Flow in Locally Constricted Tubes at Low Reynolds Numbers

1970 ◽  
Vol 37 (1) ◽  
pp. 9-16 ◽  
Author(s):  
Jen-Shih Lee ◽  
Yuan-Cheng Fung
Keyword(s):  
Reynolds Number ◽  
Blood Flow ◽  
Shear Stress ◽  
Cylindrical Tube ◽  
Reynolds Numbers ◽  
Velocity Measurements ◽  
Number Range ◽  
Low Reynolds Numbers ◽  
Circular Cylindrical Tube ◽  
Velocity Pressure

With an objective to understand arteriosclerosis, the blood flow in a circular cylindrical tube with a local constriction is analyzed. Numerical results are presented for the streamlines and the distributions of velocity, pressure, vorticity, and shear stress in the Reynolds number range 0–25. These results have applications to other fluid-mechanical problems such as gauges for velocity measurements, etc.

Strut Interference Effects on Pitot Tube Velocity Measurements

2007 ◽  
Author(s):  
Sandra K. S. Boetcher ◽  
Ephraim M. Sparrow
Keyword(s):  
Reynolds Number ◽  
Reynolds Numbers ◽  
The Body ◽  
Pitot Tube ◽  
Velocity Measurements ◽  
Measuring Device ◽  
Number Range ◽  
Low Reynolds Numbers ◽  
Velocity Measuring ◽  
The Impact

The possible impact of the presence of the strut portion of a Pitot tube on the efficacy of the tube as a velocity-measuring device has been evaluated by numerical simulation. At sufficiently low Reynolds numbers, there is a possibility that the precursive effects of the strut could alter the flow field adjacent to the static taps on the body of the Pitot tube and might even affect the impact pressure measured at the nose. The simulations were performed in dimensionless form with the Reynolds number being the only prescribed parameter, but the dimensions were taken from a short-shanked Pitot tube. Over the Reynolds number range from 1500 to 4000, a slight effect of the strut was identified. However, the variation due to the presence of the shank of the velocity measured by the Pitot tube operating in that range of Reynolds numbers was only 1.5%.

A note on vortex streets behind circular cylinders at low Reynolds numbers

1971 ◽  
Vol 45 (1) ◽  
pp. 203-208 ◽  
Author(s):  
D. J. Tritton
Keyword(s):  
Reynolds Number ◽  
Reynolds Numbers ◽  
Circular Cylinders ◽  
Number Range ◽  
Low Reynolds Numbers ◽  
Current State ◽  
Reynolds Number Range ◽  
Vortex Streets ◽  
Low Reynolds

A discussion is given of the current state of knowledge of vortex streets behind circular cylinders in the Reynolds number range 50 to 160. This was prompted by Gaster's (1969) report that he could not find the transition at a Reynolds number of about 90 observed by Tritton (1959) and Berger (1964a). A further brief experiment confirming the existence of the transition is described Reasons for rejecting Gaster's interpretation are advanced. Possible (mutually alternative) explanations of the discrepant observations are suggested.

Flow separation from a stationary meniscus

2009 ◽  
Vol 633 ◽  
pp. 137-145 ◽  
Author(s):  
J. SÉBILLEAU ◽  
L. LIMAT ◽  
J. EGGERS
Keyword(s):  
Reynolds Number ◽  
Free Surface ◽  
Critical Reynolds Number ◽  
Cylindrical Tube ◽  
Reynolds Numbers ◽  
Flow Lines ◽  
Low Reynolds Numbers ◽  
High Reynolds Numbers ◽  
High Reynolds ◽  
Meniscus Region

We consider the steady flow near a free surface at intermediate to high Reynolds numbers, both experimentally and theoretically. In our experiment, an axisymmetric capillary meniscus is suspended from a cylindrical tube, held slightly above a horizontal water surface. A flow of dyed water is released through the tube into the reservoir, and flow lines are thus recorded. At low Reynolds numbers, flow lines follow the free surface, and injected water spreads horizontally inside the container. Increasing the Reynolds number, the injected fluid penetrates to a certain distance into the bath, but ultimately follows the free surface. Above a critical Reynolds number of approximately 60, the flow separates from the free surface in the meniscus region and a jet projects vertically into the bath. We find no indication that the flow reattaches at higher Reynolds numbers, nor are our findings sensitive to surface contamination. We show theoretically and confirm experimentally that the separating streamline forms a right angle with the free surface.

VIV Suppression Device Development and the Perils of Reynolds Number

2017 ◽  
Author(s):  
Don W. Allen ◽  
Nicole Liu
Keyword(s):  
Reynolds Number ◽  
Small Diameter ◽  
Reynolds Numbers ◽  
Number Range ◽  
Low Reynolds Numbers ◽  
Helical Strakes ◽  
Low Reynolds ◽  
Offshore Industry ◽  
High Reynolds ◽  
Viv Suppression

Most deepwater tubulars experiencing high currents frequently require vortex-induced vibration (VIV) suppression to maintain an acceptable fatigue life. While helical strakes and fairings are by far the most popular VIV suppression devices used in the offshore industry today, a myriad of small alternations to these basic devices can significantly impact the observed levels of suppression effectiveness. Additionally, numerous novel VIV reduction devices are continually being developed and some new devices are progressing towards the product readiness phase. It is quite common to first test suppression devices at low Reynolds numbers due to the availability of smaller scale facilities that are typically more budget-friendly than larger scale facilities. For larger scale testing, it is usually simpler and less expensive to evaluate prototype suppression devices on shorter pipe sections that are spring mounted rather than test on longer flexible pipes. This paper utilizes results from historical VIV experiments to evaluate the merits of various test setups and scales and to underscore the importance of Reynolds number. An assortment of testing scales are presented including: a) small diameter tests at low Reynolds numbers; b) moderate diameter tests that incorporate at least part of the critical Reynolds number range; c) short pipe tests conducted at prototype Reynolds numbers; and d) long pipe tests conducted at high Reynolds numbers but at less than full scale suppression geometry. The use of computational fluid dynamics (CFD) is also briefly discussed.

Experiments on the flow past a circular cylinder at low Reynolds numbers

1959 ◽  
Vol 6 (4) ◽  
pp. 547-567 ◽  
Author(s):  
D. J. Tritton
Keyword(s):  
Reynolds Number ◽  
Circular Cylinder ◽  
Experimental Evidence ◽  
Theoretical Calculations ◽  
Reynolds Numbers ◽  
Vortex Street ◽  
Circular Cylinders ◽  
Number Range ◽  
Low Reynolds Numbers ◽  
Experimental Values

Part I describes measurements of the drag on circular cylinders, made by observing the bending of quartz fibres, in a stream with the Reynolds number range 0·5-100. Comparisons are made with other experimental values (which cover only the upper part of this range) and with the various theoretical calculations.Part II advances experimental evidence for there being a transition in the mode of the vortex street in the wake of a cylinder at a Reynolds number around 90. Investigations of the nature of this transition and the differences between the flows on either side of it are described. The interpretation that the change is between a vortex street originating in the wake and one originating in the immediate vicinity of the cylinder is suggested.

A Reassessment of Metering Orifices for Low Reynolds Numbers

1965 ◽  
Vol 180 (1) ◽  
pp. 331-356 ◽  
Author(s):  
L. J. Kastner ◽  
J. C. McVeigh
Keyword(s):  
Experimental Study ◽  
Reynolds Number ◽  
Flow Rate ◽  
Discharge Coefficient ◽  
Low Reynolds Number ◽  
Reynolds Numbers ◽  
Number Range ◽  
Low Reynolds Numbers ◽  
Discharge Coefficients ◽  
Low Reynolds

In view of the importance of accurate measurement of flow rate at low Reynolds numbers, there have been numerous attempts to develop metering devices having constant discharge coefficients in the range of pipe Reynolds numbers between about 3000 and 200 and even below this latter value, and some of these attempts have achieved a reasonable degrees of success. Nevertheless, some confusion exists regarding the dimensions and range of utility of certain designs which have been recommended and further information is necessary in order that the situation may be clarified. The aims of the present investigation, which is believed to be wider in scope than any published in this field in recent years, were to review and correlate existing knowledge and to make an experimental study of the properties of various types of orifice in the low range of Reynolds numbers. Arising from this it was hoped that a design might be evolved which not only had a satisfactorily constant discharge coefficient throughout the range but was also simple to manufacture and reproduce, even for small orifice diameters of the order of 0.5 in or less, and it is believed that some success in attaining this aim was achieved. The first section of the paper contains a review of previous investigations classified into three main groups. In the second part of the paper, experiments with various types of orifice plate are described and it is shown that a properly proportioned single-bevelled orifice has as good a performance in the low Reynolds number range as that of any of the more complicated shapes.

Vortex shedding from spheres

1974 ◽  
Vol 62 (2) ◽  
pp. 209-221 ◽  
Author(s):  
Elmar Achenbach
Keyword(s):  
Reynolds Number ◽  
Vortex Shedding ◽  
Critical Reynolds Number ◽  
Measurement Techniques ◽  
Reynolds Numbers ◽  
Wake Flow ◽  
Present Measurement ◽  
Number Range ◽  
Low Reynolds Numbers ◽  
The Relationship

Vortex shedding from spheres has been studied in the Reynolds number range 400 < Re < 5 × 106. At low Reynolds numbers, i.e. up to Re = 3 × 103, the values of the Strouhal number as a function of Reynolds number measured by Möller (1938) have been confirmed using water flow. The lower critical Reynolds number, first reported by Cometta (1957), was found to be Re = 6 × 103. Here a discontinuity in the relationship between the Strouhal and Reynolds numbers is obvious. From Re = 6 × 103 to Re = 3 × 105 strong periodic fluctuations in the wake flow were observed. Beyond the upper critical Reynolds number (Re = 3.7 × 105) periodic vortex shedding could not be detected by the present measurement techniques.The hot-wire measurements indicate that the signals recorded simultaneously at different positions on the 75° circle (normal to the flow) show a phase shift. Thus it appears that the vortex separation point rotates around the sphere. An attempt is made to interpret this experimental evidence.

Measurements in a Turbine Cascade Flow Under Ultra Low Reynolds Number Conditions

2001 ◽  
Author(s):  
Kenneth W. Van Treuren ◽  
Terrence Simon ◽  
Marc von Koller ◽  
Aaron R. Byerley ◽  
James W. Baughn ◽  
...  
Keyword(s):  
Reynolds Number ◽  
Turbulence Intensity ◽  
Low Reynolds Number ◽  
Reynolds Numbers ◽  
Vortex Generators ◽  
Separation Region ◽  
Suction Surface ◽  
Number Range ◽  
Low Reynolds Numbers ◽  
Low Reynolds

With the new generation of gas turbine engines, low Reynolds number flows have become increasingly important. Designers must properly account for transition from laminar to turbulent flow and separation of the flow from the suction surface, which is strongly dependent upon transition. Of interest to industry are Reynolds numbers based upon suction surface length and flow exit velocity below 150,000 and as low as 25,000. In this paper, the extreme low end of this Reynolds number range is documented by way of pressure distributions, loss coefficients and identification of separation zones. Reynolds numbers of 25,000 and 50,000 and with 1% and 8–9% turbulence intensity of the approach flow (Free Stream Turbulence Intensity, FSTI) were investigated. At 25,000 Reynolds number and low FSTI, the suction surface displayed a strong and steady separation region. Raising the turbulence intensity resulted in a very unsteady separation region of nearly the same size on the suction surface. Vortex generators were added to the suction surface, but they appeared to do very little at this Reynolds number. At the higher Reynolds number of 50,000, the low-FSTI case was strongly separated on the downstream portion of the suction surface. The separation zone was eliminated when the turbulence level was increased to 8–9%. Vortex generators were added to the suction surface of the low-FSTI case. In this instance, the vortices were able to provide the mixing needed to reestablish flow attachment. This paper shows that massive separation at very low Reynolds numbers (25,000) is persistent, in spite of elevated FSTI and added vortices. However, at a higher Reynolds number, there is opportunity for flow reattachment either with elevated freestream turbulence or with added vortices. This may be the first documentation of flow behavior at such low Reynolds numbers. Though undesirable to operate under these conditions, it is important to know what to expect and how performance may be improved if such conditions are unavoidable.

An Examination of the Effect of Reynolds Number on Airfoil Performance

2011 ◽  
Author(s):  
Tim Burdett ◽  
Jason Gregg ◽  
Kenneth Van Treuren
Keyword(s):  
Experimental Data ◽  
Reynolds Number ◽  
Wind Turbines ◽  
Large Scale ◽  
Reynolds Numbers ◽  
Energy Sources ◽  
Small Scale ◽  
Number Range ◽  
Low Reynolds Numbers ◽  
Low Reynolds

The standard of living throughout the world has increased dramatically over the last 30 years and is projected to continue to rise. This growth leads to an increased demand on conventional energy sources, such as fossil fuels. However, these are finite resources. Thus, there is an increasing demand for alternative energy sources, such as wind energy. Much of current wind turbine research focuses on large-scale (>1 MW), technologically-complex wind turbines installed in areas of high average wind speed (>20 mph). An alternative approach is to focus on small-scale (1–10kW), technologically-simple wind turbines built to produce power in low wind regions. While these turbines may not be as efficient as the large-scale systems, they require less industrial support and a less complicated electrical grid since the power can be generated at the consumer’s location. To pursue this approach, a design methodology for small-scale wind turbines must be developed and validated. This paper addresses one element of this methodology, airfoil performance prediction. In the traditional design process, an airfoil is selected and published lift and drag curves are used to optimize the blade twist and predict performance. These published curves are typically generated using either experimental testing or a numeric code, such as PROFIL (the Eppler Airfoil Design and Analysis Code) or XFOIL. However, the published curves often represent performance over a different range of Reynolds numbers than the actual design conditions. Wind turbines are typically designed from 2-D airfoil data, so having accurate airfoil data for the design conditions is critical. This is particularly crucial for small-scale, fixed-pitched wind turbines, which typically operate at low Reynolds numbers (<500,000) where airfoil performance can change significantly with Reynolds number. From a simple 2-D approach, the ideal operating condition for an airfoil to produce torque is the angle of attack at which lift is maximized and drag is minimized, so prediction of this angle will be compared using experimental and simulated data. Theoretical simulations in XFOIL of the E387 airfoil, designed for low Reynolds numbers, suggest that this optimum angle for design is Reynolds number dependent, predicting a difference of 2.25° over a Reynolds number range of 460,000 to 60,000. Published experimental data for the E387 airfoil demonstrate a difference of 2.0° over this same Reynolds number range. Data taken in the Baylor University Subsonic Wind Tunnel for the S823 airfoil shows a similar trend. This paper examines data for the E387 and S823 airfoils at low Reynolds numbers (75,000, 150,000, and 200,000 for the S823) and compares the experimental data with XFOIL predictions and published PROFIL predictions.

scholarly journals Modelling boundary-layer transition on wings operating in ground effect at low Reynolds numbers

2018 ◽  
Vol 233 (11) ◽  
pp. 2820-2837 ◽  
Author(s):  
LS Roberts ◽  
MV Finnis ◽  
K Knowles
Keyword(s):  
Reynolds Number ◽  
Shear Stress ◽  
Wind Tunnel ◽  
Transport Model ◽  
Three Dimensional ◽  
Ground Effect ◽  
Reynolds Numbers ◽  
Low Reynolds Numbers ◽  
Shear Stress Transport Model ◽  
Low Reynolds

The transition-sensitive, three-equation k- kL- ω eddy-viscosity closure model was used for simulations of three-dimensional, single-element and multi-element wing configurations operating in close proximity to the ground. The aim of the study was to understand whether the model correctly simulated the transitional phenomena that occurred in the low Reynolds number operating conditions and whether it offered an improvement over the classical fully turbulent k-ω shear stress transport model. This was accomplished by comparing the simulation results to experiments conducted in a 2.7 m × 1.7 m closed-return, three-quarter-open-jet wind tunnel. The model was capable of capturing the presence of a laminar separation bubble on the wing and predicted sectional forces and surface-flow structures generated by the wings in wind tunnel testing to within 2.5% in downforce and 4.1% in drag for a multi-element wing. It was found, however, that the model produced insufficient turbulent kinetic energy during shear-layer reattachment, predicted turbulent trailing-edge separation prematurely in areas of large adverse pressure gradients, and was found to be very sensitive to inlet turbulence quantities. Despite these deficiencies, the model gave results that were much closer to wind-tunnel tests than those given by the fully turbulent k-ω shear stress transport model, which tended to underestimate downforce. Significant differences between the transitional and fully turbulent models in terms of pressure field, wake thickness and turbulent kinetic energy production were found and highlighted the importance of using transitional models for wings operating at low Reynolds numbers in ground effect. The k- kL- ω model has been shown to be appropriate for the simulation of separation-induced transition on a three-dimensional wing operating in ground effect at low Reynolds number.

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