# Partial singular integro-differential equations models for dryout in boilers

Mphaka, Mphaka Joane Sankoela (2000) Partial singular integro-differential equations models for dryout in boilers. University of Southampton, Department of Mathematics, Doctoral Thesis , 158pp.

## Description/Abstract

A two-dimensional model for the annular two-phase flow of water and steam, along with
the dryout, in steam generating 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 in the model. The mass exchange rate depends on the details of the flow conditions and
it is calculated using some simple thermodynamic models. The change of phase at the free
surface between the liquid layer and the vapour core is modelled by proposing a suitable Stefan
problem. Appropriate boundary conditions for the model, at the onset of the annular flow
region and at the dryout point, are stated and discussed. The resulting unsteady nonlinear
singular integro-differential equation for the liquid film free surface is solved asymptotically
and numerically (using some regularisation techniques) in the steady state case, for a number
of industrially relevant cases. Predictions for the length to the dryout point from the entry
of the annular regime are made. The influence of the constant parameter values in the model
(e.g. the traction r provided by the fast flowing vapour core on the liquid layer and the mass
transfer parameter 77) on the length to the dryout point is investigated.
The linear stability of the problem where the temperature of the pipe wall is assumed to be
a constant is investigated numerically. It is found that steady state solutions to this problem
are always unstable to small perturbations. From the linear stability results, the influence
on the instability of the problem by each of the constant parameter values in the model is
investigated. In order to provide a benchmark against which the results for this problem
may be compared, the linear stability of some related but simpler problems is analysed. The
results reinforce our conclusions for the full problem.

Item Type: Thesis (Doctoral)
Subjects: T Technology > TK Electrical engineering. Electronics Nuclear engineering
Q Science > QA Mathematics
Divisions : University Structure - Pre August 2011 > School of Mathematics
ePrint ID: 50627
Accepted Date and Publication Date:
Status