Abstract
We carry out Direct Numerical Simulation (DNS) of flows in closed straight ducts with complex peripheral shape. To perform the simulations the Navier-Stokes equations in cylindrical coordinates are discretized by a second-order finite difference scheme, and the immersed-boundary technique is used to resolve the flow close to walls of complex shape. The basic geometry is a circular pipe of radius R, with imposed sinusoidal perturbations of the type \(\eta R \sin (N_{w}\theta )\). Simulations by varying N w at fixed η were performed to investigate the effect of the perturbation wavenumber. Additional simulations by fixing N w and varying η also allow to investigate the influence of the amplitude of the wall corrugations. The modifications of the near-wall structures due to change in the shape of the walls are well depicted through contour plots of the radial component of the vorticity. The presence of geometrical disturbances anchors the structures at the locations where curvature changes, and the shape of the structures is strongly linked to the amplitude of the wall corrugation. Our interest is also in understanding the influence of the shape of the surface on wall friction. We were expecting some changes in the profile of the total stress with respect to that of the circular pipe, which instead were not found. This is a first indication that changes in the near-wall region do not affect the outer region, and that Townsend’s similarity hypothesis holds.
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References
Darcy, H.: Au mouvement de l’eau dans les tuyaux. Recherches experimentales pp. 1–268 (1857)
Reynolds, O.: On the dynamical theory of incompressible viscous fluids and the determination of the criterion. Philos. Trans. R. Soc. 186, 123–164 (1895)
Prandtl, L.: Turbulent flow. NACA TM 453, 1–23 (1927)
Nikuradse, J.: Turbulente strömung in nicht-kreisförmigen rohren. Ing. Arch. 1, 306–332 (1930)
Schlichting, H.: Boundary-Layer Theory. Mc-Graw-Hill, New York (1968)
Schiller, L.: Uber den stromungswidersfand von rohren verschiedenen querschnitts und rauhigkeifsgrades. Zeitschrift fur angewandte Matbematik und Mechanik pp. 1–12 (1922)
Bradshaw, P.: Turbulent secondary flows. Annu. Rev. Fluid Mech. 19, 57–74 (1987)
Marin, O., Vinuesa, R., Obabko, A.V., Schlatter, P.: Characterization of the secondary flow in hexagonal ducts. Phys. Fluids 28(12), 125101 (2016)
Vidal, A., Vinuesa, R., Schlatter, P., Nagib, H.M.: Influence of corner geometry on the secondary flow in turbulent square ducts. Int. J. Heat Fluid Flow 67, 69–78 (2017)
Lammers, P., Jovanovic, J., Frohnapfel, B., Delgado, A.: Erlangen pipe flow: the concept and dns results for microflow control of near-wall turbulence. Microfluid Nanofluid 13, 429–440 (2012)
Daschiel, G., Krieger, V., Jovanovic, J., Delgado, A.: Numerical simulation of turbulent flow through schiller’s wavy pipe. J. Fluid Mech. 761, 241–260 (2014)
Smits, A.J., McKeon, B.J., Marusic, I.: High-reynolds number wall turbulence. Ann. Rev. Fluid Mech. 43, 353–375 (2011)
Bernardini, M., Pirozzoli, S., Orlandi, P.: Velocity statistics in turbulent channel flow up to Re τ = 4000. J. Fluid Mech. 742, 171–191 (2014)
Hoyas, S., Jiménez, J.: Scaling of velocity fluctuations in turbulent channels up to R e τ = 2003. Phys. Fluids 18, 011702 (2006)
Walsh, M., Weinstein, L.M.: Drag and heat transfer on surfaces with small longitudinal fins. AIAA Paper pp. 78–1161 (1978)
Choi, H., Moin, P.J.: Direct numerical simulation of turbulent flow over riblets. J. Fluid Mech. 255, 503–538 (1993)
Orlandi, P., Leonardi, S., Antonia, R.A.: Turbulent channel flow with either transverse or longitudinal roughness elements on one wall. J. Fluid Mech. 561, 279–305 (2006)
Verzicco, R., Orlandi, P.: A finite-difference scheme for the three-dimensional incompressible flows in cylindrical coordinates. J. Comp. Phys. 123, 402–414 (1996)
Fadlun, A., Verzicco, R., Orlandi, P., Mohd-Yusof, J.: Combined immersed boundary finite-difference methods for three-dimensional complex flow simulations. J. Comput. Phys. 161, 35–60 (2000)
Orlandi, P., Leonardi, S.: DNS Of turbulent channel flows with two- and three-dimensional roughness. J. Turbul. 7(53), 1468–5248 (2006)
Burattini, P., Leonardi, S., Orlandi, P., Antonia, R.A.: Comparison between experiments and direct numerical simulations in a channel flow with roughness on one wall. J. Fluid Mech. 600, 403–426 (2008)
Uhlmann, M., Pinelli, A., Kawahara, G., Sekimoto, A.: Marginally turbulent flow in a square duct. J. Fluid Mech. 588, 153–162 (2007)
White, F.M.: Viscous Fluid Flow. Mc-Graw-Hill, New York (2006)
Duan, S., Yovanovich, M.M., Muzychka, Y.S.: Pressure drop for fully developed turbulent flow in circular and noncircular ducts. J. Fluids Eng. 134(6), 061201 (2012)
Orlandi, P.: Time evolving simulations as a tentative reproduction of the reynolds experiments on flow transition in circular pipes. Phys. Fluids 20, 101516 (2008)
Orlandi, P.: The importance of wall-normal reynolds stress in turbulent rough channel flows. Phys. Fluids 25, 110813 (2013)
Orlandi, P., Bernardini, M., Pirozzoli, S.: Poiseuille and Couette flows in the transitional and fully turbulent regime. J. Fluid Mech. 770, 424–441 (2015)
Vinuesa, R., Prus, C., Schlatter, P., Nagib, H.M.: Influence of corner geometry on the secondary flow in turbulent square ducts. Meccanica 51, 3025–3042 (2016)
Pirozzoli, S., Modesti, D., Orlandi, P., Grasso, F.: Turbulence and secondary motions in square duct flow. J. Fluid Mech 840, 631–655 (2018)
Orlandi, P., Leonardi, S.: Direct numerical simulation of three-dimensional turbulent rough channels: parameterization and flow physics. J. Fluid Mech. 606, 399–415 (2008)
Townsend, A.: The structure of Turbulent Shear Flows. Cambridge University Press, Cambridge (1976)
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We acknowledge that some of the results reported in this paper have been achieved using the PRACE Research Infrastructure resource MARCONI based at CINECA, Casalecchio di Reno, Italy.
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Orlandi, P., Modesti, D. & Pirozzoli, S. DNS of Turbulent Flows in Ducts with Complex Shape. Flow Turbulence Combust 100, 1063–1079 (2018). https://doi.org/10.1007/s10494-018-9911-9
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DOI: https://doi.org/10.1007/s10494-018-9911-9