Session A34: Phase Change I

Pool Boiling in Earth and micro-gravity during sub-cooling temperatures

Pool boiling simulations are carried out to study the effects of gravity, sub-cooling and super-heating. The purpose is to explore how the sub-cooling and super-heating in varying environments affects the bubble dynamics: bubble formation, bubble departure, sliding and coalescence bubbles; and the heat transfer statistical analysis. Direct Numerical Simulations of pool boiling were performed using our in-house high fidelity solver, where the liquid-vapor interface is tracked with a level set formulation. The gorening equations are advanced in time with a fractional step method. The ghost-fluid formulation is used to take into account sharp jumps in pressure, velocity and temperature across the multiphase boundary, and the interface is represented using the level set technique. A mathematical model based on Halton sequence is used to construct nucleation sites density, and ski Python package is used to track bubbles and determine their properties. Microgravity two-dimensional simulations indicate that the bubble departure size increases with decrease in gravity due to the buoyancy effects. In very low gravity, a central bubble remains attached to the surface due to lack of equilibrium between buoyant force and wall adhesion force. Heat transfer temporal variations in space averaged heat flux indicate that the time to reach steady state increases when gravity decreases. Sub-cooling studies indicate that heat transfer decreases when increasing the degree of sub-cooling. Besides, bubble departure becomes too slow when the sub-cooling degree increases. The time to reach steady state is constant for all sub-cooling cases.   

Computational modeling of air bubble oscillations in a cavitation-induced acoustic field using multi-phase multicomponent model

Recent experiments have shown that a mm-sized air bubble undergoes nonlinear shape oscillations when subjected to an acoustic field produced by the collapse of a nearby vapor bubble. To better understand this phenomenon, we leverage a diffuse interface two-phase, two-component compressible flow model. The model is based on a multiphase extension of the Euler equations that accounts also for surface tension, and heat conduction. We perform high-fidelity numerical simulations in cylindrical coordinates. Our simulations agree well with experiments and show that surface tension and heat conduction play an important role in the coordinated oscillations of the two bubbles. Our results are important for cavitation applications where air entrainment is significant.

    

Methodology for statistical evaluation of bubbly flows using grouped bubble cells

The present study aims to introduce an improved evaluation method of the statistical properties of bubbly two-phase flow for situations where bubble count density may exhibit low and/or strongly varying values. In these cases (sheet cavitation, boiling flows, etc.), accurate statistical descriptions are challenging at every location in the flow field (particularly in areas with a low bubble count density). As a result, methods of evaluating closure terms for pdf-transport models, such as the stochastic field method, are deemed to uncertainty. In the proposed methodology, bubbles are clustered to form groups of a fixed size. The volume associated with each of the grouped bubble clusters is dynamically calculated by a Voronoi tessellation, based on a prior Delaunay triangulation. We found that the proposed methodology is useful for evaluating statistical terms in pdf-transport models, as the effects of bubble number density versus those of bubble size growth are properly separated. Significant improvements in the statistical accuracy are observed in comparison to traditional evaluation techniques. In the study, we apply the method in two different examples: (i) a synthetic bubble distribution with predefined analytical field values, and (ii) experimental data captured from a plunging jet. We discuss the assessment of inherent systematic errors and the resulting achieved statistical accuracy. The objective of the study is to share our experiences and provide a best practice recommendation.   

Reynolds numbers effects on cavitation inception in secondary vortices in a turbulent shear layer

The unsteady pressure field and the distributions of nuclei in and around quasi-streamwise vortices (QSVs), in a shear layer behind a backward facing step, are experimentally investigated. The QSVs are the preferred sites of inception and the cavitation inception index, or the void fractions at the same index, increases with Reynolds number (Re). To explain these observations, tomographic particle tracking is used for calculating the velocity and pressure fields for non-cavitating flow. The pressure is lower, and its minima last longer within the QSVs compared to the surrounding flow. As a result of stretched vortex dynamics, the pressure minima are likely to be preceded by axial vorticity stretching and followed by contraction. Consequently, the regions of low pressure are localized and intermittent, consistent with the multi-point appearance of cavitation. With increasing Re, the pressure minima decay slower and the pressure correlations remain significant for longer. These trends can be explained as a result of viscous diffusion. The effects of nuclei availability are studied under controlled seeding of microbubbles using holography. For the current conditions, cavitation inception is dominated by pressure and relatively insensitive to nuclei distributions. 

    

Synchronization of Vortex Dynamics and Cavitation in Flexible Cantilevered Hydrofoils

We numerically study the combined vortex and cavity synchronization/lock-in in a flexible cantilevered hydrofoil at a high Reynolds number. The fluid-structure interaction of this system is of interest in characterizing the cavitation-induced vibrations of marine propellers. For an elastically mounted hydrofoil, cavitating conditions result in large vibrations at low angles of attack, with distinct lock-in and post-lock-in regimes, stemming from the interaction of vortex and cavity dynamics. However, in the case of an elastic structure, flexural and torsional modes can alter the nature of synchronization. In the current work, we aim to explore the mechanism associated with the vortex-cavity excitation of a flexible hydrofoil by answering three questions: (a) What are the regimes of lock-in which can be delineated owing to the presence of a multi-modal nonlinear structure? (b) What are the response characteristics of the flexural and torsional modes? and (c) How does the presence of cavitation alter the vortex dynamics and consequently hydrodynamic loads acting on the structure in contrast to non-cavitating conditions?

    

Experiments and Modeling of Aviation Fuel Cavitation in a Geometry Relevant to Aircraft Fuel Pumps

The results of both experiments and modeling of aircraft fuel cavitation are reported. The experiments are performed in a generic geometry that is relevant to that which occurs in aircraft fuel pumps. This involves a radial flow between parallel disks with a 0.4 mm gap between the disks. JP-8 or JP-5 aviation fuel is pumped through the central injection port of the lower disk at a user-selected pressure. The sudden flow turning and associated radial acceleration in the fuel creates extremely low static pressures, resulting in cavitation. This is a situation that often occurs in aircraft fuel systems. The top plate is transparent, which allows for high-speed imaging of the dynamics and extent of the cavitating region. An array of disk static pressure taps allows the radial pressure variation to also be measured. Experimental results are reported for a wide range of fuel injection pressures. A novel spatial Rayleigh-Plesset formulation is used to model the fuel cavitation. The model predictions of the radial location of bubble collapse and the radial pressure profiles are shown to be in excellent agreement with the experiments. This approach will be valuable in the future for predicting and understanding aviation fuel cavitation in other geometries.   

Transition Mechanisms in Sheet to Cloud Cavitation.

We investigate sheet to cloud cavitation over a wedge using numerical simulations performed at Reynolds number, Re=200,000, and cavitation numbers ranging from σ=1.44 to σ=2.18. The multiphase fluid is described using a homogeneous mixture model, and the governing equations are the compressible Navier Stokes equations for the liquid/vapor mixture, along with a transport equation for the vapor mass fraction. The numerical method, a characteristic-based filtering approach for shock and interface capturing, is first validated by comparison with experiments, showing good agreement. A systematic parametric investigation for different cavitation numbers is then carried out. The two primary mechanisms known to destabilize the sheet cavity, viz. the re-entrant jet and condensation shock mechanisms, are captured in the simulations. The observations are then used to propose a novel description of the condensation shock mechanism, which can be initiated by a re-entrant jet that transforms into a shock front as it travels upstream through the vapor cavity. The results presented here are part of an ongoing investigation on identifying the physical conditions that lead to the transition between the re-entrant jet and condensation shock mechanisms, a knowledge of which is yet to be elucidated.   

Sub-grid scale characteristics of Godunov-based schemes for cavitating two-phase flows

Numerical accuracy of large-eddy simulations for cavitating flows decreases near discontinuities such as shock waves generated by vapor-bubble collapse, vapor-liquid phase boundaries, and complexities of solid boundaries. The errors can often be attributed to explicit sub-grid scale models. An alternative methodology, implicit large-eddy simulation, leverages the numerical discretization error of monotone, sharp-interface capturing schemes to mimic the physical dissipation rate. The characteristics of the numerical dissipation rate and implicit sub-grid scale are detailed for a class of high-order Godunov-based schemes for cavitating flows discretized in generalized curvilinear coordinates. Because variable reconstruction is performed locally, the scheme can capture both discontinuities and low Mach number features. Leading terms of modified equation analysis confirm the dissipative behaviors. A series of cases are undertaken including a two-phase shock tube, decaying homogeneous isotropic turbulence, and cavitating flow over a cylinder, which employs a sharp-interface immersed boundary method for compressible flow. The turbulence spectra, statistics and void fraction profiles show good agreement with direct numerical simulation.