Hostname: page-component-78c5997874-4rdpn Total loading time: 0 Render date: 2024-11-17T09:17:53.176Z Has data issue: false hasContentIssue false
  • English
  • Français

On turbulent friction in straight ducts with complex cross-section: the wall law and the hydraulic diameter

Published online by Cambridge University Press:  03 May 2018

Sergio Pirozzoli Open the ORCID record for Sergio Pirozzoli [Opens in a new window]
Sergio Pirozzoli*
Affiliation:
Dipartimento di Ingegneria Meccanica e Aerospaziale, Sapienza UniversitĂ  di Roma Via Eudossiana 18, 00184 Roma, Italy
*
†Email address for correspondence: [email protected]
Get access Rights & Permissions [Opens in a new window]

Abstract

We develop predictive formulae for frictional resistance in ducts with complex cross-sectional shape based on the use of the log law and neglect of wall shear stress non-uniformities. The traditional hydraulic diameter naturally emerges from the analysis as the controlling length scale for common duct shapes such as triangles and regular polygons. The analysis also suggests that a new effective diameter should be used in more general cases, yielding corrections of a few percent to friction estimates based on the traditional hydraulic diameter. Fair, but consistent, predictive improvement is shown for duct geometries of practical relevance, including rectangular and annular ducts, and circular rod bundles.

JFM classification

Boundary Layers: Boundary Layers Boundary Layers: Pipe flow boundary layer
Type
JFM Rapids
Information
Journal of Fluid Mechanics , Volume 846 , 10 July 2018 , R1
Check for updates
Copyright
© 2018 Cambridge University Press 

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

Bernardini, M., Pirozzoli, S. & Orlandi, P. 2014 Velocity statistics in turbulent channel flow up to Re 𝜏 = 4000. J. Fluid Mech. 742, 171–191.CrossRefGoogle Scholar
Blasius, H. 1913 Das Ähnlichkeitsgesetz bei ReibungsvorgĂ€ngen in FlĂŒssigkeiten. In Mitteilungen ĂŒber Forschungsarbeiten auf dem Gebiete des Ingenieurwesens (ed. deutscher Ingenieure, Verein), vol. 131, pp. 1–41. Springer.Google Scholar
Cain, D. & Duffy, J. 1971 An experimental investigation of turbulent flow in elliptical ducts. Intl J. Mech. Sci. 13, 451–459.CrossRefGoogle Scholar
Colebrook, C. F. 1939 Turbulent flow in pipes, with particular reference to the transition region between the smooth and rough pipe laws. J. Inst. Civil Engng 11, 133–156.CrossRefGoogle Scholar
Deissler, R. G. & Taylor, M. F.1958 Analysis of turbulent flow and heat transfer in noncircular passages. NACA Tech. Rep. TN-4384.Google Scholar
Jones, O. C. 1976 An improvement in the calculation of turbulent friction in rectangular ducts. Trans. ASME J. Fluids Engng 98, 173–181.CrossRefGoogle Scholar
Jonsson, V. K. & Sparrow, E. M. 1966 Experiments on turbulent-flow phenomena in eccentric annular ducts. J. Fluid Mech. 25, 65–86.CrossRefGoogle Scholar
Keulegan, G. H. 1938 Laws of turbulent flow in open channels. J. Res. Natl Bur. Stand. 21, 707–741.CrossRefGoogle Scholar
Leutheusser, H. J. 1963 Turbulent flow in rectangular ducts. J. Hydraul. Div. ASCE 89 (3), 1–19.CrossRefGoogle Scholar
Marin, O., Vinuesa, R., Obabko, A. V. & Schlatter, P. 2016 Characterization of the secondary flow in hexagonal ducts. Phys. Fluids 28 (12), 125101.CrossRefGoogle Scholar
Maubach, K. 1970 Reibungsgesetze turbulenter Strömungen. Chemie Ingenieur Technik 42 (15), 995–1004.CrossRefGoogle Scholar
Nikitin, N. 2006 Direct numerical simulation of turbulent flows in eccentric pipes. Comput. Math. Math. Phys. 46, 489–504.CrossRefGoogle Scholar
Nikuradse, J. 1930 Turbulente Strömung in nicht-kreisförmigen Rohren. Ing.-Arch. 1, 306–332.CrossRefGoogle Scholar
Nouri, J. M., Umur, H. & Whitelaw, J. H. 1993 Flow of Newtonian and non-Newtonian fluids in concentric and eccentric annuli. J. Fluid Mech. 253, 617–641.CrossRefGoogle Scholar
Pirozzoli, S., Modesti, D., Orlandi, P. & Grasso, F. 2018 Turbulence and secondary motions in square duct flow. J. Fluid Mech. 840, 631–655.CrossRefGoogle Scholar
Prandtl, L.1926 Über die ausgebildete Turbulenz. In Int. Congress for Applied Mechanics. Also ‘Turbulent Flow’, NACA-TM 435, 1927.Google Scholar
Rehme, K. 1972 Pressure drop performance of rod bundles in hexagonal arrangements. Intl J. Heat Mass Transfer 15 (12), 2499–2517.CrossRefGoogle Scholar
Rehme, K. 1973 Simple method of predicting friction factors of turbulent flow in non-circular channels. Intl J. Heat Mass Transfer. 16 (5), 933–950.CrossRefGoogle Scholar
Schiller, L. 1923 Über den Strömungswiderstand von Rohren verschiedenen Querschnitts und Rauhigkeitsgrades. Z. Angew. Math. Mech. 3 (1), 2–13.CrossRefGoogle Scholar
Spalart, P. R., Garbaruk, A. & Stabnikov, A. 2018 On the skin friction due to turbulence in ducts of various shapes. J. Fluid Mech. 838, 369–378.CrossRefGoogle Scholar
Vinuesa, R., Noorani, A., Lozano-Durán, A., Khoury, G. K. E., Schlatter, P., Fischer, P. F. & Nagib, H. M. 2014 Aspect ratio effects in turbulent duct flows studied through direct numerical simulation. J. Turbul. 15 (10), 677–706.CrossRefGoogle Scholar