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Mathematical modeling of an nonequilibrium flow consisting of water, steam, and air

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Conclusion

Four models have been suggested for the description of a one-dimensional flow with a water-steam-air makeup in a system for accident localization from coolant losses, and three have been suggested with proven hyperbolic properties. The region of application of the homogeneous model and the inhomogeneous model using a correlation for phase sliding is practically the entire two-phase region. The proposed bubble-flow model is applicable up to α≤0.5.

It is necessary to determine experimentally the region of application of the model of a highly inhomogeneous dispersed flow made up of air and gas, since the expression obtained for the speed of sound in this flow coincides with the speed of sound in a flow with projectile structure.

It is not difficult to obtain steady systems from the three hyperbolic systems of equations. Solving them with respect to the spatial derivatives, one can obtain an expression for the critical mass flow density.

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Abbreviations

A:

area

α:

speed of sound

cp :

specific heat at constant pressure

fR :

drag force referred to unit volume of the flow

G:

density of the mass flow

g:

gravitational acceleration

h:

specific enthalpy

p:

pressure

q‴:

thermal power referred to unit volume of the flow

R:

gas constant

T:

absolute temperature

w:

velocity

\(\bar w\) :

(wg=wf)/2

Δwj:

(wex-wj)

z:

linear coordinate

ϑ:

angular coordinate

α:

volume gas content

Δ:

finite difference

ϖ:

partial differential

λ:

eigenvalue

μ:

rate of phase transitions

ρ:

density

τ:

time

L:

air

D:

steam

f:

water

g:

gas

ex:

phase which yields mass

p, T, ρ...:

const p, T, ρ...

I:

impulse equation

Literature Cited

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Authors
  1. N. I. Kolev
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Additional information

Institute of Nuclear Investigations and Nuclear Power, Bulgarian Academy of Sciences, Sofia. Translated from Atomnaya Energiya, Vol. 57, No. 4, pp. 272–277, October, 1984.

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Kolev, N.I. Mathematical modeling of an nonequilibrium flow consisting of water, steam, and air. At Energy 57, 734–741 (1984). https://doi.org/10.1007/BF01123649

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