Nuclear Engineering ETDs

Publication Date

6-26-1978

Abstract

This work involves development of improvements to two analytical methods to predict the instantaneous position of the moving phase-change front in one-dimensional Stefan-like problems. These techniques, the refined integral heat balance and the upper and lower bounds averaging methods, are useful in practical applications for reactor safety analysis, under hypothesized conditions leading to molten fuel relocation problems. With such applications in mind, the two methods are applied to four different one-dimensional problems which involve change-of­phase, with or without a convective boundary condition at the moving front. Comparison with the exact solution has been presented whenever possible; ultimately, all solutions have been illustrated graphically in dimensionless terms. Results of both methods are in good agreement with known exact solutions, indicating that such methods offer improvement in accuracy above known approximate analytical methods of other investigators, as well as illustrating the convenience of their use. Solutions to various problems involving a thermally unstable frozen crust in forced flow on a cold wall of infinite or finite extent, with or without simultaneous melting of the wall, are presented using the refined integral heat balance technique. The thermal stability of the crust that forms on a semi-infinite wall, without melting of the wall, has been shown to be governed by two dimensionless parameters; the wall-crust thermal ratio and the modified Stefan number. The growth and decay of a frozen crust subjected to a convective boundary condition onto a wall of finite thickness, without wall melting, has been presented for the first time in the known literature for the particular case of an insulated wall. It has been shown that the transient behavior of such crust depends upon the wall thickness in addition to the other two parameters mentioned. Another original contribution to the solidification heat transfer literature concerning the thermal stability of a growing crust onto a semi-infinite wall undergoing simultaneous melting is presented. In this dual change-of-phase problem, the mathematical modeling entails solving four ordinary differential equations (two being second order - second degree) simultaneously to obtain the instantaneous values of the time dependent functions; namely, the crust thickness, molten wall layer thickness, inter­face temperature and the thermal wave thickness through the solid wall. The transient behavior of such functions has been shown to be dependent upon five dimensionless parameters: the wall-crust thermal ratio, modified Stefan number for freezing, Stefan number for melting, wall melting point, and the fusion temperature of the flowing liquid. The molten layer through the wall has been shown to be thermally stable undergoing a continuous growth in thickness while the frozen crust grows until it reaches a maximum thickness, where it undergoes reduction via melting; eventually, remelting causes the crust to disappear. The last section of this work includes calculational results of interest to LMFBR safety assessments; namely, molten cladding freezing in the upper plenum region (particularly the insulator and reflector zones) of the FFTF core design and fuel freezing potential in the lower shield plug due to downward fuel debris relocation following a hypothetical core disruptive accident (HCDA). An accurate prediction of the blockage time in the upper plenum region of the fuel subassembly following upward streaming of molten cladding from the heated core region is presented. It has been shown that simultaneous melting of the stainless steel cladding in the reflector zone during the blockage time interval is unlikely, where primary blockage is expected in the reflector zone rather than the insulator region. Such blockage time is predicted to be a fraction of a second from the time at which the melting cladding, from the active core, enters the reflector zone, and depends upon the superheating of molten cladding and flow conditions. An assessment of molten fuel freezing in the lower shield plug of the CRBR core design following a "bottled-core" situation, caused by early blockage of stainless steel in the upper reflector region is analyzed, indicating that simultaneous wall melting in the shield block during the molten fuel drainage time (~ 1 sec) is expected at early times and may be instantaneously upon contact with the flowing fuel, depending upon the initial wall temperature and molten fuel superheating conditions.

Document Type

Dissertation

Language

English

Degree Name

Nuclear Engineering

Level of Degree

Doctoral

Department Name

Nuclear Engineering

First Committee Member (Chair)

August William Cronenberg

Second Committee Member

Fred Cooper

Third Committee Member

Lee Alfred Bertram

Fourth Committee Member

Chen-Yen Cheng

Fifth Committee Member

H. Eric Nuttall Jr.

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