A long-standing interest in phenomena influencing wave propagation along pipes, ducts and tunnels has focussed on the influence of unsteady skin friction on the duct walls. Dundee’s work in this area led to the only method available worldwide for estimating the values of unsteady wall shear stress coefficients without the need for empirical coefficients. Recent work has been undertaken in collaboration with Dr Shuisheng He at the University of Aberdeen.
Most engineering designs will be entirely satisfactory even if the influence of unsteady friction is completely ignored. The exceptions are related to very rapid changes in flow. Unsteady friction has only a small influence on the amplitudes of, say, the largest pressure caused by sudden valve closure in a pipe. It can have a significant influence, however, on rates of decay of successive pressure peaks as waves bounce back and forth. As a consequence, it needs to be considered by engineers using pressure measurements to infer information about the condition of a pipeline - for leak-detection purposes, say. Unsteady friction also influences the rate at which a steep wavefront can develop into a shock wave.
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| Aberdeen rig - overview | Aberdeen rig - control valve |
Dundee’s contribution
Vardy first published on unsteady friction in 1980, but meaningful progress began with a inspired PhD student Kuo-Lun (Colun) Hwang. He extended an approach developed by Werner Zielke in the 1960s when he was a student with Vic Streeter and Ben Wylie at the University of Michigan in Ann Arbor. Zielke's work dealt with laminar flow, but Hwang extended it to turbulent flow by allowing for non-uniform viscosity distributions in the flow cross-section. For the past 20 years or so, this work has been developed jointly by Vardy and his close friend and colleague, Dr Jim Brown.
A crucial advantage of this method in comparison with all others known to DTR is that it requires no empirical data except values already available for steady flows. A disadvantage is that the viscosity, although non-uniform in space, is assumed frozen in time. This turns out to be an excellent approximation for short periods after a sudden flow disturbance when unsteady contributions to wall shear stresses are greatest. Thereafter, however, the “frozen” behaviour breaks down abruptly and so the method is not well suited to predicting long-term decay.
Latterly, Vardy & Brown have given increasing attention to the consequences of time-dependent viscosity. So far, these analyses are restricted to spatially-uniform, time-dependence such as might be expected in laminar flows with strong heating or cooling. With Shuisheng He, however, work is now focussed on flows that vary simultaneously in space and time. This is being done through detailed experimental and numerical studies of turbulent flows. This work has been supported financially by the EPSRC and much of it has been undertaken by a highly talented Research Fellow, Dr Chanchala Aryaratne, who has recently moved to the University of Sussex. To date, most of the theoretical work has been based on CFD-RANS analysis. During the past few years, however, greater emphasis has been placed on CFD-DNS analysis. This is hugely demanding of computing resources, but it has the potential to increase the reliability of predictions far beyond the limits of current methods, whether theoretical or experimental.
An Unsteady Friction website developed through this collaboration is hosted at the University of Aberdeen. The site includes descriptions of an extensive experimental facility at Aberdeen funded by the EPSRC. It also includes details of a major international collaboration enabling experiments at larger scale at Deltares in The Netherlands. This programme was funded jointly by the EU and a consortium of universities and industry.
WARNING: Errors in Vardy & Brown, J Hyd Engrg, ASCE (2007): 133(11), 1219-1228
Attention is drawn to two errors and an omission in a recent paper by Vardy & Brown on unsteady skin friction. The errors are not fundamental to the main purpose of the paper, but they have the potential to cause unnecessary wasted time for researchers using the results of the paper in detail.
Error-1: The coefficients listed after Eq.17 on page 1226 are incorrect. Correct values are given in J Hyd Engrg, ASCE (2009): 135(1), 71.
Error-2: The graphs presented in Fig 2a are labelled Re = 108, 107, 106, 105, 104, 103. Unfortunately, the data used to draw these graphs were taken from the wrong columns of a spreadsheet. The graphs shown in the figure are actually for Re = 107.5, 106.5, 105.5, 104.5, 103.5, 102.5. This error applies to Fig 2a only. The graphs shown in Fig 2b are labelled correctly.
Omission: Graphical results are presented for a very large range of roughnesses – up to ks/D = 0.1 – and for a large range of Reynolds numbers - up to Re = 108 . In addition, interpolation for mulae are presented to enable the data to be used in computer software. However, the limits of validity of the interpolation formulae are not detailed. The authors consider the formulae to be sufficient for practical purposes over the whole range presented. Note, however, that the accuracy of the B** formulae reduces slightly at very small and very large values of ks/D, especially at very large Reynolds numbers.
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| Delft test rig - overview | Delft test rig - rotating disc valve |
Selected References
Ariyaratne C, He S & Vardy AE (2010) Wall friction and turbulence dynamics in decelerating pipe flows, J Hydraulics Research, 48(6), 810-821
He S, Ariyaratne C & Vardy AE (2008) A computational study of wall friction and turbulence dynamics in accelerating pipe flows, Computers & Fluids, 37(6), 674-689
He S, Ariyaratne C & Vardy AE (2011) Wall shear stress in accelerating turbulent pipe flow, J Fluid Mechanics, 685, 440-460
Seddighi M, He S, Pokrajac D, O’Donoghue T & Vardy AE (2015) Turbulence in a transient channel flow with a wall of pyramids roughness, J Fluid Mechanics, 781, 226-260
Vardy AE, Bergant A, He S, Ariyaratne C, Koppel T, Annus I, Tijsseling AS & Hou Q (2009) ‘Unsteady skin friction experimentation in a large diameter pipe’, Proc 3rd IAHR int. mtg. of the WG on Cavitation and Dynamic Problems in Hydraulic Machinery and Systems, Brno, Czech Republic, 14-16 Oct, Ed: Pavel Rudolf, Pt.II, 593-602
Vardy AE & Brown JMB (1995) Transient, turbulent, smooth pipe friction, J Hydraulic Research, 33(4), 435-456
Vardy AE & Brown JMB (2003) Transient turbulent friction in smooth pipe flows, J Sound & Vibration, 259(5), 1011-1036
Vardy AE & Brown JMB (2004) Efficient approximation of unsteady friction weighting functions, Journal of Hydraulic Engineering, ASCE, 130(11), 1097-1107
Vardy AE & Brown JMB (2004) Transient turbulent friction in fully-rough pipe flows, J Sound & Vibration, 270(2), 233-257
Vardy AE & Brown JMB (2007) Approximation of turbulent wall shear stresses in highly transient pipe flows, J Hydraulic Engineering, ASCE, 133(11), 1219-1228 [also see above and see an Erratum in 135(1), 71]
Vardy AE & Brown JMB (2010) Evaluation of unsteady wall shear stress by Zielke’s method, J Hydraulic Engineering, ASCE, Technical Note, 136(7), 453-456; Discussion and Closure 139(5), 562-565
Vardy AE & Brown JMB (2010) Influence of time-dependent viscosity on wall shear stresses in unsteady pipe flows, J Hydraulic Research, 48(2), 225-237
Vardy AE & Brown JMB (2011) Laminar Pipe Flow with Time-dependent Viscosity, J Hydroinformatics, 13(4), 729-740
Vardy AE, Brown JMB, He S, Ariyaratne C & Gorji S (2015) On the applicability of frozen-viscosity models of unsteady wall shear stress, J Hydraulic Engineering, ASCE, 141(1) , January 2015: 04014064, doi: 10.1061/(ASCE)HY.1943-7900.0000930
Vardy AE & Hwang K-L (1991) A characteristics model of transient friction in pipes. J Hydraulic Research, 29(5), 669-684
Vardy AE, Hwang K-L & Brown JMB (1993) A weighting function model of transient turbulent pipe friction, J Hydraulic Research, 31(4), 533-548
