Tabulated chemistry approach for detonation simulations

Abstract

Chemistry modeling in detonations typically relies on two broad approaches: simplified models with one- or two-step chemistry, and detailed chemistry. These approaches require choosing between computational efficiency or physical accuracy. To reduce the cost of chemistry while maintaining accurate physics, tabulated chemistry has been used extensively for flames/deflagrations in the low Mach number framework. In the simplest tabulated chemistry model for premixed flames, a progress variable, describing the progress of reactions in the system, is transported in the simulation. This progress variable is then used to look up all other species, transport properties, and thermodynamic variables from a pre-computed table. The present work extends the tabulated chemistry method to detonations. Even in non-reacting compressible flow simulations, the enthalpy and specific heat capacity are required; to describe these thermodynamic variables, the temperature is selected as a second table coordinate. The two table coordinates are able to capture virtually all variations in the progress variable source term. 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 $H_2$-$O_2$ mixtures. The tabulated chemistry simulations are able to reproduce the detailed chemistry results in terms of propagation speed, cellular structures, and source term statistics. For hydrogen detonations, the computational cost of scalar transport is reduced by a factor of 9 and the cost of the chemistry is reduced by a factor of 17. More substantial computational savings are expected for hydrocarbon fuels.

Novelty and significance statement

Detonations are often challenging to simulate due to the significant cost of integrating accurate chemical models. In deflagrations, this cost has been reduced by pre-computing the chemistry and collecting the information into a lookup table to be used at runtime. Although chemistry tabulation has been adapted recently for supersonic combustion, such as in scramjets, the typical assumptions of these approaches do not apply to detonations. We propose a new tabulated chemistry approach, valid for detonations and reproducing critical parameters such as induction zone length and detonation velocity. The key novelty lies in (1) the use of progress variable and temperature as the coordinates for tabulation, and (2) the selection of one-dimensional Zel’dovich–von Neumann–Döring detonations as the relevant physical problem to be tabulated. The new model significantly reduces the cost of simulations.