This is the first of a series of two papers reporting on a study of reflooding of a hot vertical tube. A mechanistic model of reflood is developed using a multifield modeling approach to analyze experimental data reported previously [1]. In Part 1 of this paper, the mathematical model for the thermohydraulic processes during reflood is derived from the general two-field conservation equations, and its structure is examined. Linear stability of the equation system is analyzed incorporating consideration of phase pressure differences. For inverted annular flow, the system is stable to short-wavelength perturbations and captures long-wavelength interfacial instabilities. The length of the most unstable waves is also derived in the analysis and agrees well with the available data. For dispersed flow, the system is predicted to become unstable if the Weber number exceeds a critical value of 8. In Part 2 [2], constitutive relations for reflood are fomulated and model is numerically solved for comparison with experimental data.

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