Verified and validated calculation of unsteady dynamics of viscous hydrogen–air detonations

Abstract

The dynamics of one-dimensional, piston-driven hydrogen-air detonations are predicted in the presence of physical mass, momentum and energy diffusion. The calculations are automatically verified by the use of an adaptive wavelet-based computational method which correlates a user-specified error tolerance to the error in the calculations. The predicted frequency of 0.97 MHz for an overdriven pulsating detonation agrees well with the 1.04 MHz frequency observed by Lehr in a shock-induced combustion experiment around a spherical projectile, thus giving a limited validation for the model. A study is performed in which the supporting piston velocity is varied, and the long time behaviour is examined for an initially stoichiometric mixture at 293.15 K and 1 atm. Several distinct propagation behaviours are predicted: a stable detonation, a high-frequency pulsating detonation, a pulsating detonation with two competing modes, a low-frequency pulsating detonation and a propagating detonation with many active frequencies. In the low-frequency pulsating mode, the long time behaviour undergoes a phenomenon similar to period-doubling. Harmonic analysis is used to examine how the frequency of the pulsations evolves as the supporting piston velocity is varied. It is found that the addition of viscosity shifts the neutral stability boundary by about 2 % with respect to the supporting piston velocity. As the supporting piston velocity is lowered, the intrinsic instability grows in strength, and the effect of viscosity is weakened such that the results are indistinguishable from the inviscid predictions.

Mean structure of one-dimensional unstable detonations with friction

“…The issue of including viscous effects was discussed in Fickett & Davis (1979), and in Romick et al (2011a), Romick, Aslam & Powers (2011b) and Romick et al (2012). The latter studies investigated the effects of mass, momentum and energy diffusion on the dynamics of unsteady detonation, with a one-step irreversible Arrhenius kinetic model.…”

Equation Level Matching: An Extension of the Method of Matched Asymptotic Expansion for Problems of Wave Propagation

“…Rewriting the equations in terms of the variables ξ = χ/δ and µ = τ /δ, it is easy to see (same argument) that the expansion here matches the one in § 3.3 -the equations reduce to those in (29)(30)(31) and (34)(35).…”

Evolution of detonation formation initiated by a spatially distributed, transient energy source

“…It is also found that the transition to chaos is a function of activation energy and the transitional activation energy is moderately sized (E = E ′ /(R ′ T ′ 0 ) ∼ 25). It should be pointed out that both the 1-D and 2-D results contained in this work focus on small activation energies in which case the instabilities observed in Romick et al (2012) and Romick et al (2015) may be absent.…”

“…While the current process appears to be independent of transport effects this does not imply that these other cases will be as well. Romick et al (2012) and Romick et al (2015) show that detonation dynamics in one dimension are influenced by viscosity and inviscid cases lead to chaos more quickly than viscous cases. It is also found that the transition to chaos is a function of activation energy and the transitional activation energy is moderately sized (E = E ′ /(R ′ T ′ 0 ) ∼ 25).…”