The Use of the Inverse Problem Methodology in Analysis of Fluid Flow Through Granular Beds With Non-Uniform Grain Sizes

• Autorzy: Sobieski Wojciech , Trykozko Anna

Identyfikatory

DOI

10.31648/ts.6772

• Języki publikacji: EN

Abstrakty

EN

The pressure drop during water flow through two gravel beds with 2-8 and 8-16 [mm] grain size was measured across a wide range of filtration velocities, and the optimal method for calculating the coefficients for Darcy’s law and Forchheimer’s law was selected. The laws and the experimental data were used to develop a computational program based on the Finite Element Method (FEM). The results were compared, and errors were analyzed to determine which law better describes flow data. Various methods of measuring porosity and average grain diameter, representative of the sample, were analyzed. The data were used to determine the limits of applicability of both laws. The study was motivated by the observation that computational formulas in the literature produce results that differ by several orders of magnitude, which significantly compromises their applicability. The present study is a continuation of our previous research into artificial granular materials with similarly sized particles. In our previous work, the results produced by analytical and numerical models were highly consistent with the experimental data. The aim of this study was to determine whether the inverse problem methodology can deliver equally reliable results in natural materials composed of large particles. The experimental data were presented in detail to facilitate the replication, reproduction and verification of all analyses and calculations.

Słowa kluczowe

EN

granular media; reverse problem; Darcy; Forchheimer

• Wydawca: Wydawnictwo Uniwersytetu Warmińsko-Mazurskiego w Olsztynie
• Czasopismo: Technical Sciences / University of Warmia and Mazury in Olsztyn
• Rocznik: 2021
• Tom: nr 24(1)
• Strony: 83--104
• Opis fizyczny: Bibliogr. 34 poz., rys., tab., wykr.

Twórcy

autor

Sobieski Wojciech

• Katedra Mechaniki i Podstaw Konstrukcji Maszyn, Uniwersytet Warmińsko-Mazurski, 10-736 Olsztyn, ul. Oczapowskiego 11

• https://orcid.org/0000-0003-1434-5520

autor

Trykozko Anna

• Interdyscyplinarne Centrum Modelowania Matematycznego i Komputerowego Uniwersytetu Warszawskiego, 02-106 Warszawa, ul. Pawińskiego 5a

• https://orcid.org/0000-0002-0674-7944

Bibliografia

• Anderson B.A., Sarkar A., Thompson J.F., Singh R.P. 2004. Commercial-Scale Forced-Air Cooling Of Packaged Strawberries. Transactions of the ASAE, 47(1): 183-190. American Society of Agricultural Engineers.
• Battenburg D. van, Milton-Tayler D. 2005. Discussion of SPE 879325, Beyond Beta factors: a complete model for Darcy, Forchheimer, and Trans-Forchheimer flow in porous media. Journal of Petroleum Technology, 57: 72-74.
• Bear J. 1972. Dynamics of Fluids in Porous Media. Elsevier, Amsterdam.
• Bloshanskaya L., Ibragimov A., Siddiqui F., Soliman M. 2016. Productivity Index for Darcy and pre-/post-Darcy Flow (Analytical Approach). Journal of Porous Media, 20(9).
• Breugem W.P., Boersma B.J., Uittenbogaard R.E. 2004. Direct numerical simulations of plane channel flow over a 3D Cartesian grid of cubes. In: Applications of porous media. Eds. A.H. Reis, A.F. Miguel. Évora: Évora Geophysics Center, p. 27-35.
• Carminati A., Kaestner A., Ippisch O., Koliji A., Lehmann P., Hassanein R., Vontobel P., Lehmann E., Laloui L., Vulliet L. 2007. Water flow between soil aggregates. Transport in Porous Media, 68(2): 219-236.
• Darcy H. 1856. Les Fontaines Publiques De La Ville De Dijon. Victor Dalmont, Paris, France.
• Ergun S. 1952. Fluid flow through packed columns. Chemical and Engineering Progress, 48: 89-94.
• Forchheimer P. 1901. Wasserbewegung durch boden. Zeit. Ver. Deutsch. Ing., 45: 1781-1788.
• Fourar M., Lenormand R., Karimi-Fard M. 2005. Inetria Effects in High-Rate Flow Through Heterogeneous Porous Media. Transport in Porous Media, 60: 353-370.
• GAMBIT 2.2 Tutorial Guide. 2004. Fluent, Incorporated.
• Hansen T.E. 2007. Flow in micro porous silicon carbide. Master Thesis. Department of Micro and Nanotechnology, Technical University of Denmark, March 2nd.
• Hassanizadeh S.M., Gray W.G. 1987. High Velocity Flow in Porous Media. Transport in Porous Media, 2: 521-531.
• Hellström J.G.I., Lundström T.S. 2006. Flow through Porous Media at Moderate Reynolds Number. International Scientific Colloquium, Modelling for Material Processing, Riga, June 8-9.
• Huang H., Ayoub J. 2008. Applicability of the Forchheimer Equation for Non-Darcy Flow in Porous Media. SPE Journal, 13: 112-122.
• Kaasschieter E.F. 1988. Preconditioned conjugate gradients for solving singular systems. Journal of Computational and Applied Mathematics, 24: 265-275.
• Koponen A., Kataja M., Timonen J. 1996. Tortuous flow in porous media. Physical Review E., 54(1): 406-410.
• Koponen A., Kataja M., Timonen J. 1997. Permeability and effective porosity of porous media. Physical Review E., 56(3): 3319-3325.
• Lucquin B., Pironneau O. 1998. Introduction to Scientific Computing. Wiley, New York.
• Matyka M., Khalili A., Koza Z. 2008. Tortuosity-porosity relation in the porous media flow. Physical Review E, 78: 026306.
• Mota M., Teixeira J., Yelshin A. 1999. Image analysis of packed beds of spherical particles of different sizes. Separation and Purification Technology, 15(1-4): 59-68.
• Nabovati A., Sousa C.M. 2007. Fluid Flow Simulation In Random porous media at pore level using Latice Boltzmann method. Journal of Engineering Science and Technology, 2(3): 226-237.
• Nałęcz T. 1991. Ćwiczenia laboratoryjne z mechaniki płynów. Wydawnictwo ART, Olsztyn.
• Neethirajan S., Karunakaran C., Jayas D.S., White N.D.G. 2006. X-ray Computed Tomography Image Analysis to explain the Airflow Resistance Differences in Grain Bulks. Biosystems Engineering, 94(4): 545-555.
• Peszyńska M., Trykozko A., Augustson K. 2009a. Computational upscaling of inertia effects from porescale to mesoscale. In: ICCS 2009 Proceedings, LNCS 5544. Part I. Eds. G. Allen, J. Nabrzyski, E. Seidel, D. van Albada, J. Dongarra, P. Sloot. Springer-Verlag, Berlin-Heidelberg, p. 695-704.
• Peszyńska M., Trykozko A., Augustson K., Sobieski W. 2009b. Computational Upscaling of Inertia Effects from Porescale to Mesoscale. Conference on Mathematical and Computational Issues in the Geosciences SIAM GS, Leipzig, 15-18 June.
• Sawicki J., Szpakowski W., Weinerowska K., Wołoszyn E., Zima P. 2004. Laboratorium z mechaniki płynów i hydrauliki. Politechnika Gdańska, Gdańsk.
• Sidiropoulou M.G., Moutsopoulos K.N., Tsihrintzis V.A. 2007. Determination of Forchheimer equation coefficients a and b. Hydrological Processes, 21(4): 534-554.
• Sobieski W. 2010. Examples of Using the Finite Volume Method for Modeling Fluid-Solid Systems. Technical Sciences, 13: 256-265.
• Sobieski W., Trykozko A. 2011. Sensitivity aspects of Forchheimer’s approximation. Transport in Porous Media, 89(2): 155-164.
• Sobieski W., Trykozko A. 2014a. Darcy’s and Forchheimer’s laws in practice. Part 1. The experiment. Technical Sciences, 17(4): 321-335.
• Sobieski W., Trykozko A. 2014b. Darcy’s and Forchheimer’s laws in practice. Part 2. The numerical model. Technical Sciences, 17(4): 337-350.
• Wu J., Tu B., Yun M. 2008. A resistance model for flow through porous media. Transport in Porous Media, 71(3): 331-342.
• Yu B.-M., Li J.-H. 2004. A geometry model for tortuosity of flow path in porous media. Chinese Physics Letters, 21(8): 1569-1571.

Uwagi

Opracowanie rekordu ze środków MEiN, umowa nr SONP/SP/546092/2022 w ramach programu "Społeczna odpowiedzialność nauki" - moduł: Popularyzacja nauki i promocja sportu (2022-2023)