Two-phase magma flow with phase exchange: Part I. Physical modeling of a volcanic conduit

IF 4.6 Q2 MATERIALS SCIENCE, BIOMATERIALS
Gladys Narbona-Reina, Didier Bresch, Alain Burgisser, Marielle Collombet
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引用次数: 0

Abstract

In a review paper in this same volume, we present the state of the art on modeling of compressible viscous flows ranging from single-phase to two-phase systems. It focuses on mathematical properties related to weak stability because they are important for numerical resolution and on the homogenization process that leads from a microscopic description of two separate phases to an averaged two-phase model. This review serves as the foundation for Parts I and II, which present averaged two-phase models with phase exchange applicable to magma flow during volcanic eruptions. Here, in Part I, after introducing the physical processes occurring in a volcanic conduit, we detail the steps needed at both microscopic and macroscopic scales to obtain a two-phase transient conduit flow model ensuring: (1) mass and volatile species conservation, (2) disequilibrium degassing considering both viscous relaxation and volatile diffusion, and (3) dissipation of total energy. The resulting compressible/incompressible system has eight transport equations on eight unknowns (gas volume fraction and density, dissolved water content, liquid pressure, and the velocity and temperature of both phases) as well as algebraic closures for gas pressure and bubble radius. We establish valid sets of boundary conditions such as imposing pressures and stress-free conditions at the conduit outlet and either velocity or pressure at the inlet. This model is then used to obtain a drift-flux system that isolates the effects of relative velocities, pressures, and temperatures. The dimensional analysis of this drift-flux system suggests that relative velocities can be captured with a Darcy equation and that gas–liquid pressure differences partly control magma acceleration. Unlike the vanishing small gas–liquid temperature differences, bulk magma temperature is expected to vary because of gas expansion. Mass exchange being a major control of flow dynamics, we propose a limit case of mass exchange by establishing a relaxed system at chemical equilibrium. This single-velocity, single-temperature system is a generalization of an existing volcanic conduit flow model. Finally, we compare our full compressible/incompressible system to another existing volcanic conduit flow model where both phases are compressible. This comparison illustrates that different two-phase systems may be obtained depending on the governing unknowns chosen. Part II presents a 1.5D version of the model established herein that is solved numerically. The numerical outputs are compared to those of another steady-state, equilibrium degassing, isothermal model under conditions typical of an effusive eruption at an andesitic volcano.

两相岩浆流动与相交换:第一部分:火山导管的物理建模
在同卷的一篇综述论文中,我们介绍了从单相系统到两相系统的可压缩粘性流建模技术现状。论文重点讨论了与弱稳定性相关的数学特性,因为这些特性对数值分辨率非常重要,同时还讨论了从两个独立相的微观描述到平均两相模型的均质化过程。本综述是第一部分和第二部分的基础,这两部分介绍了适用于火山喷发过程中岩浆流动的具有相交换的平均两相模型。在第一部分中,在介绍了火山导管中发生的物理过程之后,我们详细说明了在微观和宏观尺度上获得两相瞬态导管流模型所需的步骤,以确保:(1)质量和挥发性物种守恒;(2)考虑粘性松弛和挥发性扩散的非平衡脱气;以及(3)总能量耗散。由此产生的可压缩/不可压缩系统包含八个未知量(气体体积分数和密度、溶解水含量、液体压力以及两相的速度和温度)的八个传输方程,以及气体压力和气泡半径的代数闭包。我们建立了有效的边界条件集,例如在导管出口处施加压力和无应力条件,在入口处施加速度或压力。然后利用该模型得到一个漂移-流动系统,该系统可隔离相对速度、压力和温度的影响。对这一漂移-流动系统的尺寸分析表明,相对速度可以用达西方程来捕捉,气液压力差在一定程度上控制着岩浆加速度。与消失的微小气液温差不同,岩浆体积温度预计会因气体膨胀而变化。质量交换是流动动力学的主要控制因素,因此我们提出了一种质量交换的极限情况,即建立一个处于化学平衡状态的松弛系统。这种单一速度、单一温度的系统是对现有火山导管流模型的概括。最后,我们将我们的完全可压缩/不可压缩系统与另一个现有的两相都可压缩的火山导管流模型进行了比较。这种比较说明,根据所选的控制未知量,可以得到不同的两相系统。第二部分介绍了本文所建立模型的 1.5D 版本,并对其进行了数值求解。在安山岩火山喷发的典型条件下,将数值输出结果与另一个稳态、平衡脱气、等温模型的输出结果进行比较。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
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来源期刊
ACS Applied Bio Materials
ACS Applied Bio Materials Chemistry-Chemistry (all)
CiteScore
9.40
自引率
2.10%
发文量
464
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