Turbulent and Transitional Flow in Porous Media An Experimental Investigation

Sammanfattning: Fluid flow through porous media takes place in many natural processes such as ground water flows, capillary flows in plants and flow in human organs and muscles. It is also of outmost importance to have knowledge of this flow in a number of industrial processes such as paper making, making of fiber boards, composites manufacturing, filtering, forming and sintering of iron ore pellets and drying and impregnation of wood. Despite the significance of porous media flow and the vast amount of work that has been performed to investigate it, knowledge of some fundamentals is missing. Little is, for instance, known about flow field at the inlet, mid-section and outlet of porous bed as well as transitional and turbulent flow in porous media on the microscopic level. On a macroscopic level Darcy law is extended to the so called Ergun or Forchheimer Equations when Re becomes larger than about 10 to fit experimental data. The actual value depends both on the porous media and how Re is defined. The deviation from Darcy flow can for modest Re be explained by inertia but may, as Re increases, also be attributed to turbulence. The macroscopic way of modelling the flow field during transition from inertia dominated to turbulent flow is just to continue with the Forchheimer Equation or possibly some version of it. In any case experimental data yields that, on a macroscopic level, the transition from Darcy flow to inertia dominated and turbulent flow is smooth. To get a better understanding of this process the transition from laminar to turbulent flow in porous media is here studied with new experimental methods. To mimic inter-connected pores, a simplified geometry is studied consisting of a pipe with a relatively large diameter that is split into two parallel pipes with different diameters. This is a pore-doublet set-up and the pressure drop over all pipes is recorded by pressure transducers for different flow rates. The model is also extended to three parallel pipes. In the other main set-up the flow in a bed of spheres is studied with indexed matched fluids and with classical 2D-PIV and Stereoscopic-PIV. This is done in order to be able to understand the conditions in different flow regimes and in different position of the porous media even before and after it. The measurements are performed at a large range of Reynolds numbers, 30 < Rep < 4000 and the bed consists of relatively many spheres. The size of the porous bed is 0.10 x 0.10 x 0.31 m3 and the spheres are 12.5 mm in diameter. Statistical methods and frequency analysis are performed to investigate the data collected. Positive skewness of pressure drop fluctuations indicates early stage of presence of turbulent patches in the flow in the set-up with pipes. The measured flow distribution and pressure drop fluctuations highlights six distinct flow patterns in the pipe network based on variation in flow regime of each pipe and the level of pressure fluctuations. Correlation between the pressure drop between the two pipes shows that fluctuations in the flow in one pipe is mirrored in the other pipe much better than when both of them become fully turbulent. Some detailed results are that the frequency analysis reveals two different frequency band events in the pipes. The gain factor shows that both frequency band events originate from the larger pipe until the early presence of turbulent patches in the smaller pipe. The low frequency fluctuations makes the flow in the pipes to be out of phase while the high frequency band fluctuations try to bring the flow in the pipes back to equilibrium state. The 2D-PIV measurements showed that the flow is no longer in the creeping regime at Rep ≈ 100 while intregrated pressure drop data yield that it is. This shows that detailed measurements can yield more information of the overall flow field than measurements of integrated quantities. Also the velocity distribution is self-similar with respect to Rep for laminar flow and for turbulent flow. The PIV measurement also yields that the probability for relatively low and high velocities decreases with Rep while recirculation zones that appear in inertia dominated flows are suppressed by the turbulent flow at higher Rep. Finally and to my best knowledge, for the first time stereoscopic particle image velocimetry has been used to investigate the flow dynamic in a randomly packed bed of mono sized spherical particles. This reveals a highly three-dimensional flow.