scholarly journals Self-force via energy–momentum and angular momentum balance equations

2011 ◽  
Vol 52 (1) ◽  
pp. 012906 ◽  
Author(s):  
Yurij Yaremko
Keyword(s):  
Angular Momentum ◽  
Momentum Balance ◽  
Balance Equations ◽  
Self Force

Application of an Angular Momentum Balance Method for Investigating Numerical Accuracy in Swirling Flow

2003 ◽  
Vol 125 (4) ◽  
pp. 723-730
Author(s):  
H. Nilsson ◽  
L. Davidson
Keyword(s):  
Fluid Dynamics ◽  
Computational Fluid Dynamics ◽  
Angular Momentum ◽  
Swirling Flow ◽  
Linear Momentum ◽  
Correct Solution ◽  
Momentum Balance ◽  
Numerical Accuracy ◽  
Water Turbine ◽  
Water Turbines

This work derives and applies a method for the investigation of numerical accuracy in computational fluid dynamics. The method is used to investigate discretization errors in computations of swirling flow in water turbines. The work focuses on the conservation of a subset of the angular momentum equations that is particularly important to swirling flow in water turbines. The method is based on the fact that the discretized angular momentum equations are not necessarily conserved when the discretized linear momentum equations are solved. However, the method can be used to investigate the effect of discretization on any equation that should be conserved in the correct solution, and the application is not limited to water turbines. Computations made for two Kaplan water turbine runners and a simplified geometry of one of the Kaplan runner ducts are investigated to highlight the general and simple applicability of the method.

Constitutive relations for polar continua based on statistical mechanics and spatial averaging

2020 ◽  
Vol 476 (2233) ◽  
pp. 20190407
Author(s):  
Bob Svendsen
Keyword(s):  
Angular Momentum ◽  
Constitutive Relations ◽  
Volume Averaging ◽  
Mass Point ◽  
Momentum Balance ◽  
Spatial Averaging ◽  
Material Frame Indifference ◽  
Phase Space Transport ◽  
Polar Continua ◽  
Material Frame

The purpose of the current work is the formulation of macroscopic constitutive relations, and in particular continuum flux densities, for polar continua from the underlying mass point dynamics. To this end, generic microscopic continuum field and balance relations are derived from phase space transport relations for expectation values of point fields related to additive mass point quantities. Given these, microscopic energy, linear momentum and angular momentum, balance relations are obtained in the context of the split of system forces into non-conservative and conservative parts. In addition, divergence–flux relations are formulated for the conservative part of microscopic supply-rate densities. For the case of angular momentum, two such relations are obtained. One of these is force-based, and the other is torque-based. With the help of physical and material theoretic restrictions (e.g. material frame-indifference), reduced forms of the conservative flux densities are obtained. In the last part of the work, formulation of macroscopic constitutive relations from their microscopic counterparts is investigated in the context of different spatial averaging approaches. In particular, these include (weighted) volume-averaging based on a localization function, surface averaging of normal flux densities based on Cauchy flux theory and volume averaging with respect to centre of mass.

Dynamical modelling of an anaerobic digestion fluidized bed reactor

1997 ◽  
Vol 36 (5) ◽  
pp. 285-292 ◽  
Author(s):  
Benjamin Bonnet ◽  
Denis Dochain ◽  
Jean-Philippe Steyer
Keyword(s):  
Fluidized Bed ◽  
Solid Phase ◽  
Biofilm Reactor ◽  
Momentum Balance ◽  
Balance Equations ◽  
Biological Variables ◽  
Dynamical Simulation ◽  
Model Derivation ◽  
The Stability ◽  
Bed Expansion

One of the main difficulties in modelling a Fluidized Bed Biofilm Reactor (FBBR) is to take into account hydraulic phenomena (such as bed expansion) and its interactions with the biological variables. In this paper, we shall present a dynamical model of the process, analyse the stability of the hydrodynamics and illustrate its performances in simulation. A key feature of the model is that it combines mass balance of the process components with momentum balance equations in order to emphasise the different hydrodynamics of the liquid phase and of the solid phase, and the interactions between both phases. The model derivation finally leads to a set of partial differential equations (PDE). This model is intended to be used as a basis for the derivation of controllers and for dynamical simulation.

scholarly journals THE INFLUENCE OF “INJECTED” AND “THERMAL” MAGNONS ON A SPIN WAVE CURRENT AND DRAG EFFECT IN HYBRID STRUCTURES

2018 ◽  
Vol 185 ◽  
pp. 01022
Author(s):  
Igor Lyapilin ◽  
Mikhail Okorokov
Keyword(s):  
Spin Wave ◽  
Metal Structure ◽  
Relaxation Mechanism ◽  
Seebeck Effect ◽  
Hybrid Structures ◽  
Momentum Balance ◽  
Drag Effect ◽  
Balance Equations ◽  
Spin Seebeck Effect ◽  
Magnetic Insulator

The formation of the two: injected and thermally excited, different in energies magnon subsystems and the influence of its interaction with phonons and between on drag effect under spin Seebeck effect conditions in the magnetic insulator part of the metal/ferromagnetic insulator/metal structure is studied. The analysis of the macroscopic momentum balance equations of the systems of interest conducted for different ratios of the drift velocities of the magnon and phonon currents show that the injected magnons relaxation on the thermal ones is possible to be dominant over its relaxation on phonons. This interaction will be the defining in the forming of the temperature dependence of the spin-wave current under spin Seebeck effect conditions, and inelastic part of the magnon-magnon interaction is the dominant spin relaxation mechanism.

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