Physics of reshock and mixing in single-mode Richtmyer-Meshkov instability.
Physics of reshock and mixing in single-mode Richtmyer-Meshkov instability.
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DOI：
10.1103/physreve.76.026319
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发表时间：
2006-12
期刊：
影响因子：
--
通讯作者：
O. Schilling;M. Latini;W. Don
中科院分区：
文献类型：
--
作者：
O. Schilling;M. Latini;W. Don
采用九阶加权基本无振荡（韦诺）激波捕捉方法研究了二维单模Richtmyer-Meshkov不稳定性中的再震和混合现象。初始条件和计算域改编自柯林斯和雅各布斯的马赫数1.21空气（丙酮）/ SF6激波管实验[J. Fluid Mech. 464，113（2002）]：将来自该实验的五阶和九阶韦诺模拟的气泡和尖峰振幅的增长与线性和非线性振幅增长模型的预测进行比较，并且显示出与Latini、Schilling和Don [Phys. Fluids 19，024104（2007）]的重震之前的实验数据非常一致。在本研究中，密度，涡度，斜压涡度生产，和模拟密度纹影场首次提出定性描述的再震过程。斜压环流沉积界面上的Samtaney-Zabusky模型的预测和线性不稳定理论的同意。正、负环流在界面上的时间演化被认为是在重震前后：结果表明，环流的大小是相等的，以及重震后，直到反射稀疏层的相互作用引起流动对称性破缺和不同的正负环流的大小的演变。后重震混合层的增长被证明是在一般良好的协议与三个模型预测的线性增长后的短时间重震。接下来，全面调查的本地和全球的混合性能作为时间的函数进行。沿沿着激波传播方向的混合流体的分布和量的特征在于使用平均摩尔分数分布，快速动力学反应模型，和混合分数。利用脉动动能、脉动涡度拟能、压力方差、密度方差和斜压涡度产生方差的谱，定量分析了混合层中能量的模态分布。结果表明，范围广泛的尺度已经存在之前的重震，表明单模Richtmyer-Meshkov不稳定性发展非平凡的光谱内容从它的成立。在二维湍流的经典惯性子范围标度的预测的频谱的比较表明，后重震频谱可能是一致的，这些标度在波数范围小于十年。在重震时，所有场（密度除外）的波动在所有尺度上都被放大。重震强烈地放大了环流、剖面和混合分数，以及能谱和统计，导致增强的混合，然后是衰变。的摩尔和混合分数的配置文件成为几乎自相似的后期时间后，再冲击;混合分数表现出一种接近统一的整个层在最新的时间，这意味着几乎完全混合的气体。为了直接量化由再震引起的波动放大，在再震之后和之前立即比较先前考虑的量。最后，调查的衰减波动的情况下，额外的波与混合层的相互作用后再冲击，在计算域的末端的边界条件被改变，从反射到流出，让反射稀疏波退出域。结果表明，反射稀疏在打破对称性和实现后期统计各向同性的速度场有重要的作用。
The ninth-order weighted essentially nonoscillatory (WENO) shock-capturing method is used to investigate the physics of reshock and mixing in two-dimensional single-mode Richtmyer-Meshkov instability to late times. The initial conditions and computational domain were adapted from the Mach 1.21 air (acetone)/ SF6 shock tube experiment of Collins and Jacobs [J. Fluid Mech. 464, 113 (2002)]: the growth of the bubble and spike amplitudes from fifth- and ninth-order WENO simulations of this experiment were compared to the predictions of linear and nonlinear amplitude growth models, and were shown to be in very good agreement with the experimental data prior to reshock by Latini, Schilling, and Don [Phys. Fluids 19, 024104 (2007)]. In the present investigation, the density, vorticity, baroclinic vorticity production, and simulated density Schlieren fields are first presented to qualitatively describe the reshock process. The baroclinic circulation deposition on the interface is shown to agree with the predictions of the Samtaney-Zabusky model and with linear instability theory. The time evolution of the positive and negative circulation on the interface is considered before and after reshock: it is shown that the magnitudes of the circulations are equal before as well as after reshock, until the interaction of the reflected rarefaction with the layer induces flow symmetry breaking and different evolutions of the magnitude of the positive and negative circulation. The post-reshock mixing layer growth is shown to be in generally good agreement with three models predicting linear growth for a short time following reshock. Next, a comprehensive investigation of local and global mixing properties as a function of time is performed. The distribution and amount of mixed fluid along the shock propagation direction is characterized using averaged mole fraction profiles, a fast kinetic reaction model, and mixing fractions. The modal distribution of energy in the mixing layer is quantified using the spectra of the fluctuating kinetic energy, fluctuating enstrophy, pressure variance, density variance, and baroclinic vorticity production variance. It is shown that a broad range of scales already exists prior to reshock, indicating that the single-mode Richtmyer-Meshkov instability develops nontrivial spectral content from its inception. The comparison of the spectra to the predictions of classical inertial subrange scalings in two-dimensional turbulence shows that the post-reshock spectra may be consistent with many of these scalings over wave number ranges less than a decade. At reshock, fluctuations in all fields (except for the density) are amplified across all scales. Reshock strongly amplifies the circulation, profiles, and mixing fractions, as well as the energy spectra and statistics, leading to enhanced mixing followed by a decay. The mole and mixing fraction profiles become nearly self-similar at late times following reshock; the mixing fraction exhibits an approach toward unity across the layer at the latest time, signifying nearly complete mixing of the gases. To directly quantify the amplification of fluctuations by reshock, the previously considered quantities are compared immediately after and before reshock. Finally, to investigate the decay of fluctuations in the absence of additional waves interacting with the mixing layer following reshock, the boundary condition at the end of the computational domain is changed from reflecting to outflow to allow the reflected rarefaction wave to exit the domain. It is demonstrated that the reflected rarefaction has an important role in breaking symmetry and achieving late-time statistical isotropy of the velocity field.