# zbMATH — the first resource for mathematics

Flow simulations over porous media – comparisons with experiments. (English) Zbl 1390.76849
Summary: A closure model is presented to compute turbulent flow over and through porous media. The model is based on the Darcy and Forchheimer term which are also applied to a Reynolds-stress turbulence model. The implementation of the model into a flow solver is validated with wind-tunnel experiments of a 2D-wing with a porous trailing edge. Pressure and PIV measurements are performed for the determination of integral force coefficients and the understanding of the detailed flow field. The measurement data are discussed and compared with the results of the numerical computations. The simulations match most of the experiments very well and reproduce the flow phenomena correctly. The remaining differences are studied in detail by parameter variations in order to understand the flow phenomena. The results yield confidence for using the closure model with minor modifications for more general applications.

##### MSC:
 76S05 Flows in porous media; filtration; seepage 76M25 Other numerical methods (fluid mechanics) (MSC2010) 76-05 Experimental work for problems pertaining to fluid mechanics
TAU; XFOIL
Full Text:
##### References:
 [1] Herr, M.; Rossignol, K.-S.; Delfs, J.; Mößner, M.; Lippitz, N., Specification of porous materials for low-noise trailing-edge applications, 20th AIAA/CEAS aeroacoustics conference, AIAA-2014-3041. atlanta, georgia, (2014) [2] Nakayama, A.; Kuwahara, F., A macroscopic turbulence model for flow in a porous medium, J Fluids Eng, 121, 427-433, (1999) [3] Getachew, D.; Minkowycz, W. J.; Lage, J. L., A modified form of the $$\kappa - ɛ$$ model for turbulent flows of an incompressible fluid in porous media, Int J Heat Mass Trans, 43, 2909-2915, (2000) · Zbl 1094.76529 [4] Mößner, M.; Radespiel, R., Numerical simulations of turbulent flow over porous media, 21st AIAA computational fluid dynamics conference, AIAA 2013-2963. san diego, california, (2013) · Zbl 1390.76849 [5] Mößner, M.; Radespiel, R., Modelling of turbulent flow over porous media using a volume averaging approach and a Reynolds stress model, Comput Fluids, 108, 25-42, (2015) · Zbl 1390.76199 [6] Bear, J.; Bachmat, Y., Introduction to modeling of transport phenomena in porous media, Theory and applications of transport in porous media, 4, (1990), Kluwer Academic Publishers · Zbl 0743.76003 [7] Whitaker, S., The method of volume averaging, Theory and applications of transport in porous media, 13, (1999), Kluwer Academic [8] Cécora, R.-D.; Eisfeld, B.; Probst, A.; Crippa, S.; Radespiel, R., Differential Reynolds stress modeling for aeronautics, 50th AIAA aerospace sciences meeting, AIAA 2012-0465. nashville, tennessee, (2012) [9] Probst, A.; Radespiel, R., Implementation and extension of a near-wall Reynolds-stress model for application to aerodynamic flows on unstructured meshes, 46th AIAA sciences meeting and exhibit, AIAA 2008-770. reno, nevada, (2008) [10] Jakirlić, S., Reynolds-spannungs-modellierung komplexer turbulenter Strömungen, (1997), Universität Erlangen-Nürnberg, Ph.D. thesis [11] Whitaker, S., The Forchheimer equation: a theoretical development, Trans Porous Media, 25, 27-91, (1996) [12] Schwamborn, D.; Gerhold, T.; Heinrich, R., The DLR TAU-code: recent applications in research and industry, (Wesseling, P.; Oñate, E.; Périaux, J., ECCOMAS CFD 06, (2006), TU delft, The Netherlands) [13] Breugem, W.-P., The influence of wall permeability on laminar and turbulent flows, (2005), Technische Universiteit Delft, Ph.D. thesis [14] Herr, M.; Rossignol, K.-S.; Delfs, J.; Lippitz, N.; Mößner, M., Specification of Porous Materials for Low-Noise Trailing-Edge Applications, (2014), 20th AIAA/CEAS Aeroacoustics Conference Atlanta Georgia, Ph.D. thesis [15] Macdonald, I. F.; El-Sayed, M. S.; Mow, K.; Dullien, F. A.L., Flow through porous media - the ergun equation revisited, Ind Eng Chem Fundam, 18, 3, 199-208, (1979) [16] Drela, M., XFOIL: an analysis and design system for low Reynolds number airfoils, (Mueller, T. J., Low Reynolds number aerodynamics, Lecture Notes in Engineering, 54, (1989), Springer Berlin Heidelberg), 1-12 [17] XFLR5. http://www.xflr5.com/xflr5.htm; 2014. [18] Ochoa-Tapia, J. A.; Whitaker, S., Momentum transfer at the boundary between a porous medium and a homogeneous fluid - I. theoretical development, Int J Heat Mass Trans, 38, 2635-2646, (1995) · Zbl 0923.76320
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.