Flow of Newtonian and non-Newtonian fluids in concentric and eccentric annuli

Abstract

Three components of mean velocity and the corresponding Reynolds shear stresses have been measured in fully developed concentric and eccentric annulus flows of a Newtonian fluid at bulk-flow Reynolds numbers of 8900 and 26600 and a weakly elastic shear-thinning polymer at effective bulk-flow Reynolds numbers of 1150, 6200 and 9600. The diameter ratio was 0.5 with eccentricities of 0, 0.5 and 1.0, and the use of a Newtonian fluid of refractive index identical to that of the Perspex working section facilitated the measurements by laser velocimetry.With the Newtonian fluid, the distribution of static pressure measurements on the outer wall is shown to be linear, with friction factors for concentric-annulus flows some 8% higher than in a smooth round pipe and for the eccentric flows of eccentricities of 0.5 and 1.0 it was lower by, respectively 8 and 22.5% than that of the concentric-annulus flow. In the former case, the law of the wall was confirmed on both inner and outer walls of the annulus at both Reynolds numbers. This was also the case for the outer wall in the eccentric-annulus flows, except in the smallest gap, but the near-inner-wall flow was not represented by a logarithmic region particularly in the smallest gap. The locations of zero shear stress and zero velocity gradient were displaced by amounts which were, like the secondary flows measured in the eccentric annulus of 0.5, almost within the measurement precision. In the eccentric-annulus flow with eccentricity of 1.0, there was a secondary flow with two circulation cells on each side of the plane of symmetry and with a maximum velocity of 2.2% of the bulk velocity.The measurements with the non-Newtonian fluid were less detailed since refraction limited the flow accessible to the light beams. The average wall shear stress coefficient was similar to that for the Newtonian fluid in the laminar region of the concentric-annulus flow and higher for the two eccentric-annulus flows. Transition was extended to an effective Reynolds number well above that for the Newtonian fluid with a drag reduction of up to 63%. The near-outer-wall flows had logarithmic forms between the Newtonian curve and that of the maximum drag-reduction asymptote, and all fluctuation levels were less than those for the Newtonian fluid, particularly the radial and tangential components.