Gerardo Trapaga

Mathematical modeling of the isothermal impingement of liquid droplets in spraying processes

A mathematical representation has been developed and computed results are presented describing the spreading of droplets impacting onto a solid substrate. Problems of this type are of major practical interest in plasma spraying (PS) and in spray forming (SF) operations. While the present study was confined to the fluid flow aspects of the process, information has been generated on both the final splat dimensions and on the time required to complete the spreading process. Through this treatment, it is possible to relate these quantities (the splat size and the spreading time) to the operating conditions,i.e., droplet size and droplet velocity, and material properties. The theoretical predictions were found to be in good agreement with both Madejski’s asymptotic solution[17] and with available experimental results. For typical SF conditions (droplet sizes in the 100-µm range and droplet velocities in the 100 m/s range), the spreading times were of the order of microseconds,i.e., significantly shorter than the estimated solidification time.

Mathematical modelling of high velocity oxygen fuel thermal spraying of nanocrystalline materials: an overview

An emerging application of nanocrystalline materials involves the deposition of nanocrystalline coatings using high velocity oxygen fuel (HVOF) thermal spraying. Since the physical, mechanical, and chemical characteristics of a nanocrystalline coating are critically influenced by the HVOF operating parameter, mathematical modelling is increasingly being used to establish a fundamental understanding of the process, to maximize coating performance, and to minimize the amount of experimentation required. In this paper, the modelling of HVOF thermal-spray processes, including combustion, gas dynamics, momentum, and thermal transfer between the particle and gas phase, as well as the impact of particles onto a substrate is reviewed. Particular attention is paid to topics that are particularly relevant to the thermal spraying of nanocrystalline coatings.

Solidification kinetics of a near eutectic Al-Si alloy, unmodified and modified with Sr

The purpose of this work was to explore the differences in solidification kinetics between unmodified and Sr modified eutectic Al-Si alloy as revealed by Fourier Thermal Analysis (FTA) and grain-growth kinetics characterization. Thermal analysis were performed in cylindrical stainless steel cups coated with a thin layer of boron nitride, using two type-K thermocouples connected to a data acquisition system. Grain growth kinetics characterization was carried out using solid fraction evolution and grain density data. FTA results for the non modified and modified alloys suggest that there are changes in the solidification rate during eutectic nucleation followed, during growth, by similar solidification rate evolutions, suggesting that this parameter is governed principally by the heat extraction conditions. On the other hand the change of the grain growth parameters estimated for the experimental probes suggest that the presence of Sr may modify the relationship between grain growth rate and undercooling in eutectic Al-Si.

Structural and electrical properties of Ge1Sb2Te4 face centered cubic phase

The aim of this article is to study the properties of the crystalline face centered cubic Ge1Sb2Te4 phase as a function of annealing and measuring temperature. This material is one of the stoichiometric members of the Ge:Sb:Te family, which is widely used in the phase change data storage and one candidate for multistate recording. The electrical properties of this material have been investigated using two independent methods, the four probe impedance and the Hall measurements, and the results are interpreted in terms of structural parameters obtained from x-ray diffraction and transmission electron microscopy results. Experimental results have shown the polycrystalline nature of the film and that the transport properties have a strong dependence on the annealing temperature. An increase in the annealing temperature leads to an increase in the grain size, carrier concentration, mobility, and to a decrease in the volume fraction of grain boundaries. The mobility is limited by scattering of charge carries at...

Mathematical Modeling of Fluid Flow in a Water Physical Model of an Aluminum Degassing Ladle Equipped with an Impeller-Injector

In this work, a 3D numerical simulation using a Euler–Euler-based model implemented into a commercial CFD code was used to simulate fluid flow and turbulence structure in a water physical model of an aluminum ladle equipped with an impeller for degassing treatment. The effect of critical process parameters such as rotor speed, gas flow rate, and the point of gas injection (conventional injection through the shaft vs a novel injection through the bottom of the ladle) on the fluid flow and vortex formation was analyzed with this model. The commercial CFD code PHOENICS 3.4 was used to solve all conservation equations governing the process for this two-phase fluid flow system. The mathematical model was reasonably well validated against experimentally measured liquid velocity and vortex sizes in a water physical model built specifically for this investigation. From the results, it was concluded that the angular speed of the impeller is the most important parameter in promoting better stirred baths and creating smaller and better distributed bubbles in the liquid. The pumping effect of the impeller is increased as the impeller rotation speed increases. Gas flow rate is detrimental to bath stirring and diminishes the pumping effect of the impeller. Finally, although the injection point was the least significant variable, it was found that the “novel” injection improves stirring in the ladle.

Dielectric properties of Ge2Sb2Te5 phase-change films

The static (es) and high-frequency (e∞) dielectric constants of amorphous and NaCl-type crystalline Ge2Sb2Te5 were measured and the relaxation effects in films were studied using impedance spectroscopy. On the basis of a simple method that allows obtaining the dielectric constant in the low resistivity planar structure, static and high frequency dielectric constants and their temperature dependencies were calculated in both phases. A surprising value of es ≈ 750 in crystalline films was obtained, but the effective dielectric constant, eeff, estimated from the Maxwell-Wagner effective medium model, is significantly lower (eeff ≈ 34.9). Such a high value of es obtained by electrical impedance measurements has been explained by Maxwell-Wagner relaxation, the separation of charges at the interface between grains and grain boundaries. Additionally, three relaxation processes (alpha, beta, and Ohmic relaxation) were observed in the amorphous phase and four relaxations (dipolar relaxation of grains, Ohmic relaxa...

Numerical analyses of fluid dynamics of an atomization configuration

Computational fluid dynamic techniques were used to analyze the gas flow behavior of a typical atomization configuration. The calculated results are summarized as follows. The atomization gas flow at the atomizers exit may be either subsonic at ambient pressure or sonic at an underexpanded condition, depending on the magnitude of the inlet gas pressure. When the atomization gas separates to become a free annular gas jet, a closed recirculating vortex region is formed between the liquid delivery tube and the annular jets inner boundary. Upon entering the atomization chamber, an underexpanded sonic gas flow is further accelerated to supersonic velocity during expansion. This pressure adjustment establishes itself in repetitive expansion and compression waves. A certain protrusion of the liquid delivery tube is crucial to obtain a stable subatmospheric pressure region at its exit. The vortex flow under the liquid delivery tube tends to transport liquid metal to the high kinetic energy gas located outside the liquid delivery tube, thereby leading to an efficient atomization.

Method to Cope with Zero Flows in Newton Solvers for Water Distribution Systems

AbstractThis paper presents and discusses a simple method to deal with zero flows in Newton solvers for water distribution systems, in particular in a previously published global gradient algorithm. The method consists in replacing the Hazen-Williams head loss–flow relationship for flows below a certain threshold with a linear relationship, which coincides with Hazen-Williams’ at zero, but has a nonzero derivative at that point, thus avoiding computational troubles associated with zero flows. Manual and automatic random testing of example networks shows that the proposed method compares well with both the algorithm adopted in water distribution modeling software and the recently proposed regularization method in convergence rate while outperforming them in computational veracity and applicability range.

Physical Modeling of Fluid Flow in Ladles of Aluminum Equipped with Impeller and Gas Purging For Degassing

In the current study a transparent water physical model was developed to study fluid flow and turbulent structure of aluminum ladles for degassing treatment with a rotating impeller and gas injection. Flow patterns and turbulent structure in the ladle were measured with the particle image velocimetry technique. The effects of process parameters such as rotor speed, gas flow rate, and type of rotor on the flow patterns and on the vortex formation were analyzed using this model, which control degassing kinetics. In addition, a comparison between two points of gas injection was performed: (a) conventional gas injection through the shaft and (b) a “novel” gas injection technique through the bottom of the ladle. Results show that the most significant process variable on the stirring degree of the bath was the angular speed of the impeller, which promotes better stirred baths with smaller and better distributed bubbles. A gas flow rate increment is detrimental to stirring. Finally, although the injection point was the less-significant variable, it was found that the “novel” injection from the bottom of the ladle improves the stirring in the ladle, promotes a better distribution of bubbles, and shows to be a promising alternative for gas injection.

Isothermal phase transformation kinetics in stoichiometric and eutectic Ge:Sb:Te films

The aim of this work is to compare the isothermal crystallization kinetics in stoichiometric Ge:Sb:Te as well as in un-doped and Ge doped Sb:Te eutectic films. Experimental results have shown a different crystallization mechanism in the investigated films. In Ge2Sb2Te5 and Ge1Sb2Te4 films the analysis of the kinetic results showed that at the beginning of crystallisation a metastable phase appeared with the Ge1Sb4Te7 composition, this is followed by the nucleation and growth of the stable fcc phase up to full crystallization. In contrast Ge4Sb1Te5 films show diffusion control growing from small dimension grains with decreasing nucleation rate. Sb:Te eutectic films doped by Ge have shown that the addition of Ge increased the effective activation energy of crystallization, but the mechanism of crystallization (diffusion-controlled growth of particles of appreciable initial volume) did not depend on Ge concentration.