CORRECTIONS- Numerical Study of the Three-Component Gaseous Diffusion Equations in the Transition Region Between Kundsen and Molecular Diffusion

1972 ◽  
Vol 11 (2) ◽  
pp. 286-286 ◽  
Author(s):  
R Rimick ◽  
C Geankoplos
Keyword(s):  
Transition Region ◽  
Molecular Diffusion ◽  
Numerical Study ◽  
Diffusion Equations ◽  
Gaseous Diffusion

Numerical Study of Mass Dispersion in Laminar and Turbulent Flows Through a Pipeline

2002 ◽  
Author(s):  
Horacio Antonio Flo´rez Guzma´n
Keyword(s):  
Turbulent Flows ◽  
Molecular Diffusion ◽  
Numerical Study ◽  
Computer Code ◽  
Finite Difference Schemes ◽  
Entire Volume ◽  
Two Fluids ◽  
Mass Dispersion ◽  
Miscible Fluid ◽  
Domain Discretization

A computer code for solving the equations of mass diffusion has been developed and applied to study the molecular-level mixing between two fluids inside a pipe. First, one fluid occupies the entire volume within the pipe, and then a second miscible fluid is forced into the pipe, developing a mixing process through the interface between the fluids. This phenomenon occurs as the combination of molecular diffusion, variation of velocity over the cross-section and turbulence. The code developed for this study is based on the finite element method for domain discretization and standard finite difference schemes for temporal discretization. Comparison with experimental data shows that the code is able to reproduce the physical trends and gives good predictions for engineering applications. A grid independence analysis is presented for all computations.

Mathematical Modelling of Methane-Air Combustion in a Channel with a Porous Axial Insert

2014 ◽  
Vol 698 ◽  
pp. 660-663
Author(s):  
Anastasia I. Baygulova ◽  
Aleksey M. Bubenchikov ◽  
Oleg V. Matvienko
Keyword(s):  
Turbulent Combustion ◽  
Energy Equation ◽  
Numerical Study ◽  
Particulate Material ◽  
Diffusion Equations ◽  
Stoichiometric Mixture ◽  
Axial Zone ◽  
Averaged Equations ◽  
Irreversible Chemical Reaction ◽  
Interpenetrating Continua

In the paper we construct a mathematical model of turbulent flow, combustion and heat transfer in an axisymmetric chamber with an axial zone of a compacted particulate material. The averaged equations written using the model of interacting and interpenetrating continua contain diffusion equations of individual components, the energy equation for the gas and the porous structure, the motion equation for a mixture of gaseous components, as well as the equation of the turbulence model. This system is closed by the equations of continuity and condition of the mixture. In the flow, an irreversible chemical reaction of stoichiometric mixture of methane and oxygen proceeds. Numerical study of porosity influencing the nature of turbulent combustion is conducted.

A Numerical Study of Turbulent Flow in Helical Static Mixers

2006 ◽  
Author(s):  
Ramin K. Rahmani ◽  
Anahita Ayasoufi ◽  
Theo G. Keith
Keyword(s):  
Turbulent Flow ◽  
Molecular Diffusion ◽  
Stokes Equations ◽  
Numerical Study ◽  
Critical Role ◽  
Three Dimensional ◽  
Turbulent Dispersion ◽  
Working Fluid ◽  
Static Mixer ◽  
Static Mixers

Many processing applications call for the addition of small quantities of chemicals to working fluid. Hence, fluid mixing plays a critical role in the success or failure of these processes. An optimal combination of turbulent dispersion down to eddies of the Kolmogoroff scale and molecular diffusion would yield fast mixing on a molecular scale which in turn favors the desired reactions. Helical static mixers can be used for those applications. The range of practical flow Reynolds numbers for these mixers in industry is usually from very small (Re ∼ 0) to moderate values (Re ∼ 5000). In this study, a helical static mixer is investigated numerically using Lagrangian methods to characterize mixer performance under turbulent flow regime conditions. A numerical simulation of turbulent flows in helical static mixers is employed. The model solves the three-dimensional, Reynolds-averaged Navier-Stokes equations, closed with the Spalart-Allmaras turbulence model, using a second-order-accurate finite-volume numerical method. Numerical simulations are carried out for a six-element mixer, and the computed results are analyzed to elucidate the complex, three-dimensional features of the flow. Using a variety of predictive tools, mixing results are obtained and the performance of static mixer under turbulent flow condition is studied.

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