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A Compressible Fluid Flow Model Coupling Channel and Porous Media Flows and Its Application to Fuel Cell Materials

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Abstract

A multi-dimensional, compressible fluid flow solver, valid in both channel and porous media, is derived by volume-averaging the Navier–Stokes equations. By selecting an appropriate average density/velocity pair, a continuous, stable solution is obtained for both pressure and velocity. The proposed model is validated by studying the pressure drop of two commonly used experimental setups to measure in-plane and through-plane permeability of fuel cell porous media. Numerical results show that the developed model is able to reproduce the experimentally measured pressure drop at varying flow rates. Further, it highlights that previously used methods of extracting permeability, which rely on the use of simplified one-dimensional models, are not appropriate when high flow rates are used to study the porous media. At high flow rates, channel–porous media interactions cannot be neglected and can result in incorrect permeability estimations. For example, at flow rates of 1 SLPM a discrepancy of 12% in pressure drop was observed when using previous permeability values instead of the values obtained in the article using the proposed 3D model. Given that at high flow rate one-dimensional models might not be appropriate, previous estimations of Forchheimer permeability might not be accurate. To illustrate the suitability of the numerical model to fuel cell applications, fluid flow bypass in serpentine and interdigitated fuel cell flow channels is also investigated.

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Acknowledgements

The authors would also like to thank the Natural Sciences and Engineering Research Council of Canada (NSERC), the Automotive Fuel Cell Cooperation (AFCC) Corp., and International Cooling Towers (ICT) for their financial support.

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Authors and Affiliations

  1. Energy Systems Design Lab (ESDLab), University of Alberta, Edmonton, Canada

    Alex Jarauta, Valentin Zingan & Marc Secanell

  2. Department of Mathematical and Statistical Sciences, University of Alberta, Edmonton, Canada

    Peter Minev

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  1. Alex Jarauta
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Appendix: Lid-Driven Cavity Flow Test Case

Appendix: Lid-Driven Cavity Flow Test Case

A standard benchmark problem for testing Navier–Stokes equations is the lid-driven cavity flow problem (Donea and Huerta 2003; Cremonesi et al. 2020), which consists in the flow of an isothermal fluid in a square cavity, as shown in Fig. 19. The fluid contained inside the cavity is set into motion by the top wall which is sliding at constant velocity from left to right, while the other sides are fixed.

Fig. 19
figure 19

Lid-driven cavity flow configuration and boundary conditions

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The steady-state compressible numerical solution is computed at Re = 1000 on a \(128 \times 128\) grid by using \(Q_1\) and \(Q_2\) approximations for density and velocity, respectively. The tolerance of the Newton method is set to \(10^{-10}\). The fluid flow patterns generated in this computation are shown in Fig. 20a, b. The streamlines depicted in Fig. 20a show the formation of three vortexes, which have been already observed in previous numerical studies Donea and Huerta (2003), Ghia et al. (1982), Erturk et al. (2005), Cremonesi et al. (2020).

The numerical results are compared to those previously obtained by Ghia et al. (1982). Figure 21 shows the variation of the horizontal and vertical velocity components along the vertical and horizontal centerlines (i.e., \(y/L = 0.5\) and \(x/L = 0.5\)), respectively. The computational results obtained by the present model are in very good agreement with the available numerical data.

Fig. 20
figure 20

a Velocity field and streamlines and b pressure field for the lid-driven cavity flow at Re = 1000

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Fig. 21
figure 21

a Velocity \(x-\)component profile along the vertical centerline and b velocity \(y-\)component profile along the horizontal centerline for the lid-driven cavity flow at Re = 1000

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Jarauta, A., Zingan, V., Minev, P. et al. A Compressible Fluid Flow Model Coupling Channel and Porous Media Flows and Its Application to Fuel Cell Materials. Transp Porous Med 134, 351–386 (2020). https://doi.org/10.1007/s11242-020-01449-2

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