Aerosol nucleation and growth in a laminar diffusion chamber

 

This tutorial case considers the problem of aerosol formation via nucleation and subsequent growth via condensation in a laminar flow diffusion chamber (LFDC). A simple cylindrical pipe geometry is considered into which a comparably hotvapor mixture flows. The walls of the pipe are kept at a lower temperature, thereby inducing a cooling of the vapor mixture, causing it to become super saturated further downstream and inducing the formation of nano-scale aerosol droplets via nucleation. Further into the pipe geometry these droplets growin size as more and more of the remaining vapor condenses onto the droplets that were formed. We consider flow of DBP in a LFDC and treat the solution as independent of the circumferential direction. This allows to simulate thenucleation problem in two computational dimensions, i.e., the radial coordinateand the longitudinal coordinate. This problem has been considered by various authors, employing a low-order moment approach for the aerosol size distribution. The use of the AeroSolved code allows to extend this study and consider a complete size distribution with a number of sections. In Figure 1 we sketched the geometry that will be considered and the boundary conditions.

lfdc-fig1

 

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 a directory ‘0.org’, specify physical properties in the dictionary files in the ‘constant’ directory and specify aspects of the numerical method in the dictionary files in the 'system’ directory. The reader may 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 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 are specified in detail. These properties relate to clearly identifiable classes of physical quantities and are grouped ac- cordingly. 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 file ‘controlDict.foam’ is created from controlDict in order to create an interface for later postprocessing with ParaView.

In order to simulate the transient behavior properly, a suitably small maximal time step should be specified and/or a suitably small diffusivity. 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 computing. The actual execution of a case then can be started by issuing 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 computing is used as basis to reconstruct the solution in thetotal 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 of course also exploit other methods of post-processing to study the results of a simulation. This aspect will not be elaborated on here. After running the case of the flow of a hot vapor mixture, a number of properties is 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.

 

lfdc-fig2

 

To illustrate some of the capabilities of the AeroSolved code we consider a few physical quantities as found on the selected simulation grid. The flow inside the LFDC quickly develops and yields a well-defined temperature front at which the high temperature flow entering from the left changes into a much lower temperature as is present in the rest of the domain. A few snapshots illustrating the early development of the temperature field are shown in Figure 2. This localized temperature front is crucial in relation to the rapid cooling of the hot vapor mixture and the formation of the liquid aerosol droplet content.

lfdc-fig3

 

In Figure 3 the early development of the liquid DBP aerosol droplets is shown. After a short period of about 0.6 s, during which the temperature profile develops, we observe the formation of the first aerosol droplets near this temperature front. Downstream of this region the generated aerosol droplets grows in size and spread inside the domain, mainly downstream of the initial nucleation region. During the development of the DBP aerosol droplets, also the sizes of the droplets grow considerably due to condensation of DBP vapor onto the already formed droplets.