Flow near the permeable boundary of an aligned fiber preform: An experimental investigation using laser doppler anemometry

• Published in: Polymer composites Vol. 18; no. 1; pp. 114 - 124
• Main Authors: Gupte, Sunil K., Advani, Suresh G.
• Format: Journal Article
• Language: English
• Published: Hoboken Wiley Subscription Services, Inc., A Wiley Company 01.02.1997; Willey
• Subjects: Applied sciences; Composites; Exact sciences and technology; Forms of application and semi-finished materials; Polymer industry, paints, wood; Technology of polymers; Fiber reinforced materials; Composite materials; Flow(fluid); Prepreg; Fiber orientation; Measurement method; Anemometry
• ISSN: 0272-8397; 1548-0569
• DOI: 10.1002/pc.10266

The flow of fluid at the interface of an aligned fiber bed and an open flow is the governing phenomenon in a number of processes of industrial importance. Traditionally, this has been modeled by applying Brinkman's modification of Darcy's law to obtain the velocity profile in planar geometries in terms of an additional parameter called “apparent viscosity.” to test this ad hoc approach, a detailed experimental investigation of the flow was conducted using Laser Doppler Anemometry (LDA) in the close vicinity of the permeable boundary of aligned fiber preforms. The performs used in the experiments consisted of cylindrical fibers aligned in one direction. Two cases were investigated. In the first case, the axis of alignment was in the direction of flow and in the second case the axis of alignment was perpendicular to the flow direction. A Hele‐Shaw cell is partially filled with a fibrous preform such that an open channel flow is coupled to the Darcy flow inside the fiber bed through the permeable interface of the bed. The unfilled portion of the Hele‐Shaw cell acts as an ideal porous medium of known in‐plane permeability, which is much higher than the permeability of the fibrous/porous bed. Modeling this flow situation using a Hele‐Shaw cell is appropriate because most composite parts are long and wide in comparison with their thickness. When a viscous fluid is injected at a constant flow rate through the above arrangement, a steady state coupled flow is created. This coupling of the open flow and the Darcy flow through the fibrous bed occurs through the boundary layer zone inside the fibrous bed. Using LDA, steady state velocity profiles are accurately measured in the boundary layer zone by traversing the fibrous bed at a suitable location. For aligned fiber beds, the depth of the boundary layer zone inside the bed was found to be of the order of the mold depth, which is much larger as compared to the Brinkman's prediction. This finding indicates the presence of a length scale that is much larger than the known length scale \documentclass{article}\pagestyle{empty}\begin{document}$ \sqrt K $\end{document}, where K is the permeability of the bed made up of aligned cylindrical fibers. Based on this finding, the depth of the boundary layer thickness is incorporated in the Brinkman's solution through a boundary condition. This results in a model that compares well with the experimental data for the planar geometry and the fibrous beds considered here.