Effects of heat diffusion and turbulence on detonation development of hydrogen/air mixtures under engine-relevant conditions

Abstract

The effects of heat diffusion and turbulence on the detonation propensity of a stoichiometric hydrogen/air mixture under representative low- and high-temperature conditions in internal combustion engines are investigated using two- and three-dimensional direct numerical simulations (DNS) with detailed chemistry. Parametric studies are performed by varying the root-mean-square temperature fluctuation, $T^{\prime }$, the most energetic length scale of the temperature and velocity fluctuation, $l_T$ and $l_e$, and the turbulent velocity fluctuation, $u^{\prime }$. Two non-dimensional parameters, namely the resonance parameter $\xi$ and the reactivity parameter $\varepsilon$, are employed to identify ignition modes. The results reveal that the gradient of the temperature field experiences a rapid dissipation prior to the main ignition due to the pronounced effect of heat diffusion, leading to a decrease of the mean $\overline{\xi }$ and an increase of the mean $\overline{\varepsilon }$, especially at lower initial temperature having a long ignition delay time. Due to the decreased $\overline{\xi }$ and the increased $\overline{\varepsilon }$, these cases have a weaker detonation propensity — their ignition mode shifts from deflagration to detonation transition (DDT) to spontaneous auto-ignition. Moreover, turbulence with faster mixing time scales, characterized by the ratio of ignition delay time to eddy-turnover time, ${\tau }_{ig}/{\tau }_t$, and larger length scales of $l_e/l_T$ enhances the effect of heat dissipation, which in turn effectively decreases the temperature gradient level, and thus the detonation propensity. These effects of heat diffusion and turbulence on the ignition mode are well-characterized by the newly proposed turbulent Damköhler number, Da${}_t$, considering the turbulence intensity characterized by both ${\tau }_{ig}/{\tau }_t$ and $l_e/l_T$, which shows good correlation with the transient evolution of $\overline{\xi }$, ${\overline{\xi }}_t/\overline{\xi }$. Moreover, by employing the transient ${\overline{\xi }}_t$-${\overline{\varepsilon }}_t$ detonation regime diagram, the effects of heat diffusion and turbulence on the detonation propensity of hydrogen/air mixtures are well predicted. For the cases with a lower initial $\overline{\xi }\gtrsim {\overline{\xi }}_l$, turbulence effectively reduces ${\overline{\xi }}_t$, alleviating the detonation occurrence by shifting the combustion mode from the developing detonation regime towards the spontaneous ignition regime. On the contrary, for the cases with a higher initial $\overline{\xi }\gtrsim {\overline{\xi }}_u$, the decrease in ${\overline{\xi }}_t$ due to turbulence facilitates the occurrence of DDT and ultimately enhances the detonation propensity.

Novelty and Significance Statement

$•$ The effects of heat diffusion and turbulence on affecting the detonation propensity of H₂/air mixture at engine-relevant conditions are systematically analyzed using 2-D and 3-D DNSs with detailed chemistry.

$•$ By employing the transient detonation peninsula, ${\overline{\xi }}_t$ - ${\overline{\varepsilon }}_t$, which considers the transient thermo-chemical state of the unburned mixture, accurate predictions of the detonation propensity of H₂/air mixtures are achieved.

$•$ The turbulent Damköhler number, Da${}_t$, is introduced to incorporate the influence of turbulent intensity on the reduction of the thermal diffusion timescale. The newly proposed predictive criterion effectively characterizes the transient evolution of $\overline{\xi }$, accounting for both heat diffusive and turbulent effects.