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.

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.

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.

Temperature Control of Blow-Down, Supersonic Tunnels

1956 ◽  
Vol 60 (541) ◽  
pp. 67-70
Author(s):  
T. A. Thomson
Keyword(s):  
Heat Transfer ◽  
Boundary Layer ◽  
Reynolds Number ◽  
Mach Number ◽  
Reynolds Numbers ◽  
Stagnation Temperature ◽  
Blow Down ◽  
High Reynolds Numbers ◽  
Experimental Errors ◽  
High Reynolds

The blow-down type of intermittent, supersonic tunnel is attractive because of its simplicity and because relatively high Reynolds numbers can be obtained for a given size of test section. An adverse characteristic, however, is the fall of stagnation temperature during runs, which can affect experiments in several ways. The Reynolds number varies and the absolute velocity is not constant, even if the Mach number and pressure are; heat-transfer cannot be studied under controlled conditions and the experimental errors arising from the effect of heat-transfer on the boundary layer vary in time. These effects can become significant in quantitative experiments if the tunnel is large and the variation of temperature very rapid; the expense required to eliminate them might then be justified.

Tip and Junction Vortices Generated by the Sail of a Yawed Submarine Model at Low Reynolds Numbers

2011 ◽  
Vol 133 (3) ◽  
Author(s):  
Juan M. Jiménez ◽  
Alexander J. Smits
Keyword(s):  
Boundary Layer ◽  
Reynolds Number ◽  
Water Channel ◽  
Reynolds Numbers ◽  
Tip Vortex ◽  
Streamwise Vortices ◽  
Low Reynolds Numbers ◽  
Good Accordance ◽  
Finite Wing ◽  
Yaw Angle

Results are presented on the behavior of the tip and junction vortices generated by the sail of a SUBOFF submarine model at yaw angles from 6 deg to 17 deg for a Reynolds number of 94×103 based on model length. The measurements were conducted in a water channel on a spanwise plane 1.3 chord lengths downstream from the trailing edge of the sail. In the vicinity of the sail hull junction, the presence of streamwise vortices in the form of horseshoe or necklace vortices locally dominates the flow. As the yaw angle is increased from 6 deg to 9 deg, the circulation of the sail tip vortex increases, and is in good accordance with predictions from finite wing theory. However, as the yaw angle is further increased, the sail boundary layer separates with an overall drop in circulation. In contrast, the circulation value for the junction vortex increases with yaw angle, and only drops slightly at the highest yaw angle.

An experimental insight into the effect of confinement on tip vortex cavitation of an elliptical hydrofoil

1999 ◽  
Vol 390 ◽  
pp. 1-23 ◽  
Author(s):  
OLIVIER BOULON ◽  
MATHIEU CALLENAERE ◽  
JEAN-PIERRE FRANC ◽  
JEAN-MARIE MICHEL
Keyword(s):  
Boundary Layer ◽  
Lift Coefficient ◽  
Three Dimensional ◽  
Tangential Velocity ◽  
Velocity Profiles ◽  
Tip Clearance ◽  
Tip Vortex ◽  
Flat Plates ◽  
Tip Vortex Cavitation ◽  
Cavitation Inception

The present paper is devoted to an analysis of tip vortex cavitation under confined situations. The tip vortex is generated by a three-dimensional foil of elliptical planform, and the confinement is achieved by flat plates set perpendicular to the span, at an adjustable distance from the tip. In the range of variation of the boundary-layer thickness investigated, no significant interaction was observed between the tip vortex and the boundary layer which develops on the confinement plate. In particular, the cavitation inception index for tip vortex cavitation does not depend significantly upon the length of the plate upstream of the foil. On the contrary, tip clearance has a strong influence on the non-cavitating structure of the tip vortex and consequently on the inception of cavitation in its core. The tangential velocity profiles measured by a laser-Doppler velocimetry (LDV) technique through the vortex, between the suction and the pressure sides of the foil, are strongly asymmetric near the tip. They become more and more symmetric downstream and the confinement speeds up the symmetrization process. When the tip clearance is reduced to a few millimetres, the two extrema of the velocity profiles increase. This increase results in a decrease of the minimum pressure in the vortex centre and accounts for the smaller resistance to cavitation observed when tip clearance is reduced. For smaller values of tip clearance, a reduction of tip clearance induces on the contrary a significant reduction in the maxima of the tangential velocity together with a significant increase in the size of the vortex core estimated along the confinement plate. Hence, the resistance to cavitation is much higher for such small values of tip clearance and in practice, no tip vortex cavitation is observed for tip clearances below 1.5 mm. The cavitation number for the inception of tip vortex cavitation does not correlate satisfactorily with the lift coefficient, contrary to classical results obtained without any confinement. Owing to the specificity introduced by the confinement, the usual procedure developed in an infinite medium to estimate the vortex strength from LDV measurements is not applicable here. Hence, a new quantity homogeneous to a circulation had to be defined on the basis of the maximum tangential velocity and the core size, which proved to be better correlated to the cavitation inception data.

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.

Turbulent boundary layer statistics at very high Reynolds number

2015 ◽  
Vol 779 ◽  
pp. 371-389 ◽  
Author(s):  
M. Vallikivi ◽  
M. Hultmark ◽  
A. J. Smits
Keyword(s):  
Boundary Layer ◽  
Reynolds Number ◽  
High Reynolds Number ◽  
Reynolds Numbers ◽  
Working Fluid ◽  
Mean Velocity ◽  
High Reynolds Numbers ◽  
Layer Flow ◽  
High Reynolds ◽  
Very High

Measurements are presented in zero-pressure-gradient, flat-plate, turbulent boundary layers for Reynolds numbers ranging from $\mathit{Re}_{{\it\tau}}=2600$ to $\mathit{Re}_{{\it\tau}}=72\,500$ ($\mathit{Re}_{{\it\theta}}=8400{-}235\,000$). The wind tunnel facility uses pressurized air as the working fluid, and in combination with MEMS-based sensors to resolve the small scales of motion allows for a unique investigation of boundary layer flow at very high Reynolds numbers. The data include mean velocities, streamwise turbulence variances, and moments up to 10th order. The results are compared to previously reported high Reynolds number pipe flow data. For $\mathit{Re}_{{\it\tau}}\geqslant 20\,000$, both flows display a logarithmic region in the profiles of the mean velocity and all even moments, suggesting the emergence of a universal behaviour in the statistics at these high Reynolds numbers.

Tip-Vortex Induced Cavitation on a Ducted Propulsor

2003 ◽  
Author(s):  
Christopher J. Chesnakas ◽  
Stuart D. Jessup
Keyword(s):  
Reynolds Number ◽  
High Speed ◽  
Three Dimensional ◽  
Tip Vortex ◽  
Number Range ◽  
Vortical Structures ◽  
Tip Vortices ◽  
Tip Vortex Cavitation ◽  
Cavitation Inception ◽  
Ducted Rotor

An extensive experimental investigation was carried out to examine tip-vortex induced cavitation on a ducted propulsor. The flowfield about a 3-bladed, ducted rotor operating in uniform inflow was measured in detail with three-dimensional LDV; cavitation inception was measured; and a correlated hydrophone/high-speed video system was used to identify and characterize the early, sub-visual cavitation events. Two geometrically-similar, ducted rotors were tested over a Reynolds number range from 1.4×106 to 9×106 in order to determine how the tip-vortex cavitation scales with Reynolds number. Analysis of the data shows that exponent for scaling tip-vortex cavitation with Reynolds number is smaller than for open rotors. It is shown that the parameters which are commonly accepted to control tip-vortex cavitation, vortex circulation and vortex core size, do not directly control cavitation inception on this ducted rotor. Rather it appears that cavitation is initiated by the stretching and deformation of secondary vortical structures resulting from the merger of the leakage and tip vortices.

scholarly journals On the Flow Along Swept Leading Edges

1967 ◽  
Vol 18 (2) ◽  
pp. 165-184 ◽  
Author(s):  
M. Gaster
Keyword(s):  
Boundary Layer ◽  
Reynolds Number ◽  
Wave Length ◽  
Leading Edge ◽  
Propagation Speed ◽  
Reynolds Numbers ◽  
Amplification Ratio ◽  
Tollmien Schlichting ◽  
High Reynolds ◽  
Attachment Line

SummaryFlight tests on the Handley Page suction wing showed that turbulence at the wing root can propagate along the leading edge and cause the whole flow to be turbulent. The flow on the attachment line of a swept wing was studied in a low speed wind tunnel with particular reference to this problem of turbulent contamination.The critical Reynolds number, RθL, of the attachment-line boundary layer for the spanwise spread of turbulence was found to be about 100 for sweep angles in the range 40°–60°. A device was developed to act as a barrier to the turbulent root flow so that a clean laminar flow could exist outboard. This device was shown to be effective up to an Rθ of at least 170, so that experiments were possible on a laminar boundary layer at Reynolds numbers above the lower critical value. A spark was used to introduce spots of turbulence into the attachment-line boundary layer and the propagation speeds of the leading and trailing edges were measured. The spots expanded, the leading edge moving faster than the trailing edge, at high Reynolds numbers, and contracted at low values.The behaviour of Tollmien-Schlichting waves was also investigated by exciting the flow with sound emanating from a small hole on the attachment line. Measurements of the perturbation phase and amplitude were made downstream of the source and, although accurate values of wave length and propagation speed could be found, difficulties were experienced in evaluating the amplification ratio. Nevertheless, all small disturbances decayed at a sufficient distance from the source hole up to the highest available Reynolds number of 170.

Effect of Free-Stream Turbulence on Heat Transfer through a Turbulent Boundary Layer

1978 ◽  
Vol 100 (4) ◽  
pp. 671-677 ◽  
Author(s):  
J. C. Simonich ◽  
P. Bradshaw
Keyword(s):  
Heat Transfer ◽  
Boundary Layer ◽  
Reynolds Number ◽  
Free Stream ◽  
Reynolds Numbers ◽  
Skin Friction Coefficient ◽  
Reynolds Analogy ◽  
Low Reynolds Numbers ◽  
Free Stream Turbulence ◽  
High Reynolds

Measurements in a boundary layer in zero pressure gradient show that the effect of grid-generated free-stream turbulence is to increase heat transfer by about five percent for each one percent rms increase of the longitudinal intensity. In fact, even a Reynolds analogy factor, 2 × (Stanton number)/(skin-friction coefficient), increases significantly. It is suggested that the irreconcilable differences between previous measurements are attributable mainly to the low Reynolds numbers of most of those measurements. The present measurements attained a momentum-thickness Reynolds number of 6500 (chord Reynolds number approximately 6.3 × 106) and are thought to be typical of high-Reynolds-number flows.

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