A Two-Dimensional Analysis of a Heated Free Jet at Low Reynolds Numbers

1971 ◽  
Vol 93 (3) ◽  
pp. 355-363 ◽  
Author(s):  
S. Krishnan ◽  
L. R. Glicksman
Keyword(s):  
Variable Viscosity ◽  
Fluid Dynamic ◽  
Reynolds Numbers ◽  
Two Dimensional ◽  
Rotating Drum ◽  
Low Reynolds Numbers ◽  
Free Jet ◽  
Approximate Integral ◽  
Jet Behavior ◽  
Flow Through

To spin polymers and glass into continuous fibers, hot molten material is made to flow through a nozzle into air, thus forming a free liquid jet. This cools as it proceeds through the air and the solid fiber is collected on a rotating drum. This maintains a tension on the jet causing it to attenuate as it cools. An approximate integral technique is presented to investigate the relative importance of two-dimensional fluid mechanics for a variable viscosity glass jet in the region of the jet within four to five nozzle diameters of the nozzle exit. The results, when compared with those of an existing analysis based on one-dimensional velocity and temperature profiles, indicate that two-dimensional fluid dynamic effects exert very little influence on the jet shape while small changes in the temperature distribution cause significant changes in the jet behavior. A limited number of experiments performed with a chlorinated polymer provided a very simple and inexpensive means of modeling glass flow and also served to verify the results of the existing analysis over a different range of property values as compared to glass.

The Dynamics of a Heated Free Jet of Variable Viscosity Liquid at Low Reynolds Numbers

1968 ◽  
Vol 90 (3) ◽  
pp. 343-354 ◽  
Author(s):  
L. R. Glicksman
Keyword(s):  
Variable Viscosity ◽  
Reynolds Numbers ◽  
Rotating Drum ◽  
Molten Material ◽  
Low Reynolds Numbers ◽  
One Dimensional ◽  
Tension Distribution ◽  
Free Jet ◽  
Nozzle Temperature ◽  
Good Agreement

To spin polymers or glass into continuous fibers, molten material is forced through a nozzle into air forming a free liquid jet. The jet is cooled as it proceeds through the air and the cold fiber is collected on a rotating drum. The drum maintains tension on the jet causing it to attenuate as it cools. The behavior of a variable viscosity jet of glass was studied analytically and experimentally. In the analysis, it was assumed that the velocity and temperature distributions within the jet were one dimensional. Predictions of the jet shape, the temperature distribution and the tension in the jet as a function of the material properties and the process variables were obtained. Measurements of the jet shape and the tension distribution in the jet were made for various values of the flow rate, the collecting drum speed, and the nozzle temperature. The analytical predictions were found to be in error in the region of the jet within three to four nozzle diameters of the nozzle exit; below this point the theoretical and experimental results were in good agreement.

Cellular flow in a partially filled rotating drum: regular and chaotic advection

2017 ◽  
Vol 825 ◽  
pp. 631-650 ◽  
Author(s):  
Francesco Romanò ◽  
Arash Hajisharifi ◽  
Hendrik C. Kuhlmann
Keyword(s):  
Three Dimensional ◽  
Reynolds Numbers ◽  
Chaotic Advection ◽  
Two Dimensional ◽  
Rotating Drum ◽  
Three Dimensional Flow ◽  
Dimensional Flow ◽  
Heteroclinic Connection ◽  
Two Dimensional Flow ◽  
Chaotic Streamlines

The topology of the incompressible steady three-dimensional flow in a partially filled cylindrical rotating drum, infinitely extended along its axis, is investigated numerically for a ratio of pool depth to radius of 0.2. In the limit of vanishing Froude and capillary numbers, the liquid–gas interface remains flat and the two-dimensional flow becomes unstable to steady three-dimensional convection cells. The Lagrangian transport in the cellular flow is organised by periodic spiralling-in and spiralling-out saddle foci, and by saddle limit cycles. Chaotic advection is caused by a breakup of a degenerate heteroclinic connection between the two saddle foci when the flow becomes three-dimensional. On increasing the Reynolds number, chaotic streamlines invade the cells from the cell boundary and from the interior along the broken heteroclinic connection. This trend is made evident by computing the Kolmogorov–Arnold–Moser tori for five supercritical Reynolds numbers.

scholarly journals Force and flowfield measurements to understand unsteady aerodynamics of cycloidal rotors in hover at ultra-low Reynolds numbers

2019 ◽  
Vol 11 ◽  
pp. 175682931983367
Author(s):  
Carolyn M Reed ◽  
David A Coleman ◽  
Moble Benedict
Keyword(s):  
Separation Bubble ◽  
Fluid Dynamic ◽  
Unsteady Aerodynamics ◽  
Leading Edge ◽  
Reynolds Numbers ◽  
Dynamic Stall ◽  
Static Case ◽  
Low Reynolds Numbers ◽  
Curvature Effects ◽  
Low Reynolds

This paper provides a fundamental understanding of the unsteady fluid-dynamic phenomena on a cycloidal rotor blade operating at ultra-low Reynolds numbers (Re ∼ 18,000) by utilizing a combination of instantaneous blade force and flowfield measurements. The dynamic blade force coefficients were almost double the static ones, indicating the role of dynamic stall. For the dynamic case, the blade lift monotonically increased up to ±45° pitch amplitude; however, for the static case, the flow separated from the leading edge after around 15° with a large laminar separation bubble. There was significant asymmetry in the lift and drag coefficients between the upper and lower halves of the trajectory due to the flow curvature effects (virtual camber). The particle image velocimetry measured flowfield showed the dynamic stall process during the upper half to be significantly different from the lower half because of the reversal of dynamic virtual camber. Even at such low Reynolds numbers, the pressure forces, as opposed to viscous forces, were found to be dominant on the cyclorotor blade. The power required for rotation (rather than pitching power) dominated the total blade power.

Two-Dimensional Unsteady Viscous Flows

2017 ◽  
Author(s):  
Jian-Jun Shu
Keyword(s):  
Circular Cylinder ◽  
Flow Field ◽  
Hydrodynamic Force ◽  
Viscous Flows ◽  
Reynolds Numbers ◽  
Fundamental Solutions ◽  
Time Dependent ◽  
Two Dimensional ◽  
Low Reynolds Numbers ◽  
Rotational Motions

A number of new closed-form fundamental solutions for the two-dimensional generalized unsteady Oseen and Stokes flows associated with arbitrary time-dependent translational and rotational motions have been developed. As an example of application, the hydrodynamic force acting on a circular cylinder translating in an unsteady flow field at low Reynolds numbers is calculated using the new generalized fundamental solutions.

Effects of the Divergence Angle on the Onset of Asymmetric Flow Through a Planar Diffuser

2009 ◽  
Author(s):  
Majid Nabavi ◽  
Luc Mongeau
Keyword(s):  
Reynolds Number ◽  
Flow Regime ◽  
Critical Reynolds Number ◽  
Reynolds Numbers ◽  
Two Dimensional ◽  
Asymmetric Flow ◽  
Symmetric Flow ◽  
Turbulent Flow Regime ◽  
Flow Through ◽  
Gradual Expansion

In this study, two-dimensional laminar incompressible and turbulent compressible flow through the planar diffuser (gradual expansion) for different divergence half angles of the diffuser (θ), and different Reynolds numbers (Re) was numerically studied. The effects of θ on the critical Reynolds number at which the onset of asymmetric flow is observed, were investigated. In the laminar flow regime, it was observed that for every values of θ, there is a critical Re beyond which the flow is asymmetric. However, in the turbulent flow regime, for θ ≥ 20°, even at low Reynolds number the flow is asymmetric. Only for θ ≤ 10°, symmetric flow was observed below a critical Re.

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