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

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

Numerical simulation of exact two-dimensional governing equations for internal condensing flows

The paper outlines a two-dimensional computational methodology and presents results for laminar/laminar condensing flows inside mm- scale ducts. The methodology has been developed using MATLAB/COMSOL platform and is currently capable of simulating film-wise condensation for steady and unsteady flows. The results obtained are shown to be in agreement with an independently developed quasi-one-dimensional technique as well as a two-dimensional technique. The results are further validated with the help of vertical tube condensation experiments. The developed code is employed to investigate effects of transverse gravity on condensate motion inside a horizontal channel. It is found that in mm-scale channels, the flows in 0g are much different than flows in horizontal channels. The differences in film thickness, velocity profiles and pressure drops between horizontal and 0g channel are presented in this paper. The paper also investigates the response of the flow variables to inlet mass flow rate fluctuations for different cooling methods employed at the heat transfer surface

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

Steady and unsteady simulations for annular internal condensing flows, part I: Algorithm and its accuracy

This paper presents an algorithm for accurately solving the full two-dimensional governing equations, along with the interface conditions that govern laminar/laminar annular/stratified internal condensing flows. The simulation approach - which can be generalized to adiabatic and evaporating flows, a 3-D level-set technique, and so on - uses a sharp-interface model, separate liquid and vapor domain computational solutions with interface conditions embedded as boundary conditions, and a moving grid technique to locate the dynamic wavy interface (in amplitude and phase) by a method of characteristics solution of the interface tracking equation. The moving grid is spatially fixed for a defined number of instants, but changes when the current marker instant advances in time

Steady and unsteady computational results of full two dimensional governing equations for annular internal condensing flows

This paper presents steady and unsteady computational results obtained from numerical solutions of the full two-dimensional governing equations for annular internal condensing flows in a channel. This is achieved by active integration of our own home grown codes and utilization of COMSOL Multiphysics® CFD and Heat Transfer modules. This has allowed for an accurate wave simulation technique for the highly sensitive, shear-driven, annular condensing flows. The simulation capability uses an approach of separately solving (via COMSOL) the unsteady liquid and vapor domain governing equations over their respective fixed domains resulting from an assumed sharp interface location, tracking the interface (by solving its evolution equation in MATLAB®) using a moving grid, and then iteratively re-solving the unsteady liquid and vapor domain governing equations while satisfying the remaining interface conditions. Here liquid and vapor domain unsteady equations are solved on fixed grids and suitable boundary conditions are imposed with the help of COMSOL\u27s CFD and Heat Transfer Modules. Interface evolution equation is a wave equation which is solved (with the help of the well-defined characteristics equation underlying this problem) with 4th order accuracy in time. The resulting accurate prediction of interface location is used to iteratively redefine the liquid/vapor domains with COMSOL Multiphysics®. The approach ensures accurate prediction of interface location and interface variables towards accurate satisfaction of all the time-varying interface conditions. For example, at any point on the interface, the mass flux values computed from three different methods - one using predicted kinematics of vapor velocity and local interface profile, one using predicted kinematics of liquid velocity and local interface profile, and one based on the energy balance - show excellent agreement with one another. Figure 1 highlights the difference in the streamlines patterns and film thickness variations for a shear driven steady condensing flow in a horizontal channel and its analogous gravity driven condensing flow in an inclined channel. The horizontal flows exhibit much thicker films (and poorer heat-transfer rates) with the liquid tending to lift upwards from the condensing-surface. The basic features of the flows as well as their stability (see Figure 2) are obtained for the case of negligible externally imposed fluctuations. The computational simulation results agree with experimentally measured values of heat-flux and the length of the annular regime. This unsteady wave simulation capability is able to capture the destabilizing wave growth tendencies that govern the transition from the annular regime of a shear-driven steady flow to its non-annular regime. This unsteady wave simulation capability is used to predict the heat transfer rates and length of annular regimes for condensing flows. It is also being used to track the transition from the annular regime of a shear-driven steady flow to other non-annular regime. In addition, results obtained for inclined, horizontal, and zero-gravity cases (with and without surface-tension) bring out the differences between shear driven and gravity assisted/driven flows. This accurate simulation capability leads to significant improvements over our previous simulation capabilities and over other existing fixed grid solution techniques

Fundamental assessments and new enabling proposals for heat transfer correlations and flow regime maps for shear driven condensers in the annular/stratified regime

Modern-day applications need mm-scale shear-driven flow condensers. Condenser designs need to ensure large heat transfer rates for a variety of flow conditions. For this, good estimates for heat-transfer rate correlations and correlations for the length of the annular regime (beyond which plug-slug flows typically occur) are needed. For confident use of existing correlations (particularly the more recent ones supported by large data sets) for shear-pressure driven internal condensing flows, there is a great need to relate the existing correlation development approaches to direct flow-physics based fundamental results from theory, computations, and experiments. This paper addresses this need for millimeter scale shear driven and annular condensing flows. In doing so, the paper proposes/compares a few new and reliable non-dimensional heat-transfer coefficient correlations as well as a key flow regime transition criteria/correlation

Innovative realizations of high heat-flux boiling and condensing flows for milli-meter and micro-meter scale applications

For shear driven mm-scale flows, the traditional boiler and condenser operations pose serious problems of degraded performance (low heat-flux values, high pressure drops, and device-and-system level instabilities). The innovative devices are introduced for functionality and high heat load capabilities needed for shear dominated electronic cooling situations that arise in milli-meter scale operations, certain gravity-insensitive avionics-cooling and zero-gravity applications

A quasi one-dimensional method and results for steady annular/stratified shear and gravity driven condensing flows

This paper presents an effective quasi one-dimensional (1-D) computational simulation methodology for steady annular/stratified internal condensing flows of pure vapor. In-channel and in-tube flows are considered for a range of gravity component values in the direction of the flow. For these flows, three sets of results are presented and they are obtained from: (i) a full 2-D CFD based approach, (ii) the quasi-1D approach introduced here, and (iii) relevant experimental results for gravity driven condensing flows of FC-72. Besides demonstrating differences between shear and gravity driven annular flows, the paper also presents a map that distinguishes shear driven, gravity driven, and “mixed” driven flows within the non-dimensional parameter space that govern these duct flows. The paper also demonstrates that μm-scale hydraulic diameter ducts typically experience shear/pressure driven flows

Shear-driven annular flow-boiling in millimeter-scale channels: Direct numerical simulations for convective component of the overall heat transfer coefficient

Many contemporary high heat-flux cooling applications are facilitated by controlled operation of millimeter-scale flow-boilers that operate in the steady annular or steady-in-the-mean (with superposed large amplitude standing waves in the liquid film) annular regimes – with micrometer-scale liquid film thicknesses. That is, a thin evaporating liquid film flow covers the heated boiling-surface – with or without superposed micron/sub-micron-scale nucleate boiling regime. Therefore, to begin with, to characterize convective boiling component of experimentally measured values of heat transfer coefficient (HTC), it becomes important to fully characterize the underlying steady annular flows under the assumption of suppressed nucleation. For such steady cases, and liquid thickness values in the range of tens to hundreds of micrometers that are much smaller than the mm-scale hydraulic diameter of the ducts, this paper presents a direct numerical simulations (DNS) approach for laminar liquid and laminar vapor flows. Representative detailed steady solutions for annular flow-boiling of FC-72 in a horizontal channel (heated from below) are presented, the flow-physics is studied, and HTC values are correlated. Furthermore, a one-dimensional correlations-based design tool is developed and discussed, along with its future extensions for covering laminar liquid and turbulent vapor are annular flow realizations that may also occur in the aforementioned operations of flow-boiling

Sensitivity of shear-driven internal condensing flows to pressure fluctuations and its utilization for heat flux enhancements

The reported experimental results are for annular zones of fully condensing flows of pure FC-72 (perfluorohexane) vapor. The flow condenses on the bottom surface (316 stainless steel) of a horizontal, rectangular cross-section duct. The sides and top of the duct are made of clear plastic. The annular portion of the flow in the test-section is driven, under negligible to zero gravity effects along the flow direction, by pressure-difference and cooling conditions. Since the annular regime condensate motion is primarily driven by an effective interfacial shear stress, all such flows are termed shear-driven flows. The experimental system in which this condenser is used is able to control quasi-steady (termed quasi-steady) values of inlet mass flow rate, inlet (or exit) pressure, and wall cooling conditions. For the experimental results reported here, the mean (time-averaged) inlet mass flow rate, mean inlet pressure, and condensing-surface cooling conditions were held fixed at their quasi-steady values. Under these conditions, it was found that the imposition of small inlet pressure fluctuations (relative to the mean inlet pressure) induces significant mass flow rate fluctuations at the condenser inlet, and that there is a change in the very nature of the quasi-steady annular condensing flow regime. The resulting phenomena change the mean local heat flux values with significant (\u3e200%) enhancements. There are accompanying time-varying changes in the liquid–vapor configurations within the annular and the non-annular regimes. This changes the mean and fluctuation amplitude values (with induced harmonics) in the pressure at any interior location within the annular regime. It is shown here that the heat flux enhancement phenomenon is real and occurs regardless of the method of cooling for a suitable range of fluctuation frequencies and amplitudes. This paper experimentally investigates how the strength of this sensitivity varies with amplitude and frequency of pressure or mass flow rate fluctuations imposed at the inlet of the condenser. Associated theory and rudimentary experiments (not reported here) suggest that similar enhancement may be observed in annular flows which do not completely condense before the exit, provided that suitable arrangements at the condenser exit allow similar or equivalent liquid–vapor interfacial wave structures with the help of similar acoustic wave reflections in the vapor phase