Numerical Study on Tip Vortex Cavitation Inception on a Foil

In this paper, the inception of tip vortex cavitation in weak water has been predicted using a numerical simulation, and a new scaling concept with variable exponent has also been suggested for cavitation inception index. The numerical simulations of the cavitating flows over an elliptic planform hydrofoil were performed by using the RANS approach with a Eulerian cavitation model. To ensure the accuracy of the present simulations, the effects of the turbulence model and grid resolution on the tip vortex flows were investigated. The turbulence models behaved differently in the boundary layer of the tip region where the tip vortex is developed, which resulted in different pressure and velocity fields in the vortex region. Furthermore, the Reynolds stress model for the finest grid showed a better agreement with the experimental data. The tip vortex cavitation inception numbers for the foil, predicted by using both wetted and cavitating flow simulation approaches, were compared with the measured cavitation index values, showing a good correlation. The current cavitation scaling study also suggested new empirical relations as a function of the Reynolds number substitutable for the two classic constant scaling exponents. This scaling concept showed how the scaling law changes with the Reynolds number and provided a proper scaling value for any given Reynolds numbers under turbulent flow conditions.

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Tip Vortex Cavitation Inception Scaling for High Reynolds Number Applications

Journal of Fluids Engineering ◽

10.1115/1.3130245 ◽

2009 ◽

Vol 131 (7) ◽

Cited By ~ 19

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.

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Tip Vortex Cavitation Inception Scaling for High Reynolds Number Application

Volume 1: Fora, Parts A, B, C, and D ◽

10.1115/fedsm2003-45316 ◽

2003 ◽

Cited By ~ 1

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.

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Tip-Vortex Induced Cavitation on a Ducted Propulsor

Volume 1: Fora, Parts A, B, C, and D ◽

10.1115/fedsm2003-45320 ◽

2003 ◽

Cited By ~ 7

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.

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Experimental Study of Scale Effects on the Scaling Law for Tip Vortex Cavitation Noise

Volume 2, Fora: Cavitation and Multiphase Flow; Fluid Measurements and Instrumentation; Microfluidics; Multiphase Flows: Work in Progress; Fluid-Particle Interactions in Turbulence ◽

10.1115/fedsm2014-21449 ◽

2014 ◽

Author(s):

Jisoo Park ◽

Cheolsoo Park ◽

Youngmin Choo ◽

Woojae Seong

Keyword(s):

High Speed ◽

Scale Effects ◽

Scaling Law ◽

Size Variation ◽

Tip Vortex ◽

Cavitation Noise ◽

Scaling Exponents ◽

Tip Vortex Cavitation ◽

Cavitation Inception ◽

Vortex Model

Novel scaling law for the tip vortex cavitation (TVC) noise is derived from the physical basis of TVC, employing the Rankine vortex model, the Rayleigh-Plesset equation, the lifting surface theory, and the number of bubbles generated per unit time (N0). All terms appearing in the scaling law have physical or mathematical grounds except for N0. Therefore, to experimentally validate the N0 term, experiments are designed to keep the same TVC patterns as velocities and dimensions vary. Optimal shooting conditions with a velocity and size variation are determined from the scaling exponents, cavitation numbers and Reynolds numbers at each condition. To avoid wall effects and flow field interaction, two hydrofoils are optimally arranged by using computational fluid dynamics (CFD) for size variation. Images taken by a high speed camera are used to count N0, considering similitude of the spectra of nuclei. Scaling exponents curve fitted from five velocities and cavitation inception numbers have an exponent value of 0.371, which is closely placed on scaling exponents curve deduced from Schlichting’s friction coefficients fitting with Reynolds number. The tendency that N0 is proportional to a velocity and inversely proportional to a size can be confirmed by this study.

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Observation and Scaling of Tip Vortex Cavitation on Elliptical Hydrofoils

ASME-JSME-KSME 2011 Joint Fluids Engineering Conference: Volume 2, Fora ◽

10.1115/ajk2011-33015 ◽

2011 ◽

Cited By ~ 3

Author(s):

Shigeki Nagaya ◽

Risa Kimoto ◽

Kenji Naganuma ◽

Takayuki Mori

Keyword(s):

Water Quality ◽

Reynolds Number ◽

High Speed ◽

Tip Vortex ◽

Video Observation ◽

Tip Vortex Cavitation ◽

Air Content ◽

Sheet Cavitation ◽

High Speed Video ◽

Systems Research

Experimental study on tip vortex cavitation (TVC) was carried out for elliptical hydrofoils with various chord lengths. The purpose of the experiment was to clarify the influences of Reynolds number and water quality on tip vortex cavitation. Experiments were made in a large cavitation tunnel of the Naval Systems Research Center, TRDI/Ministry of Defense Japan. The elliptical hydrofoils tested were NACA 0012 cross section with chord lengths of 500mm, 250mm and 50mm. Reynolds number based on hydrofoil chord length was 2×105 < ReC < 7.4×106. Water quality of the tunnel was characterized by air content and nuclei distribution. Air content of the tunnel was varied between 30% and 80%. Nuclei distribution was measured by a cavitation susceptibility meter (CSM) with center-body venturi. Cavitation inception was determined from high speed video observation. A standard formula, (σL/σS) = (ReL/ReS)n, was applied for the scaling. In the present study, exponent of the scaling law n was found to be 0.2 < n < 0.4. High speed video observation showed that the process of the TVC inception strongly depends on water quality. In the experiments, unsteady behaviors of TVC were also investigated. Strong interactions between sheet cavitation and TVC were observed.

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Numerical Investigation of Tip-Vortex Cavitation Noise of an Elliptic Wing Using Coupled Eulerian-Lagrangian Approaches

Applied Sciences ◽

10.3390/app10175897 ◽

2020 ◽

Vol 10 (17) ◽

pp. 5897 ◽

Cited By ~ 1

Author(s):

Garam Ku ◽

Cheolung Cheong ◽

Hanshin Seol

Keyword(s):

Flow Field ◽

Numerical Method ◽

Vortex Flow ◽

Acoustic Pressure ◽

Tip Vortex ◽

Experimental Result ◽

Cavitation Noise ◽

Navier Stokes Equation ◽

Tip Vortex Cavitation ◽

Cavitation Inception

In this study, a numerical methodology is developed to investigate the tip-vortex cavitation of NACA16-020 wings and their flow noise. The numerical method consists of a sequential one-way coupled application of Eulerian and Lagrangian approaches. First, the Eulerian method based on Reynolds-averaged Navier–Stokes equation is applied to predict the single-phase flow field around the wing, with particular emphasis on capturing high-resolution tip-vortex flow structures. Subsequently, the tip-vortex flow field is regenerated by applying the Scully vortex model. Secondly, the Lagrangian approach is applied to predict the tip-vortex cavitation inception and noise of the wing. The initial nuclei are distributed upstream of the wing. The subsequent time-varying size and position of each nucleus are traced by solving spherically symmetric bubble dynamics equations for the nuclei in combination with the flow field predicted from the Eulerian approach. The acoustic pressure at the observer position is computed by modelling each bubble as a point source. The numerical results of the acoustic pressure spectrum are best matched to the measured results when the nuclei number density of freshwater is used. Finally, the current numerical method is applied to the flows of various cavitation numbers. The results reveal that the cavitation inception determined by the predicted acoustic pressure spectrum well matched the experimental result.

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Assessment of Different Turbulence Models for Predicting Laminar Separation Bubble Over Thick Airfoils

ASME 2015 Gas Turbine India Conference ◽

10.1115/gtindia2015-1277 ◽

2015 ◽

Cited By ~ 1

Author(s):

Saravana Kumar Lakshmanan ◽

Alok Mishra ◽

Ashoke De

Keyword(s):

Reynolds Number ◽

Numerical Study ◽

Separation Bubble ◽

Turbulence Models ◽

Laminar Separation Bubble ◽

Laminar Separation ◽

Performance Variables ◽

Rans Models ◽

High Angles Of Attack ◽

Aerodynamic Lift

Accurate laminar-turbulent prediction is very much important to understand the complete performance characteristics of any airfoil which operates at low and medium Reynolds number. In this article, a numerical study has been performed over two different thick airfoils operating at low Reynolds number using k-ω SST, k-kl-ω and Spalart-Allmaras (SA) RANS models. The unsteady two dimensional (2D) simulations are performed over NACA 0021 and NACA 65-021 at Re 120,000 for a range of angle of attacks. The performances of these models are assessed through aerodynamic lift, drag and pressure coefficients. To obtain better comparison, the simulated results are compared with the experimental measurements and XFOIL results as well. In this present study, it is found that the k-kl-ω transition model is capable of predicting correct lift, drag coefficient and separation bubble as reported in experiments. At high angles of attack, this model fails to predict performance variables accurately. The SA and SST models are fail to predict laminar separation bubble. However, At high angle of attack, SA model shows better predictions compared to k-kl-ω and k-ω SST models.

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Heat Transfer Predictions for U-Shaped Coolant Channels With Skewed Ribs and With Smooth Walls

ASME 1996 Turbo Asia Conference ◽

10.1115/96-ta-007 ◽

1996 ◽

Cited By ~ 8

Author(s):

Bernhard Bonhoff ◽

Uwe Tomm ◽

Bruce V. Johnson

Keyword(s):

Heat Transfer ◽

Reynolds Number ◽

Computational Study ◽

Flow Direction ◽

Turbine Blades ◽

Turbulence Models ◽

Reynolds Stress Model ◽

Internal Cooling ◽

Smooth Wall ◽

Wall Model

A computational study was performed for the flow and heat transfer in coolant passages with two legs connected with a U-bend and with dimensionless flow conditions typical of those in the internal cooling passages of turbine blades. The first model had smooth surfaces on all walls. The second model had opposing ribs staggered and angled at 45° to the main flow direction on two walls of the legs, corresponding to the coolant passage surfaces adjacent to the pressure and suction surfaces of a turbine airfoil. For the ribbed model, the ratio of rib height to duct hydraulic diameter equaled 0.1, and the ratio of rib spacing to rib height equaled 10. Comparisons of calculations with previous measurements are made for a Reynolds number of 25,000. With these conditions, the predicted heat transfer is known to be strongly influenced by the turbulence and wall models. The k-e model, the low Reynolds number RNG k-e and the differential Reynolds-stress model (RSM) were used for the smooth wall model calculation. Based on the results with the smooth walls, the calculations for the ribbed walls were performed using the RSM and k-e turbulence models. The high secondary flow induced by the ribs leads to an increased heat transfer in both legs. However, the heat transfer was nearly unchanged between the smooth wall model and the ribbed model within the bend region. The agreement between the predicted segment-averaged and previously-measured Nusselt numbers was good for both cases.

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