A fourth-order PDE denoising model with an adaptive relaxation method

In this paper, an adaptive relaxation method and a discontinuity treatment of edges are proposed to improve the digital image denoising process by using the fourth-order partial differential equation (known as the YK model) first proposed by You and Kaveh. Since the YK model would generate some speckles into the denoised image, a relaxation method is incorporated into the model to reduce the formation of isolated speckles. An additional improvement is employed to handle the discontinuity on the edges of the image. In order to stop the iteration automatically, a control of the iteration is integrated into the denoising process. Numerical results demonstrate that such modifications not only make the denoised image look more natural, but also achieve a higher value of PSNR

Modelling the cold crucible pouring dynamics

The paper uses the mathematical modelling technique to investigate cold crucible operation with a non-consumable nozzle made of copper segments. The combination of two coils, one for the main crucible and the other for the nozzle with different power supplies, requires to superpose the effects of the two independent AC electromagnetic force fields. This leads to complex transitional flow structures and turbulence of the melt, contributing to the melt shape dynamics and the heat loss to the walls to satisfy the narrow balance between the thin solidified protective layer while avoiding the blockage of the outflow if the nozzle is frozen. The sensitivity of the outflow to the nozzle diameter is investigated. The beneficial features of the cold crucible melting to purify the melt from particulate contamination are explained using the particle tracking during the pouring process

The impact of two and three dimensional assumptions on coupled structural mechanics and microstructure solidification modelling

It is usual for computational efficiency to simulate growing alloy dendrites during solidification using a two-dimensional model. However, the fidelity of such simulations is to be questioned, since observations show that three-dimensional models lead to significantly more realistic results in comparison to experiments under many situations. Even in thin sample cases, the properties affecting, for example, mechanical behaviour are intrinsically three-dimensional. However, partly due to the lack of published work on the, topic the impact of 2D assumptions on the evolution and structural mechanical behaviour of dendrites has not been properly explored. In this study, solidification using the Cellular Automata (CA) method was coupled to a Finite Volume Structural Mechanics Solver (FVSMS) capable of both 2D and 3D modelling, applied to a selection of representative problems which clearly demonstrate that structural mechanics is another factor in the modelling of dendrites where two-dimensional assumptions can lead to significantly altered behaviour when compared to three-dimensional reality

A study of the complex dynamics of dendrite solidification coupled to structural mechanics

The impact of structural mechanics is often overlooked when modelling the solidification of dendritic microstructures, despite experimental observations that the interaction between these processes can be a factor leading to the development of crystal mosaicity throughout the microstructure which can itself lead to more serious defects. When considered at all, the structural mechanical behaviour of columnar dendrites is often considered as being analogous to a cantilever beam both in interpretations of experimental results and in existing numerical modelling. While this is not an unreasonable assumption when considering a dendrite in isolation, this is a scenario that infrequently occurs. In this paper a parametric study is presented using a Cellular Automata solidification solver coupled to a Finite Volume Structural Mechanics solver. These results highlight the complex non-linear behaviour that arises when considering dendrite interaction, demonstrating the significantly different microstructures that can be obtained by varying only the force experienced by the system

Modelling three-dimensional microstructure evolution influenced by concurrent structural mechanical mechanisms

The interdependence between structural mechanics and microstructure solidification is an inherently three-dimensional phenomenon, where the complex physical processes and mechanical interactions can lead to dendrites growing at orientations influenced by twisting and out of plane bending. These effects can have a significant impact on the formation of defects and the overall macroscopic material properties of the structure. However, all attempts to numerically model this process so far have been limited to two dimensional representations of the problem, which necessitates ignoring any potential behaviour that may arise from these more complex deformation events. For this reason, the two-dimensional numerical methods presented in previous papers, which couple a Finite Volume Structural Mechanics Solver to a Cellular Automata solidification solver, have been expanded so that problems may now be simulated in three dimensions. Results are presented which do not aim to predict any specific mechanism but rather highlight the new capabilities of this improved three-dimensional modelling framework

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

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

Effect of water temperature and induced acoustic pressure on cavitation erosion behaviour of aluminium alloys

Cavitation erosion is a major challenge for marine and fluid machinery systems. This study investigated the erosion performance of two as-cast aluminium alloys exposed to acoustic cavitation in water at temperatures of 10–50°C and those were then compared with an extruded wrought alloy tested specifically at the temperature of maximum erosion. The results showed that the as-cast A380 alloy displayed exceptional resistance to cavitation erosion, with the lowest mass loss and surface roughness. This finding suggests that the as-cast A380 alloy is a suitable choice for lightweight, high-performance components in applications where cavitation resistance is critical

Investigation of mechanical properties of Al3Zr intermetallics at room and elevated temperatures using nanoindentation

This work deals with the measurement of mechanical properties of single and polycrystalline Al3Zr specimens from ambient to elevated temperatures using nano-indentation experiments. In this study, we employed three kinds of intermetallic specimens produced from Al3Zr crystals chemically extracted from an Al-3 wt% Zr alloy. The properties such as elastic modulus and hardness were determined under quasistatic loading conditions. Constant multicycle indentation testing (MCT) was further performed using a Vickers indenter to understand the fatigue response of intermetallics at high load low cycle conditions. The results showed that hardness and elastic modulus of Al3Zr intermetallics depended on the crystal structure/orientation, with polycrystalline samples showing higher elastic modulus than single crystal specimens at room temperature conditions. MCT experiments revealed that contact pressure of more than 7 GPa was needed to fracture a crack-free crystal under dynamic loading conditions. Consequently the properties of intermetallics at temperatures up to 700 ◦C were determined for the first time, using high-temperature nano-indentation technique. Elevated temperature measurements indicated that intermetallics had high creep resistance at low and intermediate temperatures, but exhibited significant plastic deformation and creep close to the melting point of pure aluminium

Ultrasonic cavitation erosion mechanism of free-floating Al3Zr intermetallics

In this paper, we investigate the cavitation-induced erosion and breakdown mechanism of free floating Al3Zr crystals exposed to ultrasonic vibrations in water at different exposure times using in-situ high-speed imaging technique and scanning electron microscopy (SEM). The post-mortem microstructural examination of the damaged crystals shows that the micron-sized hierarchical crack network structure is initially formed in the outer layer of the crystals. Subsequently, the cracked surface undergoes delamination with subsequent layer-by-layer breakdown into micro-fragments in the range of 5-50 μm. This process is accelerated every time the fragment is dragged into the cavitation zone by the recirculating acoustic flow conditions