A singular integro-differential equation model for dryout in LMFBR boiler tubes

Cuminato, J.A., Fitt, A.D., Mphaka, M.J.S. and Nagamine, A. (2009) A singular integro-differential equation model for dryout in LMFBR boiler tubes. IMA Journal of Applied Mathematics, 75 (2), 269-290. (doi:10.1093/imamat/hxp039).

Abstract

A 2D steady model for the annular two-phase flow of water and steam in the steam-generating boiler pipes of a liquid metal fast breeder reactor is proposed. The model is based on thin-layer lubrication theory and thin aerofoil theory. The exchange of mass between the vapour core and the liquid film due to evaporation of the liquid film is accounted for using some simple thermodynamics models, and the resultant change of phase is modelled by proposing a suitable Stefan problem. Appropriate boundary conditions for the flow are discussed. The resulting non-linear singular integro-differential equation for the shape of the liquid film free surface is solved both asymptotically and numerically (using some regularization techniques). Predictions for the length to the dryout point from the entry of the annular regime are made. The influence of both the traction provided by the fast-flowing vapour core on the liquid layer and the mass transfer parameter on the dryout length is investigated.

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