Research Problems on Chaotic Advection in Three Dimensions and at Higher Reynolds Number.

1994 ◽  
Author(s):  
M. Tabor ◽  
I. Klapper
Keyword(s):  
Reynolds Number ◽  
Three Dimensions ◽  
Chaotic Advection ◽  
Research Problems

scholarly journals Turbulent Coagulation of Aerosol Particles: New Insights From Direct Numerical Simulations and Holographic Imaging Experiments

2003 ◽  
Author(s):  
Lance R. Collins ◽  
Hui Meng ◽  
Aruj Ahluwalia ◽  
Lujie Cao ◽  
Gang Pan
Keyword(s):  
Reynolds Number ◽  
Numerical Simulations ◽  
Search Algorithm ◽  
Concentration Field ◽  
Direct Numerical Simulations ◽  
Three Dimensions ◽  
Collision Kernel ◽  
Coagulation Rate ◽  
Subsequent Work ◽  
Turbulent Fluctuations

Particle collisions driven by turbulent fluctuations play a key role in such diverse problems as cloud formation, aerosol powder manufacturing and inhalation drug therapy to name a few. In all of these examples (and many others) turbulent fluctuations increase the rate of collisions relative to the background collision rate driven by Brownian motion. Furthermore, turbulence can spontaneously generate very large fluctuations in the particle concentration field. This “clustering” is caused by the inertial mismatch between the heavy particles and the lighter surrounding gas; vortices in the flow “centrifuge” the heavier particles out of vortex cores and into the straining regions that lie in between the vortices. Because collision is a binary process, concentration fluctuations further enhance the turbulent coagulation rate by as much as two orders of magnitude. An effect of this size must be accounted for in a rational model of turbulent coagulation. Sundaram & Collins (J. Fluid Mech. 1997) showed that the radial distribution function (RDF) of the particle population, evaluated at contact, precisely corrects the collision kernel for clustering. Subsequent work has explored the dependence of the RDF on the system parameters (e.g., particle size, concentration, response time and Reynolds number) using direct numerical simulations. These results have improved our understanding and ability to predict the effect of the first three parameters; however, owing to the limited range of Reynolds number that can be reached in a numerical simulation, questions remain over the scaling of the RDF with Reynolds number. This is a critical issue for high-Reynolds-number applications such as cloud physics, where values of the Reynolds number can be 1–2 orders of magnitude greater than can be simulated. We will present our highest Reynolds number simulations to date and show our attempts to resolve this issue. Recently, the ability to measure three-dimensional particle positions using holography has been realized (e.g., Meng & Pu, J. Opt. Soc. Am. 2003). With holography, the optical image that is produced contains fringes that, upon inverting the laser, reproduce the original image in three dimensions. The hologram can then be scanned using a digital camera to obtain the particle positions. An important consideration with this study is the need to differentiate individual particles. We developed a search algorithm that locates particle centers, even in the presence of optical aberations and speckle noise. The algorithm has been used to obtain the first experimental RDF measurements to date. Thus far we see good agreement between the experimentally obtained RDF and the simulations. Besides validating the simulations, experiments can span a much broader range of Reynolds numbers, providing critical data that may help resolve the open questions associated with this parameter.

Numerical study of a vortex ring impacting a flat wall

2010 ◽  
Vol 660 ◽  
pp. 430-455 ◽  
Author(s):  
MING CHENG ◽  
JING LOU ◽  
LI-SHI LUO
Keyword(s):  
Reynolds Number ◽  
Vortex Ring ◽  
Three Dimensions ◽  
Angle Of Incidence ◽  
Secondary Vortex ◽  
Primary Ring ◽  
Flat Wall ◽  
Hydrodynamic Behaviour ◽  
Moderate Reynolds Number ◽  
Wall Interaction

We numerically study a vortex ring impacting a flat wall with an angle of incidence θ ≥ 0°) in three dimensions by using the lattice Boltzmann equation. The hydrodynamic behaviour of the ring–wall interacting flow is investigated by systematically varying the angle of incidence θ in the range of 0° ≤ θ ≤ 40° and the Reynolds number in the range of 100 ≤ Re ≤ 1000, where the Reynolds number Re is based on the translational speed and initial diameter of the vortex ring. We quantify the effects of θ and Re on the evolution of the vortex structure in three dimensions and other flow fields in two dimensions. We observe three distinctive flow regions in the θ–Re parameter space. First, in the low-Reynolds-number region, the ring–wall interaction dissipates the ring without generating any secondary rings. Second, with a moderate Reynolds number Re and a small angle of incidence θ, the ring–wall interaction generates a complete secondary vortex ring, and even a tertiary ring at higher Reynolds numbers. The secondary vortex ring is convected to the centre region of the primary ring and develops azimuthal instabilities, which eventually lead to the development of hairpin-like small vortices through ring–ring interaction. And finally, with a moderate Reynolds number and a sufficiently large angle of incidence θ, only a secondary vortex ring is generated. The secondary vortex wraps around the primary ring and propagates from the near end of the primary ring, which touches the wall first, to the far end, which touches the wall last. The rings develop a helical structure. Our results from the present study confirm some existing experimental observations made in the previous studies.

scholarly journals On the detection of internal interfacial layers in turbulent flows

2019 ◽  
Vol 872 ◽  
pp. 198-217 ◽  
Author(s):  
Duosi Fan ◽  
Jinglei Xu ◽  
Matthew X. Yao ◽  
Jean-Pierre Hickey
Keyword(s):  
Boundary Layer ◽  
Reynolds Number ◽  
Turbulent Flows ◽  
Channel Flow ◽  
Outer Region ◽  
Fuzzy Cluster ◽  
Three Dimensions ◽  
Cluster Method ◽  
Strong Concentration ◽  
Interfacial Layers

A novel approach to identify internal interfacial layers, or IILs, in wall-bounded turbulent flows is proposed. Using a fuzzy cluster method (FCM) on the streamwise velocity component, a unique and unambiguous grouping of the uniform momentum zones (UMZs) is achieved, thus allowing the identification of the IILs. The approach overcomes some of the key limitations of the histogram-based IIL identification methods. The method is insensitive to the streamwise domain length, can be used on inhomogeneous grids, uses all the available flow field data, is trivially extended to three dimensions and does not need user-defined parameters (e.g. number of bins) other than the number of zones. The number of zones for a given snapshot can be automatically determined by an a priori algorithm based on a kernel density estimation algorithm, or KDE. This automated approach is applied to compute the average number of UMZs as a function of Reynolds number $Re_{\unicode[STIX]{x1D70F}}$ in turbulent channel flows in several numerical simulations. This systematic approach reveals a dependence of the Reynolds number on the average number of UMZs in the channel flow; this supports previously reported observations in the boundary layer. The fuzzy clustering approach is applied to the turbulent boundary layer (experimental, planar particle image velocimetry) and channel flow (numerical, direct numerical simulation) at varying Reynolds numbers. The interfacial layers are characterized by a strong concentration of spanwise vorticity, with the outer-most layer located at the upper edge of the log layer. The three-dimensional interface identification reveals a streak-like organization. The large-scale motion (LSM) at the outer region of the channel flow boundary layer modulates the outer IIL. The corrugations of the outer IIL are aligned with the LSM and the conditional correlation of the inner and outer IIL height shows that extreme near-wall events leave their mark on the outer IIL corrugations.

A Theory of Lubrication With Turbulent Flow and Its Application to Slider Bearings

1960 ◽  
Vol 27 (1) ◽  
pp. 1-4 ◽  
Author(s):  
L. N. Tao
Keyword(s):  
Exact Solution ◽  
Reynolds Number ◽  
Turbulent Flow ◽  
Closed Form ◽  
Governing Equation ◽  
Reynolds Equation ◽  
Three Dimensions ◽  
Slider Bearing ◽  
Numerical Example ◽  
Special Case

The governing equation of turbulent lubrication in three dimensions, equivalent to the Reynolds equation of laminar lubrication, is derived. The problem of a slider bearing with no side leakage is then analyzed. An exact solution is found in closed form. Bearing characteristics are also established. It is found that the Reynolds number is an important parameter in the problem of turbulent lubrication. Furthermore, it is shown that the laminar lubrication may be considered as the special case of the present study. A numerical example is also included.

Flows produced by the combined oscillatory rotation and translation of a circular cylinder in a quiescent fluid

2014 ◽  
Vol 764 ◽  
pp. 148-170 ◽  
Author(s):  
Christopher Koehler ◽  
Philip Beran ◽  
Marcos Vanella ◽  
Elias Balaras
Keyword(s):  
Reynolds Number ◽  
Circular Cylinder ◽  
Bluff Body ◽  
Stokes Equations ◽  
Time Windows ◽  
Two Dimensions ◽  
Three Dimensions ◽  
Immersed Boundary ◽  
Dimensionless Time ◽  
Quiescent Fluid

AbstractFlows produced by a circular cylinder undergoing oscillatory rotation and translation in a quiescent fluid have been studied via direct numerical simulations. The incompressible Navier–Stokes equations were solved for large dimensionless time windows using an immersed boundary method with adaptive Cartesian grid refinement. Parametric studies were conducted in two dimensions on the Reynolds number, Keulegan–Carpenter number and phase shift. In addition to the previously reported net thrust case (Blackburn et al., Phys. Fluids, vol. 11, 1999, pp. 4–6), the study catalogued the appearance of several streaming jet regimes with varying deflection angles, deflected and horizontal vortex shedding regimes, and a double mirrored jet regime with varying inter-jet angles, as well as several chaotic cases. Visualizations are presented to clarify each observed flow regime and to illustrate the parameter space. Connections are drawn between these canonical bluff-body deflected wakes and a similar phenomenon observed in aerofoils oscillating at high reduced frequencies in a cross-flow. Also, the discovery of the streaming jet regimes with varying deflection angles opens the door for using these flows as a low-Reynolds-number propulsive mechanism requiring only a two-degree-of-freedom actuator. Simulation results suggest that the flow phenomena observed in two dimensions persist in three dimensions, despite spanwise fluctuations.

scholarly journals Coherent structures and chaotic advection in three dimensions

2010 ◽  
Vol 654 ◽  
pp. 1-4 ◽  
Author(s):  
STEPHEN WIGGINS
Keyword(s):  
Dynamical Systems ◽  
Fluid Mechanics ◽  
Coherent Structures ◽  
Three Dimensional ◽  
Point Of View ◽  
Three Dimensions ◽  
Chaotic Advection ◽  
Periodic Flow ◽  
Two Dimensional ◽  
Time Periodic

In the 1980s the incorporation of ideas from dynamical systems theory into theoretical fluid mechanics, reinforced by elegant experiments, fundamentally changed the way in which we view and analyse Lagrangian transport. The majority of work along these lines was restricted to two-dimensional flows and the generalization of the dynamical systems point of view to fully three-dimensional flows has seen less progress. This situation may now change with the work of Pouransari et al. (J. Fluid Mech., this issue, vol. 654, 2010, pp. 5–34) who study transport in a three-dimensional time-periodic flow and show that completely new types of dynamical systems structures and consequently, coherent structures, form a geometrical template governing transport.

Microswimmer-induced chaotic mixing

2015 ◽  
Vol 779 ◽  
pp. 669-683 ◽  
Author(s):  
Mir Abbas Jalali ◽  
Atefeh Khoshnood ◽  
Mohammad-Reza Alam
Keyword(s):  
Reynolds Number ◽  
Periodic Orbits ◽  
Complex Geometry ◽  
Low Reynolds Number ◽  
Two Dimensions ◽  
Chaotic Advection ◽  
Entire Volume ◽  
Low Reynolds ◽  
The Stokes Equation ◽  
Linear Nature

Efficient mixing, typically characterised by chaotic advection, is hard to achieve in low Reynolds number conditions because of the linear nature of the Stokes equation that governs the motion. Here we show that low Reynolds number swimmers moving in quasi-periodic orbits can result in considerable stretching and folding of fluid elements. We accurately follow packets of tracers within the fluid domain and show that their trajectories become chaotic as the swimmer’s trajectory densely fills its invariant torus. The mixing process is demonstrated in two dimensions using the Quadroar swimmer that autonomously propels and tumbles along quasi-periodic orbits with multi-loop turning trajectories. We demonstrate and discuss that the streamlines of the flow induced by the Quadroar closely resemble the oscillatory flow field of the green alga Chlamydomonas reinhardtii. Our findings can thus be utilized to understand the interactions of microorganisms with their environments, and to design autonomous robotic mixers that can sweep and mix an entire volume of complex geometry containers.

Mixing Enhancement in a Chaotic Micromixer Using Pulsating Flow

2014 ◽  
Author(s):  
Mohammad Karami ◽  
Mojtaba Jarrahi ◽  
Ebrahim Shirani ◽  
Hassan Peerhossaini
Keyword(s):  
Reynolds Number ◽  
Lyapunov Exponent ◽  
Steady Flow ◽  
Concentration Distribution ◽  
Pulsating Flow ◽  
Chaotic Advection ◽  
Mixing Enhancement ◽  
Mean Flow ◽  
Number Range ◽  
Velocity Amplitude

This study determines the simultaneous effects of spatial disturbance and flow pulsation on micromixing by using three different metrics: concentration distribution, Lyapunov exponent and axial vorticity. Numerical simulations are performed for both steady and pulsating flows through a microchannel made up of C-curved repeating units. Moreover, a straight microchannel is analyzed to compare the effects of chaotic advection and molecular diffusion, the main mechanisms of transverse mixing in the chaotic and straight mixer respectively. Simulations are carried out in the steady flow for the Reynolds number range 1≤Re≤50 and in the pulsating flow for velocity amplitude ratios 1≤β≤2.5, and the ratio of the peak oscillatory velocity component to the mean flow velocity, Strouhal numbers 0.1≤St≤0.5. It was found that chaotic advection improves mixing without significant increase in pressure drop. The analysis of concentration distribution implied that full mixing occurs after Reynolds number 50 in the steady flow. When the flow is pulsatile, small and moderate values of the Strouhal number (0.1≤St≤0.3) and high values of velocity amplitude ratio (β ≥ 2) are favorable conditions for mixing enhancement. Moreover, mixing has an oscillating trend along the microchannel due to the coexistence of regular and chaotic zones in the fluid. These results correlate closely with those obtained using two other metrics, analysis of the Lyapunov exponent and axial vorticity.

scholarly journals Rotational Maneuvers of Copepod Nauplii at Low Reynolds Number

Fluids ◽  
2020 ◽  
Vol 5 (2) ◽  
pp. 78
Author(s):  
Kacie T. M. Niimoto ◽  
Kyleigh J. Kuball ◽  
Lauren N. Block ◽  
Petra H. Lenz ◽  
Daisuke Takagi
Keyword(s):  
Reynolds Number ◽  
Rotational Motion ◽  
High Speed ◽  
The Body ◽  
Three Dimensions ◽  
Linear Path ◽  
Physical Mechanisms ◽  
High Speed Video ◽  
Video Observations ◽  
Principal Axes

Copepods are agile microcrustaceans that are capable of maneuvering freely in water. However, the physical mechanisms driving their rotational motion are not entirely clear in small larvae (nauplii). Here we report high-speed video observations of copepod nauplii performing acrobatic feats with three pairs of appendages. Our results show rotations about three principal axes of the body: yaw, roll, and pitch. The yaw rotation turns the body to one side and results in a circular swimming path. The roll rotation consists of the body spiraling around a nearly linear path, similar to an aileron roll of an airplane. We interpret the yaw and roll rotations to be facilitated by appendage pronation or supination. The pitch rotation consists of flipping on the spot in a maneuver that resembles a backflip somersault. The pitch rotation involved tail bending and was not observed in the earliest stages of nauplii. The maneuvering strategies adopted by plankton may inspire the design of microscopic robots, equipped with suitable controls for reorienting autonomously in three dimensions.

A nonlinear instability burst in plane parallel flow

1972 ◽  
Vol 51 (4) ◽  
pp. 705-735 ◽  
Author(s):  
L. M. Hocking ◽  
K. Stewartson ◽  
J. T. Stuart ◽  
S. N. Brown
Keyword(s):  
Differential Equation ◽  
Reynolds Number ◽  
Critical Value ◽  
Three Dimensions ◽  
Parabolic Differential Equation ◽  
Nonlinear Instability ◽  
Two Dimensional ◽  
Slowly Varying Function ◽  
Plane Poiseuille Flow ◽  
Long Time

An infinitesimal centre disturbance is imposed on a fully Ldveloped plane Poiseuille flow at a Reynolds numberRslightly greater than the critical valueRcfor instability. After a long time,t, the disturbance consists of a modulated wave whose amplitudeAis a slowly varying function of position and time. In an earlier paper (Stewartson & Stuart 1971) the parabolic differential equation satisfied byAfor two-dimensional disturbances was found; the theory is here extended to three dimensions. Although the coefficients of the equation are coinples, a start is made on elucidating the properties of its solutions by assuming that these coefficients are real. It is then found numerically and confirmed analytically that, for a finite value of (R-Rc)t, the amplitudeAdevelops an infinite peak at the wave centre. The possible relevance of this work to the phenomenon of transition is discussed.

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