Skip to main content
×
Home
    • Aa
    • Aa
  • Get access
    Check if you have access via personal or institutional login
  • Cited by 36
  • Cited by
    This article has been cited by the following publications. This list is generated based on data provided by CrossRef.

    WADA, Yuki FURUICHII, Noriyuki TERAO, Yoshiya and TSUJI, Yoshiyuki 2015. Experimental study on the mean velocity profile in the high Reynolds number turbulent pipe flow. Transactions of the JSME (in Japanese), Vol. 81, Issue. 826, p. 15-00091.


    McKeon, B. J. Sharma, A. S. and Jacobi, I. 2013. Experimental manipulation of wall turbulence: A systems approach. Physics of Fluids, Vol. 25, Issue. 3, p. 031301.


    LeHew, J. Guala, M. and McKeon, B. J. 2011. A study of the three-dimensional spectral energy distribution in a zero pressure gradient turbulent boundary layer. Experiments in Fluids, Vol. 51, Issue. 4, p. 997.


    Ng, H. C. H. Monty, J. P. Hutchins, N. Chong, M. S. and Marusic, I. 2011. Comparison of turbulent channel and pipe flows with varying Reynolds number. Experiments in Fluids, Vol. 51, Issue. 5, p. 1261.


    McKEON, B. J. and SHARMA, A. S. 2010. A critical-layer framework for turbulent pipe flow. Journal of Fluid Mechanics, Vol. 658, p. 336.


    Podvin, Bérengère Fraigneau, Yann Jouanguy, Julien and Laval, J.-P. 2010. On Self-Similarity in the Inner Wall Layer of a Turbulent Channel Flow. Journal of Fluids Engineering, Vol. 132, Issue. 4, p. 041202.


    Priimak, V. G. 2010. Waves and spatially localized structures in the turbulent flows of a viscous fluid: Calculation results. Mathematical Models and Computer Simulations, Vol. 2, Issue. 5, p. 543.


    Willis, Ashley P. Hwang, Yongyun and Cossu, Carlo 2010. Optimally amplified large-scale streaks and drag reduction in turbulent pipe flow. Physical Review E, Vol. 82, Issue. 3,


    Sharma, Atul and McKeon, Beverley 2009. 47th AIAA Aerospace Sciences Meeting including The New Horizons Forum and Aerospace Exposition.

    Liou, William W. and Fang, Yichuan 2003. Bursting Frequency Predictions for Compressible Turbulent Boundary Layers. AIAA Journal, Vol. 41, Issue. 6, p. 1022.


    Liou, William W. Fang, Yichuan and Baty, Roy S. 2000. Global numerical prediction of bursting frequency in turbulent boundary layers. International Journal of Numerical Methods for Heat & Fluid Flow, Vol. 10, Issue. 8, p. 862.


    Chang, Peter A. Piomelli, Ugo and Blake, William K. 1999. Relationship between wall pressure and velocity-field sources. Physics of Fluids, Vol. 11, Issue. 11, p. 3434.


    Hites, Michael Nagib, Hassan Wark, Candace Hites, Michael Nagib, Hassan and Wark, Candace 1997. 28th Fluid Dynamics Conference.

    Nikitin, N. V. 1994. Direct numerical modeling of three-dimensional turbulent flows in pipes of circular cross section. Fluid Dynamics, Vol. 29, Issue. 6, p. 749.


    Priymak, V. G. and Miyazaki, T. 1994. Long-wave motions in turbulent shear flows. Physics of Fluids, Vol. 6, Issue. 10, p. 3454.


    Tantirige, S.C. Iribarne, A.P. Ojha, M. and Trass, O. 1994. The turbulent boundary layer over single V-shaped grooves. International Journal of Heat and Mass Transfer, Vol. 37, Issue. 15, p. 2261.


    Chase, D.M. 1992. Fluctuating wall-shear stress and pressure at low streamwise wavenumbers in turbulent boundary-layer flow at low Mach numbers. Journal of Fluids and Structures, Vol. 6, Issue. 4, p. 395.


    1991. Second-order near-wall turbulence closures - A review. AIAA Journal, Vol. 29, Issue. 11, p. 1819.


    Zai-chao, Liang and Shi-he, Liu 1990. Fuzzy cluster analysis of turbulent scales. Applied Mathematics and Mechanics, Vol. 11, Issue. 8, p. 767.


    LAI, J. C. S. BULLOCK, K. J. and KRONAUER, R. E. 1989. Structural similarity of turbulence in fully developed smooth pipe flow. AIAA Journal, Vol. 27, Issue. 3, p. 283.


    ×

Structural similarity for fully developed turbulence in smooth tubes

  • W. R. B. Morrison (a1) and R. E. Kronauer (a2)
  • DOI: http://dx.doi.org/10.1017/S0022112069002072
  • Published online: 01 March 2006
Abstract

The structure of fully developed turbulence in smooth circular tubes has been studied in detail in the Reynolds number range between 10,700 and 96,500 (R based on centre velocity and radius). The data was taken as longitudinal and transverse correlations of the longitudinal component of turbulence in narrow frequency bands. By taking Fourier transforms of the correlations, crosspower spectral densities are formed with frequency, ω, and longitudinal or transverse wave-number, kx or kz, as the independent variables. In this form the data shows the distribution of turbulence intensity among waves of different size and inclination, and permits an estimate of the phase velocity of the individual waves.

Data taken at radii where the mean velocity profile is logarithmic show that the waves of smaller size (higher (k2x + k2z)½) decrease in intensity more rapidly with distance from the wall than the larger waves, and also possess lower phase velocity. This suggests that the waves might constitute a geometrically similar family such that the variation of intensity with wall distance is a unique function with a scale established by (k2x + k2z)−½). The hypothesis fits the data very well for waves of small inclination, α = tan−1(kx/kz), and permits a collapse of the intensity data at the several radii into a single ‘wave-strength’ distribution. The function of intensity with wall distance which effects this collapse has a peak at a wall distance roughly equal to 0·6(k2x + k2z)−½). For waves whose inclination is not small, it would not be expected that the intensity data could collapse in this way since the measured longitudinal component of turbulence represents a combination of two turbulence components when resolved in the wave co-ordinate system.

Although the similarity hypothesis is strictly true only for data taken where the mean velocity profile is logarithmic, a simple correction procedure has been discovered which permits the extension of the similarity concept to the sublayer region as well. This procedure requires only that the observed total turbulence intensity at any station in the sublayer be reduced by a factor which depends solely on the y+ distance from the wall (i.e. on the distance from the wall, scaled by the viscid parameters of the sublayer). The correction factor is independent of Reynolds number and applies equally to waves of all sizes. In this way, all of the turbulence waves down to the very smallest of any significance, are found to satisfy slightly modified similarity conditions.

From the data taken a t Reynolds numbers between 96,500 and 46,000 wave ‘strength’ is seen to be distributed more or less uniformly over a range bounded at one extreme by the largest waves which the tube can contain (k2x + k2z ≅ (2/a)2, where a is the tube radius) and at the other extreme by the smallest waves which can be sustained against the dissipative action of viscosity (k2x + k2z ≅ (0·04v/Uτ)2, where Uτ is the shear velocity). As the Reynolds number of the flow is lowered, the spread between the bounds becomes smaller. If the data is projected to a Reynolds number of order lo3 the bounds coalesce and turbulence should no longer be sustainable.

Copyright
Recommend this journal

Email your librarian or administrator to recommend adding this journal to your organisation's collection.

Journal of Fluid Mechanics
  • ISSN: 0022-1120
  • EISSN: 1469-7645
  • URL: /core/journals/journal-of-fluid-mechanics
Please enter your name
Please enter a valid email address
Who would you like to send this to? *
×
MathJax