Multispecies aerosol formation in a lid-driven cavity

 

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.

cavity_fig1

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:

  • 0.org: the initial vapor (Y) and liquid (Z) mass fractions for air and DBP are specified as well as the sections (M) in which the aerosol size-distribution is approximated. Similarly, pressure, temperature and fluid velocity components are initialized and boundary conditions specified.
  • constant: a large number of physical properties of the flow and species contained in the cavity is specified in detail. These properties relate to clearly identifiable classes of physical quantities and are grouped accordingly. The format for their specifications is directly following OpenFOAM conventions. Finally, details of the computational grid are contained in the directory polyMesh.
  • system: numerical parameters that govern the discretization and methods of solution are specified in a number of files. In addition, a linked ‘controlDict.foam’ file is created from controlDict in order to create an interface for later postprocessing with ParaView.

 

cavity_fig2

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’ script in which the decomposed representation for parallel processing is used as a basis to reconstruct the solution in the total domain, after which it could be sampled in specific ways for later evaluation. In the tutorial we use only ‘paraview’ for simple post-processing - the user may also exploit other methods of post-processing to study the results of a simulation. This aspect will not be elaborated on here.

 

cavity_fig3

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 vortical structure of the velocity magnitude in Figure 2. Cold fluid is initially swept into the domain and in later stages is seen to occupy much of the inner domain of the cavity. The aerosol that forms is characterized by a wide range of scales. One may readily infer the pattern of the sectional size distribution by visualizing the different sections. As an example, in Figure 4 we show the M0 section containing the smallest droplets that are formed, at different times. Figure 5 similarly shows the evolution of M4. We observe a clear imprint of the vortical flow structures on the locations at which aerosol droplets nucleate and grow via condensation. Moreover, the larger droplets first appear at a later moment than the smaller droplets, which is directly recognized in the simulation results. This illustrates some of the capabilities of the AeroSolved code in approximating the formation of an aerosol in a cooled lid-driven cavity.

cavity_fig4

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.


cavity_fig5

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.