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Longitudinal flow between cylinders in square and triangular arrays Galloway, Leslie Robert

Abstract

Friction factors have been determined experimentally for longitudinal flow of water and various aqueous solutions of polyethylene glycol between regular enclosed arrays of cylinders. Two different geometries were investigated: a 4 × 4 square array enclosed by a square duct and a 19-rod equilateral triangular array enclosed by a hexagonal duct. Four different pitch-to-diameter ratios were studied in each geometry. These covered a range of 1.07 to 2.00 in the square array and 1.11 to 2.06 in the triangular array. No spacers were used in the rod bundle. The Reynolds number range investigated was approximately 2.5 to 40,000 (equivalent diameter based on total wetted perimeter). The fully developed friction factors for all eight arrays were correlated by the Nikuradse equation for smooth round tubes when the Reynolds number exceeded 10,000 and when the equivalent diameter, used in both the Reynolds number and the friction factor, was taken as four times the hydraulic raduis based on total wetted perimeter. In laminar flow no equivalent diameter was found that would consolidate the results of all eight arrays. Deviations from the laminar flow theory of Sparrow and Loeffler for infinite arrays could be consistently accounted for by the wall effect in the present study. The critical Reynolds number for each array ranged between 90 and 450 (equivalent diameter based on total perimeter) and the transition from laminar to turbulent flow appeared to extend over a large Reynolds number range. Friction factors in both laminar and turbulent flow were apparently established in a very short distance from the entrance to the rod bundle, since no entrance effect was detected, even as close as 9.6 total equivalent diameters from the entrance. Local friction factors were also measured in the entrance and fully developed region of a round smooth tube with a sharp-edged entrance. The Reynolds number range covered was 394 to 77,000. The inside tube diameter, determined by forcing the fully developed laminar flow friction factors to fit Poiseuille's equation, was in excellent agreement with the measured diameter, and the fully developed turbulent flow friction factor results, based on the computed diameter, were in good agreement with Nikuradse's equation for a smooth round tube. The Newtonian behavior of the polyethylene glycol solutions over all rates of shear encountered in the present study was thus established. Good agreement was also obtained between the local laminar flow friction factors, measured in the entrance region of the tube, and those predicted theoretically by Langhaar for a rounded entrance. In turbulent flow, the friction factor became fully developed within 50 tube diameters of the entrance.

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