A Colebrook equation for impinging radial wall jets

Pease, Leonard F.; Fuher, Arich; Bamberger, Judith A.; Minette, Michael J.

doi:10.1017/jfm.2022.1095

A Colebrook equation for impinging radial wall jets

Journal Article · Wed Mar 26 00:00:00 EDT 2025 · Journal of Fluid Mechanics

DOI:https://doi.org/10.1017/jfm.2022.1095· OSTI ID:2587227

^[1]; Fuher, Arich ^[1]; ^[1]; ^[1]

Pacific Northwest National Laboratory (PNNL), Richland, WA (United States)

Here, in this study, we evaluate the skin coefficient of friction for steady turbulent radial wall jets across smooth and rough surfaces. Although the Colebrook equation has been used successfully for many decades to evaluate friction factors for flows through smooth and rough pipes, how roughness affects the skin friction coefficient for steady turbulent radial wall jets remains unclear. Here we explore a Colebrook-type equation for skin friction coefficients associated with single-phase turbulent radial wall jets arising from orthogonally impinging circular jets. The fully iterative solution, based on well-established concepts of turbulent wall-bounded flow, is presented along with a power-law approximation and a non-iterative approximation for the friction coefficient derived therefrom. We find the skin coefficient of friction defined on the peak radial velocity to be a function of position over rough but not smooth surfaces in contrast to pipe friction factors that remain independent of axial position. These results follow expected trends, explain prior heterogeneity in power-law expressions for the skin friction coefficient and have significant implications for the industrial use of jets in mixing vessels.

View Accepted Manuscript (DOE)

Research Organization:: Pacific Northwest National Laboratory (PNNL), Richland, WA (United States)

Sponsoring Organization:: USDOE

Grant/Contract Number:: AC05-76RL01830

OSTI ID:: 2587227

Report Number(s):: PNNL-SA--153954

Journal Information:: Journal of Fluid Mechanics, Journal Name: Journal of Fluid Mechanics Vol. 1008; ISSN 1469-7645; ISSN 0022-1120

Publisher:: Cambridge University Press (CUP)Copyright Statement

Country of Publication:: United States

Language:: English

References (29)

Mass transfer in a turbulent radial wall jet Dawson, D. A.; Trass, O. The Canadian Journal of Chemical Engineering, Vol. 44, Issue 3 https://doi.org/10.1002/cjce.5450440301	journal	June 1966
Vollständige Darstellung der turbulenten Geschwindigkeitsverteilung in glatten Leitungen Reichardt, H. ZAMM - Zeitschrift für Angewandte Mathematik und Mechanik, Vol. 31, Issue 7 https://doi.org/10.1002/zamm.19510310704	journal	January 1951
On the LambertW function Corless, R. M.; Gonnet, G. H.; Hare, D. E. G. Advances in Computational Mathematics, Vol. 5, Issue 1 https://doi.org/10.1007/BF02124750	journal	December 1996
Non-unique turbulent boundary layer flows having a moderately large velocity defect: a rational extension of the classical asymptotic theory Scheichl, B.; Kluwick, A. Theoretical and Computational Fluid Dynamics, Vol. 27, Issue 6 https://doi.org/10.1007/s00162-012-0266-x	journal	April 2012
A note on mass transfer in turbulent wall jets Rao, V. Kuppu International Journal of Heat and Mass Transfer, Vol. 23, Issue 12 https://doi.org/10.1016/0017-9310(80)90230-6	journal	December 1980
The near wall mixing length formulation revisited Grifoll, J.; Giralt, Francesc International Journal of Heat and Mass Transfer, Vol. 43, Issue 19 https://doi.org/10.1016/S0017-9310(00)00009-0	journal	October 2000
The Turbulent Boundary Layer Clauser, Francis H. Advances in Applied Mechanics https://doi.org/10.1016/S0065-2156(08)70370-3	book	January 1956
An experimental study of a radial wall jet formed by the normal impingement of a round synthetic jet Krishnan, Gopi; Mohseni, Kamran European Journal of Mechanics - B/Fluids, Vol. 29, Issue 4 https://doi.org/10.1016/j.euromechflu.2010.03.001	journal	July 2010
Experimental study of a round jet impinging on a flat surface: Flow field and vortex characteristics in the wall jet van Hout, R.; Rinsky, V.; Grobman, Y. G. International Journal of Heat and Fluid Flow, Vol. 70 https://doi.org/10.1016/j.ijheatfluidflow.2018.01.010	journal	April 2018
Wall shear stress measurements and parametric analysis of impinging wall jets Loureiro, J. B. R.; Silva Freire, A. P. International Journal of Heat and Mass Transfer, Vol. 55, Issue 23-24 https://doi.org/10.1016/j.ijheatmasstransfer.2012.06.028	journal	November 2012
Heat transfer and associated coherent structures of a single impinging jet from a round nozzle Rönnberg, Kristian; Duwig, Christophe International Journal of Heat and Mass Transfer, Vol. 173 https://doi.org/10.1016/j.ijheatmasstransfer.2021.121197	journal	July 2021
Turbulent flow in a machine honed rough pipe for large Reynolds numbers: General roughness scaling laws Afzal, Noor; Seena, Abu; Bushra, A. Journal of Hydro-environment Research, Vol. 7, Issue 1 https://doi.org/10.1016/j.jher.2011.08.002	journal	March 2013
The wall shear stress produced by the normal impingement of a jet on a flat surface Phares, Denis J.; Smedley, Gregory T.; Flagan, Richard C. Journal of Fluid Mechanics, Vol. 418 https://doi.org/10.1017/S002211200000121X	journal	September 2000
The wall jet Glauert, M. B. Journal of Fluid Mechanics, Vol. 1, Issue 06 https://doi.org/10.1017/S002211205600041X	journal	December 1956
An experimental investigation of a wall jet Bakke, P. Journal of Fluid Mechanics, Vol. 2, Issue 5 https://doi.org/10.1017/S0022112057000270	journal	July 1957
Impingement of an axisymmetric jet on unheated and heated flat plates Özdemir, İ. Bedii; Whitelaw, J. H. Journal of Fluid Mechanics, Vol. 240 https://doi.org/10.1017/S002211209200017X	journal	July 1992
Efficient Resolution of the Colebrook Equation Clamond, Didier Industrial & Engineering Chemistry Research, Vol. 48, Issue 7 https://doi.org/10.1021/ie801626g	journal	February 2009
Impinging Circular Turbulent Jets Beltaos, Spyridon; Rajaratnam, Nallamuthu Journal of the Hydraulics Division, Vol. 100, Issue 10 https://doi.org/10.1061/JYCEAJ.0004072	journal	October 1974
Does fully developed turbulence exist? Reynolds number independence versus asymptotic covariance Barenblatt, G. I.; Goldenfeld, Nigel Physics of Fluids, Vol. 7, Issue 12 https://doi.org/10.1063/1.868685	journal	December 1995
Log laws or power laws: The scaling in the overlap region Zagarola, M. V.; Perry, A. E.; Smits, A. J. Physics of Fluids, Vol. 9, Issue 7 https://doi.org/10.1063/1.869328	journal	July 1997
Impingement of circular turbulent jets on rough boundaries Rajaratnam, N.; Mazurek, K. A. Journal of Hydraulic Research, Vol. 43, Issue 6 https://doi.org/10.1080/00221680509500388	journal	November 2005
Oblique Impingement of Circular Turbulent jets Beltaos, S. Journal of Hydraulic Research, Vol. 14, Issue 1 https://doi.org/10.1080/00221687609499685	journal	January 1976
Flow Field and Scouring Effects of Steady and Pulsating jets Impinging on a Movable bed Kobus, H.; Leister, P.; Westrich, B. Journal of Hydraulic Research, Vol. 17, Issue 3 https://doi.org/10.1080/00221687909499582	journal	July 1979
Large-eddy simulation of impinging jets on smooth and rough surfaces Wu, Wen; Banyassady, Rayhaneh; Piomelli, Ugo Journal of Turbulence, Vol. 17, Issue 9 https://doi.org/10.1080/14685248.2016.1181761	journal	June 2016
Investigation of a Turbulent Radial Wall Jet Poreh, M.; Tsuei, Y. G.; Cermak, J. E. Journal of Applied Mechanics, Vol. 34, Issue 2 https://doi.org/10.1115/1.3607705	journal	June 1967
Hot-Wire Measurements in a Radial Turbulent Jet Heskestad, Gunnar Journal of Applied Mechanics, Vol. 33, Issue 2 https://doi.org/10.1115/1.3625059	journal	June 1966
The Turbulent Wall Jet Measurements and Modeling Launder, B. E.; Rodi, W. Annual Review of Fluid Mechanics, Vol. 15, Issue 1 https://doi.org/10.1146/annurev.fl.15.010183.002241	journal	January 1983
Turbulent flow in Pipes, with Particular Reference to the Transition Region Between the Smooth and Rough pipe Laws. Colebrook, C. F. Journal of the Institution of Civil Engineers, Vol. 11, Issue 4 https://doi.org/10.1680/ijoti.1939.13150	journal	February 1939
On Turbulent Flow Near a Wall Van Driest, E. R. Journal of the Aeronautical Sciences, Vol. 23, Issue 11 https://doi.org/10.2514/8.3713	journal	November 1956

Similar Records

A review of explicit friction factor equations

Journal Article · Sat Jun 01 00:00:00 EDT 1985 · J. Energy Resour. Technol.; (United States) · OSTI ID:6282591

On the Mechanism of Turbulent Shear Flows

Journal Article · Mon Jul 15 00:00:00 EDT 2019 · Journal of Experimental and Theoretical Physics · OSTI ID:22917705

Relaxation of the turbulent boundary layer after an abrupt change from rough to smooth wall

Journal Article · Wed Sep 01 00:00:00 EDT 1993 · Journal of Fluids Engineering; (United States) · OSTI ID:5617872

Related Subjects

friction losses
law of the wall
radial wall jets
skin coefficient of friction

A Colebrook equation for impinging radial wall jets

Citation Formats

References (29)

Similar Records

Related Subjects