Skip to main content Accessibility help
×
Home

Effect of adverse pressure gradients on turbulent wing boundary layers

  • Á. Tanarro (a1) (a2), R. Vinuesa (a1) (a2) and P. Schlatter (a1) (a2)

Abstract

The characteristics of turbulent boundary layers (TBLs) subjected to adverse pressure gradients are analysed through well-resolved large-eddy simulations. The geometries under study are the NACA0012 and NACA4412 wing sections, at $0^{\circ }$ and $5^{\circ }$ angle of attack, respectively, both of them at a Reynolds number based on inflow velocity and chord length of $Re_{c}=400\,000$ . The turbulence statistics show that adverse pressure gradients (APGs) have a significant effect on the mean velocity, velocity fluctuations and turbulent kinetic energy budget, and this effect is more prominent on the outer region of the boundary layer. Furthermore, the effect of flow history is assessed by means of an integrated Clauser pressure-gradient parameter $\overline{\unicode[STIX]{x1D6FD}}$ (Vinuesa et al., Flow Turbul. Combust., vol. 99, 2017, pp. 565–587), through the study of cases with matching local values of $\unicode[STIX]{x1D6FD}$ and the friction Reynolds number $Re_{\unicode[STIX]{x1D70F}}$ to isolate this effect. Our results show a noticeable effect of the flow history on the outer region, however the differences in the near-wall peak of the tangential velocity fluctuations appear to be mostly produced by the local APG magnitude. The one-dimensional power-spectral density shows energetic small scales in the outer region of APG TBLs, whereas these energetic scales do not appear in zero-pressure-gradient (ZPG) TBLs, suggesting that small scales near the wall are advected towards the outer layer by the APG. Moreover, the linear coherence spectra show that the spectral outer peak of high-Reynolds-number ZPG TBLs is highly correlated with the near-wall region (Baars et al., J. Fluid Mech., vol. 823, 2017, R2), unlike APG TBLs which do not show such a correlation. This result, together with the different two-dimensional spectra of APG and high-Reynolds-number ZPG TBLs, suggests different energisation mechanisms due to APG and increase in Reynolds number. To the authors’ knowledge, this is the first in-depth analysis of the TBL characteristics over wings, including detailed single-point statistics, spectra and coherence.

  • View HTML
    • Send article to Kindle

      To send this article to your Kindle, first ensure no-reply@cambridge.org is added to your Approved Personal Document E-mail List under your Personal Document Settings on the Manage Your Content and Devices page of your Amazon account. Then enter the ‘name’ part of your Kindle email address below. Find out more about sending to your Kindle. Find out more about sending to your Kindle.

      Note you can select to send to either the @free.kindle.com or @kindle.com variations. ‘@free.kindle.com’ emails are free but can only be sent to your device when it is connected to wi-fi. ‘@kindle.com’ emails can be delivered even when you are not connected to wi-fi, but note that service fees apply.

      Find out more about the Kindle Personal Document Service.

      Effect of adverse pressure gradients on turbulent wing boundary layers
      Available formats
      ×

      Send article to Dropbox

      To send this article to your Dropbox account, please select one or more formats and confirm that you agree to abide by our usage policies. If this is the first time you use this feature, you will be asked to authorise Cambridge Core to connect with your <service> account. Find out more about sending content to Dropbox.

      Effect of adverse pressure gradients on turbulent wing boundary layers
      Available formats
      ×

      Send article to Google Drive

      To send this article to your Google Drive account, please select one or more formats and confirm that you agree to abide by our usage policies. If this is the first time you use this feature, you will be asked to authorise Cambridge Core to connect with your <service> account. Find out more about sending content to Google Drive.

      Effect of adverse pressure gradients on turbulent wing boundary layers
      Available formats
      ×

Copyright

This is an Open Access article, distributed under the terms of the Creative Commons Attribution licence (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted re-use, distribution, and reproduction in any medium, provided the original work is properly cited.

Corresponding author

Email address for correspondence: rvinuesa@mech.kth.se

References

Hide All
del Álamo, J. C., Jiménez, J., Zandonade, P. & Moser, R. D. 2004 Scaling of the energy spectra of turbulent channels. J. Fluid Mech. 500, 135144.
Baars, W. J., Hutchins, N. & Marusic, I. 2017 Self-similarity of wall-attached turbulence in boundary layers. J. Fluid Mech. 823, R2.
Bobke, A., Vinuesa, R., Örlü, R. & Schlatter, P. 2017 History effects and near equilibrium in adverse-pressure-gradient turbulent boundary layers. J. Fluid Mech. 820, 667692.
Chandran, D., Baidya, R., Monty, J. P. & Marusic, I. 2017 Two-dimensional energy spectra in high-Reynolds-number turbulent boundary layers. J. Fluid Mech. 826, R1.
Clauser, F. H. 1954 Turbulent boundary layers in adverse pressure gradients. J. Aero. Sci. 21 (2), 91108.
Clauser, F. H. 1956 The turbulent boundary layer. Adv. Appl. Mech. 4, 151.
Coles, D. 1956 The law of the wake in the turbulent boundary layer. J. Fluid Mech. 1 (2), 191226.
Coles, D. & Wadcock, A. J. 1979 Flying-hot-wire study of flow past an NACA 4412 airfoil at maximum lift. AIAA J. 17 (4), 321329.
Dong, S., Karniadakis, G. E. & Chryssostomidis, C. 2014 A robust and accurate outflow boundary condition for incompressible flow simulations on severely-truncated unbounded domains. J. Comput. Phys. 261, 83105.
Eitel-Amor, G., Örlü, R. & Schlatter, P. 2014 Simulation and validation of a spatially evolving turbulent boundary layer up to Re 𝜃 = 8300. Intl J. Heat Fluid Flow 47, 5769.
Fischer, P., Lottes, J. & Kerkemeier, S.2008 Nek5000: Open source spectral element CFD solver. Available at: https://nek5000.mcs.anl.gov.
Flores, O. & Jiménez, J. 2010 Hierarchy of minimal flow units in the logarithmic layer. Phys. Fluids 22 (7), 071704.
Harun, Z., Monty, J. P., Mathis, R. & Marusic, I. 2013 Pressure gradient effects on the large-scale structure of turbulent boundary layers. J. Fluid Mech. 715, 477498.
Hosseini, S. M., Vinuesa, R., Schlatter, P., Hanifi, A. & Henningson, D. S. 2016 Direct numerical simulation of the flow around a wing section at moderate Reynolds number. Intl J. Heat Fluid Flow 61, 117128.
Hoyas, S. & Jiménez, J. 2006 Scaling of the velocity fluctuations in turbulent channels up to Re 𝜏 = 2003. Phys. Fluids 18 (1), 011702.
Hutchins, N. & Marusic, I. 2007a Evidence of very long meandering features in the logarithmic region of turbulent boundary layers. J. Fluid Mech. 579, 128.
Hutchins, N. & Marusic, I. 2007b Large-scale influences in near-wall turbulence. Phil. Trans. R. Soc. Lond. A 365 (1852), 647664.
Jansen, K. 1996 Large-eddy simulation of flow around a NACA 4412 airfoil using unstructured grids. In Annual Research Briefs, pp. 225232. Center for Turbulence Research, NASA Ames/Stanford University.
Jeong, J. & Hussain, F. 1995 On the identification of a vortex. J. Fluid Mech. 285, 6994.
Jiménez, J., Hoyas, S., Simens, M. P. & Mizuno, Y. 2010 Turbulent boundary layers and channels at moderate Reynolds numbers. J. Fluid Mech. 657, 335360.
Jones, W. P. & Launder, B. E. 1972 Some properties of sink-flow turbulent boundary layers. J. Fluid Mech. 56, 337351.
Kitsios, V., Sekimoto, A., Atkinson, C., Sillero, J. A., Borrell, G., Gungor, A. G., Jiménez, J. & Soria, J. 2017 Direct numerical simulation of a self-similar adverse pressure gradient turbulent boundary layer at the verge of separation. J. Fluid Mech. 829, 392419.
Lee, J. H. 2017 Large-scale motions in turbulent boundary layers subjected to adverse pressure gradients. J. Fluid Mech. 810, 323361.
Maciel, Y., Gungor, A. G. & Simens, M. P. 2017 Structural differences between small and large momentum-defect turbulent boundary layers. Intl J. Heat Fluid Flow 67, 95110.
Maciel, Y., Wei, T., Gungor, A. G. & Simens, M. P. 2018 Outer scales and parameters of adverse-pressure-gradient turbulent boundary layers. J. Fluid Mech. 844, 535.
Marusic, I., Mathis, R. & Hutchins, N. 2010 Predictive model for wall-bounded turbulent flow. Science 329 (5988), 193196.
Menter, F. R. 1994 Two-equation eddy-viscosity turbulence models for engineering applications. AIAA J. 32 (8), 15981605.
Monkewitz, P. A., Chauhan, K. A. & Nagib, H. M. 2007 Self-consistent high-Reynolds-number asymptotics for zero-pressure-gradient turbulent boundary layers. Phys. Fluids 19 (11), 115101.
Monty, J. P., Harun, Z. & Marusic, I. 2011 A parametric study of adverse pressure gradient turbulent boundary layers. Intl J. Heat Fluid Flow 32 (3), 575585.
Nagano, Y., Tagawa, M. & Tsuji, T. 1993 Effects of adverse pressure gradients on mean flows and turbulence statistics in a boundary layer. In Turbulent Shear Flows 8, pp. 721. Springer.
Nagib, H. M. & Chauhan, K. A. 2008 Variations of von Kármán coefficient in canonical flows. Phys. Fluids 20 (10), 101518.
Nagib, H. M., Chauhan, K. A. & Monkewitz, P. A. 2007 Approach to an asymptotic state for zero pressure gradient turbulent boundary layers. Phil. Trans. R. Soc. Lond. A 365 (1852), 755770.
Negi, P. S., Vinuesa, R., Hanifi, A., Schlatter, P. & Henningson, D. S. 2018 Unsteady aerodynamic effects in small-amplitude pitch oscillations of an airfoil. Intl J. Heat Fluid Flow 71, 378391.
Patel, V. & Sotiropoulos, F. 1997 Longitudinal curvature effects in turbulent boundary layers. Prog. Aerosp. Sci. 33 (1–2), 170.
Patera, A. T. 1984 A spectral element method for fluid dynamics: Laminar flow in a channel expansion. J. Comput. Phys. 54 (3), 468488.
Pinkerton, R. M. 1938 The variation with Reynolds number of pressure distribution over an airfoil section. NACA Ann. Rep. 24, 6584.
Rodríguez, I., Lehmkuhl, O., Borrell, R. & Oliva, A. 2013 Direct numerical simulation of a NACA0012 in full stall. Intl J. Heat Fluid Flow 43, 194203.
Sanmiguel Vila, C., Örlü, R., Vinuesa, R., Schlatter, P., Ianiro, A. & Discetti, S. 2017 Adverse-pressure-gradient effects on turbulent boundary layers: statistics and flow-field organization. Flow Turbul. Combust. 99, 589612.
Sato, M., Asada, K., Nonomura, T., Kawai, S. & Fujii, K. 2016 Large-eddy simulation of NACA 0015 airfoil flow at Reynolds number of 1. 6 × 106. AIAA J. 55 (2), 673679.
Schlatter, P., Li, Q., Brethouwer, G., Johansson, A. V. & Henningson, D. S. 2010 Simulations of spatially evolving turbulent boundary layers up to Re 𝜃 = 4300. Intl J. Heat Fluid Flow 31 (3), 251261.
Schlatter, P. & Örlü, R. 2012 Turbulent boundary layers at moderate Reynolds numbers: inflow length and tripping effects. J. Fluid Mech. 710, 534.
Schlatter, P., Stolz, S. & Kleiser, L. 2004 LES of transitional flows using the approximate deconvolution model. Intl J. Heat Fluid Flow 25 (3), 549558.
Sillero, J., Jiménez, J., Moser, R. D. & Malaya, N. P. 2011 Direct simulation of a zero-pressure-gradient turbulent boundary layer up to Re 𝜃 = 6650. J. Phys.: Conf. Ser. 318, 022023.
Sillero, J. A., Jiménez, J. & Moser, R. D. 2014 Two-point statistics for turbulent boundary layers and channels at Reynolds numbers up to 𝛿+ ≃ 2000. Phys. Fluids 26 (10), 105109.
Skåre, P. E. & Krogstad, P. å. 1994 A turbulent equilibrium boundary layer near separation. J. Fluid Mech. 272, 319348.
Spalart, P. R. & Watmuff, J. H. 1993 Experimental and numerical study of a turbulent boundary layer with pressure gradients. J. Fluid Mech. 249, 337371.
Tanarro, Á., Mallor, F., Offermans, N., Peplinski, A., Vinuesa, R. & Schlatter, P. 2019 Using adaptive mesh refinement to simulate turbulent wings at high Reynolds numbers. In Proc. Intern. Symp. on Turbulence and Shear Flow Phenomena (TSFP-11), Southampton, UK, July 30–August 2.
Townsend, A. A. 1976 The Structure of Turbulent Shear Flow. Cambridge University Press.
Vinuesa, R., Bobke, A., Örlü, R. & Schlatter, P. 2016 On determining characteristic length scales in pressure-gradient turbulent boundary layers. Phys. Fluids 28 (5), 055101.
Vinuesa, R., Hosseini, S. M., Hanifi, A., Henningson, D. S. & Schlatter, P. 2017a Pressure-gradient turbulent boundary layers developing around a wing section. Flow Turbul. Combust. 99 (3–4), 613641.
Vinuesa, R., Negi, P. S., Atzori, M., Hanifi, A., Henningson, D. S. & Schlatter, P. 2018 Turbulent boundary layers around wing sections up to Re c = 1 000 000. Intl J. Heat Fluid Flow 72, 8699.
Vinuesa, R., Örlü, R., Sanmiguel Vila, C., Ianiro, A., Discetti, S. & Schlatter, P. 2017b Revisiting history effects in adverse-pressure-gradient turbulent boundary layers. Flow Turbul. Combust. 99 (3–4), 565587.
Wadcock, A. J.1987 Investigation of low-speed turbulent separated flow around airfoils. NACA CR 177450.
MathJax
MathJax is a JavaScript display engine for mathematics. For more information see http://www.mathjax.org.

JFM classification

Related content

Powered by UNSILO

Effect of adverse pressure gradients on turbulent wing boundary layers

  • Á. Tanarro (a1) (a2), R. Vinuesa (a1) (a2) and P. Schlatter (a1) (a2)

Metrics

Full text views

Total number of HTML views: 0
Total number of PDF views: 0 *
Loading metrics...

Abstract views

Total abstract views: 0 *
Loading metrics...

* Views captured on Cambridge Core between <date>. This data will be updated every 24 hours.

Usage data cannot currently be displayed.