Applied Mathematics and Mechanics

, Volume 13, Issue 11, pp 1039–1046 | Cite as

The solution for transient two-phase flow by split flux vector method

  • Weng Rong-zhou 
Article
  • 27 Downloads

Abstract

In this paper the transient two-phase flow equations and their eigenvalues are first introduced. The flux vector is then split into subvectors which just contain a specially signed eigenvalue. Using one-sided spatial difference operators finite difference equations and their solutions are obtained. Finally comparison with experiment shows the predicted results produce good agreement with experimental data.

Key words

two-phase flow vector flux split flux vector method 

Nomenclature

cp J/kg°C

specific heat at constant pressure

c m/s

sonic velocity

d m

diametric of tube

f

friction coefficient

G kg/m2s

mass velocity

g m/s2

gravitational acceleration

ht J/kg

specific enthalpy of saturated liquid

hg J/kg

specific enthalpy of saturated vapour

hgt J/kg

enthalpy of evaporation

P N/m2

pressure

T °C,k

temperature

t s

time

u m/s

velocity

Vg m3/kg

specific volume of saturated vapour

Vf m3/kg

specific volume of saturated liquid

Z m

length

α

void fraction

β m3.K/J

property relationship

λ

eigenvalue

ρ kg/m3

density

ρm kg/m3

mean density

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. [1]
    Courant, R., E. Isaacson and M. Rees, On the solution of nonlinear hyperbolic differential equation by finite differences.Communications on Pure and Applied Mathematics.5 (1952), 243–255.MATHMathSciNetGoogle Scholar
  2. [2]
    Whitham, G. B.,Linear and Non-Linear Waves, Wiley, New York (1974).Google Scholar
  3. [3]
    Gonzalez-Santal, J. M. and R. T. Lahey, Jr., An exact solution for flow of transients in two-phase system by method of characteristics,J. Heat Transfer,95, 470 (1973).Google Scholar
  4. [4]
    Moretti, G., The λ-scheme,Computers and Fluid,7 (1979), 191–205.MATHMathSciNetCrossRefGoogle Scholar
  5. [5]
    Chakravarthy, S. R., D. A. Anderson, and M. Salas, The splist-coefficient matrix method for hyperbolie stytems of gas dynamic equations,AIAA Paper 80 0268, Pasadena, California (1980).Google Scholar
  6. [6]
    Steger, J. L., Coefficient matrices for implicit finite-difference solution of the inviscid fluid conservation law equation,Comput. Methods Appl. Mech. Eng.,13 (1978), 175–188.MATHMathSciNetCrossRefGoogle Scholar
  7. [7]
    Banerjee, E. and W. T. Hancox, On the development of methods for analysing transient flow-boiling,Int. J. Multiphase Flow.4 (1978), 437–460.MATHCrossRefGoogle Scholar
  8. [8]
    Steger, J. L. and R. F. Warming, Flux vector splitting of the inviscid gasdynamic equations with application to finite-difference methods,J. of Comp. Physics 40 (1981), 263–293.MATHMathSciNetCrossRefGoogle Scholar
  9. [9]
    Kim-choon, N. G., Some aspects of transient two-phase flow, Ph. D. Thesis, University of Strathelyde, Glasgow.Google Scholar

Copyright information

© Shanghai University of Technology (SUT) 1992

Authors and Affiliations

  • Weng Rong-zhou 
    • 1
  1. 1.Huaqiao UniversityQuanzhou

Personalised recommendations