Low-Reynolds-Number Turbulent Boundary Layers

1981 ◽  
Vol 103 (4) ◽  
pp. 624-630 ◽  
Author(s):  
B. R. White
Keyword(s):  
Boundary Layer ◽  
Shape Factor ◽  
Reynolds Numbers ◽  
Viscous Sublayer ◽  
Factor H ◽  
Boundary Layer Flows ◽  
Viscous Effects ◽  
Boundary Layer Height ◽  
Wind Tunnel Data ◽  
Logarithmic Velocity Profile

This paper presents experimental wind-tunnel data that show the universal logarithmic velocity profile for zero-pressure-gradient turbulent boundary layer flows is valid for values of momentum-deficit Reynolds numbers Rθ as low as 600. However, for values of Rθ between 425 and 600, the von Ka´rma´n and additive constants vary and are shown to be functions of Rθ and shape factor H. Furthermore, the viscous sublayer in the range 425<Rθ<600 can no longer maintain its characteristically small size. It is forced to grow, due to viscous effects, into a super sublayer (6-9 percent of the boundary layer height) that greatly exceeds conventional predictions of sublayer heights.

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.

An Approach to Three-Dimensional Turbulent Boundary Layers

1966 ◽  
Author(s):  
A. D. Carmichael
Keyword(s):  
Boundary Layer ◽  
Boundary Layers ◽  
Shape Factor ◽  
Basic Assumption ◽  
Three Dimensional ◽  
Cross Flow ◽  
Turbulent Boundary Layers ◽  
Factor H ◽  
Simple Method ◽  
The Cross

A relatively simple method for predicting some of the characteristics of three-dimensional turbulent boundary layers is presented. The basic assumption of the method is that the cross-flow is small. An empirical correlation of a basic shape factor of the cross-flow boundary layer against the streamwise shape factor H is provided. This correlation, together with data for the streamwise boundary layer, is used to predict the cross flow. The solution is very sensitive to the accuracy of the streamwise boundary-layer data which is predicted by conventional two-dimensional methods.

Investigation of Boundary Layer Flows Over a Flat Plate With Different-Size Transverse Square Grooves at s/w = 10

2007 ◽  
Author(s):  
Redha Wahidi ◽  
Walid Chakroun ◽  
Sami Al-Fahad
Keyword(s):  
Boundary Layer ◽  
Flat Plate ◽  
Skin Friction ◽  
Turbulence Intensity ◽  
Viscous Sublayer ◽  
Velocity Profiles ◽  
Boundary Layer Flows ◽  
Mean Velocity ◽  
Uncertainty Range ◽  
The Mean

Turbulent boundary layer flows over a flat plate with multiple transverse square grooves spaced 10 element widths apart were investigated. Mean velocity profiles, turbulence intensity profiles, and the distributions of the skin-friction coefficients (Cf) and the integral parameters are presented for two grooved walls. The two transverse square groove sizes investigated are 5mm and 2.5mm. Laser-Doppler Anemometer (LDA) was used for the mean velocity and turbulence intensity measurements. The skin-friction coefficient was determined from the gradient of the mean velocity profiles in the viscous sublayer. Distribution of Cf in the first grooved-wall case (5mm) shows that Cf overshoots downstream of the groove and then oscillates within the uncertainty range and never shows the expected undershoot in Cf. The same overshoot is seen in the second grooved-wall case (2.5mm), however, Cf continues to oscillate above the uncertainty range and never returns to the smooth-wall value. The mean velocity profiles clearly represent the behavior of Cf where a downward shift is seen in the Cf overshoot region and no upward shift is seen in these profiles. The results show that the smaller grooves exhibit larger effects on Cf, however, the boundary layer responses to these effects in a slower rate than to those of the larger grooves.

The Shape-Factor Relationship for Turbulent Boundary Layers

1983 ◽  
Vol 34 (2) ◽  
pp. 147-161 ◽  
Author(s):  
M.M.M. El Telbany ◽  
J. Niknejad ◽  
A.J. Reynolds
Keyword(s):  
Boundary Layer ◽  
Boundary Layers ◽  
Shape Factor ◽  
Factor H ◽  
Boundary Layer Development ◽  
The Common ◽  
Modified Formula ◽  
The Relationship ◽  
Layer Development ◽  
Common Shape

SummaryConsideration is given to the relationship H1 = f(H) linking the common shape factor H and the mass-flow shape parameter H1 which is used in entrainment models of boundary-layer development. A formula suggested by Green et al is found to be most nearly consistent with the measurements presented. However, a more exact prediction of H1 is obtained by introducing a factor involving the Reynolds number based on the local momentum thickness θ; thus H1 = f(H, Reθ). Predictions obtained by incorporating the appropriately modified entrainment equation into the well-known method of Green et al prove not to give an improved representation of the development of boundary layers studied experimentally by the authors and others. It is concluded that the modified formula for H1 is primarily useful in giving an improved specification of the overall boundary layer thickness δ = θ(H1 + H), and hence of other features of the developing profile.

Effects of Free Stream Turbulence on Intermittent Boundary Layer Flows

1995 ◽  
Author(s):  
Anestis I. Kalfas ◽  
Robin L. Elder
Keyword(s):  
Boundary Layer ◽  
Stream Flow ◽  
Free Stream ◽  
Leading Edge ◽  
Reynolds Numbers ◽  
Flow Transition ◽  
Flow Conditions ◽  
Boundary Layer Flows ◽  
Laminar Separation ◽  
Free Stream Turbulence

This paper considers the effects of free stream turbulence intensity on intermittent boundary layer flows related to turbomachinery. The present experimental investigation has been undertaken under free stream flow conditions dominated by grid generated turbulence and Reynolds numbers appropriate for turbomachinery applications. Unseparated flow transition in the boundary layer has been considered using a flat plate with the C4 leading edge which has been designed to avoid laminar separation. This configuration provided the opportunity to study the effect of a realistic turbomachinery leading edge shape on transition. Boundary layer type hot-wire probes have been used in order to acquire detailed information about the effect of the free stream conditions and the leading edge configuration on the structure of the boundary layer. Furthermore, information about the intermittency distribution throughout the boundary layer has been obtained using statistical analysis of the velocity record of the flow field.

An Analysis of Axisymmetric Turbulent Flow Past a Long Cylinder

1972 ◽  
Vol 94 (1) ◽  
pp. 200-204 ◽  
Author(s):  
F. M. White
Keyword(s):  
Boundary Layer ◽  
Shape Factor ◽  
Boundary Layer Thickness ◽  
Axial Flow ◽  
Reynolds Numbers ◽  
Small Radius ◽  
Law Of The Wall ◽  
Curvature Effects ◽  
Flow Past ◽  
Long Cylinder

An analysis is presented which predicts the properties of an arbitrarily thick turbulent boundary layer for incompressible axial flow past a long cylinder. The approach makes use of a modified form of the law-of-the-wall, deduced by G. N. V. Rao, which properly accounts for transverse curvature effects. Using this law, the theory which follows is equivalent to an exact solution to the axisymmetric equations of continuity and momentum for zero pressure gradient. Numerical results show that curvature increases skin friction and overall drag and decreases the boundary layer thickness and the integral thicknesses. The velocity profile is flattened and the shape factor approaches unity at large curvature. Comparison with several sources of friction data show better overall agreement than previous theories, except for an unexplained discrepancy with data for moving nylon fibers at very small radius Reynolds numbers.

Mobility Deposition Effect of Aerosol Particles in the Boundary Layer

2013 ◽  
Vol 300-301 ◽  
pp. 924-927
Author(s):  
Ming Chi Chiou ◽  
Wen Zong Hsu
Keyword(s):  
Boundary Layer ◽  
Particle Deposition ◽  
Particle Concentration ◽  
Fluid Motion ◽  
Viscous Sublayer ◽  
Boundary Layer Flows ◽  
Random Surface ◽  
Surface Renewal ◽  
Developed Turbulence ◽  
Deposition Effect

The particle concentration and convection velocity profile has been obtained by the adaptation of the random surface renewal model to the particle continuity and momentum equations of the nonisothermal turbulence boundary-layer flows In general, the investigations of particle deposition mainly include incompressible fluid laden by spherical and dilute particles in the fully developed turbulence boundary layer flows. This means that the fluid motion is unaffected by the presence of the particles and that the collisions between particles can be neglected. the relative quiescent viscous sublayer, resulting in the increase in thermophoretic deposition with increased Prandtl number.

Turbulent oscillatory boundary layers at high Reynolds numbers

1989 ◽  
Vol 206 ◽  
pp. 265-297 ◽  
Author(s):  
B. L. Jensen ◽  
B. M. Sumer ◽  
J. Fredsøe
Keyword(s):  
Boundary Layer ◽  
Stream Flow ◽  
Free Stream ◽  
Reynolds Numbers ◽  
Velocity Variation ◽  
Boundary Layer Flows ◽  
Oscillatory Boundary Layer ◽  
Rough Bed ◽  
High Reynolds ◽  
Rough Beds

This study deals with turbulent oscillatory boundary-layer flows over both smooth and rough beds. The free-stream flow is a purely oscillating flow with sinusoidal velocity variation. Mean and turbulence properties were measured mainly in two directions, namely in the streamwise direction and in the direction perpendicular to the bed. Some measurements were made also in the transverse direction. The measurements were carried out up to Re = 6 × 106 over a mirror-shine smooth bed and over rough beds with various values of the parameter a/ks covering the range from approximately 400 to 3700, a being the amplitude of the oscillatory free-stream flow and ks the Nikuradse's equivalent sand roughness. For smooth-bed boundary-layer flows, the effect of Re is discussed in greater detail. It is demonstrated that the boundary-layer properties change markedly with Re. For rough-bed boundary-layer flows, the effect of the parameter a/ks is examined, at large values (O(103)) in combination with large Re.

scholarly journals On the Asymptotic Approach to Thermosolutal Convection in Heated Slow Reactive Boundary Layer Flows

2008 ◽  
Vol 2008 ◽  
pp. 1-15
Author(s):  
Stanford Shateyi ◽  
Precious Sibanda ◽  
Sandile S. Motsa
Keyword(s):  
Boundary Layer ◽  
Boundary Layer Flow ◽  
Chemical Species ◽  
Reynolds Numbers ◽  
Thermosolutal Convection ◽  
Boundary Layer Flows ◽  
Instability Waves ◽  
Tollmien Schlichting ◽  
Layer Flow ◽  
Negative Buoyancy

The study sought to investigate thermosolutal convection and stability of two dimensional disturbances imposed on a heated boundary layer flow over a semi-infinite horizontal plate composed of a chemical species using a self-consistent asymptotic method. The chemical species reacts as it diffuses into the nearby fluid causing density stratification and inducing a buoyancy force. The existence of significant temperature gradients near the plate surface results in additional buoyancy and decrease in viscosity. We derive the linear neutral results by analyzing asymptotically the multideck structure of the perturbed flow in the limit of large Reynolds numbers. The study shows that for small Damkohler numbers, increasing buoyancy has a destabilizing effect on the upper branch Tollmien-Schlichting (TS) instability waves. Similarly, increasing the Damkohler numbers (which corresponds to increasing the reaction rate) has a destabilizing effect on the TS wave modes. However, for small Damkohler numbers, negative buoyancy stabilizes the boundary layer flow.

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