Visualization of the Transition To Turbulent Flow In Porous Media
Authors: McFarland J.D. , Dranchuk P.M. 
Published: March 2010

Abstract
Flow experiments were conducted on four synthetic porous media in order to determine the Reynolds number at the point of transition to turbulent flow. Two sphere sizes were employed, of 0.25 and 0.5 in. diameter, and two packing arrangements, a Cubic No.1 and an Orthorhombic No.2.
The streaming birefringence visualization technique was used to observe the transition to turbulence in flowing milling yellow dye solutions. This technique offers the advantageof eliminating the flow disturbance that results when intrusive measuring techniques are employed, and provides good reproducibility and sharp definition of the transition. The non-Newtonian nature of the birefringent milling yellow dye solution required that the effective viscosity in the Reynolds number at the transition to turbulence be calculated from the Forchheimer equation adapted for non-Newtonian flow.
The results indicate that the transition to turbulent flow takes place over a range of Reynolds numbers from 0.241 to 4.56, where the Reynolds number is based on superficial velocity and a length parameter equal to the product of the permeability und the inertial resistance coefficient of the puck. These results compare favourably with those in the literature when a Reynolds number based on superficial velocity and sphere diameter is used for this comparison.

Introduction
It has long been known that Darcy's Law fails to describe flow through porous media at high rates. Early investigators(1) thought that failure of the law occurred when the flow regime changed from laminar to turbulent. However, recent studies(2–6) indicate that pressure drop ceases to be a linear function of flow rate well before turbulence is developed. It is suggested that the departure from linearity is due to the increased significance of inertial forces, but that flow continues to be laminar and that true turbulence develops at much higher flow rates.
Although the latter explanation is widely accepted as correct, some people still use the term turbulent to describe such flows, others use non-Darcy and turbulent interchangeable, and still others(7) tend to use inertialnd turbulent in a confusing manner. The matter is not one of semantics alone, for it appears that in flow through porous media three different flow regimes are possible; namely, viscous, visco-inertial and turbulent. Furthermore, it appears possible that a different mathematical expression may be required to describe flow in each regime.
The most widely used techniques for determining the point of transition to turbulence in bead packs have been dye injection and hot-wire anemometry. Both methods have posed problems. The use of a dye resulted in rapid fluid coloration, which made visual studies difficult. On the other hand, the intrusion of a hot wire into a pore space resulted in distortion of the flow pattern there.
On the basis of these observations, the object of the study described herein was to determine the Reynoldsnumber at the point of transition to turbulent flow in porous media by employing the streaming birefringence flow visualization technique to observe that transition in bead packs.