A numerical solution for the material and momentum balance equations for finite concentration chromatography

1976 ◽  
Vol 80 (24) ◽  
pp. 2656-2661 ◽  
Author(s):  
Jon F. Parcher ◽  
T. H. Ho ◽  
Henry W. Haynes
Keyword(s):  
Numerical Solution ◽  
Momentum Balance ◽  
Balance Equations ◽  
Finite Concentration

Theory of the propagation of finite concentration bands in gas chromatography. A numerical solution of the ideal problem

1985 ◽  
Vol 89 (10) ◽  
pp. 2076-2082 ◽  
Author(s):  
Pierre Rouchon ◽  
Marc Schoenauer ◽  
Patrick Valentin ◽  
Claire Vidal-Madjar ◽  
Georges Guiochon
Keyword(s):  
Gas Chromatography ◽  
Numerical Solution ◽  
Finite Concentration ◽  
The Ideal

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.

scholarly journals Numerical simulation of indoor microclimate using free software

2021 ◽  
Vol 33 (5) ◽  
pp. 259-270
Author(s):  
Anna Alexandrovna Tsynaeva ◽  
Ekaterina Alexandrovna Tsynaeva
Keyword(s):  
Numerical Simulation ◽  
Velocity Field ◽  
Numerical Solution ◽  
Thermal Energy ◽  
Numerical Study ◽  
Free Software ◽  
Momentum Balance ◽  
Navier Stokes Equation ◽  
Temperature Deviation ◽  
Residential Space

The work is devoted to the numerical study of indoor microclimate. Accurately predicting the distributed microclimate inside the residential space equipped with a microclimate control system called the «smart house» allows to save thermal energy significantly. Mathematical modeling was carried out by means of the Navier-Stokes equation, the energy equation, the continuity equation. The system of equations used was closed using the k-w-sst turbulence model. The resulting numerical solution was performed in the Code_Saturn, which has a free license. The Salome free software package was used to build a grid. In this context, a second–order scheme (SOLU) was used to resolve the velocity field, a MULTIGRID scheme was used for the pressure field, automatic settings were used for the kinetic energy of turbulence and her dissipation and for the temperature field, the maximum number of iterations for each cycle was equal to 10000, the Solver Precision accuracy was 10-8. The SIMPLEC algorithm is used to obtain a connected solution of the momentum balance and continuity equations. The paper provides an example of numerical solution verification, which is showed the relative temperature deviation from the values obtained by other authors was no more than 0.8-1.2%. Numerical simulation of the air velocity field in the residential space showed values from 0.12 to 0.15 m/s. Based on the results of the obtained solution, an analysis of the saving of thermal energy was carried out when regulating the supply of heat.

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