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

Abstract

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.

Elementary Assessments and Simulations Based Proposals for New Heat Transfer Correlations and Flow Regime Maps for Annular/Stratified Regime of Shear Driven Internal Condensing Flows

“…The results obtained in this study uses a highly efficient and sufficiently accurate quasi 1D flow simulation tool [2], and has been validated by comparing the results from correlation results obtained from the nearly exact 2D modelling and steady solutions [3,19,20]. Since results from 1D tool agrees well with results from the 2D steady tool, it justifies the earlier described 1D modelling approximations discussed earlier in this section.…”

“…This research provides a structured approach in assessing the efficacy of existing semiempirical heat transfer correlations [11,[16][17][18] and further assists in the development of such correlations for other flow regimes. Furthermore, results from existing study are compared with results obtained and proposed in the study using an approximate Quasi 1D [2] condensing flow simulation tool with a combination of experimental data [13,14] and nearly exact 2D steady/unsteady simulation tools [3,[19][20][21].…”

“…The details of the formulation and implementation of these algorithms are discussed in detail in [2]. Consistency of the simulation results are explained in [3,19,20] and their equivalency with the experimental results are described in [13][14][15].…”

“…This study assumes zero transverse gravity obtaining the correlation for the non-dimensional annular length. However detailed discussion of the effects of the transverse gravity can be obtained from [3,[19][20][21].…”

An Assessment of Flow Regime Maps and a Numerical Heat Transfer Correlation for the Stratified/Annular Regime of Shear-Driven Internal Condensing Flows

“…An assessment of the structure of some of these heattransfer correlations is conducted in section 3. The results from the studies available in literature ( [14][15][16][17][18]) are compared with results that are obtained in this study using a combination of an approximate Quasi-1D condensing flow simulation tool ( [5,19]) and an exact scientific 2D steady simulation code ( [19][20][21][22][23]). The mathematical models and the two simulation tools used in this study are described in section 2.…”