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Comparison of experiments and simulations for zero pressure gradient turbulent boundary layers at moderate Reynolds numbers

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Abstract

A detailed comparison between recent direct numerical simulation (DNS) and experiments of a turbulent boundary layer under zero pressure gradient at Re θ  = 2,500 and 4,000 (based on the free-stream velocity and momentum-loss thickness) is presented. The well-resolved DNS is computed in a long spatial domain (Schlatter and Örlü in J Fluid Mech 659:116, 2010a), including the disturbance strip, while the experiments consist of single hot-wire probe and oil-film interferometry measurements. Remarkably, good agreement is obtained for integral quantities such as skin friction and shape factor, as well as mean and fluctuating streamwise velocity profiles, higher-order moments and probability density distributions. The agreement also extends to spectral/structural quantities such as the amplitude modulation of the small scales by the large-scale motion and temporal spectral maps throughout the boundary layer. Differences within the inner layer observed for statistical and spectral quantities could entirely be removed by spatially averaging the DNS to match the viscous-scaled length of the hot-wire sensor, thereby explaining observed differences solely by insufficient spatial resolution of the hot-wire sensor. For the highest Reynolds number, Re θ  = 4,000, the experimental data exhibit a more pronounced secondary spectral peak in the outer region (y/δ 99 = 0.1) related to structures with length on the order of 5–7 boundary layer thicknesses, which is weaker and slightly moved towards lower temporal periods in the DNS. The cause is thought to be related to the limited spanwise box size which constrains the growth of the very large structures. In the light of the difficulty to obtain “canonical” flow conditions, both in DNS and the wind tunnel where effects such as boundary treatment, pressure gradient and turbulence tripping need to be considered, the present cross-validation of the data sets, at least for the present Re θ -range, provides important reference data for future studies and highlights the importance of taking spatial resolution effects into account when comparing experiment and DNS. For the considered flow, the present data also provide quantitative guidelines on what level of accuracy can be expected for the agreement between DNS and experiments.

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Notes

  1. See also the featuring Focus on Fluids article by Hutchins (2012).

  2. Note that the data for pipe flows from experiments are inconclusive. Recent hot-wire measurements in the Superpipe with matched L + values surprisingly show “that the magnitude of the near-wall peak is invariant with Reynolds number in location and magnitude” (Hultmark et al. 2010), a finding that has been confirmed in the same facility by means of nano-scale thermal anemometry probes (Hultmark et al. 2012). A recent compilation of new DNS and experiments by Örlü and Alfredsson (2012), albeit limited to Re τ ⩽ 3,000, depicts, however, a clear increase with Re, indicating the need for new experiments for Re τ  > 3,000.

References

  • Alfredsson PH, Johansson AV, Haritonidis JH, Eckelmann H (1988) The fluctuating wall-shear stress and the velocity field in the viscous sublayer. Phys Fluids 31:1026–1033

    Article  Google Scholar 

  • Alfredsson PH, Örlü R, Schlatter P (2011) The viscous sublayer revisited–exploiting self-similarity to determine the wall position and friction velocity. Exp Fluids 51:271–280

    Article  Google Scholar 

  • Alfredsson PH, Örlü R, Segalini A (2012) A new formulation for the streamwise turbulence intensity distribution in wall-bounded turbulent flows. Eur J Mech B Fluid 36:167–175

    Article  Google Scholar 

  • Bernardini M, Pirozzoli S (2011) Inner/outer layer interactions in turbulent boundary layers: a refined measure for the large-scale amplitude modulation mechanism. Phys Fluids 23:061701

    Article  Google Scholar 

  • Bertolotti FP, Herbert T, Spalart PR (1992) Linear and nonlinear stability of the Blasius boundary layer. J Fluid Mech 242:441–474

    Article  MathSciNet  MATH  Google Scholar 

  • Bhatia J, Durst F, Jovanovic J (1982) Corrections of hot-wire anemometer measurements near walls. J Fluid Mech 123:411–431

    Article  Google Scholar 

  • Bruun HH (1995) Hot-wire anemometry: principles and signal analysis. Oxford University Press Inc, New York

    Google Scholar 

  • Buschmann MH, Indinger T, Gad-el-Hak M (2009) Near-wall behavior of turbulent wall-bounded flows. Int J Heat Fluid Flow 30:993–1006

    Article  Google Scholar 

  • Chauhan KA, Monkewitz PA, Nagib HM (2009) Criteria for assessing experiments in zero pressure gradient boundary layers. Fluid Dyn Res 41:021404

    Article  Google Scholar 

  • Chevalier M, Schlatter P, Lundbladh A, Henningson DS (2007) SIMSON—a pseudo-spectral solver for incompressible boundary layer flow. Technical report, Royal Institute of Technology, Stockholm, Sweden

  • Coles DE (1968) The young person’ s guide to the data. In: Coles DE, Hirst EA (eds) AFOSR-IFP-stanford conference on computation of turbulent boundary layers. pp 1–45

  • DeGraaff DB, Eaton JK (2000) Reynolds-number scaling of the flat-plate turbulent boundary layer. J Fluid Mech 422:319–346

    Article  MATH  Google Scholar 

  • del Álamo JC, Jiménez J (2009) Estimation of turbulent convection velocities and corrections to Taylor’s approximation. J Fluid Mech 640:5–26

    Article  MathSciNet  MATH  Google Scholar 

  • del Álamo JC, Jiménez J, Zandonade P, Moser RD (2004) Scaling of the energy spectra of turbulent channels. J Fluid Mech 500:135–144

    Article  MATH  Google Scholar 

  • Dryden HL (1936) Air flow in the boundary layer near a plate. NACA Technical report No. 562

  • Dryden HL, Schubauer GB, Mock WC, Skramstad HK (1937) Measurements of intensity and scale of wind-tunnel turbulence and their relation to the critical Reynolds number of spheres. NACA Technical report No. 581

  • Erm LP, Joubert PN (1991) Low-Reynolds-number turbulent boundary layers. J Fluid Mech 230:1–44

    Article  Google Scholar 

  • Fernholz HH, Finley PJ (1996) The incompressible zero-pressure-gradient turbulent boundary layer: an assessment of the data. Prog Aerosp Sci 32:245–311

    Article  Google Scholar 

  • Ferrante A, Elghobashi SE (2005) Reynolds number effect on drag reduction in a microbubble-laden spatially developing turbulent boundary layer. J Fluid Mech 543:93–106

    Article  MATH  Google Scholar 

  • Hoyas S, Jiménez J (2006) Scaling of the velocity fluctuations in turbulent channels up to Re τ  = 2003. Phys Fluids 18:011702

    Article  Google Scholar 

  • Hultmark M, Bailey SCC, Smits AJ (2010) Scaling of near-wall turbulence in pipe flow. J Fluid Mech 649:103–113

    Article  MATH  Google Scholar 

  • Hultmark M, Vallikivi M, Bailey SCC, Smits AJ (2012) Turbulent pipe flow at extreme Reynolds numbers. Phys Rev Lett 108:094501

    Article  Google Scholar 

  • Hutchins N (2012) Caution: tripping hazards. J Fluid Mech 710:1–4

    Article  MathSciNet  Google Scholar 

  • Hutchins N, Marusic I (2007) Evidence of very long meandering features in the logarithmic region of turbulent boundary layers. J Fluid Mech 579:1–28

    Article  MATH  Google Scholar 

  • Hutchins N, Nickels TB, Marusic I, Chong MS (2009) Hot-wire spatial resolution issues in wall-bounded turbulence. J Fluid Mech 635:103–136

    Article  MATH  Google Scholar 

  • Jiménez J, Hoyas S, Simens MP, Mizuno Y (2010) Turbulent boundary layers and channels at moderate Reynolds numbers. J Fluid Mech 657:335–360

    Article  MATH  Google Scholar 

  • Karlsson RI (1980) Studies of skin friction in turbulent boundary layers on smooth and rough walls. Ph.D. thesis, Chalmers University of Technology, Göteborg, Sweden

  • Khujadze G, Oberlack M (2004) DNS and scaling laws from new symmetry groups of ZPG turbulent boundary layer flow. Theor Comput Fluid Dyn 18:391–411

    Article  MATH  Google Scholar 

  • Kim J, Moin P, Moser RD (1987) Turbulence statistics in fully developed channel flow at low Reynolds number. J Fluid Mech 177:133–166

    Article  MATH  Google Scholar 

  • Klewicki JC (2010) Reynolds number dependence, scaling, and dynamics of turbulent boundary layers. J Fluid Eng 132:094001

    Article  Google Scholar 

  • Klewicki JC, Falco R (1990) On accurately measuring statistics associated with small-scale structure in turbulent boundary layers using hot-wire probes. J Fluid Mech 219:119–142

    Article  Google Scholar 

  • Lee JH, Sung HJ (2011) Direct numerical simulation of a turbulent boundary layer up to Re θ  = 2500. Int J Heat Fluid Flow 32:1–10

    Article  Google Scholar 

  • Lenaers P, Li Q, Brethouwer G, Schlatter P, Örlü R (2012) Rare backflow and extreme wall-normal velocity fluctuations in near-wall turbulence. Phys Fluids 24:035110

    Article  Google Scholar 

  • Lindgren B, Johansson AV (2002) Evaluation of the flow quality in the MTL wind-tunnel. Technical report, Royal Institute of Technology, Stockholm, Sweden

  • Marusic I, Mathis R, Hutchins N (2010a) Predictive model for wall-bounded turbulent flow. Science 329:193–196

    Article  MathSciNet  MATH  Google Scholar 

  • Marusic I, McKeon BJ, Monkewitz PA, Nagib HM, Smits AJ, Sreenivasan KR (2010b) Wall-bounded turbulent flows at high Reynolds numbers: recent advances and key issues. Phys Fluids 22:065103

    Article  Google Scholar 

  • Mathis R, Hutchins N, Marusic I (2009) Large-scale amplitude modulation of the small-scale structures in turbulent boundary layers. J Fluid Mech 628:311–337

    Article  MATH  Google Scholar 

  • Mathis R, Marusic I, Hutchins N, Sreenivasan K (2011) The relationship between the velocity skewness and the amplitude modulation of the small scale by the large scale in turbulent boundary layers. Phys Fluids 23:121702

    Article  Google Scholar 

  • Metzger M, Klewicki JC (2001) A comparative study of near-wall turbulence in high and low Reynolds number boundary layers. Phys Fluids 13:692–701

    Article  Google Scholar 

  • Monkewitz PA, Chauhan KA, Nagib HM (2008) Comparison of mean flow similarity laws in zero pressure gradient turbulent boundary layers. Phys Fluids 20:105102

    Article  Google Scholar 

  • Monkewitz PA, Duncan RD, Nagib HM (2010) Correcting hot-wire measurements of stream-wise turbulence intensity in boundary layers. Phys Fluids 22:091701

    Article  Google Scholar 

  • Monty JP, Chong MS (2009) Turbulent channel flow: comparison of streamwise velocity data from experiments and direct numerical simulation. J Fluid Mech 633:461–474

    Article  MATH  Google Scholar 

  • Nagib HM, Christophorou C, Rüedi JD, Monkewitz PA, Österlund JM (2004) Can we ever rely on results from wall-bounded turbulent flows without direct measurements of wall shear stress? AIAA 2004-2392

  • Nagib HM, Chauhan KA, Monkewitz PA (2007) Approach to an asymptotic state for zero pressure gradient turbulent boundary layers. Philos Trans R Soc 365:755–770

    Article  MATH  Google Scholar 

  • Nickels TB (2004) Inner scaling for wall-bounded flows subject to large pressure gradients. J Fluid Mech 521:217–239

    Article  MathSciNet  MATH  Google Scholar 

  • Örlü R (2009) Experimental studies in jet flows and zero pressure-gradient turbulent boundary layers. Ph.D. thesis, Royal Institute of Technology, Stockholm, Sweden

  • Örlü R, Alfredsson PH (2010) On spatial resolution issues related to time-averaged quantities using hot-wire anemometry. Exp Fluids 49:101–110

    Article  Google Scholar 

  • Örlü R, Alfredsson PH (2012) Comment on the scaling of the near-wall streamwise variance peak in turbulent pipe flows. Exp Fluids 54:1431

    Article  Google Scholar 

  • Örlü R, Schlatter P (2011) On the fluctuating wall shear stress in zero pressure-gradient turbulent boundary layer flows. Phys Fluids 23:021704

    Article  Google Scholar 

  • Örlü R, Fransson JHM, Alfredsson PH (2010) On near wall measurements of wall bounded flows–the necessity of an accurate determination of the wall position. Prog Aerosp Sci 46:353–387

    Article  Google Scholar 

  • Osaka H, Kameda T, Mochizuki S (1998) Re-examination of the Reynolds-number-effect on the mean flow quantities in a smooth wall turbulent boundary layer. JSME Int J Ser B 41:123–129

    Article  Google Scholar 

  • Österlund JM (1999) Experimental studies of zero pressure-gradient turbulent boundary layer flow. Ph.D. thesis, Royal Institute of Technology, Stockholm, Sweden

  • Österlund JM, Johansson AV, Nagib HM, Hites MH (2000) A note on the overlap region in turbulent boundary layers. Phys Fluids 12:1–4

    Article  MATH  Google Scholar 

  • Perry AE, Marusic I, Jones MB (2002) On the streamwise evolution of turbulent boundary layers in arbitrary pressure gradients. J Fluid Mech 461:61–91

    Article  MathSciNet  MATH  Google Scholar 

  • Purtell L, Klebanoff PS, Buckley F (1981) Turbulent boundary layer at low Reynolds number. Phys Fluids 25:802–811

    Article  Google Scholar 

  • Schlatter P, Örlü R (2010a) Assessment of direct numerical simulation data of turbulent boundary layers. J Fluid Mech 659:116–126

    Article  MATH  Google Scholar 

  • Schlatter P, Örlü R (2010b) Quantifying the interaction between large and small scales in wall-bounded turbulent flows: a note of caution. Phys Fluids 22:051704

    Article  Google Scholar 

  • Schlatter P, Örlü R (2012) Turbulent boundary layers at moderate Reynolds numbers: inflow length and tripping effects. J Fluid Mech 710:5–34

    Article  Google Scholar 

  • Schlatter P, Örlü R, Li Q, Brethouwer G, Fransson JHM, Johansson AV, Alfredsson PH, Henningson DS (2009) Turbulent boundary layers up to Re θ  = 2500 studied through simulation and experiment. Phys Fluids 21:051702

    Article  Google Scholar 

  • Schlatter P, Li Q, Brethouwer G, Johansson AV, Henningson DS (2010) Simulations of spatially evolving turbulent boundary layers up to Re θ =4300. Int J Heat Fluid Flow 31:251–261

    Article  Google Scholar 

  • Segalini A, Örlü R, Schlatter P, Alfredsson PH, Rüedi JD, Talamelli A (2011) A method to estimate turbulence intensity and transverse Taylor microscale in turbulent flows from spatially averaged hot-wire data. Exp Fluids 51:693–700

    Article  Google Scholar 

  • Segalini A, Örlü R, Alfredsson PH (2013) Uncertainty analysis of the von Kármán constant. Exp Fluids 54:1460

    Article  Google Scholar 

  • Smits AJ, Matheson N, Joubert PN (1983) Low-Reynolds-number turbulent boundary layers in zero and favorable pressure gradients. J Ship Res 27:147–157

    Google Scholar 

  • Smits AJ, McKeon BJ, Marusic I (2011a) High–Reynolds number wall turbulence. Annu Rev Fluid Mech 43:353–375

    Article  Google Scholar 

  • Smits AJ, Monty JP, Hultmark M, Bailey SCC, Hutchins N, Marusic I (2011b) Spatial resolution correction for wall-bounded turbulence measurements. J Fluid Mech 676:41–53

    Article  MATH  Google Scholar 

  • Spalart PR (1988) Direct simulation of a turbulent boundary layer up to R θ  = 1410. J Fluid Mech 187:61–98

    Article  MATH  Google Scholar 

  • Talamelli A, Segalini A, Örlü R, Schlatter P, Alfredsson PH (2013) Correcting hot-wire spatial resolution effects in third- and fourth-order velocity moments in wall-bounded turbulence. Exp Fluids 54:1496

    Article  Google Scholar 

  • van der Hegge Zijnen B (1924) Measurements of the velocity distribution in the boundary layer along a plane surface. Ph.D. thesis, Delft University of Technology, The Netherlands

  • Wallace JM (2012) Highlights from 50 years of turbulent boundary layer research. J Turbulence 13(N53)

  • Wu X, Moin P (2010) Transitional and turbulent boundary layer with heat transfer. Phys Fluids 22:085105

    Article  Google Scholar 

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Acknowledgments

Prof. P. Henrik Alfredsson and Dr. Georg Eitel-Amor are acknowledged for comments on the manuscript. The first author wishes to thank Dr. J. D. Rüedi for discussions related to oil-film interferometry. Computer time provided by the Swedish National Infrastructure for Computing (SNIC) is gratefully acknowledged.

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  1. Linné FLOW Centre, Swedish e-Science Research Centre (SeRC), KTH Mechanics, 100 44, Stockholm, Sweden

    Ramis Örlü & Philipp Schlatter

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  1. Ramis Örlü
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  2. Philipp Schlatter
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Correspondence to Ramis Örlü.

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Örlü, R., Schlatter, P. Comparison of experiments and simulations for zero pressure gradient turbulent boundary layers at moderate Reynolds numbers. Exp Fluids 54, 1547 (2013). https://doi.org/10.1007/s00348-013-1547-x

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