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Título:EXPERIMENTS ON THE ADDITIONAL DYNAMIC PRESSURE IN THE FLOW RELATIVE BETWEEN SOLID PARTICLES AND VISCOUS FLUID Instituição:PONTIFÍCIA UNIVERSIDADE CATÓLICA DO RIO DE JANEIRO - PUC-RIO Autor(es):ROBERTO GUIMARAES PEREIRA
Experiments concerning the relative motion of solid particles and viscous fluids, confined within cylinders of arbitrary cross-section (circular and quadrangular) have been conducted. For all cases experimentally investigated and for a flow regime extending from a very low particle Reynolds Number (Re less than 0.1) up to far beyond the Oseen s Regime, it has been shown that the additional pressure force to viscous drag ratio (Delta plus A/D) can be directly evaluated by means of parameters of the unperturbed flow. Accordingly to a recent theory (Brenner, 1962) the above statement which uses a Oseen s type linearization of the equation of motion, should only be expected for the very low particle Reynolds Number regime (Re < 2). Brenner (1962), using momentum and energy theorems applied to the relative motion of a particle and a confined viscous fluid has shown that, as a result of the relative motion, a finete shearing force acting on the cylinder walls must existis, even if the walls are infinitely distant from the particle perturbation. The generality of Brenner s theory concerning the cylinder geometry was also verified in the Stokes and in the Oseen s regimes. Experiments conducted in a short (1 m) circular cylinder, filled with a Newtonian fluid, provided the base line data set used to qualify the experimental technique used, within very low experimental uncertainties. Experiments conducted in a long square cylinder (3 m), allowed verification of the theory far beyond the theorectical regime. Measurements of the additional pressure drop created by the relative motion between a solid particle and the viscous fluid, confined in the square
cylinder, cleary defined three regions: i) up to about Re ~ 50 it was found that the pressure force to Viscous drag ratio Delta P+A/D approximately 2.093 which should be expected only for Re < 2. By
elementary momentum considerations, applied to the fluid control volume around the particle present in the flow, it can easily be show that this value of Delta P+A/D diferente than 1 confirms the existence of a
finete shearing force on the far walls of the cylinder; ii) beyond Re = 50 and up to Re ~ 2500 a very complex and not completely understood transition occurs. At about Re ~ 50 an abrupt transition takes place forcing the value of Delta P+A/D to decrease. The ratio Delta P+A/D decreases asymptotically towards the value 1.0 wich corresponds to the situation of an unbounded fluid as can be predicted by the Momentum Principle; iii) for particle Reynolds Number Re > 2500, the Delta P+A/D approaches very closely the value 1.0. The largest flow regime investigated was Re ~ 36000 but, physically, there seems to be no reason to expect any change in the described behaviour. This work also discusses an accurate method for
directly measuring the viscous drag force and the diminute dynamic pressure (~ 1 to 10 (-3) mm Hg) created by the motion of the particle.