Trajectory and flow properties for a rod spinning in a viscous fluid. Part 1. An exact solution

2008 ◽  
Vol 612 ◽  
pp. 153-200 ◽  
Author(s):  
ROBERTO CAMASSA ◽  
TERRY JO LEITERMAN ◽  
RICHARD M. MCLAUGHLIN
Keyword(s):  
High Speed ◽  
Cone Angle ◽  
Fluid Motion ◽  
Three Dimensional ◽  
Prolate Spheroid ◽  
Laboratory Frame ◽  
Flow Properties ◽  
Nano Scale ◽  
Hydrodynamic Solution ◽  
Recent Developments

An exact mathematical solution for the low-Reynolds-number quasi-steady hydrodynamic motion induced by a rod in the form of a prolate spheroid sweeping a symmetric double cone is developed, and the influence of the ensuing fluid motion upon passive particles is studied. The resulting fluid motion is fully three-dimensional and time varying. The advected particles are observed to admit slow orbits around the rotating rods and a fast epicyclic motion roughly commensurate with the rod rotation rate. The epicycle amplitudes, vertical fluctuations, arclengths and angle travelled per rotation are mapped as functions of their initial coordinates and rod geometry. These trajectories exhibit a rich spatial structure with greatly varying trajectory properties. Laboratory frame asymmetries of these properties are explored using integer time Poincaré sections and far-field asymptotic analysis. This includes finding a small cone angle invariant in the limit of large spherical radius whereas an invariant for arbitrary cone angles is obtained in the limit of large cylindrical radius. The Eulerian and Lagrangian flow properties of the fluid flow are studied and shown to exhibit complex structures in both space and time. In particular, spatial regions of high speed and Lagrangian velocities possessing multiple extrema per rod rotation are observed. We establish the origin of these complexities via an auxiliary flow in a rotating frame, which provides a generator that defines the epicycles. Finally, an additional spin around the major spheroidal axis is included in the exact hydrodynamic solution resulting in enhanced vertical spatial fluctuation as compared to the spinless counterpart. The connection and relevance of these observations with recent developments in nano-scale fluidics is discussed, where similar epicycle behaviour has been observed. The present study is of direct use to nano-scale actuated fluidics.

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.

scholarly journals Volumetric quantification of fluid flow reveals fish's use of hydrodynamic stealth to capture evasive prey

2014 ◽  
Vol 11 (90) ◽  
pp. 20130880 ◽  
Author(s):  
Brad J. Gemmell ◽  
Deepak Adhikari ◽  
Ellen K. Longmire
Keyword(s):  
High Speed ◽  
Prey Capture ◽  
Fluid Motion ◽  
Three Dimensional ◽  
Trophic Levels ◽  
Small Fish ◽  
Major Pathway ◽  
Image Velocimetry ◽  
Highly Sensitive ◽  
Volumetric Quantification

In aquatic ecosystems, predation on zooplankton by fish provides a major pathway for the transfer of energy to higher trophic levels. Copepods are an abundant zooplankton group that sense hydromechanical disturbances produced by approaching predators and respond with rapid escapes. Despite this capability, fish capture copepods with high success. Previous studies have focused on the predatory strike to elucidate details of this interaction. However, these raptorial strikes and resulting suction are only effective at short range. Thus, small fish must closely approach highly sensitive prey without triggering an escape in order for a strike to be successful. We use a new method, high-speed, infrared, tomographic particle image velocimetry, to investigate three-dimensional fluid patterns around predator and prey during approaches. Our results show that at least one planktivorous fish ( Danio rerio ) can control the bow wave in front of the head during the approach and consumption of prey (copepod). This alters hydrodynamic profiles at the location of the copepod such that it is below the threshold required to elicit an escape response. We find this behaviour to be mediated by the generation of suction within the buccopharyngeal cavity, where the velocity into the mouth roughly matches the forward speed of the fish. These results provide insight into how animals modulate aspects of fluid motion around their bodies to overcome escape responses and enhance prey capture.

Ship Motion Computations Using a High Froude Number Time Domain Strip Theory

2006 ◽  
Vol 50 (01) ◽  
pp. 15-30
Author(s):  
D. S. Holloway ◽  
M. R. Davis
Keyword(s):  
Froude Number ◽  
Time Domain ◽  
High Speed ◽  
Equations Of Motion ◽  
Fluid Motion ◽  
Three Dimensional ◽  
Viscous Effects ◽  
Strip Theory ◽  
Large Amplitude Motions ◽  
The Time Domain

High-speed strip theories are discussed, and a time domain formulation making use of a fixed reference frame for the two-dimensional fluid motion is described in detail. This, and classical (low-speed) strip theory, are compared with the experimental results of Wellicome et al. (1995) up to a Froude number of 0.8, as well as with our own test data for a semi-SWATH, demonstrating the marked improvement of the predictions of the former at high speeds, while the need to account for modest viscous effects at these speeds is also argued. A significant contribution to time domain computations is a method of stabilizing the integration of the ship's equations of motion, which are inherently unstable due to feedback from implicit added mass components of the hydrodynamic force. The time domain high-speed theory is recommended as a practical alternative to three-dimensional methods. It also facilitates the investigation of large-amplitude motions with stern or bow emergence and forms a simulation base for the investigation of ride control systems and local or global loads.

scholarly journals Propulsive design principles in a multi-jet siphonophore

2018 ◽  
Author(s):  
Kelly R. Sutherland ◽  
Sean P. Colin ◽  
John H. Costello ◽  
Brad J. Gemmell
Keyword(s):  
High Speed ◽  
Swimming Performance ◽  
Dimensional Space ◽  
Fluid Motion ◽  
Three Dimensional ◽  
Flow Parameters ◽  
Image Velocimetry ◽  
Summary Statement ◽  
High Pressure Region ◽  
Three Dimensional Space

AbstractCoordination of multiple propulsors can provide performance benefits in swimming organisms. Siphonophores are marine colonial organisms that orchestrate the motion of multiple swimming zooids for effective swimming. However, the kinematics at the level of individual swimming zooids (nectophores) have not been examined in detail. We used high speed, high resolution microvideography and particle image velocimetry (PIV) of the physonect siphonophore, Nanomia bijuga, to study the motion of the nectophores and the associated fluid motion during jetting and refilling. The integration of nectophore and velum kinematics allow for a high-speed (maximum ~1 m s−1), narrow (1-2 mm) jet and rapid refill as well as a 1:1 ratio of jetting to refill time. Overall swimming performance is enhanced by velocity gradients produced in the nectophore during refill, which lead to a high pressure region that produces forward thrust. Generating thrust during both the jet and refill phases augments the distance travelled by 17% over theoretical animals, which generate thrust only during the jet phase. The details of velum kinematics and associated fluid mechanics elucidate how siphonophores effectively navigate three-dimensional space and could be applied to exit flow parameters in multijet underwater vehicles.Summary statement:Colonial siphonophores produce high speed jets and generate forward thrust during refill using a flexible velum to achieve effective propulsion.

scholarly journals Splash-cup plants accelerate raindrops to disperse seeds

2013 ◽  
Vol 10 (79) ◽  
pp. 20120880 ◽  
Author(s):  
Guillermo J. Amador ◽  
Yasukuni Yamada ◽  
Matthew McCurley ◽  
David L. Hu
Keyword(s):  
High Speed ◽  
Cone Angle ◽  
Three Dimensional ◽  
Dispersal Distance ◽  
Optimal Angle ◽  
Three Dimensional Printing ◽  
A Value ◽  
Dispersal Distances ◽  
Drop Impacts ◽  
Dimensional Printing

The conical flowers of splash-cup plants Chrysosplenium and Mazus catch raindrops opportunistically, exploiting the subsequent splash to disperse their seeds. In this combined experimental and theoretical study, we elucidate their mechanism for maximizing dispersal distance. We fabricate conical plant mimics using three-dimensional printing, and use high-speed video to visualize splash profiles and seed travel distance. Drop impacts that strike the cup off-centre achieve the largest dispersal distances of up to 1 m. Such distances are achieved because splash speeds are three to five times faster than incoming drop speeds, and so faster than the traditionally studied splashes occurring upon horizontal surfaces. This anomalous splash speed is because of the superposition of two components of momentum, one associated with a component of the drop's motion parallel to the splash-cup surface, and the other associated with film spreading induced by impact with the splash-cup. Our model incorporating these effects predicts the observed dispersal distance within 6–18% error. According to our experiments, the optimal cone angle for the splash-cup is 40°, a value consistent with the average of five species of splash-cup plants. This optimal angle arises from the competing effects of velocity amplification and projectile launching angle.

High-speed brightfield 3-D imaging and 3-D image analysis of thick and overlapped cell clusters in cytological preparations

1994 ◽  
Vol 52 ◽  
pp. 218-219
Author(s):  
Robert W. Mackin
Keyword(s):  
Image Analysis ◽  
High Speed ◽  
Three Dimensional ◽  
Image Data ◽  
Ccd Camera ◽  
Objective Lens ◽  
Array Processor ◽  
Vaginal Smears ◽  
Low Contrast ◽  
Computer Controlled

This paper presents two advances towards the automated three-dimensional (3-D) analysis of thick and heavily-overlapped regions in cytological preparations such as cervical/vaginal smears. First, a high speed 3-D brightfield microscope has been developed, allowing the acquisition of image data at speeds approaching 30 optical slices per second. Second, algorithms have been developed to detect and segment nuclei in spite of the extremely high image variability and low contrast typical of such regions. The analysis of such regions is inherently a 3-D problem that cannot be solved reliably with conventional 2-D imaging and image analysis methods.High-Speed 3-D imaging of the specimen is accomplished by moving the specimen axially relative to the objective lens of a standard microscope (Zeiss) at a speed of 30 steps per second, where the stepsize is adjustable from 0.2 - 5μm. The specimen is mounted on a computer-controlled, piezoelectric microstage (Burleigh PZS-100, 68/μm displacement). At each step, an optical slice is acquired using a CCD camera (SONY XC-11/71 IP, Dalsa CA-D1-0256, and CA-D2-0512 have been used) connected to a 4-node array processor system based on the Intel i860 chip.

Effects of Three-Dimensional Pressure Gradients on High-Speed Turbulent Boundary Layers

2021 ◽  
Author(s):  
Scott J. Peltier ◽  
Brian E. Rice ◽  
Ethan Johnson ◽  
Venkateswaran Narayanaswamy ◽  
Marvin E. Sellers
Keyword(s):  
Boundary Layers ◽  
High Speed ◽  
Three Dimensional ◽  
Turbulent Boundary Layers ◽  
Pressure Gradients

EXPERIMENTAL INVESTIGATION OF FLOW RESPONSE TO STATIONARY DISTURBANCE IN ROTATING-DISK FLOW

2019 ◽  
Vol XVI (2) ◽  
pp. 13-22
Author(s):  
Muhammad Ehtisham Siddiqui
Keyword(s):  
Boundary Layer ◽  
Boundary Layer Flow ◽  
Three Dimensional ◽  
Rotating Disk ◽  
Careful Analysis ◽  
Laboratory Frame ◽  
Transition To Turbulence ◽  
Turbulent Regime ◽  
Mean Velocity ◽  
Layer Flow

Three-dimensional boundary-layer flow is well known for its abrupt and sharp transition from laminar to turbulent regime. The presented study is a first attempt to achieve the target of delaying the natural transition to turbulence. The behaviour of two different shaped and sized stationary disturbances (in the laboratory frame) on the rotating-disk boundary layer flow is investigated. These disturbances are placed at dimensionless radial location (Rf = 340) which lies within the convectively unstable zone over a rotating-disk. Mean velocity profiles were measured using constant-temperature hot-wire anemometry. By careful analysis of experimental data, the instability of these disturbance wakes and its estimated orientation within the boundary-layer were investigated.

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