Speaker
Dr
Bent Fritsche
(HTG)
Description
Spacecraft re-entering the Earth atmosphere in an uncontrolled manner may get stabilised by restoring aerodynamic torques, if they have an appropriate shape and mass distribution. While the aerodynamic force (mainly drag) is usually a second-order effect compared to the gravitational acceleration by the Earth at altitudes above 150 km, sometimes the aerodynamic torques can already compete with the Earth gravitation gradient-induced torques at altitudes around 250 km and below. Therefore it is of interest to have an understanding of how to compute the aerodynamic torques in this altitude regime.
The usual approach to compute the aerodynamic coefficients at high altitudes is to construct a surface model of the spacecraft, where the surface is either modelled with plane face elements or discretized into small triangular or quadrangular "panels". The aerodynamic coefficients are then computed for each surface element and summed up with an Integral or Monte-Carlo method, utilizing that the flow around the spacecraft can be considered as free-molecular.
While the Monte-Carlo method can give quite accurate coefficients for a given configuration, it does not allow to parametrize the object of interest. This is different to analytical solutions, where the geometric dimensions and mass distribution appear as explicit parameters, and where the influence of configuration changes on the results are direct. On the other hand, the possibility to get analytical solutions is limited to convex geometric shapes. This can be extended to concave shapes by using some kind of shadowing algorithms, but in this case the additional effort needed to examine the shadowed areas can foil the advantages of the analytical approach compared to the numerical analysis.
In any case, the combination of different methods can give an added value. For basic geometries analytical solutions are known. Comparing these solutions with Monte-Carlo results can serve as a calibration method for the Monte-Carlo method's statistical uncertainties. For more complex geometries the Monte-Carlo method can give a measure of the effect of shadowing and multiple reflections, which cannot be considered exactly, or not at all, in analytical solutions or integral methods.
Due to the special form of the free-molecular gas-surface interaction and its momentum transfer some simplifications are possible especially for the typical high-speed conditions in orbit, which can be used to extend the validity of the analytical solutions or at least extend their approximate range of validity. This will be used in the paper for a simplified categorization of spacecraft without extensive multiple internal reflections w.r.t. to their aerodynamic characteristics.
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Primary author
Dr
Bent Fritsche
(HTG)
