Papers by Bishnupriya Nayak
Materials Research Express
Numerical solution of Euler equations employing enthalpy-based equation of state for simulating shock wave propagation in porous materials, 2019
Shock wave propagation through porous materials is investigated using numerical simulations of on... more Shock wave propagation through porous materials is investigated using numerical simulations of one dimensional Euler equations of inviscid fluid flow, with the basic aim to demonstrate the application of the enthalpy-based equation of state. A one dimensional hydrodynamics solution method employing the flux-corrected transport algorithm, which does not make use of artificial viscosity, is used for all simulations. Benchmark results on the Sedov-von Neumann-Taylor blast wave problem are given thereby showing the capabilities of the algorithm for capturing strong shock profiles. Next, numerical results for plate impact problems are obtained for porous Cu, Al, Fe and W, and compared with experimental data available in the literature. It is shown that shock waves attenuate very fast even in materials of small size and low porosity. Excellent agreement is also found with experimental data on pressure versus particle velocity in the four target materials for different porosities. Thus the enthalpy-based approach, using a few experimental data of solids at normal conditions, is shown to be capable of quantitative prediction of shock wave parameters of porous materials. An accurate but simple approach for in-line calculation of the enthalpy parameters is discussed in the Appendix together with numerical results.
Enthalpy-based equation of state based on a modified soft sphere model for the fluid phase, which... more Enthalpy-based equation of state based on a modified soft sphere model for the fluid phase, which includes vaporization and ionization effects, is formulated for highly porous materials. Earlier developments and applications of enthalpy-based approach had not accounted for the fact that shocked states of materials with high porosity (e.g., porosity more than two for Cu) are in the expanded fluid region. We supplement the well known soft sphere model with a generalized Lennard-Jones formula for the zero temperature isotherm, with parameters determined from cohesive energy, specific volume and bulk modulus of the solid at normal condition. Specific heats at constant pressure, ionic and electronic enthalpy parameters and thermal excitation effects are calculated using the modified approach and used in the enthalpy-based equation of state. We also incorporate energy loss from the shock due to expansion of shocked material in calculating porous Hugoniot. Results obtained for Cu, even up to initial porosities ten, show good agreement with experimental data.
A generalized enthalpy-based equation of state, which includes thermal electron excitations and n... more A generalized enthalpy-based equation of state, which includes thermal electron excitations and non-equilibrium thermal energies, is formulated for binary solid and porous mixtures. Our approach gives rise to an extra contribution to mixture volume, in addition to those corresponding to average mixture parameters. This excess term involves the difference of thermal enthalpies of the two components , which depend on their individual temperatures. We propose to use the Hugoniot of the components to compute non-equilibrium temperatures in the mixture. These are then compared with the average temperature obtained from the mixture Hugoniot, thereby giving an estimate of non-equilibrium effects. The Birch–Murnaghan model for the zero-temperature isotherm and a linear thermal model are then used for applying the method to several mixtures, including one porous case. Comparison with experimental data on the pressure–volume Hugoniot and shock speed versus particle speed shows good agreement.
Annals of Nuclear Energy, 2013
Fusion reactivities (hrvi) of some neutronic and aneutronic fusion fuels are evaluated numericall... more Fusion reactivities (hrvi) of some neutronic and aneutronic fusion fuels are evaluated numerically using cross-section data available from IAEA site. Comparison of new reactivities with the fitting formula published in earlier works shows that these fits are accurate only in certain temperature ranges. Here, new polynomial fits for fusion reactivities are proposed. Agreement of the new fittings with numerical values of hrvi is found to be quite good.
Journal of Applied Physics, 2016
A generalized enthalpy based equation of state, which includes thermal electron excitations expli... more A generalized enthalpy based equation of state, which includes thermal electron excitations explicitly, is formulated from simple considerations. Its application to obtain Hugoniot of materials needs simultaneous evaluation of pressure-volume curve and temperature, the latter requiring solution of a differential equation. The errors involved in two recent papers (J. Appl. Phys., 92, 5917, 2002; 92, 5924, 2002) which employed this approach are brought out and discussed. In addition to developing the correct set of equations, the present work also provides a numerical method to implement this approach. Constant pressure specific heat of ions and electrons and ionic enthalpy parameter, needed for applications, are calculated using a three component equation of state. The method is applied to porous Cu with different initial porosities. Comparison of results with experimental data shows good agreement. It is found that temperatures along the Hugoniot of porous materials are significantly modified due to electronic effects.
Laser and Particle Beams, 2012
Conditions for thermonuclear ignition are determined by three parameters: fuel density, temperatu... more Conditions for thermonuclear ignition are determined by three parameters: fuel density, temperature and hot-spot size. A simple three temperature model is developed to calculate the critical burn-up parameter or the minimum ρR product. Extensive results obtained are compared with earlier one temperature model for DT and DD fuels. While the two approaches are found to provide similar results for DT fuel except at low temperature regime (∼10 keV), three temperature modeling is found to be necessary for DD fuel. This is argued to be due to the lower fusion reactivity and energy production in DD reactions.
A generalized enthalpy based equation of state, which includes thermal electron excitations expli... more A generalized enthalpy based equation of state, which includes thermal electron excitations explicitly, is formulated from simple considerations. Its application to obtain Hugoniot of materials needs simultaneous evaluation of pressure-volume curve and temperature, the latter requiring solution of a differential equation. The errors involved in two recent papers [Huayun et al., J. Appl. Phys. 92, 5917 (2002); 92, 5924 (2002)], which employed this approach, are brought out and discussed. In addition to developing the correct set of equations, the present work also provides a numerical method to implement this approach. Constant pressure specific heat of ions and electrons and ionic enthalpy parameter, needed for applications, are calculated using a three component equation of state. The method is applied to porous Cu with different initial porosities. Comparison of results with experimental data shows good agreement. It is found that temperatures along the Hugoniot of porous materials are significantly modified due to electronic effects. V C 2016 AIP Publishing LLC. [http://dx.doi.org/10.1063/1.4944430]
Uploads
Papers by Bishnupriya Nayak