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.

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 steady flow due to a rotating sphere at low and moderate Reynolds numbers

1980 ◽  
Vol 101 (2) ◽  
pp. 257-279 ◽  
Author(s):  
S. C. R. Dennis ◽  
S. N. Singh ◽  
D. B. Ingham
Keyword(s):  
Reynolds Number ◽  
Numerical Solutions ◽  
Equations Of Motion ◽  
Reynolds Numbers ◽  
Low Reynolds Numbers ◽  
Finite Set ◽  
Flow Variables ◽  
Theoretical Results ◽  
Radial Variable ◽  
Good Agreement

The problem of determining the steady axially symmetrical motion induced by a sphere rotating with constant angular velocity about a diameter in an incompressible viscous fluid which is at rest at large distances from it is considered. The basic independent variables are the polar co-ordinates (r, θ) in a plane through the axis of rotation and with origin at the centre of the sphere. The equations of motion are reduced to three sets of nonlinear second-order ordinary differential equations in the radial variable by expanding the flow variables as series of orthogonal Gegenbauer functions with argument μ = cosθ. Numerical solutions of the finite set of equations obtained by truncating the series after a given number of terms are obtained. The calculations are carried out for Reynolds numbers in the range R = 1 to R = 100, and the results are compared with various other theoretical results and with experimental observations.The torque exerted by the fluid on the sphere is found to be in good agreement with theory at low Reynolds numbers and appears to tend towards the results of steady boundary-layer theory for increasing Reynolds number. There is excellent agreement with experimental results over the range considered. A region of inflow to the sphere near the poles is balanced by a region of outflow near the equator and as the Reynolds number increases the inflow region increases and the region of outflow becomes narrower. The radial velocity increases with Reynolds number at the equator, indicating the formation of a radial jet over the narrowing region of outflow. There is no evidence of any separation of the flow from the surface of the sphere near the equator over the range of Reynolds numbers considered.

A Theory of Sharp-Edged Orifices

1937 ◽  
Vol 4 (2) ◽  
pp. A53-A54
Author(s):  
W. E. Howland
Keyword(s):  
Experimental Data ◽  
Reynolds Number ◽  
Discharge Coefficient ◽  
Reynolds Numbers ◽  
Experimental Results ◽  
Low Reynolds Numbers ◽  
Circular Orifice ◽  
Coefficient Of Discharge ◽  
Theoretical Considerations ◽  
Good Agreement

Abstract The author presents a figure in which the coefficient of discharge Cd, velocity Cv, and contraction Cc determined by several investigators are plotted logarithmically as points against Reynolds’ numbers. Curves for the coefficients drawn by the author, based on theoretical considerations, show good agreement with the experimental data, thus throwing some light upon the basic phenomena of the discharge of sharp-edged orifices. The variation of the coefficient of discharge of a circular orifice as a function of the Reynolds number is explained as a purely viscous phenomenon for low Reynolds numbers, and by means of a momentum analysis for higher speeds. The analysis presented by the author leads to the development of several formulas for the discharge coefficient, which formulas are in fair agreement with experimental results.

Vortex-induced instabilities and accelerated collapse due to inertial effects of density stratification

2010 ◽  
Vol 646 ◽  
pp. 415-439 ◽  
Author(s):  
HARISH N DIXIT ◽  
RAMA GOVINDARAJAN
Keyword(s):  
Reynolds Number ◽  
Stability Analysis ◽  
Reynolds Numbers ◽  
Passive Scalar ◽  
Density Stratification ◽  
Low Reynolds Numbers ◽  
Density Interface ◽  
Lower Reynolds Number ◽  
Number Flow ◽  
Good Agreement

A vortex placed at a density interface winds it into an ever-tighter spiral. We show that this results in a combination of a centrifugal Rayleigh–Taylor (CRT) instability and a spiral Kelvin–Helmholtz (SKH) type of instability. The SKH instability arises because the density interface is not exactly circular, and dominates at large times. Our analytical study of an inviscid idealized problem illustrates the origin and nature of the instabilities. In particular, the SKH is shown to grow slightly faster than exponentially. The predicted form lends itself for checking by a large computation. From a viscous stability analysis using a finite-cored vortex, it is found that the dominant azimuthal wavenumber is smaller for lower Reynolds number. At higher Reynolds numbers, disturbances subject to the combined CRT and SKH instabilities grow rapidly, on the inertial time scale, while the flow stabilizes at low Reynolds numbers. Our direct numerical simulations are in good agreement with these studies in the initial stages, after which nonlinearities take over. At Atwood numbers of 0.1 or more, and a Reynolds number of 6000 or greater, both stability analysis and simulations show a rapid destabilization. The result is an erosion of the core, and breakdown into a turbulence-like state. In studies at low Atwood numbers, the effect of density on the inertial terms is often ignored, and the density field behaves like a passive scalar in the absence of gravity. The present study shows that such treatment is unjustified in the vicinity of a vortex, even for small changes in density when the density stratification is across a thin layer. The study would have relevance to any high-Péclet-number flow where a vortex is in the vicinity of a density-stratified interface.

The plane Symmetric sudden-expansion flow at low Reynolds numbers

1993 ◽  
Vol 248 ◽  
pp. 567-581 ◽  
Author(s):  
F. Durst ◽  
J. C. F. Pereira ◽  
C. Tropea
Keyword(s):  
Maximum Flow ◽  
Reynolds Numbers ◽  
Sudden Expansion ◽  
Channel Height ◽  
Low Reynolds Numbers ◽  
Plane Symmetric ◽  
Numerical Predictions ◽  
Flow Through ◽  
Volume Method ◽  
Good Agreement

Detailed velocity measurements and numerical predictions are presented for the flow through a plane nominally two-dimensional duct with a Symmetric sudden expansion of area ratio 1:2. Both the experiments and the predictions confirm a symmetry-breaking bifurcation of the flow leading to one long and one short Separation zone for channel Reynolds numbers above 125, based on the upstream channel height and the maximum flow velocity upstream. With increasing Reynolds numbers above this value, the short separated region remains approximately constant in length whereas the long region increases in length.The experimental data were obtained using a one-component laser-Doppler anemometer at many Reynolds number values, with more extensive measurements being performed for the three Reynolds numbers 70, 300 and 610. Predictions were made using a finite volume method and an explicit quadratic Leith type of temporal discretization. In general, good agreement was found between measured and predicted velocity profiles for all Reynolds numbers investigated.

An Alternative Analysis of the Plane Stick-Slip Problem

1983 ◽  
Vol 50 (4a) ◽  
pp. 863-868 ◽  
Author(s):  
A. Dutta
Keyword(s):  
Reynolds Numbers ◽  
Exit Plane ◽  
Alternative Analysis ◽  
Variable Technique ◽  
Stick Slip ◽  
Low Reynolds Numbers ◽  
Mathematical Procedure ◽  
Present Solution ◽  
Separation Of Variable ◽  
Good Agreement

The plane stick-slip problem has been solved analytically using the separation of variable technique. The essence of the mathematical procedure is to solve the problem separately for the “stick” and the “slip” regions and then to match the two solutions at the exit plane. The present solution, which is relatively easy to evaluate, yields results that compare favorably with those obtained by the Wiener-Hopf technique. Furthermore, the stick-slip solution has been used to estimate the expansion of a two-dimensional plane Newtonian jet at very low Reynolds numbers. For capillary numbers less than 0.1, the approximate method predicts swell ratios that are in fairly good agreement with those obtained from a more elaborate numerical solution of the jet swell problem.

Numerical Solutions of Viscous Flow through a Pipe Orifice at Low Reynolds Numbers

1968 ◽  
Vol 10 (2) ◽  
pp. 133-140 ◽  
Author(s):  
R. D. Mills
Keyword(s):  
Numerical Solutions ◽  
Stokes Equations ◽  
Viscous Incompressible Fluid ◽  
Reynolds Numbers ◽  
Navier Stokes ◽  
Axially Symmetric ◽  
Navier Stokes Equations ◽  
Low Reynolds Numbers ◽  
Flow Through ◽  
Good Agreement

Numerical solutions of the Navier-Stokes equations have been obtained in the low range of Reynolds numbers for steady, axially symmetric, viscous, incompressible fluid flow through an orifice in a circular pipe with a fixed orifice/pipe diameter ratio. Streamline patterns and vorticity contours are presented as functions of Reynolds number. The theoretically determined discharge coefficients are in good agreement with experimental results of Johansen (2).

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