This tutorial case considers the formation of an aerosol by strongly cooling a supersaturated mixture of species that are initially in their vapor phase. The well-known flow in a lid-driven cavity is used as a generic example, allowing to study aerosol nucleation and evolution via condensation and evaporation in a spatially in a homogeneous setting. We adopt the standard geometry as shown schematically in Figure 1. An aerosol formation is studied in the flow that develops in a square domain with top wall moving with a constant horizontal velocity U to the right and stationary side and bottom walls.
Schematic sketch of the driven cavity geometry.
A solid wall on top of the cavity moves a constant velocity U to the right thereby driving the flow in the cavity of which the other walls are stationary.
The case considered here starts from an initially hot mixture of vapors from various species. These are at rest at t = 0 in a square cavity with solid no-slip walls kept at a lower temperature. In the course, of time the cold temperature of the walls is having effects also deeper into the domain. This drives a nucleation process by which small liquid aerosol droplets are formed. The penetration of colder fluid swept into the inner domain of the cavity is characterized by a striking vortical structure, which also imposes its pattern on the aerosol size distribution as a function of space and time. An intriguing non-uniform pattern emerges with narrow bands of aerosol formed by rapid cooling of the vapors. As time passes, this develops further into a strongly mixed and highly complex pattern of liquid aerosol droplets and remaining regions of vapor. A graphical illustration is presented in Figure 2. The simulation of the problem employs the AeroSolved code, closely adopting the framework of the OpenFOAM platform. The user is required to provide an initial condition in the directory ‘0.org’ of the case, specify physical properties in the dictionary files in the ‘constant’ directory and specify aspects of the numerical method in the dictionary files in a ‘system’ directory. The reader may readily observe the type of quantities and the format of their specification in the Case. Files provided:
Illustration of the magnitude of the fluid velocity (u2 + v2)1/2 at different times t= 0.5, 1, 1.5 in (a), (b), and (c), respectively.
Red refers to a magnitude equal to 1 while dark blue is linked to zero velocity magnitude.
To facilitate managing, setting up, running and evaluating a case, four shell scripts are provided. With ‘clean.sh’ one can restore a default setting, creating a similar point of reference for the simulations. Using ‘prep.sh’ the user can issue for a number of required preparations to be made, such as a computational grid and the decomposition of the problem for later parallel processing. The actual execution of a case can be thereafter started by executing the ‘run.sh’ script. Finally, gathering data in a manner suitable for further post-processing by the user is made easy using the ‘post.sh’
Figure 3: Illustration of the temperature T in the cavity at different times t=0.5, 1, 1.5 in (a), (b), and (c), respectively.
Red refers to a magnitude equal to 368.8 K while dark blue is linked to 273 K.
After running the case of aerosol formation in a cooled lid-driven cavity, a number of physical properties are available for further study. Before the actual simulation results are investigated it is worth checking the log files and make sure that the solution process has been executed properly. To illustrate some of the capabilities of the AeroSolved code we consider a few physical quantities as found on the selected simulation grid of 128 × 128 grid cells (cf. the blockMeshDict file in the constant/polyMesh directory. In Figure 3, the initial evolution of the temperature field is presented. One clearly discerns a structure similar to the
Figure 4: Evolution of the M0 section in the size distribution of the aerosol at different times t=0.8, 1.1, 1.5 (s) in (a), (b), and (c) respectively.
Red refers to a magnitude equal to 3.7 1011 m-3 while dark blue is linked to 0 m-3.
Figure 5: Evolution of the M4 section in the size distribution of the aerosol at different times t=1.1, 1.5, 2 (s) in (a), (b), and (c) respectively.
Red refers to a magnitude equal to 1.16 1010 m-3 while dark blue is linked to 0 m-3.