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Relaxation of turbulent pipe flow downstream of a square bar roughness element

Published online by Cambridge University Press:  19 July 2021

Liuyang Ding Open the ORCID record for Liuyang Ding [Opens in a new window]  and
Alexander J. Smits Open the ORCID record for Alexander J. Smits [Opens in a new window]
Liuyang Ding*
Affiliation:
Department of Mechanical and Aerospace Engineering, Princeton University, Princeton, NJ08544, USA
Alexander J. Smits
Affiliation:
Department of Mechanical and Aerospace Engineering, Princeton University, Princeton, NJ08544, USA
*
†Email address for correspondence: [email protected]
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Abstract

The relaxation of turbulent pipe flow downstream of a single square bar roughness element is studied at distances up to $120R$ ($R$ is the pipe radius). Three bar heights, $h/R = 0.04$, 0.1 and 0.2, are investigated. The data suggest three stages for the relaxing flow. Immediately following the square bar is the development of a separated shear layer, where we find that the peak Reynolds stress scales linearly with $h/R$ and the disturbance profile is characterised by $h$. The bulk shear stress and turbulence intensity in this stage scale as $(h/R)^{2}$ and reach their maximum near the reattachment point. The second stage features the redistribution of turbulence towards the pipe centre and a power law in the decay of turbulence. The extent of this region is characterised by a streamwise length scale, ${x_c}$, which measures the extent of the redistribution process. The final stage of recovery is found to be long-lasting and oscillatory owing to asynchronous recovery between the mean velocity and the Reynolds stress. The oscillation wavelength scales with ${x_c}$ and decreases with increasing $h/R$. In contrast, the deficits in the mean shear and the bulk shear stress increase with $h/R$. For all three bar sizes, the flow recovery is not complete until the streamwise distance exceeds 500$h$–1000$h$.

JFM classification

Turbulent Flows: Pipe flow Turbulent Flows: Turbulence modelling
Type
JFM Papers
Information
Journal of Fluid Mechanics , Volume 922 , 10 September 2021 , A34
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Copyright
© The Author(s), 2021. Published by Cambridge University Press

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References

REFERENCES

Adams, E.W. & Johnston, J.P. 1988 Effects of the separating shear layer on the reattachment flow structure. Part 2: reattachment length and wall shear stress. Exp. Fluids 6 (7), 493–499.CrossRefGoogle Scholar
Adrian, R.J. & Westerweel, J. 2011 Particle Image Velocimetry. Cambridge University Press.Google Scholar
Antonia, R.A. & Luxton, R.E. 1971 The response of a turbulent boundary layer to a step change in surface roughness. Part 1. Smooth to rough. J. Fluid Mech. 48 (4), 721–761.CrossRefGoogle Scholar
Antonia, R.A. & Luxton, R.E. 1972 The response of a turbulent boundary layer to a step change in surface roughness. Part 2. Rough-to-smooth. J. Fluid Mech. 53 (4), 737–757.CrossRefGoogle Scholar
Armaly, B.F., Durst, F., Pereira, J.C.F. & Schönung, B. 1983 Experimental and theoretical investigation of backward-facing step flow. J. Fluid Mech. 127, 473–496.CrossRefGoogle Scholar
Bradshaw, P. & Wong, F.Y.F. 1972 Reattachment and relaxation of a turbulent shear layer. J. Fluid Mech. 52, 113–135.CrossRefGoogle Scholar
Castro, I.P. 1979 Relaxing wakes behind surface-mounted obstacles in rough wall boundary layers. J. Fluid Mech. 93 (4), 631–659.CrossRefGoogle Scholar
Castro, I.P. & Epik, E. 1998 Boundary layer development after a separated region. J. Fluid Mech. 374, 91–116.CrossRefGoogle Scholar
Castro, I.P. & Fackrell, J.E. 1978 A note on two-dimensional fence flows, with emphasis on wall constraint. J. Wind Engng Ind. Aerodyn. 3 (1), 1–20.CrossRefGoogle Scholar
Castro, I.P. & Haque, A. 1987 The structure of a turbulent shear layer bounding a separation region. J. Fluid Mech. 179, 439–468.CrossRefGoogle Scholar
Chapman, D.R., Kuehn, D.M. & Larson, H.K. 1958 Investigation of separated flows in supersonic and subsonic streams with emphasis on the effect of transition. NACA Rep. 1356.Google Scholar
Chung, D., Marusic, I., Monty, J.P., Vallikivi, M. & Smits, A.J. 2015 On the universality of inertial energy in the log layer of turbulent boundary layer and pipe flows. Exp. Fluids 56 (7), 1–10.CrossRefGoogle Scholar
Daly, B.J. & Harlow, F.H. 1970 Transport equations in turbulence. Phys. Fluids 13 (11), 2634–2649.CrossRefGoogle Scholar
Durst, F., Founti, M. & Wang, A.B. 1989 Experimental investigation of the flow through an axisymmetric constriction. In Turbulent Shear Flows, vol. 6, pp. 338–350. Springer.CrossRefGoogle Scholar
Eaton, J.K. & Johnston, J.P. 1981 A review of research on subsonic turbulent flow reattachment. AIAA J. 19 (9), 1093–1100.CrossRefGoogle Scholar
Efros, V. & Krogstad, P. 2011 Development of a turbulent boundary layer after a step from smooth to rough surface. Exp. Fluids 51 (6), 1563–1575.CrossRefGoogle Scholar
Good, M.C. & Joubert, P.N. 1968 The form drag of two-dimensional bluff-plates immersed in turbulent boundary layers. J. Fluid Mech. 31 (3), 547–582.CrossRefGoogle Scholar
Goswami, S. & Hemmati, A. 2020 Response of turbulent pipeflow to multiple square bar roughness elements at high Reynolds number. Phys. Fluids 32 (7), 075110.CrossRefGoogle Scholar
Hanson, R.E. & Ganapathisubramani, B. 2016 Development of turbulent boundary layers past a step change in wall roughness. J. Fluid Mech. 795, 494–523.CrossRefGoogle Scholar
Ismail, U., Zaki, T.A. & Durbin, P.A. 2018 Simulations of rib-roughened rough-to-smooth turbulent channel flows. J. Fluid Mech. 843, 419–449.CrossRefGoogle Scholar
van der Kindere, J. & Ganapathisubramani, B. 2018 Effect of length of two-dimensional obstacles on characteristics of separation and reattachment. J. Wind Engng Ind. Aerodyn. 178, 38–48.CrossRefGoogle Scholar
Kostas, J., Soria, J. & Chong, M. 2002 Particle image velocimetry measurements of a backward-facing step flow. Exp. Fluids 33 (6), 838–853.CrossRefGoogle Scholar
Kuehn, D.M. 1980 Effects of adverse pressure gradient on the incompressible reattaching flow over a rearward-facing step. AIAA J. 18 (3), 343–344.CrossRefGoogle Scholar
Launder, B.E., Reece, G. Jr. & Rodi, W. 1975 Progress in the development of a Reynolds-stress turbulence closure. J. Fluid Mech. 68 (3), 537–566.CrossRefGoogle Scholar
Le, H., Moin, P. & Kim, J. 1997 Direct numerical simulation of turbulent flow over a backward-facing step. J. Fluid Mech. 330, 349–374.CrossRefGoogle Scholar
Li, M., de Silva, C.M., Rouhi, A., Baidya, R., Chung, D., Marusic, I. & Hutchins, N. 2019 Recovery of wall-shear stress to equilibrium flow conditions after a rough-to-smooth step change in turbulent boundary layers. J. Fluid Mech. 872, 472–491.CrossRefGoogle Scholar
McKeon, B.J., Swanson, C.J., Zagarola, M.V., Donnelly, R.J. & Smits, A.J. 2004 Friction factors for smooth pipe flow. J. Fluid Mech. 511, 41–44.CrossRefGoogle Scholar
Mohammed-Taifour, A. & Weiss, J. 2016 Unsteadiness in a large turbulent separation bubble. J. Fluid Mech. 799, 383–412.CrossRefGoogle Scholar
Ötügen, M.V. 1991 Expansion ratio effects on the separated shear layer and reattachment downstream of a backward-facing step. Exp. Fluids 10 (5), 273–280.CrossRefGoogle Scholar
Pope, S.B. 2001 Turbulent Flows. IOP Publishing.Google Scholar
Smits, A.J. & Wood, D.H. 1985 The response of turbulent boundary layers to sudden perturbations. Annu. Rev. Fluid Mech. 17 (1), 321–358.CrossRefGoogle Scholar
Smits, A.J., Young, S.T.B. & Bradshaw, P. 1979 The effect of short regions of high surface curvature on turbulent boundary layers. J. Fluid Mech. 94 (2), 209–242.CrossRefGoogle Scholar
Tomas, J.M., Pourquie, M.J.B.M. & Jonker, H.J.J. 2015 The influence of an obstacle on flow and pollutant dispersion in neutral and stable boundary layers. Atmos. Environ. 113, 236–246.CrossRefGoogle Scholar
Van Buren, T., Floryan, D., Ding, L., Hellström, L.H.O. & Smits, A.J. 2020 Turbulent pipe flow response to a step change in surface roughness. J. Fluid Mech. 904, A38.CrossRefGoogle Scholar
Westphal, R.V., Johnston, J.P. & Eaton, J.K. 1984 Experimental study of flow reattachment in a single-sided sudden expansion. NASA CR-3765.Google Scholar
Yakhot, V., Bailey, S.C.C. & Smits, A.J. 2010 Scaling of global properties of turbulence and skin friction in pipe and channel flows. J. Fluid Mech. 652, 65–73.CrossRefGoogle Scholar