Abstract
Based on an analogy to the Colebrook-White equation, a technique has been developed to allow polymer-solution extrapolation or “scaling” from one pipe size to another at constant values of ΔB. Each experimental data point can be transferred to a new pipe size by a simple, pocket-calculator method which preserves the experimental value of ΔB exactly. Thus scaling can be easily accomplished, without resorting to iteration or graphical techniques. The “negative-roughness” idea can also explain the loss of ΔB or drag reduction with increasing flow velocity.
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Abbreviations
- A, B :
-
constants in velocity profile equation
- ΔB :
-
constants corresponding to roughness (actual or negative)
- D :
-
pipe diameter, m
- k s :
-
height of sand-type roughness, m
- N :
-
nondimensional negative roughness parameter
- Re :
-
Reynolds number, UD/v
- U :
-
average velocity in pipe, m/sec
- u + :
-
local velocity in pipe, nondimensionalized with u *
- u * :
-
friction velocity, m/sec
- y :
-
radial distance from pipe wall, m
- y + :
-
nondimensional distance from wall, yu */ν
- λ :
-
Darcy friction factor
- v :
-
kinematic viscosity, m2/sec
- 1:
-
experimental data
- 2:
-
predicted
References
Colebrook, C.; White, C. 1937: Experiments with fluid friction in roughened pipes. Proc. Royal Soc. A. 161, 376–381
De Loof, J.; de Lagarde, B.; Petry, M.; Simon, A. 1977: Pressure drop reduction in large industrial ducts by macromolecular additives. Part I: Polymer efficiency. In: 2nd Int Conference on Drag Reduction, pp. B2-13-36
Elata, C.; Lehrer, J.; Kahanovitz, A. 1966: Turbulent shear flow of polymer solutions. Isr. J. Technol. 4, 87–95
Fabula, A.; Lumley, J.; Taylor, W. 1966: Some interpretations of the Toms effect. In: Modern developments in the mechanics of continua. New York: Academic Press
Granville, P. 1977: Scaling-up of pipe-flow frictional data for drag-reducing polymer solutions. In: 2nd Int. Conference on Drag Reduction pp.B1-1-12
Granville, P. 1968: Frictional resistance and velocity similarity laws of drag-reducing polymer solutions. J. of Ship Research 12, 201–222
Granville, P. 1984: A method for predicting additive drag reduction from small diameter pipe flows In: 3rd Int. Conference on Drag Reduction. (Eds. Sellin, R. H. J.; Moses, R. T.) pp. C.3–1–8. Bristol: University of Bristol
Hoyt, J.; Sellin, R. 1988: Drag reduction by centrally-injected polymer “threads”. Rheologica Acta 27, 518–522
Matthys, E.; Sabersky, R. 1982: A method of predicting the ‘diameter effect’ for heat transfer and friction of drag-reducing fluids. Int. J. Heat mass Transfer 25, 1343–1351
Meyer, W. 1966: A correlation of the frictional characteristics for turbulent flow of dilute viscoelastic non-Newtonian fluids in pipes. AICHE J. 12, 522–525
Moody, L. 1944: Friction factors for pipe flow. Trans ASME 66, 671–684
Ollis, M. 1981: The scaling of drag reducing turbulent pipe flow. PhD Thesis, University of Bristol
Schlichting, H. 1979: Boundary-layer theory. New York: McGraw-Hill (7th. ed)
Sellin, R.; Ollis, M. 1983: Effect of pipe diameter on polymer drag reduction. I & EC Product Research and Development. 22, 445–452
Wang, C.-B. 1969: Pipe flow of dilute polymer solutions. PhD Thesis, University of Wisconsin, USA
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Hoyt, J.W. “Negative roughness” and polymer drag reduction. Experiments in Fluids 11, 142–146 (1991). https://doi.org/10.1007/BF00190290
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DOI: https://doi.org/10.1007/BF00190290