Experimental investigation on water flow in cubic arrays of spheres

• Published in: Journal of hydrology (Amsterdam) Vol. 492; pp. 61 - 68
• Main Authors: Huang, K., Wan, J.W., Chen, C.X., He, L.Q., Mei, W.B., Zhang, M.Y.
• Format: Journal Article
• Language: English
• Published: Kidlington Elsevier B.V 07.06.2013; Elsevier
• Subjects: Arrays; Earth sciences; Earth, ocean, space; Ergun equation; Exact sciences and technology; Fluid dynamics; Fluid flow; Forchheimer equation; Head drop experiments; Hydrogeology; Hydrology. Hydrogeology; Inertial; Mathematical analysis; Non-linear flow; Porous media; Turbulence; Turbulent flow; Head drop experiments; Non-linear flow; Ergun equation; Forchheimer equation; experimental studies; porosity; ground water; turbulent flow; velocity; turbulence; steady flow; one-dimensional models; discontinuities; prediction; particles; Darcy's law; porous media
• ISSN: 0022-1694; 1879-2707
• DOI: 10.1016/j.jhydrol.2013.03.039

•Four test tubes with cubic arrays of spheres in diameter 3mm, 5mm, 8mm and 10mm.•Darcy’s law should be an approximate expression by neglecting the inertial term.•Nonlinearity is attributed to inertial term other than turbulence.•Forchheimer equation can well predict the flow in porous medium.•Coefficients in the Ergun type equations are relevant to pore characteristic. One-dimensional uniform flow in homogeneous porous media was experimentally investigated. Head drop experiments were conducted in four test tubes with cubic arrays of spheres in diameter 3mm, 5mm, 8mm and 10mm. The experimental results indicate that Darcy’s law should be an approximate expression by neglecting the inertial term for flow at low velocity. Nonlinearity is attributed to inertial term in porous medium before the turbulent flow emerges. Forchheimer equation with constant coefficients can well predict the flow in porous medium. The relationship between the diameter of the particles and the coefficients a and b in the equations were verified. Different Ergun type equations were used to predict the head drop and compared to the experimental data. It shows that the Irmay equation could well predict the fluid flow in cubic arrays of spheres, while the prediction of head drop by Ergun equation was much higher than observed data. It indicates that the coefficients α and β in the Ergun type equations have certain relations with porosity or the pore structure and would vary for different medium. The discontinuity observed was interpreted by transition from steady flow to weakly turbulence and compared with previous studies.