A Theoretical Investigation of the Maximum-Lift Coefficient

1935 ◽  
Vol 2 (1) ◽  
pp. A21-A27
Author(s):  
Th. von Kármán ◽  
Clark B. Millikan
Keyword(s):  
Boundary Layer ◽  
Experimental Investigation ◽  
Reynolds Number ◽  
Velocity Distribution ◽  
Theoretical Investigation ◽  
Laminar Boundary Layer ◽  
Lift Coefficient ◽  
Boundary Layer Theory ◽  
First Approximation ◽  
Transition Points

Abstract In the present paper the application of a laminar boundary-layer theory, previously developed by the authors, to the problem of the maximum-lift coefficient of airfoils is discussed. The calculations are carried through in detail for a first approximation, called a single-roof profile, to the potential velocity distribution over the upper surface of an airfoil. The results indicate a large variation in Clmax with turbulence but the quantitative dependence on Reynolds’ number and turbulence is not satisfactory. The calculations are then repeated for a so-called double-roof profile which approximates to the flow over the upper surface of an N.A.C.A. 2412 airfoil. These results are compared with those obtained from an experimental investigation on the same airfoil. The agreement is considered to indicate that for moderate values of R and Clmax the phenomenon of the maximum-lift coefficient is controlled by a contest between the separation and transition points of the laminar boundary layer over the nose of the airfoil. The difficulties involved in extending the theory to larger values of R, or to airfoils whose Cl vs. α curves are not approximately linear up to the stall, are mentioned.

A Theoretical Investigation of the Maximum-lift Coefficient

1935 ◽  
Vol 39 (295) ◽  
pp. 619-632
Author(s):  
TH. Von karman ◽  
Clark B. Millikan
Keyword(s):  
Experimental Investigation ◽  
Reynolds Number ◽  
Wind Tunnel ◽  
Theoretical Investigation ◽  
Lift Coefficient ◽  
Wind Tunnels ◽  
California Institute ◽  
California Institute Of Technology ◽  
Junior Author ◽  
Institute Of Technology

The problem of the maximum lift of airfoils has concerned the authors greatly since there were first discovered in the spring of 1932 serious discrepancies in this characteristic between results obtained in the wind tunnel of the Guggenheim Aeronautics Laboratory at the California Institute of Technology (GALCIT) and those reported from certain other wind tunnels. An elaborate experimental investigation by the junior author and A. L. Klein indicated that the value of CLmax for a given airfoil was strongly affected both by Reynolds number and by the degree of turbulence in the tunnel wind stream.

Note on the velocity distribution in the wake behind a flat plate placed along the stream

1936 ◽  
Vol 32 (3) ◽  
pp. 385-391 ◽  
Author(s):  
L. Rosenhead ◽  
J. H. Simpson
Keyword(s):  
Boundary Layer ◽  
Reynolds Number ◽  
Velocity Distribution ◽  
Flat Plate ◽  
Great Distance ◽  
Large Reynolds Number ◽  
Small Viscosity ◽  
First Approximation ◽  
Image Position ◽  
Forward Edge

1. The velocity distribution in fluid of small viscosity, or at large Reynolds number, in the laminar boundary layer associated with a thin flat plate along the main direction of flow, has been worked out by Blasius on the basis of the Prandtl theory. These original investigations covered the region from the forward edge of the plate to the downstream edge. In a recent paper Goldstein investigated the velocity distribution in the wake immediately behind the downstream edge over a region within about 0·5lfrom it,lbeing the length of the plate. LaterTollmien obtained a first approximation to the flow at a great distance down-stream. Goldstein § extended Tollmien's solution by finding a second approximation and by joining it up with his previous work on the flow very near the plate.

scholarly journals An Experimental Investigation of Nozzle-Exit Boundary Layers of Highly Heated Free Jets

1992 ◽  
Vol 114 (2) ◽  
pp. 469-475
Author(s):  
J. Lepicovsky
Keyword(s):  
Boundary Layer ◽  
Experimental Investigation ◽  
Reynolds Number ◽  
Boundary Layers ◽  
Laminar Boundary Layer ◽  
Nozzle Exit ◽  
Total Pressure ◽  
Free Jets ◽  
Exit Boundary ◽  
Mach Numbers

An experimental investigation of the effects of nozzle operating conditions on the development of nozzle-exit boundary layers of highly heated air free jets is reported in this paper. The total pressure measurements in the nozzle-exit boundary layer were obtained at a range of jet Mach numbers from 0.1 to 0.97 and jet total temperatures up to 900 K. The analysis of results shows that the nozzle-exit laminar boundary-layer development depends only on the nozzle-exit Reynolds number. For the nozzle-exit turbulent boundary layer, however, it appears that the effects of the jet total temperature on the boundary-layer integral characteristics are independent from the effect of the nozzle-exit Reynolds number. This surprising finding has not yet been reported. Further, laminar boundary-layer profiles were compared with the Pohlhausen solution for a flat-wall converging channel and an acceptable agreement was found only for low Reynolds numbers. For turbulent boundary layers, the dependence of the shape factor on relative Mach numbers at a distance of one momentum thickness from the nozzle wall resembles Spence’s prediction. Finally, the calculated total pressure loss coefficient was found to depend on the nozzle-exit Reynolds number for the laminar nozzle-exit boundary layer, while for the turbulent exit boundary layer this coefficient appears to be constant.

scholarly journals An Experimental Investigation of Nozzle-Exit Boundary Layers of Highly Heated Free Jets

1990 ◽  
Author(s):  
J. Lepicovsky
Keyword(s):  
Boundary Layer ◽  
Experimental Investigation ◽  
Reynolds Number ◽  
Boundary Layers ◽  
Laminar Boundary Layer ◽  
Nozzle Exit ◽  
Total Pressure ◽  
Free Jets ◽  
Exit Boundary ◽  
Mach Numbers

An experimental investigation of the effects of nozzle operating conditions on the development of nozzle-exit boundary layers of highly heated air free jets is reported in this paper. The total pressure measurements in the nozzle-exit boundary layer were obtained at a range of jet Mach numbers from 0.1 to 0.97 and jet total temperatures up to 900 K. The analysis of results shows that the nozzle-exit laminar boundary-layer development depends only on the nozzle-exit Reynolds number. For the nozzle-exit turbulent boundary layer, however, it appears that the effects of the jet total temperature on the boundary-layer integral characteristics are independent from the effect of the nozzle-exit Reynolds number. This surprizing finding has not yet been reported. Further, laminar boundary-layer profiles were compared with the Pohlhausen solution for a flat-wall converging channel and an acceptable agreement was found only for low Reynolds numbers. For turbulent boundary layers, the dependence of the shape factor on relative Mach numbers at a distance of one momentum thickness from the nozzle wall resembles Spence’s prediction. Finally, the calculated total pressure loss coefficient was found to depend on the nozzle-exit Reynolds number for the laminar nozzle-exit boundary layer, while for the turbulent exit boundary layer this coefficient appears to be constant.

Separation in oscillating laminar boundary-layer flows

1971 ◽  
Vol 47 (1) ◽  
pp. 21-31 ◽  
Author(s):  
R. A. Despard ◽  
J. A. Miller
Keyword(s):  
Experimental Data ◽  
Boundary Layer ◽  
Experimental Investigation ◽  
Reynolds Number ◽  
Reverse Flow ◽  
Oscillation Amplitude ◽  
Hot Wire ◽  
Boundary Layer Flows ◽  
Laminar Boundary Layers ◽  
History Of

The results of an experimental investigation of separation in oscillating laminar boundary layers is reported. Instantaneous velocity profiles obtained with multiple hot-wire anemometer arrays reveal that the onset of wake formation is preceded by the initial vanishing of shear at the wall, or reverse flow, throughout the entire cycle of oscillation. Correlation of the experimental data indicates that the frequency, Reynolds number and dynamic history of the boundary layer are the dominant parameters and oscillation amplitude has a negligible effect on separation-point displacement.

The Critical Height of Distributed Roughness to Cause Boundary Layer Transition

1959 ◽  
Vol 63 (588) ◽  
pp. 722-722
Author(s):  
R. L. Dommett
Keyword(s):  
Boundary Layer ◽  
Reynolds Number ◽  
Laminar Boundary Layer ◽  
Boundary Layer Transition ◽  
Critical Height ◽  
Layer Transition ◽  
Local Conditions ◽  
Additional Advantage ◽  
Boundary Layer Equations ◽  
General Method

It has been found that there is a critical height for “sandpaper” type roughness below which no measurable disturbances are introduced into a laminar boundary layer and above which transition is initiated at the roughness. Braslow and Knox have proposed a method of predicting this height, for flow over a flat plate or a cone, using exact solutions of the laminar boundary layer equations combined with a correlation of experimental results in terms of a Reynolds number based on roughness height, k, and local conditions at the top of the elements. A simpler, yet more general, method can be constructed by taking additional advantage of the linearity of the velocity profile near the wall in a laminar boundary layer.

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