Ablative performance of carbon-carbon nosetips in simulated re-entry environments

A summary is presented of ablation performance data for carbon-carbon nosetip models obtained over a range of pressures from 10 to 168 atm. Two classes of tests are reviewed: (1) steady state, in which a constant environment is imposed on the model, and (2) ramp, in which the pressure is increased from 10 to 80 atmospheres to simulate re-entry pressure history. Comparison of arc test parameters with typical reentry vehicle parameters is included, to assess the adequacy of the test simulation. Based on this comparison, recommendations are made for facility developments which would yield improved simulation capability for reentry vehicle nosetip ablative performance

A finite element approach for vector- and tensor-valued surface PDEs

We derive a Cartesian componentwise description of the covariant derivative of tangential tensor fields of any degree on general manifolds. This allows to reformulate any vector- and tensor-valued surface PDE in a form suitable to be solved by established tools for scalar-valued surface PDEs. We consider piecewise linear Lagrange surface finite elements on triangulated surfaces and validate the approach by a vector- and a tensor-valued surface Helmholtz problem on an ellipsoid. We experimentally show optimal (linear) order of convergence for these problems. The full functionality is demonstrated by solving a surface Landau-de Gennes problem on the Stanford bunny. All tools required to apply this approach to other vector- and tensor-valued surface PDEs are provided

Phase-field simulations of solidification in binary and ternary systems using a finite element method

We present adaptive finite element simulations of dendritic and eutectic solidification in binary and ternary alloys. The computations are based on a recently formulated phase-field model that is especially appropriate for modelling non-isothermal solidification in multicomponent multiphase systems. In this approach, a set of governing equations for the phase-field variables, for the concentrations of the alloy components and for the temperature has to be solved numerically, ensuring local entropy production and the conservation of mass and inner energy. To efficiently perform numerical simulations, we developed a numerical scheme to solve the governing equations using a finite element method on an adaptive non-uniform mesh with highest resolution in the regions of the phase boundaries. Simulation results of the solidification in ternary Ni$_{60}$Cu$_{40-x}$Cr$_{x}$ alloys are presented investigating the influence of the alloy composition on the growth morphology and on the growth velocity. A morphology diagram is obtained that shows a transition from a dendritic to a globular structure with increasing Cr concentrations. Furthermore, we comment on 2D and 3D simulations of binary eutectic phase transformations. Regular oscillatory growth structures are observed combined with a topological change of the matrix phase in 3D. An outlook for the application of our methods to describe AlCu eutectics is given.Comment: 5 pages, 3 figures, To appear in the proceedings of 14th "International Conference on Crystal Growth", ICCG-14, 9-13 August 2004 Grenoble Franc

Phase field analysis of eutectic breakdown.

In this paper an isotropic multi-phase-field model is extended to include the effects of anisotropy and the spontaneous nucleation of an absent phase. This model is derived and compared against a published single phase model. Results from this model are compared against results from other multi-phase models, additionally this model is used to examine the break down of a regular two dimensional eutectic into a single phase dendritic front

Nematic liquid crystals on curved surfaces - a thin film limit

We consider a thin film limit of a Landau-de Gennes Q-tensor model. In the limiting process we observe a continuous transition where the normal and tangential parts of the Q-tensor decouple and various intrinsic and extrinsic contributions emerge. Main properties of the thin film model, like uniaxiality and parameter phase space, are preserved in the limiting process. For the derived surface Landau-de Gennes model, we consider an L2-gradient flow. The resulting tensor-valued surface partial differential equation is numerically solved to demonstrate realizations of the tight coupling of elastic and bulk free energy with geometric properties.Comment: 20 pages, 4 figure