README.md

SPARTA

The Stochastic PArallel Rarefied-gas Time-accurate Analyzer (SPARTA) software library has been used to get the drag coefficient of the satellite given different atmospheric conditions. SPARTA is a Direct Simulation Monte Carlo (DSMC) simulator, suited for rarefied flow simulations.

Installation

The SPARTA documentation can be accessed here.

Moreover, it can be installed and compiled by running the following commands:

git clone https://github.com/sparta/sparta
cd sparta
mkdir build
cd build
module load openmpi
cmake -LH ../cmake
make

The spa_ compiled file will then be found in build/src.

This folder can be added to path using the following command:

echo "export PATH=\$PATH:/path/to/sparta/build/src" >> ~/.bash_profile

Satellite configurations

Different CubeSat configurations have been modeled, each with different solar panels configurations.

The naming scheme has been taken as CS ABCD:

• CS: CubeSat
• A: Solar panels above and below the main body
• B: Extension of the solar panels in A (straight behind)
• C: Solar panels on the main body
• D: Extension of the solar panels in C (behind, at a 15deg angle from the centerline)

The following figure illustrates this naming scheme:

The number of solar panels (of size 300x100mm) has been counted for one side of the satellite.

As an example, the 3U deployable solar array from EnduroSat could be used. Including PCB, these have a mass of 0.27 kg and a thickness of 1.75 mm. At EOL, they have a power efficiency of at least 29%.

Finally, the area of the solar panels of each satellite has been computed across three different planes. This later simplifies solar power calculations. These x, y, and z planes are defined as in the figure below:

Satellite name	# of solar panels (x2)	Reference length [m]	Reference surface area [m2]	SA x-area [m2]	SA y-area [m2]	SA z-area [m2]	Illustration
CS 0020	2	0.3	0.01	0	0.042426	0.042426
CS 1020	4	0.341421	0.0104	0	0.102426	0.042426
CS 0021	4	0.589778	0.041058285	0.031058	0.083343	0.083343
CS 2020	6	0.541421	0.0108	0	0.162426	0.042426
CS 1021	6	0.589778	0.041458285	0.031058	0.143343	0.083343
CS 3020	8	0.741421	0.0112	0	0.222426	0.042426
CS 2021	8	0.589778	0.041858285	0.031058	0.203343	0.083343
CS 2120	10	0.6	0.0108	0	0.282426	0.042426
CS 3021	10	0.741421	0.042258285	0.031058	0.263343	0.083343

Atmospheric conditions

The atmospheric conditions in which the simulation has been made have been varied, as to gather different drag values, for interpolation later on. The geopotential altitudes have been varied between 85 km and 150 km.

This leads to the following parameters:

Altitude [km]	Velocity [m/s]	Density [kg/m3]	Dynamic pressure [Pa]	Temperature [K]	Pressure [Pa]	Mixture [mol/mol]
85	3510.90	1.27915E-06 (σ=5.54578E-07)	7.88373E+00	140.264 (σ=10.3875)	3.47635E-02 (σ=1.65223E-02)	95.298% CO2, 1.909% N2, 1.960% Ar, 0.422% CO, 0.250% O, 0.162% O2 (σ=1.199% CO2, 0.293% N2, 0.303% Ar, 0.376% CO, 0.232% O, 0.039% O2)
115	3495.84	2.21588E-08 (σ=1.45383E-08)	1.35400E-01	114.185 (σ=9.53312)	4.84327E-04 (σ=3.18527E-04)	87.489% CO2, 4.340% N2, 4.041% Ar, 2.341% CO, 1.409% O, 0.380% O2 (σ=6.234% CO2, 1.968% N2, 1.308% Ar, 1.931% CO, 1.018% O, 0.180% O2)
150	3475.51	1.94535e-10 (σ=8.33132e-11)	1.17491E-03	172.404 (σ=23.5187)	7.27188E-06 (σ=3.21932E-06)	65.826% CO2, 11.923% N2, 4.910% Ar, 7.796% CO, 8.533% O, 1.012% O2 (σ=13.260% CO2, 4.501% N2, 0.592% Ar, 3.837% CO, 4.956% O, 0.198% O2)

These values have been gathered by running the run_atmo_study in feasible_altitudes.py. As can be seen in the code, they are atmospheric values that are averaged for a satellite that flies in a circular orbit inclined at 45deg for 2 Martian years (1300 days).

Commands

This section compiles the commands that have been used both as SPARTA inputs, and to run SPARTA and convert results.

Run SPARTA

Once SPARTA has been compiled, and the path to the spa_ file added to path, the following commands can be used.

To run SPARTA on a given input script (for instance, satellite input script in.sat), the following command can be used:

spa_ < in.sat

SPARTA can be run on different CPU cores in parallel, if it was compiled with MPI. Note that, doing so, the computer may run out of memory faster. The following command can be used for this:

mpirun -np 16 spa_ < in.sat

When all of the input files have been created, they can all be run by using the following command while in the inputs folder:

bash run_all.sh

Analyse results

In the input file, pictures can be generated at given time steps (with file extension .ppm). With ImageMagick installed, the following command can be used to transform them to an animated .gif file:

convert image*ppm movie.gif

Most CAD softwares such as CATIA generate a binary STL file. To convert it to an ASCII STL file, the following command can be used (with stl_B2A.py from the tools folder):

python2 stl_B2A.py model.stl

Additionally, the -rs option can be added to rescale the binary STL from mm to m when translating it to ASCII:

python2 stl_B2A.py model.stl -rs

Finally, to convert an ASCII STL file to a surface that SPARTA understands, the following command can be used (with stl2surf.py from the tools folder):

python2 stl2surf.py model_ascii.stl data.model

The SPARTA data files describing the geometry can be converted to ParaView by using the following command (from the paraview/surf folder):

pvpython ../../tools/surf2paraview.py ../../setup/data/data.CS_XXXX CS_XXXX

Similarly, values for the particles in the grid can be converted to ParaView by using the command below (from the paraview/grid folder):

pvpython ../../tools/grid2paraview_original.py def/grid.CS_XXX_YYkm_I vals_CS_XXX_YYkm_I -r ../../setup/results_sparta/CS_XXX/vals_YYkm_I.*.dat 

In the command above, grid.CS_XXXX_._YYkm_I is a file describing the grid geometry for satellite CS_XXXX, at an altitude of YY km, at a grid refinement level I.

These two last commands can be run automatically by running bash paraview_convert.sh in the paraview folder.

SPARTA commands

The list of commands below is part of the inputs that has been used to run the SPARTA simulation of the CS_0021 satellite at 85km. The complete list of commands used can directly be seen in the in.CS_0021_85km input file. This file contain a more detailed description of the mixture, the complete list of computes, fixes, and dumps that have been setup, and all of the refinements applied.

The documentation has been adapted from the one that is distributed with SPARTA.

• seed 12345: the random number generator seed is 12345.
• dimension 3: the simulation is in 3 dimensions.
• global gridcut 1e-3 comm/sort yes surfmax 10000 splitmax 100 nrho 1.7717e+19 fnum 5.5228e+12 vstream -3510.9000 0.0 0.0 temp 140.2640:
  • gridcut: acquire ghost cells up to 1e-3 meters away.
  • comm/sort: sort messages by PID.
  • surfmax: 10000 surface elements are allowed by grid cell.
  • nrho: the free stream has a number density of 1.7717e+19 particles per cubic meter.
  • fnum: the ratio of physical particles (nrho) to simulation particles is of 5.5228e+12. A bigger values thus means less simulated particles.
  • vtream: the free stream has a velocity of -3510.9 m/s in the x direction, and nothing in the other directions.
  • temp: the free stream has a temperature of 140.264 K.
• boundary o o o: the particles can freely exit the simulation volume.
• create_box -0.5500 0.5500 -0.3500 0.3500 -0.3500 0.3500: the simulation volume extends from +/-0.55 meters in the x direction, and from +/-0.35 meters in the y and z directions.
• create_grid 66 42 42: the grid cuts the x length in 66 elements, and the y and z lengths in 42.
• balance_grid rcb cell: a recursive coordinate bisectioning algorithm is used to assign the spatially-compact clumps of grid cells to processors.
• species ../atmo.species CO2 N2 Ar CO O O2: the atmo species consists in CO2 N2 Ar CO O O2 and have properties as defined in the atmo.species file
• mixture atmo CO2 frac 0.9530: the CO2 species is present at a molecular fraction of 95.3% in the atmo flow.
• read_surf ../data/data.CS_0021 trans 0.1500 0 0: read the surface of the CS_0021 satellite that is in the data.CS_0021 file, and translate this surface in the simulation volume by 0.15 meters in the x direction only.
• surf_collide 1 diffuse 293.15 0.9979: the particles collide with the surface in a diffuse way, with an accommodation coefficient of 0.9979. The surface has a temperature of 293.15 K. This collision model has the id 1.
• surf_modify all collide 1: apply the collision model with id 1 to all the surfaces in the simulation.
• region sat_front block 0.1000 0.3000 -0.1 0.1 -0.1 0.1: define a region with if sat_front, that goes from 0.1 meters to 0.3 meters in the x direction, and extend in +/-0.1 meters in the y and z directions.
• fix in emit/face atmo xhi zhi zlo yhi ylo: create a fix with id in that emits the flow atmo from all of the faces of the simulation volume (xhi zhi zlo yhi ylo) excepts the face behind the satellite in the x direction. The flow is also emitted from the site because, while it has globally only a x velocity, its randomness still makes particles enter from other directions.
• timestep 3.5603e-06: the simulation time step is of 3.5603e-06 seconds.
• compute forces surf all all fx fy fz: create a compute with id forces that measures the force in each direction (fx fy fz) on all surfaces.
• fix avg ave/surf all 5 15 75 c_forces[*] ave running: cerate a fix on the forces compute (c_forces), taking all of its columns ([*]), and computing a running average per over the entire surface (ave/surf). This running average is computed every 75 epochs, the input values are used 15 times to compute it, and the values are taken every 5 epochs.
• compute sum_force reduce sum f_avg[*]: create a fix with id sum_force on the f_avg[*] fix to reduce the arrays of values to a vector by summing (sum) their values on all faces.
• compute knudsen lambda/grid f_nrho_avg f_T_avg CO2 kall: create a fix with id knudsen that results in two columns (because kall is used): the first one with the mean free path per cell, the second one with the Knudsen number relative to each cell size. This compute needs as inputs:
  • f_nrho_avg: a fix with the average number density per cell.
  • f_T_avg: a fix with the average temperature per cell.
  • CO2: the name of a species that will be used to get reference properties.
• stats 75: print stats in the console every 75 epochs. Warning, this must coincide with the time at which relevant fixes and computes are made.
• stats_style step cpu np nscoll nexit c_sum_force[*] c_avg_ppc: change what is printed in the stats:
  • step: last epoch that has been run.
  • cpu: CPU time since the start of the run.
  • np: number of simulated particles.
  • nscoll: number of collision computed.
  • nexit: number of particles exiting the simulation volume.
  • c_sum_force[*]: average force in the three directions.
  • c_avg_ppc: average number of particles per cell.
• dump 0 grid all 150 ../results_sparta/CS_0021/vals_85km_0.*.dat id f_n_avg f_nrho_avg f_massrho_avg f_u_avg f_T_avg c_knudsen[*]: create a dump with id 0 that will save per-grid values every 150 epochs in the vals_85km_0.*.dat file (with * being the epoch number). The values saved are the grid cell id, as well as a series of fixes and computes.
• write_grid ../results_sparta/CS_0021/grid_85km_0.dat: save the current grid geometry in the grid_85km_0.dat file.
• run 2025: run the simulation for 2025 epochs. Warning, this must be a multiple of the stats frequency (here, 75).
• timestep 3.7037e-06: change the time step to a lower value of 3.7037e-06 seconds.
• adapt_grid all refine coarsen value c_knudsen[2] 5 20 combine min thresh less more region sat_front one: refine the grid by a factor of 2 where the grid-Knudsen number compute by c_knudsen[2] gets below 5. Coarsen previously refined cells if their Knudsen number is above 20. Only refine in the region with id sat_front when one of the grid points is in the region.
• scale_particles all 4: scales all of the present particles by a factor of 4.
• global fnum 1.3807e+12: reduce the fraction of real particles to simulated particles to 1.3807e+12 to increase the number of simulated particles.
• undump 0: remove the dump with id 0.
• dump 1 grid all 150 ../results_sparta/CS_0021/vals_85km_1.*.dat id f_n_avg f_nrho_avg f_massrho_avg f_u_avg f_T_avg c_knudsen[*] and write_grid ../results_sparta/CS_0021/grid_85km_1.dat: make a new dump and save the refined grid.
• run 450: run the simulation for 450 more epochs.

Input files

The script comp_inputs.py has been used to generate the relevant input files for the SPARTA simulations.

These input files have been made for each satellite, for each of the satellite configurations, as specified at the top of comp_inputs.py.

These can be found in the inputs, and are of the format in.*.

The input files make SPARTA start with a very coarse grid, and progressively refine it based on the Knudsen numbers that are computed. At each grid refinement, the number of simulated particles is increased accordingly, and so is the time step.

Note that all SPARTA simulations assume that the satellite accommodation coefficient is based on the adsorption of atomic oxygen (as in this paper).

Results

Running SPARTA for the different altitudes, the force in each direction has been saved in .dat files in the results folder.

The satellites that do not have solar panels extended in their back have not been run, since they are deemed too unstable. These are the followings: CS 0020, CS 1020, CS 2020, CS 3020.

Then, analyse_results.py has been used to compute the drag force from all of the simulations.

At each altitude, the dynamic pressure (in Pa) has been computed as follows:

For each altitude, the Mach number has also been computed, using the formula below with molecular values of CO2.

The compression ratio between the free stream and the end of the atmosphere inlet is also reported in the table below.

For each satellite configuration, the reference surface S has been taken as the frontal area of the CubeSat. Values for these reference surface area can be found in the table of this section.

The drag coefficients have then been computed at each altitude by using the following equation:

Later on, when using these drag coefficients, the same reference surface must be used.

This leads to the drag coefficients of the table below, with the Knudsen numbers included as well:

Satellite name	Altitude [km]	Knudsen number [-]	Dynamic pressure [Pa]	Mach number [-]	Compression ratio [-]	Drag [N]	Drag coefficient [-]
CS 0021	85	1.96934E-01	7.8837E+00	18.9145	37.82965	4.13356e-01	1.277012
CS 0021	115	1.10556E+01	1.3540E-01	20.8736	50.49326	1.00289e-02	1.803986
CS 0021	150	1.17386E+03	1.1749E-03	16.8886	60.37834	8.03958e-05	1.666586
CS 1021	85	1.96934E-01	7.8837E+00	18.9145	35.10988	4.80367E-01	1.469716
CS 1021	115	1.10556E+01	1.3540E-01	20.8736	50.17104	1.06509e-02	1.897386
CS 1021	150	1.17386E+03	1.1749E-03	16.8886	60.29815	8.57891e-05	1.761229
CS 2021	85	1.96934E-01	7.8837E+00	18.9145	35.27233	5.68135E-01	1.721637
CS 2021	115	1.10556E+01	1.3540E-01	20.8736	49.77842	1.13702e-02	2.006168
CS 2021	150	1.17386E+03	1.1749E-03	16.8886	59.51885	9.20775e-05	1.872265
CS 2120	85	1.93579E-01	7.8837E+00	18.9145	36.17590	4.91818E-01	5.776334
CS 2120	115	1.08673E+01	1.3540E-01	20.8736	50.10605	5.83676E-03	3.991432
CS 2120	150	1.15386E+03	1.1749E-03	16.8886	58.88298	5.32386E-05	4.195638
CS 3021	85	1.56655E-01	7.8837E+00	18.9145	42.28136	6.52884E-01	1.959728
CS 3021	115	8.79440E+00	1.3540E-01	20.8736	58.14033	1.22516E-02	2.141222
CS 3021	150	9.33769E+02	1.1749E-03	16.8886	64.84591	9.96816E-05	2.007698