A Parallel Cellular Automata Lattice Boltzmann Method for Convection-Driven Solidification.

This article presents a novel coupling of numerical techniques that enable three-dimensional convection-driven microstructure simulations to be conducted on practical time scales appropriate for small-size components or experiments. On the microstructure side, the cellular automata method is efficient for relatively large-scale simulations, while the lattice Boltzmann method provides one of the fastest transient computational fluid dynamics solvers. Both of these methods have been parallelized and coupled in a single code, allowing resolution of large-scale convection-driven solidification problems. The numerical model is validated against benchmark cases, extended to capture solute plumes in directional solidification and finally used to model alloy solidification of an entire differentially heated cavity capturing both microstructural and meso-/macroscale phenomena.

Cavitation-induced shock wave behaviour in different liquids.

This paper follows our earlier work where a strong high frequency pressure peak has been observed as a consequence of the formation of shock waves due to the collapse of cavitation bubbles in water, excited by an ultrasonic source at 24 kHz. We study here the effects of liquid physical properties on the shock wave characteristics by replacing water as the medium successively with ethanol, glycerol and finally a 1:1 ethanol-water solution. The pressure frequency spectra obtained in our experiments (from more than 1.5 million cavitation collapsing events) show that the expected prominent shockwave pressure peak was barely detected for ethanol and glycerol, particularly at low input powers, but was consistently observed for the 1:1 ethanol-water solution as well as in water, with a slight shift in peak frequency for the solution. We also report two distinct features of shock waves in raising the frequency peak at MHz (inherent) and contributing to the raising of sub-harmonics (periodic). Empirically constructed acoustic pressure maps revealed significantly higher overall pressure amplitudes for the ethanol-water solution than for other liquids. Furthermore, a qualitative analysis revealed that mist-like patterns are developed in ethanol-water solution leading to higher pressures.

Comparison of frequency domain and time domain methods for the numerical simulation of contactless ultrasonic cavitation.

The use of a top-mounted electromagnetic induction coil has been demonstrated as a contactless alternative to traditional ultrasonic treatment (UST) techniques that use an immersed mechanical sonotrode for the treatment of metals in the liquid state. This method offers similar benefits to existing UST approaches, including degassing, grain refinement, and dispersion of nanoparticles, while also preventing contact contamination due to erosion of the sonotrode. Contactless treatment potentially extends UST to high temperature or reactive melts. Generally, the method relies on acoustic resonance to reach pressure levels suitable for inertial cavitation and as a result the active cavitation volume tends to lie deep in the melt rather than in the small volume surrounding the immersed sonotrode probe. Consequently, (i) with suitable tuning of the coil supply frequency for resonance, the treatment volume can be made arbitrarily large, (ii) the problem of shielding and pressure wave attenuation suffered by the immersed sonotrode is avoided. However, relying on acoustic resonance presents problems: (i) the emergence of bubbles alters the speed of sound, resonance is momentarily lost, and cavitation becomes intermittent, (ii) as sound waves travel through and reflect on all the materials surrounding the melt, the sound characteristics of the crucible and supporting structures need to be carefully considered. The physics of cavitation coupled with this intermittent behaviour poses a challenge to sonotrode modelling orthodoxy, a problem we are trying to address in this publication. Two alternative approaches will be discussed, one of which is in the time domain and one in the frequency domain, which couple the solution of a bubble dynamics solver with that of an acoustics solver, to give an accurate prediction of the acoustic pressure generated by the induction coil. The time domain solver uses a novel algorithm to improve simulation time, by detecting an imminent bubble collapse and prescribing its subsequent behaviour, rather than directly solving a region that would normally require extremely small time steps. This way, it is shown to predict intermittent cavitation. The frequency domain solver for the first time couples the nonlinear Helmholtz model used for studying cavitation, with a background source term for the contribution of Lorentz forces. It predicts comparable RMS pressures to the time domain solver, but not the intermittent behaviour due to the underlying harmonic assumption. As further validation, the frequency domain method is also used to compare the generated acoustic pressure with that of traditional UST using a mechanical sonotrode.

Scale up design study on process vessel dimensions for ultrasonic processing of water and liquid aluminium.

Scaling up ultrasonic cavitation melt treatment (UST) requires effective flow management with minimised energy requirements. To this end, container dimensions leading to the resonance play a crucial role in amplifying pressure amplitude for cavitation. To quantify the importance of resonance length during the treatment of liquid aluminium, we used calibrated high-temperature cavitometers (in the range of 8-400 kHz), to measure and record the acoustic pressure profiles inside the cavitation-induced environment of liquid Al and deionized water (used as an analogue to Al) excited at 19.5 kHz. To achieve a comprehensive map of the acoustic pressure field, measurements were conducted at three different cavitometer positions relative to the vibrating sonotrode probe and for a number of resonant and non-resonant container lengths based on the speed of sound in the treated medium. The results showed that the resonance length affected the pressure magnitude in liquid Al in all cavitometer positions, while water showed no sensitivity to resonance length. An important practical application of UST in aluminium processing concerns grain refinement. For this reason, grain size analysis of UST-treated Al-Cu-Zr-Ti alloy was used as an indicator of the melt treatment efficiency. The result showed that the treatment in a resonance tank of L=λAl (the wavelength of sound in Al) gave the best structure refinement as compared to other tested lengths. The data given here contribute to the optimisation of the ultrasonic process in continuous casting, by providing an optimum value for the critical compartment (e.g. in a launder of direct-chill casting) dimension.

Mechanisms of ultrasonic de-agglomeration of oxides through in-situ high-speed observations and acoustic measurements.

Ultrasonic de-agglomeration and dispersion of oxides is important for a range of applications. In particular, in liquid metal, this is one of the ways to produce metal-matrix composites reinforced with micron and nano sized particles. The associated mechanism through which the de-agglomeration occurs has, however, only been conceptualized theoretically and not yet been validated with experimental observations. In this paper, the influence of ultrasonic cavitation on SiO2 and MgO agglomerates (commonly found in lightweight alloys as reinforcements) with individual particle sizes ranging between 0.5 and 10 µm was observed for the first time in-situ using high-speed imaging. Owing to the opacity of liquid metals, a de-agglomeration imaging experiment was carried out in de-ionised water with sequences captured at frame rates up to 50 kfps. In-situ observations were further accompanied by synchronised acoustic measurements using an advanced calibrated cavitometer, to reveal the effect of pressure amplitude arising from oscillating microbubbles on oxide de-agglomeration. Results showed that ultrasound-induced microbubble clusters pulsating chaotically, were predominantly responsible for the breakage and dispersion of oxide agglomerates. Such oscillating cavitation clusters were seen to capture the floating agglomerates resulting in their immediate disintegration. De-agglomeration of oxides occurred from both the surface and within the bulk of the aggregate. Microbubble clusters oscillating with associated emission frequencies at the subharmonic, 1st harmonic and low order ultra-harmonics of the driving frequency were deemed responsible for the breakage of the agglomerates.

Enhancement of Mechanical Properties of Pure Aluminium through Contactless Melt Sonicating Treatment.

A new contactless ultrasonic sonotrode method was previously designed to provide cavitation conditions inside liquid metal. The oscillation of entrapped gas bubbles followed by their final collapse causes extreme pressure changes leading to de-agglomeration and the dispersion of oxide films. The forced wetting of particle surfaces and degassing are other mechanisms that are considered to be involved. Previous publications showed a significant decrease in grain size using this technique. In this paper, the authors extend this research to strength measurements and demonstrate an improvement in cast quality. Degassing effects are also interpreted to illustrate the main mechanisms involved in alloy strengthening. The mean values and Weibull analysis are presented where appropriate to complete the data. The test results on cast Al demonstrated a maximum of 48% grain refinement, a 28% increase in elongation compared to 16% for untreated material and up to 17% increase in ultimate tensile strength (UTS). Under conditions promoting degassing, the hydrogen content was reduced by 0.1 cm3/100 g.

In-situ observations and acoustic measurements upon fragmentation of free-floating intermetallics under ultrasonic cavitation in water.

Grain refinement in alloys is a well-known effect of ultrasonic melt processing. Fragmentation of primary crystals by cavitation-induced action in liquid metals is considered as one of the main driving mechanisms for producing finer and equiaxed grain structures. However, in-situ observations of the fragmentation process are generally complex and difficult to follow in opaque liquid metals, especially for the free-floating crystals. In the present study, we develop a transparent test rig to observe in real time the fragmentation potential of free-floating primary Al3Zr particles under ultrasonic excitation in water (an established analogue medium to liquid aluminium for cavitation studies). An effective treatment domain was identified and fragmentation time determined using acoustic pressure field mapping. For the first time, real-time high-speed imaging captured the dynamic interaction of shock waves from the collapsing bubbles with floating intermetallic particles that led to their fragmentation. The breakage sequence as well as the cavitation erosion pattern were studied by means of post-treatment microscopic characterisation of the fragments. Fragment size distribution and crack patterns on the fractured surface were then analysed and quantified. Application of ultrasound is shown to rapidly (<10 s) reduce intermetallic size (from 5 mm down to 10 µm), thereby increasing the number of potential nucleation sites for the grain refinement of aluminium alloys during melt treatment.

On the governing fragmentation mechanism of primary intermetallics by induced cavitation.

One of the main applications of ultrasonic melt treatment is the grain refinement of aluminium alloys. Among several suggested mechanisms, the fragmentation of primary intermetallics by acoustic cavitation is regarded as very efficient. However, the physical process causing this fragmentation has received little attention and is not yet well understood. In this study, we evaluate the mechanical properties of primary Al3Zr intermetallics by nano-indentation experiments and correlate those with in-situ high-speed imaging (of up to 1 Mfps) of their fragmentation process by laser-induced cavitation (single bubble) and by acoustic cavitation (cloud of bubbles) in water. Intermetallic crystals were chemically extracted from an Al-3 wt% Zr alloy matrix. Mechanical properties such as hardness, elastic modulus and fracture toughness of the extracted intermetallics were determined using a geometrically fixed Berkovich nano-diamond and cube corner indenter, under ambient temperature conditions. The studied crystals were then exposed to the two cavitation conditions mentioned. Results demonstrated for the first time that the governing fragmentation mechanism of the studied intermetallics was due to the emitted shock waves from the collapsing bubbles. The fragmentation caused by a single bubble collapse was found to be almost instantaneous. On the other hand, sono-fragmentation studies revealed that the intermetallic crystal initially underwent low cycle fatigue loading, followed by catastrophic brittle failure due to propagating shock waves. The observed fragmentation mechanism was supported by fracture mechanics and pressure measurements using a calibrated fibre optic hydrophone. Results showed that the acoustic pressures produced from shock wave emissions in the case of a single bubble collapse, and responsible for instantaneous fragmentation of the intermetallics, were in the range of 20-40 MPa. Whereas, the shock pressure generated from the acoustic cavitation cloud collapses surged up to 1.6 MPa inducing fatigue stresses within the crystal leading to eventual fragmentation.

Numerical Modelling of the Ultrasonic Treatment of Aluminium Melts: An Overview of Recent Advances.

The prediction of the acoustic pressure field and associated streaming is of paramount importance to ultrasonic melt processing. Hence, the last decade has witnessed the emergence of various numerical models for predicting acoustic pressures and velocity fields in liquid metals subject to ultrasonic excitation at large amplitudes. This paper summarizes recent research, arguably the state of the art, and suggests best practice guidelines in acoustic cavitation modelling as applied to aluminium melts. We also present the remaining challenges that are to be addressed to pave the way for a reliable and complete working numerical package that can assist in scaling up this promising technology.

Contactless Ultrasonic Cavitation in Alloy Melts.

A high frequency tuned electromagnetic induction coil is used to induce ultrasonic pressure waves leading to cavitation in alloy melts. This presents an alternative 'contactless' approach to conventional immersed probe techniques. The method can potentially offer the same benefits of traditional ultrasonic treatment (UST) such as degassing, microstructure refinement and dispersion of particles, but avoids melt contamination due to probe erosion prevalent in immersed sonotrodes, and it can be used on higher temperature and reactive alloys. An added benefit is that the induction stirring produced by the coil, enables a larger melt treatment volume. Model simulations of the process are conducted using purpose-built software, coupling flow, heat transfer, sound and electromagnetic fields. Modelling results are compared against experiments carried out in a prototype installation. Results indicate strong melt stirring and evidence of cavitation accompanying acoustic resonance. Up to 63% of grain refinement was obtained in commercial purity (CP-Al) aluminium and a further 46% in CP-Al with added Al-5Ti-1B grain refiner.

Ultrasonic liquid metal processing: The essential role of cavitation bubbles in controlling acoustic streaming.

The acoustic streaming behaviour below an ultrasonic sonotrode in water was predicted by numerical simulation and validated by experimental studies. The flow was calculated by solving the transient Reynolds-Averaged Navier-Stokes equations with a source term representing ultrasonic excitation implemented from the predictions of a nonlinear acoustic model. Comparisons with the measured flow field from Particle Image Velocimetry (PIV) water experiments revealed good agreement in both velocity magnitude and direction at two power settings, supporting the validity of the model for acoustic streaming in the presence of cavitating bubbles. Turbulent features measured by PIV were also recovered by the model. The model was then applied to the technologically important area of ultrasonic treatment of liquid aluminium, to achieve the prediction of acoustic streaming for the very first time that accounts for nonlinear pressure propagation in the presence of acoustic cavitation in the melt. Simulations show a strong dependence of the acoustic streaming flow direction on the cavitating bubble volume fraction, reflecting PIV observations. This has implications for the technological use of ultrasound in liquid metal processing.

Numerical modelling of acoustic streaming during the ultrasonic melt treatment of direct-chill (DC) casting.

Acoustic streaming and its attendant effects in the sump of a direct-chill (DC) casting process are successfully predicted under ultrasonic treatment for the first time. The proposed numerical model couples acoustic cavitation, fluid flow, heat and species transfer, and solidification to predict the flow pattern, acoustic pressure, and temperature fields in the sump. The model is numerically stable with time steps of the order of 0.01 s and therefore computationally attractive for optimization studies necessitating simulation times of the order of a minute. The sump profile is altered by acoustic streaming, with the slurry region depressed along the centreline of the billet by a strong central jet. The temperature gradient in the transition zone is increased, potentially interfering with grain refinement. The cooling rate in the sump is also altered, thereby modifying the dendrite arm spacing of the as-cast billet. The relative position of the sonotrode affects the sump profile, with the sump depth decreased by around 5 mm when the sonotrode is moved above the graphite ring level by 100 mm. The acoustic streaming jet penetrates into the slurry zone and, as a result, the growth direction of dendritic grains in the off-centre position is altered.

Experimental and numerical investigation of acoustic pressures in different liquids.

In an attempt to quantify the instantaneous pressure field in cavitating liquids at large forcing signals, pressures were measured in four different liquids contained in vessels with a frequency mode in resonance with the forcing signal. The pressure field in liquid metal was quantified for the first time, with maximum pressures of the order of 10-15 MPa measured in liquid aluminium. These high pressures are presumed to be responsible for deagglomeration and fragmentation of dendritic intermetallics and other inclusions. Numerical modelling showed that acoustic shielding attenuates pressure far from the sonotrode and it is prominent in the transparent liquids studied but less so in aluminium, suggesting that aluminium behaviour is different. Due to acoustic shielding, the numerical model presented cannot adequately capture the pressure field away from the intense cavitation zone, but gives a good qualitative description of the cavitation activity. The results obtained contribute to understanding the process of ultrasonic melt treatment (UST) of metal alloys, while facilitating further the guidelines formulation and reproducible protocols for controlling UST at industrial levels.

Microwave modeling and validation in food thawing applications.

Developing temperature fields in frozen cheese sauce undergoing microwave heating were simulated and measured. Two scenarios were investigated: a centric and offset placement on the rotating turntable. Numerical modeling was performed using a dedicated electromagnetic Finite Difference Time Domain (FDTD) module that was two-way coupled to the PHYSICA multiphysics package. Two meshes were used: the food material and container were meshed for the heat transfer and the microwave oven cavity and waveguide were meshed for the microwave field. Power densities obtained on the structured FDTD mesh were mapped onto the unstructured finite volume method mesh for each time-step/turntable position. On heating for each specified time-step the temperature field was mapped back onto the FDTD mesh and the electromagnetic properties were updated accordingly. Changes in thermal/electric properties associated with the phase transition were fully accounted for as well as heat losses from product to cavity. Detailed comparisons were carried out for the centric and offset placements, comparing experimental temperature profiles during microwave thawing with those obtained by numerical simulation.

Dynamics of two interacting hydrogen bubbles in liquid aluminum under the influence of a strong acoustic field.

Ultrasonic melt processing significantly improves the properties of metallic materials. However, this promising technology has not been successfully transferred to the industry because of difficulties in treating large volumes of melt. To circumvent these difficulties, a fundamental understanding of the efficiency of ultrasonic treatment of liquid metals is required. In this endeavor, the dynamics of two interacting hydrogen bubbles in liquid aluminum are studied to determine the effect of a strong acoustic field on their behavior. It is shown that coalescence readily occurs at low frequencies in the range of 16 to 20 kHz; forcing frequencies at these values are likely to promote degassing. Emitted acoustic pressures from relatively isolated bubbles that resonate with the driving frequency are in the megapascal range and these cavitation shock waves are presumed to promote grain refinement by disrupting the growth of the solidification front.