scholarly journals Mathematical Model for Metal Transfer Study in Additive Manufacturing with Electron Beam Oscillation

Crystals ◽  
2021 ◽  
Vol 11 (12) ◽  
pp. 1441
Author(s):  
Alexey Shcherbakov ◽  
Daria Gaponova ◽  
Andrey Sliva ◽  
Alexey Goncharov ◽  
Alexander Gudenko ◽  
...  
Keyword(s):  
Electron Beam ◽  
High Speed ◽  
Metal Transfer ◽  
Continuity Condition ◽  
Finite Difference Approximation ◽  
Navier Stokes ◽  
Difference Approximation ◽  
Deposition Processes ◽  
Spatial Oscillation ◽  
The Individual

A computer model has been developed to investigate the processes of heat and mass transfer under the influence of concentrated energy sources on materials with specified thermophysical characteristics, including temperature-dependent ones. The model is based on the application of the volume of fluid (VOF) method and finite-difference approximation of the Navier–Stokes differential equations formulated for a viscous incompressible medium. The “predictor-corrector” method has been used for the coordinated determination of the pressure field which corresponds to the continuity condition and the velocity field. The modeling technique of the free liquid surface and boundary conditions has been described. The method of calculating surface tension forces and vapor recoil pressure has been presented. The algorithm structure is given, the individual modules of which are currently implemented in the Microsoft Visual Studio environment. The model can be applied for studying the metal transfer during the deposition processes, including the processes with electron beam spatial oscillation. The model was validated by comparing the results of computational experiments and images obtained by a high-speed camera.

Potential Core of a Submerged Laminar Jet

1988 ◽  
Vol 110 (4) ◽  
pp. 392-398 ◽  
Author(s):  
Shiro Akaike ◽  
Mitsumasa Nemoto
Keyword(s):  
Numerical Solution ◽  
Flow Pattern ◽  
Stokes Equations ◽  
Finite Difference Approximation ◽  
Navier Stokes ◽  
Difference Approximation ◽  
Potential Core ◽  
Laminar Jet ◽  
Cone Type ◽  
Developing Region

This study is intended to clarify the flow pattern in the flow developing region of an axisymmetric laminar water jet issuing into the surrounding calm water. The jet, initially having a potential core region of some extent at the nozzle exit, was studied. The numerical solution of the Navier-Stokes equations in the developing region was obtained using a finite-difference approximation. The velocity profile was measured using a miniature cone-type hot probe. Flow visualization by the hydrogen bubble method was also performed. Experiments were carried out for the jet Reynolds number ranging from 100 to 600. The flow pattern in the developing region was made clear. The experimental results were compared with the numerical solution.

SCALING OF FLUID RECOVERY FROM PERCOLATION FRACTALS

Fractals ◽  
1994 ◽  
Vol 02 (02) ◽  
pp. 269-272 ◽  
Author(s):  
IAN D WEDGWOOD ◽  
DONALD M MONRO
Keyword(s):  
Stokes Equations ◽  
Petroleum Reservoirs ◽  
Finite Difference Approximation ◽  
Navier Stokes ◽  
Difference Approximation ◽  
Viscous Effects ◽  
Navier Stokes Equation ◽  
Navier Stokes Equations ◽  
Reservoir Models ◽  
Wide Range

We report on the recovery of fluid driven through percolation lattices across a range of scales using a finite difference approximation to the Navier-Stokes equation. This is important in the study of recovery from petroleum reservoirs, in which flow occurs over a wide range of scales, from the microscopic pores right up to the full reservoir. This variation of scale presents difficulties, since flow at the pore level is subject to predominantly viscous effects, whereas at the larger scales the viscous effects may become negligible in comparison with inertial effects. The Navier-Stokes equations may differ greatly with scale. Theoretical rock structures are created using percolation lattices and the flow properties of identical rock structures are then examined as a function of scale. The resultant recovery rates exhibit similarity across scale which would simplify the study of geological reservoir models.

Determination of Main-Term and Cross-Term Gas Diffusivities in Heavy Oil Systems Considering Local Oil Swelling Effect

2020 ◽  
Vol 143 (2) ◽  
Author(s):  
Hyun Woong Jang ◽  
Daoyong Yang
Keyword(s):  
Liquid Phase ◽  
Heavy Oil ◽  
Molecular Diffusion ◽  
Numerical Solutions ◽  
The Other ◽  
Finite Difference Approximation ◽  
Difference Approximation ◽  
Dissolved Gas ◽  
Cross Term ◽  
The Individual

Abstract To inject gas into a heavy oil reservoir, molecular diffusion of the dissolved gas into heavy oil is one of the crucial mechanisms to lower its viscosity while swelling the diluted oil. Various efforts have been made to predict the diffusivity of such gas dissolved in heavy oil with or without considering the oil swelling. Practically, the oil swelling is always considered in an excessively simplified manner so that such swelling is not able to exhibit its true effect on the estimated diffusivity. In most studies where the oil swelling is considered, the liquid-phase hydrocarbon is assumed to swell equally at every location because the height of liquid-phase in a diffusion vessel is simply extended proportionally to the oil swelling direction. Such a proportional swell is often realized during numerical solutions by uniformly extending the numerical cells, regardless of the amount of dissolved gas contained in each of them. In addition, no studies have been made to examine the contribution of one gas over the other for a gas mixture-liquid system. In this study, a pragmatic approach is proposed to determine the main- and cross-term diffusivities of gas–liquid systems considering local swelling effect. More specifically, diffusivities of CO2 and a CO2–C3H8 mixture in a Lloydminster heavy oil are respectively estimated by implementing the finite difference approximation (FDA) with the face-centered explicit scheme. For the CO2–C3H8 mixture, the individual diffusivity of each gas in the mixture is firstly computed independent of the other gas in the mixture. Then, the cross-term diffusivity is included to verify the effect of the other gas in heavy oil for the diffusion of one gas, while the local oil swelling is implemented during the estimation of the individual gas diffusivities. It is found that the obtained diffusivities of pure CO2 and each individual component of the CO2–C3H8 mixture in the Lloydminster heavy oil are reasonable and accurate to reproduce the measured oil swelling factors obtained from the dynamic volume analysis (DVA) tests.

Centrifugal Effects in Thrust Bearings and Seals Under Laminar Conditions

1981 ◽  
Vol 103 (1) ◽  
pp. 126-136 ◽  
Author(s):  
Oscar Pinkus ◽  
J. W. Lund
Keyword(s):  
High Speed ◽  
Stokes Equations ◽  
Load Capacity ◽  
Finite Difference Methods ◽  
Navier Stokes ◽  
Negative Consequences ◽  
Centrifugal Forces ◽  
Thrust Bearings ◽  
Dominant Component ◽  
The Individual

An analysis is conducted and solutions are provided for the effect of centrifugal forces on the hydrodynamics of high-speed thrust bearings and seals. First, a scrutiny of the individual inertia terms of the Navier-Stokes equations delineates the circumstances under which the centrifugal term (u2/r) becomes the dominant component. A Reynolds equation incorporating centrifugal forces is then derived for finite sectorial configurations operating under incompressible laminar conditions. Thermal effects are included. The equation is solved by finite difference methods. The results show that at the upper limits of laminar operation centrifugal forces reduce considerably the load capacity and alter the pattern of lubricant flow. As a result, at sufficiently high velocities the inflow of lubricant at the inner radius of a sectorial configuration may bring about the scavenging of lubricant from wide portions of the bearing surface, producing a form of thrust bearing cavitation. Design features which would reduce the negative consequences of centrifugal action are outlined, including the introduction of radial tapers.

scholarly journals Numerical Solution of the Navier–Stokes Equations Using Multigrid Methods with HSS-Based and STS-Based Smoothers

Symmetry ◽  
2020 ◽  
Vol 12 (2) ◽  
pp. 233
Author(s):  
Galina Muratova ◽  
Tatiana Martynova ◽  
Evgeniya Andreeva ◽  
Vadim Bavin ◽  
Zeng-Qi Wang
Keyword(s):  
Stokes Equations ◽  
Hermitian Matrix ◽  
Multigrid Methods ◽  
Finite Difference Approximation ◽  
Navier Stokes ◽  
Difference Approximation ◽  
Algebraic Equations ◽  
Navier Stokes Equations ◽  
Linear Algebraic Equations ◽  
Discretized Systems

Multigrid methods (MGMs) are used for discretized systems of partial differential equations (PDEs) which arise from finite difference approximation of the incompressible Navier–Stokes equations. After discretization and linearization of the equations, systems of linear algebraic equations (SLAEs) with a strongly non-Hermitian matrix appear. Hermitian/skew-Hermitian splitting (HSS) and skew-Hermitian triangular splitting (STS) methods are considered as smoothers in the MGM for solving the SLAE. Numerical results for an algebraic multigrid (AMG) method with HSS-based smoothers are presented.

scholarly journals Numerical Simulation of Combustion and Rotor-Stator Interaction in a Turbine Combustor

2003 ◽  
Vol 9 (5) ◽  
pp. 363-374 ◽  
Author(s):  
Dragos D. Isvoranu ◽  
Paul G. A. Cizmas
Keyword(s):  
Numerical Algorithm ◽  
Stokes Equations ◽  
Species Conservation ◽  
Finite Difference Approximation ◽  
Navier Stokes ◽  
Difference Approximation ◽  
Combustion Model ◽  
Combustion Gases ◽  
Fully Implicit ◽  
Correction Technique

This article presents the development of a numerical algorithm for the computation of flow and combustion in a turbine combustor. The flow and combustion are modeled by the Reynolds-averaged Navier-Stokes equations coupled with the species-conservation equations. The chemistry model used herein is a two-step, global, finite-rate combustion model for methane and combustion gases. The governing equations are written in the strong conservation form and solved using a fully implicit, finite-difference approximation. The gas dynamics and chemistry equations are fully decoupled. A correction technique has been developed to enforce the conservation of mass fractions. The numerical algorithm developed herein has been used to investigate the flow and combustion in a one-stage turbine combustor.

Image quality vs data obtainment in biological electron microscopy

1986 ◽  
Vol 44 ◽  
pp. 42-43
Author(s):  
J. E. Johnson
Keyword(s):  
Electron Microscopy ◽  
Endoplasmic Reticulum ◽  
Electron Beam ◽  
Image Quality ◽  
High Speed ◽  
Early Period ◽  
Early Years ◽  
Fluorescent Screen ◽  
Embedding Medium

In the early years of biological electron microscopy, scientists had their hands full attempting to describe the cellular microcosm that was suddenly before them on the fluorescent screen. Mitochondria, Golgi, endoplasmic reticulum, and other myriad organelles were being examined, micrographed, and documented in the literature. A major problem of that early period was the development of methods to cut sections thin enough to study under the electron beam. A microtome designed in 1943 moved the specimen toward a rotary “Cyclone” knife revolving at 12,500 RPM, or 1000 times as fast as an ordinary microtome. It was claimed that no embedding medium was necessary or that soft embedding media could be used. Collecting the sections thus cut sounded a little precarious: “The 0.1 micron sections cut with the high speed knife fly out at a tangent and are dispersed in the air. They may be collected... on... screens held near the knife“.

Formation of Standing Waves in Radial Tires

1984 ◽  
Vol 12 (1) ◽  
pp. 44-63 ◽  
Author(s):  
Y. D. Kwon ◽  
D. C. Prevorsek
Keyword(s):  
High Speed ◽  
Critical Speed ◽  
Unit Length ◽  
Standing Waves ◽  
Rolling Resistance ◽  
Damping Coefficient ◽  
Circular Membrane ◽  
Critical Speeds ◽  
Steel Cord ◽  
The Individual

Abstract Radial tires for automobiles were subjected to high speed rolling under load on a testing wheel to determine the critical speeds at which standing waves started to form. Tires of different makes had significantly different critical speeds. The damping coefficient and mass per unit length of the tire wall were measured and a correlation between these properties and the observed critical speed of standing wave formation was sought through use of a circular membrane model. As expected from the model, desirably high critical speed calls for a high damping coefficient and a low mass per unit length of the tire wall. The damping coefficient is particularly important. Surprisingly, those tire walls that were reinforced with steel cord had higher damping coefficients than did those reinforced with polymeric cord. Although the individual steel filaments are elastic, the interfilament friction is higher in the steel cords than in the polymeric cords. A steel-reinforced tire wall also has a higher density per unit length. The damping coefficient is directly related to the mechanical loss in cyclic deformation and, hence, to the rolling resistance of a tire. The study shows that, in principle, it is more difficult to design a tire that is both fuel-efficient and free from standing waves when steel cord is used than when polymeric cords are used.

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