Mechanical and Civil Engineering Seminar: PhD Thesis Defense

Abstract:

The coupling between shocks and chemistry in detonations poses a challenge for simulations. In this thesis, a simulation framework is developed to address key components of detonation modeling: numerical stability of shocks and discontinuities, and computational efficiency in chemistry modeling.

To ensure numerical stability in the vicinity of shocks, a variety of methods have been used, including shock-capturing schemes such as weighted essentially non-oscillatory schemes, as well as the addition of artificial diffusivities to the governing equations. In this work, all necessary viscous/diffusion terms are derived from first principles by spatially-filtering the Euler equations. Sub-filter scale (SFS) terms arise in the momentum and energy equations. Analytical closure is provided for each of them by leveraging the jump conditions for a shock. For contact discontinuities, the analytical SFS terms are identically zero; to prevent artificial oscillations due to dispersive errors, a numerical correction term is applied to the enthalpy transport. Implemented within a centered difference code, this filtered framework performs well for a range of shock-dominated flows without introducing excessive diffusion.

Detonation simulations also face a trade-off between computational efficiency and physical accuracy of the chemistry modeling. To reduce the cost of chemistry without sacrificing the physics, tabulated chemistry has often been used for deflagrations in the low Mach number framework. In this approach, a progress variable is transported in the simulation and is used to look up all required chemical source terms, transport properties, and thermodynamic quantities from a pre-computed table. This work extends the tabulated chemistry approach to detonations. To describe the enthalpy and specific heat capacity, temperature is chosen as a second table coordinate. The Zel'dovich-von Neumann-Döring (ZND) model is found to be the most appropriate one-dimensional problem for generation of the table. The ZND tabulation approach is validated for both one-dimensional stable and pulsating, and two-dimensional regular and irregular detonations in various hydrogen-oxygen mixtures. The tabulated chemistry simulations reproduce the detailed chemistry results in terms of propagation speed, cellular structures, and source term statistics at a reduced computational cost.