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.

On High-Performance Airfoil at Very Low Reynolds Number

2016 ◽  
Vol 28 (3) ◽  
pp. 273-285
Author(s):  
Katsuya Hirata ◽  
◽  
Ryo Nozawa ◽  
Shogo Kondo ◽  
Kazuki Onishi ◽  
...  
Keyword(s):  
Reynolds Number ◽  
Flat Plate ◽  
High Performance ◽  
Low Reynolds Number ◽  
Three Dimensional ◽  
Reynolds Numbers ◽  
Aerodynamic Characteristics ◽  
Slow Flow ◽  
Low Reynolds Numbers ◽  
Low Reynolds

[abstFig src='/00280003/02.jpg' width=""300"" text='Iso-Q surfaces of very-slow flow past an iNACA0015' ] The airfoil is often used as the elemental device for flying/swimming robots, determining its basic performances. However, most of the aerodynamic characteristics of the airfoil have been investigated at Reynolds numbers Re’s more than 106. On the other hand, our knowledge is not enough in low Reynolds-number ranges, in spite of the recent miniaturisation of robots. In the present study, referring to our previous findings (Hirata et al., 2011), we numerically examine three kinds of high-performance airfoils proposed for very-low Reynolds numbers; namely, an iNACA0015 (the NACA0015 placed back to front), an FPBi (a flat plate blended with iNACA0015 as its upper half) and an FPBN (a flat plate blended with the NACA0015 as its upper half), in comparison with such basic airfoils as a NACA0015 and an FP (a flat plate), at a Reynolds number Re = 1.0 × 102 using two- and three-dimensional computations. As a result, the FPBi shows the best performance among the five kinds of airfoils.

Two Dimensional Jet at Low Reynolds Numbers

2007 ◽  
Author(s):  
Akinori Muramatsu ◽  
Tatsuo Motohashi
Keyword(s):  
Reynolds Number ◽  
Outer Part ◽  
Reynolds Numbers ◽  
Streamwise Velocity ◽  
Momentum Conservation ◽  
Control Surface ◽  
Two Dimensional ◽  
Low Reynolds Numbers ◽  
Vortical Motion ◽  
The Difference

A numerical simulation of two-dimensional jets was carried out using a SOLA method. The two-dimensional jets were discharged from a slit in a wall at Reynolds numbers below 50. The difference between the calculated flow fields and those of the Bickley jet is due to the non-uniformity of the pressure field near the jet exit at the wall. The jet spreads faster than the Bickley jet. The decay of the streamwise velocity on the center line is more rapid than that of the Bickley jet. The streamwise velocity profile is different from that of the Bickley jet, and a reversed flow is generated in the outer part of the jet. The jet develops instability through two processes. First, small fluctuations grow exponentially. Second, vortical motion such as so-called ‘flapping motion’ of the jet develops in the downstream region. The critical Reynolds number, as determined by the growth of an integral of kinetic energy, is approximately 16.5. Integrals of momentum and pressure are calculated on a control surface in order to confirm the momentum conservation law. When the Reynolds number exceeds 20, the generation of fluctuations contributes to streamwise variations in the integrals of momentum and pressure.

A Numerical Investigation of Laminar Flow Past Nonspherical Solids and Droplets

1995 ◽  
Vol 117 (1) ◽  
pp. 170-175 ◽  
Author(s):  
J. K. Comer ◽  
C. Kleinstreuer
Keyword(s):  
Laminar Flow ◽  
Drag Coefficient ◽  
Reynolds Numbers ◽  
Shear Stresses ◽  
Spherical Droplet ◽  
Total Drag ◽  
Interfacial Transport ◽  
Aspect Ratios ◽  
Flow Past ◽  
Steady Laminar

Steady laminar flow past solitary spheroids and nonspherical droplets has been numerically analyzed. Specifically, interfacial transport properties such as surface pressures, interfacial velocities, shear stresses and separation angles as well as the resulting drag coefficients are evaluated for specified aspect ratios (0.2 ≤ E = b/a ≤ 1.0) and intermediate gas stream Reynolds numbers (40 ≤ Re ≤ 120). For one case, it was determined that the use of the traditional spherical-droplet assumption would result in a 30 percent underprediction of the total drag coefficient.

The drag on oscillating flat plates in liquids at low Reynolds numbers

1971 ◽  
Vol 48 (2) ◽  
pp. 229-239 ◽  
Author(s):  
Cornelius C. Shih ◽  
Harry J. Buchanan
Keyword(s):  
Reynolds Number ◽  
Drag Coefficient ◽  
Reynolds Numbers ◽  
Motor Oil ◽  
Flat Plates ◽  
Low Reynolds Numbers ◽  
Two Fluids ◽  
Low Reynolds ◽  
The Relationship ◽  
Graphical Presentation

An experimental investigation was conducted to describe the fluid flow about oscillating flat plates and to determine the magnitude and nature of forces acting on the plates at low Reynolds numbers. In the experiment, the Reynolds number was varied from 1·01 to 1057·0; three period parameters, 1·57, 2·07 and 4·71, were applied; two fluids, water and SAE 30 motor oil, and three flat plates of various sizes with or without end plates were used. The analysis of data resulted in graphical presentation of the relationships among the drag coefficient, the Reynolds number and period parameter. The drag coefficient becomes less dependent on the Reynolds number for values greater than 250. The relationship between the drag coefficient and period parameter is pronounced throughout the entire range of the Reynolds number tested.

The Forces on a Cylinder Oscillating Sinusoidally in Water: Further Experiments

1978 ◽  
Vol 100 (3) ◽  
pp. 297-301
Author(s):  
C. Dalton ◽  
J. P. Hunt ◽  
A. K. M. F. Hussain
Keyword(s):  
Reynolds Number ◽  
Continuous Function ◽  
Drag Coefficient ◽  
Steady Flow ◽  
Parametric Study ◽  
Reynolds Numbers ◽  
Wave Forces ◽  
Force Coefficient ◽  
Low Reynolds Numbers ◽  
Flow Drag

This paper deals with wave forces on a single cylinder. The wave forces are simulated in a laboratory by oscillating a cylinder sinusoidally in water otherwise at rest. This effort is a parametric study relating a force coefficient to such variables as instantaneous Reynolds number, period parameter, and d/νT. The force is not decomposed into drag and inertia components, but is represented as a continuous function of the previously mentioned parameters. The idea is to determine how the acceleration affects the force. Considerable deviation from a Reynolds-number only dependence is noted for low Reynolds numbers. The steady-flow drag coefficient value is asymptotically obtained for large Reynolds numbers.

Low Reynolds number flow around and heat transfer from a heated circular cylinder

2010 ◽  
Vol 1 (1-2) ◽  
pp. 15-20 ◽  
Author(s):  
B. Bolló
Keyword(s):  
Reynolds Number ◽  
Circular Cylinder ◽  
Lift Coefficient ◽  
Reynolds Numbers ◽  
Low Reynolds Numbers ◽  
Reynolds Number Flow ◽  
Two Dimensional Flow ◽  
Number Flow ◽  
Low Reynolds ◽  
Increasing Temperature

Abstract The two-dimensional flow around a stationary heated circular cylinder at low Reynolds numbers of 50 < Re < 210 is investigated numerically using the FLUENT commercial software package. The dimensionless vortex shedding frequency (St) reduces with increasing temperature at a given Reynolds number. The effective temperature concept was used and St-Re data were successfully transformed to the St-Reeff curve. Comparisons include root-mean-square values of the lift coefficient and Nusselt number. The results agree well with available data in the literature.

scholarly journals Erratum: “The effect of permeability on the flow past permeable disks at low Reynolds numbers” [Phys. Fluids 29, 097103 (2017)]

2020 ◽  
Vol 32 (11) ◽  
pp. 119901
Author(s):  
Cathal Cummins ◽  
Ignazio Maria Viola ◽  
Enrico Mastropaolo ◽  
Naomi Nakayama
Keyword(s):  
Reynolds Numbers ◽  
Low Reynolds Numbers ◽  
Flow Past ◽  
Low Reynolds

scholarly journals Plunging Airfoil: Reynolds Number and Angle of Attack Effects

Aerospace ◽  
2021 ◽  
Vol 8 (8) ◽  
pp. 216
Author(s):  
Emanuel A. R. Camacho ◽  
Fernando M. S. P. Neves ◽  
André R. R. Silva ◽  
Jorge M. M. Barata
Keyword(s):  
Reynolds Number ◽  
High Performance ◽  
Angle Of Attack ◽  
Systems Design ◽  
Reynolds Numbers ◽  
Navier Stokes ◽  
Low Reynolds Numbers ◽  
Operational Conditions ◽  
Naca0012 Airfoil ◽  
The Mean

Natural flight has consistently been the wellspring of many creative minds, yet recreating the propulsive systems of natural flyers is quite hard and challenging. Regarding propulsive systems design, biomimetics offers a wide variety of solutions that can be applied at low Reynolds numbers, achieving high performance and maneuverability systems. The main goal of the current work is to computationally investigate the thrust-power intricacies while operating at different Reynolds numbers, reduced frequencies, nondimensional amplitudes, and mean angles of attack of the oscillatory motion of a NACA0012 airfoil. Simulations are performed utilizing a RANS (Reynolds Averaged Navier-Stokes) approach for a Reynolds number between 8.5×103 and 3.4×104, reduced frequencies within 1 and 5, and Strouhal numbers from 0.1 to 0.4. The influence of the mean angle-of-attack is also studied in the range of 0∘ to 10∘. The outcomes show ideal operational conditions for the diverse Reynolds numbers, and results regarding thrust-power correlations and the influence of the mean angle-of-attack on the aerodynamic coefficients and the propulsive efficiency are widely explored.

scholarly journals The Profile Drag of Yawed Wings of Infinite Span

1951 ◽  
Vol 3 (3) ◽  
pp. 211-229 ◽  
Author(s):  
A.D. Young ◽  
T.B. Booth
Keyword(s):  
Boundary Layer ◽  
Pressure Gradient ◽  
Drag Coefficient ◽  
Experimental Evidence ◽  
Flat Plate ◽  
Transition Point ◽  
Reynolds Numbers ◽  
External Pressure ◽  
Basic Assumptions ◽  
Angle Of Yaw

SummaryA method is developed for calculating the profile drag of a yawed wing of infinite span, based on the assumption that the form of the spanwise distribution of velocity in the boundary layer, whether laminar or turbulent, is insensitive to the chordwise pressure distribution. The form is assumed to be the same as that accepted for the boundary layer on an unyawed plate with zero external pressure gradient. Experimental evidence indicates that these assumptions are reasonable in this context. The method is applied to a flat plate and the N.A.C.A. 64-012 section at zero incidence for a range of Reynolds numbers between 106 and 108, angles of yaw up to 45°, and a range of transition point positions. It is shown that the drag coefficients of a flat plate varies with yaw as cos½ Λ (where Λ is the angle of yaw) if the boundary layer is completely laminar, and it varies as if the boundary layer is completely turbulent. The drag coefficient of the N.A.C.A. 64-012 section, however, varies closely as cos½ Λ for transition point positions between 0 and 0.5 c. Further calculations on wing sections of other shapes and thicknesses and more detailed experimental checks of the basic assumptions at higher Reynolds numbers are desirable.

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