Impact of web permeability on high speed web transport

Abstract

Measurements of drag on a moving web in a multi-span festoon show a stronger than expected dependency on the porosity of the web with a highly non-linear relationship. The experiments suggest a wall shear stress 3-4 times larger than non-porous webs or historical Couette flow data for solid walls. Previous DNS studies of boundary layers with passive porous surfaces predict a much smaller increase in wall shear stress for a porous wall of only 40%. Other DNS studies of porous walls with periodic transpiration do show a large increase in drag under certain periodic conditions of modest amplitude. Although those results are more aligned in magnitude with this study, the exact reason for the observed high drag for porous webs in this present study is not understood because there was no external disturbance applied to the web. Previously reported experimental data reported a strong linear correlation between wall shear stress and web permeability. The present paper refines those measurements in more detail and shows a highly nonlinear relationship between wall shear stress and permeability, but we offer no physical explanation for this relationship. It can be hypothesized that natural flutter of the web results in a similar mechanism shown in the periodic DNS study, but when the natural flutter was reduced by increasing web tension, there was only a small decrease of the drag.

Because of the prevalence of such flows in many industrial processes using festoons for web accumulation, and the large drag increase that accompanies porous webs, the topic is a very relevant problem. With multiple parallel spans in a festoon, any transpiration in one layer must act in the opposite manner on the adjacent span. This coupling may play a role in the amplification of the drag. Higher drag through a festoon creates processing limitations for light weight porous webs such as non-wovens by restricting maximum speeds or requiring higher than desired web tension to process at high speeds. A festoon is a series of many parallel web paths between idler rolls resulting in a multiple set of planar Couette flows between the moving webs. Length/gap ratios approach 100, with distance between the webs ranging from several millimeters to several hundred millimeters.