Numerical Simulation of Nitrogen Nozzle Expansion using Kinetic and Continuum Approaches

Paper number

IAC-08.E2.1.4

Author

Mr. Martin Grabe, DLR German Aerospace Center, Germany

Year

2008

Abstract

Attitude control of satellites is often accomplished by expanding a gas through the nozzle of small thrusters. The
very low background pressure leads to a heavily underexpanded plume, which may impinge on the surrounding
surfaces causing contamination, thermal loads and unwanted forces. A thorough understanding of the plume
expansion is thus of high importance for the design of the spacecraft and its mission.
Experimental investigations of nozzle expansion in a spacelike
environment are quite intricate and numerical
methods may help to evaluate many technical configurations much more quickly. A gas expansion into vacuum
involves a drastic decrease in density over several orders of magnitude, which causes the continuum assumption
inherent in the wellknown
NavierStokesequations
of fluid mechanics to fail. Hence the classical methods of
Computational Fluid Dynamics (CFD), relying on these equations, will produce wrong results in the domain of
high rarefaction, where nonequilibrium
effects prevail.
The well tried engineering method of choice for rarefied gas flows is termed Direct Simulation Monte Carlo
(DSMC), a probabilistic simulation method which recognizes the molecular nature of the gas. DSMC is capable
to accurately simulate gas flows over a wide range of densities and is able to capture nonequilibrium
effects
without additional modelling and assumptions. However, the method is computationally expensive, particularly
in regions of high density. It is thus attempted to use CFD to model the nearisentropic
core of the nozzle flow
and use DSMC for the nonequilibrium
regions to save on computer resources and time. The line along which
the two methods are coupled is determined by a suitable continuumbreakdown
parameter from the CFD
solution. Since the expanding flow is for the most part hypersonic, it is initially assumed that the DSMC solution
will not influence the flow in the continuum domain (downstream coupling). Density, temperature and velocity
are extracted along the coupling boundary from the continuum solution and set as boundary values for the
particle method.
In the investigated case of the axisymmetric nitrogen expansion from a conical nozzle, the isolines of the applied
breakdownparameters
were found to be nearly parallel to the flow for most part of the expansion. This
corresponds to a de facto effusion if viewed from a point moving with the flow, i. e. a considerable number of
particle leaves the DSMC domain towards the continuum zone simply because of their thermal velocity
component. This particle flux is not accounted for in a pure downstream coupling and leads to an unphysical
discontinuity in density over the boundary between the two domains. While the results thus obtained are not
satisfactory near the nozzle exit plane, they agree well with experimental results in the farfield of the plume.
A simple downstream coupling of kinetic and continuum approaches to accurately and efficiently simulate a gas
expanding into vacuum is found to be insufficient, contrary to previous assumptions. Better results in the
nearfield of the plume may be obtained by continuously updating the solution in the continuum domain using
the results of the DSMC solution.

Abstract document

IAC-08.E2.1.4.pdf

Manuscript document

IAC-08.E2.1.4.pdf (🔒 authorized access only).

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