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This paper describes the modeling of boiling multisize bubbly flows and its application to the simulation of the DEBORA experiment. We follow the method proposed originally by Kamp, assuming a given mathematical expression for the bubble diameter pdf. The original model is completed by the addition of some new terms for vapor compressibility and phase change. The liquid-to-interface heat transfer term, which essentially determines the bubbles condensation rate in the DEBORA experiment, is also modeled with care. First numerical results realized with the Neptune_CFD code are presented and discussed.

This paper
describes the modeling of
boiling multisize bubbly flows and its application to
the simulation of the DEBORA experiment (see [

In real flows, a
bubble diameter spectrum is often observed, rather than a single bubble
diameter. In order to take this diameter spectrum into account, Kamp et al. (see
[

The outline of
the paper is the following. The classical two-fluid model for boiling bubbly
flows is summarized in Section

The two-fluid model we use for our boiling bubbly flow
calculations is constituted of the following six balance equations
(e.g., [

(i)
two mass balance equations:

(ii)
two momentum balance equations:

(iii)
two total enthalpy balance equations:

Kamp et al. (see
[

In the original
work of Kamp, the term

Let

Substituting the
expression (

In the previous
paragraph, we made the assumption of no phase change in order to derive the
compressibility terms in the equations for

In subcooled
boiling flows, as this is the case for the DEBORA experiment, vapor bubbles are
essentially nucleated onto the heated wall surface (heterogeneous nucleation)
rather than in the liquid bulk, because the liquid is subcooled in the major
part of the flow. Therefore, we can neglect a possible homogeneous nucleation
in comparison to the heterogeneous nucleation. The newly nucleated bubbles are
supposed to be generated with a unique size: the so-called detachment diameter

For a relatively
low speed flow, the local instantaneous interfacial balance of total energy (see
[

The DEBORA experiment, carried out at the French Commissariat
à l’Energie Atomique (see [

Here we evaluate the different models presented above on a particular DEBORA experimental test. The controlling parameters of this test are the following.

Test pressure: 14.59 bar.

Inlet mass flux density (liquid only):

Liquid inlet temperature:

Wall to fluid heat flux density:

comparison of the different models on the void fraction profile.

comparison of the different models on the vapor velocity profile.

comparison of the different models on the liquid temperature profile.

comparison of the different models on the interfacial area profile.

comparison of the different models on the Sauter mean diameter profile.

comparison of the different models on the mean diameter

Each figure compares the results of five calculations together with the experimental values.

According to these comparisons, the model giving better
results on the void fraction, the vapor mean velocity, the liquid temperature,
and the interfacial area concentration seems to be the one using
(

A multisize model for boiling bubbly flows has been presented
in detail. This model is not completely achieved (e.g., a bubble breakup term
is missing in the equations). Nevertheless, we made first calculations to
evaluate the capabilities of this model in its present state. Five different
calculations have been done and compared to a single experimental test of the
DEBORA experiment. It has been shown that the results are sensitive to the
expressions used for the liquid-to-interface heat transfer (

Several issues can be raised for future developments:

a bubble breakup model should be added for completeness of the model;

a bubble collapse model is missing too;

the physical model given by Ranz and Marschall [

Neptune_CFD is a three-dimensional two-fluid
code developed more especially for nuclear reactor applications within
the framework of the Neptune project, financially supported by CEA
(Commissariat à l'Energie Atomique), EDF (Electricité de France), IRSN
(Institut de Radioprotection et de S