Numerical Simulations of Rarefied Gas Flow with ''Direct Simulation Monte Carlo'' Method

In this chapter, various types of aerospace and physical two-dimensional applications will be studied in the presence of rarefied gases. For this purpose the DSMC method has been applied to several cases of interest that will be discussed in detail in the next sections. The program used to study two-dimensional flows is the 2D version of DSMC Bird’s program [10], written in Fortran programming language. The avaiable source-code is called “DS2.f90” and it is possible to carry out only two-dimensional studies. The source code was compiled using the Intel-Fortran compiler and has also a complete graphical interface through which it is possible to select the various cases to be studied and post-process the results.
As the 0D and 1D version, the Fortran code consists of a main body called “main program” and a series of subroutines, which are called in a time loop over the flow time by the main program itself.

Specifically, the various subroutines contain exactly the same steps of the DSMC method described before. Also in this case there are some particular subroutines that specify a molecular set of data for a specific type of gas and are designed to give the possibility to study gas flows already set and ready for use. Some of these include also gas mixtures, with the possibility of chemical reactions, dissociations and further internal degrees of freedom (vibrational, rotational, and electronic).

The program reads in input a “.dat” file which must contain all the data needed for the sutdy of a generic 2D flow. This file, which will be described in detail in the appendix, must be completely set manually by the user or using the program’s graphical interface. The latter gives also the possibility to import and generate complex geometry with only straight lines and arc curves. The outputs resulting from the simulation contains all the information (macroscopic properties) within the domain and on the body surfaces, both for the total gas and for each individual species (if there is a mixture).

If the flow is steady-state, there is a single file containing time-mediated informations; while if the flow is unsteady, the program will print a successive set of files, each of which represents a temporal instant mediated in the samples (ensemble average). It is to point out that all (or almost) the simulations that will be made in this work will be stationary.

Examining two-dimensional cases gives, from a physical point of view, direct results of the main effects of low-density phenomena. Also in this case, from the point of view of the geometry generation, it is very simple to modify the input file to implement different scenarios, so that it is possible to examine multiple cases and compare the proposed DSMC model from Bird [10] with a Navier-Stokes continuum code.

In this sense, a series of tests were carried out to study some interesting geometry with the optimal choise of the code parameters resulting from the awareness of the studies conducted in the previous 1D applications chapter. The two-dimensional cases that have been chosen are the following:
* The circular cylinder;
* The ESA Vega launcher.

The flow past a circular cylinder has been chosen for its “simplicity” and the possibility to compare the results with the literature and a continuum Navier-Stoke solver, in which the cylinder mesh grid generation is very simple. It is also possible to highlight the effects of the rarefaction in a direct way, underlining the limit of the continuous method at high Knudsen numbers. The ESA Vega launcher, instead, was chosen to emphasize the ability of the method to deal with a complex geometry, which is very difficult from the point of view of continuum methods. In fact, the geometry was imported only using the couple (x; y) of the Vega surface points, without any grid generation.