We examine the evolution of cellular detonation patterns in a two-dimensional channel with yielding confinement on one side. It is shown that in a narrow channel of fixed width the number of cells first increase with decreasing level of confinement. Subsequently, with increasingly weaker confinement, the cells then grow in size and the total number of cells in the channel decreases. For sufficiently weak confinement, the flow becomes laminar with no detonation cells. We examine the relative importance of two fluid mechanisms underlying the observed evolution: global curvature of the detonation shock front due to induced flow divergence caused by the yielding confinement, and energy loss associated with transverse shock wave transmission to the confining material. In order to determine which effect is dominant, we compare two types of numerical calculations. One involves specialized calculations in which the explosive boundary, along which impermeable flow conditions are applied, is deflected through a range of specified angles upon detonation arrival. This set-up mimics the effect of yielding confinement in terms of induced flow divergence, but removes the transverse wave energy loss that would otherwise occur due to wave transmission into the confiner material. The second involves multi-material simulations which can account for transverse wave energy loss into the confining material. Shock polar theory is used to select confiner densities in the multi-material calculations that provide equivalent material interface deflection angles at the detonation shock to the angles imposed in the deflected solid wall calculations. We determine that the induced global curvature of the wave primarily drives both the evolution of the cellular pattern and eventual stabilization of the detonation front, characterized by laminar flow solutions. In wider channels, we show that the detonation front will likely remain unstable even for very weak confinement, as the mean curvature of the front only becomes significant near the edge of the explosive domain.

我们检查了在一侧产生限制的二维通道中细胞爆轰模式的演变。结果表明，在固定宽度的狭窄通道中，细胞数量首先随着限制水平的降低而增加。随后，随着限制越来越弱，细胞的大小随之增加，通道中的细胞总数减少。对于足够弱的限制，气流会变成层流而没有爆轰孔。我们检查了观察到的演化背后的两种流体机制的相对重要性：由于屈服限制引起的诱导的流动发散，爆炸冲击波前沿的整体曲率，以及与横向冲击波传输到约束材料相关的能量损失。为了确定哪种效果占主导地位，我们比较两种类型的数值计算。其中一项涉及专门的计算，在爆炸发生时，爆炸边界（沿边界施加不透水的流动条件）会偏转一定范围的指定角度。这种设置模仿了诱导流散度的屈服限制效果，但是消除了由于波传输到限制材料中而可能发生的横向波能量损失。第二个涉及多材料模拟，可以模拟横向波能量损失到约束材料中。激波极地理论用于在多材料计算中选择约束密度，从而在爆震时提供与在挠性实心壁计算中施加的角度相等的材料界面偏转角。我们确定，感应波的整体曲率主要驱动细胞模式的演变以及以层流解决方案为特征的引爆前沿的最终稳定。在更宽的通道中，我们表明，即使在非常弱的约束下，爆轰锋也可能会保持不稳定，因为该锋的平均曲率仅在爆炸区域的边缘附近才变得显着。