Experimental investigation on water flow in cubic arrays of spheres

- Four test tubes with cubic arrays of spheres in diameter 3 mm, 5 mm, 8 mm and 10 mm.
- 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 3 mm, 5 mm, 8 mm and 10 mm. 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.