Chebyshev polynomials expansion method for solving the one-dimensional transport equation in spherical geometry

Kerntechnik ◽  
2010 ◽  
Vol 75 (1-2) ◽  
pp. 47-49
Author(s):  
F. Yaşa
Keyword(s):  
Transport Equation ◽  
Chebyshev Polynomials ◽  
Spherical Geometry ◽  
Expansion Method ◽  
One Dimensional ◽  
The One

Two-Fluid CFD Model of Adiabatic Air-Water Upward Bubbly Flow Through a Vertical Pipe With a One-Group Interfacial Area Transport Equation

2009 ◽  
Author(s):  
Deoras Prabhudharwadkar ◽  
Chris Bailey ◽  
Martin Lopez de Bertodano ◽  
John R. Buchanan
Keyword(s):  
Experimental Data ◽  
Transport Equation ◽  
Bubbly Flow ◽  
Interfacial Area ◽  
Correct Prediction ◽  
Interfacial Area Transport ◽  
One Dimensional ◽  
Interfacial Area Transport Equation ◽  
The One ◽  
Two Fluid

This paper describes in detail the assessment of the CFD code CFX to predict adiabatic liquid-gas two-phase bubbly flow. This study has been divided into two parts. In the first exercise, the effect of Lift Force, Wall Force and the Turbulent Diffusion Force have been assessed using experimental data from the literature for air-water upward bubbly flows through a pipe. The data used here had a characteristic near wall void peaking which was largely influenced by the joint action of the three forces mentioned above. The simulations were performed with constant bubble diameter assuming no bubble interactions. This exercise resulted in selection of the most appropriate closure form and closure coefficients for the above mentioned forces for the range of flow conditions chosen. In the second exercise, the One-Group Interfacial Area Transport equation was introduced in the two-fluid model of CFX. The interfacial area density plays important role in the correct prediction of interfacial mass, momentum and energy transfer and is affected by bubble breakup and coalescence processes in adiabatic flows. The One-Group Interfacial Area Transport Equation (IATE) has been developed and implemented for one-dimensional models and validated using cross-sectional area averaged experimental data over the last decade by various researchers. The original one-dimensional model has been extended to multidimensional flow predictions in this study and the results are presented in this paper. The paper also discusses constraints posed by the commercial CFD code CFX and the solutions worked out to obtain the most accurate implementation of the model.

scholarly journals A simple moment model to study the effect of diffusion on the coagulation of nanoparticles due to Brownian motion in the free molecule regime

2012 ◽  
Vol 16 (5) ◽  
pp. 1331-1338 ◽  
Author(s):  
Wenxi Wang ◽  
Qing He ◽  
Nian Chen ◽  
Mingliang Xie
Keyword(s):  
Method Of Moments ◽  
Taylor Series Expansion ◽  
Expansion Method ◽  
Particle Coagulation ◽  
Average Volume ◽  
One Dimensional ◽  
The One ◽  
And Diffusion ◽  
Dimensional Domain ◽  
Series Expansion Method

In the study a simple model of coagulation for nanoparticles is developed to study the effect of diffusion on the particle coagulation in the one-dimensional domain using the Taylor-series expansion method of moments. The distributions of number concentration, mass concentration, and particle average volume induced by coagulation and diffusion are obtained.

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