The Representation of Regenerator Fluid Carryover by Bypass Flows

1984 ◽  
Vol 106 (1) ◽  
pp. 216-220 ◽  
Author(s):  
P. J. Banks
Keyword(s):  
Numerical Solutions ◽  
Fluid Flows ◽  
Porous Matrix ◽  
Heat Transfer Process ◽  
The Other ◽  
Sensible Heat ◽  
Governing Equations ◽  
Fluid Stream ◽  
The Matrix ◽  
Two Fluid

A regenerator transfers sensible heat between two fluid streams by means of a porous matrix through which the streams are passed alternately. The fluid contained in the matrix passages is carried over from one fluid stream to the other, and contributes to the heat transfer process. It has been suggested that this contribution may be predicted by treating the fluid carryover as fluid flows bypassing the matrix. The validity of this representation is explained, and its accuracy is explored in a case for which numerical solutions of the governing equations are available. A published analysis of the representation is discussed and completed.

Consequences of viscous anisotropy in a deforming, two-phase aggregate. Part 1. Governing equations and linearized analysis

2013 ◽  
Vol 734 ◽  
pp. 424-455 ◽  
Author(s):  
Yasuko Takei ◽  
Richard F. Katz
Keyword(s):  
Shear Stress ◽  
Numerical Solutions ◽  
Shear Plane ◽  
High Porosity ◽  
Governing Equations ◽  
Two Phase ◽  
The Matrix ◽  
Continuum Scale ◽  
Torsional Flow ◽  
Matrix Shear

AbstractIn partially molten regions of Earth, rock and magma coexist as a two-phase aggregate in which the solid grains of rock form a viscously deformable framework or matrix. Liquid magma resides within the permeable network of pores between grains. Deviatoric stress causes the distribution of contact area between solid grains to become anisotropic; in turn, this causes anisotropy of the matrix viscosity at the continuum scale. In this two-paper set, we predict the consequences of viscous anisotropy for flow of two-phase aggregates in three configurations: simple shear, Poiseuille, and torsional flow. Part 1 presents the governing equations and an analysis of their linearized form. Part 2 (Katz & Takei, J. Fluid Mech., vol. 734, 2013, pp. 456–485) presents numerical solutions of the full, nonlinear model. In our theory, the anisotropic viscosity tensor couples shear and volumetric components of the matrix stress/strain rate. This coupling, acting over a gradient in shear stress, causes segregation of liquid and solid. Liquid typically migrates toward higher shear stress, but under specific conditions, the opposite can occur. Furthermore, it is known that in a two-phase aggregate with a porosity-weakening viscosity, matrix shear causes porosity perturbations to grow into a banded or sheeted structure. We show that viscous anisotropy reduces the angle between these emergent high-porosity features and the shear plane. Laboratory experiments produce similar, high-porosity features. We hypothesize that the low angle of porosity bands in such experiments is the result of viscous anisotropy. We therefore predict that experiments incorporating a gradient in shear stress will develop sample-wide liquid–solid segregation due to viscous anisotropy.

Analysis of Real-Gas and Matrix-Conduction Effects in Cyclic Cryogenic Regenerators

1973 ◽  
Vol 95 (2) ◽  
pp. 199-205 ◽  
Author(s):  
M. F. Modest ◽  
C. L. Tien
Keyword(s):  
Numerical Solutions ◽  
Operating Conditions ◽  
Physical Parameters ◽  
Governing Equations ◽  
Real Gas ◽  
The Matrix ◽  
Compression And Expansion ◽  
Temperature Levels ◽  
The One ◽  
Gas Conduction

The one-dimensional governing equations for the thermal performance of cryogenic regenerators are developed and simplified by neglecting gas conduction and pressure drop along the matrix. The present formulation includes the effects of matrix conduction and real-gas behavior, which can be quite important in actual situations but were neglected in all previous analyses. The time dependence of the governing equations is eliminated by integration over the compression and expansion periods. Numerical solutions of the resulting time-independent equations are presented for various values of physical parameters and temperature levels. Comparison with the corresponding cases neglecting real-gas and matrix-conduction effects demonstrates the significant nature of these effects for many operating conditions.

scholarly journals Electro-Magnetohydrodynamic Two Fluid Flow of Ionized-Gases with Hall and Rotation Effects

2021 ◽  
Vol 26 (4) ◽  
pp. 128-144
Author(s):  
T. Linga Raju
Keyword(s):  
Fluid Flow ◽  
Numerical Solutions ◽  
Hartmann Number ◽  
Transverse Magnetic ◽  
Rotation Parameter ◽  
Physical Parameters ◽  
Governing Equations ◽  
Flow And Heat Transfer ◽  
Hall Parameter ◽  
Two Fluid

Abstract An electro-magnetohydrodynamic (EMHD) two fluid flow and heat transfer of ionized gases through a horizontal channel surrounded by non-conducting plates in a rotating framework with Hall currents is investigated. The Hall effect is considered with an assumption that the gases are completely ionized and the strength of the applied transverse magnetic field is strong. The governing equations are solved analytically for the temperature and velocity distributions in two fluid flow regions. The numerical solutions are demonstrated graphically for various physical parameters such the Hartmann number, Hall parameter, rotation parameter, and so on. It was noticed that an increment is either due to the Hall parameter or the rotation parameter reduces the temperature in the two regions.

Pembobotan Berdasarkan Tingkat Kesamaan Semantik pada Metode Fuzzy Semi-Supervised Co-Clustering untuk Pengelompokkan Dokumen Teks

2014 ◽  
Vol 6 (2) ◽  
pp. 46-51
Author(s):  
Galang Amanda Dwi P. ◽  
Gregorius Edwadr ◽  
Agus Zainal Arifin
Keyword(s):  
Supervised Learning ◽  
Semantic Similarity ◽  
The Other ◽  
Classification Result ◽  
Document Similarity ◽  
The Matrix ◽  
Index Terms ◽  
Membership Value ◽  
Degree Of Similarity

Nowadays, a large number of information can not be reached by the reader because of the misclassification of text-based documents. The misclassified data can also make the readers obtain the wrong information. The method which is proposed by this paper is aiming to classify the documents into the correct group.  Each document will have a membership value in several different classes. The method will be used to find the degree of similarity between the two documents is the semantic similarity. In fact, there is no document that doesn’t have a relationship with the other but their relationship might be close to 0. This method calculates the similarity between two documents by taking into account the level of similarity of words and their synonyms. After all inter-document similarity values obtained, a matrix will be created. The matrix is then used as a semi-supervised factor. The output of this method is the value of the membership of each document, which must be one of the greatest membership value for each document which indicates where the documents are grouped. Classification result computed by the method shows a good value which is 90 %. Index Terms - Fuzzy co-clustering, Heuristic, Semantica Similiarity, Semi-supervised learning.

scholarly journals Numerical Analysis of Viscoelastic Rotating Beam with Variable Fractional Order Model Using Shifted Bernstein–Legendre Polynomial Collocation Algorithm

2021 ◽  
Vol 5 (1) ◽  
pp. 8
Author(s):  
Cundi Han ◽  
Yiming Chen ◽  
Da-Yan Liu ◽  
Driss Boutat
Keyword(s):  
Numerical Analysis ◽  
Fractional Order ◽  
Governing Equation ◽  
Numerical Solutions ◽  
Bernstein Polynomials ◽  
Matrix Product ◽  
Algebraic Equations ◽  
Rotating Beam ◽  
The Matrix ◽  
The Time Domain

This paper applies a numerical method of polynomial function approximation to the numerical analysis of variable fractional order viscoelastic rotating beam. First, the governing equation of the viscoelastic rotating beam is established based on the variable fractional model of the viscoelastic material. Second, shifted Bernstein polynomials and Legendre polynomials are used as basis functions to approximate the governing equation and the original equation is converted to matrix product form. Based on the configuration method, the matrix equation is further transformed into algebraic equations and numerical solutions of the governing equation are obtained directly in the time domain. Finally, the efficiency of the proposed algorithm is proved by analyzing the numerical solutions of the displacement of rotating beam under different loads.

scholarly journals Mathematical study on two-fluid model for flow of K–L fluid in a stenosed artery with porous wall

2021 ◽  
Vol 3 (4) ◽  
Author(s):  
R. Ponalagusamy ◽  
Ramakrishna Manchi
Keyword(s):  
Theoretical Study ◽  
Fluid Model ◽  
Porous Wall ◽  
Governing Equations ◽  
Rate Of Increase ◽  
Special Cases ◽  
Stenosed Artery ◽  
Flow Through ◽  
Two Fluid Model ◽  
Two Fluid

AbstractThe present communication presents a theoretical study of blood flow through a stenotic artery with a porous wall comprising Brinkman and Darcy layers. The governing equations describing the flow subjected to the boundary conditions have been solved analytically under the low Reynolds number and mild stenosis assumptions. Some special cases of the problem are also presented mathematically. The significant effects of the rheology of blood and porous wall of the artery on physiological flow quantities have been investigated. The results reveal that the wall shear stress at the stenotic throat increases dramatically for the thinner porous wall (i.e. smaller values of the Brinkman and Darcy regions) and the rate of increase is found to be 18.46% while it decreases for the thicker porous wall (i.e. higher values of the Brinkman and Darcy regions) and the rate of decrease is found to be 10.21%. Further, the streamline pattern in the stenotic region has been plotted and discussed.

scholarly journals An augmented Lagrangian method for solving total variation (TV)-based image registration model

2020 ◽  
Vol 14 ◽  
pp. 174830262097353
Author(s):  
Noppadol Chumchob ◽  
Ke Chen
Keyword(s):  
Image Registration ◽  
Augmented Lagrangian ◽  
Numerical Solutions ◽  
Augmented Lagrangian Method ◽  
Closed Form Solution ◽  
Numerical Algorithms ◽  
Lagrangian Method ◽  
Form Solution ◽  
The Other ◽  
Other Hand

Variational methods for image registration basically involve a regularizer to ensure that the resulting well-posed problem admits a solution. Different choices of regularizers lead to different deformations. On one hand, the conventional regularizers, such as the elastic, diffusion and curvature regularizers, are able to generate globally smooth deformations and generally useful for many applications. On the other hand, these regularizers become poor in some applications where discontinuities or steep gradients in the deformations are required. As is well-known, the total (TV) variation regularizer is more appropriate to preserve discontinuities of the deformations. However, it is difficult in developing an efficient numerical method to ensure that numerical solutions satisfy this requirement because of the non-differentiability and non-linearity of the TV regularizer. In this work we focus on computational challenges arising in approximately solving TV-based image registration model. Motivated by many efficient numerical algorithms in image restoration, we propose to use augmented Lagrangian method (ALM). At each iteration, the computation of our ALM requires to solve two subproblems. On one hand for the first subproblem, it is impossible to obtain exact solution. On the other hand for the second subproblem, it has a closed-form solution. To this end, we propose an efficient nonlinear multigrid (NMG) method to obtain an approximate solution to the first subproblem. Numerical results on real medical images not only confirm that our proposed ALM is more computationally efficient than some existing methods, but also that the proposed ALM delivers the accurate registration results with the desired property of the constructed deformations in a reasonable number of iterations.

An example of steady laminar flow at large Reynolds number

1960 ◽  
Vol 9 (4) ◽  
pp. 593-602 ◽  
Author(s):  
Iam Proudman
Keyword(s):  
Boundary Layer ◽  
Reynolds Number ◽  
Boundary Layers ◽  
Tangential Velocity ◽  
Fluid Flows ◽  
The Other ◽  
Large Reynolds Number ◽  
Rotational Flows ◽  
Flow Domain ◽  
Source Of Information

The purpose of this note is to describe a particular class of steady fluid flows, for which the techniques of classical hydrodynamics and boundary-layer theory determine uniquely the asymptotic flow for large Reynolds number for each of a continuously varied set of boundary conditions. The flows involve viscous layers in the interior of the flow domain, as well as boundary layers, and the investigation is unusual in that the position and structure of all the viscous layers are determined uniquely. The note is intended to be an illustration of the principles that lead to this determination, not a source of information of practical value.The flows take place in a two-dimensional channel with porous walls through which fluid is uniformly injected or extracted. When fluid is extracted through both walls there are boundary layers on both walls and the flow outside these layers is irrotational. When fluid is extracted through one wall and injected through the other, there is a boundary layer only on the former wall and the inviscid rotational flow outside this layer satisfies the no-slip condition on the other wall. When fluid is injected through both walls there are no boundary layers, but there is a viscous layer in the interior of the channel, across which the second derivative of the tangential velocity is discontinous, and the position of this layer is determined by the requirement that the inviscid rotational flows on either side of it must satisfy the no-slip conditions on the walls.

Thermal Post-Buckling Analysis of Functionally Graded Composite Plates with Nonlinear Aerodynamic Forces

2010 ◽  
Vol 123-125 ◽  
pp. 280-283
Author(s):  
Chang Yull Lee ◽  
Ji Hwan Kim
Keyword(s):  
Material Properties ◽  
Numerical Solutions ◽  
Virtual Work ◽  
Shear Deformation Theory ◽  
Composite Plates ◽  
Buckling Analysis ◽  
Functionally Graded ◽  
Governing Equations ◽  
Functionally Graded Composite ◽  
Post Buckling

The post-buckling of the functionally graded composite plate under thermal environment with aerodynamic loading is studied. The structural model has three layers with ceramic, FGM and metal, respectively. The outer layers of the sandwich plate are different homogeneous and isotropic material properties for ceramic and metal. Whereas the core is FGM layer, material properties vary continuously from one interface to the other in the thickness direction according to a simple power law distribution in terms of the volume fractions. Governing equations are derived by using the principle of virtual work and numerical solutions are solved through a finite element method. The first-order shear deformation theory and von-Karman strain-displacement relations are based to derive governing equations of the plate. Aerodynamic effects are dealt by adopting nonlinear third-order piston theory for structural and aerodynamic nonlinearity. The Newton-Raphson iterative method applied for solving the nonlinear equations of the thermal post-buckling analysis

Thermal Modeling of Unlooped and Looped Pulsating Heat Pipes

2001 ◽  
Vol 123 (6) ◽  
pp. 1159-1172 ◽  
Author(s):  
Mohammad B. Shafii ◽  
Amir Faghri ◽  
Yuwen Zhang
Keyword(s):  
Heat Transfer ◽  
Finite Difference ◽  
Heat Pipes ◽  
Analytical Models ◽  
Charge Ratio ◽  
Sensible Heat ◽  
Governing Equations ◽  
Heating Wall ◽  
Heat Mode ◽  
Explicit Finite Difference

Analytical models for both unlooped and looped Pulsating Heat Pipes (PHPs) with multiple liquid slugs and vapor plugs are presented in this study. The governing equations are solved using an explicit finite difference scheme to predict the behavior of vapor plugs and liquid slugs. The results show that the effect of gravity on the performance of top heat mode unlooped PHP is insignificant. The effects of diameter, charge ratio, and heating wall temperature on the performance of looped and unlooped PHPs are also investigated. The results also show that heat transfer in both looped and unlooped PHPs is due mainly to the exchange of sensible heat.

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