Evaluation of stochastic void models for bubble worth calculations Page: 2 of 7
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AN EVALUATION OF STOCHASTIC VOID MODELS
FOR BUBBLE WORTH CALCULATIONS
E. U. Vaughan and T. J. Hoffman
The reactivity due to the collapse of a large number of small bubbles in
a reactor core has been analyzed with Behrens' method,12 Benoist's method,3
and the probability table method ' Each analysis has used a different stochas-
tic model for the bubble distribution within the reactor core: the Nicholson-
Goldsmith calculations have employed a "closely-spaced holes" model; the
Gelbard-Lell calculations have employed a "random cube" model; the Hoffman-
Petrie calculations have employed a "nuclear model". However, any of the
models can be used with any of the methods. In this paper, the three void
models are evaluated. Based on this analysis, the closely-spaced holes model
is reconnended. as the most suitable for analysis of bubble collapse in a
molten, LMFBR core.
To study the void distribution, the moment-generating function is used:
G n(q) = n (
where <sn> is the n-th moment of the next collision. site distribution in the
bubbly system.
In the Hoffman-Petrie calculations with the nuclear model, an explicit
expression for the distribution of next collision sites was obtained. With
the substitution of this expression into Eq. 1, the following moment-generating
function is obtained for this model
GHP (q) + q/k+-( /Et exp (-qd)]4 .
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Vaughan, E. U. & Hoffman, T. J. Evaluation of stochastic void models for bubble worth calculations, article, January 1, 1979; United States. (https://digital.library.unt.edu/ark:/67531/metadc1106644/m1/2/: accessed April 24, 2024), University of North Texas Libraries, UNT Digital Library, https://digital.library.unt.edu; crediting UNT Libraries Government Documents Department.