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Large-scale coherent structures in compressible turbulent boundary layers

Published online by Cambridge University Press:  22 January 2021

Matthew Bross Open the ORCID record for Matthew Bross [Opens in a new window] ,
Sven Scharnowski  and
Christian J. Kähler
Matthew Bross*
Affiliation:
Institute of Fluid Mechanics and Aerodynamics, Universität der Bundeswehr München, 85577Neubiberg, Germany
Sven Scharnowski
Affiliation:
Institute of Fluid Mechanics and Aerodynamics, Universität der Bundeswehr München, 85577Neubiberg, Germany
Christian J. Kähler
Affiliation:
Institute of Fluid Mechanics and Aerodynamics, Universität der Bundeswehr München, 85577Neubiberg, Germany
*
†Email address for correspondence: matthew.bross@unibw.de
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Abstract

The presence of large-scale coherent structures in various wall bounded turbulent flows, often called superstructures in turbulent boundary layers (TBLs), has been of great interest in recent years. These meandering high- and low-momentum structures can extend up to several boundary layer thicknesses in the streamwise direction and contain a relatively large portion of the layer's turbulent kinetic energy. Therefore, studying these features is important for understanding the overall dynamics of turbulent boundary layers and for the development of flow control strategies or near-wall flow modifications. However, compared to the extensive number of incompressible investigations, much less is known about the structural characteristics for compressible turbulent boundary layer flows. Therefore, in this investigation turbulent boundary layers developing on a flat plate with zero pressure gradient (ZPG) over a range of Reynolds numbers and Mach numbers are considered in order to examine the effect of compressibility on superstructures. More specifically, measurements are performed on a flat plate model in the Trisonic Wind Tunnel Munich (TWM) for the Mach number range $0.3 \leq Ma \leq 3.0$ and a friction Reynolds number range of $4700 \leq Re_{\tau } \leq 29\,700$ or $11\,730 \leq Re_{\delta _2} = \rho _e u_e \theta ^*/\mu _{w} \leq 74\,800$. Velocity fields are recorded using planar particle image velocimetry methods (PIV and stereo-PIV) in three perpendicular planes. Using multi-point correlation and spectral analysis methods it was found that the most energetic frequencies have slightly longer streamwise wavelengths for the supersonic case when compared to the subsonic case. Furthermore, a distinct increase in the spanwise spacing of the superstructures was found for the supersonic cases when compared to the subsonic and transonic turbulent boundary layers.

JFM classification

Compressible Flows: Compressible boundary layers Turbulent Flows: Turbulent boundary layers Boundary Layers: Boundary layer structure
Type
JFM Papers
Information
Journal of Fluid Mechanics , Volume 911 , 25 March 2021 , A2
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Copyright
© The Author(s), 2021. Published by Cambridge University Press

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References

REFERENCES

Adrian, R.J., Meinhart, C.D. & Tomkins, C.D. 2000 Vortex organization in the outer region of the turbulent boundary layer. J.Fluid Mech. 422, 1–54.CrossRefGoogle Scholar
Ames Research Staff 1953 Equations, tables and charts for compressible flow. Tech. Rep. 1135. NASA Tech. Report.Google Scholar
Baars, W.J., Hutchins, N. & Marusic, I. 2017 Reynolds number trend of hierarchies and scale interactions in turbulent boundary layers. Phil. Trans. R. Soc. A 375 (2089), 1–18.Google ScholarPubMed
Baidya, R., Scharnowski, S., Bross, M. & Kähler, C.J. 2020 Interactions between a shock and turbulent features in a Mach 2 compressible boundary layer. J.Fluid Mech. 893, A15.CrossRefGoogle Scholar
Balakumar, B.J. & Adrian, R.J. 2007 Large- and very-large-scale motions in channel and boundary-layer flows. Phil. Trans. R. Soc. A 365 (1852), 665–681.Google ScholarPubMed
Beresh, S.J., Clemens, N.T. & Dolling, D.S. 2002 Relationship between upstream turbulent boundary-layer velocity fluctuations and separation shock unsteadiness. AIAA J. 40 (12), 2412–2422.CrossRefGoogle Scholar
Bradshaw, P. 1977 Compressible turbulent shear layers. Annu. Rev. Fluid Mech. 9 (1), 33–52.CrossRefGoogle Scholar
Bross, M., Fuchs, T. & Kähler, C.J. 2019 Interaction of coherent flow structures in adverse pressure gradient turbulent boundary layers. J.Fluid Mech. 873, 287–321.CrossRefGoogle Scholar
Bross, M., Scharnowski, S. & Kähler, C.J. 2018 Influence of leading edge tripping devices on supersonic turbulent boundary layer characteristics. In 5th International Conference on Experimental Fluid Mechanics, July 2–4, Munich, Germany.Google Scholar
Buchmann, N.A., Cierpka, C., Knopp, T., Schanz, D., Schröder, A., Hain, R. & Kähler, C.J. 2014 Large Scale Adverse Pressure Gradient Turbulent Boundary Layer Investigation by means of PIV and PTV. In 17th International Symposium on the Applications of Laser and Imaging Techniques to Fluid Mechanics, July 7–10, Lisbon, Portugal.Google Scholar
Buchmann, N.A., Kücükosman, Y.C., Ehrenfried, K. & Kähler, C.J. 2016 Wall pressure signature in compressible turbulent boundary layers. In Progress in Wall Turbulence 2 (ed. M. Stanislas, J. Jimenez & I. Marusic), pp. 93–102. Springer International Publishing.Google Scholar
Coles, D. 1956 The law of the wake in the turbulent boundary layer. J.Fluid Mech. 1 (2), 191–226.CrossRefGoogle Scholar
Elsinga, G.E., Adrian, R.J., van Oudheusden, B.W. & Scarano, F. 2010 Three-dimensional vortex organization in a high-Reynolds-number supersonic turbulent boundary layer. J.Fluid Mech. 644, 35–60.Google Scholar
Elsinga, G.E. & Westerweel, J. 2012 Tomographic-PIV measurement of the flow around a zigzag boundary layer trip. Exp. Fluids 52 (4), 865–876.CrossRefGoogle Scholar
Fernholz, H.H. & Finley, P.J. 1980 A critical commentary on mean flow data for two-dimensional compressible turbulent boundary layers. In AGARDograph 253.Google Scholar
Fernholz, H.H. & Finley, P.J. 1996 The incompressible zero-pressure-gradient turbulent boundary layer: an assessment of the data. Prog. Aerosp. Sci. 32 (4), 245–311.CrossRefGoogle Scholar
Ganapathisubramani, B., Clemens, N.T. & Dolling, D.S. 2006 Large-scale motions in a supersonic turbulent boundary layer. J.Fluid Mech. 556, 271–282.CrossRefGoogle Scholar
Ganapathisubramani, B., Clemens, N.T. & Dolling, D.S. 2007 Effects of upstream boundary layer on the unsteadiness of shock-induced separation. J.Fluid Mech. 585, 369–394.CrossRefGoogle Scholar
Ganapathisubramani, B., Hutchins, N., Hambleton, W.T., Longmire, E.K. & Marusic, I. 2005 Investigation of large-scale coherence in a turbulent boundary layer using two-point correlations. J.Fluid Mech. 524, 57–80.Google Scholar
Ganapathisubramani, B., Hutchins, N., Monty, J.P., Chung, D. & Marusic, I. 2012 Amplitude and frequency modulation in wall turbulence. J.Fluid Mech. 712, 61–91.Google Scholar
Hain, R., Kähler, C.J. & Radespiel, R. 2009 Dynamics of laminar separation bubbles at low-Reynolds-number aerofoils. J.Fluid Mech. 630, 129–153.CrossRefGoogle Scholar
Hopkins, E.J. & Inouye, M. 1971 An evaluation of theories for predicting turbulent skin friction and heat transfer on flat plates at supersonic and hypersonic mach. AIAA J. 9, 993–1003.Google Scholar
Hutchins, N. 2012 Caution: tripping hazards. J.Fluid Mech. 710, 1–4.CrossRefGoogle Scholar
Hutchins, N. & Marusic, I. 2007 a Evidence of very long meandering features in the logarithmic region of turbulent boundary layers. J.Fluid Mech. 579, 1–29.CrossRefGoogle Scholar
Hutchins, N. & Marusic, I. 2007 b Large-scale influences in near-wall turbulence. Phil. Trans. R. Soc. A 365, 647–664.CrossRefGoogle ScholarPubMed
Hutchins, N., Monty, J.P., Ganapathisubramani, B., Ng, H.C.H. & Marusic, I. 2011 Three-dimensional conditional structure of a high-Reynolds-number turbulent boundary layer. J.Fluid Mech. 673, 255–285.CrossRefGoogle Scholar
Kähler, C.J., Sammler, B. & Kompenhans, J. 2002 Generation and control of tracer particles for optical flow investigations in air. Exp. Fluids 33, 736–742.CrossRefGoogle Scholar
von Kármán, T. 1934 Turbulence and skin friction. J.Aero. Sci. 1, 1–20.CrossRefGoogle Scholar
Kevin, K., Monty, J. & Hutchins, N. 2019 The meandering behaviour of large-scale structures in turbulent boundary layers. J.Fluid Mech. 865, R1.CrossRefGoogle Scholar
Kline, S.J., Reynolds, W.C., Schraub, F.A. & Runstadler, P.W. 1967 The structure of turbulent boundary layers. J.Fluid Mech. 30, 741–773.CrossRefGoogle Scholar
Kokmanian, K., Scharnowski, S., Bross, M., Duvvuri, S., Fu, M.K., Kähler, C.J. & Hultmark, M. 2019 Development of a nanoscale hot-wire probe for supersonic flow applications. Exp. Fluids 60 (10), 150.CrossRefGoogle Scholar
Kovasznay, L.S.G. 1953 Turbulence in supersonic flow. J.Aero. Sci. 20 (10), 657–674.CrossRefGoogle Scholar
Kovasznay, L.S.G., Kibens, V. & Blackwelder, R.F. 1970 Large-scale motion in the intermittent region of a turbulent boundary layer. J.Fluid Mech. 41 (2), 283–325.CrossRefGoogle Scholar
Laskari, A., de Kat, R., Hearst, R.J. & Ganapathisubramani, B. 2018 Time evolution of uniform momentum zones in a turbulent boundary layer. J.Fluid Mech. 842, 554–590.CrossRefGoogle Scholar
Marusic, I., Chauhan, K.A., Kulandaivelu, V. & Hutchins, N. 2015 Evolution of zero-pressure-gradient boundary layers from different tripping conditions. J.Fluid Mech. 783, 379–411.CrossRefGoogle Scholar
Marusic, I. & Heuer, W.D.C. 2007 Reynolds number invariance of the structure inclination angle in wall turbulence. Phys. Rev. Lett. 99, 114504.CrossRefGoogle ScholarPubMed
Meinhart, C.D. & Adrian, R.J. 1995 On the existence of uniform momentum zones in a turbulent boundary layer. Phys. Fluids 7, 694–696.CrossRefGoogle Scholar
Monty, J.P., Hutchins, N., NG, H.C.H., Marusic, I. & Chong, M.S. 2009 A comparison of turbulent pipe, channel and boundary layer flows. J.Fluid Mech. 632, 431–442.CrossRefGoogle Scholar
Morkovin, M.V. 1962 Effects of compressibility on turbulent flows. In Mecanique de la Turbulence (ed. A. Favre). CNRS.Google Scholar
Pirozzoli, S. & Bernardini, M. 2011 Turbulence in supersonic boundary layers at moderate Reynolds number. J.Fluid Mech. 688, 120–168.CrossRefGoogle Scholar
Raffel, M., Willert, C., Scarano, F., Kähler, C.J., Wereley, S.T. & Kompenhans, J. 2018 Particle Image Velocimetry: A Practical Guide. Springer.CrossRefGoogle Scholar
Ragni, D., Schrijer, F., van Oudheusden, B.W. & Scarano, F. 2011 Particle tracer response across shocks measured by PIV. Exp. Fluids 50 (1), 53–64.CrossRefGoogle Scholar
Reuther, N. & Kähler, C.J. 2018 Evaluation of large-scale turbulent/non-turbulent interface detection methods for wall-bounded flows. Exp. Fluids 59, 121.CrossRefGoogle Scholar
Ringuette, M.J., Wu, M. & Martín, M.P. 2008 Coherent structures in direct numerical simulation of turbulent boundary layers at Mach 3. J.Fluid Mech. 594, 59–69.CrossRefGoogle Scholar
Samie, M., Marusic, I., Hutchins, N., Fu, M.K., Fan, Y., Hultmark, M. & Smits, A.J. 2018 Fully resolved measurements of turbulent boundary layer flows up to $Re_{\tau }=20\,000$. J.Fluid Mech. 851, 391–415.CrossRefGoogle Scholar
Sanmiguel Vila, C., Vinuesa, R., Discetti, S., Ianiro, A., Schlatter, P. & Örlü, R. 2017 On the identification of well-behaved turbulent boundary layers. J.Fluid Mech. 822, 109–138.CrossRefGoogle Scholar
Scharnowski, S., Bross, M. & Kähler, C.J. 2019 Accurate turbulence level estimations using PIV/PTV. Exp. Fluids 60 (1), 1.CrossRefGoogle Scholar
Schoenherr, K.E. 1932 Resistance of flat surfaces moving through a fluid. S. Nav. Arch. Mar. Engng 40, 273–313.Google Scholar
Sciacchitano, A. 2019 Uncertainty quantification in particle image velocimetry. Meas. Sci. Technol. 30 (9), 092001.CrossRefGoogle Scholar
Sillero, J.A., Jiménez, J. & Moser, R.D. 2013 One-point statistics for turbulent wall-bounded flows at Reynolds numbers up to $\delta ^+ \approx 2000$. Phys. Fluids 25 (10), 105102.CrossRefGoogle Scholar
de Silva, C.M., Hutchins, N. & Marusic, I. 2016 Uniform momentum zones in turbulent boundary layers. J.Fluid Mech. 786, 309–331.CrossRefGoogle Scholar
de Silva, C.M., Kevin, K., Baidya, R., Hutchins, N. & Marusic, I. 2018 Large coherence of spanwise velocity in turbulent boundary layers. J.Fluid Mech. 847, 161–185.CrossRefGoogle Scholar
de Silva, C.M., Philip, J., Hutchins, N. & Marusic, I. 2017 Interfaces of uniform momentum zones in turbulent boundary layers. J.Fluid Mech. 820, 451–478.CrossRefGoogle Scholar
Smith, M.W. & Smits, A.J. 1995 Visualization of the structure of supersonic turbulent boundary layers. Exp. Fluids 18 (4), 288–302.CrossRefGoogle Scholar
Smits, A.J. & Dussauge, J.P. 2006 Turbulent Shear Layers in Supersonic Flow. Springer.Google Scholar
Smits, A.J., Matheson, N. & Joubert, P.N. 1983 Low-Reynolds-number turbulent boundary layers in zero and favorable pressure gradients. J.Ship Res. 27 (3), 147–157.CrossRefGoogle Scholar
Smits, A.J., Spina, E.F., Alving, A.E., Smith, R.W., Fernando, E.M. & Donovan, J.F. 1989 A comparison of the turbulence structure of subsonic and supersonic boundary layers. Phys. Fluids A 1 (11), 1865–1875.CrossRefGoogle Scholar
Spina, E.F., Donovan, J.F. & Smits, A.J. 1991 On the structure of high-Reynolds-number supersonic turbulent boundary layers. J.Fluid Mech. 222, 293–327.CrossRefGoogle Scholar
Sutherland, W. 1883 The viscosity of gases and molecular force. Phil. Mag. Ser. 5 36 (223), 507–531.CrossRefGoogle Scholar
Taylor, G.I. 1938 The spectrum of turbulence. Proc. R. Soc. A 164 (919), 476–490.CrossRefGoogle Scholar
Van Driest, E.R. 1951 Turbulent boundary layer in compressible fluids. J.Aero. Sci. 18, 145–160.CrossRefGoogle Scholar
Van Driest, E.R. 1956 On turbulent flow near a wall. J.Aero. Sci. 23, 1007–1011.CrossRefGoogle Scholar
Wallace, J.M. 2012 Highlights from 50 years of turbulent boundary layer research. J.Turbul. 13, 1–70.CrossRefGoogle Scholar
Walz, A. 1966 Strömungs- und Temperaturgrenzschichten. Braun Verlag, Karlsruhe, English translation Boundary Layers of Flow and Temperature, MIT Press, 1969.Google Scholar
Welch, P.D. 1967 The use of fast fourier transform for the estimation of power spectra: a method based on time averaging over short, modified periodograms. IEEE Trans. Audio Electroacoust. 15 (2), 70–73.CrossRefGoogle Scholar
Wenzel, C., Selent, B., Kloker, M. & Rist, U. 2018 DNS of compressible turbulent boundary layers and assessment of data/scaling-law quality. J.Fluid Mech. 842, 428–468.CrossRefGoogle Scholar
Williams, O.J.H., Sahoo, D., Baumgartner, M.L. & Smits, A.J. 2018 Experiments on the structure and scaling of hypersonic turbulent boundary layers. J.Fluid Mech. 834, 237–270.CrossRefGoogle Scholar