Review—Mean Flow in Turbulent Boundary Layers Disturbed to Alter Skin Friction

1986 ◽  
Vol 108 (2) ◽  
pp. 127-140 ◽  
Author(s):  
P. R. Bandyopadhyay
Keyword(s):  
Boundary Layer ◽  
Drag Reduction ◽  
Skin Friction ◽  
Boundary Layers ◽  
Convex Surface ◽  
Outer Boundary ◽  
Turbulent Boundary Layers ◽  
Mean Flow ◽  
Polymer Addition ◽  
Convex Curvature

Recent developments in methods of reducing drag in turbulent boundary layers have been briefly reviewed. The behavior of the mean flow in several drag reducing boundary-layer flows of current interest, viz., those over longitudinal surface riblets, outer-layer devices (OLD’s), and longitudinal convex surface curvature, has been examined. The boundary layer on a surface with longitudinal concave curvature has been studied to complement the results of convex curvature. The riblets alter the flow in their vicinity only and cause no drag penalty. However, the OLD’s disturb the entire boundary layer, and it is the slow downstream (≃150 δ0) relaxation back to the equilibrium state that produces a region of lower skin friction; a net drag reduction results when the wall-drag reduction exceeds the drag penalty due to the device. The net drag reduction achieved by the riblets and OLD’s remains a modest 10 percent compared with the more spectacular levels reached by polymer addition and microbubble injection in water. Over mild convex curvatures, the outer-boundary-layer response is a function of the curvature ratio (δ0/R), and the relaxation rate after a length of convex curvature is a function of the curved length ratio (Δs0/δi). Boundary layers exhibit an asymmetric response to streamwise surface curvatures; the response is slower to a concave curvature than to a convex. Detailed turbulence and accurate wall shear stress measurements in the altered boundary layers are needed to understand the drag-reducing mechanisms involved.

Experimental investigation of three-dimensional turbulent boundary layers on ‘infinite’ swept curved wings

1990 ◽  
Vol 211 ◽  
pp. 95-122 ◽  
Author(s):  
V. Baskaran ◽  
Y. G. Pontikis ◽  
P. Bradshaw
Keyword(s):  
Boundary Layer ◽  
Boundary Layers ◽  
Three Dimensional ◽  
Initial Boundary ◽  
Turbulent Boundary Layers ◽  
Radius Of Curvature ◽  
Turbulence Structure ◽  
Mean Flow ◽  
Convex Curvature ◽  
Curved Ducts

Mean flow and turbulence measurements have been made in three-dimensional turbulent boundary layers in curved ducts, simulating adverse pressure gradients on two ‘infinite’ swept curved wing surfaces with concave and convex curvature respectively. The ratio of the initial boundary-layer thickness to the surface radius of curvature in both cases is approximately 0.01, the value used in the earlier two-dimensional turbulent boundary-layer studies on the effects of concave and convex curvature by Hoffmann, Muck & Bradshaw (1985) and Muck, Hoffmann & Bradshaw (1985) respectively. The pressure-driven crossflow has nearly the same streamwise distribution as in the ‘infinite’ swept flat-surface experiment of Bradshaw & Pontikos (1985), which used a similar duct. The results of the present study show that the coupled effects of mean flow three-dimensionality and prolonged mild surface curvature of either sign have rather a weak influence on the turbulence structure, unlike the significant influence of the above extra strain rates when applied individually. In the concave case, the effect of the crossflow appears to oppose the destabilizing effect of curvature in addition to suppressing spanwise wavy inhomogeneities In contrast, the weak combined influence of convex curvature and crossflow, both of which, separately, tend to attenuate turbulence, implies that the interaction between the two effects is grossly nonlinear. Implications of the present results for turbulence modelling are briefly discussed.

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.

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.

Direct numerical simulation of complete transition to turbulence via oblique breakdown at Mach 3

2011 ◽  
Vol 674 ◽  
pp. 5-42 ◽  
Author(s):  
CHRISTIAN S. J. MAYER ◽  
DOMINIC A. VON TERZI ◽  
HERMANN F. FASEL
Keyword(s):  
Boundary Layer ◽  
Turbulent Boundary Layer ◽  
Skin Friction ◽  
Boundary Layers ◽  
Wave Spectrum ◽  
Linear Stability Theory ◽  
Transition To Turbulence ◽  
Transitional Region ◽  
Mean Flow ◽  
Mach 3

A pair of oblique waves at low amplitudes is introduced in a supersonic flat-plate boundary layer at Mach 3. Its downstream development and the concomitant process of laminar to turbulent transition is then investigated numerically using linear-stability theory, parabolized stability equations and direct numerical simulations (DNS). In the present paper, the linear regime is studied first in great detail. The focus of the second part is the early and late nonlinear regimes. It is shown how the disturbance wave spectrum is filled up by nonlinear interactions and which flow structures arise and how these structures locally break down to small scales. Finally, the study answers the question whether a fully developed turbulent boundary layer can be reached by oblique breakdown. It is shown that the skin friction develops such as is typical of transitional and turbulent boundary layers. Initially, the skin friction coefficient increases in the streamwise direction in the transitional region and finally decays when the early turbulent state is reached. Downstream of the maximum in the skin friction, the flow loses its periodicity in time and possesses characteristic mean-flow and spectral properties of a turbulent boundary layer. The DNS data clearly demonstrate that oblique breakdown can lead to a fully developed turbulent boundary layer and therefore it is a relevant mechanism for transition in two-dimensional supersonic boundary layers.

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.

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.

Developing turbulent boundary layers with system rotation

1985 ◽  
Vol 157 ◽  
pp. 405-448 ◽  
Author(s):  
J. H. Watmuff ◽  
H. T. Witt ◽  
P. N. Joubert
Keyword(s):  
Skin Friction ◽  
Boundary Layers ◽  
Large Scale ◽  
Turbulent Boundary Layers ◽  
Momentum Balance ◽  
Reynolds Stresses ◽  
Mean Flow ◽  
Mean Velocity ◽  
Secondary Circulations ◽  
Spatially Periodic

Measurements are presented for low-Reynolds-number turbulent boundary layers developing in a zero pressure gradient on the sidewall of a duct. The effect of rotation on these layers is examined. The mean-velocity profiles affected by rotation are described in terms of a common universal sublayer and modified logarithmic and wake regions.The turbulence quantities follow an inner and outer scaling independent of rotation. The effect appears to be similar to that, of increased or decreased layer development. Streamwise-energy spectra indicate that, for a given non-dimensional wall distance, it is the low-wavenumber spectral components alone that are affected by rotation.Large spatially periodic spanwise variations of skin friction are observed in the destabilized layers. Mean-velocity vectors in the cross-stream plane clearly show an array of vortex-like structures which correlate strongly with the skin-friction pattern. Interesting properties of these mean-flow structures are shown and their effect on Reynolds stresses is revealed. Near the duct centreline, where we have measured detailed profiles, the variations are small and there is a reasonable momentum balance.Large-scale secondary circulations are also observed but the strength of the pattern is weak and it appears to be confined to the top and bottom regions of the duct. The evidence suggests that it has minimally affected the flow near the duct centreline where detailed profiles were measured.

Simple Methods for Determining the Virtual Origin of Turbulent Boundary Layers in Hypersonic Flow on Sharp-Edged Flat Plates

1974 ◽  
Vol 41 (3) ◽  
pp. 551-553
Author(s):  
E. J. Hopkins
Keyword(s):  
Boundary Layer ◽  
Skin Friction ◽  
Hypersonic Flow ◽  
Boundary Layers ◽  
Turbulent Boundary Layers ◽  
Boundary Layer Transition ◽  
Simple Relationship ◽  
Flat Plates ◽  
Layer Transition ◽  
Virtual Origin

For hypersonic Mach numbers up to about 8, the virtual origin for turbulent skin-friction calculations is shown to be close to the beginning of boundary-layer transition. A simple relationship between the beginning and end of boundary-layer transition is presented.

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