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.

A Model for High-Reynolds-Number Flow Past Rough-Walled Circular Cylinders

1977 ◽  
Vol 99 (3) ◽  
pp. 486-493 ◽  
Author(s):  
O. Gu¨ven ◽  
V. C. Patel ◽  
C. Farell
Keyword(s):  
Boundary Layer ◽  
Surface Roughness ◽  
Circular Cylinder ◽  
Turbulent Boundary Layer ◽  
Pressure Coefficient ◽  
Empirical Relation ◽  
Reynolds Numbers ◽  
Boundary Layer Separation ◽  
Circular Cylinders ◽  
Mean Flow

A simple analytical model for two-dimensional mean flow at very large Reynolds numbers around a circular cylinder with distributed roughness is presented and the results of the theory are compared with experiment. The theory uses the wake-source potential-flow model of Parkinson and Jandali together with an extension to the case of rough-walled circular cylinders of the Stratford-Townsend theory for turbulent boundary-layer separation. In addition, a semi-empirical relation between the base-pressure coefficient and the location of separation is used. Calculation of the boundary-layer development, needed as part of the theory, is accomplished using an integral method, taking into account the influence of surface roughness on the laminar boundary layer and transition as well as on the turbulent boundary layer. Good agreement with experiment is shown by the results of the theory. The significant effects of surface roughness on the mean-pressure distribution on a circular cylinder at large Reynolds numbers and the physical mechanisms giving rise to these effects are demonstrated by the model.

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.

Study of Possibility of Simulation of Thick Turbulent Boundary Layer on a Flat Plate of Limited Length

2012 ◽  
Vol 7 (3) ◽  
pp. 44-56
Author(s):  
Vladimir Kornilov
Keyword(s):  
Boundary Layer ◽  
Turbulent Boundary Layer ◽  
Flat Plate ◽  
Effective Means ◽  
Leading Edge ◽  
Circular Cylinders ◽  
Mean Velocity ◽  
Velocity Scale ◽  
Limited Length ◽  
Fluctuation Boundary

The experiments directed to the study of possibility of simulation of thick equilibrium (according to Clauser) incompressible turbulent boundary layer on a flat plate of limited length have been performed. It is shown that the artificial generators manufactured from circular cylinders (pins) of adjustable height h, which were mounted normal to the wall in a staggered order in two rows in х in vicinity of the plate leading edge are quite effective means of artificial boundary layer thickening. In most cases both the averaged and fluctuation boundary-layer characteristics at a downstream distance about 530 cylinder diameters have values typical for naturally-developed turbulent boundary layer. Mean velocity profiles in the artificially thickened boundary layer taken in wall-law variables are approximated with a good accuracy by the wellknown velocity law valid for canonic boundary layer and they are generalized by a unified dependence using empirical velocity scale

Effect of Tripping Laminar-to-Turbulent Boundary Layer Transition on Tip Vortex Cavitation

1997 ◽  
Vol 41 (01) ◽  
pp. 1-9
Author(s):  
T. Pichon ◽  
A. Pauchet ◽  
A. Astolfi ◽  
D. H. Fruman ◽  
J-Y. Billard
Keyword(s):  
Boundary Layer ◽  
Turbulent Boundary Layer ◽  
Flat Plate ◽  
Cross Section ◽  
Lift Coefficient ◽  
Reynolds Numbers ◽  
Boundary Layer Transition ◽  
Tip Vortex ◽  
Layer Transition ◽  
Tip Vortex Cavitation

It is by now well established that, for Reynolds numbers larger than those corresponding to the conditions of laminar-to-turbulent boundary layer transition over a flat plate (≈0.5 × 106) and for a variety of wing shapes and cross sections, desinent cavitation numbers divided by the Reynolds number to the power 0.4 correlate with the square of the lift coefficient. In the case of foils having an NACA 16020 cross section and for Reynolds numbers below or close to those leading to transition over a flat plate, the results are very much different from those obtained for well-developed turbulent boundary layer conditions. Thus, a research program has been conducted in order to investigate the effect of boundary layer manipulation on cavitation occurrence. It consisted in determining the critical cavitation numbers, the lift coefficients, and the velocities in the tip vortex of foils having either a smooth surface or tripping roughness (promoters) near the leading edge. Tests were performed using elliptical foils of NACA 16020 cross section having the promoters extending over 60, 80 and 90 percent of the semi-span. The region near the tip was kept smooth in order to distinguish laminar-to-turbulent transition effects from tip vortex cavitation inhibition effects associated with artificial roughness at the wing tip. Results obtained at very low Reynolds numbers, ≥ 0.24 × 106, with the foil tripped on both the pressure and suction sides collapse rather well with those previously obtained at much larger Reynolds numbers with the smooth foil, and correlate with the square of the lift coefficient. The differences between the tripped and smooth foil results are due to the modification of the lift characteristics through the modification of the wing boundary layer, as shown by flow visualization studies, and as a result of the local tip vortex intensity.

The Application of Different Tripping Techniques to Determine the Characteristics of the Turbulent Boundary Layer Over a Flat Plate

2017 ◽  
Vol 140 (1) ◽  
Author(s):  
Anton Silvestri ◽  
Farzin Ghanadi ◽  
Maziar Arjomandi ◽  
Benjamin Cazzolato ◽  
Anthony Zander
Keyword(s):  
Boundary Layer ◽  
Turbulent Boundary Layer ◽  
Flat Plate ◽  
Boundary Layer Thickness ◽  
Reynolds Numbers ◽  
Wind Tunnels ◽  
Hot Wire ◽  
Flow Speeds ◽  
Different Diameters ◽  
Insight Into

In the present study, the optimal two-dimensional (2D) tripping technique for inducing a naturally fully developed turbulent boundary layer in wind tunnels has been investigated. Various tripping techniques were tested, including wires of different diameters and changes in roughness. Experimental measurements were taken on a flat plate in a wind tunnel at a number of locations along the flat plate and at a variety of flow speeds using hot-wire anemometry to measure the boundary layer resulting from each tripping method. The results have demonstrated that to produce a natural turbulent boundary layer using a 2D protuberance, the height of the trip must be less than the undisturbed boundary layer thickness. Using such a trip was shown to reduce the development length of the turbulent boundary layer by approximately 50%. This was shown to hold true for all Reynolds numbers investigated (Rex=1.2×105−1.5×106). The present study provides an insight into the effect of the investigated trip techniques on the induced transition of a laminar boundary layer into turbulence.

Momentum Thickness Measurements for Thick Axisymmetric Turbulent Boundary Layers

2003 ◽  
Vol 125 (3) ◽  
pp. 569-575 ◽  
Author(s):  
Kimberly M. Cipolla ◽  
William L. Keith
Keyword(s):  
Boundary Layer ◽  
Turbulent Boundary Layer ◽  
Flat Plate ◽  
Boundary Layers ◽  
Control Volume ◽  
Scaling Law ◽  
Reynolds Numbers ◽  
Momentum Thickness ◽  
Spatial Growth ◽  
Thickness Measurements

Experimental measurements of the mean wall shear stress and boundary layer momentum thickness on long, thin cylindrical bodies are presented. To date, the spatial growth of the boundary layer and the related boundary layer parameters have not been measured for cases where δ/a (a=cylinder radius) is much greater than one. Moderate Reynolds numbers 104<Reθ<105 encountered in hydrodynamic applications are considered. Tow tests of cylinders with diameters of 0.61, 0.89, and 2.5 mm and lengths ranging from approximately 30 meters to 150 meters were performed. The total drag (axial force) was measured at tow speeds up to 17.4 m/sec. These data were used to determine the tangential drag coefficients on each test specimen, which were found to be two to three times greater than the values for the corresponding hypothetical flat-plate cases. Using the drag measurements, the turbulent boundary layer momentum thickness at the downstream end of the cylindrical bodies is determined, using a control volume analysis. The results show that for the smallest diameter cylinders, there is no indication of relaminarization, and a fully developed turbulent boundary layer exists. A scaling law for the momentum thickness versus length Reynolds number is determined from the data. The results indicate that the spatial growth of the boundary layers over the entire length is less than for a comparable flat-plate case.

scholarly journals Large-eddy simulation of separation and reattachment of a flat plate turbulent boundary layer

2015 ◽  
Vol 785 ◽  
pp. 78-108 ◽  
Author(s):  
W. Cheng ◽  
D. I. Pullin ◽  
R. Samtaney
Keyword(s):  
Boundary Layer ◽  
Turbulent Boundary Layer ◽  
Pressure Gradient ◽  
Flat Plate ◽  
Skin Friction ◽  
Separation Bubble ◽  
Reynolds Numbers ◽  
Wall Model ◽  
Large Eddy ◽  
Layer Flow

We present large-eddy simulations (LES) of separation and reattachment of a flat-plate turbulent boundary-layer flow. Instead of resolving the near wall region, we develop a two-dimensional virtual wall model which can calculate the time- and space-dependent skin-friction vector field at the wall, at the resolved scale. By combining the virtual-wall model with the stretched-vortex subgrid-scale (SGS) model, we construct a self-consistent framework for the LES of separating and reattaching turbulent wall-bounded flows at large Reynolds numbers. The present LES methodology is applied to two different experimental flows designed to produce separation/reattachment of a flat-plate turbulent boundary layer at medium Reynolds number $Re_{{\it\theta}}$ based on the momentum boundary-layer thickness ${\it\theta}$. Comparison with data from the first case at $Re_{{\it\theta}}=2000$ demonstrates the present capability for accurate calculation of the variation, with the streamwise co-ordinate up to separation, of the skin friction coefficient, $Re_{{\it\theta}}$, the boundary-layer shape factor and a non-dimensional pressure-gradient parameter. Additionally the main large-scale features of the separation bubble, including the mean streamwise velocity profiles, show good agreement with experiment. At the larger $Re_{{\it\theta}}=11\,000$ of the second case, the LES provides good postdiction of the measured skin-friction variation along the whole streamwise extent of the experiment, consisting of a very strong adverse pressure gradient leading to separation within the separation bubble itself, and in the recovering or reattachment region of strongly-favourable pressure gradient. Overall, the present two-dimensional wall model used in LES appears to be capable of capturing the quantitative features of a separation-reattachment turbulent boundary-layer flow at low to moderately large Reynolds numbers.

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