I. The Analysis of the Rewetting of a Vertical Slab Using a Wiener-Hopf Technique. II. Asymptotic Expansions of Integrals with Three Coalescing Saddle Points

Author: Mueller, James Robert

Year: 1982

Degree: Dissertation (Ph.D.)

Advisor: Cohen, Donald S.

Committee Member: Unknown, Unknown

Option: Applied Mathematics

DOI: 10.7907/8q9c-pe97

Abstract

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Part I: A problem which arises in the analysis of the emergency core cooling system of a nuclear reactor is the rewetting of the fuel rods following a loss of coolant accident. Due to the high initial temperatures in the rods, the emergency coolant initially flashes to steam on contact, effectively insulating the rods from the coolant. It is observed experimentally, however, that a constant velocity traveling quench front is set up on the surface of the rod, moving from the cold to the hot end.

We approximate the rod by an infinite two-dimensional slab with adiabatic boundary conditions ahead of the quench front, and a constant heat transfer coefficient behind in the wet region. The temperature at the front is found using Fourier transforms and an exact Wierner-Hopf Factorization. Using a reversion of series, the dimensionless velocity of the quench front (Peclet number) for a small dimensionless heat transfer coefficient A (Biot number) is found approximately to lowest order in A. This approximate quench front velocity is found to be in agreement with the known front velocity for a one-dimensional slab.

Part II: Contour integrals of the form I([...]) = [...]dz are considered for a large parameter [...]. In problems of interest, the exponent w is assumed to have simple saddle points at z = [...], i=1,2,3 which are allowed to coalesce, forming a single saddle of order three. Using a conformal map, the integral I is shown to be asymptotically equivalent to the study of the canonical integral J([...]) = [...]dt, which has simple saddles at t = 0, ± [...]. By applying the method of steepest descent, the complete asymptotic behavior of J([...]) is obtained for [...], uniformly as [...].

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