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.

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.

scholarly journals Aerodynamics of Flapping Wing at Low Reynolds Numbers: Force Measurement and Flow Visualization

2011 ◽  
Vol 2011 ◽  
pp. 1-8 ◽  
Author(s):  
Abhijit Banerjee ◽  
Saurav K. Ghosh ◽  
Debopam Das
Keyword(s):  
Reynolds Number ◽  
Flow Field ◽  
Flow Visualization ◽  
Force Measurement ◽  
Reynolds Numbers ◽  
Flapping Flight ◽  
Water Tank ◽  
Cross Sectional ◽  
Piv Measurement ◽  
The Difference

Flow field of a butterfly mimicking flapping model with plan form of various shapes and butterfly-shaped wings is studied. The nature of the unsteady flow and embedded vortical structures are obtained at chord cross-sectional plane of the scaled wings to understand the dynamics of insect flapping flight. Flow visualization and PIV experiments are carried out for the better understanding of the flow field. The model being studied has a single degree of freedom of flapping. The wing flexibility adds another degree to a certain extent introducing feathering effect in the kinematics. The mechanisms that produce high lift and considerable thrust during the flapping motion are identified. The effect of the Reynolds number on the flapping flight is studied by varying the wing size and the flapping frequency. Force measurements are carried out to study the variations of lift forces in the Reynolds number (Re) range of 3000 to 7000. Force experiments are conducted both at zero and finite forward velocity in a wind tunnel. Flow visualization as well as PIV measurement is conducted only at zero forward velocity in a stagnant water tank and in air, respectively. The aim here is to measure the aerodynamic lift force and visualize the flow field and notice the difference with different Reynolds number (Re), and flapping frequency (f), and advance ratios (J=U∞/2ϕfR).

Pulsatile Blood Flow in a Channel of Small Exponential Divergence—I. The Linear Approximation for Low Mean Reynolds Number

1975 ◽  
Vol 97 (3) ◽  
pp. 353-360 ◽  
Author(s):  
D. J. Schneck ◽  
Simon Ostrach
Keyword(s):  
Reynolds Number ◽  
Vascular Endothelium ◽  
Coronary Circulation ◽  
Viscous Incompressible Fluid ◽  
Axial Direction ◽  
Reynolds Numbers ◽  
Pulsatile Blood Flow ◽  
Viscous Effects ◽  
Radial Velocity Component ◽  
Phase Lags

The pulsating flow of a viscous, incompressible fluid through rigid circular channels having walls which diverge at a slow exponential rate is examined analytically. Linearized solutions for low mean Reynolds numbers reveal that viscous effects lead to radially dependent phase shifts between different layers of fluid oscillating in the axial direction, and characteristic phase lags between flow and pressure curves. When the Reynolds number and channel divergence are each small, the flow does not separate, but there is a downstream attenuation of both flow and pressure, together with the appearance of a finite radial velocity component. Utilizing data relevant to basal conditions existing in the major blood vessels of the human coronary circulation, it is found (in the absence of any persistent flow anomalies) that the shear stress at the wall is at least one to two orders of magnitude lower than values reported to be damaging to vascular endothelium.

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.

scholarly journals Laminar-to-turbulent transition of pipe flows through puffs and slugs

2008 ◽  
Vol 614 ◽  
pp. 425-446 ◽  
Author(s):  
MINA NISHI ◽  
BÜLENT ÜNSAL ◽  
FRANZ DURST ◽  
GAUTAM BISWAS
Keyword(s):  
Reynolds Number ◽  
Pipe Flow ◽  
Axial Direction ◽  
Reynolds Numbers ◽  
Turbulent Pipe Flow ◽  
Test Facility ◽  
Pipe Flows ◽  
Laminar To Turbulent Transition ◽  
Turbulent Transition ◽  
Slug Flows

Laminar-to-turbulent transition of pipe flows occurs, for sufficiently high Reynolds numbers, in the form of slugs. These are initiated by disturbances in the entrance region of a pipe flow, and grow in length in the axial direction as they move downstream. Sequences of slugs merge at some distance from the pipe inlet to finally form the state of fully developed turbulent pipe flow. This formation process is generally known, but the randomness in time of naturally occurring slug formation does not permit detailed study of slug flows. For this reason, a special test facility was developed and built for detailed investigation of deterministically generated slugs in pipe flows. It is also employed to generate the puff flows at lower Reynolds numbers. The results reveal a high degree of reproducibility with which the triggering device is able to produce puffs. With increasing Reynolds number, ‘puff splitting’ is observed and the split puffs develop into slugs. Thereafter, the laminar-to-turbulent transition occurs in the same way as found for slug flows. The ring-type obstacle height, h, required to trigger fully developed laminar flows to form first slugs or puffs is determined to show its dependence on the Reynolds number, Re = DU/ν (where D is the pipe diameter, U is the mean velocity in the axial direction and ν is the kinematic viscosity of the fluid). When correctly normalized, h+ turns out to be independent of Reτ (where h+ = hUτ/ν, Reτ = DUτ/ν and $U_{\tau}\,{=}\,\sqrt{\tau_{w}/ \rho}$; τw is the wall shear stress and ρ is the density of the fluid).

scholarly journals Effect of Ambient Reynolds Number on Small Wind Turbine Subjected to Low Wind Speed Conditions

2021 ◽  
Vol 12 (2) ◽  
pp. 223-231
Author(s):  
Joel Mbwiga ◽  
Cuthbert Z Kimambo ◽  
Joseph Kihedu
Keyword(s):  
Reynolds Number ◽  
Wind Turbine ◽  
Wind Turbines ◽  
Reynolds Numbers ◽  
Design Parameters ◽  
Power Performance ◽  
Airfoil Surface ◽  
Small Wind Turbine ◽  
Low Wind Speed ◽  
The Difference

Wind flow over the airfoil surface is adversely affected by the differences between the design and ambient values of a dimensionless quantity called Reynolds number. Wind turbine designed for high Reynolds Number shows lower maximum power performance when installed in low-speed wind regime. Tanzanian experience shows that some imported modern wind turbines depict lower power performance compared to the drag-type locally manufactured wind turbines. The most probable reason is the difference between design and local ambient Reynolds numbers. The turbine design parameters have their properties restricted to the range of Reynolds numbers for which the turbine was designed for. When a wind turbine designed for a certain range of Reynolds numbers is made to operate in the Reynolds number out of that range, it behaves differently from the embodied design specifications. The small wind turbine of higher Reynolds number will suffer low lift forces with probably occasional stalls.  

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.

scholarly journals Study of Blood Flow with Effects of Slip in Arterial Stenosis Due to Presence of Transverse Magnetic Field

2013 ◽  
Vol 4 (2) ◽  
pp. 215-226
Author(s):  
Sarfraz Ahmed
Keyword(s):  
Magnetic Field ◽  
Reynolds Number ◽  
Blood Flow ◽  
Transverse Magnetic Field ◽  
Hartmann Number ◽  
Fluid Velocity ◽  
Equations Of Motion ◽  
Circulatory System ◽  
Transverse Magnetic ◽  
Arterial Stenosis

The flow of blood in human circulatory system can be controlled by applying appropriate magnetic field. It is also well known that non-Newtonian nature of blood significantly influences the flows, particularly in the cases where blood vessels are curved, branching or narrow etc. Stenosis refers to localized narrowing of an artery and is a frequent result of arterial disease and is caused mainly due to intravascular atherosclerotic plaque which develops at the arterial wall and protrudes into the lumen of the vessel. Such constrictions disturb normal blood flow through the artery. Here study is made on the flow of blood through a stenosed artery with the effect of slip at the boundary in presence of transverse magnetic field considering blood as Casson fluid (non- Newtonian fluid). The equations of motion has have been solved numerically. The effect of various parameters on the flow characteristics like Hartmann number, Reynolds number has been discussed. Numerical results were obtained for different values of the Hartmann number M and Reynolds number Re. It is observed that the fluid velocity decreases as the Hartmann number increases.

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 past a flat plate at low Reynolds numbers

1958 ◽  
Vol 3 (4) ◽  
pp. 329-343 ◽  
Author(s):  
E. Janssen
Keyword(s):  
Reynolds Number ◽  
Drag Coefficient ◽  
Flat Plate ◽  
Truncation Error ◽  
Reynolds Numbers ◽  
Experimental Result ◽  
Total Drag ◽  
Low Reynolds Numbers ◽  
Flow Past ◽  
The Difference

The flow past a flat plate at Reynolds numbers in the range 0·1 to 10·0 is investigated by an analogue method. The solution gives the stream function and the vorticity in the flow field surrounding the plate. From these are obtained the local coefficient of friction, the pressure distribution along the plate, and the total drag coefficient. The drag coefficient approaches the analytical values of Haaser (1950) and of Tomotika & Aoi (1953) as the Reynolds number decreases toward 0·1. The drag coefficient approaches the Blasius solution as the Reynolds number increases. At Reynolds number 10·0 the drag coefficient is still above the Blasius value, but is below the value obtained experimentally by Janour (1951). The difference from the experimental result is attributed for the most part to truncation error.

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