Analysis by the Dissipation Theorem of Turbulent Flow in a Pipe

Monday, 2 October 2017: 14:00
Chesapeake 12 (Gaylord National Resort and Convention Center)
J. Newman (University of California, Berkeley)
More than a year ago, I proposed analyzing turbulent flow and predicting friction and mass transfer by relating one statistical quantity for the flow to other statistical quantities on a local basis. This is what we do with laminar flow, where the stress is related to the viscosity and the velocity gradient. Excellent data could be found on turbulent mass transfer in the system where one cylinder rotates within a larger stationary cylinder. Excellent data on fluid friction and pressure drop are found for turbulent pipe flow. The dissipation theorem has been applied to this system. In the course of doing this, several aspects of the earlier work have been refined. Furthermore, one can make predictions of the eddy viscosity and the dissipation that accord with old measurements. Of course, some empiricism is required, but one strives to keep this on a local level where the volumetric dissipation is related to the eddy viscosity. The behavior of the system is surprising, and the literature data are quite different from what one might have expected.