NONLINEAR DYNAMICS OF A 2 PHASE FLOW SYSTEM IN AN EVAPORATOR - THE EFFECTS OF (I) A TIME-VARYING PRESSURE-DROP (II) AN AXIALLY VARYING HEAT-FLUX

In this paper we study the phenomena of density wave oscillations (DWO ) in a vertical heated channel. The homogeneous equilibrium model is u sed to simulate the flow in the two-phase region. The equations are so lved numerically using a 'shooting-method' technique. This in its turn employs an implicit backward finite difference scheme. The scheme can incorporate the movement of the interface. It is very elegant and doe s not involve storage of variables in large N x N matrices. This schem e is sufficiently general and can be used to simulate the dynamic beha viour when: (i) the heat flux imposed at the surface is non-constant, i.e. exhibits an axial variation; and (ii) the imposed pressure drop i s varied periodically at a fixed frequency. A possible explanation for the conflicting reports of the effect of a periodic variation in heat flux is provided using a linear stability analysis and the D-partitio n method. The interaction of the natural frequency of the DWO and the fixed forcing frequency of the imposed pressure drop gives rise to var ious phenomena viz relaxation oscillations, sub-harmonic oscillations, quasi-periodic and chaotic solutions. To aid the experimentalist desc ribe this infinite-dimensional system on the basis of his experimental results we discuss the characterisation using only the velocity time series data. This is done employing the method of delay coordinate emb edding. The phase portraits, stroboscopic map and correlation dimensio n of the actual attractor are compared with that of the reconstructed attractor from the velocity time series. (C) 1997 Elsevier Science S.A .