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

1.2. Application highlights
1.2 Application highlights
Spacecraft re-entry into planetary atmospheres, the function of thrusters used on spacecraft to adjust 
orbits, and the behavior of outgassed plumes are all important problems in rarefied atmospheric 
gas dynamics. In the field of materials processing, a variety of vapor-phase processing and plasma-
etch applications are used to produce thin films. In both atmospheric dynamics and materials 
processing, the densities of the gases are quite low. However, in the relatively new development 
of microsystems, such as micro electro-mechanical systems (MEMS), gases flow in micron-sized 
channels are at relatively high densities. Each of these distinct applications of high-Knudsen-
number flows is now of practical scientific and engineering importance.
This section will highligth a number of applicantions that have been successfully undertaken 
using a NASA’s DSMC software. The examples that will be presented are only for demonstration 
purposes of the capabilities and possible fields of application of the DSMC method. For further 
details on any of these investigations it is necessary to refer to the associated references.
Martian Atmosphere entry vehicle
With the development of aerospace technology and understanding the environments of Mars at-
mosphere, the success probability of Mars exploration mission significantly grows in 21
st 
century. 
Martian atmosphere mainly composed of 95:7% CO
2
, 2:7% N
2
, and 1:6% Ar is quite different from 
Earth’s. The density is only 1:0% of Earth’s atmosphere and the temperature is lower than Earth’s. 
The atmosphere and climates in Mars vary severely and quasi-randomly with Mars geographic po-
sition and seasons, which makes the atmosphere parameters having evident scatter characteristic. 
As a result, these uncertainties of atmosphere parameter do not be neglected in entry vehicles aero-
dynamics computations in virtue of its interdependency with the trajectory design. An attempt 
has been made to analyze impact of Martian atmosphere parameter uncertainties on entry vehicle 
aerodynamics for hypersonic rarefied conditions with a DSMC code. Fig. 1.1 shows the pressure 
contours and distribution on the surface of the entry vehicle.
Figure 1.1: Pressure contours and distribution on the surface of a entry vehicle (of the Martian
Atmosphere) at a certain angle of attack. [18]
Matteo Cimini 3
1.2. Application highlights
Shuttle plume loads on a space station
The first example that is reported is that of the simulation of plume flowfields generated by the
Space Shuttle and the resultant impingement loads on a space station. In this case a combined
CFD / DSMC method is used. The analysis of such rendezvous and docking maneuvers is tipically
done with an engineering model that computes impingement loads based on an undisturbed plume
flowfield prediction. DSMC analysis was used to refine the plume flowfield and impingement pre-
dictions of these models. As such, the first task was to use the DSMC methodology to compute the
associated flowfields for the various RCS thruster combinations that are used during docking. In
the analysis, traditional computational fluid dynamics is used to compute the near filed continuum
portion of the flowfield. Then DSMC is used to compute the remainder of the flowfield. Fig. 1.2
shows the centerline density distribution as three of the RCS engines fire. This analysis revealed the
relatively strong interaction region between the nose and the tail jets which had not been previously
accounted for in the original plume models used in the engineering analysis.
The next step was to compute the aerodynamic loads generated by the RCS plumes on a space
station geometry. The complexity of the geometry, combined with the need to couple into the so-
lution one or more plume flowfields, provides an excellent example of the capabilities of the DSMC
method. The resultant pressure distribution for one such case is shown in Fig. 1.3.
Figure 1.2: Shuttle Norm-Z plume flowfield computed using a combined CFD/DSMC ap-
proach. [22]
Matteo Cimini 4
1.2. Application highlights
Figure 1.3: Predicted surface pressure on a space station from Shuttle Norm-Z jets at 5 m 
from docking. [22]
High altitude X-38 aerodynamics
The aerodynamic characteristics of a vehicle like the Space Shuttle change significantly during re-
entry due to the transitioning of the flow from the free molecular limit into the continuum regime. 
These regime will be clarified better in the next chapter. This was invistigated in detail for the 
Space Shuttle by Rault [32] using a commercial code. Such effects need to be accurately quantified 
because of their impact on the design of the reentry trajectory. The X-38 represents NASA’s latest 
interest in a manned re-entry vehicle. It is being designed to serve as a crew return vehicle for the 
ISS. Just like the Shuttle, the aerodynamic characteristics of the X-38 will change significantly as 
it flies back to Earth from the International Space Station. A DSMC software was used by [32] 
to predict the aerodynamics of the X-38 in the transitional and free molecular regime down to an 
altitude of approximatley 92 km. The surface pressure distribution at 120 km, is shown in Fig. 1.4.
Figure 1.4: Surface pressure distribution on X-38 vehicle at 120km. [22]
Matteo Cimini 5
1.2. Application highlights
RCS thruster/freestream interaction
On orbit, vehicles employ a RCS for maneuvering purposes. As a vehicle descends into an atmo-
sphere, either to deorbit or for some form of aeromaneuvering, the reaction control system is the
only form of active control available for the vehicle in the free molecular regime. Once the vehicle
more deeply penetrates the atmosphere, and the freestream density has reached a sufficient level,
traditional aerodynamic control surfaces (rudders, body flaps, etc.) can be used to trim the vehicle
in the desired attitude. Until that time, as the vehicle descends there is a progressively stronger
interaction between the RCS plume flowfiled and the oncoming freestream. This interaction may
reduce or enhance the anticipated effectiveness of the RCS through a change in the surface pressure
distribution and a subsequent change of the vehicle’s aerodynamic characteristics.
A representative solution is shown in Fig. 1.5 and reproduce a simplified experiment, involving
a sonic jet in a low density cross flow over a sharp leading edge plate, that was carried out at the
Defense Research Agency in Farnborough. The lobe on top of the plate is the plume surface from
a continuum calculation, which is used as an inflow boundary for the DSMC computation. Fig. 1.5
illustrates how strong the interaction can be as clearly evident shocks form to redirect the flow past
the jet.
Figure 1.5: Experimental investigation into a freestream/jet interaction. [22]
Mars global surveyor mission anomaly
From an aeronautics perspective, NASA’s Mars Global Surveyor (MGS) vehicle was historic in that
it was the first vehicle to utilize aerobraking as a means of achieving mission objectives. Aerobrak-
ing was used in conjunction with propulsive burns to attain the desired final orbit for the vehicle,
as opposed to using propulsive means exclusively. This reduce the amount of propellant needed for
the circularization phase of the mission, and thus reduced the overall mass of the vehicle.
Extensivecalculationoftheaerodynamicloadsandaerothermodynamicenvironmentwascarried
out using a commercial DSMC software (NASA’s DAC software) to provide the necessary confir-
mation that the aerobraking could be performed successfully. An example of heating distribution
solution is shown in Fig. 1.6.
Matteo Cimini 6
1.2. Application highlights
Figure 1.6: Surface heating distribution for Mars Global Surveyor vehicle. [22]
Aerothermodynamics of missile defense system
As a Department of Defense subcontractor, Raytheon Missile Systems analyzed kill vehicle designs
for the Navy Lightweight Exo-Atmospheric Projectile (LEAP) program that would provide the
largest battlespace possible, given aerothermal and aerooptical limitations, as the system utilized
an optical tracking system for terminal intercept.
Using a DSMC commercial code (NASA’s DAC software) surface heating and divert thruster
plume data were obtained at endo- and exo-atmospheric flight confitions that cannot be accurately
modeled with CFD methods. For the aerothermal analysis, vehicle surface heat fluxes are obtained
from steady-state DSMC. Fig. 1.7 shows the surface heating contours on the optical tracking system
and the flowfield temperature profile as the vehicle flies at a 25
 angle of attack.
Figure 1.7: Predicted flowfield temperature and surface heating contours for a candidate
missile system. [22]
Matteo Cimini 7
1.2. Application highlights
Europa water vapor plumes
Europa is the smallest of the four moons orbiting Jupiter, and the sixth-closest to the planet. It
is also the sixth-largest moon in the Solar System. Recent observations of water vapor plumes at
Europa may present an exceptional opportunity to study the composition of the subsurface ocean
and the geology of the ice crust.
Tidal forces experienced throughout the orbit cause interior heating that maintains a proposed
water ocean in a liquid state . While the existence of this ocean is well supported by evidence, many
of the characteristics of the surmounting ice layer are undetermined. This includes the thickness of
the ice, its temperature profile, and whether or not there is convection within the ice.
The Direct Simulation Monte Carlo method was used to model the plume expansion assuming a
supersonic vent source. The structure of the plume was determined, including the number density,
temperature, and velocity fields. For example, Fig. 1.8 shows the comparison of OH number
densities in the low and high mass flow rate cases.
Figure 1.8: Comparison of OH number densities of vapor plumes at Europa in the low (left)
and high (right) mass flow rate cases. The black contours on the right indicate H
2
O number
density [6]
Matteo Cimini 8
1.3. Objectives of the work
1.3 Objectives of the work
This work has three objectives:
 to describe the molecular models, the elastic collisions, the basic kinetic theory and the
Chapman-Enskog theory used in the method;
 to describe the procedures implemented in the DSMC method with particular emphasis on
the most important one;
 to discuss selected one- and two-dimensional applications of DSMC.
In the second chapter the need for a molecular description, the simple gas theory and binary elastic
collisions will be described. In paricular, the various model used in the DSMC method, as for
example the Variable Hard Sphere (or VHS) model, the velocity distribution function and the
Chapman-Enskog theory will be introduced. For the latter, viscosity models will be described for
each molecular model. In the third chapter all the most important procedures of the DSMC method
will be described, as for example the collision and the molecule move procedures. Furthermore
a current dillemma for the DSMC method will be discussed. In the last two chaptes the one-
dimensionalandthetwo-dimensionalapplicationswillbestudiedindetail. Inparticular, fortheone-
dimensional applications, the Couette flow and the steady state normal shockwave will be studied
with particular attention for the simulation parameters. For the two-dimensional application a
circular cylinder will be studied with both DSMC and Navier-Stokes codes and a critical comparison
of the two methods will be made. Furthermore a single applications on the ESA Vega launcher will
be studied through the DSMC method. Finally, conclusions will be provided.
Matteo Cimini 9