Oscillatory Darcy Flow in Porous Media

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• 作者：Tao Zhu ; Michael Manhart
• 关键词：Oscillatory porous media flow ; Unsteady Darcy equation ; Time scale ; Direct numerical simulation ; Womersley number
• 刊名：Transport in Porous Media
• 出版年：2016
• 出版时间：January 2016
• 年：2016
• 卷：111
• 期：2
• 页码：521-539
• 全文大小：1,825 KB
• 参考文献：Batchelor, G.K.: An Introduction to Fluid Dynamics. Cambridge University Press, Cambridge (1967)
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• 作者单位：Tao Zhu (1)
  Michael Manhart (1)
  
  1. Technische Universität München, Fachgebiet Hydromechanik, Arcisstr. 21, 80333, Munich, Germany
  
• 刊物类别：Earth and Environmental Science
• 刊物主题：Earth sciences
  Geotechnical Engineering
  Industrial Chemistry and Chemical Engineering
  Civil Engineering
  Hydrogeology
  Mechanics, Fluids and Thermodynamics
  
• 出版者：Springer Netherlands
• ISSN：1573-1634

文摘

We investigate the flow in a porous medium subjected to an oscillatory (sinusoidal) pressure gradient. Direct numerical simulation (DNS) has been performed to benchmark the analytical solutions of the unsteady Darcy equation with two different expressions of the time scale: one given by a consistent volume averaging of the Navier–Stokes equation with a steady-state closure for the flow-resistance term, another given by volume averaging of the kinetic energy equation with a closure for the dissipation rate. For small and medium frequencies, the analytical solutions with the time scale obtained by the energy approach compare well with the DNS results in terms of amplitude and phase lag. For large dimensionless frequencies (\(\omega \tau \gtrsim 10\)), we observe a slightly smaller damping of the amplitude than predicted by the unsteady Darcy equation with the low-frequency time scale. This can be explained by a change in the velocity fields towards a potential flow solution. Note that at those high frequencies, the flow amplitudes remain below 1 % of those of the steady-state flows. Our DNSs, however, indicate that the time scale predicted by the steady-state closure for the flow-resistance term is too small. In general, this study supports the use of the unsteady form of Darcy’s equation with constant coefficients to solve time-periodic Darcy flow, provided the proper time scale has been found. Keywords Oscillatory porous media flow Unsteady Darcy equation Time scale Direct numerical simulation Womersley number