A Hybrid-Dimensional Coupled Pore-Network/Free-Flow Model Including Pore-Scale Slip and Its Application to a Micromodel
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A Hybrid‑Dimensional Coupled Pore‑Network/Free‑Flow Model Including Pore‑Scale Slip and Its Application to a Micromodel Experiment K. Weishaupt1 · A. Terzis2 · I. Zarikos3 · G. Yang4 · B. Flemisch1 · D. A. M. de Winter5 · R. Helmig1 Received: 25 April 2020 / Accepted: 3 September 2020 / Published online: 14 September 2020 © The Author(s) 2020
Abstract Modeling coupled systems of free flow adjacent to a porous medium by means of fully resolved Navier–Stokes equations is limited by the immense computational cost and is thus only feasible for relatively small domains. Coupled, hybrid-dimensional models can be much more efficient by simplifying the porous domain, e.g., in terms of a pore-network model. In this work, we present a coupled pore-network/free-flow model taking into account pore-scale slip at the local interfaces between free flow and the pores. We consider two-dimensional and three-dimensional setups and show that our proposed slip condition can significantly increase the coupled model’s accuracy: compared to fully resolved equidimensional numerical reference solutions, the normalized errors for velocity are reduced by a factor of more than five, depending on the flow configuration. A pore-scale slip parameter 𝛽pore required by the slip condition was determined numerically in a preprocessing step. We found a linear scaling behavior of 𝛽pore with the size of the interface pore body for threedimensional and two-dimensional domains. The slip condition can thus be applied without incurring any run-time cost. In the last section of this work, we used the coupled model to recalculate a microfluidic experiment where we additionally exploited the flat structure of the micromodel which permits the use of a quasi-3D free-flow model. The extended coupled model is accurate and efficient. Keywords Coupling · Free flow · Pore-network model · Porous medium · Micromodel
* K. Weishaupt [email protected]‑stuttgart.de 1
Department of Hydromechanics and Modelling of Hydrosystems, University of Stuttgart, Stuttgart, Germany
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Department of Mechanical Engineering, Stanford University, Stanford, CA, USA
3
Institute of Nuclear and Radiological Sciences and Technology, Energy and Safety, NCSR Demokritos, Athens, Greece
4
School of Mechanical Engineering, Shanghai Jiao Tong University, Shanghai, China
5
Environmental Hydrogeology Group, Department of Earth Sciences, Utrecht University, Utrecht, The Netherlands
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1 Introduction Coupled systems of free flow over a porous medium play an important role in many environmental, biological and technical processes. Examples include evaporation from soil governed by atmospheric air flow (Vanderborght et al. 2017), intervascular exchange in living tissue (Chauhan et al. 2011), preservation of food (Verboven et al. 2006), fuel cell water management (Gurau and Mann 2009) or heat exchange systems (Yang et al. 2018). Considerable effort has been spent on modeling these kinds of systems where a discrete resolution of the complex p
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