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.

An approximate theory for the streaming motion past axisymmetric bodies at Reynolds numbers of from 1 to approximately 100

1977 ◽  
Vol 82 (3) ◽  
pp. 583-604 ◽  
Author(s):  
Michael S. Kolansky ◽  
Sheldon Weinbaum ◽  
Robert Pfeffer
Keyword(s):  
Boundary Layer ◽  
Reynolds Number ◽  
Pressure Gradient ◽  
Reynolds Numbers ◽  
Bluff Bodies ◽  
Approximate Theory ◽  
Viscous Term ◽  
Number Range ◽  
Curvature Effects ◽  
Flow Past

In Weinbaum et al. (1976) a simple new pressure hypothesis is derived which enables one to take account of the displacement interaction, the geometrical change in streamline radius of curvature and centrifugal effects in the thick viscous layers surrounding two-dimensional bluff bodies in the intermediate Reynolds number range O(1) < Re < O(102) using conventional Prandtl boundary-layer equations. The new pressure hypothesis states that the streamwise pressure gradient as a function of distance from the forward stagnation point on the displacement body is equal to the wall pressure gradient as a function of distance along the original body. This hypothesis is shown to be equivalent to stretching the streamwise body co-ordinate in conventional first-order boundary-layer theory. The present investigation shows that the same pressure hypothesis applies for the intermediate Reynolds number flow past axisymmetric bluff bodies except that the viscous term in the conventional axisymmetric boundary-layer equation must also be modified for transverse curvature effects O(δ) in the divergence of the stress tensor. The approximate solutions presented for the location of separation and the detailed surface pressure and vorticity distribution for the flow past spheres, spheroids and paraboloids of revolution at various Reynolds numbers in the range O(1) < Re < O(102) are in good agreement with available numerical Navier–Stokes solutions.

Effect of Transverse Curvature on Turbulent-Boundary-Layer Characteristics

1958 ◽  
Vol 2 (04) ◽  
pp. 33-51
Author(s):  
Yun-Sheng Yu
Keyword(s):  
Boundary Layer ◽  
Circular Cylinder ◽  
Turbulent Boundary Layer ◽  
Velocity Profile ◽  
Pressure Gradient ◽  
Boundary Layer Thickness ◽  
Axial Flow ◽  
Shearing Stress ◽  
Transverse Curvature ◽  
Similarity Laws

Tests made on the turbulent boundary layer on a circular cylinder in axial flow at zero pressure gradient are described. From the measurements, similarity laws of the velocity profile are formulated, and various boundary-layer characteristics are evaluated and compared with the flatplate results. It is found that the effect of transverse curvature is to increase the surface shearing stress and to decrease the boundary-layer thickness, and that the latter variation is more pronounced than the former.

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.

A Numerical Investigation Into the Sources of Endwall Loss in Axial Flow Turbines

2012 ◽  
Author(s):  
John Denton ◽  
Graham Pullan
Keyword(s):  
Boundary Layer ◽  
Layer Thickness ◽  
Boundary Layer Thickness ◽  
Axial Flow ◽  
Turbine Cascade ◽  
Plane Model ◽  
Blade Row ◽  
Axial Turbines ◽  
Different Sources ◽  
Good Agreement

Endwall loss, often termed “secondary loss”, in axial turbines has been intensively studied for many years, despite this the physical origin of much of the loss is not really understood. This lack of understanding is a serious impediment to our ability to predict the loss and to the development of methods for reducing it. This paper aims to study the origins of the loss by interrogating the results from detailed and validated CFD calculations. The calculation method is first validated by comparing its predictions to detailed measurements in a turbine cascade. Very good agreement between the calculations and the measurements is obtained. The solution is then examined in detail to highlight the sources of entropy generation in the cascade, several different sources of loss are found to be significant. The same blade row is then used to study the effects of the of the inlet boundary layer thickness on the loss. It is found that only the inlet boundary layer loss and the mixing loss vary greatly with inlet boundary layer thickness. Finally a complete 50% reaction stage, with identical stator and rotor blade profiles, is examined using both steady calculations, with a mixing plane model, and the time average of unsteady calculations. It is found that the endwall flow in the rotor is completely different from that in the stator. Because of this it is considered that results from endwall flow and loss measurements in cascades are of limited relevance to the endwall flow in a real turbine. The results are also used to discuss the validity of the mixing plane model.

Tip Vortex Cavitation Inception Scaling for High Reynolds Number Applications

2009 ◽  
Vol 131 (7) ◽  
Author(s):  
Young T. Shen ◽  
Scott Gowing ◽  
Stuart Jessup
Keyword(s):  
Boundary Layer ◽  
Reynolds Number ◽  
Boundary Layer Thickness ◽  
Reynolds Numbers ◽  
Present Theory ◽  
Full Scale ◽  
Tip Vortex ◽  
Tip Vortex Cavitation ◽  
Cavitation Inception ◽  
High Reynolds

Tip vortices generated by marine lifting surfaces such as propeller blades, ship rudders, hydrofoil wings, and antiroll fins can lead to cavitation. Prediction of the onset of this cavitation depends on model tests at Reynolds numbers much lower than those for the corresponding full-scale flows. The effect of Reynolds number variations on the scaling of tip vortex cavitation inception is investigated using a theoretical flow similarity approach. The ratio of the circulations in the full-scale and model-scale trailing vortices is obtained by assuming that the spanwise distributions of the section lift coefficients are the same between the model-scale and the full-scale. The vortex pressure distributions and core sizes are derived using the Rankine vortex model and McCormick’s assumption about the dependence of the vortex core size on the boundary layer thickness at the tip region. Using a logarithmic law to describe the velocity profile in the boundary layer over a large range of Reynolds number, the boundary layer thickness becomes dependent on the Reynolds number to a varying power. In deriving the scaling of the cavitation inception index as the ratio of Reynolds numbers to an exponent m, the values of m are not constant and are dependent on the values of the model- and full-scale Reynolds numbers themselves. This contrasts traditional scaling for which m is treated as a fixed value that is independent of Reynolds numbers. At very high Reynolds numbers, the present theory predicts the value of m to approach zero, consistent with the trend of these flows to become inviscid. Comparison of the present theory with available experimental data shows promising results, especially with recent results from high Reynolds number tests. Numerical examples of the values of m are given for different model- to full-scale sizes and Reynolds numbers.

Heat Transfer Around a Cylindrical Protuberance Mounted in a Plane Turbulent Boundary Layer

2005 ◽  
Vol 128 (2) ◽  
pp. 153-161 ◽  
Author(s):  
Takayuki Tsutsui ◽  
Masafumi Kawahara
Keyword(s):  
Heat Transfer ◽  
Boundary Layer ◽  
Aspect Ratio ◽  
Turbulent Boundary Layer ◽  
Layer Thickness ◽  
Boundary Layer Thickness ◽  
Reynolds Numbers ◽  
Heat Transfer Characteristics ◽  
Low Aspect Ratio ◽  
Maximum Value

Heat transfer characteristics around a low aspect ratio cylindrical protuberance placed in a turbulent boundary layer were investigated. The diameters of the protuberance, D, were 40 and 80mm, and the height to diameter aspect ratio H∕D ranged from 0.125 to 1.0. The Reynolds numbers based on D ranged from 1.1×104 to 1.1×105 and the thickness of the turbulent boundary layer at the protuberance location, δ, ranged from 26 to 120mm for these experiments. In this paper we detail the effects of the boundary layer thickness and the protuberance aspect ratio on heat transfer. The results revealed that the overall heat transfer for the cylindrical protuberance reaches a maximum value when H∕δ=0.24.

Numerical Computation of Laminar Separation and Reattachment of Flow Over Surface Mounted Ribs

1991 ◽  
Vol 113 (2) ◽  
pp. 190-198 ◽  
Author(s):  
Ying-Jong Hong ◽  
Shou-Shing Hsieh ◽  
Huei-Jan Shih
Keyword(s):  
Boundary Layer ◽  
Layer Thickness ◽  
Boundary Layer Thickness ◽  
Initial Boundary ◽  
Reynolds Numbers ◽  
Laminar Separation ◽  
Aspect Ratios ◽  
Entire Flow ◽  
Vertical Step ◽  
Fluid Characteristics

Numerical results are presented concerning the fluid characteristics of steady-state laminar flow over surface mounted ribs. Computations are carried out using a false transient stream function-vorticity form. The effects of the aspect ratios (width-to-depth) of the ribs and Reynolds numbers as well as initial boundary-layer thickness on entire flow field, separated region, and reattachment length are presented and discussed. The computed reattachment distance compares reasonably well with those data reported by previous studies. A correlation is provided in terms of the rib aspect ratio, Reynolds number, and the ratio of boundary-layer thickness and rib height. The pressure drop is excessive along the upstream vertical step face and it recovers thereafter, which agrees qualitatively with those of the previous studies for the flow over backward-facing steps.

Tip Vortex Cavitation Inception Scaling for High Reynolds Number Application

2003 ◽  
Author(s):  
Young T. Shen ◽  
Stuart Jessup ◽  
Scott Gowing
Keyword(s):  
Boundary Layer ◽  
Reynolds Number ◽  
Boundary Layer Thickness ◽  
Reynolds Numbers ◽  
Present Theory ◽  
Full Scale ◽  
Tip Vortex ◽  
Tip Vortex Cavitation ◽  
Cavitation Inception ◽  
High Reynolds

Tip vortices that are generated by marine lifting surfaces such as propeller blades, ship rudders, hydrofoil wings, and anti-roll fins can lead to cavitation. Prediction of the onset of this cavitation depends on model tests at Reynolds numbers much lower than those for the corresponding full-scale flows. The effect of Reynolds number variations on the scaling of tip vortex cavitation inception is investigated using a theoretical flow similarity approach. The ratio of the circulations in the full-scale and model-scale trailing vortices is obtained by assuming that the spanwise section lift coefficient distributions are the same between model and full-scale. The vortex pressure distributions and core sizes are derived using the Rankine vortex model and McCormick’s assumption about the dependence of the vortex core size on the boundary layer thickness at the tip region. Using a logarithmic law to describe the velocity profile in the boundary layer over a large range of Reynolds number, the boundary layer thickness becomes dependent on the Reynolds number to a varying power. In deriving the cavitation inception scaling in the traditional scaling format of σif / σim = (Ref/Rem)n, the values of n are not constant and depend on the values of Ref and Rem themselves. This contrasts traditional scaling for which n is treated as a fixed value that is independent of Reynolds numbers. At very high Reynolds numbers, the present theory predicts the value of n to approach zero, consistent with the trend of these flows to become inviscid. Comparison of the present theory with available experimental data shows promising results, especially with recent results from high Reynolds number tests. Numerical examples are given of the values of n for different model to full-scale sizes and Reynolds numbers.

Calculation of the axisymrnetric boundary layer on a long thin cylinder

1980 ◽  
Vol 372 (1751) ◽  
pp. 555-564 ◽  
Keyword(s):  
Boundary Layer ◽  
Asymptotic Expansion ◽  
Skin Friction ◽  
Layer Thickness ◽  
Boundary Layer Thickness ◽  
Axial Flow ◽  
Thin Cylinder ◽  
Residual Series ◽  
Convergent Expansion ◽  
Significant Figures

The laminar boundary layer in axial flow along a long thin cylinder is investigated, following Seban & Bond (1951), by expanding in powers of a variable £ that represents the ratio of the boundary layer thickness to the cylinder radius. The resulting series for the skin friction r, of which 20 terms are calculated, is analysed, and, by working in terms of the inverse series, for r _1, the radius of convergence is estimated to be £ = 0.37416. An Euler transformation then yields a more convergent expansion in terms of a new variable By using the known asymptotic expansion of r for large £, we deduce how t—1 behaves near 2 = 1 , and extraction of the leading terms leaves an even more convergent residual series. Although neither the original series nor the asymptotic expansion give very accurate results over the substantial range 0-2 < £ < 100, the present analysis gives r to about six, or more, significant figures throughout the range. Similar success is achieved in calculating the displacement area.

scholarly journals Numerical investigations of flow around subsea covers at high Reynolds numbers

2021 ◽  
Vol 1201 (1) ◽  
pp. 012013
Author(s):  
G Yin ◽  
Y Zhang ◽  
M C Ong
Keyword(s):  
Boundary Layer ◽  
Reynolds Number ◽  
Numerical Simulations ◽  
Layer Thickness ◽  
Boundary Layer Thickness ◽  
Reynolds Numbers ◽  
Navier Stokes ◽  
Stream Velocity ◽  
Layer Flow ◽  
High Reynolds

Abstract Two-dimensional (2D) numerical simulations of flow over wall-mounted rectangular and trapezoidal ribs subjected to a turbulent boundary layer flow with the normalized boundary layer thickness of δ/D = 0.73,1.96,2.52 (D is the height of the ribs) have been carried out by using the Reynolds-averaged Navier-Stokes (RANS) equations combined with the k – ω SST (Shear Stress Transport) turbulence model. The angles of the two side slopes of trapezoidal rib varies from 0° to 60°. The Reynolds number based on the free-stream velocity U ∞ and D are 1 × 106 and 2 × 106. The results obtained from the present numerical simulations are in good agreement with the published experimental data. Furthermore, the effects of the angle of the two side slopes of the trapezoidal ribs, the Reynolds number and the boundary layer thickness on the hydrodynamic quantities are discussed.

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