How can we model the effects of air bubble condensation on its trajectory?
Vapor bubble condensation in sub-cooled boiling flows is an important subject of study in the nuclear engineering field for optimizing design and safety of the nuclear system. Sub-cooled boiling flow consists of complicated dynamic phenomena of vapor bubble-water interaction due to the boiling, condensation, break-up and coalescence of the bubble. Understanding the behavior of the vapor bubble is important because it has a large effect on the heat transfer characteristics of the nuclear system.
In the past, many researchers attempted to analyze the behavior of the bubble experimentally, and it has not been possible to get the complete information about the bubble behavior. This is in part due to the fact that the interface between the liquid and vapor phases is very difficult to analyze since it has a complex shape and varying area. Hence, the recent approach is to model and simulate the behavior of vapor bubbles numerically, where the parameters of interest usually are: bubble size, bubble shape, rising trajectory, and bubble velocity. In other words, numerical approach has become handy in completing the understanding of such condensing vapor bubble and can therefore be used as a complement to laboratory experiments.
Bubble condensation occurs by conjugate heat transfer mechanism due to the temperature difference between the vapor and liquid phases. The CFD-ACE+ VOF module can simulate the rising vapor bubble. However, in order to simulate the bubble condensation, source terms need to be added through user subroutines. The mass transfer between the phases during bubble condensation can be simulated by adding mass source terms (which may depend on other variables) to the pressure correction equation (similarly, heat source/sink can be added to the enthalpy equation and an additional force can be added to the momentum equation).
Even though vapor bubble condensation involves heat and mass transfer through the interface, in this user tip we demonstrate the behavior of single condensing vapor bubble by accounting for the mass source term only.
A 2D simulation of a liquid/vapor system representing a rising water vapor bubble in a column of liquid water (see figure 1) is chosen to demonstrate the implementation of the bubble condensation phenomenon.
Figure 1. Rising bubble in liquid water column.
Note that the mesh was created using the Structured Block Coarsening feature of CFD-GEOM, allowing reducing the total number of cells while keeping the bubble interface well resolved by maintaining a good mesh density as the bubble rises and becomes smaller.
In this example, the vapor phase is treated as the ‘primary’ fluid of the free surface module, and the liquid phase as the ‘secondary’ fluid. The mass source is specified to volume conditions of the computational domain as “Mass Source (Primary Fluid)” and “Mass Source (Secondary Fluid)”, as shown in Figure 2. This implementation requires the implementation of the usource user subroutine. The sources specified by the user inside usource are then passed to the solver at the beginning of each time step.
Figure 2. Mass source specification in CFD-ACE-GUI for VOF fluids.
Please find herewith the sample case files used in this example. You may use this tip and the accompanying files as a starting point for CFD modeling of bubble condensation. For demonstration purpose, in this tip it is assumed that the mass of the primary fluid (vapor phase) is negligible compared to the mass of the secondary fluid (liquid phase), and hence a mass source term is added only to the primary fluid.
Also, to model condensation, we assume a constant condensation rate (kg/s), from which we calculate the mass to be condensed every time step. This mass needs to be subtracted from the vapor phase, and here we choose an algorithm that distributes the total source term over all the cells containing vapor phase. Each cell will be given a mass source term proportional to the amount of vapor mass in that cell at the beginning of each time-step, thus preventing removing more mass than was present.
The user may develop more sophisticated functions to identify cells where the bubble interface may lie and then apply the source term appropriately to those cells only. Further, the user can develop subroutines to account for the more complex heat transfer phenomenon through the bubble interface as well.
Figure 3. Vapor bubble rise without (left) and with (right) condensation.
Note that condensation can presently be modeled only through user subroutines.
Note: tested with V2010.0
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2003/12%Last update: 2011-04-21 17:47
Author: ESI-CFD Support Team
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