DEVELOPMENT OF UNSTEADY TWO-DIMENSIONAL COMPUTATIONAL SIMULATION TOOLS FOR ANNULAR INTERNAL CONDENSING FLOWS – AND THEIR USE FOR RESULTS ON HEAT-TRANSFER RATES, FLOW PHYSICS, FLOW STABILITY, AND FLOW SENSITIVITY

Abstract

This work presents a numerical method for solving the full two-dimensional governing equations, along with the interface conditions, that govern the annular/stratified internal condensing flows in a channel. The simulation approach uses a sharp-interface model and a moving grid technique to accurately locate the dynamic wavy interface as a solution of the interface tracking equation - which is a wave equation and arises from one of the interface conditions. In the proposed method of characteristics, a 4th order time-step accuracy is used for locating the characteristics curves on a specially designed moving grid. The approach allows the evolving interface locations to correctly capture the wave phenomena (both in amplitude and phase) on a coarse spatial grid – allowing it to be coarser than the mesh-size needed for the CFD solutions. This, along with embedded interface conditions used for the separate domain CFD for the two phases, allows accurate satisfaction of all the interface conditions - including the more difficult to satisfy interfacial mass-flux equalities. The improvement allows stability analysis for shear driven flows considered here, enabling it to overcome inaccuracies associated with our earlier approach. The unsteady wave simulation capability has been used to successfully implement a unique computational version of non-linear stability analysis. The kinetic energy values associated with the spatial and temporal evolution of interfacial disturbances mark the approximate location beyond which the annular regime typically transitions to a non-annular regime (experimentally known to be a plug-slug regime). The transition location estimate is supported by two other independent considerations. The reported results also elucidate flow-physics differences between different types of shear driven horizontal channel flows (i.e., with or without transverse gravity) as well as differences between shear driven and gravity driven flows. The computational predictions of heat-flux values and the length of the annular regime agree with the experimentally measured values obtained from relevant in-house experimental runs. The computational physics results have also been used to develop engineering tools such as heat transfer correlations and flow regime maps