Session AJ: Bubbles I: Cavitation

Numerical simulation of shock/bubble-cloud interaction problems

The interaction of a shock wave with a dilute bubble cloud is computed using a continuum two-phase model incorporating the effect of a distribution of nuclei sizes. The bubble dynamics are evaluated using a Rayleigh-Plesset-type equation including the effects of heat transfer, liquid viscosity and compressibility. A finite-volume WENO scheme coupled with an approximate HLLC Riemann solver is developed to solve the shock problems. Linear and shock wave propagation through a one-dimensional bubble screen is computed and the effect of phase cancellations among the different-sized bubbles is quantified. The size distribution in the screen is found to increase the cushioning of the shock loading. Computations of shock/bubble-cloud interaction in two dimensions are also presented.   

Numerical Simulations of Bubble Dispersion over a Hydrofoil

The production and entrainment of bubbles in ship wakes is not completely understood despite the fact that it has many practical applications. For example, bubbles trapped in the large vortical structures in the ship wake can form clusters that are able to persist for large distances leaving a long trail of bubbles, which increases the ship's signature; an important consideration in the defence environment. The fundamental mechanisms behind the complicated bubbly flow can be understood using data from numerical simulations. The objective of the study is to investigate the accuracy of current state-of-art numerical models for simulating bubbly flows. A spectral element-Fourier code will be used to carry out direct numerical simulations (DNS) with Lagrangian particle tracking to study the interaction of the upstream bubble distribution with a hydrofoil at different angles of attack and Reynolds numbers, and the effect on the resulting downstream bubble distribution.   

Partial Cavity Flows at High Reynolds Numbers

Partial cavity flows created for friction drag reduction were examined on a large-scale. Partial cavities were investigated at Reynolds numbers up to 120 million, and stable cavities with frictional drag reduction of more than 95{\%} were attained at optimal conditions. The model used was a 3 m wide and 12 m long flat plate with a plenum on the bottom. To create the partial cavity, air was injected at the base of an 18 cm backwards-facing step 2.1 m from the leading edge. The geometry at the cavity closure was varied for different flow speeds to optimize the closure of the cavity. Cavity gas flux, thickness, frictional loads, and cavity pressures were measured over a range of flow speeds and air injection fluxes. High-speed video was used extensively to investigate the unsteady three dimensional cavity closure, the overall cavity shape and oscillations.   

Ventilated Supercavities

The topic of supercavitation is of considerable interest to drag reduction and/or speed augmentation in marine vehicles. Supercavitating vehicles need to be supplied with an artificial cavity through ventilation until they accelerate to conditions at which a natural supercavity can be sustained. A study has been carried out in the high-speed water tunnel at St. Anthony Falls Laboratory to investigate some aspects of the flow physics of such a supercavitating vehicle. During the present experimental work, the ventilated supercavity formed behind a sharp-edged disk was investigated utilizing several different configurations. Results regarding cavity shape, cavity closure and ventilation requirements versus cavitation number and Froude number are presented. Additionally, effects related to flow choking in a water tunnel test section are discussed. Results obtained are similar in character to previously reported results, but differ significantly in measured values. Cavity shape, particularly aft of the maximum cavity diameter, is found to be a strong function of the model support scheme chosen.   

Effect of the cavity closure condition on the flow of liquid around a supercavitating wedge

The problem for a one non-symmetric supercavitating wedge in a jet is considered. The single- and double-spiral-vortex models proposed by Tulin are used to describe the flow of the liquid at the rear part of the cavity. Both problems are solved in a closed form using the methods of complex analysis. The models are compared with respect to different parameters of the flow. It is obtained that the flow around the wedge, in the front part of the cavity and the lift and drag coefficients are not affected by the choice of the model. On the other hand, the flow at the tail part of the cavity and the length of the cavity depend strongly on the chosen model.   

Tip vortex cavitation suppression via mass injection

Tip vortex cavitation (TVC) suppression by mass injection in the core of the vortex was studied with an elliptical plan-form hydrofoil NACA-66 modified in a re-circulating water tunnel of known nuclei distribution. The chord based Re was O(106) for all experiments. Water and Polyox WSR 301 solution for a range of concentrations (10 to 500pmm) and relative flow rates (Qjet / Qcore of 0.033 to 0.27) were injected. Also, different injection port size and angle of attack were studied. It was found that the TVC suppression effect was different for inception and desinence. The baseline (no injection) inception cavitation number was more than the average negative pressure coefficient, -Cp of the vortex, while mass addition reduced the inception cavitation number to approximately the --Cp value. TVC desinence for the baseline case was found to match the estimated --Cp value and polymer injection provided some cavitation suppression. Flow measurements were made to understand the underlying physics of TVC. The mechanisms and scalability that lead to TVC suppression by mass injection are discussed.   

Dynamic of cavitation bubble in a flowing liquid with a pressure gradient

In the present study, a high energy pulsed laser is used to generate a millimetric cavitation bubble within a water flow over a symmetric hydrofoil. The bubble is initiated at different locations in the vicinity of the hydrofoil leading edge. A high speed camera is used to observe the motion of the bubble as it travels along the hydrofoil suction side. Besides the standoff parameter, we have found that the pressure gradient plays a major role on bubble dynamic and subsequent phenomena. For a specific initial location of the bubble, the micro-jet is no more directed towards the hydrofoil surface, as commonly observed in still water. In this case, we have also observed a spectacular behaviour of the cavity rebound, which migrates towards the solid surface despite of the outward direction of the micro-jet. This result differs from the behaviour of a bubble near a solid surface in water at rest or water flowing uniformly since the micro-jet is normally directed toward the solid.   

Cavitation induced by high speed impact of a solid surface on a liquid jet

A solid surface may suffer from severe erosion if it impacts a liquid jet at high speed. The physics behind the erosion process remains unclear. In the present study, we have investigated the impact of a gun bullet on a laminar water jet with the help of a high speed camera. The bullet has a flat front and 11 mm diameter, which is half of jet diameter. The impact speed was varied between 200 and 500 ms$^{-1}$. Immediately after the impact, a systematic shock wave and high speed jetting were observed. As the compression waves reflect on the jet boundary, a spectacular number of vapour cavities are generated within the jet. Depending on the bullet velocity, these cavities may grow and collapse violently on the bullet surface with a risk of cavitation erosion. We strongly believe that this transient cavitation is the main cause of erosion observed in many industrial applications such as Pelton turbines.   

Cavitation Bubble in Shear Flow

In the orifice of liquid injectors at high pressure, cavitation occurs behind the sharp corners, where a strong pressure drop is present due to quick change in the flow direction. In addition, a high level of shear is present inside the boundary layer. Therefore, it is important to understand the influence of the shear on the cavitation. In this study, the deformation of a cavitation bubble in shear and extensional flows is numerically investigated. The Navier-Stokes equations are solved to observe the three-dimensional behavior of the bubble as it grows and collapses. During the collapse phase of the bubble, two re-entrant jets are observed on two sides of the bubble due to interaction of the bubble with the background flow. Re-entrant jets with enough strength could breakup the bubble into smaller bubbles. Post processing of the results is done to cast the disturbance by the bubble on the liquid velocity field in terms of spherical harmonics. It is found that a quadrupole moment is created in addition to the monopole source. As the bubble collapses regions of high vorticity are created near the bubble interface.