Hostname: page-component-cd9895bd7-dk4vv Total loading time: 0 Render date: 2024-12-19T23:16:48.777Z Has data issue: false hasContentIssue false

Time-resolved topology of turbulent boundary layer separation over the trailing edge of an airfoil

Published online by Cambridge University Press:  18 March 2020

Austin Ma
Affiliation:
Department of Mechanical Engineering, University of Alberta, Edmonton, AlbertaT6G 2R3, Canada
Bradley Gibeau
Affiliation:
Department of Mechanical Engineering, University of Alberta, Edmonton, AlbertaT6G 2R3, Canada
Sina Ghaemi*
Affiliation:
Department of Mechanical Engineering, University of Alberta, Edmonton, AlbertaT6G 2R3, Canada
*
Email address for correspondence: [email protected]

Abstract

The unsteady organization of a separated turbulent boundary layer was investigated upstream from the trailing edge of a NACA 4418 airfoil. The angle of attack was $9^{\circ }$ in the pre-stall regime. Two particle image velocimetry fields of view were of interest: a streamwise–wall-normal plane at midspan of the airfoil and a streamwise–spanwise plane parallel to and near the surface of the airfoil. In the near-surface streamwise–spanwise plane, the mean velocity field revealed a saddle point near midspan and a pair of counter-rotating foci at the sides. This pattern is reminiscent of a stall cell, which has been traditionally associated with flow separation on thick airfoils at and slightly beyond the angle of attack of maximum lift. Isolating the low frequencies showed that the instantaneous separation front consisted of several smaller structures that also resembled a stall cell pattern, but they were an order of magnitude smaller than the one found in the mean pattern. These instantaneous stall cells were of two types: forward and backward. The forward stall cells were formed by strong high-speed streaks from upstream, while backward stall cells formed as a result of strong backflow just downstream from the separation front, resulting in a foci pair and a saddle point on their upstream side. In both cases, the foci pairs acted to mobilize high-speed momentum of the associated streak into a rotational motion, causing these streaks to dissipate. Finally, proper orthogonal decomposition revealed that low-order modes were associated with the movement and distortion of the separation front.

Type
JFM Papers
Copyright
© The Author(s), 2020. Published by Cambridge University Press

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

Abbott, I. H. & Von Doenhoff, A. E. 1959 Theory of Wing Sections, including a Summary of Airfoil Data. Courier Corporation.Google Scholar
Alving, A. E. & Fernholz, H. H. 1996 Turbulence measurements around a mild separation bubble and downstream of reattachment. J. Fluid Mech. 322, 297328.10.1017/S0022112096002807CrossRefGoogle Scholar
Angele, K. P. & Muhammad-Klingmann, B. 2006 PIV measurements in a weakly separating and reattaching turbulent boundary layer. Eur. J. Mech. (B/Fluids) 25 (2), 204222.10.1016/j.euromechflu.2005.05.003CrossRefGoogle Scholar
Broeren, A. P. & Bragg, M. B. 2001 Spanwise variation in the unsteady stalling flowfields of two-dimensional airfoil models. AIAA J. 39 (9), 16411651.10.2514/2.1501CrossRefGoogle Scholar
Coles, D. & Wadcock, A. 1979 Flying-hot-wire study of two-dimensional mean flow past an NACA 4412 airfoil at maximum lift. AIAA J. 17 (4), 321329.10.2514/3.61127CrossRefGoogle Scholar
Délery, J. 2013 Three-Dimensional Separated Flow Topology: Critical Points, Separation Lines and Vortical Structures, pp. 914. John Wiley & Sons.10.1002/9781118578544CrossRefGoogle Scholar
Dell’Orso, H. & Amitay, M. 2018 Parametric investigation of stall cell formation on a NACA 0015 airfoil. AIAA J. 56, 113.10.2514/1.J056850CrossRefGoogle Scholar
Dengel, P. & Fernholz, H. H. 1990 An experimental investigation of an incompressible turbulent boundary layer in the vicinity of separation. J. Fluid Mech. 212, 615636.10.1017/S0022112090002117CrossRefGoogle Scholar
Depardon, S., Lasserre, J. J., Boueilh, J. C., Brizzi, L. E. & Borée, J. 2005 Skin friction pattern analysis using near-wall PIV. Exp. Fluids 39 (5), 805818.10.1007/s00348-005-0014-8CrossRefGoogle Scholar
Duquesne, P., Maciel, Y. & Deschênes, C. 2015 Unsteady flow separation in a turbine diffuser. Exp. Fluids 56 (8), 156.CrossRefGoogle Scholar
Elyasi, M. & Ghaemi, S. 2019 Experimental investigation of coherent structures of a three-dimensional separated turbulent boundary layer. J. Fluid Mech. 859, 132.10.1017/jfm.2018.788CrossRefGoogle Scholar
Ghaemi, S., Ragni, D. & Scarano, F. 2012 PIV-based pressure fluctuations in the turbulent boundary layer. Exp. Fluids 53 (6), 18231840.10.1007/s00348-012-1391-4CrossRefGoogle Scholar
Gibeau, B. & Ghaemi, S. 2020 The mode B structure of streamwise vortices in the wake of a two-dimensional blunt trailing edge. J. Fluid Mech. 884, A12.10.1017/jfm.2019.931CrossRefGoogle Scholar
Gregory, N., Quincey, V. G., O’Reilly, C. L. & Hall, D. J.1971 Progress report on observations of three-dimensional flow patterns obtained during stall development on aerofoils, and on the problem of measuring two-dimensional characteristics. C.P. No. 1146. Aeronautical Research Council.Google Scholar
Heinzel, G., Rüdiger, A. & Schilling, R.2002 Spectrum and spectral density estimation by the discrete Fourier transform (DFT), including a comprehensive list of window functions and some new at-top windows. Tech. Rep. Albert Einstein Institut.Google Scholar
Holm, R. & Gustavsson, J.1999 A PIV study of separated flow around a 2D airfoil at high angles of attack in a low speed wind tunnel. FFA TN, 52.Google Scholar
Jeong, J. & Hussain, F. 1995 On the identification of a vortex. J. Fluid Mech. 285, 6994.10.1017/S0022112095000462CrossRefGoogle Scholar
Jones, L. E., Sandberg, R. D. & Sandham, N. D. 2008 Direct numerical simulations of forced and unforced separation bubbles on an airfoil at incidence. J. Fluid Mech. 602, 175207.10.1017/S0022112008000864CrossRefGoogle Scholar
Liu, T., Woodiga, S. & Ma, T. 2011 Skin friction topology in a region enclosed by penetrable boundary. Exp. Fluids 51 (6), 15491562.10.1007/s00348-011-1171-6CrossRefGoogle Scholar
Lu, F. K. 2010 Surface oil flow visualization. Eur. Phys. J. 182 (1), 5163.Google Scholar
McCullough, G. & Gault, D.1951 Examples of three representative types of airfoil-section stall at low speed. NACA Tech. Note 2502.Google Scholar
Manolesos, M., Papadakis, G. & Voutsinas, S. G. 2014 Experimental and computational analysis of stall cells on rectangular wings. Wind Energy 17 (6), 939955.CrossRefGoogle Scholar
Manolesos, M. & Voutsinas, S. G. 2014a Geometrical characterization of stall cells on rectangular wings. Wind Energy 17 (9), 13011314.Google Scholar
Manolesos, M. & Voutsinas, S. G. 2014b Study of a stall cell using stereo particle image velocimetry. Phys. Fluids 26 (4), 045101.CrossRefGoogle Scholar
Meinhart, C. D., Wereley, S. T. & Santiago, J. G. 2000 A PIV algorithm for estimating time-averaged velocity fields. Trans. ASME J. Fluids Engng 122 (2), 285289.CrossRefGoogle Scholar
Moss, G. F. & Murdin, P. M.1970. Two-dimensional low-speed tunnel tests on the NACA 0012 section including measurements made during pitching oscillations at the stall. C.P. No. 1145. Aeronautical Research Council.Google Scholar
Na, Y. & Moin, P. 1998 Direct numerical simulation of a separated turbulent boundary layer. J. Fluid Mech. 374, 379405.CrossRefGoogle Scholar
Ragni, D. & Ferreira, C. 2016 Effect of 3D stall-cells on the pressure distribution of a laminar NACA64-418 wing. Exp. Fluids 57 (8), 127.CrossRefGoogle Scholar
Scarano, F. & Riethmuller, M. L. 1999 Iterative multigrid approach in PIV image processing with discrete window offset. Exp. Fluids 26 (6), 513523.CrossRefGoogle Scholar
Schlichting, H. & Gersten, K. 2016 Boundary-Layer Theory, vol. 474. Springer.Google Scholar
Sears, W. R. & Telionis, D. P. 1975 Boundary-layer separation in unsteady flow. SIAM J. Appl. Maths 28 (1), 215235.CrossRefGoogle Scholar
Simpson, R. L. 1981 A review of some phenomena in turbulent flow separation. Trans. ASME J. Fluids Engng 103 (4), 520533.CrossRefGoogle Scholar
Simpson, R. L. 1989 Turbulent boundary-layer separation. Annu. Rev. Fluid Mech. 21 (1), 205232.CrossRefGoogle Scholar
Sirovich, L. 1987 Turbulence and the dynamics of coherent structures. Parts I–III. Q. Appl. Maths 45, 561590.CrossRefGoogle Scholar
Song, S. & Eaton, J. 2002 The effects of wall roughness on the separated flow over a smoothly contoured ramp. Exp. Fluids 33 (1), 3846.CrossRefGoogle Scholar
Squire, L. C., Maltby, R. L., Keating, R. F. A. & Stanbrook, A.1962. Flow visualization in wind tunnels using indicators. Part I. The surface oil flow technique. Tech. Rep.: AGARDOGRAPH.Google Scholar
Surana, A., Grunberg, O. & Haller, G. 2006 Exact theory of three-dimensional flow separation. Part 1. Steady separation. J. Fluid Mech. 564, 57103.CrossRefGoogle Scholar
Thompson, B. E. & Whitelaw, J. H. 1985 Characteristics of a trailing-edge flow with turbulent boundary-layer separation. J. Fluid Mech. 157, 305326.CrossRefGoogle Scholar
Tobak, M. & Peake, D. J. 1982 Topology of three-dimensional separated flows. Annu. Rev. Fluid Mech. 14 (1), 6185.CrossRefGoogle Scholar
Wadcock, A. J.1987 Investigation of low-speed turbulent separated flow around airfoils. NASA Contractor Rep. 177450.Google Scholar
Weihs, D. & Katz, J. 1983 Cellular patterns in poststall flow over unswept wings. AIAA J. 21 (12), 17571759.CrossRefGoogle Scholar
Westerweel, J. & Scarano, F. 2005 Universal outlier detection for PIV data. Exp. Fluids 39 (6), 10961100.CrossRefGoogle Scholar
Winkelman, A. E. & Barlow, J. B. 1980 Flowfield model for a rectangular planform wing beyond stall. AIAA J. 18 (8), 10061008.CrossRefGoogle Scholar
Yon, S. A. & Katz, J. 1998 Study of the unsteady flow features on a stalled wing. AIAA J. 36 (3), 305312.10.2514/2.372CrossRefGoogle Scholar
Zaman, K. B. M. Q., Mckinzie, D. J. & Rumsey, C. L. 1989 A natural low-frequency oscillation of the flow over an airfoil near stalling conditions. J. Fluid Mech. 202, 403442.CrossRefGoogle Scholar

Ma et al. supplementary movie 1

Time-resolved animation of the skin-friction lines over 1.5 s. The flow is slowed down by a factor of 12 in the video and the background contours shows the instantaneous streamwise velocity.

Download Ma et al. supplementary movie 1(Video)
Video 24.2 MB

Ma et al. supplementary movie 2

A video of the formation of a forward stall cell due to local concentration of downstream momentum. The colors in the background correspond to instantaneous streamwise velocity.

Download Ma et al. supplementary movie 2(Video)
Video 4.3 MB

Ma et al. supplementary movie 3

A video of the formation of a backward stall cell due to a strong backflow. The colors in the background correspond to instantaneous streamwise velocity.

Download Ma et al. supplementary movie 3(Video)
Video 6.7 MB