We consider a three-dimensional unsteady flow with one, two, or four rotating detonation waves arising in an annular gap of an axially symmetric device between two parallel planes perpendicular to its symmetry axis. The corresponding problem is formulated and studied. It is assumed that there is a reservoir with quiescent homogeneous propane–air combustible mixture with given stagnation parameters; the mixture flows from the reservoir into the annular gap through its external cylindrical surface toward the symmetry axis, and the parameters of the mixture are determined by the pressure in the reservoir and the static pressure in the gap. The detonation products flow out from the gap into a space bounded on one side by an impermeable wall that is an extension of a side of the gap. Through a hole on the other side of the gap and through a conical output section with a half-opening angle of \(45^{\circ }\), the gas flows out from the engine into the external space. We formulate a model of detonation initiation by energy supply in which the direction of rotation of the detonation wave is defined by the position of the energy-release zone of the initiator with respect to the solid wall situated in a plane passing through the symmetry axis. After a while, this solid wall disappears (burns out). We obtain and analyze unsteady shock-wave structures that arise during the formation of a steady rotating detonation. We measure and compare thrust characteristics for different numbers of detonation waves. It was shown that the thrust weakly depends on the number of waves while the specific impulse increases with increasing number of waves. The study of rotating detonation at various values of the stagnation pressure was conducted. The calculation results show that at a stagnation pressure less than the critical value, the realization of rotating detonation is impossible. It is established that, depending on the stagnation pressure, qualitatively different shock-wave structures can be observed. The analysis is carried out within single-stage combustion kinetics by the numerical method based on the Godunov scheme with the use of an original software system developed for multi-parameter calculations and visualization of flows. The calculations were carried out on the Lomonosov supercomputer at Moscow State University.

我们考虑一个三维非定常流动，该流动具有一个，两个或四个旋转的爆轰波，这些爆轰波出现在两个对称于垂直于其对称轴的平行平面之间的轴向对称装置的环形间隙中。提出并研究了相应的问题。假设有一个储层，其丙烷和空气可燃混合物均处于静止状态，并具有给定的停滞参数。混合物从容器中通过其外圆柱表面朝对称轴流入环形间隙，混合物的参数由容器中的压力和间隙中的静压力决定。爆炸产物从间隙流出到一侧，该间隙的一侧由不可渗透的壁界定，该壁是间隙的一侧的延伸。\（45 ^ {\ circ} \），气体从发动机流出到外部空间。我们建立了一种通过能量供应引发爆炸的模型，其中，爆炸波的旋转方向由引发剂的能量释放区相对于位于穿过对称轴的平面中的固体壁的位置定义。一段时间后，此坚固的壁消失（烧毁）。我们获得并分析了在稳定旋转爆轰形成过程中产生的不稳定冲击波结构。我们测量和比较不同数量的爆震波的推力特性。结果表明，推力几乎不依赖于波浪数，而比冲随着波浪数的增加而增加。研究了在不同的停滞压力下的旋转爆轰。计算结果表明，在停滞压力小于临界值时，不可能实现旋转爆轰。已经确定，根据停滞压力，可以观察到质的不同的冲击波结构。通过基于Godunov方案的数值方法，并使用为多参数计算和流动可视化开发的原始软件系统，通过数值方法在单级燃烧动力学中进行分析。计算是在莫斯科国立大学的罗蒙诺索夫超级计算机上进行的。通过基于Godunov方案的数值方法，并使用为多参数计算和流动可视化开发的原始软件系统，通过数值方法在单级燃烧动力学中进行分析。计算是在莫斯科国立大学的罗蒙诺索夫超级计算机上进行的。通过基于Godunov方案的数值方法，并使用为多参数计算和流动可视化开发的原始软件系统，通过数值方法在单级燃烧动力学中进行分析。计算是在莫斯科国立大学的罗蒙诺索夫超级计算机上进行的。