Low-Reynolds-Number Turbulent Boundary Layers in Zero and Favorable Pressure Gradients

1983 ◽  
Vol 27 (03) ◽  
pp. 147-157 ◽  
Author(s):  
A. J. Smits ◽  
N. Matheson ◽  
P. N. Joubert
Keyword(s):  
Friction Coefficient ◽  
Skin Friction ◽  
Boundary Layers ◽  
Leading Edge ◽  
Reynolds Numbers ◽  
Skin Friction Coefficient ◽  
Turbulent Boundary Layers ◽  
Pressure Gradients ◽  
Mean Flow ◽  
Low Reynolds

This paper reports the results of an extensive experimental investigation into the mean flow properties of turbulent boundary layers with momentum-thickness Reynolds numbers less than 3000. Zero pressure gradient and favorable pressure gradients were studied. The velocity profiles displayed a logarithmic region even at very low Reynolds numbers (as low as Rθ = 261). The results were independent of the leading-edge shape, and the pin-type turbulent stimulators performed well. It was found that the shape and Clauser parameters were a little higher than the correlation proposed by Coles [10], and the skin friction coefficient was a little lower. The skin friction coefficient behavior could be fitted well by a simple power-law relationship in both zero and favorable pressure gradients.

Turbulent Boundary Layers in Low Reynolds Number Shallow Open Channel Flows

1999 ◽  
Vol 121 (3) ◽  
pp. 684-689 ◽  
Author(s):  
Ram Balachandar ◽  
Shyam S. Ramachandran
Keyword(s):  
Reynolds Number ◽  
Boundary Layers ◽  
Open Channel ◽  
Reynolds Numbers ◽  
Skin Friction Coefficient ◽  
Turbulent Boundary Layers ◽  
Channel Flows ◽  
Open Channel Flows ◽  
Mean Velocity ◽  
Low Reynolds

The results of an experimental investigation of turbulent boundary layers in shallow open channel flows at low Reynolds numbers are presented. The study was aimed at extending the database toward lower values of Reynolds number. The data presented are primarily concerned with the longitudinal mean velocity, turbulent-velocity fluctuations, boundary layer shape parameter and skin friction coefficient for Reynolds numbers based on the momentum thickness (Reθ) ranging from 180 to 480. In this range, the results of the present investigation in shallow open channel flows indicate a lack of dependence of the von Karman constant κ on Reynolds number. The extent to which the mean velocity data overlaps with the log-law decreases with decreasing Reθ. The variation of the strength of the wake with Reθ is different from the trend proposed earlier by Coles.

Investigation of Flat-Plate Hypersonic, Turbulent Boundary Layers With Heat Transfer

1961 ◽  
Vol 28 (3) ◽  
pp. 323-329 ◽  
Author(s):  
Eva M. Winkler
Keyword(s):  
Heat Transfer ◽  
Boundary Layer ◽  
Friction Coefficient ◽  
Mach Number ◽  
Flat Plate ◽  
Skin Friction ◽  
Boundary Layers ◽  
Skin Friction Coefficient ◽  
Turbulent Boundary Layers ◽  
Reynolds Analogy

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.

Prediction of Transpired Turbulent Boundary Layers With Arbitrary Pressure Gradients

1997 ◽  
Vol 119 (3) ◽  
pp. 526-532 ◽  
Author(s):  
Miodrag Oljaca ◽  
James Sucec
Keyword(s):  
Experimental Data ◽  
Skin Friction ◽  
Boundary Layers ◽  
Integral Method ◽  
Skin Friction Coefficient ◽  
Turbulent Boundary Layers ◽  
Pressure Gradients ◽  
Wide Range ◽  
Better Than ◽  
Good Agreement

An integral method, using Coles combined inner and outer law as the velocity profile, is developed for calculation of turbulent boundary layers with blowing or suction and pressure gradients. The resulting ordinary differential equations are solved numerically for the distribution of skin friction coefficient and integral thickness along the surface. Comparisons of predicted skin friction coefficients with experimental data are made for a wide range of blowing and suction rates and for various pressure gradients, including adverse, zero and a strong favorable gradient. In addition to good agreement with experimental data for constant blowing fractions F, the method is also successfully tested on cases where the blowing fraction is variable with position. Predictions, in general, exhibit satisfactory agreement with the data. The integral method predictions are comparable to, or better than, a number of finite difference procedures in a limited number of cases where comparisons were made.

scholarly journals Self-similar compressible turbulent boundary layers with pressure gradients. Part 1. Direct numerical simulation and assessment of Morkovin’s hypothesis

2019 ◽  
Vol 880 ◽  
pp. 239-283 ◽  
Author(s):  
Christoph Wenzel ◽  
Tobias Gibis ◽  
Markus Kloker ◽  
Ulrich Rist
Keyword(s):  
Numerical Simulation ◽  
Boundary Layer ◽  
Mach Number ◽  
Direct Numerical Simulation ◽  
Boundary Layers ◽  
Turbulent Boundary Layers ◽  
Shear Stresses ◽  
Pressure Gradients ◽  
Mean Flow ◽  
Self Similar

A direct numerical simulation study of self-similar compressible flat-plate turbulent boundary layers (TBLs) with pressure gradients (PGs) has been performed for inflow Mach numbers of 0.5 and 2.0. All cases are computed with smooth PGs for both favourable and adverse PG distributions (FPG, APG) and thus are akin to experiments using a reflected-wave set-up. The equilibrium character allows for a systematic comparison between sub- and supersonic cases, enabling the isolation of pure PG effects from Mach-number effects and thus an investigation of the validity of common compressibility transformations for compressible PG TBLs. It turned out that the kinematic Rotta–Clauser parameter $\unicode[STIX]{x1D6FD}_{K}$ calculated using the incompressible form of the boundary-layer displacement thickness as length scale is the appropriate similarity parameter to compare both sub- and supersonic cases. Whereas the subsonic APG cases show trends known from incompressible flow, the interpretation of the supersonic PG cases is intricate. Both sub- and supersonic regions exist in the boundary layer, which counteract in their spatial evolution. The boundary-layer thickness $\unicode[STIX]{x1D6FF}_{99}$ and the skin-friction coefficient $c_{f}$, for instance, are therefore in a comparable range for all compressible APG cases. The evaluation of local non-dimensionalized total and turbulent shear stresses shows an almost identical behaviour for both sub- and supersonic cases characterized by similar $\unicode[STIX]{x1D6FD}_{K}$, which indicates the (approximate) validity of Morkovin’s scaling/hypothesis also for compressible PG TBLs. Likewise, the local non-dimensionalized distributions of the mean-flow pressure and the pressure fluctuations are virtually invariant to the local Mach number for same $\unicode[STIX]{x1D6FD}_{K}$-cases. In the inner layer, the van Driest transformation collapses compressible mean-flow data of the streamwise velocity component well into their nearly incompressible counterparts with the same $\unicode[STIX]{x1D6FD}_{K}$. However, noticeable differences can be observed in the wake region of the velocity profiles, depending on the strength of the PG. For both sub- and supersonic cases the recovery factor was found to be significantly decreased by APGs and increased by FPGs, but also to remain virtually constant in regions of approximated equilibrium.

Control of Separated Boundary-Layer on Subsonic Airfoil Using Vortex Generator Jet Devices

2006 ◽  
Author(s):  
A. Kourta ◽  
G. Petit ◽  
J. C. Courty ◽  
J. P. Rosenblum
Keyword(s):  
Boundary Layer ◽  
Friction Coefficient ◽  
Skin Friction ◽  
Three Dimensional ◽  
Vortex Generator ◽  
Leading Edge ◽  
Skin Friction Coefficient ◽  
Synthetic Jets ◽  
High Lift ◽  
Longitudinal Vortices

The control of subsonic high lift induced separation on airfoil may improve the flight envelope of current aircraft or even simplify the complex and heavy high-lift devices on commercial airframes. Until now, synthetic jets have proved a really interesting efficiency to delay or remove even leading-edge located separated areas on high-lift configuration but are not efficient for real scale aircrafts. In case of pressure-like separation (i.e. from trailing-edge), synthetic jets can be replaced by so the called “Vortex Generator Jets” which create strong longitudinal vortices that increase mixing in inner boundary layer and consequently the skin friction coefficient is increased to prevent separation. In this study, numerical simulations were undertaken on a generic three dimensional flat plate in order to quantify the effect of the longitudinal vortices on the natural skin friction coefficient. Both counter and co-rotative devices were tested at different exhaust velocities and distances between each others. Finally co-rotative vortex generators jets were tested on a three dimensional generic airfoil ONERA D. Results show a delay of the separation occurence but this solution does not seem to be as robust as synthetic jets. The study of jets spacing with respect to the efficiency of the devices shows a maximum for a given ratio of spacing to exhaust velocity.

scholarly journals Low-Reynolds-number turbulent boundary layers

1991 ◽  
Vol 230 ◽  
pp. 1-44 ◽  
Author(s):  
Lincoln P. Erm ◽  
Peter N. Joubert
Keyword(s):  
Reynolds Number ◽  
Boundary Layers ◽  
Low Reynolds Number ◽  
Turbulent Boundary Layers ◽  
Stream Velocity ◽  
Wall Region ◽  
Mean Flow ◽  
Low Reynolds ◽  
High Reynolds ◽  
Turbulent Wall

An investigation was undertaken to improve our understanding of low-Reynolds-number turbulent boundary layers flowing over a smooth flat surface in nominally zero pressure gradients. In practice, such flows generally occur in close proximity to a tripping device and, though it was known that the flows are affected by the actual low value of the Reynolds number, it was realized that they may also be affected by the type of tripping device used and variations in free-stream velocity for a given device. Consequently, the experimental programme was devised to investigate systematically the effects of each of these three factors independently. Three different types of device were chosen: a wire, distributed grit and cylindrical pins. Mean-flow, broadband-turbulence and spectral measurements were taken, mostly for values of Rθ varying between about 715 and about 2810. It was found that the mean-flow and broadband-turbulence data showed variations with Rθ, as expected. Spectra were plotted using scaling given by Perry, Henbest & Chong (1986) and were compared with their models which were developed for high-Reynolds-number flows. For the turbulent wall region, spectra showed reasonably good agreement with their model. For the fully turbulent region, spectra did show some appreciable deviations from their model, owing to low-Reynolds-number effects. Mean-flow profiles, broadband-turbulence profiles and spectra were found to be affected very little by the type of device used for Rθ ≈ 1020 and above, indicating an absence of dependence on flow history for this Rθ range. These types of measurements were also compared at both Rθ ≈ 1020 and Rθ ≈ 2175 to see if they were dependent on how Rθ was formed (i.e. the combination of velocity and momentum thickness used to determine Rθ). There were noticeable differences for Rθ ≈ 1020, but these differences were only convincing for the pins, and there was a general overall improvement in agreement for Rθ ≈ 2175.

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