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REVIEW ARTICLES

Review of Wall Turbulence as Described by Composite Expansions

[+] Author and Article Information
Ronald L. Panton

Mechanical Engineering Department, University of Texas, Austin, TX 78712

Appl. Mech. Rev 58(1), 1-36 (Mar 08, 2005) (36 pages) doi:10.1115/1.1840903 History: Online March 08, 2005
Copyright © 2005 by ASME
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References

Figures

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Composite velocity profiles from experiments on pipe flow. Data from Zagarola and Smits 53.
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Wake velocity profiles from experiments on pipe flow. Data from Zagarola and Smits 53.
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Wake velocity profiles for different types of flows. Data sources cited in the caption are listed in the Refs. 6611253.
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Mathematical model composite velocity profiles in inner variables for several values of Re
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Mathematical model comparison of the composite, the common part and the exact answer for Re=1000
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Schematic of interaction of Reynolds stress inner function and wake function
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Reynolds stress inner function from channel flow experiments. Data sources Antonia et al. 110, Harder and Tiederman 111, and Wei and Willmarth 112.
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Reynolds stress inner function from channel flow DNS. Data sources cited in the caption are listed in Refs. 113114115116117101102.
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Reynolds stress inner function from pipe flow experiments. Data from Toonder and Nieuwstadt 104.
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Reynolds stress inner function from pipe flow DNS. Data from Eggels et al. 118 and Unger and Friedrich 119.
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Composite expansion compared with Reynolds stress from pipe flow experiments. Data from Toonder and Nieuwstadt 104.
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Reynolds number dependence ratio of Rotta–Clauser thickness to Coles thickness
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Independence of log law from pressure gradient. Data from Ludwieg and Tillmann 63.
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Boundary layer growth in flow direction. Data from Österlund 60.
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Boundary layer growth rate proportional to friction velocity. Data from Österlund 60.
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Defect law for boundary layers at various Re* . Data from Österlund 60.
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Wake law for boundary layers at various Re* . Data from Österlund 60.
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Boundary layer velocity profiles. DNS (Spalart 69) calculation compared with composite expansion.
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Equilibrium boundary layer parameters. Free stream velocity exponent as function of pressure gradient parameter.
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Equilibrium boundary layer parameters. Coles’ wake parameter as function of pressure gradient parameter.
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Velocity defect profiles, equilibrium boundary layers showing log region. Data from East et al. 72. Flow (1); beta=−0.25, (2) −0.15, (3) 0.00, (4) 0.47, (5) 1.87, (6) 7.27, (7) 61.6.
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Velocity wake profiles for equilibrium boundary layers. Wiegardt flow, dp/dx=0, two flows from Bradshaw and one from Clauser, each with three different streamwise stations. Data are in Coles and Hirst 5.
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Velocity wake profiles for equilibrium boundary layers from East et al. 72 compared with Coles’ law. Flows (1); beta=−0.25, (2) −0.15, (3) 0.00, (4) 0.47.
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Velocity wake profiles for equilibrium boundary layers from East et al. 72 compared with Coles’ law. Flows (4); beta=0.47, (5) 1.87, (6) 7.27, (7) 61.6.
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Velocity wake profiles for equilibrium boundary layers from Skare and Krogstad 73 Π=6.9 (beta=20)
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Reynolds stress wake law for a boundary layer with dp/dx=0. Data from Degraaff and Eaton 74. Computation using Coles’ velocity law shown for reference.
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Reynolds stress wake law for a boundary layer with dp/dx=0. DNS data from Spalart 69. Computation using Coles’ velocity law shown for reference.
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Reynolds stress in a boundary layer with dp/dx=0. DNS data from Spalart 69. Composite derived from Coles’ law and g0 from Eq. (5.36).
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Reynolds stress wake profiles for equilibrium boundary layers from East et al. 72. Computation using Coles’ velocity law shown for reference. Flows (1); beta=−0.25, (2) −0.15, (3) 0.00, (4) 0.47.
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Reynolds stress wake profiles for equilibrium boundary layers from East et al. 72. Computation using Coles’ velocity law shown for reference. Flows (4); beta=0.47, (5) 1.87, (6) 7.27, (7) 61.6.
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Reynolds stress wake profiles for equilibrium boundary layers from Skare and Krogstad 73. Computation using Coles’ velocity law is shown for reference. Π=6.9 (beta=16.6).
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Spectrum of wall pressure under an atmospheric boundary layer at Re*=109. Data from Klewicki and Miner 84.
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Wall-pressure spectrum. Contour plot in phase-velocity/wave number space. Graph from Wills 89.
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Wall-pressure spectrum. Contour plot normalized for constant level in overlap region. Data from Panton and Robert 92.
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Wall-pressure spectrum. Overlap function at K=10. From Panton and Robert 92.
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Wall-pressure spectrum. Overlap function at K=30. From Panton and Robert 92.
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Defect law with U0 scale for boundary layers at various Re* . Data from Österlund 61.
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Insensitivity of wake strength at high Re* . Data of Smith and Walker 99 corrected by East et al. 72.
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Reynolds stress wall function for Ames channel flow DNS. Data from Moser et al. 102.
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Composite expansion for Reynolds stress and Ames channel flow DNS. Data from Moser et al. 102.
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Composite expansion for velocity and Ames channel flow DNS at Re* =590. Data from Moser et al. 102.
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Log law diagnostic function gamma for channel flow. Composite expansion and Ames DNS at Re* =590.
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Log law diagnostic function gamma for channel flow. Composite expansion at Re* =500 and 1000.
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Log law diagnostic function gamma for boundary layer. Composite expansion at Re* =500, 1000, and 5000.
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Relative shape of Barenblatt’s power law to the log law. Displayed in the inner variable y+.
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Wake law representation of Barenblatt’s power law. Coles’ wake law shown for comparison.
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Von Kármán constant for higher-order overlap law of Buschmann and Gad-el-Hak 20

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