collide style args keyword value ...
none args = none vss args = mix-ID file mix-ID = ID of mixture to use for group definitions file = filename that lists species with their VSS model parameters
relax value = constant or variable
collide none collide vss all ../data/air.vss collide vss species all.vss relax variable
Define what style of particle-particle collisions will be performed by SPARTA each timestep. If collisions are performed, particles are sorted into grid cells every timestep and the appropriate collision model is invoked on a per-grid-cell basis. Collisions alter the velocity of participating particles as well as their rotational and vibrational energies. The rotational and vibrational properties of each species are set in the file read by the species command.
The collision style determines how many pairs of particles are considered for collisions, the criteria for which collisions actually occurs, and the outcome of individual collision, which alters the velocities of the two particles. If chemistry is enabled, via the react command, particles involved in collisions may also change species, or a particle may be deleted, or a new particle created. The collide_modify command can also be used to alter aspects of how collisions are performed. For example, it can be used to turn on/off the tracking of vibrational energy and its exchange in collisions.
A mix-ID argument is specified for each collision style. It must contain all the species defined for use by the simulation, via the species command. The group definitions in the mixture assign one or more particle species to each group. These groupings are used to determine how pairs of particles are chosen to collide with each other, in the following manner.
Consider a cell with N particles and a mixture with M groups. Based on its species, each particle is assigned to one of the M groups. Each unique pair of groups is considered, including each group paired with itself. For each pair of groups a value Nattempt (see equation 11.3 in (Bird94)) is calcualted which is the number of collisions to attempt. This is a function of N1 and N2 (the number of particles in each group), the grid cell volume, and other parameters of the collision style.
For each collision attempt, a random pair of particles is selected, with one particle from each group. Whether the collision occurs or not is a function of the relative velocities of the two particles, their respectives species, and other parameters of the collision style; see equation 11.4 in (Bird94).
The none style means that no particle-particle collisions will be performed, i.e. the simulation models free-molecular flow.
The vss style implements the Variable Soft Sphere (VSS) model for collisions. As discussed below, with appropriate parameter choices, it can also compute the Variable Hard Sphere (VHS) model and the Hard Sphere (HS) model. See chapters 2.6 and 2.7 in (Bird94) for details.
In DSMC, the variable-soft-sphere (VSS) interaction of Koura and Matsumoto and the variable-hard-sphere (VHS) interaction of Bird are used to approximate molecular interactions. Both models yield transport properties proportional to a power (omega) of the gas temperature. This temperature dependence of the transport properties is similar to the Inverse Power Law model (IPL) for which Chapman-Enskog theory provides closed form solutions for the transport properties.
Both VSS and VHS interactions define parameters diam = molecular diameter, which is a function of the molecular speed, and alpha = angular-scattering parameter, which relates the scattering angle to the impact parameter. Setting alpha = 1 produces isotropic (hard sphere) interactions, which converts the VSS model into a VHS model.
The file argument is for a collision data file which contains definitions of VSS model parameters for some number of species. Example files are included in the data directory of the SPARTA distribution, with a "*.css" suffix. The file can contain species not used by this simulation; they will simply be ignored. All species currently defined by the simulation must be present in the file.
The format of the file depends of the setting of the optional relax keyword, as explained below. Comments or blank lines are allowed in the file. Comment lines start with a "#" character. All other lines must have the following format with parameters separated by whitespace.
If the relax keyword is specified as constant, which is the default, then each line has 4 parameters following the species ID:
species-ID diam omega tref alpha
The species-ID is a string that will be matched to one of the species defined by the simulation, via the species command. The meaning of additional properties is as follows:
The methodolgy for deriving VSS/VHS parameters from these properties is explained in Chapter 3 of (Bird94). Parameter values for the most common gases are given in Appendix A of the same book. These values are based on the first-order approximation of the Chapman-Enskog theory. Infinite-order parameters are described in (Gallis04).
In the constant case rotational and vibrational relaxation during a collision is treated in the same constant manner for every collision, using the rotational and vibrational relaxation numbers from the species data file, as read by the species command.
If the relax keyword is specified as variable, then each line has 8 parameters following the species ID:
species-ID diam omega tref alpha Zrotinf T* C1 C2
The first 4 parameters are the same as above. Parameters 5 and 6 affect rotational relaxation; parameters 7 and 8 affect vibrational relaxation. In this case the rotational and vibrational relaxation during a collision is treated as a variable and is computed for each collision. This calculation is only performed for polyatomic species, using equations A5 and A6 on pages 413 and 414 in (Bird94). Zrotinf and T* are parameters in the numerator and denominator of eq A5. C1 and C2 are in eq A6. The units of these parameters is as follows:
Note that a collision data file with the 4 extra relaxation parameters (per species) can be used when the relax keyword is specified as constant. In that case, the extra parameters are simply ignored.
collide_modify, mixture, react
Style = none is the default (no collisions). If the vss style is specified, then relax = constant is the default.
(Koura92) K. Koura and H. Matsumoto, "Variable soft sphere molecular model for air species," Phys Fluids A, 4, 1083 (1992).
(Bird94) G. A. Bird, Molecular Gas Dynamics and the Direct Simulation of Gas Flows, Clarendon Press, Oxford (1994).
(Gallis04) M. A. Gallis, J. R. Torczynski, and D. J. Rader, "Molecular gas dynamics observations of Chapman-Enskog behavior and departures therefrom in nonequilibrium gases," Phys Rev E, 69, 042201 (2004).