Investigation of micro-shock waves in a planar magnetogasdynamic flow using the discontinuous Galerkin finite element method

IF 2.8 Q2 MECHANICS
Alberto Gallottini, L. Könözsy
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引用次数: 0

Abstract

The present work focuses on the numerical investigation of micro-shock wave propagation in a two-dimensional magnetogasdynamic flow in the framework of the Dis- continuous Galerkin-Finite Element Method (DG-FEM). The Lorentz force has been im- plemented in the compressible, viscous Navier–Stokes equations as a source term using first-order spatial and fourth-order temporal Runge–Kutta discretization schemes. To in- vestigate the effect of the electrical conductivity on the micro-shock wave propagation, a two-dimensional micro-shock channel problem with hydraulic diameter of 2.5 mm, length of 82 mm, and no-slip boundary conditions at the left and at the right wall is considered as a benchmark problem. In this case, acoustic waves are generated behind after the rupture of the membrane that separates two states of the same gas originally at different pressure and density and both initially at rest. The magnetic field is taken into account as uniform and stationary throughout the microchannel, and the numerical simulations are performed in a short physical time, before the reflection of the waves on the lateral wall. A detailed parametric study of the temperature, density, pressure, and u-velocity is carried out by a variation of the electrical conductivity of the magnetogasdynamic flow, under the assumption of low magnetic Reynolds numbers. It has been found that the jumps of the acoustic waves become significantly intensified when the electrical conductivity of the gas is increased. It has also been observed that the presence of the Lorentz force causes an acceleration in the gasflow towards the outlet section of the microchannel at the low Knudsen number of 0.05. The outcome of this research work could be relevant to biomedical applications where the ability to control the flow in a microchannel has a significant impact on the development of small devices aimed to deliver pharmaceutical drugs in specific locations.
用不连续伽辽金有限元法研究平面磁气动力流中的微激波
本文采用非连续伽辽金有限元法(DG-FEM)对二维磁气动力学流中微激波的传播进行了数值研究。采用一阶空间和四阶时间龙格-库塔离散格式,将洛伦兹力作为源项引入可压缩粘性Navier-Stokes方程中。为了研究电导率对微激波传播的影响,以一个水力直径为2.5 mm、长度为82 mm、左右壁面无滑移边界条件的二维微激波通道问题为基准问题。在这种情况下,声波是在分离同一气体的两种状态的膜破裂后产生的,这两种状态最初处于不同的压力和密度,最初都处于静止状态。考虑磁场在整个微通道中是均匀和平稳的,并在较短的物理时间内进行了数值模拟,然后将波反射到侧壁上。在低磁雷诺数的假设下,通过磁气动力学流的电导率变化,对温度、密度、压力和u型速度进行了详细的参数研究。研究发现,当气体的电导率增加时,声波的跳变明显增强。还观察到,在低克努森数为0.05时,洛伦兹力的存在导致气体流向微通道出口段的加速。这项研究工作的结果可能与生物医学应用有关,在生物医学应用中,控制微通道流量的能力对旨在在特定位置输送药物的小型设备的开发具有重大影响。
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
CiteScore
6.90
自引率
3.20%
发文量
0
审稿时长
8 weeks
期刊介绍: The Journal of Applied and Computational Mechanics aims to provide a medium for dissemination of innovative and consequential papers on mathematical and computational methods in theoretical as well as applied mechanics. Manuscripts submitted to the journal undergo a blind peer reviewing procedure conducted by the editorial board. The Journal of Applied and Computational Mechanics devoted to the all fields of solid and fluid mechanics. The journal also welcomes papers that are related to the recent technological advances such as biomechanics, electro-mechanics, advanced materials and micor/nano-mechanics. The scope of the journal includes, but is not limited to, the following topic areas: -Theoretical and experimental mechanics- Dynamic systems & control- Nonlinear dynamics and chaos- Boundary layer theory- Turbulence and hydrodynamic stability- Multiphase flows- Heat and mass transfer- Micro/Nano-mechanics- Structural optimization- Smart materials and applications- Composite materials- Hydro- and aerodynamics- Fluid-structure interaction- Gas dynamics
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