scholarly journals A Conservative Macroscopic Model for Binary-mixture Fluidized Beds

2021 ◽  
Author(s):  
Mohamed Sobhi Alagha ◽  
Pal Szentannai
Keyword(s):  
Binary Mixture ◽  
Fluidized Beds ◽  
Vertical Mixing ◽  
Computational Cost ◽  
Mass Conservation ◽  
Macroscopic Model ◽  
Two Phase ◽  
Phase Theory ◽  
Macroscopic Modeling ◽  
Macroscopic Models

Two approaches are commonly used for modeling the vertical mixing of binary-mixture fluidized beds, Computational Fluid Dynamics (CFD) and macroscopic modeling. A common realization of the latter one is the Gibiralo–Rowe (G-R) model, which uses the Two-Phase Theory. This macroscopic model obviously overperforms CFDs regarding computational cost; however, determining its coefficients is a still challenging issue. Although several methods were published for solving this, the general problem with most of them remains their neglecting the conservation of mass. In the present new procedure, the mass conservation is applied to correct the values of the G-R model coefficients estimated from known equations. The present model was validated on a wide variety of fluidized bed systems. The results show that this conservative and macroscopic model gives more accurate predictions than the recently published other macroscopic models, and this one is, in general, better than the CFD model from the perspective of prediction accuracy as well.

Macroscopic models for melting derived from averaging microscopic Stefan problems I: Simple geometries with kinetic undercooling or surface tension

2000 ◽  
Vol 11 (2) ◽  
pp. 153-169 ◽  
Author(s):  
A. A. LACEY ◽  
L. A. HERRAIZ
Keyword(s):  
Free Boundary ◽  
Multiple Scales ◽  
Two Dimensions ◽  
Macroscopic Model ◽  
Mushy Region ◽  
Free Boundaries ◽  
Two Phase ◽  
Macroscopic Models ◽  
Stefan Problems ◽  
Kinetic Undercooling

A mushy region is assumed to consist of a fine mixture of two distinct phases separated by free boundaries. For simplicity, the fine structure is here taken to be periodic, first in one dimension, and then a lattice of squares in two dimensions. A method of multiple scales is employed, with a classical free-boundary problem being used to model the evolution of the two-phase microstructure. Then a macroscopic model for the mush is obtained by an averaging procedure. The free-boundary temperature is taken to vary according to Gibbs–Thomson and/or kinetic-undercooling effects.

scholarly journals Analysis and Enhancements of a Prolific Macroscopic Model of Epilepsy

Scientifica ◽  
2016 ◽  
Vol 2016 ◽  
pp. 1-10
Author(s):  
Christopher Fietkiewicz ◽  
Kenneth A. Loparo
Keyword(s):  
Dynamical Systems ◽  
Direct Current ◽  
Systems Analysis ◽  
Reduction Method ◽  
Model Specification ◽  
Macroscopic Model ◽  
Macroscopic Modeling ◽  
Macroscopic Models ◽  
Dynamical Systems Analysis ◽  
Models Of Epilepsy

Macroscopic models of epilepsy can deliver surprisingly realistic EEG simulations. In the present study, a prolific series of models is evaluated with regard to theoretical and computational concerns, and enhancements are developed. Specifically, we analyze three aspects of the models: (1) Using dynamical systems analysis, we demonstrate and explain the presence of direct current potentials in the simulated EEG that were previously undocumented. (2) We explain how the system was not ideally formulated for numerical integration of stochastic differential equations. A reformulated system is developed to support proper methodology. (3) We explain an unreported contradiction in the published model specification regarding the use of a mathematical reduction method. We then use the method to reduce the number of equations and further improve the computational efficiency. The intent of our critique is to enhance the evolution of macroscopic modeling of epilepsy and assist others who wish to explore this exciting class of models further.

Simulation of Two Phase Flow Dynamics in Flexible Riser Exit Geometries for Oil and Gas Applications

2018 ◽  
Vol 39 ◽  
pp. 1-13
Author(s):  
Ikpe E. Aniekan ◽  
Owunna Ikechukwu ◽  
Satope Paul
Keyword(s):  
Oil And Gas ◽  
Two Phase Flow ◽  
Flow Analysis ◽  
Computational Cost ◽  
Maximum Velocity ◽  
Oil Well ◽  
Phase Flow ◽  
Two Phase ◽  
The Third ◽  
Riser Pipe

Four different riser pipe exit configurations were modelled and the flow across them analysed using STAR CCM+ CFD codes. The analysis was limited to exit configurations because of the length to diameter ratio of riser pipes and the limitations of CFD codes available. Two phase flow analysis of the flow through each of the exit configurations was attempted. The various parameters required for detailed study of the flow were computed. The maximum velocity within the pipe in a two phase flow were determined to 3.42 m/s for an 8 (eight) inch riser pipe. After thorough analysis of the two phase flow regime in each of the individual exit configurations, the third and the fourth exit configurations were seen to have flow properties that ensures easy flow within the production system as well as ensure lower computational cost. Convergence (Iterations), total pressure, static pressure, velocity and pressure drop were used as criteria matrix for selecting ideal riser exit geometry, and the third exit geometry was adjudged the ideal exit geometry of all the geometries. The flow in the third riser exit configuration was modelled as a two phase flow. From the results of the two phase flow analysis, it was concluded that the third riser configuration be used in industrial applications to ensure free flow of crude oil and gas from the oil well during oil production.

scholarly journals Investigation of representing hysteresis in macroscopic models of two-phase flow in porous media using intermediate scale experimental data

2017 ◽  
Vol 53 (1) ◽  
pp. 199-221 ◽  
Author(s):  
Abdullah Cihan ◽  
Jens Birkholzer ◽  
Luca Trevisan ◽  
Ana Gonzalez-Nicolas ◽  
Tissa Illangasekare
Keyword(s):  
Experimental Data ◽  
Porous Media ◽  
Two Phase Flow ◽  
Flow In Porous Media ◽  
Phase Flow ◽  
Two Phase ◽  
Intermediate Scale ◽  
Macroscopic Models

A simplified two-phase macroscopic model for reinforced soils

2010 ◽  
Vol 28 (1) ◽  
pp. 85-92 ◽  
Author(s):  
Ehsan Seyedi Hosseininia ◽  
Orang Farzaneh
Keyword(s):  
Macroscopic Model ◽  
Two Phase ◽  
Reinforced Soils

scholarly journals Patch-Recovery Filters for Curvature in Discontinuous Galerkin-Based Level-Set Methods

2016 ◽  
Vol 19 (2) ◽  
pp. 329-353 ◽  
Author(s):  
Florian Kummer ◽  
Tim Warburton
Keyword(s):  
Discontinuous Galerkin ◽  
Level Set ◽  
Numerical Study ◽  
Level Set Methods ◽  
Computational Cost ◽  
Pressure Jump ◽  
Two Phase ◽  
Two Fluids ◽  
Whole Process ◽  
Numerical Instabilities

AbstractIn two-phase flow simulations, a difficult issue is usually the treatment of surface tension effects. These cause a pressure jump that is proportional to the curvature of the interface separating the two fluids. Since the evaluation of the curvature incorporates second derivatives, it is prone to numerical instabilities. Within this work, the interface is described by a level-set method based on a discontinuous Galerkin discretization. In order to stabilize the evaluation of the curvature, a patch-recovery operation is employed. There are numerous ways in which this filtering operation can be applied in the whole process of curvature computation. Therefore, an extensive numerical study is performed to identify optimal settings for the patch-recovery operations with respect to computational cost and accuracy.

Highly Efficient and Accurate Gas-Alkane Binary Mixture Interfacial Tension Equations for a Broad Range of Temperatures, Pressures, and Compositions

SPE Journal ◽  
2021 ◽  
pp. 1-19
Author(s):  
Yingnan Wang ◽  
Nadia Shardt ◽  
Janet A. W. Elliott ◽  
Zhehui Jin
Keyword(s):  
Experimental Data ◽  
Binary Mixture ◽  
Interfacial Tension ◽  
Binary Mixtures ◽  
Oil Recovery ◽  
Computational Cost ◽  
Petroleum Engineering ◽  
Pure Species ◽  
Highly Efficient ◽  
Wide Range

Summary Gas-alkane interfacial tension (IFT) is an important parameter in the enhanced oil recovery (EOR) process. Thus, it is imperative to obtain an accurate gas-alkane mixture IFT for both chemical and petroleum engineering applications. Various empirical correlations have been developed in the past several decades. Although these models are often easy to implement, their accuracy is inconsistent over a wide range of temperatures, pressures, and compositions. Although statistical mechanics-based models and molecular simulations can accurately predict gas-alkane IFT, they usually come with an extensive computational cost. The Shardt-Elliott (SE) model is a highly accurate IFT model that for subcritical fluids is analytic in terms of temperature T and composition x. In applications, it is desirable to obtain IFT in terms of temperature T and pressure P, which requires time-consuming flash calculations, and for mixtures that contain a gas component greater than its pure species critical point, additional critical composition calculations are required. In this work, the SE model is combined with a machine learning (ML) approach to obtain highly efficient and highly accurate gas-alkane binary mixture IFT equations directly in terms of temperature, pressure, and alkane molar weights. The SE model is used to build an IFT database (more than 36,000 points) for ML training to obtain IFT equations. The ML-based IFT equations are evaluated in comparison with the available experimental data (888 points) and with the SE model, as well as with the less accurate parachor model. Overall, the ML-based IFT equations show excellent agreement with experimental data for gas-alkane binary mixtures over a wide range of T and P, and they outperform the widely used parachor model. The developed highly efficient and highly accurate IFT functions can serve as a basis for modeling gas-alkane binary mixtures for a broad range of T, P, and x.

Convolutional Neural Networks for the Localization of Plastic Velocity Gradient Tensor in Polycrystalline Microstructures

2021 ◽  
pp. 1-41
Author(s):  
David Montes de Oca Zapiain ◽  
Apaar Shanker ◽  
Surya Kalidindi
Keyword(s):  
Neural Networks ◽  
Convolutional Neural Networks ◽  
Velocity Gradient ◽  
Optimization Problems ◽  
Computational Cost ◽  
Two Phase ◽  
Design And Optimization ◽  
Gradient Fields ◽  
Generalized Spherical Harmonics ◽  
New Research

Abstract Recent work has demonstrated the potential of convolutional neural networks (CNNs) in producing low-computational cost surrogate models for the localization of mechanical fields in two-phase microstructures. The extension of the same CNNs to polycrystalline microstructures is hindered by the lack of an efficient formalism for the representation of the crystal lattice orientation in the input channels of the CNNs. In this paper, we demonstrate the benefits of using generalized spherical harmonics (GSH) for addressing this challenge. A CNN model was successfully trained to predict the local plastic velocity gradient fields in polycrystalline microstructures subjected to a macroscopically imposed loading condition. Specifically, it is demonstrated that the proposed approach improves significantly the accuracy of the CNN models, when compared with the direct use of Bunge-Euler angles to represent the crystal orientations in the input channels. Since the proposed approach implicitly satisfies the expected crystal symmetries in the specification of the input microstructure to the CNN, it opens new research directions for the adoption of CNNs in addressing a broad range of polycrystalline microstructure design and optimization problems.

scholarly journals The Finite Element Numerical Investigation of Free Surface Newtonian and Non-Newtonian Fluid Flows in the Rectangular Tanks

2020 ◽  
Vol 2020 ◽  
pp. 1-18
Author(s):  
Puyang Gao
Keyword(s):  
Finite Element ◽  
Free Surface ◽  
Level Set ◽  
Newtonian Fluid ◽  
Mass Conservation ◽  
Free Surface Flow ◽  
Surface Flow ◽  
Two Phase ◽  
Navier Stokes Equation ◽  
Correction Technique

In this paper, we develop a new computational framework to investigate the sloshing free surface flow of Newtonian and non-Newtonian fluids in the rectangular tanks. We simulate the flow via a two-phase model and employ the fixed unstructured mesh in the computation to avoid the mesh distortion and reconstruction. As for the solution of Navier–Stokes equation, we utilize the SUPG finite element method based on the splitting scheme. The same order interpolation functions are then used for velocity and pressure. Moreover, the moving interface is captured via the concise level set method. We take advantage of the implicit discontinuous Galerkin method to handle the solution of level set and its reinitialization equations. A mass correction technique is also added to ensure the mass conservation property. The dam break-free surface flow is simulated firstly to demonstrate the validity of our mathematical model. In addition, the sloshing Newtonian fluid in the tank with flat and rough bottoms is considered to illustrate the feasibility and robustness of our computational scheme. Finally, the development of free surface for non-Newtonian fluid is also studied in the two tanks, and the influence of power-law index on the sloshing fluid flow is analyzed.

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