Hostname: page-component-78c5997874-v9fdk Total loading time: 0 Render date: 2024-11-05T04:54:10.343Z Has data issue: false hasContentIssue false
  • English
  • Français

Flow along a long thin cylinder

Published online by Cambridge University Press:  25 April 2008

O. R. TUTTY
O. R. TUTTY*
Affiliation:
School of Engineering Sciences, University of Southampton, Highfield, Southampton SO17 1BJ, UK
Get access Rights & Permissions [Opens in a new window]

Abstract

Two different approaches have been used to calculate turbulent flow along a long thin cylinder where the flow is aligned with the cylinder. A boundary-layer code is used to predict the mean flow for very long cylinders (length to radius ratio of up to O(106)), with the effects of the turbulence estimated through a turbulence model. Detailed comparison with experimental results shows that the mean properties of the flow are predicted within experimental accuracy. The boundary-layer model predicts that, sufficiently far downstream, the surface shear stress will be (almost) constant. This is consistent with experimental results from long cylinders in the form of sonar arrays. A periodic Navier–Stokes problem is formulated, and solutions generated for Reynolds number from 300 to 5×104. The results are in agreement with those from the boundary-layer model and experiments. Strongly turbulent flow occurs only near the surface of the cylinder, with relatively weak turbulence over most of the boundary layer. For a thick boundary layer with the boundary-layer thickness much larger than the cylinder radius, the mean flow is effectively constant near the surface, in both temporal and spatial frameworks, while the outer flow continues to develop in time or space. Calculations of the circumferentially averaged surface pressure spectrum show that, in physical terms, as the radius of the cylinder decreases, the surface noise from the turbulence increases, with the maximum noise at a Reynolds number of O(103). An increase in noise with a decrease in radius (Reynolds number) is consistent with experimental results.

Type
Papers
Information
Journal of Fluid Mechanics , Volume 602 , 10 May 2008 , pp. 1 - 37
Copyright
Copyright © Cambridge University Press 2008

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

REFERENCES

Bokde, A. L. W., Lueptow, R. M. & Abraham, B. 1999 Spanwise structure of wall pressure on a cylinder in axial flow. Phys Fluids 11, 151–161.CrossRefGoogle Scholar
Bull, M. K. 1996 Wall-pressure fluctuations beneath turbulent boundary layers: some relections on forty years of research. J. Sound Vib. 190, 299–315.CrossRefGoogle Scholar
Cippola, K. M. & Keith, W. L. 2003 a High Reynolds number thick axisymmetric turbulent boundary layer measurements. Exps. Fluids 35, 477–485.CrossRefGoogle Scholar
Cippola, K. M. & Keith, W. L. 2003 b Momentum thickness measurements for thick turbulent axisymmetric boundary layers. Trans. ASME I: J. Fluids Engng 125, 569–575.Google Scholar
Corcos, J. M. 1963 Resolution of pressure in turbulence. J. Accoust. Soc. Am. 35, 192–199.CrossRefGoogle Scholar
Denli, N. & Landweber, L. 1979 Thick axisymmetric turbulent boundary layer on a circular cylinder. J. Hydronautics 13, 92–104.CrossRefGoogle Scholar
Farabee, T. M. & Casarella, M. J. 1991 Spectral features of wall pressure fluctuations beneath turbulent boundary layers. Phys. Fluids A 10, 2410–2420.CrossRefGoogle Scholar
Furey, D., Cippola, K. M. & Atsavappranee, P. 2004 Investigation of the turbulent boundary layer flow on a microfliament towed array. In Proc. 25th Symp. on Naval Hydrodynamics. St Johns, Canada.Google Scholar
Glauert, M. B. & Lighthill, M. J. 1955 The axisymmetric boundary layer on a long thin cylinder. Proc. R. Soc. Lond. A 224, 188–203.Google Scholar
Knight, A. 1996 Flow noise calculations for extened hydrophones in fluid and solid-filled arrays. J. Accoust. Soc. Am. 100, 245–251.CrossRefGoogle Scholar
Lueptow, R. M. 1988 Turbulent boundary layer on a cylinder in axial flow. Tech. Rep. 8389. US NUSC Tech. Mem.Google Scholar
Lueptow, R. M. 1990 Turbulent boundary layer on a cylinder in axial flow. AIAA J. 28, 1706–1706.CrossRefGoogle Scholar
Lueptow, R. M. & Haritonidis, J. H. 1987 The structure of the turbulent boundary layer on a cylinder axial flow. Phys. Fluids 30, 2993–3005.CrossRefGoogle Scholar
Lueptow, R. M. & Jackson, C. P. 1991 Near-wall streaky structure in a turbulent boundary layer on a cylinder. Phys Fluids 3, 2822–2824.CrossRefGoogle Scholar
Lueptow, R. M., Leehey, P. & Stellinger, T. 1985 The thick, turbulent boundary layer on a cylinder: mean and fluctuating velocities. Phys Fluids 28, 3495–3505.CrossRefGoogle Scholar
Luxton, R. M., Bull, M. K. & Rajagopalan, S. 1984 The thick turbulent boundary layer on a long fine cylinder in axial flow. Aero. J. 88, 186–199.CrossRefGoogle Scholar
Marschall, R. A., Stinson, D. L., Pearce, R. E., Boyer, E. & Embury, B. 1993 The use of an innovative solid towed array for exploring the Antartic marine environment. In Proc. Oceans 93; Engineering in Harmony with Ocean, vol. 2, pp. II/35–II/40.Google Scholar
Moin, P. & Kim, J. 1982 Numerical investigation of turbulent channel flow. J. Fluid Mech. 118, 341–377.CrossRefGoogle Scholar
Nepomuceno, H. G. & Lueptow, R. M. 1997 Pressure and shear stress measurements at the wall in a turbulent boundary layer on a cylinder. Phys Fluids 9, 2732–2739.CrossRefGoogle Scholar
Neves, J. C. & Moin, P. 1994 Effects of convex transverse curvature on wall bounded turbulence. Part 2. The pressure fluctuations. J. Fluid Mech 272, 383–406.CrossRefGoogle Scholar
Neves, J. C., Moin, P. & Moser, R. D. 1992 Numerical study of axial turbulent flow over long cylinders. Tech. Rep. 54. Department of Mechanical Engineering, Stanford University.Google Scholar
Neves, J. C., Moin, P. & Moser, R. D. 1994 Effects of convex transverse curvature on wall bounded turbulence. Part 1. The velocity and vorticity. J. Fluid Mech 272, 349–381.CrossRefGoogle Scholar
Nikitin, N. 2006 Third-order accurate semi-implicit Runge–Kutta scheme of the incompressible Navier–Stokes equations. Intl J. Numer. Meth. Fluids 51, 221–233.CrossRefGoogle Scholar
Potter, J. R., Delory, E., Constantin, S. & Badiu, S. 2000 The ‘thinarray’; a lightweight, ultra-thin (8 mm OD) towed array for use with small vessels of opportunity. In Proc. Intl Symp. on Underwater Technology, pp. 49–53. Tokyo.Google Scholar
Seban, R. A. & Bond, R. 1951 Skin-friction and heat-transfer characteristics of a laminar boundary layer on a cylinder in axial compressible flow. J. Aero. Sci. 18, 671–675.CrossRefGoogle Scholar
Snarski, S. R. & Lueptow, R. M. 1995 Wall pressure and coherent structures in a turbulent boundary layer on a cylinder in axial flow. J. Fluid Mech. 286, 137–171.CrossRefGoogle Scholar
Spalart, P. R. & Allmaras, S. R. 1994 A one-equation turbulence model for aerodynamic flows. Recherche Aerospatiale 1, 5–21.Google Scholar
Stewartson, K. 1955 The asymptotic boundary layer on a circular cylinder in axial incompressible flow. Q. Appl. Maths 13, 113–122.CrossRefGoogle Scholar
Tutty, O. R., Price, W. G. & Parsons, A. T. 2002 Boundary layer flow on a long thin cylinder. Phys. Fluids 14, 628–637.CrossRefGoogle Scholar
Wedin, H. & Kerswell, R. R. 2004 Exact coherent structures in pipe flow: travelling wave solutions. J. Fluid Mech. 508, 333–371.CrossRefGoogle Scholar
Wietrzak, A. & Lueptow, R. M. 1994 Wall shear stress and velocity in a turbulent axisymmetric boundary layer. J. Fluid Mech. 259, 191–218.CrossRefGoogle Scholar
Willmarth, W. W. & Yang, C. S. 1970 Wall-pressure fluctuations beneath turbulent boundary layers on a flat plate and a cylinder. J. Fluid Mech. 41, 47–80.CrossRefGoogle Scholar
Willmarth, W. W., Winkel, R. E., Sharma, L. K. & Bogar, T. J. 1976 Axially symmetric turbulent boundary layers on cylinders: mean velocity profiles and wall pressure fluctuations. J. Fluid Mech. 76, 35–64.CrossRefGoogle Scholar