Sergey Gavrilyuk

Modelling wave dynamics of compressible elastic materials

An Eulerian conservative hyperbolic model of isotropic elastic materials subjected to finite deformation is addressed. It was developed by Godunov [S.K. Godunov, Elements of continuum mechanics, Nauka, Moscow, 1978 (in Russian) and G.H. Miller, P. Colella, A high-order Eulerian Godunov method for elastic-plastic flow in solids, J. Comput. Phys. 167 (2001) 131-176]. Some modifications are made concerning a more suitable form of governing equations. They form a set of evolution equations for a local cobasis which is naturally related to the Almansi deformation tensor. Another novelty is that the equation of state is given in terms of invariants of the Almansi tensor in a form which separates hydrodynamic and shear effects. This model is compared with another hyperbolic non-conservative model which is widely used in engineering sciences. For this model we develop a Riemann solver and determine some reference solutions which are compared with the conservative model. The numerical results for different tests show good agreement of both models for waves of very small and very large amplitude. However, for waves of intermediate amplitude important discrepancies between results are clearly visible.

Progress in the Development of Compressible, Multiphase Flow Modeling Capability for Nuclear Reactor Flow Applications

In nuclear reactor safety and optimization there are key issues that rely on in-depth understanding of basic two-phase flow phenomena with heat and mass transfer. Within the context of multiphase flows, two bubble-dynamic phenomena – boiling (heterogeneous) and flashing or cavitation (homogeneous boiling), with bubble collapse, are technologically very important to nuclear reactor systems. The main difference between boiling and flashing is that bubble growth (and collapse) in boiling is inhibited by limitations on the heat transfer at the interface, whereas bubble growth (and collapse) in flashing is limited primarily by inertial effects in the surrounding liquid. The flashing process tends to be far more explosive (and implosive), and is more violent and damaging (at least in the near term) than the bubble dynamics of boiling. However, other problematic phenomena, such as crud deposition, appear to be intimately connecting with the boiling process. In reality, these two processes share many details.