Analytical and numerical computation of ring-symmetric spacecraft exhaust plumes
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A doubleheader approach to the computation of a ring- symmetric spacecraft exhaust plume is presented. We plan to use the present analytic approximation in conjunction with a model for backflow from the exhaust plume of an orbiting spacecraft, induced by oncoming ambient molecules. This process takes place in the regions of centered rarefaction waves (CRW) that flank the central plume. A semi-inverse marching characteristic scheme (SI MA) is formulated specifically for accurate computation of a CRW in two-dimensional axisymmetric coordinates, as a variant of the classical inverse marching method. It replicates a Prandtl- Meyer flow exactly, resulting in an accurate marching scheme for axisymmetric CRW. The analytic approximation to a ring- symmetric CRW is formulated in two phases. An analysis of the flow near the corner using characteristic coordinates, results in fan-wise gradients of flow variables (Riemann invariants). These gradients are then used to extrapolate the flow field along fan characteristics from the presumably Prandtl- Meyer flow at the corner, while matching exactly the cylindrically diverging flow along the unreflected portion of the CRW leading characteristic. The resulting approximation compares favorably with numerical (SIMA) computations, even at about 10 corner radii away from the corner. Closed-form expressions are obtained for lateral plume opacity at the CRW fringes.
NPS Report NumberNPS-72-86-003CR
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