Series ◽  
High Speed ◽  
Isotropic Turbulence ◽  
Fluid Motion ◽  
Three Dimensional ◽  
Time History ◽  
Sample Volume ◽  
Velocity Autocorrelation Function ◽  
Digital Cameras ◽  
Velocity Autocorrelation

High-speed in-line digital holographic cinematography was used to investigate the diffusion of droplets in locally isotropic turbulence. Droplets of diesel fuel (0.3–0.9mm diameter, specific gravity of 0.85) were injected into a 37×37×37mm3 sample volume located in the center of a 160-liter tank. The turbulence was generated by 4 spinning grids, located symmetrically in the corners of the tank, and was characterized prior to the experiments. The sample volume was back illuminated with two perpendicular collimated beams of coherent laser light and time series of in-line holograms were recorded with two high-speed digital cameras at 500 frames/sec. Numerical reconstruction generated a time series of high-resolution images of the droplets throughout the sample volume. We developed an algorithm for automatically detecting the droplet trajectories from each view, for matching the two views to obtain the three-dimensional tracks, and for calculating the time history of velocity. We also measured the mean fluid motion using 2-D PIV. The data enabled us to calculate the Lagrangian velocity autocorrelation function.

Secondary motion in convection layers generated by lateral heating of a solute gradient

2002 ◽  
Vol 455 ◽  
pp. 1-19 ◽  
Author(s):  
CHO LIK CHAN ◽  
WEN-YAU CHEN ◽  
C. F. CHEN
Keyword(s):  
Stability Analysis ◽  
Linear Stability ◽  
Linear Stability Analysis ◽  
Fluid Motion ◽  
Three Dimensional ◽  
Convection Cell ◽  
Experimental Conditions ◽  
Longitudinal Plane ◽  
Secondary Motion ◽  
Solute Gradient

The three-dimensional motion observed by Chen & Chen (1997) in the convection cells generated by sideways heating of a solute gradient is further examined by experiments and linear stability analysis. In the experiments, we obtained visualizations and PIV measurements of the velocity of the fluid motion in the longitudinal plane perpendicular to the imposed temperature gradient. The flow consists of a horizontal row of counter-rotating vortices within each convection cell. The magnitude of this secondary motion is approximately one-half that of the primary convection cell. Results of a linear stability analysis of a parallel double-diffusive flow model of the actual ow show that the instability is in the salt-finger mode under the experimental conditions. The perturbation streamlines in the longitudinal plane at onset consist of a horizontal row of counter-rotating vortices similar to those observed in the experiments.

scholarly journals On a third order initial boundary value problem in a plane domain

2012 ◽  
Vol 17 (3) ◽  
pp. 312-326
Author(s):  
Neringa Klovienė
Keyword(s):  
Boundary Value Problem ◽  
Boundary Value ◽  
Auxiliary Problem ◽  
Fluid Motion ◽  
Three Dimensional ◽  
Initial Boundary ◽  
Initial Boundary Value Problem ◽  
Plane Domain ◽  
Third Order ◽  
Initial Boundary Value

Third order initial boundary value problem is studied in a bounded plane domain σ with C4 smooth boundary ∂σ. The existence and uniqueness of the solution is proved using Galerkin approximations and a priory estimates. The problem under consideration appear as an auxiliary problem by studying a second grade fluid motion in an infinite three-dimensional pipe with noncircular cross-section.

Interaction of Transient Waves With a Circular Surface-Piercing Body

1995 ◽  
Vol 117 (3) ◽  
pp. 382-388 ◽  
Author(s):  
Xing Yu ◽  
Ronald W. Yeung
Keyword(s):  
Large Time ◽  
Fluid Motion ◽  
Three Dimensional ◽  
Transient Waves ◽  
Generalized Poisson ◽  
Poisson Solver ◽  
Potential Applications ◽  
Circular Surface ◽  
High Degree ◽  
Pseudo Spectral

A pseudo-spectral formulation for solving unsteady, three-dimensional fluid motion with a free surface in cylindrical coordinates is presented. An effective method for treating the Laplace equation, as a special application of a generalized Poisson solver, is developed. This approach is demonstrated by studying the evolution of transient surface waves near a vertical circular cylinder enclosed in open or closed domains. Results are observed to have a high degree of precision and spatial resolution even at large time. Potential applications of this method to other problems are discussed.

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