Cavity flow past a slender pointed hydrofoil

A slender-body theory for the flow past a slender, pointed hydrofoil held at a small angle of Attack to the flow, with a cavity on the upper surface, has been worked out. The approximate solution valid near the body is seen to be the sum of two components. The first consists of a distribution of two-dimensional sources located along the centroid line of the cavity to represent the variation of the cross-sectional area of the cavity. The second component represents the crossflow perpendicular to the centroid line. It is found that over the cavity boundary which envelops a constant pressure region, the magnitude of the cross-flow velocity is not constant, but varies to a moderate extent. With this variation neglected only in the neighbourhood of the hydrofoil, the cross-flow is solved by adopting the Riabouchinsky model for the two-dimensional flow. The lift is then calculated by integrating the pressure along the chord; the dependence of the lift on cavitation number and angle of attack is shown for a specific case of the triangular plan form

Assessment of RANS turbulence models and Zwart cavitation model empirical coefficients for the simulation of unsteady cloud cavitation

The numerical simulation of unsteady cavitation flows is sensitive to the selected models and associated parameters. Consequently, three Reynolds Average Navier-Stokes (RANS) turbulence models and the Zwart cavitation model were selected to assess their performance for the simulation of cloud cavitation on 2D hydrofoils. The experimental cavitation tests from a NACA65012 hydrofoil at different hydrodynamic conditions were used as a reference to tune the modeling parameters and the experimental tests from a NACA0015 were finally used to validate them. The effects of near wall grid refinement, time step, iterations and mesh elements were also investigated. The results indicate that the Shear Stress Transport (SST) model is sensitive to near wall grid resolution which should be fine enough. Moreover, the cavitation morphology and dynamic behavior are sensitive to the selection of the Zwart empirical vaporization, Fv, and condensation, Fc, coefficients. Therefore, a multiple linear regression approach with the single objective of predicting the shedding frequency was carried out that permitted to find the range of coefficient values giving the most accurate results. In addition, it was observed that they provided a better prediction of the vapor volume fraction and of the instantaneous pressure pulse generated by the main cloud cavity collapse.Postprint (published version

Unsteady Propulsion by an Intermittent Swimming Gait

Inviscid computational results are presented on a self-propelled swimmer modeled as a virtual body combined with a two-dimensional hydrofoil pitching intermittently about its leading edge. Lighthill (1971) originally proposed that this burst-and-coast behavior can save fish energy during swimming by taking advantage of the viscous Bone-Lighthill boundary layer thinning mechanism. Here, an additional inviscid Garrick mechanism is discovered that allows swimmers to control the ratio of their added mass thrust-producing forces to their circulatory drag-inducing forces by decreasing their duty cycle, DC, of locomotion. This mechanism can save intermittent swimmers as much as 60% of the energy it takes to swim continuously at the same speed. The inviscid energy savings are shown to increase with increasing amplitude of motion, increase with decreasing Lighthill number, Li, and switch to an energetic cost above continuous swimming for sufficiently low DC. Intermittent swimmers are observed to shed four vortices per cycle that form into groups that are self-similar with the DC. In addition, previous thrust and power scaling laws of continuous self-propelled swimming are further generalized to include intermittent swimming. The key is that by averaging the thrust and power coefficients over only the bursting period then the intermittent problem can be transformed into a continuous one. Furthermore, the intermittent thrust and power scaling relations are extended to predict the mean speed and cost of transport of swimmers. By tuning a few coefficients with a handful of simulations these self-propelled relations can become predictive. In the current study, the mean speed and cost of transport are predicted to within 3% and 18% of their full-scale values by using these relations

Observations of Cavitation on a Three-Dimensional Oscillating Hydrofoil

A test apparatus was designed and constructed to observe the effect of sinusoidal pitching oscillations on the cavitation of three-dimensional hydrofoils. The apparatus is capable of oscillating hydrofoils at a rate up to 50 Hz and provides for adjustments in oscillation amplitude and mean angle of attack. Observations of the effect of pitching oscillation on cavitation have been made for a NACA 64-309 (modified) hydrofoil operating at its designed mean angle of attack of 7 degrees with an oscillation amplitude of 2 degrees. Photographs illustrating the interaction between natural cavity shedding frequencies and the foil reduced frequency are included

A Note on the Linear and Nonlinear Theories for Fully Cavitated Hydrofoils

The lifting problem of fully cavitated hydrofoils has recently received some attention. The nonlinear problem of two-dimensional fully cavitated hydrofoils has been treated by the author, using a generalized free streamline theory. The hydrofoils investigated in Ref. 1 were those with sharp leading and trailing edges which are assumed to be the separation points of the cavity streamlines. Except for this limitation, the nonlinear theory is applicable to hydrofoils of arbitrary geometric profile, operating at any cavitation number, and for almost all angles of attack as long as the cavity wake is fully developed. By using an elegant linear theory, Tulin has treated the problem of a fully cavitated flat plate set at a small angle of attack and operated at arbitrary cavitation number. In the case of hydrofoils of arbitrary profile operating at zero cavitation number, some interesting simple relationships are given by Tulin for the connection between the lift, drag and moment of a supercavitating hydrofoil and the lift, moment and the third moment of an equivalent airfoil (unstalled). In the present investigation, Tulin's linear theory is first extended to calculate the hydrodynamic lift and drag on a fully cavitated hydrofoil of arbitrary camber at arbitrary cavitation number. A numerical example is given for a circular hydrofoil subtending an arc angle of 160, for which the corresponding nonlinear solution is available. A direct comparison between these two theories is made explicitly for the flat plate and the circular arc hydrofoil. Some important aspects of the results are discussed subsequently

Cloud cavitation on an oscillating hydrofoil

Cloud cavitation, often formed by the breakdown of a sheet or vortex cavity, is believed to be responsible for much of the noise and erosion damage that occurs under cavitating conditions. For this paper, cloud cavitation was produced through the periodic forcing of the flow by an oscillating hydrofoil. The present work examines the acoustic signal generated by the collapse of cloud cavitation, and compares the results to those obtained by studies of single travelling bubble cavitation. In addition, preliminary studies involving the use of air injection on the suction surface of the hydrofoil explore its mitigating effects on the cavitation noise

A Note on Partial Cavitation of Flat Plate Hydrofoils

Recently Tulin and Wu have treated the problem of fully developed cavitation on flat plate and cambered foils. In these treatments, the length of the cavity is always greater than the chord of the hydrofoil and the cavity is assumed to start at the leading edge of the plate. The purpose of this note is to extend Tulin's work to account for partial cavitation, i.e., when the cavitation bubble is less than the hydrofoil chord

Pressure Pulses Generated by Cloud Cavitation

This paper describes an experimental investigation of the large unsteady and impulsive pressures which are experienced on the suction surface of both an oscillating and static hydrofoil as a result of cloud cavitation. The present experiments used piezo-electric transducers to measure unsteady pressures at four locations along the chord of the foil and at two locations along the walls of the tunnel test section. These transducers measured very large positive pressure pulses with amplitudes of the order of tens of atmospheres and with durations of the order of tenths of milliseconds. Two distinct types of pressure pulse were identified. "Local" pulses occurred at a single transducer location and were randomly distributed in position and time; several local impulses could be recorded by each transducer during an oscillation cycle. On the other hand, "global" impulses were registered by all the transducers almost simultaneously. Correlation of the transducer output with high speed movies of the cavitation revealed that they were produced by a large scale collapse of the bubble cloud. The location of the global impulses relative to the foil oscillation was quite repeatable and produced substantial far-field noise. The high speed movies also showed that the local impulses were caused both by crescent-shaped regions of low void fraction and by small bubbly structures. These regions appeared to be bounded by bubbly shock waves which were associated with the large pressure pulses. The paper also quantifies the effect of reduced frequency, cavitation number and tunnel velocity on the strength of the pressure pulses by presenting the acoustic impulse for a range of flow conditions. The reduced frequency is an important parameter in the determination of the total impulse level and the local and global pulse distribution. Large impulses are present on the foil surface even at cavitation numbers which do not result in large levels of acoustic radiation or global impulse. The total impulse increases with increasing tunnel velocity

Shock Wave Measurements in Cloud Cavitation

One of the most destructive (and noisy) forms of cavitation is that referred to as "cloud cavitation" because it involves a large collection of bubbles which behave as a coherent whole. The present paper presents the results of an experimental study of the processes of collapse of a cavitation bubble cloud, specifically that generated by an oscillating hydrofoil in a water tunnel. Measurements of the far-field noise show that this is comprised of substantial pulses radiated from the cloud at the moment of collapse. Also, transducers within the cavitation zone encounter very large pressure pulses (or shock waves) with amplitudes of the order of tens of atmospheres and typical durations of the order of tenths of a millisecond. These shock waves appear to be responsible for the enhanced noise and damage potential which results from that phenomenon