Session M29: Multiphase Flows: Cavitation and Aerated Flows

Pressure field and cavitation inception in secondary vortices in a turbulent shear layer

Cavitation inception in a turbulent shear layer starts at multiple points along quasi-streamwise vortices (QSVs) stretched between the primary spanwise structures. Being pressure-dependent, this experimental study characterizes the pressure field in QSVs in a shear layer developing behind a 10mm high backward facing step. The time-resolved volumetric velocity distribution is measured using tomographic particle tracking. Interpolation of data to a grid with 200 µm spacing using a constrained cost minimization process that makes the velocity divergence-free and material acceleration curl-free, and subsequent integration of the material acceleration, provides the pressure distribution. Regions of QSVs are detected using k-means clustering using a series of variables involving velocity gradients. The pressure is indeed lower, and its minima last longer within the QSVs compared to the surrounding flow. These pressure minima are more likely to appear after a period of axial vorticity stretching and before contraction events. The QSVs have a typical diameter of 1 mm and are 2-5 mm long, and contain contraction and stretching bands with a typical size of 1 mm. Accordingly, the regions of low pressure are localized, consistent with the dimensions of cavitation inception events.   

LES of cavitation inception in a shear layer

Cavitation inception in a shear layer is numerically investigated using a backward-facing step configuration, with an inflow turbulent boundary-layer of Reτ=1500 and at two values of cavitation number. PDFs of pressure and vapor volume fraction show that inception has a higher probability of being observed in the axial position of 0.4 < x/Lr < 0.8, where Lr is the reattachment length, agreeing well with experimental data. An analysis of the incipient topological structures is performed and it is revealed that inception is more likely to occur at the cores of the elongated vortical structures. These structures are found to have a rotation rate 4x higher than their straining rate.   

Analysis of the slip velocity between the two phases in a high-speed cavitating flow

The liquid / vapor mixture in a cavitating flow is usually considered as a homogeneous medium in the current models, but it is shown in this study that the two phases have very different dynamics. Two separate experiments have been performed to measure simultaneously the liquid and vapor velocity fields in two-dimensional sheet cavities on a small-scale Venturi type section. One is based on optical Particle Image Velocimetry (PIV), using a laser light sheet illumination, and the second one is based on fast X-ray imaging. In the first case two components of the velocity are obtained at mid-span of the test section, while in the latter case, the velocity fields are integrated in the width of the test section. One other difference is that optical PIV enables to get the entire velocity field in the whole sheet cavity, while X-ray imaging provides higher resolution results in portions of the cavitation area only.  It is shown first that the two techniques measure similar time-averaged velocities both in the liquid and the vapor phases. The resulting slip velocities between the two phased obtained in both cases are thus in good agreement and reach about 50% of the liquid velocity in a large part of the cavitation area. In general, the vapor velocity is significantly lower than the liquid one, including in the re-entrant jet close to the bottom wall. It is also shown that the non-dimensional slip velocity is almost constant in the sheet cavity and does also not depend on the Reynolds number or the cavitation number. Eventually, the dynamics of the two phases in the area of the re-entrant jet is specifically discussed, based on the data obtained from X-ray imaging: the instantaneous results indicate that the mechanism is based on a liquid reverse flow that subsequently entrains some bubbles in the upstream direction.   

Shock wave emission and evolution mechanisms in aerated cavitating aviation fuel flow in a converging-diverging nozzle

Fuel cavitation in an aircraft fuel system can lead to unexpected material degradation and damage to the fuel system components due to the violent collapse of cavitation bubbles near boundaries and the emitted shock waves. In this study, shock wave propagation and generation mechanisms in fuel cavitation are experimentally characterized in aerated cavitating flow in a converging-diverging nozzle via high-speed digital imaging and signal processing technique that we denote as synthetic schlieren. Two independent stationery and sustained mechanisms responsible for shock wave generation in the diverging section of the nozzle have been observed in the choked flow regime. A detailed systematic quantitative data is obtained to characterize shock wave intensity and velocity in aerated flow regimes of two jet fuels (JP5 and JP8) under different bubble injection rates, nozzle back pressures, and void fractions. A strong similarity is obtained between shock speeds from our experimental data and nonlinear solutions of the governing equations for nonbarotropic homogeneous flow. Results from our study shed some light on the complex physics of fuel cavitation and may lead to improved design of fuel system components.   

Pressure reconstruction of a planar turbulent flow field within a multiply-connected domain with arbitrary boundary shapes

This paper presents a detailed report for the first time documenting the implementation procedures and validation results for pressure reconstruction of a planar turbulent flow field within a multiply-connected domain that has arbitrary inner and outer boundary shapes. The pressure reconstruction algorithm used in the current study is the rotating parallel-ray omni-directional integration algorithm offers high-level of accuracy in the reconstructed pressure. While preserving the nature and advantage of the parallel ray omni-directional pressure reconstruction at places with flow data, the new implementation of the algorithm is capable of processing an arbitrary number of inner void areas with arbitrary boundary shapes. Validation of the multiply-connected domain pressure reconstruction code is conducted using the Johns Hopkins DNS isotropic turbulence databases, with 1000 statistically independent pressure gradient field realizations embedded with random noise used to gauge the code performance. For further validation, the code is also applied for pressure reconstruction from the DNS data (Johnsen and Colonius 2009) about a shock-induced non-spherical bubble collapse in water. It demonstrated that the parallel-ray omni-directional integration algorithm outperforms the Poisson equation approach in terms of the accuracy of the reconstructed pressure.     

Removal of free-stream bubbles in a research water tunnel using an inline cyclone separator

This study evaluates the efficacy of an inline cyclone separator as a means of continuously reducing the free-stream bubble concentration in a research water tunnel. Two sets of experiments are conducted at a cyclone inlet velocity (4.5 m/s) that should remove 100 μm bubble based on a simplified analysis. In the first test, an initial dense field of bubbles is created by intentionally cavitating the pump. Then, the pressure is increased and the time evolution of bubble size distribution in the test section, with and without the cyclone are compared. In the second experiment, the pressure is reduced to a level that causes pump cavitation while monitoring the evolution of bubble statistics, also with and without the cyclone. The bubble size distributions are measured using digital inline holography. Large (>75μm) and small bubbles are reconstructed separately using low-pass & high-pass filtering, and the bubbles are detected using a machine learning based algorithm. In the first experiment, the cyclone doubles the decay rate of bubble concentration, and in the second, it suppresses the increase in bubble density by an order of magnitude. Both experiments indicate that most of the bubbles larger than 60 μm are effectively removed, consistent with expectations.   

Smashed into vapor, cavitation from water slamming

Cliff diving can really hurt. The pain stems from the high pressure generated at impact, which von Karman showed approaches infinity when striking flat (von Karman, 1929).  Yet in contrast to the high pressures found from hard experience we show that a cylinder impacting on a water surface can decrease the local pressure enough to cavitate the liquid in the very early moments (~100 μs).  The liquid cavitates because its slight compressibility allows large pressure waves to form that reflect and create negative pressure regions.  Impact velocities as low as ~3 m/s suffice to cavitate the liquid.  We formulate a new cavitation number to predict the onset of cavitation in these low-speed water slamming scenarios.  These findings imply that cavitation is possible in a variety of free-surface impacts such as boats slamming, cliff diving, and ocean landing of spacecraft.    

Investigation of unsteady cavitation dynamics over a hydrofoil subject to controlled pitching motion

We present a numerical study to examine the influence of low-amplitude controlled pitching motion on the unsteady turbulent cavitating flow over a NACA66 hydrofoil section at Re= 800000. We simulate multiphase flow dynamics in an Arbitrary Lagrangian-Eulerian coordinate, utilizing a highly validated variational finite element approach and homogeneous mixture-based cavitation model with a hybrid URANS-LES approach for turbulence effects. To decouple the cavitation shedding dynamics from trailing edge vortex dynamics, we employ prescribed sinusoidal pitching motion to the hydrofoil at select harmonics of the cavitation shedding frequency. The cavity growth and detachment are forced to delay, limiting the cavity to a thin attached harmonic oscillating layer driven by the pitching frequency for majority of its life, while minimizing cloud shedding. Additionally, increased negative vorticity over the suction surface by pitching motion is adjusted to balance the trailing edge vortex, enforcing a reorganization of the turbulent wake. This targeted decoupling control strategy achieves a significant reduction in the drag forces over the hydrofoil, with slight increase in the lift. The observations are seen to be consistent over a range of cavitation numbers above super-cavitating regime.   

Not Participating

The pressure wave dynamics and associated cavitation in a water-filled cylinder are studied experimentally. The use of single-piston and double-piston drivers enables the system loading to be varied between near-constant acceleration and impulsive loading. The pressure in the air-filled volume is varied to enable the onset of cavitation to be induced or suppressed. The piston(s) acceleration is measured via photonic Doppler velocimetry, enabling the loading to be precisely quantified. The resultant wave activity and fluid cavitation are monitored via piezoelectric pressure transducers and direct visualization of liquid interfaces via high-speed videography through a glass window. The results are compared to predictions of a quasi-one-dimensional model of fluid motion and wave-tracking of acoustic waves. The onset of cavitation is predicted in comparison to homogeneous and heterogeneous nucleation models.   

Coupling of the mixture model with the Rayleigh-Plesset equation

In numerical experiments for engineering applications cavitation is commonly addressed through the mixture model, which considers a scalar, indicating the vapor fraction transported by the flow. The sink and source terms of the transport equation, which rule the dynamics of the cavity, can be expressed through different models. They rely on the use of coefficients which accelerate/decelerate the vaporization and condensation processes and which are usually calibrated through optimization methods. According to the Sauer-Schnerr (SS) model the vapor fraction is related to the bubble dynamics and a simplified version of the Rayleigh-Plesset (RP) equation is exploited to evaluate the bubble radius growth/decrease. We propose the coupling of the SS model with the complete RP equation. Retaining all the terms of the RP equation allows to observe the typical rebounds of bubbles and their influence on the vapor phase development. We test the proposed model by considering a benchmark case, for which experimental data are available. The results are also compared with those obtained with the standard formulation of SS model. We point out how the accurately reproduced high-frequency dynamics of the cavity may be important  for the acoustic characterization of cavitating flows.