Modeling Welding by Surface Heating

1992 ◽  
Vol 114 (4) ◽  
pp. 439-449 ◽  
Author(s):  
I. C. Sheng ◽  
Y. Chen
Keyword(s):  
Energy Equation ◽  
Solid Phase ◽  
Equations Of Motion ◽  
Fluid Phase ◽  
Equation Of Motion ◽  
Avrami Equation ◽  
Moving Heat Source ◽  
Stress Evolution ◽  
Fluid Mixture ◽  
Traction Boundary Conditions

A mathematical model has been developed in describing the temperature distribution, the flow of the molten fluid and the stress field in the solid during welding. In modeling the properties of the material during welding, the solid phase is assumed to behave as a thermoviscoplastic solid obeying Bodner-Partom/Walker type constitutive equation, whereas the fluid phase as a thermoviscous incompressible fluid. Three regions exist: pure solid, pure fluid, and the transition (solid-fluid mixture). In the formulation of the boundary value problem, the energy equation is coupled to the equation of motion through the terms of mechanical work and the latent heat of the phases, whereas the equations of motion of the solid and the fluid are decoupled. Appropriate thermal and traction boundary conditions are detailed in the text. Phase transformation activities during cooling are monitored by CCT diagram and Avrami equation. An arbitrary Lagrangian and Eulerian method is used to accommodate the kinematic description of both the solid and the fluid phases. A representative plane perpendicular to the moving heat source is analyzed. Results of sample calculations are presented to show the temperature and the stress evolution in time. Residual stress and microstructure patterns are presented.

scholarly journals Stellar corona models

1979 ◽  
Vol 83 ◽  
pp. 241-242
Author(s):  
A. G. Hearn ◽  
I. M. Vardavas
Keyword(s):  
Energy Balance ◽  
Continuity Equation ◽  
Energy Equation ◽  
Equations Of Motion ◽  
Weak Shock ◽  
Equation Of Motion ◽  
Hot Stars ◽  
Coupled Equations ◽  
Radiation Losses ◽  
Hot Corona

A new method of calculating models for stellar coronae is being developed with the aim of providing models of coronae around hot stars capable of explaining the observed mass loss as a stellar wind from a hot corona. The method gives a stationary solution to the coupled equations of motion, continuity and energy balance. The equation of motion contains only the gradient of the gas pressure and the acceleration due to gravity. Radiation pressure is not yet included. The continuity equation assumes spherical symmetry. The energy equation includes heating by weak shock waves, heating by the absorption of photospheric radiation through continuous opacity, radiation losses, heating or cooling by conductivity and the effect on the energy balance of the velocity of the expanding atmosphere. The model is assumed to be optically thin. The velocity distribution is calculated from the solution going through the critical point.

Equations of Motion of Two-Phase Variable Mass Systems With Solid Base

1994 ◽  
Vol 61 (4) ◽  
pp. 855-860 ◽  
Author(s):  
F. O. Eke ◽  
Song-Min Wang
Keyword(s):  
Solid Phase ◽  
Equations Of Motion ◽  
Variable Mass ◽  
Fluid Phase ◽  
Solid Base ◽  
Phase Variable ◽  
Dynamical Equations ◽  
Two Phase ◽  
Attitude Stability ◽  
Variable Mass Systems

This paper develops dynamical equations for variable mass systems that can be viewed, at any given instant, as comprising a solid phase and a fluid phase. The equations of translational and rotational motion are presented, and several versions of each are given. It is shown that some versions have major advantages over others because they involve parameters that are relatively easy to estimate in practical problems, and make close-form solutions possible without the usual penalty of drastic simplifying assumptions. A simple rocket example is presented, and shows that instability cannot be ruled out for such systems. It is shown that system and combustion chamber geometry play a crucial role in the attitude stability of such systems.

scholarly journals CFD-based numerical simulation of cyclone separator for separating stigmas from petals of saffron

2020 ◽  
Author(s):  
Javad Nemati ◽  
Babak Beheshti ◽  
Ali Mohammad Borghei
Keyword(s):  
Separation Efficiency ◽  
Solid Phase ◽  
Equations Of Motion ◽  
Fluid Phase ◽  
Reynolds Stress Model ◽  
Continuous Phase ◽  
Solid Particles ◽  
Inlet Section ◽  
Ansys Fluent ◽  
Discrete Phase

This study numerically modeled the flow of a fluid (air) and solid particles (saffron flower) inside a cyclone using the finite volume method (FVM) in ANSYS Fluent. The continuous phase was simulated under steady state conditions, as the initial condition, using the Reynolds Stress Model (RSM) for turbulence at three constant inlet air velocities of 1.5 m/s, 2.5 m/s, and 3.5 m/s over the inlet section. One-way coupling was assumed to govern all numerical analyses. The fluid phase and particles were treated as the continuous medium (within a Eulerian framework) and discrete phase (within a Lagrangian framework), respectively. The equations governing the gas phase included the compressible Navier–Stokes and the conservation of mass. The discrete phase equations included the equations of motion for three different particles including petals, stigmas, and anthers. According to the numerical results, the cyclone separation efficiency was calculated, and the static pressure and velocity contours were plotted. The results showed the capability of the CFD-based simulation for an accurate demonstration of the behavior of the fluid–solid phase. Accordingly, it can be used to predict the efficiency of stigma separation from petals of saffron using airflow in the cyclone. According to the results, the highest cyclonic separation efficiency of 89% was achieved at an inlet air velocity of 3.5 m/s, which was very close to the experimental data.

A Poroelastic-Viscoelastic Limit for Modeling Brain Biomechanics

2015 ◽  
Vol 1753 ◽  
Author(s):  
Md. Mehedi Hasan ◽  
Corina S. Drapaca
Keyword(s):  
Brain Tissue ◽  
Solid Phase ◽  
Soil Mechanics ◽  
Equations Of Motion ◽  
Elastic Solid ◽  
Two Phase ◽  
Fluid Mixture ◽  
Brain Responses ◽  
Brain Biomechanics ◽  
The Central Nervous System

ABSTRACTThe brain, a mixture of neural and glia cells, vasculature, and cerebrospinal fluid (CSF), is one of the most complex organs in the human body. To understand brain responses to traumatic injuries and diseases of the central nervous system it is necessary to develop accurate mathematical models and corresponding computer simulations which can predict brain biomechanics and help design better diagnostic and therapeutic protocols. So far brain tissue has been modeled as either a poroelastic mixture saturated by CSF or as a (visco)-elastic solid. However, it is not obvious which model is more appropriate when investigating brain mechanics under certain physiological and pathological conditions. In this paper we study brain’s mechanics by using a Kelvin-Voight (KV) model for a one-phase viscoelastic solid and a Kelvin-Voight-Maxwell-Biot (KVMB) model for a two-phase (solid and fluid) mixture, and explore the limit between these two models. To account for brain’s evolving microstructure, we replace in the equations of motion the classic integer order time derivatives by Caputo fractional order derivatives and thus introduce corresponding fractional KV and KVMB models. As in soil mechanics we use the displacements of the solid phase in the classic (fractional) KVMB model and respectively of the classic (fractional) KV model to define a poroelastic-viscoelastic limit. Our results show that when the CSF and brain tissue in the classic (fractional) KVMB model have similar speeds, then the model is indistinguishable from its equivalent classic (fractional) KV model.

scholarly journals Pole-skipping and hydrodynamic analysis in Lifshitz, AdS2 and Rindler geometries

2021 ◽  
Vol 2021 (6) ◽  
Author(s):  
Haiming Yuan ◽  
Xian-Hui Ge
Keyword(s):  
Boundary Condition ◽  
Green’S Function ◽  
Green's Function ◽  
Equations Of Motion ◽  
Equation Of Motion ◽  
Boundary Theory ◽  
Hydrodynamic Analysis ◽  
Dimensionless Variables ◽  
Pass Through ◽  
Special Points

Abstract The “pole-skipping” phenomenon reflects that the retarded Green’s function is not unique at a pole-skipping point in momentum space (ω, k). We explore the universality of pole-skipping in different geometries. In holography, near horizon analysis of the bulk equation of motion is a more straightforward way to derive a pole-skipping point. We use this method in Lifshitz, AdS2 and Rindler geometries. We also study the complex hydrodynamic analyses and find that the dispersion relations in terms of dimensionless variables $$ \frac{\omega }{2\pi T} $$ ω 2 πT and $$ \frac{\left|k\right|}{2\pi T} $$ k 2 πT pass through pole-skipping points $$ \left(\frac{\omega_n}{2\pi T},\frac{\left|{k}_n\right|}{2\pi T}\right) $$ ω n 2 πT k n 2 πT at small ω and k in the Lifshitz background. We verify that the position of the pole-skipping points does not depend on the standard quantization or alternative quantization of the boundary theory in AdS2× ℝd−1 geometry. In the Rindler geometry, we cannot find the corresponding Green’s function to calculate pole-skipping points because it is difficult to impose the boundary condition. However, we can still obtain “special points” near the horizon where bulk equations of motion have two incoming solutions. These “special points” correspond to the nonuniqueness of the Green’s function in physical meaning from the perspective of holography.

Kinematic and Dynamic Parameters of a Liquid-Solid Pipe Flow Using DPIV∕Accelerometry

2007 ◽  
Vol 129 (11) ◽  
pp. 1415-1421 ◽  
Author(s):  
Joseph Borowsky ◽  
Timothy Wei
Keyword(s):  
Pipe Flow ◽  
Solid Phase ◽  
Fluid Phase ◽  
Central Moment ◽  
Steady Flows ◽  
Dynamic Parameters ◽  
Two Phase ◽  
Turbulence Structures ◽  
Two Phases ◽  
Flat Profile

An experimental investigation of a two-phase pipe flow was undertaken to study kinematic and dynamic parameters of the fluid and solid phases. To accomplish this, a two-color digital particle image velocimetry and accelerometry (DPIV∕DPIA) methodology was used to measure velocity and acceleration fields of the fluid phase and solid phase simultaneously. The simultaneous, two-color DPIV∕DPIA measurements provided information on the changing characteristics of two-phase flow kinematic and dynamic quantities. Analysis of kinematic terms indicated that turbulence was suppressed due to the presence of the solid phase. Dynamic considerations focused on the second and third central moments of temporal acceleration for both phases. For the condition studied, the distribution across the tube of the second central moment of acceleration indicated a higher value for the solid phase than the fluid phase; both phases had increased values near the wall. The third central moment statistic of acceleration showed a variation between the two phases with the fluid phase having an oscillatory-type profile across the tube and the solid phase having a fairly flat profile. The differences in second and third central moment profiles between the two phases are attributed to the inertia of each particle type and its response to turbulence structures. Analysis of acceleration statistics provides another approach to characterize flow fields and gives some insight into the flow structures, even for steady flows.

scholarly journals Surface Wave Speed of Functionally Graded Magneto-Electro-Elastic Materials with Initial Stresses

2014 ◽  
Vol 44 (3) ◽  
pp. 49-64 ◽  
Author(s):  
Li Li ◽  
P. J. Wei
Keyword(s):  
Surface Wave ◽  
Boundary Conditions ◽  
Elastic Material ◽  
Short Circuit ◽  
Equations Of Motion ◽  
Open Circuit ◽  
Functionally Graded ◽  
Initial Stresses ◽  
Shear Surface ◽  
Traction Boundary Conditions

Abstract The shear surface wave at the free traction surface of half- infinite functionally graded magneto-electro-elastic material with initial stress is investigated. The material parameters are assumed to vary ex- ponentially along the thickness direction, only. The velocity equations of shear surface wave are derived on the electrically or magnetically open circuit and short circuit boundary conditions, based on the equations of motion of the graded magneto-electro-elastic material with the initial stresses and the free traction boundary conditions. The dispersive curves are obtained numerically and the influences of the initial stresses and the material gradient index on the dispersive curves are discussed. The investigation provides a basis for the development of new functionally graded magneto-electro-elastic surface wave devices.

scholarly journals Conducting dusty fluid flow through a constriction in a porous medium

2016 ◽  
Vol 5 (1) ◽  
pp. 29
Author(s):  
Madhura K R ◽  
Uma M S
Keyword(s):  
Porous Medium ◽  
Hartmann Number ◽  
Equations Of Motion ◽  
Fluid Phase ◽  
Dust Particles ◽  
Governing Equations ◽  
Electrically Conducting ◽  
Electrically Conducting Fluid ◽  
Flow Through ◽  
Constricted Channel

<p><span lang="EN-IN">The flow of an unsteady incompressible electrically conducting fluid with uniform distribution of dust particles in a constricted channel has been studied. The medium is assumed to be porous in nature. The governing equations of motion are treated analytically and the expressions are obtained by using variable separable and Laplace transform techniques. The influence of the dust particles on the velocity distributions of the fluid are investigated for various cases and the results are illustrated by varying parameters like Hartmann number, deposition thickness on the walls of the cylinder and the permeability of the porous medium on the velocity of dust and fluid phase.</span></p>

Dynamic Characteristics of a Hydrostatic Gas Bearing Driven by Oscillating Exhaust Pressure

1984 ◽  
Vol 106 (4) ◽  
pp. 477-483 ◽  
Author(s):  
C. B. Watkins ◽  
H. D. Branch ◽  
I. E. Eronini
Keyword(s):  
Reynolds Equation ◽  
Numerical Solutions ◽  
Equations Of Motion ◽  
Equation Of Motion ◽  
Source Model ◽  
Regular Perturbation ◽  
Response Characteristics ◽  
Finite Difference Approximations ◽  
Bode Plots ◽  
Gas Bearing

Vibration of a statically loaded, inherently compensated hydrostatic journal bearing due to oscillating exhaust pressure is investigated. Both angular and radial vibration modes are analyzed. The time-dependent Reynolds equation governing the pressure distribution between the oscillating journal and sleeve is solved together with the journal equation of motion to obtain the response characteristics of the bearing. The Reynolds equation and the equation of motion are simplified by applying regular perturbation theory for small displacements. The numerical solutions of the perturbation equations are obtained by discretizing the pressure field using finite-difference approximations with a discrete, nonuniform line-source model which excludes effects due to feeding hole volume. An iterative scheme is used to simultaneously satisfy the equations of motion for the journal. The results presented include Bode plots of bearing-oscillation gain and phase for a particular bearing configuration for various combinations of parameters over a range of frequencies, including the resonant frequency.

scholarly journals Determination of Phase-Eigenvalues by Rational Factorization and Enhanced Simulation of Two-Phase Mass Flow

2019 ◽  
Vol 2 (2) ◽  
pp. 61-77
Author(s):  
Puskar R. Pokhrel ◽  
Bhadra Man Tuladhar
Keyword(s):  
Fluid Dynamics ◽  
Debris Flows ◽  
Lateral Pressure ◽  
Solid Phase ◽  
Fluid Phase ◽  
Factorization Method ◽  
Phase Interaction ◽  
Two Phase ◽  
Simulation Results

In this paper, we present simple and exact eigenvalues for both the solid- and fluid-phases of the real two-phase general model developed by Pudasaini (2012); we call these phase-eigenvalues, the solid- phase-eigenvalues and the fluid-phase-eigenvalues. Results are compared by applying the derived phase- eigenvalues that incorporate the phase-interactions in the two-phase debris movements against the simple and classical solid and fluid eigenvalues without any phase interaction. We have constructed several different set of eigenvalues including the coupled phase eigenvalues by using rational factorization method. At first, we consider for general debris height; factorizing the solid and fluid lateral pressure contributions by considering the negligible pressure gradient; negligible solid lateral pressure; negligible fluid lateral pressure; negligible solid and fluid lateral pressure. Secondly, for a thin debris ow height, we also construct the fourth set of eigenvalues in three different cases. These phase-eigenvalues incorporate strong interaction between the solid and fluid dynamics. The simulation results are produced by taking all these different sets of coupled phase-eigenvalues and are compared with the classical uncoupled set of solid and fluid eigenvalues. The results indicate the importance of phase-eigenvalues and supports for a complete description of the phase- eigenvalues for the enhanced description of real two-phase debris flows and landslide motions.

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