Further Development of a Boundary Layer Profile for a given Pressure Distribution

1941 ◽  
Vol 45 (362) ◽  
pp. 35-50 ◽  
Author(s):  
H. Görtler
Keyword(s):  
Boundary Layer ◽  
Velocity Profile ◽  
Pressure Distribution ◽  
Recent Work ◽  
Boundary Layers ◽  
Laminar Boundary Layer ◽  
Numerical Evaluation ◽  
Further Development ◽  
Boundary Layer Profile

The following paper forms a continuation of a recent work by Prandtl (I) “On the Calculation of Boundary Layers.” It deals with the problem of developing in detail the method, proposed in that paper, for continuing a given velocity profile in a laminar boundary layer when the pressure distribution is given; the method is tried out in practice by numerical evaluation of an example.

Recent Developments in Calculation Methods for Turbulent Boundary Layers With Pressure Gradients and Heat Transfer

1966 ◽  
Vol 33 (2) ◽  
pp. 429-437 ◽  
Author(s):  
J. C. Rotta
Keyword(s):  
Heat Transfer ◽  
Boundary Layer ◽  
Temperature Distribution ◽  
Velocity Profile ◽  
Boundary Layers ◽  
Turbulent Boundary Layers ◽  
Pressure Gradients ◽  
Calculation Methods ◽  
Recent Developments ◽  
Incompressible Boundary

A review is given of the recent development in turbulent boundary layers. At first, for the case of incompressible flow, the variation of the shape of velocity profile with the pressure gradient is discussed; also the temperature distribution and heat transfer in incompressible boundary layers are treated. Finally, problems of the turbulent boundary layer in compressible flow are considered.

Development of a laminar boundary layer under conditions of continuous incipient separation

1976 ◽  
Vol 76 (1) ◽  
pp. 55-66 ◽  
Author(s):  
N. Curle
Keyword(s):  
Boundary Layer ◽  
Pressure Distribution ◽  
Laminar Boundary Layer ◽  
Shape Parameter ◽  
Uniform Pressure ◽  
Continuous Change ◽  
Similar Series ◽  
Image Position ◽  
Incipient Separation

SynopsisThis paper, extending the work of Stratford [6] considers a boundary layer with uniform pressure when x < x0, and with the pressure in x > x0 so chosen that the layer is just on the point of separation for all x >x0. The required pressure distribution is shown to beThe displacement and momentum thicknesses are also derived as series in powers of ξ (and log ξ), and the shape parameter H then obtained as a similar series. The continuous change in H from the Blasius value (when ξ = 0) towards the Falkner-Skan [3] separation value is convincingly demonstrated, with the aid of the leading terms of an asymptomatic expansion for large ξ.

Velocity Profiles of Turbulent Boundary Layers

1969 ◽  
Vol 73 (698) ◽  
pp. 143-147 ◽  
Author(s):  
M. K. Bull
Keyword(s):  
Experimental Data ◽  
Boundary Layer ◽  
Turbulent Boundary Layer ◽  
Velocity Profile ◽  
Boundary Layers ◽  
Experimental Work ◽  
Constant Pressure ◽  
Velocity Profiles ◽  
Turbulent Boundary Layers ◽  
Boundary Layer Equations

Although a numerical solution of the turbulent boundary-layer equations has been achieved by Mellor and Gibson for equilibrium layers, there are many occasions on which it is desirable to have closed-form expressions representing the velocity profile. Probably the best known and most widely used representation of both equilibrium and non-equilibrium layers is that of Coles. However, when velocity profiles are examined in detail it becomes apparent that considerable care is necessary in applying Coles's formulation, and it seems to be worthwhile to draw attention to some of the errors and inconsistencies which may arise if care is not exercised. This will be done mainly by the consideration of experimental data. In the work on constant pressure layers, emphasis tends to fall heavily on the author's own data previously reported in ref. 1, because the details of the measurements are readily available; other experimental work is introduced where the required values can be obtained easily from the published papers.

Decreasing the Side Wall Contamination in Wind Tunnels

1983 ◽  
Vol 105 (4) ◽  
pp. 435-438 ◽  
Author(s):  
T. Motohashi ◽  
R. F. Blackwelder
Keyword(s):  
Boundary Layer ◽  
Reynolds Number ◽  
Boundary Layers ◽  
Laminar Boundary Layer ◽  
Three Dimensional ◽  
Side Wall ◽  
Wind Tunnels ◽  
Turbulent Fluid ◽  
Side Walls ◽  
Suction Slot

To study boundary layers in the transitional Reynolds number regime, the useful spanwise and streamwise extent of wind tunnels is often limited by turbulent fluid emanating from the side walls. Some or all of the turbulent fluid can be removed by sucking fluid out at the corners, as suggested by Amini [1]. It is shown that by optimizing the suction slot width, the side wall contamination can be dramatically decreased without a concomitant three-dimensional distortion of the laminar boundary layer.

scholarly journals On the identification of well-behaved turbulent boundary layers

2017 ◽  
Vol 822 ◽  
pp. 109-138 ◽  
Author(s):  
C. Sanmiguel Vila ◽  
R. Vinuesa ◽  
S. Discetti ◽  
A. Ianiro ◽  
P. Schlatter ◽  
...  
Keyword(s):  
Boundary Layer ◽  
Reynolds Number ◽  
Velocity Profile ◽  
Skin Friction ◽  
Boundary Layers ◽  
Shape Factor ◽  
Outer Region ◽  
The Other ◽  
Diagnostic Plot ◽  
Other Hand

This paper introduces a new method based on the diagnostic plot (Alfredsson et al., Phys. Fluids, vol. 23, 2011, 041702) to assess the convergence towards a well-behaved zero-pressure-gradient (ZPG) turbulent boundary layer (TBL). The most popular and well-understood methods to assess the convergence towards a well-behaved state rely on empirical skin-friction curves (requiring accurate skin-friction measurements), shape-factor curves (requiring full velocity profile measurements with an accurate wall position determination) or wake-parameter curves (requiring both of the previous quantities). On the other hand, the proposed diagnostic-plot method only needs measurements of mean and fluctuating velocities in the outer region of the boundary layer at arbitrary wall-normal positions. To test the method, six tripping configurations, including optimal set-ups as well as both under- and overtripped cases, are used to quantify the convergence of ZPG TBLs towards well-behaved conditions in the Reynolds-number range covered by recent high-fidelity direct numerical simulation data up to a Reynolds number based on the momentum thickness and free-stream velocity $Re_{\unicode[STIX]{x1D703}}$ of approximately 4000 (corresponding to 2.5 m from the leading edge) in a wind-tunnel experiment. Additionally, recent high-Reynolds-number data sets have been employed to validate the method. The results show that weak tripping configurations lead to deviations in the mean flow and the velocity fluctuations within the logarithmic region with respect to optimally tripped boundary layers. On the other hand, a strong trip leads to a more energized outer region, manifested in the emergence of an outer peak in the velocity-fluctuation profile and in a more prominent wake region. While established criteria based on skin-friction and shape-factor correlations yield generally equivalent results with the diagnostic-plot method in terms of convergence towards a well-behaved state, the proposed method has the advantage of being a practical surrogate that is a more efficient tool when designing the set-up for TBL experiments, since it diagnoses the state of the boundary layer without the need to perform extensive velocity profile measurements.

scholarly journals Similarity Behavior in Transitional Boundary Layers Over a Range of Adverse Pressure Gradients and Turbulence Levels

1990 ◽  
Author(s):  
J. P. Gostelow ◽  
G. J. Walker
Keyword(s):  
Boundary Layer ◽  
Form Factor ◽  
Velocity Profile ◽  
Transition Region ◽  
Boundary Layers ◽  
Free Stream ◽  
Local Equilibrium ◽  
Pressure Gradients ◽  
Lag Effects ◽  
Free Stream Turbulence

Boundary layer transition has been investigated experimentally under low, moderate and high free-stream turbulence levels and varying adverse pressure gradients. Under high turbulence levels and adverse pressure gradients a pronounced subtransition was present. A strong degree of similarity in intermittency distributions was observed, for all conditions, when the Narasimha procedure for determination of transition inception was used. Effects of free-stream turbulence on the velocity profile are particularly strong for the laminar boundary layer upstream of the transition region. This could reflect the influence of the turbulence on the shear stress distribution throughout the layer and this matter needs further attention. The velocity profiles in wall coordinates undershoot the turbulent wall layer asymptote near the wall over most of the transition region. The rapidity with which transition occurs under adverse pressure gradients produces strong lag effects on the velocity profile; the starting turbulent boundary layer velocity profile may depart significantly from local equilibrium conditions. The practice of deriving integral properties and skin friction for transitional boundary layers by a linear combination of laminar and turbulent values for equilibrium layers is inconsistent with the observed lag effects. The velocity profile responds sufficiently slowly to the perturbation imposed by transition that much of the anticipated drop in form factor will not have occurred prior to the completion of transition. This calls into question both experimental techniques which rely on measured form factor to characterize transition and boundary layer calculations which rely on local equilibrium assumptions in the vicinity of transition.

On the generation of spatially growing waves in a boundary layer

1965 ◽  
Vol 22 (3) ◽  
pp. 433-441 ◽  
Author(s):  
M. Gaster
Keyword(s):  
Boundary Layer ◽  
Boundary Layers ◽  
Laminar Boundary Layer ◽  
Wave Number ◽  
Wave System ◽  
Velocity Fluctuations ◽  
Forced Wave ◽  
General Terms ◽  
Complex Wave ◽  
Complex Wave Number

The solution is obtained in general terms for the velocity fluctuations generated in a laminar boundary layer by an oscillating disturbance on the boundry wall. The form of excitation is chosen to represent a vibrating ribbon of the type used by Schubauer to force disturbance in boundary layers. The forced wave system generated by the ribbon is shown to be a spatially growing one, which is described far downstream by an eigenmode of the system which has a complex wave-number.

Prediction of the Becalmed Region for LP Turbine Profile Design

1997 ◽  
Author(s):  
Volker Schulte ◽  
Howard P. Hodson
Keyword(s):  
Boundary Layer ◽  
Boundary Layers ◽  
Turbulent Flows ◽  
Laminar Boundary Layer ◽  
Turbine Blades ◽  
Boundary Layer Separation ◽  
Suction Surface ◽  
High Lift ◽  
Lp Turbine ◽  
Profile Loss

Recent attention has focused on the so called ‘becalmed region’ that is observed inside the boundary layers of turbomachinery blading and is associated with the process of wake-induced transition. Significant reductions of profile loss have been shown for high lift LP turbine blades at low Reynolds-numbers due the effects of the becalmed region on the diffusing flow at the rear of the suction surface. In this paper the nature and the significance of the becalmed region are examined using experimental observations and computational studies. It is shown that the becalmed region may be modelled using the unsteady laminar boundary layer equations. Therefore, it is predictable independently of the transition or turbulence models employed. The effect of the becalmed region on the transition process is modelled using a spot-based intermittency transition model. An unsteady differential boundary layer code was used to numerically simulate a deterministic experiment involving an isolated turbulent spot. The predictability of the becalmed region means that the rate of entropy production can be calculated in that region. It is found to be of the order of that in a laminar boundary layer. It is for this reason and because the becalmed region may be encroached upon by pursuing turbulent flows that for attached boundary layers, wake-induced transition cannot significantly reduce the profile loss. However, the becalmed region is less prone to separation than a conventional laminar boundary layer. Therefore, the becalmed region may be exploited in order to prevent boundary layer separation and the increase in loss that this entails. It is shown that it should now be possible to design efficient high lift LP turbine blades.

Experiment on convex curvature effects in turbulent boundary layers

1973 ◽  
Vol 60 (1) ◽  
pp. 43-62 ◽  
Author(s):  
Ronald M. C. So ◽  
George L. Mellor
Keyword(s):  
Boundary Layer ◽  
Velocity Profile ◽  
Boundary Layers ◽  
Reynolds Stress ◽  
Convex Surface ◽  
Turbulent Boundary Layers ◽  
Turbulence Measurements ◽  
Curvature Effects ◽  
Convex Wall ◽  
Complete Set

Turbulent boundary layers along a convex surface of varying curvature were investigated in a specially designed boundary-layer tunnel. A fairly complete set of turbulence measurements was obtained.The effect of curvature is striking. For example, along a convex wall the Reynolds stress is decreased near the wall and vanishes about midway between the wall and the edge of a boundary layer where there exists a velocity profile gradient created upstream of the curved wall.

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