Two-dimensional Mixture Model Research Articles

An analytical model for the velocity and gas fraction profiles near gas-evolving electrodes

Understanding multiphase flow close to the electrode surface is crucial to the design of electrolyzers, such as alkaline water electrolyzers for the production of green hydrogen. Vertical electrodes develop a narrow gas plume near their surface. We apply the integral method to the mixture model. Considering both exponentially varying and step-function gas fraction profiles, we derive analytical relations for plume thickness, velocity profile, and gas fraction near the electrode as a function of height and current density. We verify these analytical relations with the numerical solutions obtained using two-dimensional mixture model simulations. We find that for low gas fractions, the plume thickness decreases with an increase in current density for an exponentially varying gas fraction profile. In contrast, the plume thickness increases with increasing current density at high gas fractions for an approximately step-function-shaped gas fraction profile, in agreement with experiments from the literature.

A new toolbox to distinguish the sources of spatial memory error.

Studying the sources of errors in memory recall has proven invaluable for understanding the mechanisms of working memory (WM). While one-dimensional memory features (e.g., color, orientation) can be analyzed using existing mixture modeling toolboxes to separate the influence of imprecision, guessing, and misbinding (the tendency to confuse features that belong to different memoranda), such toolboxes are not currently available for two-dimensional spatial WM tasks.Here we present a method to isolate sources of spatial error in tasks where participants have to report the spatial location of an item in memory, using two-dimensional mixture models. The method recovers simulated parameters well and is robust to the influence of response distributions and biases, as well as number of nontargets and trials.To demonstrate the model, we fit data from a complex spatial WM task and show the recovered parameters correspond well with previous spatial WM findings and with recovered parameters on a one-dimensional analogue of this task, suggesting convergent validity for this two-dimensional modeling approach. Because the extra dimension allows greater separation of memoranda and responses, spatial tasks turn out to be much better for separating misbinding from imprecision and guessing than one-dimensional tasks.Code for these models is freely available in the MemToolbox2D package and is integrated to work with the commonly used MATLAB package MemToolbox.

Numerical investigation of a mixture two-phase flow model in two-dimensional space

A two-dimensional two-phase flow model for gas-liquid mixture is presented. The model takes into account the relative velocity between the gas and liquid phases and is based on conservation equations for gas-liquid mixtures. The mixture model involves balance equations for the relative velocity and is able to handle it without any physical or artificial stabilization in the source terms. The novel aspect of the mixture model is that it is written in a conservative form and ensures the hyperbolicity of the two-phase flow equations. With this regard, the governing equations are solved with finite volume methods. We extend and apply the framework of Godunov methods of centred-type, namely, the FirstOrder Centered (FORCE) and the Slope Limiter Centered (SLIC) methods to the two-dimensional governing equations without any loss of generality in the numerical solutions. An efficient assessment of both the mixture model and the numerical methods is carried out by simulating physical problems available in the literature. Simulations agree well with those in the literature and include new insights that could be used to explain the relative velocity observations. The favourable results suggest that the two-dimensional mixture model simulations can be employed for practical engineering problems of the non-equilibrium type.

Compilation of NC lathe dynamic cutting force spectrum based on two-dimensional mixture models

The load spectrum of numerical control machine tool (NCMT) is the basis data of reliability design, life prediction, and reliability bench test with simulated actual load conditions. Static cutting force spectrum, which can be compiled by empirical formula, cannot accurately reflect the real load conditions. Hence, a method for compiling the spectrum of dynamic turning force is proposed by using two-dimensional mixture models. Dynamic turning force is measured in the laboratory based on a large amount of cutting process data collected in the user field. Mean–frequency and amplitude–frequency matrices of dynamic turning force are obtained by the rainflow counting method. The probability distributions of mean and amplitude are established by using Weibull mixture models (WMM) according to the characteristics of the dynamic turning force, and the two main problems of this method are the determination of the number of mixture components and the estimation of parameters. Gray relation analysis is used to quantify the multi-objective evaluation matrix, and thus the number of mixture components is determined. Parameters are estimated using the improved expectation maximization (EM) algorithm, where the initial values of parameters are obtained by the K-means++ and Bayesian random classification. Finally, the joint probability distribution function between the mean and amplitude is established by the Copula function. Thus, the dynamic cutting force spectrum is compiled. Case analysis results show that the mean and amplitude distribution models with high fitting precision can be obtained using the proposed method. Furthermore, the precision of the load spectrum of NCMT is improved.

Two phase discharge flow prediction in safety valves

Safety relief valves (SRV) are necessary elements in the protection of any pressurised system and the prediction of the expected discharge flows is an important consideration for the valve sizing to ensure that rupture pressures do not occur. The high speed flows that occur inside the SRV are complex particularly when a two-phase flow is involved and lead to a less capable protection device which result in larger valves compared to single phase flows. In this paper the ability of a CFD based two phase mixture model to predict the critical flows of air and water through a safety valve is examined. An industrial refrigeration safety relief valve of ¼″ inlet bore size has been tested experimentally over a pressure range of 6–15 barg and air mass qualities from 0.1 to 1 when discharging to near atmospheric conditions for a fully open condition. A two-dimensional mixture model consisting of mixture mass, momentum, and energy equations, combined with a liquid mass equation and the standard k–ε turbulence model for mixture turbulent transport has been used to predict the two phase flows through the valve. The mixture model results have been compared with the Homogenous Equilibrium Model (HEM) commonly used for in valve sizing in non flashing two phase flow conditions. The accuracy of the models over the two phase flow range are quantified and discussed.

Prediction of two-phase flow through a safety relief valve

Safety relief valves are necessary elements in any pressurised system. The flow inside the safety relief valve shows a number of interesting, yet complicated, features especially when a two-phase flow is involved. Consequently, developing an efficient and accurate means for predicting the safety relief valve performance and understanding the flow physics is a demanding objective. In this article, the ability of a two-phase mixture model to predict the critical flows of air and water through a safety valve is examined. An industrial refrigeration safety relief valve of ¼” inlet bore size has been tested experimentally over a pressure range of 6–15 barg and air mass qualities from 0.23 to 1 when discharging to near atmospheric conditions for a range of valve lift positions. A two-dimensional mixture model consisting of mixture mass, momentum and energy equations, combined with a liquid mass equation and the standard k-e turbulence model for mixture turbulent transport has been used to predict the two-phase flows though the valve. The mixture model results have been compared with the homogenous equilibrium model and the homogenous non-equilibrium model adopted by the ISO standard. It has been shown that the mixture model can be used satisfactorily to predict the mass flows for the above conditions. Overall, the accuracy of the two-phase air mass flow for given inlet liquid flow rates can be predicted to within 15%.