Numerical Investigation of Richtmyer-Meshkov Instability in Reactive Gas Mixtures

冲击波与气泡的反应性气体混合物的相互作用触发了richhtmyer - meshkov不稳定性和化学反应。在惰性激波-气泡相互作用（SBI）中，涡度通过斜压产生在界面附近沉积。入射激波在界面处传播和反射。对于浸入轻气体中的重气体气泡，传递的激波集中在气泡的下游极，导致压力和温度的强烈升高。涡量沉积导致了界面的强烈变形。流动在材料界面周围形成湍流混合区。在过去的几十年里，人们对无反应的SBI进行了深入研究。1983年，Haas和Sturtevant研究了空气中轻或重气泡的SBI，从而建立了一类全新的典型流动结构。由于冲击冲击波引起的温度和压力升高，为无需直接接触即可点燃反应性气体混合物开辟了道路。Haehn等人在2012年将SBI扩展为反应性SBI (RSBI)，研究了一种由惰性气体氙稀释的氢和氧的化学计量混合物，在冲击波冲击下点燃。研究发现，随着激波马赫数的增加，从爆燃到爆轰的反应波类型发生了变化。Haehn等人的复杂实验设置意味着显著的不确定性。Damköhler数字的不确定性在50%左右。在最小的马赫数下，30%的实验没有点燃。显然，如果没有互补的数值模拟，理解只能是不完整的。当前项目的目标是双重的。基于二维RSBI直接数值模拟的初步工作，我们首先对初始数据和燃烧模型的不确定性进行了系统的研究。我们确定了感兴趣的量，如混合速率、熵、中间反应产物质量分数，并通过非侵入性不确定性传播方法预测初始数据变化的影响。我们评估了不同反应机制的预测能力。初始数据不确定性量化还允许估计在三维空间中再现标称实验设置的缺陷的影响，这是第二个目标，旨在对Haehn等人的实验进行第一次定量数值预测。三维研究的目的是确定主要的混合机制、反应和气泡变形参数与理想的二维情况有何不同，以及这些差异如何与实验不确定性相关。在可能的第二个资助期内，我们将进一步增加工程应用的复杂性，例如通过考虑反应泡簇的相互作用。

The interaction of a shock wave with a bubble of reactive gas mixture triggers Richtmyer-Meshkov instabilities and chemical reactions. With inert shock-bubble interactions (SBI) vorticity is deposited near the interface by baroclinic production. The incident shock wave is transmitted and reflected at the interface. For a heavy-gas bubble immersed in light gas the transmitted shock focuses at the downstream pole of the bubble resulting in a strong increase of pressure and temperature. Vorticity deposition leads to a strong deformation of the interface. The flow develops a turbulent mixing zone around the material interface. Non-reacting SBI was intensely studied over the last decades. In 1983 Haas and Sturtevant investigated SBI for light- or heavy-gas bubbles in air, thus establishing an entire new class of canonical flow configurations. Temperature and pressure increase due to the impacting shock wave opens the way of igniting a reactive-gas mixture without direct contact. Ex-tending SBI to reactive SBI (RSBI), Haehn et al. investigated in 2012 a stoichiometric mixture of hydrogen and oxygen, diluted by the inert gas xenon, ignited upon shock-wave impact. It was found that with increasing shock Mach numbers different reaction-wave types develop, from deflagration to detonation. The complex experimental setup of Haehn et al. implies significant uncertainties. The uncertainty in Damköhler number is around 50%. At the smallest investigated Mach number 30% of all experiments did not ignite. It is evident that without complementary numerical simulations the understanding can only be incomplete. The objective of the current project is twofold. Based on pre-liminary work on two-dimensional RSBI direct numerical simulations, we first target systematic in-vestigation of initial-data and combustion-model uncertainties. We identify quantities of interest, such as the mixing rate, enstrophy, intermediate reaction product mass fractions, and predict by non-intrusive uncertainty-propagation methods the effect of initial-data variations. We assess the prediction capability of different reaction mechanisms. The initial-data uncertainty quantification also allows to estimate impact of imperfections in reproducing the nominal experimental setup in three dimensions which are the second objective, aiming at the first quantitative numerical prediction of the experiments of Haehn et al. The objective of the three-dimensional investigation is to identify how dominant mixing mechanisms, reaction, and bubble deformation parameters differ from the ide-alized two-dimensional case, and how these differences may be related to experimental uncertain-ties. In a possible second funding period we will further increase the complexity towards engineering applications, e.g. by considering the interaction of reacting bubble clusters.