Impulsive Loading from a Bare Explosive Charge in Space

The article of record as published may be found at https://doi.org/10.2514/3.2601

Hyperbolic conservation laws on the sphere. A geometry-compatible finite volume scheme

We consider entropy solutions to the initial value problem associated with scalar nonlinear hyperbolic conservation laws posed on the two-dimensional sphere. We propose a finite volume scheme which relies on a web-like mesh made of segments of longitude and latitude lines. The structure of the mesh allows for a discrete version of a natural geometric compatibility condition, which arose earlier in the well-posedness theory established by Ben-Artzi and LeFloch. We study here several classes of flux vectors which define the conservation law under consideration. They are based on prescribing a suitable vector field in the Euclidean three-dimensional space and then suitably projecting it on the sphere's tangent plane; even when the flux vector in the ambient space is constant, the corresponding flux vector is a non-trivial vector field on the sphere. In particular, we construct here "equatorial periodic solutions", analogous to one-dimensional periodic solutions to one-dimensional conservation laws, as well as a wide variety of stationary (steady state) solutions. We also construct "confined solutions", which are time-dependent solutions supported in an arbitrarily specified subdomain of the sphere. Finally, representative numerical examples and test-cases are presented.Comment: 22 pages, 10 figures. This is the third part of a series; see also arXiv:math/0612846 and arXiv:math/061284

A conservative coupling algorithm between a compressible flow and a rigid body using an Embedded Boundary method

This paper deals with a new solid-fluid coupling algorithm between a rigid body and an unsteady compressible fluid flow, using an Embedded Boundary method. The coupling with a rigid body is a first step towards the coupling with a Discrete Element method. The flow is computed using a Finite Volume approach on a Cartesian grid. The expression of numerical fluxes does not affect the general coupling algorithm and we use a one-step high-order scheme proposed by Daru and Tenaud [Daru V,Tenaud C., J. Comput. Phys. 2004]. The Embedded Boundary method is used to integrate the presence of a solid boundary in the fluid. The coupling algorithm is totally explicit and ensures exact mass conservation and a balance of momentum and energy between the fluid and the solid. It is shown that the scheme preserves uniform movement of both fluid and solid and introduces no numerical boundary roughness. The effciency of the method is demonstrated on challenging one- and two-dimensional benchmarks

A Moving Boundary Flux Stabilization Method for Cartesian Cut-Cell Grids using Directional Operator Splitting

An explicit moving boundary method for the numerical solution of time-dependent hyperbolic conservation laws on grids produced by the intersection of complex geometries with a regular Cartesian grid is presented. As it employs directional operator splitting, implementation of the scheme is rather straightforward. Extending the method for static walls from Klein et al., Phil. Trans. Roy. Soc., A367, no. 1907, 4559-4575 (2009), the scheme calculates fluxes needed for a conservative update of the near-wall cut-cells as linear combinations of standard fluxes from a one-dimensional extended stencil. Here the standard fluxes are those obtained without regard to the small sub-cell problem, and the linear combination weights involve detailed information regarding the cut-cell geometry. This linear combination of standard fluxes stabilizes the updates such that the time-step yielding marginal stability for arbitrarily small cut-cells is of the same order as that for regular cells. Moreover, it renders the approach compatible with a wide range of existing numerical flux-approximation methods. The scheme is extended here to time dependent rigid boundaries by reformulating the linear combination weights of the stabilizing flux stencil to account for the time dependence of cut-cell volume and interface area fractions. The two-dimensional tests discussed include advection in a channel oriented at an oblique angle to the Cartesian computational mesh, cylinders with circular and triangular cross-section passing through a stationary shock wave, a piston moving through an open-ended shock tube, and the flow around an oscillating NACA 0012 aerofoil profile.Comment: 30 pages, 27 figures, 3 table

Semi-Inverse Marching Characteristics Scheme for Supersonic Flows

The purpose of this Note is to present a modification of the inverse marching characteristics scheme for compressible flows that is designed to yield an exact computation of centered rarefaction waves, such as the Prandtl-Meyer corner expansion flow (PMF)

An integral model for thermal backscattering from the exhaust plume of space-based HF laser

The operation of a space-based HF laser may be hampered due to self contamination by corrosive exhaust products. We estimate one effect contributing to contaminating blackflow: thermal backscattering from the rarefaction fans flanking the exhaust ring-jet. Our computational model is based on a first-iterate approximation to the Boltzmann equation in integral form. Results indicate that thermal backscattering of corrosive speies (HF, DF) is negligible

Impulsive loading from a bare explosive charge in space

This document considers a platform target subjected to a normal impact of explosive products generated by detonating a bare charge in space. It is suggested that the loading impulse may be approximated by the total momentum of that portion of the fluid which impacts at the target. Assuming impulsive dynamic response, and assuming that the ensuing damage is proportional to the kinetic energy imparted to the structure by the blast, we get a particularly simple law; Damage similar to W to the 2nd power/R to the 4th power (W is charge mass, R is range). This model is an idealization of a solar panel (or antenna) extended in a paddle-like fashion from a relatively rigid and massive core structure. It is also shown that this law implies that no advantage can be realized by re-arranging the mass of a single bare charge in a cluster configuration of smaller sub-charges, which would be dispersed and detonated via an idealized 'isotropic' scheme. Keywords: Gas dynamics; Exhaust plumes; SpacecraftPrepared for: Strategic Defense Initiative Officehttp://archive.org/details/impulsiveloading00falcMIPR DGAA60045N

Analytical and numerical computation of ring-symmetric spacecraft exhaust plumes

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.Prepared for: Strategic Defense Initiative Office The Pentagon Washington, DChttp://archive.org/details/analyticalnumeri00falcN62271-86-M-0214The project at the Naval Postgraduate School is under the cognizance of Distinguished Professor A. E. Fuhs who is principal investigator

A breakdown surface model for thermal backscattering from the exhaust plume of a space-based HF laser

The purpose of this report is to present a breakdown surface model for evaluating thermal backscattering flow from the supersonic exhaust plume of a gaseous mixture of H, HF, H2, DF and He. Fluxes of these species are considered separately. The model is carefully analyzed and is shown to overestimate the flux. Actual flux levels of the heavy corrosive molecules (HD, DF) have been found to be exceedingly low. It is concluded that the contribution of thermal backscattering to contaminating flux of HF and DF can be neglectedDefense Initiative Office, Washington D.C.http://archive.org/details/breakdownsurface00falcN66271-84-M-3345N