ANALYTICAL APPROACHES FOR CALCULATION OF SHEAR STRESS ENHANCEMENT IN LAMINAR PULSED FLOWS

Analytical approaches have been developed for quantifying the enhancement of wall shear stress offered by intermittent flow pulsing, based on pressure gradient data, for the tubular and annular flow geometries commonly used in fouling and cleaning studies. The solutions are strictly only valid in the laminar regime. For the pipe geometry the two approaches, based on Fourier series integration and Green functions, respectively, both yielded results for nonregular pressure gradients in relatively short periods of computation time which were consistent with previously published solutions and CFD simulations. The Fourier series approach proved to be cumbersome for annular ducts so only the Green function approach was followed to completion. The enhancement of surface shear stress over a baseline steady laminar flow is reported for both geometries: the enhancement depends on both the magnitude of the pressure gradient and the fraction of repeat period occupied by the pulse. The enhancement of shear stress in an annular flow geometry is also reported for the case of equivalent steady flow, where the total flow for the pulse and baseline remains constant. The improvement is small when long pulses are used. A noteworthy observation is that the process conditions employed by Gillham and co-workers (2000) to enhance the cleaning of whey protein deposits during simulated alkaline cleaning-in-place tests were likely to have promoted turbulence in their system.