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.
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Abbreviations
- c p 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
- h t J/kg:
-
specific enthalpy of saturated liquid
- h g J/kg:
-
specific enthalpy of saturated vapour
- h gt J/kg:
-
enthalpy of evaporation
- P N/m2 :
-
pressure
- T °C,k:
-
temperature
- t s:
-
time
- u m/s:
-
velocity
- V g m3/kg:
-
specific volume of saturated vapour
- V f 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
- ρ m kg/m3 :
-
mean density
References
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.
Whitham, G. B.,Linear and Non-Linear Waves, Wiley, New York (1974).
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).
Moretti, G., The λ-scheme,Computers and Fluid,7 (1979), 191–205.
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).
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.
Banerjee, E. and W. T. Hancox, On the development of methods for analysing transient flow-boiling,Int. J. Multiphase Flow.4 (1978), 437–460.
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.
Kim-choon, N. G., Some aspects of transient two-phase flow, Ph. D. Thesis, University of Strathelyde, Glasgow.
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Communicated by Liu Ren-huai
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Weng, Rz. The solution for transient two-phase flow by split flux vector method. Appl Math Mech 13, 1039–1046 (1992). https://doi.org/10.1007/BF02454521
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DOI: https://doi.org/10.1007/BF02454521