Scaling of statistics in wall-bounded turbulent flows

L. Keirsbulck; G. Fourrié; L. Labraga; M. Gad-el-Hak

doi:10.1016/j.crme.2012.02.005

Scaling of statistics in wall-bounded turbulent flows
[Lois dʼéchelle des moments statistiques pour des écoulements turbulents pariétaux]

L. Keirsbulck ^1,² ; G. Fourrié ^1,² ; L. Labraga ^1,² ; M. Gad-el-Hak ³

¹ Univ. Lille Nord de France, 59000 Lille, France
² UVHC, TEMPO, 59313 Valenciennes, France
³ Department of Mechanical & Nuclear Engineering, Virginia Commonwealth University, Richmond, VA 23284-3015, USA

Comptes Rendus. Mécanique, Volume 340 (2012) no. 6, pp. 420-433.

Résumé
Abstract

Des mesures dʼanémométrie laser (Ldv) et fil chaud haute résolution ont été utilisées pour étudier la couche limite turbulente sans gradient de pression pour des nombres de Reynolds, basés sur lʼépaisseur de quantité de mouvement, compris entre 1170 et 3720. Lʼobjectif de cette étude vise à analyser le comportement de cet écoulement en région de proche paroi. Nous nous sommes particulièrement intéressés à une éventuelle dépendance vis-à-vis des nombres de Reynolds et de Kármán. Les résultats expérimentaux sont en excellent accord avec les simulations numériques directes (Dns) les plus récentes, ce qui permet une comparaison fine avec certaines quantités telles la valeur et la position du maximum de la tension de Reynolds, les facteurs de dissymétrie et dʼaplatissement en région de proche paroi et le taux de dissipation turbulente. Une dépendance systématique au nombre de Kármán de ces quantités est observée lorsque lʼadimensionnement en variables internes est utilisé. Une alternative possible consiste à utiliser des variables mixtes basées sur $u_{τ}^{3 / 2} U_{0}^{1 / 2}$ plutôt que sur $u_{τ}^{2}$ , celles-ci présentant lʼavantage de prendre en compte les échelles externes dans lʼadimensionnement des paramètres pariétaux.

High-resolution laser Doppler anemometry (Lda) and hot-wire anemometry (Hwa) measurements are utilized to study a zero-pressure-gradient turbulent boundary layer over the range of momentum thickness Reynolds number of 1170–3720. The primary objective is to investigate the near-wall behavior of this type of flow. We are particularly interested in possible Reynolds- and Kármán-number dependencies. The experimental results are in excellent agreement with most recent direct numerical simulations (Dns), which allow direct comparison of detailed results such as peak value and position of streamwise Reynolds stress, wall values of skewness and flatness factors, and turbulence dissipation rate. Systematic changes of some of these parameters with Kármán number are found when scaled with the inner parameters. A remedy seems to be the alternative mixed scaling that is based on $u_{τ}^{3 / 2} U_{0}^{1 / 2}$ , instead of $u_{τ}^{2}$ , which admits direct influence of the outer velocity scale on the wall parameters.

Reçu le : 2012-01-10
Accepté le : 2012-02-22
Publié le : 2012-03-15

DOI : 10.1016/j.crme.2012.02.005

Keywords: Turbulence, Wall-bounded flows, Lda & Hwa measurements, Scaling
Mot clés : Turbulence, Écoulements turbulents pariétaux, Mesures anémométriques laser et fil chaud, Lois dʼéchelle

Affiliations des auteurs :

L. Keirsbulck ^{1, 2} ; G. Fourrié ^{1, 2} ; L. Labraga ^{1, 2} ; M. Gad-el-Hak ³

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     author = {L. Keirsbulck and G. Fourri\'e and L. Labraga and M. Gad-el-Hak},
     title = {Scaling of statistics in wall-bounded turbulent flows},
     journal = {Comptes Rendus. M\'ecanique},
     pages = {420--433},
     publisher = {Elsevier},
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L. Keirsbulck; G. Fourrié; L. Labraga; M. Gad-el-Hak. Scaling of statistics in wall-bounded turbulent flows. Comptes Rendus. Mécanique, Volume 340 (2012) no. 6, pp. 420-433. doi : 10.1016/j.crme.2012.02.005. https://comptes-rendus.academie-sciences.fr/mecanique/articles/10.1016/j.crme.2012.02.005/

Bibliographie
Cité par

[1] I. Marusic; B.J. McKeon; P.A. Monkewitz; H.M. Nagib; A.J. Smits; K.R. Sreenivasan Wall-bounded turbulent flows at high Reynolds numbers: Recent advances and key issues, Phys. Fluids, Volume 22 (2010), p. 065103

[2] J.C. Klewicki Reynolds number dependence, scaling, and dynamics of turbulent boundary layers, J. Fluids Eng., Volume 132 (2010), p. 1

[3] R.L. Panton Review of wall turbulence as described by composite expansions, Appl. Mech. Rev., Volume 58 (2005), p. 1

[4] R. Mathis; J.P. Monty; N. Hutchins; I. Marusic Comparison of large-scale amplitude modulation in turbulent boundary layers, pipes, and channel flows, Phys. Fluids, Volume 21 (2009), p. 111703

[5] P.A. Monkewitz; R.D. Duncan; H.M. Nagib Correcting hot-wire measurements of stream-wise turbulence intensity in boundary layers, Phys. Fluids, Volume 22 (2010), p. 091701

[6] H.H. Fernholz; P.J. Finley The incompressible zero-pressure-gradient turbulent boundary layer: an assessment of the data, Prog. Aerospace Sci., Volume 32 (1996), p. 245

[7] M.H. Buschmann; T. Indinger; M. Gad-el-Hak Near-wall behavior of turbulent wall-bounded flows, Int. J. Heat Fluid Flow, Volume 30 (2009), p. 993

[8] I. Marusic; R. Mathis; N. Hutchins Predictive model for wall-bounded turbulent flow, Science, Volume 329 (2010), p. 193

[9] D.B. DeGraaff; J.K. Eaton Reynolds-number scaling of the flat-plate turbulent boundary layer, J. Fluid Mech., Volume 422 (2000), p. 319

[10] P.H. Alfredsson; A.V. Johansson; J.H. Haritonidis; H. Eckelmann The fluctuating wall-shear stress and the velocity field in the viscous sublayer, Phys. Fluids, Volume 31 (1988) no. 5, p. 1026

[11] F. Durst; J. Jovanović; J. Sender Lda measurements in the near-wall region of a turbulent pipe flow, J. Fluid Mech., Volume 295 (1995), p. 305

[12] J.F. Morrison; B.J. MeKeon; W. Jiang; A.J. Smith Scaling the streamwise velocity component in turbulent pipe flow, J. Fluid Mech., Volume 508 (2004), p. 99

[13] N. Hutchins; I. Marusic Evidence of very long meandering features in the logarithmic region of turbulent boundary layers, J. Fluid Mech., Volume 579 (2007), p. 1

[14] M. Hultmark; S.C.C. Bailey; A.J. Smits Scaling of near-wall turbulence in pipe flow, J. Fluid Mech., Volume 649 (2010), p. 103

[15] N. Hutchins; T.B. Nickels; I. Marusic; M.S. Chong Hot-wire spatial resolution issues in wall-bounded turbulence, J. Fluid Mech., Volume 635 (2009), p. 103

[16] G. Fourrié; L. Keirsbulck; L. Labraga; P. Gilliéron Bluff-body drag reduction using a deflector, Exp. Fluid, Volume 50 (2010), p. 385

[17] V.C. Patel Calibration of the Preston tube and limitations on its use in pressure gradients, J. Fluid Mech., Volume 23 (1965), p. 185

[18] W.P. Jones; B.E. Launder The prediction of laminarization with two-equation model of turbulence, Int. J. Heat Mass Transfer, Volume 15 (1972) no. 2, p. 301

[19] M.M. Metzger; J.C. Klewicki A comparison study of near-wall turbulence in high and low Reynolds number boundary layer, Phys. Fluids, Volume 13 (2001) no. 3, p. 692

[20] P.M. Ligrani; P. Bradshaw Spatial resolution and measurement of turbulence in the viscous sublayer using subminiature hot-wire probes, Exp. Fluid, Volume 5 (1987), p. 407

[21] D.A. Compton; J.K. Eaton A high-resolution laser Doppler anemometer for three-dimensional turbulent boundary layers, Exp. Fluid, Volume 22 (1996), p. 111

[22] F. Durst; H. Kikura; I. Lekakis; J. Jovanović Wall shear stress determination from near-wall mean velocity data in turbulent pipe and channel flows, Exp. Fluid, Volume 20 (1996), p. 417

[23] P. Schlatter; R. Örlü; Q. Li; G. Brethouwer; J.H. Fransson; A.V. Johansson; P.H. Alfredsson; D.S. Henningson Turbulent boundary layers up to ${Re}_{θ} = 2500$ studied through simulation and experiment, Phys. Fluids, Volume 21 (2009), p. 051702

[24] P.V. Lanspeary, M.K. Bull, Correction of sublayer turbulence measurements for wall proximity effects in hot-wire anemometry, in: 11th Australasian Fluid Mechanics Conference, December 1992.

[25] A.S. Monin; A.M. Yaglom Statistical fluid mechanics: mechanics of turbulence (J.L. Lumley, ed.), English Translation, vol. 2, MIT Press, Cambridge, Massachusetts, USA, 1971

[26] R. Örlü; J.H.M. Fransson; P.H. Alfredsson On near wall measurements of wall bounded flows – the necessity of an accurate determination of the wall position, Prog. Aerospace Sci., Volume 46 (2010) no. 8, p. 353

[27] M. Fischer; J. Jovanović; F. Durst Reynolds number effects in the near-wall region of turbulent channel flows, Phys. Fluids, Volume 13 (2001) no. 6, p. 1755

[28] D.R. Chapmann; G.D. Kuhn The limiting behaviour of turbulence near a wall, J. Fluid Mech., Volume 170 (1986), p. 265

[29] C. Chin; A.S.H. Ooi; I. Marusic; H.M. Blackburn The influence of pipe length on turbulence statistics computed from direct numerical simulation data, Phys. Fluids, Volume 22 (2010), p. 61

[30] L. Keirsbulck, L. Labraga, M. Gad el Hak, Statistical properties of wall-shear-stress fluctuations in turbulent channel flows, Int. J. Heat Fluid Flow (2012), in press.

[31] X. Wu; P. Moin A direct numerical simulation study on the mean velocity characteristics in turbulent pipe flow, J. Fluid Mech., Volume 608 (2008), p. 81

[32] R. Örlü; P. Schlatter On the fluctuating wall-shear stress in zero pressure-gradient turbulent boundary layer flows, Phys. Fluids, Volume 23 (2011), p. 021704

[33] M.P. Simens; J. Jiménez; S. Hoyas; Y. Mizuno A high-resolution code for turbulent boundary layers, J. Computat. Phys., Volume 228 (2009) no. 11, p. 4218

[34] J.H. Lee; H.J. Sun Direct numerical simulation of a turbulent boundary layer up to ${Re}_{θ} = 2500$ , Int. J. Heat Fluid Flow, Volume 32 (2011), p. 1

[35] H. Osaka; T. Kameda; S. Mochizuki Re-examination of the Reynolds number effect on the mean flow quantities in a smooth wall turbulent boundary layer, JSME Int. J., Volume 41 (1988), p. 123

[36] J. Carlier; M. Stanislas Experimental study of eddy structures in a turbulent boundary layer using particle image velocimetry, J. Fluid Mech., Volume 535 (2005), p. 143

[37] C. Ching; L. Djenidi; R. Antonia Low-Reynolds-effects in a turbulent boundary layer, Exp. Fluid, Volume 19 (1995), p. 61

[38] T. Johansson; R. Karlsson The energy budget in the near-wall region of a turbulent boundary layer (R.J. Adrian; T. Asanuma; D.F.G. Durao; F. Durst; J.H. Whitelaw, eds.), Applications of Laser Anemometry to Fluid Mechanics, Springer, 1989, p. 3

[39] P.R. Spalart Direct simulation of a turbulent boundary layer up to ${Re}_{θ} = 1410$ , J. Fluid Mech., Volume 187 (1988), p. 61

[40] J.L. Balint; J.M. Wallace; P. Vukoslavcevic The velocity and vorticity vector fields of a turbulent boundary layer. Part 2. Statistical properties, J. Fluid Mech., Volume 228 (1991), p. 53

[41] X. Wu; P. Moin Direct numerical simulation of turbulence in a nominally zero-pressure-gradient flat-plate boundary layer, J. Fluid Mech., Volume 630 (2009), p. 5

[42] H. Abe; H. Kawamura; H. Choi Very large-scale structures and their effects on the wall shear-stress fluctuations in a turbulent channel flow up to ${Re}_{τ} = 640$ , Phys. Fluids, Volume 126 (2004), p. 835

[43] R.A. Antonia; J. Kim Low-Reynolds-number effects on near-wall turbulence, J. Fluid Mech., Volume 276 (1994), p. 61

[44] J.C. DelÁdamo; J. Jiménez Spectra of the very large anisotropic scales in turbulent channels, J. Fluid Mech., Volume 500 (2004), p. 135

[45] A. Günther; D.V. Papavassiliou; M.D. Warholic; T.J. Hanratty Turbulent flow in a channel at low Reynolds number, Exp. Fluid, Volume 25 (1998), p. 503

[46] P. Purtell; P. Klebanoff; F. Buckley Turbulent boundary layer at low Reynolds number, Phys. Fluids, Volume 24 (1981), p. 802

[47] S. Hoyas; J. Jiménez Scaling of the velocity fluctuations in turbulent channels up to ${Re}_{τ} = 2003$ , Phys. Fluids, Volume 18 (2006), p. 011702

[48] H. Ueda; J.O. Hinze Fine-structure turbulence in the wall region of a turbulent boundary layer, J. Fluid Mech., Volume 67 (1975), p. 125

[49] K. Iwamoto; Y. Suzuki; N. Kasagi Reynolds number effect on wall turbulence: Toward effective feedback control, Int. J. Heat Fluid Flow, Volume 23 (2002), p. 678

[50] J. Jiménez; J.C. DelÁdamo; O. Flores The large-scale dynamics of near-wall turbulence, J. Fluid Mech., Volume 505 (2004), p. 179

[51] D. Poggi; A. Porporato; L. Ridolfi An experimental contribution to near-wall measurements by means of special laser Doppler anemometry technique, Exp. Fluid, Volume 32 (2002), p. 366

[52] L. Lyons; T.J. Hanratty; J.B. McLaughlin Direct numerical simulation of passive heat transfer in a turbulent channel flow, Int. J. Heat Mass Transfer, Volume 34 (1991) no. 4, p. 1149

[53] T. Wei; W.W. Willmarth Reynolds-number effects on the structure of a turbulent channel flow, J. Fluid Mech., Volume 204 (1989), p. 57

[54] N.N. Mansour; J. Kim; P. Moin Reynolds-stress and dissipation-rate budgets in a turbulent channel flow, J. Fluid Mech., Volume 194 (1988), p. 15

[55] B.C. Khoo; Y.T. Chew; C.J. Teo Near-wall hot-wire measurements, Part II: Turbulence time scale, convective velocity and spectra in the viscous sublayer, Exp. Fluid, Volume 31 (2001), p. 494

[56] R.D. Moser; J. Kim; N.N. Mansour Direct numerical simulation of a turbulent channel flow up to ${Re}_{τ} = 590$ , Phys. Fluids, Volume 11 (1999), p. 943

[57] J. Pallares; F.X. Grau Frequency response of an electrochemical probe to the wall shear stress fluctuations of turbulent channel flow, Int. J. Heat Mass Transfer, Volume 51 (2008), p. 4753

[58] T. Tsukahara, Y. Seki, H. Kawamura, D. Tochio, Dns of turbulent channel flow at very low Reynolds numbers, in: Proc. Fourth Int. Symp. on Turbulence and Shear Flow Phenomena, Williamsburg, USA, June 2005, p. 935.

[59] R.W. Smith, Effect of Reynolds number on the structure of turbulent boundary layers, Ph.D. thesis, Department of Mechanical and Aerospace Engineering, Princeton University, 1994.

[60] A.A. Townsend Equilibrium layers and wall turbulence, J. Fluid Mech., Volume 11 (1961), p. 97

[61] A.N. Kolmogorov The local structure of turbulence in incompressible viscous fluid for very large Reynolds number, Acad. Sci., Volume 30 (1941), p. 301

[62] S.B. Pope Turbulent Flows, Cambridge University Press, 2000

[63] R. Rubinstein; W.J.T. Bos On the unsteady behavior of turbulence models, Phys. Fluids, Volume 21 (2009), p. 041701

[64] M.H. Buschmann; M. Gad-el-Hak Kolmogorov scaling of turbulent flow in the vicinity of the wall, Phys. D: Nonlinear Phenom., Volume 239 (2010), p. 1288

[65] Z.W. Hu; C.L. Morfey; N.D. Sandham Wall pressure and shear stress spectra from direct simulations of channel flow, AIAA J., Volume 44 (2006), p. 1541

[66] J. Kim; P. Moin; R.D. Moser Turbulence statistics in fully developed channel flow at low Reynolds number, J. Fluid Mech., Volume 177 (1987), p. 133

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