scholarly journals Shape factor of the turbulent boundary layer on a flat plate and the Reynolds shear stress in the outer region

2019 ◽  
Vol 4 (2) ◽  
Author(s):  
P. Phani Kumar ◽  
J. Dey
Keyword(s):  
Boundary Layer ◽  
Shear Stress ◽  
Turbulent Boundary Layer ◽  
Flat Plate ◽  
Shape Factor ◽  
Reynolds Shear Stress ◽  
Outer Region

The accelerated fully rough turbulent boundary layer

1977 ◽  
Vol 82 (3) ◽  
pp. 507-528 ◽  
Author(s):  
Hugh W. Coleman ◽  
Robert J. Moffat ◽  
William M. Kays
Keyword(s):  
Boundary Layer ◽  
Shear Stress ◽  
Turbulent Boundary Layer ◽  
Pressure Gradient ◽  
Stress Tensor ◽  
Skin Friction ◽  
Shape Factor ◽  
Reynolds Shear Stress ◽  
Smooth Wall ◽  
Mean Velocity

The behaviour of a fully rough turbulent boundary layer subjected to favourable pressure gradients both with and without blowing was investigated experimentally using a porous test surface composed of densely packed spheres of uniform size. Measurements of profiles of mean velocity and the components of the Reynolds-stress tensor are reported for both unblown and blown layers. Skin-friction coefficients were determined from measurements of the Reynolds shear stress and mean velocity.An appropriate acceleration parameterKrfor fully rough layers is defined which is dependent on a characteristic roughness dimension but independent of molecular viscosity. For a constant blowing fractionFgreater than or equal to zero, the fully rough turbulent boundary layer reaches an equilibrium state whenKris held constant. Profiles of the mean velocity and the components of the Reynolds-stress tensor are then similar in the flow direction and the skin-friction coefficient, momentum thickness, boundary-layer shape factor and the Clauser shape factor and pressure-gradient parameter all become constant.Acceleration of a fully rough layer decreases the normalized turbulent kinetic energy and makes the turbulence field much less isotropic in the inner region (forFequal to zero) compared with zero-pressure-gradient fully rough layers. The values of the Reynolds-shear-stress correlation coefficients, however, are unaffected by acceleration or blowing and are identical with values previously reported for smooth-wall and zero-pressure-gradient rough-wall flows. Increasing values of the roughness Reynolds number with acceleration indicate that the fully rough layer does not tend towards the transitionally rough or smooth-wall state when accelerated.

High-order moments of Reynolds shear stress fluctuations in a turbulent boundary layer

1973 ◽  
Vol 58 (3) ◽  
pp. 581-593 ◽  
Author(s):  
R. A. Antonia ◽  
J. D. Atkinson
Keyword(s):  
Boundary Layer ◽  
Shear Stress ◽  
Turbulent Boundary Layer ◽  
Fourth Order ◽  
High Speed ◽  
Reynolds Shear Stress ◽  
Digital Data ◽  
Normal Velocity ◽  
The Third ◽  
Digital Data Acquisition System

The cumulant-discard approach is used to predict the third- and fourth-order moments and the probability density of turbulent Reynolds shear stress fluctuations uv, the streamwise and normal velocity fluctuations being represented by u and v respectively. Measurements of these quantities in a turbulent boundary layer are presented, with the required statistics of uv obtained by the use of a high-speed digital data-acquisition system. Including correlations between u and u up to the fourth order, the cumulant-discard predictions are in close agreement with the measurements in the inner region of the layer but only qualitatively follow the experimental results in the outer intermittent region. In this latter region, predictions for the third- and fourth-order moments of uv are also obtained by assuming that the properties of both turbulent and irrotational fluctuations are Gaussian and by using some of the available conditional averages of u, v and uv.

Measurements in an Axisymmetric Turbulent Boundary Layer Along a Circular Cylinder

1976 ◽  
Vol 27 (3) ◽  
pp. 217-228 ◽  
Author(s):  
Noor Afzal ◽  
K P Singh
Keyword(s):  
Boundary Layer ◽  
Circular Cylinder ◽  
Turbulent Boundary Layer ◽  
Constant Pressure ◽  
Reynolds Shear Stress ◽  
Longitudinal Velocity ◽  
Outer Region ◽  
Wall Region ◽  
Mean Velocity ◽  
Dimensional Boundary

SummaryIn an axisymmetric turbulent boundary layer along a circular cylinder at constant pressure, measurements have been made of mean velocity profile and turbulence characteristics: longitudinal velocity fluctuations, Reynolds shear stress, transverse correlation and spectrum. It has been found that the qualitative behaviour of an axisymmetric turbulent boundary layer is similar to that of a two-dimensional boundary layer in the wall region, where as in the outer region the effects of transverse curvature are observed.

Evolution of a moderately short turbulent boundary layer in a severe pressure gradient

1974 ◽  
Vol 64 (4) ◽  
pp. 763-774 ◽  
Author(s):  
R. G. Deissler
Keyword(s):  
Boundary Layer ◽  
Shear Stress ◽  
Turbulent Boundary Layer ◽  
Pressure Gradient ◽  
Reynolds Shear Stress ◽  
Pressure Gradients ◽  
Mean Velocity ◽  
Mass Injection ◽  
The Mean ◽  
Theoretical Results

The early and intermediate development of a highly accelerated (or decelerated) turbulent boundary layer is analysed. For sufficiently large accelerations (or pressure gradients) and for total normal strains which are not excessive, the equation for the Reynolds shear stress simplifies to give a stress that remains approximately constant as it is convected along streamlines. The theoretical results for the evolution of the mean velocity in favourable and adverse pressure gradients agree well with experiment for the cases considered. A calculation which includes mass injection at the wall is also given.

Very-large-scale motions in a turbulent boundary layer

2011 ◽  
Vol 673 ◽  
pp. 80-120 ◽  
Author(s):  
JAE HWA LEE ◽  
HYUNG JIN SUNG
Keyword(s):  
Boundary Layer ◽  
Shear Stress ◽  
Turbulent Boundary Layer ◽  
Large Scale ◽  
Spatial Organization ◽  
Reynolds Shear Stress ◽  
Three Dimensional ◽  
Hairpin Vortices ◽  
Extraction Algorithm ◽  
Normal Distance

Direct numerical simulation of a turbulent boundary layer was performed to investigate the spatially coherent structures associated with very-large-scale motions (VLSMs). The Reynolds number was varied in the range Reθ = 570–2560. The main simulation was conducted by using a computational box greater than 50δo in the streamwise domain, where δo is the boundary layer thickness at the inlet, and inflow data was obtained from a separate inflow simulation based on Lund's method. Inspection of the three-dimensional instantaneous fields showed that groups of hairpin vortices are coherently arranged in the streamwise direction and that these groups create significantly elongated low- and high-momentum regions with large amounts of Reynolds shear stress. Adjacent packet-type structures combine to form the VLSMs; this formation process is attributed to continuous stretching of the hairpins coupled with lifting-up and backward curling of the vortices. The growth of the spanwise scale of the hairpin packets occurs continuously, so it increases rapidly to double that of the original width of the packets. We employed the modified feature extraction algorithm developed by Ganapathisubramani, Longmire & Marusic (J. Fluid Mech., vol. 478, 2003, p. 35) to identify the properties of the VLSMs of hairpin vortices. In the log layer, patches with the length greater than 3δ–4δ account for more than 40% of all the patches and these VLSMs contribute approximately 45% of the total Reynolds shear stress included in all the patches. The VLSMs have a statistical streamwise coherence of the order of ~6δ; the spatial organization and coherence decrease away from the wall, but the spanwise width increases monotonically with the wall-normal distance. Finally, the application of linear stochastic estimation demonstrated the presence of packet organization in the form of a train of packets in the log layer.

Mean Velocity, Reynolds Shear Stress, and Fluctuations of Velocity and Pressure Due to Log Laws in a Turbulent Boundary Layer and Origin Offset by Prandtl Transposition Theorem

2018 ◽  
Vol 140 (7) ◽  
Author(s):  
Noor Afzal ◽  
Abu Seena
Keyword(s):  
Boundary Layer ◽  
Shear Stress ◽  
Turbulent Boundary Layer ◽  
Skin Friction ◽  
Velocity Vector ◽  
Reynolds Shear Stress ◽  
Mean Velocity ◽  
Time Period ◽  
Log Law ◽  
Turbulent Burst

The maxima of Reynolds shear stress and turbulent burst mean period time are crucial points in the intermediate region (termed as mesolayer) for large Reynolds numbers. The three layers (inner, meso, and outer) in a turbulent boundary layer have been analyzed from open equations of turbulent motion, independent of any closure model like eddy viscosity or mixing length, etc. Little above (or below not considered here) the critical point, the matching of mesolayer predicts the log law velocity, peak of Reynolds shear stress domain, and turbulent burst time period. The instantaneous velocity vector after subtraction of mean velocity vector yields the velocity fluctuation vector, also governed by log law. The static pressure fluctuation p′ also predicts log laws in the inner, outer, and mesolayer. The relationship between u′/Ue with u/Ue from structure of turbulent boundary layer is presented in inner, meso, and outer layers. The turbulent bursting time period has been shown to scale with the mesolayer time scale; and Taylor micro time scale; both have been shown to be equivalent in the mesolayer. The shape factor in a turbulent boundary layer shows linear behavior with nondimensional mesolayer length scale. It is shown that the Prandtl transposition (PT) theorem connects the velocity of normal coordinate y with s offset to y + a, then the turbulent velocity profile vector and pressure fluctuation log laws are altered; but skin friction log law, based on outer velocity Ue, remains independent of a the offset of origin. But if skin friction log law is based on bulk average velocity Ub, then skin friction log law depends on a, the offset of origin. These predictions are supported by experimental and direct numerical simulation (DNS) data.

Streamwise development of turbulent boundary-layer drag reduction with polymer injection

2008 ◽  
Vol 597 ◽  
pp. 31-66 ◽  
Author(s):  
Y. X. HOU ◽  
V. S. R. SOMANDEPALLI ◽  
M. G. MUNGAL
Keyword(s):  
Boundary Layer ◽  
Shear Stress ◽  
Turbulent Boundary Layer ◽  
Drag Reduction ◽  
Reynolds Shear Stress ◽  
Depletion Region ◽  
Stress Profile ◽  
Total Stress ◽  
Polymer Injection ◽  
Shear Stress Profile

Zero-pressure-gradient turbulent boundary-layer drag reduction by polymer injection has been studied with particle image velocimetry. Flow fields ranging from low to maximum drag reduction have been investigated. A previously developed technique – the (1 − y/δ) fit to the total shear stress profile – has been used to evaluate the skin friction, drag reduction and polymer stress. Current results agree well with the semi-log plot of drag reduction vs. normalized polymer flux which has been used by previous workers and can be used as a guide to optimize the use of polymer from a single injector. Detailed flow-field statistics show many special features that pertain to polymer flow. It is shown that the mean velocity responds quickly to the suddenly reduced wall shear stress associated with polymer injection. However, it takes a much longer time for the entire Reynolds shear stress profile to adjust to the same change. The Reynolds shear stress profiles in wall units can be higher than unity and this unique feature can be used to further judge whether the flow is in equilibrium. The streamwise evolution of drag reduction magnitude is used to divide the flow into three regions: development region; steady-state region; and depletion region. The polymer stress is estimated and found to be proportional to drag reduction in the depletion region, but not necessarily so in the other regions. The interaction between injected polymer and turbulent activity in a developing boundary-layer flow is dependent upon the flow history and it produces an equally complex relationship between polymer stress and drag reduction. The stress balance in the boundary layer and the dynamical contribution of the various stresses to the total stress are evaluated and it is seen that the polymer stresses can account for up to 25% of the total stress. This finding is in contrast to channel flows with homogeneous polymer injection where the polymer stress is found to account for up to 60% of the total stress.

On the Axisymmetric Turbulent Boundary Layer Growth Along Long Thin Circular Cylinders

2014 ◽  
Vol 136 (5) ◽  
Author(s):  
Stephen A. Jordan
Keyword(s):  
Boundary Layer ◽  
Turbulent Boundary Layer ◽  
Flat Plate ◽  
Shape Factor ◽  
Experimental Testing ◽  
Reynolds Numbers ◽  
Layer Growth ◽  
Factor H ◽  
Circular Cylinders ◽  
Length Scales

Even after several decades of experimental and numerical testing, our present-day knowledge of the axisymmetric turbulent boundary layer (TBL) along long thin circular cylinders still lacks a clear picture of many fundamental characteristics. The main issues causing this reside in the experimental testing complexities and the numerical simplifications. An important characteristic that is crucial for routine scaling is the boundary layer length scales, but the downstream growth of these scales (boundary layer, displacement, and momentum thicknesses) is largely unknown from the leading to trailing edges. Herein, we combine pertinent datasets with many complementary numerical computations (large-eddy simulations) to address this shortfall. We are particularly interested in expressing the length scales in terms of the radius-based and axial-based Reynolds numbers (Rea and Rex). Although the composite dataset gave an averaged shape factor H = 1.09 that is substantially lower than the planar value (H = 1.27), the shape factor distribution along the cylinder axis actually begins at the flat plate value then decays logarithmically to near unity. The integral length scales displayed power-law evolutions with variable exponents until high Rea (Rea > 35,000) where both scales then mimic streamwise consistency. Beneath this threshold, their streamwise growth is much slower than the flat plate (especially at low-Rea). The boundary layer thickness grew according to an empirical expression that is dependent on both Rea and Rex where its streamwise growth can far exceed the planar turbulent flow. These unique characteristics rank the thin cylinder axisymmetric TBL as a separate canonical flow, which was well documented by the previous investigations.

Some turbulent/non-turbulent properties of the outer intermittent region of a boundary layer

1974 ◽  
Vol 64 (4) ◽  
pp. 645-678 ◽  
Author(s):  
Thomas B. Hedleyt ◽  
James F. Keffer
Keyword(s):  
Boundary Layer ◽  
Turbulent Boundary Layer ◽  
Flat Plate ◽  
Outer Region ◽  
Complete Picture ◽  
Digital Sampling ◽  
Large Eddy ◽  
Trailing Edges ◽  
Instantaneous Position ◽  
Processing Techniques

A detailed study of the intermittency in the outer region of a flat-plate turbulent boundary layer has been carried out using digital sampling and processing techniques. Conditional averages are used to generate mean and fluctuating components for the turbulent and non-turbulent zones of fluid. More particularly, point averages of these variables, taken with reference to the instantaneous position of the turbulent/non-turbulent interface, have been made to show the distribution of various quantities through the turbulent front. The results indicate that significant differences exist at leading and trailing edges of the turbulent bursts and a more complete picture of the motion of an average large eddy is deduced.

Turbulent boundary layers at moderate Reynolds numbers: inflow length and tripping effects

2012 ◽  
Vol 710 ◽  
pp. 5-34 ◽  
Author(s):  
Philipp Schlatter ◽  
Ramis Örlü
Keyword(s):  
Boundary Layer ◽  
Reynolds Number ◽  
Shear Stress ◽  
Turbulent Boundary Layer ◽  
Boundary Layers ◽  
Reynolds Shear Stress ◽  
Reynolds Numbers ◽  
Normal Velocity ◽  
Low Reynolds ◽  
Inflow Conditions

AbstractA recent assessment of available direct numerical simulation (DNS) data from turbulent boundary layer flows (Schlatter & Örlü,J. Fluid Mech., vol. 659, 2010, pp. 116–126) showed surprisingly large differences not only in the skin friction coefficient or shape factor, but also in their predictions of mean and fluctuation profiles far into the sublayer. While such differences are expected at very low Reynolds numbers and/or the immediate vicinity of the inflow or tripping region, it remains unclear whether inflow and tripping effects explain the differences observed even at moderate Reynolds numbers. This question is systematically addressed by re-simulating the DNS of a zero-pressure-gradient turbulent boundary layer flow by Schlatteret al. (Phys. Fluids, vol. 21, 2009, art. 051702). The previous DNS serves as the baseline simulation, and the new DNS with a range of physically different inflow conditions and tripping effects are carefully compared. The downstream evolution of integral quantities as well as mean and fluctuation profiles is analysed, and the results show that different inflow conditions and tripping effects do indeed explain most of the differences observed when comparing available DNS at low Reynolds number. It is further found that, if transition is initiated inside the boundary layer at a low enough Reynolds number (based on the momentum-loss thickness)${\mathit{Re}}_{\theta } \lt 300$, all quantities agree well for both inner and outer layer for${\mathit{Re}}_{\theta } \gt 2000$. This result gives a lower limit for meaningful comparisons between numerical and/or wind tunnel experiments, assuming that the flow was not severely over- or understimulated. It is further shown that even profiles of the wall-normal velocity fluctuations and Reynolds shear stress collapse for higher${\mathit{Re}}_{\theta } $irrespective of the upstream conditions. In addition, the overshoot in the total shear stress within the sublayer observed in the DNS of Wu & Moin (Phys. Fluids, vol. 22, 2010, art. 085105) has been identified as a feature of transitional boundary layers.

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