ASHEE: a compressible, equilibrium-Eulerian model for volcanic ash plumes
ASHEE: a compressible, equilibrium-Eulerian model for volcanic ash plumes
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ASHEE：火山灰羽流的可压缩平衡欧拉模型
DOI：
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发表时间：
2015
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通讯作者：
L. Berselli
中科院分区：
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作者：
M. Cerminara;T. E. Ongaro;L. Berselli
摘要。开发了一种新的流体动力学模型，用于对形成火山羽流的多分散气 - 粒混合物的非平衡动力学进行数值模拟。从气体和固体分散颗粒混合物的三维N相欧拉输运方程出发，我们采用渐近展开策略推导出一阶非平衡模型的可压缩版本，该版本适用于低浓度情况（颗粒体积分数小于10⁻³）且颗粒斯托克斯数（St——即松弛时间与流动特征时间之比）不超过约0.2。这个新模型被称为ASHEE（ASH平衡欧拉模型），它比N相欧拉模型快得多，同时保留了描述气 - 粒非平衡效应的能力。直接数值模拟精确地再现了亚声速状态下各向同性、可压缩湍流的动力学。对于气 - 粒混合物，它描述了密度波动的主要特征以及湍流引起的颗粒优先聚集和聚类，从而验证了该模型在存在分散相时对高雷诺数和高温状态进行数值模拟的可靠性和适用性。另一方面，强迫羽流的大涡数值模拟能够再现平均和瞬时流动特性。特别是，再现了自相似高斯径向剖面以及大尺度相干结构的发展，包括湍流混合速率和大气空气的卷吸。将其应用于分层大气中喷发混合物注入的大涡模拟，描述了湍流火山羽流的一些重要特征，包括空气卷吸、浮力反转和最大羽流高度。对于非常细的颗粒（当非平衡效应可忽略时，St → 0），该模型简化为所谓的含尘气体模型。然而，粗颗粒在涡旋内与气相部分解耦（从而改变湍流结构），并优先聚集在涡旋边缘，最终由于重力的共同作用从羽流边缘流失。通过这些机制，气 - 粒非平衡过程能够影响火山羽流的大规模行为。
Abstract. A new fluid-dynamic model is developed to numerically simulate the non-equilibrium dynamics of polydisperse gas–particle mixtures forming volcanic plumes. Starting from the three-dimensional N-phase Eulerian transport equations for a mixture of gases and solid dispersed particles, we adopt an asymptotic expansion strategy to derive a compressible version of the first-order non-equilibrium model, valid for low-concentration regimes (particle volume fraction less than 10−3) and particle Stokes number (St – i.e., the ratio between relaxation time and flow characteristic time) not exceeding about 0.2. The new model, which is called ASHEE (ASH Equilibrium Eulerian), is significantly faster than the N-phase Eulerian model while retaining the capability to describe gas–particle non-equilibrium effects. Direct Numerical Simulation accurately reproduces the dynamics of isotropic, compressible turbulence in subsonic regimes. For gas–particle mixtures, it describes the main features of density fluctuations and the preferential concentration and clustering of particles by turbulence, thus verifying the model reliability and suitability for the numerical simulation of high-Reynolds number and high-temperature regimes in the presence of a dispersed phase. On the other hand, Large-Eddy Numerical Simulations of forced plumes are able to reproduce the averaged and instantaneous flow properties. In particular, the self-similar Gaussian radial profile and the development of large-scale coherent structures are reproduced, including the rate of turbulent mixing and entrainment of atmospheric air. Application to the Large-Eddy Simulation of the injection of the eruptive mixture in a stratified atmosphere describes some of the important features of turbulent volcanic plumes, including air entrainment, buoyancy reversal and maximum plume height. For very fine particles (St → 0, when non-equilibrium effects are negligible) the model reduces to the so-called dusty-gas model. However, coarse particles partially decouple from the gas phase within eddies (thus modifying the turbulent structure) and preferentially concentrate at the eddy periphery, eventually being lost from the plume margins due to the concurrent effect of gravity. By these mechanisms, gas–particle non-equilibrium processes are able to influence the large-scale behavior of volcanic plumes.