Comparison of Two Analyses of Boundary-Layer Data on a Flat Plate

1958 ◽  
Vol 2 (01) ◽  
pp. 21-33
Author(s):  
L. Landweber ◽  
T. T. Siao

In a recent paper (1) it was indicated that there appeared to be a need for generalizing the well-known logarithmic law of turbulent boundary layers and such a generalization was derived on the basis of a suggestion due to Townsend (2). It was found that the logarithmic formulas constitute only one member of a family of possible formulas, among which that one which best fits the boundary-layer data should be selected.

2000 ◽  
Vol 122 (3) ◽  
pp. 542-546 ◽  
Author(s):  
Anupam Dewan ◽  
Jaywant H. Arakeri

The intermittency profile in the turbulent flat-plate zero pressure-gradient boundary-layer and a thick axisymmetric boundary-layer has been computed using the Reynolds-averaged k−ε−γ model, where k denotes turbulent kinetic energy, ε its rate of dissipation, and γ intermittency. The Reynolds-averaged model is simpler compared to the conditional model used in the literature. The dissipation equation of the Reynolds-averaged model is modified to account for the effect of entrainment. It has been shown that the model correctly predicts the observed intermittency of the flows. [S0098-2202(00)02403-2]


Author(s):  
Keiji Takeuchi ◽  
Susumu Fujimoto ◽  
Eitaro Koyabu ◽  
Tetsuhiro Tsukiji

Wake-induced bypass transition of boundary layers on a flat plate subjected to favorable and adverse pressure gradients was investigated. Detailed boundary layer measurements were conducted using two hot-wire probes. A spoked-wheel-type wake generator was used to create periodic wakes in front of the flat plate. The main focus of this study was to reveal the effect of the Strouhal number, which changed by using different numbers of wake-generating bars, on the turbulence intensity distribution and the transition onset position of the boundary layer on the flat plate using two hot-wire probes.


1961 ◽  
Vol 28 (3) ◽  
pp. 323-329 ◽  
Author(s):  
Eva M. Winkler

Naturally turbulent boundary layers on a cooled flat plate have been investigated at several distances from the leading edge of the plate at a Mach number of 5.2 for three rates of steady-state heat transfer to the surface. Measurements of Pitot and static pressures and of total and wall temperatures made it possible to compute velocity profiles, static-temperature profiles, and boundary-layer parameters without resorting to assumptions. The data demonstrate that the Reynolds analogy between skin friction and heat transfer is valid for all conditions of the present experiments. With increasing rate of heat transfer to the surface, the skin-friction coefficient was found to decrease, a phenomenon opposite to that predicted by theories and empirical relations. On the basis of the present data and other published results of compressible and incompressible turbulent boundary-layer skin friction, a simple relation was devised which describes closely the variation of the skin-friction coefficient with Mach number, heat-transfer rate, and momentum-thickness Reynolds number.


Author(s):  
Ju Hyun Shin ◽  
Seung Jin Song

Rough wall turbulent boundary layers subjected to pressure gradient have engineering interest for many fluid machinery applications. A number of investigations have been made to understand surface roughness and pressure gradient effects on turbulent boundary layer characteristics, but separately. In this paper, turbulent boundary layers over a flat plate with surface roughness and favorable pressure gradient (FPG) are experimentally investigated. Boundary layers in different streamwise locations were measured using boundary layer type hot-wire anemometry. Rough wall zero pressure gradient (ZPG) turbulent boundary layers were also measured to compare the result from the investigation. The surface roughness was applied by attaching sandpapers on the flat plate. The magnitude of surface roughness is representative of land-based gas turbine compressor blade. Pressure gradient was adjusted using movable endwall of the test section. Results from the measurement show characteristics of the turbulent boundary layer growth affected by both surface roughness and favorable pressure gradient.


1968 ◽  
Vol 19 (1) ◽  
pp. 1-19 ◽  
Author(s):  
H. McDonald

SummaryRecently two authors, Nash and Goldberg, have suggested, intuitively, that the rate at which the shear stress distribution in an incompressible, two-dimensional, turbulent boundary layer would return to its equilibrium value is directly proportional to the extent of the departure from the equilibrium state. Examination of the behaviour of the integral properties of the boundary layer supports this hypothesis. In the present paper a relationship similar to the suggestion of Nash and Goldberg is derived from the local balance of the kinetic energy of the turbulence. Coupling this simple derived relationship to the boundary layer momentum and moment-of-momentum integral equations results in quite accurate predictions of the behaviour of non-equilibrium turbulent boundary layers in arbitrary adverse (given) pressure distributions.


2012 ◽  
Vol 696 ◽  
pp. 122-151 ◽  
Author(s):  
Kan Wang ◽  
Meng Wang

AbstractCompressible large-eddy simulations are carried out to study the aero-optical distortions caused by Mach 0.5 flat-plate turbulent boundary layers at Reynolds numbers of ${\mathit{Re}}_{\theta } = 875$, 1770 and 3550, based on momentum thickness. The fluctuations of refractive index are calculated from the density field, and wavefront distortions of an optical beam traversing the boundary layer are computed based on geometric optics. The effects of aperture size, small-scale turbulence, different flow regions and beam elevation angle are examined and the underlying flow physics is analysed. It is found that the level of optical distortion decreases with increasing Reynolds number within the Reynolds-number range considered. The contributions from the viscous sublayer and buffer layer are small, while the wake region plays a dominant role, followed by the logarithmic layer. By low-pass filtering the fluctuating density field, it is shown that small-scale turbulence is optically inactive. Consistent with previous experimental findings, the distortion magnitude is dependent on the propagation direction due to anisotropy of the boundary-layer vortical structures. Density correlations and length scales are analysed to understand the elevation-angle dependence and its relation to turbulence structures. The applicability of Sutton’s linking equation to boundary-layer flows is examined, and excellent agreement between linking equation predictions and directly integrated distortions is obtained when the density length scale is appropriately defined.


2013 ◽  
Vol 715 ◽  
pp. 477-498 ◽  
Author(s):  
Zambri Harun ◽  
Jason P. Monty ◽  
Romain Mathis ◽  
Ivan Marusic

AbstractResearch into high-Reynolds-number turbulent boundary layers in recent years has brought about a renewed interest in the larger-scale structures. It is now known that these structures emerge more prominently in the outer region not only due to increased Reynolds number (Metzger & Klewicki, Phys. Fluids, vol. 13(3), 2001, pp. 692–701; Hutchins & Marusic, J. Fluid Mech., vol. 579, 2007, pp. 1–28), but also when a boundary layer is exposed to an adverse pressure gradient (Bradshaw, J. Fluid Mech., vol. 29, 1967, pp. 625–645; Lee & Sung, J. Fluid Mech., vol. 639, 2009, pp. 101–131). The latter case has not received as much attention in the literature. As such, this work investigates the modification of the large-scale features of boundary layers subjected to zero, adverse and favourable pressure gradients. It is first shown that the mean velocities, turbulence intensities and turbulence production are significantly different in the outer region across the three cases. Spectral and scale decomposition analyses confirm that the large scales are more energized throughout the entire adverse pressure gradient boundary layer, especially in the outer region. Although more energetic, there is a similar spectral distribution of energy in the wake region, implying the geometrical structure of the outer layer remains universal in all cases. Comparisons are also made of the amplitude modulation of small scales by the large-scale motions for the three pressure gradient cases. The wall-normal location of the zero-crossing of small-scale amplitude modulation is found to increase with increasing pressure gradient, yet this location continues to coincide with the large-scale energetic peak wall-normal location (as has been observed in zero pressure gradient boundary layers). The amplitude modulation effect is found to increase as pressure gradient is increased from favourable to adverse.


1966 ◽  
Vol 8 (4) ◽  
pp. 426-436 ◽  
Author(s):  
A. D. Carmichael ◽  
G. N. Pustintsev

Methods of predicting the growth of turbulent boundary layers in conical diffusers using the kinetic-energy deficit equation were developed. Three different forms of auxiliary equations were used. Comparison between the measured and predicted results showed that there was fair agreement although there was a tendency to underestimate the predicted momentum thickness and over-estimate the predicted shape factor.


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