一种高阶精度大涡模拟技术用于激波/火焰相互作用

A high-order large eddy simulation for shock and flame interaction

基于Smagorinsky亚格子模型和增厚火焰技术,开发了一种高阶精度的反应流大涡模拟求解器,运用于数值研究边界层对激波与火焰相互作用的影响。该求解器的核心在于加入了基于超黏性的激波捕捉技术和时空三阶精度的两步Taylor-Galerkin紧致(TTGC)有限元格式,并通过对一维Shu-Osher问题和二维激波/气泡相互作用问题的计算,验证了求解器对激波、接触间断和湍流脉动等流动细节的捕捉精度,计算结果与实验数据吻合良好。通过对激波管内激波、火焰与边界层相互作用问题的数值模拟,发现由于激波与边界层的相互作用会产生不稳定的激波分叉现象,激波三分叉点传播速度的发展经历了水平匀速运动、小斜率线性增长和大斜率迅速增长3个阶段,由此揭示了激波分叉促进火焰加速的机理。当火焰面传入激波分叉区后,流场不均匀的回流区起到了稳定火焰的作用,一方面分叉结构内火焰面能够为激波的运动持续地供应热量,另一方面局部超声速区域为火焰的快速传播提供动力,使其能紧跟激波。通过对比相同条件下甲烷和乙烯燃烧的数值结果,发现两者爆震点触发的位置都出现在马赫杆后面,热量释放率的变化趋势也大致相同,但乙烯出现爆震的时间比甲烷早。

Coupled with the Smagorinsky sub-grid model and a thickened flame model, a high-order large eddy simulation solver for the reactive flow is developed in this paper to study the effect of the boundary layer on the shock/flame interaction. The key to this solver is the adoption of an artificial hyperviscous model and a space-time third-order Two-step Taylor- Galerkin Compact （TTGC） scheme. Calculations of the 1-D Shu-Osher problem and the 2-D shock/bubble interaction demonstrate the precision of the solver in identifying shock waves, contact discontinuities and turbulent flow. The simulation resuits are in good agreement with the experimental data. The interaction between the 2-D shock/flame and the boundary layer in an end-wall shock tube are calculated. The results show that a shock bifurcation phenomenon occurs due to the interaction between the shock and the laminar boundary layer, and the propagation speed of the triple bifurcation point experiences three regimes of horizontal uniform motion, linear growth of small slope and rapid growth of large slope, which reveals the mechanism of flame acceleration resulting from shock bifurcation. The recirculation zone of shock bifurcation plays the role of a flame holder as the reactive flow in the bifurcation can provide continuous heat for the motion of the shock wave, and the flame front closely follows the bifurcated shock and spreads forward quickly in the local supersonic region. A comparison of methane combustion in our simulation and ethylene reaction from other research under the same condition shows that the location of the detonation point are both behind the Mach stem and the variation trend of the heat release rate is also consistent with each other, but detonation occurs earlier for the ethylene.