Numerical investigations on propagating characteristics of shock waves in different triangle wedges
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摘要: 激波在收缩管内的反射与聚焦会形成高温高压区，点燃可燃混合气并诱导爆轰，因此对爆轰发动机的点火具有重要意义。本文基于二维N-S方程，结合五阶WENO格式，对马赫数为6的正激波在三角形楔面内的反射与聚焦现象进行了数值研究。结果表明，楔面顶角的变化对激波的反射类型以及聚焦均有明显的影响：随着顶角的增加，激波的反射类型从马赫反射向过渡马赫反射和双马赫反射转变，且壁面上的前向射流更加明显；三波点第一次碰撞产生的高温高压区足够满足可燃混合气体的点火条件，且其温度与压力值随顶角的增加而增大；当激波在楔面上发生临界双马赫反射时，温度与压力达到最大；当顶角增加到一定值时，激波在楔面反射转变为常规反射，不会产生激波对碰，因而没有高温高压区。Abstract: The reflection and focusing of the shock wave propagating into a convergent tube can create a high-temperature and high-pressure region, which is significant for the detonation engine to induce the mixed combustible gases to detonate in ignition. Based on the N-S equations and combined with the five order WENO scheme, the phenomena of the shock wave reflection and focusing in the triangular wedge have been numerically simulated with the Mach number as 6. The numerical results reveal that the modification of the vertex angles has an obvious influence on the kind of shock reflection and the shock wave focusing. With the vertex angle getting bigger, the shock wave transforms from the Mach reflection to the transitional-Mach and the double-Mach reflections, and the jetting on the ramp surface becomes more evident. The high-temperature and high-pressure region generated after the first collision of the triple points can then satisfy the ignition condition of the mixed combustible gases. The temperature and the pressure will rise with the vertex angle getting bigger, and approach the maximum as the shock wave reaches the critical point of the double-Mach reflection on the wedge. However, the shock wave turns to the regular reflection on the wedge when the vertex angle exceeds the angle of the critical double-Mach reflection, and the triple points will not collide. Therefore, no high-temperature and high-pressure region is generated under this condition.
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Key words:
- mechanics of explosion /
- propagating characteristics /
- shock wave /
- triple point /
- Mach reflection /
- double Mach reflection /
- jet
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图 2 激波在楔面内的传播过程(θ=10°)
Figure 2. Process of shock wave propagation in the wedge (θ=10°)
图 3 激波在楔面顶端聚焦时的高温高压区
Figure 3. High-temperature and high-pressure region generated when the shock wave focuses at the wedge vertex
图 4 激波在楔面上反射的不同波系结构(t=0.16 ms)
Figure 4. Different structures of shock wave reflection on the wedges at t=0.16 ms
图 5 激波在不同楔面上反射时的压力分布(t=0.16 ms)
Figure 5. Pressures distributed when the shock wave reflects on different wedges at t=0.16 ms
图 6 三波点碰撞产生的高温高压区
Figure 6. High-temperature and high-pressure region generated by the collision of the triple points
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