scholarly journals Temporal stability of free liquid threads with surface viscoelasticity

2018 ◽  
Vol 846 ◽  
pp. 877-901 ◽  
Author(s):  
A. Martínez-Calvo ◽  
A. Sevilla
Keyword(s):  
Reynolds Number ◽  
Equations Of Motion ◽  
Temporal Stability ◽  
Reynolds Numbers ◽  
Elasticity Parameter ◽  
Insoluble Surfactant ◽  
Stress Boundary Conditions ◽  
Stress Boundary ◽  
Maximum Amplification ◽  
Effect Of Surface

We analyse the effect of surface viscoelasticity on the temporal stability of a free cylindrical liquid jet coated with insoluble surfactant, extending the results of Timmermans & Lister (J. Fluid Mech., vol. 459, 2002, pp. 289–306). Our development requires, in particular, deriving the correct expressions for the normal and tangential stress boundary conditions at a general axisymmetric interface when surface viscosity is modelled with the Boussinesq–Scriven constitutive equation. These stress conditions are applied to obtain a new dispersion relation for the liquid thread, which is solved to describe its temporal stability as a function of four governing parameters, namely the capillary Reynolds number, the elasticity parameter, and the shear and dilatational Boussinesq numbers. It is shown that both surface viscosities have a stabilising influence for all values of the capillary Reynolds number and elasticity parameter, the effect being more pronounced at low capillary Reynolds numbers. The wavenumber of maximum amplification depends non-monotonically on the Boussinesq numbers, especially for very viscous threads at low values of the elasticity parameter. Finally, two different lubrication approximations of the equations of motion are derived. While the validity of the leading-order model is limited to small enough values of the elasticity parameter and of the Boussinesq numbers, a higher-order parabolic model is able to accurately capture the linearised behaviour for the whole range of values of the four control parameters.

Effect of Surface Roughness on Gaseous Flow Through Microchannels

2000 ◽  
Author(s):  
Stephen E. Turner ◽  
Hongwei Sun ◽  
Mohammad Faghri ◽  
Otto J. Gregory
Keyword(s):  
Surface Roughness ◽  
Reynolds Number ◽  
Friction Factor ◽  
Reynolds Numbers ◽  
Helium Flow ◽  
Local Pressure ◽  
Aspect Ratios ◽  
Corrugated Surfaces ◽  
Flow Through ◽  
Effect Of Surface

Abstract This paper presents an experimental investigation on nitrogen and helium flow through microchannels etched in silicon with hydraulic diameters between 10 and 40 microns, and Reynolds numbers ranging from 0.3 to 600. The objectives of this research are (1) to fabricate microchannels with uniform surface roughness and local pressure measurement; (2) to determine the friction factor within the locally fully developed region of the microchannel; and (3) to evaluate the effect of surface roughness on momentum transfer by comparison with smooth microchannels. The friction factor results are presented as the product of friction factor and Reynolds number plotted against Reynolds number. The following conclusions have been reached in the present investigation: (1) microchannels with uniform corrugated surfaces can be fabricated using standard photolithographic processes; and (2) surface features with low aspect ratios of height to width have little effect on the friction factor for laminar flow in microchannels.

Flow about a fluid sphere at low to moderate Reynolds numbers

1987 ◽  
Vol 177 ◽  
pp. 1-18 ◽  
Author(s):  
D. L. R. Oliver ◽  
J. N. Chung
Keyword(s):  
Reynolds Number ◽  
Equations Of Motion ◽  
Reynolds Numbers ◽  
Solid Sphere ◽  
Fluid Sphere ◽  
State Equations ◽  
Drag Coefficients ◽  
Low Reynolds Number Flows ◽  
Analytical Series ◽  
Reynolds Number Flows

The steady-state equations of motion are solved for a fluid sphere translating in a quiescent medium. A semi-analytical series truncation method is employed in conjunction with a cubic finite-element scheme. The range of Reynolds numbers investigated is from 0.5 to 50. The range of viscosity ratios is from 0 (gas bubble) to 107 (solid sphere). The flow structure and the drag coefficients agree closely with the limited available experimental measurements and also compare favourably with published finite-difference solutions. The strength of the internal circulation was found to increase with increasing Reynolds number. The flow patterns and the drag coefficient show little variation with the interior Reynolds number. Based on the numerical results, predictive equations for drag coefficients are recommended for both moderate- and low-Reynolds-number flows.

An almost-inviscid geostrophic flow

1962 ◽  
Vol 12 (1) ◽  
pp. 129-134 ◽  
Author(s):  
L. M. Hocking
Keyword(s):  
Reynolds Number ◽  
Fluid Velocity ◽  
Equations Of Motion ◽  
Axial Direction ◽  
Reynolds Numbers ◽  
Rigid Rotation ◽  
Velocity Variation ◽  
Geostrophic Flow ◽  
The Difference ◽  
Streaming Motion

An almost rigid rotation of a viscous fluid is produced by dividing the containing cylinder into two sections and rotating them at slightly different speeds. The fluid velocity can be separated into two parts, a swirl about the axis and a streaming motion in the axial planes. When the difference in the speeds of rotation of the two sections is small, the equations of motion can be linearized. The solution is found for large Reynolds numbers and provides an illustration of the way in which the conditions of geostrophic flow (no velocity variation in the axial direction and an inability to insist on undistrubed flow at infinity) are approached as the Reynolds number tends to infinity.

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.

Numerical solutions for steady flow past a circular cylinder at Reynolds numbers up to 100

1970 ◽  
Vol 42 (3) ◽  
pp. 471-489 ◽  
Author(s):  
S. C. R. Dennis ◽  
Gau-Zu Chang
Keyword(s):  
Reynolds Number ◽  
Circular Cylinder ◽  
Steady Flow ◽  
Numerical Solutions ◽  
Equations Of Motion ◽  
Reynolds Numbers ◽  
Reliable Data ◽  
Time Dependent ◽  
Cylinder Surface ◽  
Number Range

Finite-difference solutions of the equations of motion for steady incompressible flow around a circular cylinder have been obtained for a range of Reynolds numbers from R = 5 to R = 100. The object is to extend the Reynolds number range for reliable data on the steady flow, particularly with regard to the growth of the wake. The wake length is found to increase approximately linearly with R over the whole range from the value, just below R = 7, at which it first appears. Calculated values of the drag coefficient, the angle of separation, and the pressure and vorticity distributions over the cylinder surface are presented. The development of these properties with Reynolds number is consistent, but it does not seem possible to predict with any certainty their tendency as R → ∞. The first attempt to obtain the present results was made by integrating the time-dependent equations, but the approach to steady flow was so slow at higher Reynolds numbers that the method was abandoned.

Flow Interaction With Composite Wall

2006 ◽  
Author(s):  
Mahmoud Hamadiche ◽  
Natalya Kizilova
Keyword(s):  
Boundary Conditions ◽  
Temporal Stability ◽  
Fluid Flows ◽  
Displacement Boundary ◽  
Material Parameters ◽  
Amplification Rate ◽  
Eigen Values ◽  
Stress Boundary Conditions ◽  
The Comparative Study ◽  
Stress Boundary

Stability of the steady flow of a viscous liquid through the thick-walled multilayered viscoelastic tubes with different rheological properties of the layers for no stress boundary conditions at the outer surface of the tube is investigated. The eigen values of the system are found. The influence of the material parameters of the layers and the Reynolds number on the spatial and temporal amplification rate of the most unstable mode is investigated. It is shown that the system can be stabilized by increasing the shear modules of the inner and middle layers. The temporal amplification rate significantly decreases and becomes negative with increasing the shear modules of the outer layer, that corresponds to temporal stability of the system. The comparative study of the obtained dependences with the solution of the same problem at no displacement boundary conditions is carried out. The results may be applied to the fluid flows in the ducts of different technical devices as well as to the blood flow in the arteries and veins which are composed of three layers with different functions, structure and material parameters.

Temporal stability of Jeffery–Hamel flow

1994 ◽  
Vol 268 ◽  
pp. 71-88 ◽  
Author(s):  
Mahmoud Hamadiche ◽  
Julian Scott ◽  
Denis Jeandel
Keyword(s):  
Reynolds Number ◽  
Critical Reynolds Number ◽  
Temporal Stability ◽  
Reynolds Numbers ◽  
Critical Value ◽  
Volume Flux ◽  
Short Channel ◽  
Oscillatory Solutions ◽  
Half Angle ◽  
Critical Reynolds Numbers

In this study of the temporal stability of Jeffery–Hamel flow, the critical Reynolds number based on the volume flux, Rc, and that based on the axial velocity, Rec, are computed. It is found that both critical Reynolds numbers decrease very rapidly when the half-angle of the channel, α, increases, such that the quantity αRc remains very nearly constant and αRecis a nearly linear function of α. For a short channel there can be more than one value of the critical Reynolds number. A fully nonlinear analysis, for Re close to the critical value, indicates that the loss of stability is supercritical. The resulting asymmetric oscillatory solutions show staggered arrays of vortices positioned along the channel.

Calculation of incompressible flow past a circular cylinder at moderate Reynolds numbers

1969 ◽  
Vol 37 (1) ◽  
pp. 95-114 ◽  
Author(s):  
Robert Leigh Underwood
Keyword(s):  
Reynolds Number ◽  
Circular Cylinder ◽  
Differential Equations ◽  
Incompressible Flow ◽  
Equations Of Motion ◽  
Pressure Coefficient ◽  
Reynolds Numbers ◽  
Number Range ◽  
Flow Parameters ◽  
Flow Past

The steady, two-dimensional, incompressible flow past a circular cylinder is calculated for Reynolds numbers up to ten. An accurate description of the flow field is found by employing the semi-analytical method of series truncation to reduce the governing partial differential equations of motion to a system of ordinary differential equations which can be integrated numerically. Results are given for Reynolds numbers between 0.4 and 10.0 (based on diameter). The Reynolds number at which separation first occurs behind the cylinder is found to be 5.75. Over the entire Reynolds number range investigated, characteristic flow parameters such as the drag coefficient, pressure coefficient, standing eddy length, and streamline pattern compare favourably with available experimental data and numerical solution results.

Numerical Simulation of Aerodynamic Performance of Film Cooling on a Flat Plate with Surface Roughness

2013 ◽  
Vol 853 ◽  
pp. 576-581
Author(s):  
Jian Fei Wang ◽  
Yong Bin Ji ◽  
Shu Sheng Zang
Keyword(s):  
Numerical Simulation ◽  
Surface Roughness ◽  
Reynolds Number ◽  
Flat Plate ◽  
Film Cooling ◽  
Reynolds Numbers ◽  
Skin Friction Coefficient ◽  
Roughness Effect ◽  
Blowing Ratio ◽  
Effect Of Surface

This study is aimed at researching surface roughness effect on the performance of blades in terms of aerodynamics. Numerical simulation on a rough flat plate with a row of 35°round film holes under different roughness heights, Reynolds numbers and blowing ratios is conducted to see how they affect film cooling on a flat plate. In terms of aerodynamics, the increase of surface roughness height, Reynolds number and blow ratio will result in the increase of skin friction coefficient. Besides, roughness has combined effects with Reynolds number and blowing ratio So the effect of surface roughness on blades performance is too big to ignore.

Similarity Parameters for Comparing Erosive Particle Trajectories in Hot Air and Cold Air Radial Inflow Turbines

1974 ◽  
Vol 96 (4) ◽  
pp. 358-364 ◽  
Author(s):  
W. B. Clevenger ◽  
W. Tabakoff
Keyword(s):  
Reynolds Number ◽  
Equations Of Motion ◽  
Reynolds Numbers ◽  
Gas Flows ◽  
Particle Trajectories ◽  
Cold Air ◽  
Hot Gas ◽  
Hot Air ◽  
Radial Turbine ◽  
Cold Gas

The similarity parameters that can be used to relate erosive particle trajectories in hot gas and equivalent cold gas flows are derived from the equations of motion. The flow in a radial turbine is used as the basis for studying the range of applicability of these similarity parameters. The study includes the vortex and rotor regions of the radial turbine and indicates the ranges of Reynolds number within which these parameters can be used. In addition, the study shows that when general trends of particle trajectories are to be considered, and precise trajectories are not necessary, one of the similarity parameters can be used for Reynolds numbers that are not within the limits indicated for precisely similar trajectories.

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