Mathematical modeling of dispersed media flows in the presence of nucleation, coagulation and phase transitions

A model of motion of a gas-dispersed medium in the presence of processes of nucleation, coagulation and phase transitions has been constructed. A homogeneous nucleation model is used to describe the nucleation process. It is believed that the process of cluster coagulation occurs due to their Brownian motion. The analysis of the solution of the coagulation equation in the particular case of monodisperse clusters in the presence of a source and sink of particles is carried out. To determine the rate of phase transitions the Hertz-KnudsenLangmuir formula is used. The calculations were carried out on the basis of a quasi-one-dimensional model within the equilibrium approximation (when the velocities and temperatures of the phases coincide). As a result of the study the main properties of the flow of a two-phase mixture in a channel in the presence of nucleation, coagulation, and phase transformations have been established. It is shown that the vapor temperature increases along the channel and reaches the saturation temperature at some distance from the channel entrance. Calculations have shown that the coagulation process has a rather strong effect on the distribution of cluster sizes along the channel.

A Probabilistic Model for Forging Flaw Crack Nucleation Processes

A probabilistic model for quantifying the number of load cycles for nucleation of forging flaws into a crack has been developed. The model correlates low cycle fatigue (LCF) data, ultrasonic testing (UT) indication data, flaw morphology and type with the nucleation process. The nucleation model is based on a probabilistic LCF model applied to finite element analyses (FEA) of flaw geometries. The model includes statistical size and notch effects. In order to calibrate the model, we conducted experiments involving specimens that include forging flaws. The specimens were machined out from heavy duty steel rotor disks for the energy sector. The large disks, including ultrasonic indications on the millimeter scale, were cut into smaller segments in order to efficiently machine specimens including manufacturing related forging flaws. We conducted cyclic loading experiments at a variety of temperatures and high stresses in order to capture realistic engine operating conditions for flaws as they occur in service. This newly developed model can be incorporated into an existing probabilistic fracture mechanics framework and enables a reliable risk quantification allowing to support customer needs for more flexible operational profiles due to the emergence of renewable energy sources.

Forecasting Induced Earthquake Hazard Using a Hydromechanical Earthquake Nucleation Model

In response to the dramatic increase in earthquake rates in the central United States, the U.S Geological Survey began releasing 1 yr earthquake hazard models for induced earthquakes in 2016. Although these models have been shown to accurately forecast earthquake hazard, they rely purely on earthquake statistics because there was no precedent for forecasting induced earthquakes based upon wastewater injection data. Since the publication of these hazard models, multiple physics-based methods have been proposed to forecast earthquake rates using injection data. Here, we use one of these methods to generate earthquake hazard forecasts. Our earthquake hazard forecasts are more accurate than statistics-based hazard forecasts. These results imply that fluid injection data, where and when available, and the physical implications of fluid injection should be included in future induced earthquake hazard forecasts.

Langer–Schwartz–Kampmann–Wagner precipitation simulations: assessment of models and materials design application for Cu precipitation in PH stainless steels

Quantitative modelling of precipitation kinetics can play an important role in a computational material design framework where, for example, optimization of alloying can become more efficient if it is computationally driven. Precipitation hardening (PH) stainless steels is one example where precipitation strengthening is vital to achieve optimum properties. The Langer–Schwartz–Kampmann–Wagner (LSKW) approach for modelling of precipitation has shown good results for different alloy systems, but the specific models and assumptions applied are critical. In the present work, we thus apply two state-of-the-art LSKW tools to evaluate the different treatments of nucleation and growth. The precipitation modelling is assessed with respect to experimental results for Cu precipitation in PH stainless steels. The LSKW modelling is able to predict the precipitation during ageing in good quantitative agreement with experimental results if the nucleation model allows for nucleation of precipitates with a composition far from the equilibrium and if a composition-dependent interfacial energy is considered. The modelling can also accurately predict trends with respect to alloy composition and ageing temperature found in the experimental data. For materials design purposes, it is though proposed that the modelling is calibrated by measurements of precipitate composition and fraction in key experiments prior to application. Graphic abstract

A Probabilistic Model for Forging Flaw Crack Nucleation Processes

A probabilistic model for quantifying the number of load cycles for nucleation of forging flaws into a crack has been developed. The model correlates low cycle fatigue (LCF) data, ultrasonic testing (UT) indication data, flaw morphology and type with the nucleation process. The nucleation model is based on a probabilistic LCF model applied to finite element analyses (FEA) of flaw geometries. The model includes statistical size and notch effects. In order to calibrate the model, we conducted experiments involving specimens that include forging flaws. The specimens were machined out from heavy duty steel rotor disks for the energy sector. The large disks, including ultrasonic indications on the millimeter scale, were cut into smaller segments in order to efficiently machine specimens including manufacturing related forging flaws. We conducted cyclic loading experiments at a variety of temperatures and high stresses in order to capture realistic engine operating conditions for flaws as they occur in service. This newly developed model can be incorporated into an existing probabilistic fracture mechanics framework and enables a reliable risk quantification allowing to support customer needs for more flexible operational profiles due to the emergence of renewable energy sources.

Comment on “Crystallization of Supercooled Liquids: Self-Consistency Correction of the Steady-State Nucleation Rate” by Abyzov et al., Entropy 2020, 22, 558

It is shown that in the growth region (above the critical nucleation size) the transient distributions obtained numerically from the Becker-Döring equation (BDE) by Abyzov et al., Entropy 2020, 22, 558, are in accurate correspondence with the matched asymptotic (singular perturbation) solution by Shneidman, Sov. Phys. Tech. Phys. 1988, 33, 1338. The solution is unmodified by “self-consistency” corrections which affect only the steady state rate. Sensitivity of the results to selection of a specific form of the BDE (the “nucleation model”) also is briefly discussed.