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An approximation of source terms in gradient form for multiphase transport processes

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Abstract

A set of two model equations for a multiphase flow is chosen to investigate the influence of approximation formulas. The approximations have been applied to the prediction of Peclet numbers using control volume interface values, as well as for gradient terms occurring as source terms. Use of an exponential approximation for a gradient source term, instead of the conventional central-difference approximation, leads to a remarkable reduction in the number of control volumes required. Different approximation formulas for the predictions of the grid Peclet number are found to have little influence on results. The form of the model equation has also been investigated. The source terms in gradient form in the model have been combined with the convection and diffusion terms to become part of the discretization scheme.

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Abbreviations

a :

coefficient

b :

coefficient

C :

constant

D :

coefficient for diffusion

F :

coefficient for convection

H :

source term

ITER :

number of iteration

L :

length

m :

number of control volume (for continuity)

n :

number of control volume (for momentum)

U :

velocity

u′:

velocity fluctuations

Pe :

grid Peclet number

Pe L :

global Peclet number

X :

X — coordinate

Z :

αU

α:

volume fraction

α′:

volume fraction fluctuations

δx :

nodal distance

ω:

normalized difference

ν:

viscosity

ζ:

normalized differnce

ϱ:

density

ϕ:

general variable

0:

locationX/L = 0

e :

interface east momentum control volume

E :

nodal east momentum control volume

ec :

interface east continuity control volume

Ec :

nodal east continuity control volume

L :

locationX/L = 1

P :

nodal centermomentum control volume

Pc :

nodal centercontinuity control volume

t :

turbulent

U :

velocity

w :

interface west momentum equation

W :

nodal west momentum equation

wc :

interface west continuity equation

Wc :

nodal west continuity equation

α:

volume fraction

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Authors and Affiliations

  1. Dept. of Mechanical Engineering, Keio University, 3-14-1 Hiyoshi Kohoku-ku, Yokohama, Japan

    D. Fleckhaus, K. Hishida & M. Maeda

Authors
  1. D. Fleckhaus
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  2. K. Hishida
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  3. M. Maeda
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Additional information

Communicated by G. Yagawa, June 12, 1987

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Fleckhaus, D., Hishida, K. & Maeda, M. An approximation of source terms in gradient form for multiphase transport processes. Computational Mechanics 3, 361–370 (1988). https://doi.org/10.1007/BF00712149

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