A Closed Formula for the Drag of a Flat Plate with Transition in the Absence of a Pressure Gradient

1960 ◽  
Vol 64 (589) ◽  
pp. 38-39 ◽  
Author(s):  
A. R. Collar
Keyword(s):  
Reynolds Number ◽  
Pressure Gradient ◽  
Flat Plate ◽  
Transition Point ◽  
Free Stream ◽  
Analytical Form ◽  
Stream Velocity ◽  
Closed Formula ◽  
Friction Drag ◽  
Do So

Most University students of fluid mechanics are familiar with the problem of the evaluation of the skin friction drag of a flat plate in the absence of a pressure gradient: transition is specified, usually by the free stream velocity and the transition point, or directly by the transition Reynolds number. The solution is normally obtained numerically: so far as the writer is aware, the processes used have not been written down in closed analytical form, though to do so presents no difficulty.

On the asymptotic similarity of the zero-pressure-gradient turbulent boundary layer

2008 ◽  
Vol 616 ◽  
pp. 195-203 ◽  
Author(s):  
M. B. JONES ◽  
T. B. NICKELS ◽  
IVAN MARUSIC
Keyword(s):  
Boundary Layer ◽  
Reynolds Number ◽  
Turbulent Boundary Layer ◽  
Pressure Gradient ◽  
Similarity Solution ◽  
Friction Velocity ◽  
Free Stream ◽  
Outer Region ◽  
Free Stream Velocity ◽  
Stream Velocity

We investigate similarity solutions for the outer part of a zero-pressure-gradient turbulent boundary layer in the limit of infinite Reynolds number. Previous work by George (Phil. Trans. R. Soc. vol. 365, 2007 p. 789) has suggested that the only appropriate velocity scale for the outer region is U1, the free-stream velocity. This is based on the fact that scaling with U1 leads to a mathematically valid similarity solution of the momentum equation for the outer region in the asymptotic limit of infinite Reynolds number. Here we show that the classical scaling using the friction velocity also leads to a valid similarity solution for the outer flow in this limit. Therefore on this basis it is not possible to dismiss the friction velocity as a possible scaling as has been suggested by George (2007) and others. We show that both the free-stream velocity and the friction velocity are potentially valid scalings according to this theoretical criterion.

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.

scholarly journals NUMERICAL INVESTIGATION OF THE WAKE AFFECTED UNSTEADINESS ON FLAT PLATE BOUNDARY LAYER

2013 ◽  
Vol 43 (1) ◽  
pp. 15-22
Author(s):  
Sanchita Amin ◽  
Dipak Kanti Das
Keyword(s):  
Boundary Layer ◽  
Flat Plate ◽  
Free Stream ◽  
Plate Boundary ◽  
Elliptic Cylinder ◽  
Stream Velocity ◽  
Element Formulation ◽  
Weighted Residual Method ◽  
Focal Distance ◽  
Coupled Equations

The present numerical simulation has been conducted with the aim to observe the unsteady boundarylayer characteristics on a flat plate induced by a von Karman vortex street wake. This flow situation is anidealization of that occurring on turbomachinery blades where unsteady wakes are generated by the precedingrow of blades. In this research, the boundary layer is developed under zero pressure gradients while the vortexstreet is generated by an elliptic cylinder positioned in the free stream. The minor-major axes ratio of theelliptic cylinder is taken as 0.6 with an angle of attack 00. The investigation has been performed for differentcylinder-to-plate relative position and a Reynolds number of 500 based on the focal distance of the ellipticcylinder and free stream velocity. The time dependent, two dimensional flow is simulated numerically. Theconsequent mathematical model is governed by the coupled equations of mass, and momentum and solved byemploying Galerkin weighted residual method of finite element formulation. The development of the flow fieldup to certain time period is considered. Instantaneous streamlines of the disturbed flow field, instantaneousvelocity field, boundary layer integral parameters, and skin friction on different streamwise locations on theplate are presented in this paper. The result shows that the wake vortices strongly affect the boundary layerover the flat plate.DOI: http://dx.doi.org/10.3329/jme.v43i1.15771

Experimental Study on the Effect of Reynolds Number Variation on Drag Force for Various Cut Angle on D-Type Cylinders

2014 ◽  
Vol 493 ◽  
pp. 140-144
Author(s):  
Astu Pudjanarsa ◽  
Ardian Ardawalika
Keyword(s):  
Experimental Study ◽  
Reynolds Number ◽  
Drag Force ◽  
Free Stream ◽  
Force Balance ◽  
Stream Velocity ◽  
Turning Angle ◽  
Subsonic Wind Tunnel ◽  
Minimum Drag ◽  
Number Variation

Experimental study on the effect of Reynolds number variation on drag force for various cut angles on D-type cylinders was performed. Five different cut angles on different cylinders were applied including: 35o, 45o, 53o, 60o, and 65o. The free stream velocity was varied so the Reynolds number also varied.The experiment was carried out at a subsonic wind tunnel. Drag force for a cut D-type cylinder (for example 35o) was measured using a force balance and wind speed was varied so that corresponding Reynolds number of 2.4×104÷5.3×104 were achieved. Wind turning angle was kept at 0o (without turning angle). This experiment repeated for other D-type cylinders.Experiment results show that, for all D-type cylinders, drag force decreased as the Reynolds number increased, then it was increased after attain minimum drag force. For all D-type cylinders and all variations of Reynolds number the drag minimum is attained at cut angle of 53o. This value is appropriate with previous experiment results.

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