Mixture Assumption Research Articles

Three-dimensional simulation of an orifice flow with cavitation-induced air release

A model for the approximation of cavitation-induced air release in three-dimensional flow simulations is proposed. A cavitating orifice flow is investigated. It is assumed that vapor vanishes in the proximity of the orifice, and bubbles further downstream consist essentially of air. The model is based on a homogeneous mixture assumption and comprises one main parameter, which needs to be adjusted to the experimentally measured degassing fraction. Experimental validation is based on transmission light images downstream of the orifice. In the proximity of the orifice, the inclusion of air release in the CFD simulation yields a better agreement to experimentally measured cavitation intensity than the consideration of pure vapor only. It is concluded that a considerably larger amount of air is released than is dissolved in the evaporated amount of liquid. The simulation results suggest that the released air mass corresponds to about 1% of the evaporated liquid mass. These observations may be a good basis for purposeful future experiments, which are indispensable for the development of a more predictive approach of cavitation-induced air release in 3D CFD methods.

Fisher-Bayesian inversion for estimating shale gas facies

The classification of shale gas facies from seismic properties is critical for shale gas reservoir characterization. Shale gas facies are affected by many petrophysical properties. Therefore, the characterization of shale facies should be carried out by multiple parameters, which is more reasonable and accurate. However, multiparameter inversion often leads to unstable results, and coupled properties are generally a way of solving this problem. We develop a Fisher-Bayesian inversion method for estimating shale gas facies by combining the Fisher projection and Bayesian inversion method. The mathematical method adopted for the inversion is the Bayesian framework. The link between different facies and coupled properties is given by a joint prior distribution. We derive the analytical formulation of the Bayesian inversion under the Gaussian mixture assumption for coupled attributes and different shale gas facies. Our approach realizes the fusion of multidimensional petrophysical parameters and establishes a shale gas facies prediction method based on coupled properties. The application to real data sets delivers accurate and stable results, wherein shale gas facies and coupled attributes are accurately predicted and inversed.

Analyzing single and multicomponent supercritical jets using volume-based and mass-based numerical approaches

The injections of cryogenic and non-cryogenic fluids in a supercritical environment, respectively, liquid N2 into gaseous N2 and n-dodecane into gaseous N2, are investigated. The two systems are analyzed under dynamic and thermal similarity (same reduced temperatures, reduced pressures, and Reynolds numbers) using the same simplified two-dimensional configuration for the totality of the simulations. This work contributes to provide insight into the interpretation of numerical studies on single- and multicomponent systems under supercritical conditions. A comprehensive comparison of the results obtained from two numerical approaches, based on the volume of fluid and on the homogeneous mixture assumption, making use of two distinct thermophysical and mixing rule frameworks, is presented. Results show very similar and consistent fluid mechanics and mass diffusion processes predicted by the two approaches, but different thermal behaviors for binary-species configurations. The two different mixing models are found to have the greatest impact on the temperature predictions. Also, isobaric–adiabatic mixing, which is obtained with the mass-based homogeneous approach, leads eventually to a larger extension of the predicted two-phase region. Such findings have large implications in energy systems operating at high pressure, where accurate local temperature predictions are crucial.

Reinforced mixture learning

In this article, we formulate the standard mixture learning problem as a Markov Decision Process (MDP). We theoretically show that the objective value of the MDP is equivalent to the log-likelihood of the observed data with a slightly different parameter space constrained by the policy. Different from some classic mixture learning methods such as Expectation–Maximization (EM) algorithm, the proposed reinforced algorithm requires no distribution assumptions and can handle the non-convex clustered data by constructing a model-free reward to evaluate the mixture assignment based on the spectral graph theory and Linear Discriminant Analysis (LDA). Extensive experiments on both synthetic and real examples demonstrate that the proposed method is comparable with the EM algorithm when the Gaussian mixture assumption is satisfied, and significantly outperforms it and other clustering methods in most scenarios when the model is misspecified. A Python implementation of our proposed method is available at https://github.com/leyuanheart/Reinforced-Mixture-Learning.

Experimental Proof of Concept of a Noncircular Rotating Detonation Engine (RDE) for Propulsion Applications

A noncircular engine cross-section could provide great flexibility in the integration of propulsion into the airframe. In this work, a tri-arc RDE was constructed and tested as an example of noncircular cross-sectioned RDE. The operational characteristics of detonation wave propagation and thrust performance were investigated and compared with an equivalent circular RDE under the same operating conditions. High-speed camera images, short-time Fourier transform (STFT), and fast Fourier transform (FFT) were used for the investigation. The tri-arc RDE showed very similar characteristics to the circular RDE but exhibited slightly better stability and propulsion performance than the circular RDE. We consider that repeated curvature changes positively affect the stability of detonation wave propagation. The experimental data show contradicting results from the numerical analysis with a homogeneous mixture assumption in which the detonation pressures at the convex corner were greater than those at the concave corner. It is reasoned that the tri-arc injector design provides a non-uniform mixture composition, resulting in a strong detonation at the convex corner. Overall, the noncircular RDE of a tri-arc shaped cross-section is demonstrated, one which performs slightly better than an ordinary circular-shaped RDE both in detonation stability and performance.

Assessment of the applicability of binary mixture hypothesis to modeling the phase behavior of heavy oil/bitumen-solvent systems for EOR applications

Conventional production methods in heavy oil reservoirs are not efficient primarily due to the high viscosity of the oil. Several methods such as VAPEX and ES-SAGD have been developed to overcome production challenges from these reservoirs, which mainly rely on oil viscosity reduction. Solvent injection dilutes the oil and produces a complex asymmetric mixture. It is difficult to study the phase behavior of oil due to the diversity of its components, and it gets more complicated with the addition of solvent. One of the assumptions to simplify the problem is considering heavy oil as a single pseudo component and investigating the thermophysical properties of binary mixtures with diluents. This study collected and evaluated more than 1000 experimental data on various types of heavy oil/bitumen and several hydrocarbon and non-hydrocarbon solvents. The data were divided into two groups, below and above the critical temperature of the solvent, according to experimental temperatures. Modeling of mixture phase behavior as a binary mixture was performed using the advanced Peng-Robinson equation of state (APR-EoS). EoS tuning to match the experimental data was performed by optimizing the binary interaction coefficients (kij). The results showed that the binary mixture assumption could be used as a practical approach to construct pressure-composition phase diagrams. Optimized values of kij were proposed as two empirical correlations according to the dimensionless ratio Tco/Tcs (oil critical temperature to solvent critical temperature). The model constructed using these correlations showed an average deviation of about 16% compared to experimental data. It is necessary to note that the vapor-liquid-liquid three-phase regions may occur in a heavy oil/bitumen and solvent mixture. But according to the Gibbs phase rule, with two components and three phases in the system, the degree of freedom equals one. So, investigating the effects of pressure change on three-phase regions is not possible using this model.

Quantifying the effects of mixing state on aerosol optical properties

Abstract. Calculations of the aerosol direct effect on climate rely on simulated aerosol fields. The model representation of aerosol mixing state potentially introduces large uncertainties into these calculations, since the simulated aerosol optical properties are sensitive to mixing state. In this study, we systematically quantified the impact of aerosol mixing state on aerosol optical properties using an ensemble of 1800 aerosol populations from particle-resolved simulations as a basis for Mie calculations for optical properties. Assuming the aerosol to be internally mixed within prescribed size bins caused overestimations of aerosol absorptivity and underestimations of aerosol scattering. Together, these led to errors in the populations' single scattering albedo of up to −22.3 % with a median of −0.9 %. The mixing state metric χ proved useful in relating errors in the volume absorption coefficient, the volume scattering coefficient and the single scattering albedo to the degree of internally mixing of the aerosol, with larger errors being associated with more external mixtures. At the same time, a range of errors existed for any given value of χ. We attributed this range to the extent to which the internal mixture assumption distorted the particles' black carbon content and the refractive index of the particle coatings. Both can vary for populations with the same value of χ. These results are further evidence of the important yet complicated role of mixing state in calculating aerosol optical properties.

Investigation of behavior of heat storage system including paraffin with involving MWCNT nanoparticles

To create new system for heat saving and producing required cool air for building, new air conditioning system has been offered with involving several circular pipes containing paraffin. The thermal properties of paraffin have been upgraded with scattering MWCNT nano-powders and to apply the efficacy in modeling, the new material properties have been changed according to formulations based on homogeneous mixture assumption. Unsteady laminar flows have been considered in both zones and relevant source terms of melting process have been added in equations of paraffin zone. With incorporation of finite volume method, the outputs of current suggested system have been achieved and various values for size of pipe (DR) and fraction of MWCNT (ϕ) were considered. With adding nanoparticles, the conduction increases and higher heat can be absorbed by paraffin, thus, the required time for charging declines around 3.86 %. As size of pipe reduces (with considering same volume of paraffin) the melting process has been expedited. With change of DR from 0.16 to 0.12 and 0.08, the melting time reduces around 30.04 % and 12.48 %, respectively.

Non-linear hyperspectral unmixing with 3D convolutional encoders

ABSTRACT Deep learning-based methods are accepted as a viable alternative to conventional statistical and geometrical methods for hyperspectral unmixing in recent years. These methods are however mainly based on linear mixture assumption on the hyperspectral data. The vast majority of presented algorithms process individual hyperspectral pixels while neglecting the spatial relationships between pixels. In order to address these two missing aspects, we propose a convolutional autoencoder-based hyperspectral unmixing method in this paper. The proposed structure incorporates the spatial neighbourhood relation with its convolutional layers in the first stage and possible non-linearities in the observed data with the included non-linear layer in the final stage. The experiments have first revealed that Adam optimizer have the best performance among different optimization methods for the proposed network. Second, the proposed method has indicated about 20–40% accuracy improvement in terms of mean squared error (MSE) metric compared to traditional hyperspectral abundance estimation methods. Third, the contribution of the non-linear layer is verified by comparing the proposed network with the conventional LMM-based autoencoder structure without the non-linear layer. Finally, the accuracy improvement for the proposed network with non-linear layer compared to the state-of-the-art deep learning-based methods using linear mixture assumption is evaluated in terms of MSE and reported as about 10% and 20% for synthetic and real data, respectively.

Bayesian Hamiltonian Monte Carlo method for the estimation of pyrolysis parameter S1

A Gaussian mixture Hamiltonian Monte Carlo (HMC) Bayesian method has been developed for the inversion of petrophysical parameters such as pyrolysis parameter S1, which is driven by a statistical shale rock-physics model. Pyrolysis parameter S1 can be used to indicate the content of free or adsorbed hydrocarbons in source rock, and it is an important indicator to evaluate the production of shale oil reservoirs. However, most studies on pyrolysis parameters are based on pyrolysis experiments and there is no relevant study to inverse pyrolysis parameter S1 from seismic data. In addition, compared to the total organic carbon content, pyrolysis S1 is more accurate for evaluating gas and oil in shale. In particular, high values of pyrolysis S1 can directly indicate the content of shale oil. We have developed a strategy for assessing shale oil sweet spots through estimating pyrolysis S1 and other petrophysical parameters. Based on the Gaussian mixture assumptions for the prior distribution of the model, we build a joint distribution to link the pyrolysis parameter S1 with elastic attributes, and then we derive a formulation to inverse S1 with the Bayesian model. Due to the components of the Gaussian mixture, the HMC method has been used to sample the posterior distribution. Our study finds that the HMC method for sampling can improve the efficiency and allow a more robust quantification of the uncertainty; also, application to real seismic data sets indicates that the delineation of sweet spots is more accurate combined with pyrolysis S1.

Upper Bounds for the Capacity for Severely Fading MIMO Channels under a Scale Mixture Assumption.

A cornerstone in the modeling of wireless communication is MIMO systems, where a complex matrix variate normal assumption is often made for the underlying distribution of the propagation matrix. A popular measure of information, namely capacity, is often investigated for the performance of MIMO designs. This paper derives upper bounds for this measure of information for the case of two transmitting antennae and an arbitrary number of receiving antennae when the propagation matrix is assumed to follow a scale mixture of complex matrix variate normal distribution. Furthermore, noncentrality is assumed to account for LOS scenarios within the MIMO environment. The insight of this paper illustrates the theoretical form of capacity under these key assumptions and paves the way for considerations of alternative distributional choices for the channel propagation matrix in potential cases of severe fading, when the assumption of normality may not be realistic.

Comparison of three aerosol representations of NHM-Chem (v1.0) for the simulations of air quality and climate-relevant variables

Abstract. This study provides comparisons of aerosol representation methods incorporated into a regional-scale nonhydrostatic meteorology–chemistry model (NHM-Chem). Three options for aerosol representations are currently available: the five-category non-equilibrium (Aitken, soot-free accumulation, soot-containing accumulation, dust, and sea salt), three-category non-equilibrium (Aitken, accumulation, and coarse), and bulk equilibrium (submicron, dust, and sea salt) methods. The three-category method is widely used in three-dimensional air quality models. The five-category method, the standard method of NHM-Chem, is an extensional development of the three-category method and provides improved predictions of variables relating to aerosol–cloud–radiation interaction processes by implementing separate treatments of light absorber and ice nuclei particles, namely, soot and dust, from the accumulation- and coarse-mode categories (implementation of aerosol feedback processes to NHM-Chem is still ongoing, though). The bulk equilibrium method was developed for operational air quality forecasting with simple aerosol dynamics representations. The total CPU times of the five-category and three-category methods were 91 % and 44 % greater than that of the bulk method, respectively. The bulk equilibrium method was shown to be eligible for operational forecast purposes, namely, the surface mass concentrations of air pollutants such as O3, mineral dust, and PM2.5. The simulated surface concentrations and depositions of bulk chemical species of the three-category method were not significantly different from those of the five-category method. However, the internal mixture assumption of soot/soot-free and dust/sea salt particles in the three-category method resulted in significant differences in the size distribution and hygroscopicity of the particles. The unrealistic dust/sea salt complete mixture of the three-category method induced significant errors in the prediction of the mineral dust-containing cloud condensation nuclei (CCN), which alters heterogeneous ice nucleation in cold rain processes. The overestimation of soot hygroscopicity by the three-category method induced errors in the BC-containing CCN, BC deposition, and light-absorbing aerosol optical thickness (AAOT). Nevertheless, the difference in AAOT was less pronounced with the three-category method because the overestimation of the absorption enhancement was compensated by the overestimation of hygroscopic growth and the consequent loss due to in-cloud scavenging. In terms of total properties, such as aerosol optical thickness (AOT) and CCN, the results of the three-category method were acceptable.

Wave propagation characteristics and absorbed energy capability of the electrically doubly curved system reinforced by nanocomposite on viscoelastic substrate

In the current analysis, an attempt is made to extend a two-dimensional model for absorbed energy capability, and wave dispersion information of the functionally graded graphene nanoplatelets reinforced composite (FG-GPLRC) doubly curved panel coupled with a piezoelectric patch. The material properties of GPLRC layer are modeled by considering viscoelastic relations between stress and strain as well as Halpin-Tsai, and the role of mixture assumptions. FSDT and Hamilton’s principle are taken into consideration for the exact derivation of the general governing equations and boundary conditions of the FG-GPLRC panel coupled with a piezoelectric patch. For developing a precise solution approach, the analytical solution procedure is eventually used. The results demonstrate that viscoelastic parameter, wave number, applied voltage, and thickness of the piezoelectric patch have an important role in the absorbed energy capability, and wave dispersion in the FG-GPLRC panel coupled with a piezoelectric patch. The golden and fundamental result of this research is that, when the applied voltage to the piezoelectric patch increases, the energy absorption by the system decreases. Also, at the higher value of the viscoelastic factor, there is not any effect from applied voltage on the phase velocity of the system. For the design and application of the current research, some inspiration and guidance are provided by theory and simulation results.

Cavitation Model Calibration Using Machine Learning Assisted Workflow

Conventional cavitation assessment methodology in industrial and scientific applications generally depends on cavitation models utilizing homogeneous mixture assumption. These models have been extensively assessed, modified and expanded to account for deficiencies of their predecessors. Unfortunately, none of the proposed models can be classified as the universal solution for all engineering applications, with usage mainly directed by experience or general availability of the models. In this study we propose a workflow through which the empirical constants governing the phase change of the Kunz mixture cavitation model can be calibrated for a given application or a series of problems, with machine learning as a tool for parameter estimation. The proposed approach was validated on a three-dimensional propeller test case with results in excellent agreement for the case in question. Results for thrust and torque were within 2% with cavity extents differing by up to 20%. This is a significant improvement when compared to previously proposed parameters. Despite the lack of generalization due to the limited nature of the dataset on which the model was trained, the proposed parameters entail acceptable results for similar cases as well. The overall methodology is applicable to other problems as well and should lead to more accurate cavitation predictions.

Gaussian Mixture Variational Autoencoder for Semi-Supervised Topic Modeling

Topic models are widely explored for summarizing a corpus of documents. Recent advances in Variational AutoEncoder (VAE) have enabled the development of black-box inference methods for topic modeling in order to alleviate the drawbacks of classical statistical inference. Most existing VAE based approaches assume a unimodal Gaussian distribution for the approximate posterior of latent variables, which limits the flexibility in encoding the latent space. In addition, the unsupervised architecture hinders the incorporation of extra label information, which is ubiquitous in many applications. In this paper, we propose a semi-supervised topic model under the VAE framework. We assume that a document is modeled as a mixture of classes, and a class is modeled as a mixture of latent topics. A multimodal Gaussian mixture model is adopted for latent space. The parameters of the components and the mixing weights are encoded separately. These weights, together with partially labeled data, also contribute to the training of a classifier. The objective is derived under the Gaussian mixture assumption and the semi-supervised VAE framework. Modules of the proposed framework are appropriately designated. Experiments performed on three benchmark datasets demonstrate the effectiveness of our method, comparing to several competitive baselines.

Extension of unsaturated soil mechanics and its applications

Although the soil, water and air coupling theory has been deductively derived from the three-phase mixture theory, assumptions and interpretations inherent in soil mechanics are also conveniently introduced in this theory. Mechanical properties of unsaturated soils are phenomenologically integrated into the constitutive equation for a deformation problem, with effective stress expressed as a combination of partial stresses acting on each phase of the mixture. The governing equations of two seepage problems describing the movements of pore water and pore air are formulated by a priori introduction of Darcy’s law. Consequently, the coupling theory consists of a deformation problem and two seepage problems, in which the soil-water retention characteristics play the role of a mediator connecting these problems. If the theoretical structure is clarified in this way, an extension of this theory is easily made. In this paper, the extension of the theory to each of four examples and their performance is demonstrated. The features of settlement caused by absorption of soil water due to vegetation; dissolution, advection and diffusion of substances in groundwater; desaturation and state change due to vaporisation of dissolved gas from pore water; and the liquefaction potential of unsaturated soil are presented.

Fick Diffusion Coefficients of the Gaseous CH4–CO2System from Molecular Dynamics Simulations Using TraPPE Force Fields at 101.325, 506.625, 1013.25, 2533.12, and 5066.25 kPa

Gaseous Fick diffusion coefficients are calculated for the CH4–CO2 system using molecular dynamics. CH4 was modeled using the united-atom transferable potentials for phase equilibria (TraPPE) force field developed by Martin and Siepmann [J. Phys. Chem B. 1998, 102, 2569], and CO2 was modeled using the rigid TraPPE force field developed by Potoff and Siepmann [AIChE J. 2001 47, 1676]. They can adequately predict the compressibility factor of the CH4–CO2 system over a substantial temperature, pressure, and composition range. However, deviations from experimental values are observed at conditions for which the ideal gas mixture assumption is not valid. It is shown that reasonable calculations of the Fick diffusion coefficient are obtained when compared to experimental data, and a correlation is found in the literature at conditions for which the ideal gas mixture behavior is observed. Calculations are also performed where the mixture does not behave as an ideal gas and are compared to calculations from the aforementioned correlation. The methods yield different results, however the lack of experimental data at these conditions does not allow one to say which are more accurate.

Pore-scale study of reactive transport processes in catalyst layer agglomerates of proton exchange membrane fuel cells

Porous structures of agglomerates in cathode catalyst layers (CLs) of proton exchange membrane fuel cells are reconstructed, in which all the four phases are resolved including Platinum, carbon, ionomer and pore. A pore-scale reactive transport model based on the lattice Boltzmann method is developed, in which oxygen dissolution reaction at pore-ionomer interface, oxygen diffusion inside ionomer, and electrochemical reaction at ionomer-Pt interface are considered. Emphasis is put on structural parameters, especially Pt/C mass ratio, on the reactive transport process and the volumetric reaction rate (or current density). Pore-scale results show that while under high Pt loading oxygen is depleted quite close to the surface of the spherical agglomerate, it has to penetrate deep into the porous agglomerate before it is completely consumed under low Pt loading which is not captured by classical agglomerate model based on homogeneous mixture assumption. Pore-scale results also found that effects of transport inside the agglomerate decreases as reaction rate, porosity or ionomer thickness increases. Finally, local transport resistance inside the agglomerate is evaluated, and it increases as the agglomerate size increases or the dissolution reaction rate decreases.

Numerical estimation of air core length in two-phase free surface vortex

ABSTRACTThe free-surface vortex is simulated with the homogeneous mixture approach. In order to define suitable boundary conditions in the two-phase flow field, a numerical strategy is proposed on the air mass conservation in a recirculating flow system. The numerical approach is verified from an experiment. Numerical results agreed well with the experiment not only in the vortex circulation but also in the axial velocity gradient. On the homogeneous mixture assumption, the compressibility corrections for the turbulence modelling had almost no effect on the result in this case study. In order to estimate the continuous air–core length, the visible air–core interface was assumed to be characterized by the constant void fraction. With validated numerical results, vortex air core was visualized by the air volume fraction, based on the air–core length in not only the experiment but also the analytical model in the applicable range.

Impact of urban aerosol properties on cloud condensation nuclei (CCN) activity during the KORUS-AQ field campaign

Ground measurements of physical, chemical and hygroscopic properties of aerosols were made at the Olympic Park, Seoul, as part of the KORea-United States Air Quality study (KORUS-AQ) campaign in May–June 2016. The average number concentrations of aerosols larger than 10 nm in diameter and cloud condensation nuclei (CCN) at 0.6% supersaturation (S) were 10800 cm−3 and 3400 cm−3, respectively. The average geometric mean diameter (Dg) was 44 nm, and size-resolved aerosol hygroscopicity (κ) from HTDMA ranged from 0.11 to 0.24 for particle diameters in the range of 30–150 nm. Aerosols were classified into three types based on mixing state and hygroscopic growth factor (GF): Type 1 (externally mixed aerosol), Type 2 (Internally mixed and growth aerosol) and Type 3 (internally mixed and non-growth aerosol). These three aerosol types showed distinct diurnal patterns. The difference in physical and chemical properties of aerosols for different air mass sources crucially impacted aerosol hygroscopicity. Using the external mixture assumption with measured hygroscopicity data improved the results of CCN prediction compared to those from the simple internal mixture assumption because externally mixed aerosols comprised a significant portion of aerosols in this urban area. Moreover, the simple assumption of aerosol size distribution with a fixed chemical composition sufficiently explained more than 50 percent of the variation of CCN number concentrations, although the information of chemical composition was still meaningful. Overall, the measured data showed consistency with Megacity Air Pollution Studies (MAPS-Seoul) campaign held during May–June 2015, implying that these results may represent urban aerosols in spring/summer in the Korean Peninsula.