Uncontrolled hydrogen/air explosions pose a central problem in nuclear and process plant safety research. The Richtmyer–Meshkov Instability (RMI) can be an important contributing factor to flame acceleration and subsequently the deflagration-to-detonation transition. In this context, the RMI is caused by the interaction of a sharp pressure gradient, generated by a shock wave and the density gradient at a flame surface. This interaction leads to the production of baroclinic torque at the flame surface, which causes flame wrinkling. For this work, compressible direct numerical simulations of a shock wave, interacting with a perturbed statistically planar flame in a premixed medium, are conducted. After the first interaction with the flame, a second instance of shock–flame interaction (re-shock) is observed, caused by the reflection of the shock wave from an adiabatic wall on the right-hand side of the domain. The influence of the chemical reaction, shock strength, as well as initial flame surface disturbance on the flame surface area $A_{\mathrm{f}}$ and mixing width ${\delta }_{\mathrm{m}}$, are investigated. It is found that the chemical reaction has a large impact on the development of $A_{\mathrm{f}}$ and ${\delta }_{\mathrm{m}}$, as it partly smoothens emerging wrinkled structures on the flame surface for the present thermochemistry. The maximum reached $A_{\mathrm{f}}$ is hereby reduced by about $50\mathrm{\%}$ compared to cases without chemical reaction. A comparison of the development of ${\delta }_{\mathrm{m}}$ over time with predictions from an analytical model shows good agreement for the linear portion of the instability (short time frame after shock interaction). The model then fails to predict the decrease of ${\delta }_{\mathrm{m}}$ in the non-linear part of the model, due to the smoothing effects of the chemical reaction. The influence of the initial flame disturbance on the development of the flame surface area and mixing width shows a strong dependence on the selected disturbance wavenumber $k_0$. The maximum achievable flame surface area is inversely proportional to $k_0$ in the investigated range. Increasing the shock Mach number and therefore increasing the pressure gradient showed a strong impact on the development of the RMI. After the first shock interaction, numerous fresh gas funnels are created, reaching into the burned gas. Therefore, when the re-shock interaction occurs, the shock will interact with an increased and more irregular flame surface. In addition, the flame thickness is reduced by about $50\mathrm{\%}$ upon each shock interaction, due to flame compression and increase in the pressure level from the shock wave. Both effects will lead to distinct spikes in the baroclinic torque production over time upon flame interaction with the re-shock and result in a strong increase of $A_{\mathrm{f}}$ and ${\delta }_{\mathrm{m}}$.

不受控制的氢/空气爆炸是核能和加工厂安全性研究的中心问题。Richtmyer-Meshkov不稳定性（RMI）可能是导致火焰加速以及随后的爆燃-爆轰过渡的重要因素。在这种情况下，RMI是由冲击波产生的尖锐压力梯度和火焰表面的密度梯度的相互作用引起的。这种相互作用导致在火焰表面产生斜压转矩，从而引起火焰起皱。对于这项工作，进行了冲击波的可压缩直接数值模拟，与预混合介质中的扰动统计平面火焰相互作用。第一次与火焰相互作用后，观察到第二次冲击-火焰相互作用（重新电击），由域右侧的绝热壁反射的冲击波引起的。化学反应，冲击强度以及初始火焰表面扰动对火焰表面积的影响${\mathrm{一种}}_{\mathrm{F}}$ 和混合宽度 ${\delta }_{\mathrm{米}}$，正在调查中。结果发现，化学反应对有机硅的发展有很大的影响。${\mathrm{一种}}_{\mathrm{F}}$ 和 ${\delta }_{\mathrm{米}}$对于目前的热化学，它部分地平滑了火焰表面上出现的皱纹结构。达到的最大值${\mathrm{一种}}_{\mathrm{F}}$ 特此减少约 $50\mathrm{％}$与没有化学反应的情况相比。发展的比较${\delta }_{\mathrm{米}}$随着时间的推移，分析模型的预测结果表明，对于不稳定性的线性部分（冲击相互作用后的较短时间范围），一致性良好。然后，该模型无法预测${\delta }_{\mathrm{米}}$在模型的非线性部分中，由于化学反应的平滑作用。初始火焰扰动对火焰表面积和混合宽度发展的影响强烈依赖于所选的扰动波数${ķ}_0$。可达到的最大火焰表面积与${ķ}_0$在研究范围内。增加冲击马赫数，从而增加压力梯度，对RMI的发展有很大影响。在第一次冲击相互作用之后，会产生许多新鲜的气体漏斗，并进入燃烧的气体。因此，当发生重新电击相互作用时，冲击将与增加且更不规则的火焰表面相互作用。此外，火焰厚度减少了约$50\mathrm{％}$每次冲击相互作用时，由于火焰压缩和冲击波压力水平的提高。两种作用都将导致火焰与再电击相互作用时，随着时间的推移，斜压扭矩产生明显的峰值，并导致压力的强烈增加。${\mathrm{一种}}_{\mathrm{F}}$ 和 ${\delta }_{\mathrm{米}}$。