Transitional and Turbulent Flow in Porous Media

Abstract: 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 fibre 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 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. 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 beattributed to turbulence. The macroscopic way of modelling the 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 a new method. 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. Statistical method and frequency analysis are performed to investigate collected data (Papers A and B). Positive skewness of pressure drop fluctuations indicates early stage of presence of turbulent patches in the flow for each pipe. 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 (Paper B). Correlation between the pressure drop between two pipes shows that two parallel pipes follow each other fluctuations much better before 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 (Paper B). 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.