Steady and Unsteady Simulations for Annular Internal Condensing Flows in a Channel

This paper highlights: (i) numerical methods developed to solve annular/stratified internal condensing flow problems, and (ii) the assessed effects of transverse gravity and surface tension on shear driven (horizontal channels) and gravity driven (inclined channels) internal condensing flows. A comparative study of the flow physics is presented with the help of steady and unsteady computational results obtained from the numerical solutions of the full two-dimensional governing equations for annular internal condensing flows. These simulations directly apply to recently-demonstrated innovative condenser operations which make the flow regime annular over the entire length of the condenser. The simulation algorithm is based on an active integration of our own codes developed on MATLAB with the standard single-phase CFD simulation codes available on COMSOL. The approach allows for an accurate wave simulation technique for the highly sensitive shear driven annular condensing flows. This simulation approach employs a sharp-interface model and uses a moving grid technique to accurately locate the dynamic interface by the solution of the interface tracking equation (employing the method of characteristics) along with the rest of the governing equations. The 4th order time-step accuracy in the method of characteristics has enabled, for the first time, the ability to track time-varying interface locations associated with wave phenomena and accurate satisfaction of all the interface conditions — including the more difficult to satisfy interfacial mass-flux equalities. A combination of steady and unsteady simulation results are also used to identify the effects of transverse gravity, axial gravity, and surface tension on the growth of waves. The results presented bring out the differences within different types of shear driven flows and differences between shear driven and gravity driven flows. The unsteady wave simulation capability has been used here to do the stability analysis for annular shear-driven steady flows. In stability analysis, an assessment of the dynamic response of the steady solutions to arbitrary instantaneous initial disturbance are obtained. The results mark the location beyond which the annular regime transitions to a non-annular regime (experimentally known to be a plug-slug regimes). The computational prediction of heat-flux values agree with the experimentally measured values (at measurement locations) obtained from relevant runs of our in-house experiments. Also, a comparison between the computationally predicted and experimentally measured values regarding the length of the annular regime is possible, and will be presented elsewhere.

Annular/Stratified Internal Condensing Flows in Millimeter to Micrometer Scale Ducts

This paper presents computational simulations for internal condensing flows over a range of tube/channel geometries — ranging from one micro-meter to several millimeters in hydraulic diameters. Over the mm-scale, three sets of condensing flow results are presented that are obtained from: (i) full computational fluid dynamics (CFD) based steady simulations, (ii) quasi-1D steady simulations that employ solutions of singular non-linear ordinary differential equations, and (iii) experiments involving partially and fully condensing gravity driven flows of FC-72 vapor. These results are shown to be self-consistent and in agreement with one another. The paper demonstrates the existence of a unique solution for the strictly steady equations for gravity and shear driven flows. This paper also develops useful correlations for shear driven and gravity driven annular stratified internal condensing flows (covering some refrigerants and common operating conditions of interest). A useful map that marks various transitions between gravity and shear dominated annular stratified flows is also presented. For the micro-meter scale condensers, computations indentify a critical diameter condition (in non-dimensional terms), below which the flows are insensitive to the orientation of the gravity vector as the condensate is always shear driven. Large pressure drop, importance of surface tension, and vapor compressibility for μm-scale flows are also discussed. With the help of comparisons with 0g flows, the paper also discusses effects of transverse gravity on the solutions for horizontal channel flows.