Transport in Porous Media

, Volume 128, Issue 1, pp 201–220 | Cite as

On the Inertial Single Phase Flow in 2D Model Porous Media: Role of Microscopic Structural Disorder

  • Yibiao Wang
  • Azita Ahmadi
  • Didier LasseuxEmail author


In this work, single-phase incompressible laminar flow in 2D model porous media is studied and the influence of microscopic structural disorder on the flow is thoroughly investigated. Emphasis is laid upon the onset of the deviation from Darcy’s law and the identification of different inertia regimes observed before the flow becomes unsteady. For this purpose, six globally disordered pore structures were generated and the values of the critical Reynolds number at which the flow becomes unsteady corresponding to the first Hopf bifurcation were determined. Numerical simulations of steady laminar single-phase flow were then carried out to investigate the effects of the microstructures on the inertial correction to Darcy’s law. Different flow regimes, namely weak inertia, strong inertia and the regime beyond strong inertia, are identified. Comparisons are made with results presented in the literature which were restricted to ordered and locally disordered structures. The critical Reynolds number decreases and inertia intensity increases as more disorder is introduced into the pore structure. Results on flow inertia widely extend some previous studies on the subject and show that it is mainly influenced by the shape of the obstacles (either circular or square), slightly affected by the inclination of the square cylinders and hardly disturbed by the size distribution of the obstacles.


Inertial one-phase flow Non-Darcy flow Flow regimes Darcy–Forchheimer 



The financial support from the program of China Scholarship Council (No. 201506830049) and computational resources provided by the computing facility MCIA (Mésocentre de Calcul Intensif Aquitain) of the University of Bordeaux are gratefully acknowledged.


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Copyright information

© Springer Nature B.V. 2019

Authors and Affiliations

  1. 1.Arts et Métiers, CNRS, I2MTalence CedexFrance
  2. 2.CNRS, I2M, UMR 5295Talence CedexFrance

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