Abstract
The influence of post-stall angles of attack, \(\alpha\), on the turbulent flow characteristics behind a thin high aspect ratio flat plate was investigated experimentally. Time-resolved stereo particle image velocimetry was used in an open-section wind tunnel at a Reynolds number of 6600. The mean field was determined along with the wake topology, force coefficients, vortex shedding frequency, and the terms in the transport equation for the turbulent kinetic energy k. Coherent and incoherent contributions to the Reynolds stress and k-transport terms were estimated. Over the measured range of \(20^\circ \le \alpha \le 90^\circ\), quasi-periodic vortex shedding is observed and it is shown that most of the fluctuation energy contribution in the wake arises from coherent fluctuations associated with vortex shedding. As the angle of attack is reduced from \(90^\circ\), the length of the recirculation region and the drag decrease, while the shedding frequency increases monotonically. In contrast, mean lift and k are maximized at \(\alpha \approx 40^\circ\), suggesting a relationship between the bound vortex circulation and the levels of k. Structural differences in the mean strain field, wake topology, relative contributions to the k-production terms, and significant differences in the incoherent field suggest changes in the wake dynamics for \(\alpha > 40^{\circ }\) and \(20^{\circ } \le \alpha \le 40^{\circ }\). For \(\alpha > 40^\circ\), coherent contributions to the fluctuation field result in a large region close to the plate exhibiting small levels of negative mean production and generally low levels of advection, despite very high levels of production just downstream of the recirculation region.
Similar content being viewed by others
References
Abernathy FH (1962) Flow over an inclined plate. J Basic Eng 84(3):380–388
Antonia RA, Rajagopalan S (1990) Determination of drag of a circular cylinder. AIAA J 28(10):1833–1834
Arroyo MP, Greated CA (1991) Stereoscopic particle image velocimetry. Meas Sci Technol 2(12):1181
Barlow JB, Rae WH, Pope A (1999) Low-speed wind tunnel testing, 3rd edn. Wiley, New York
Bearman PW, Trueman DM (1972) An investigation of flow around rectangular cylinders. Aeronaut Quart 23(03):229–237
Bourgeois JA, Noack BR, Martinuzzi RJ (2013) Generalized phase average with applications to sensor-based flow estimation of the wall-mounted square cylinder wake. J Fluid Mech 736:316–350
Breuer M, Jovicic N (2001) Separated flow around a flat plate at high incidence: an LES investigation. J Turbul 2(18):1–15
Bruining A (1979u) Aerodynamic characteristics of a curved plate airfoil section at Reynolds numbers 60000 and 100000 and angles of attack from \(-\)10 to +90 degrees. Tech. rep., Delft University of Technology, Report LR-281
Chen JM, Fang YC (1996) Strouhal numbers of inclined flat plates. J Wind Eng Indus Aerodyn 61(2):99–112
Davies ME (1976) A comparison of the wake structure of a stationary and oscillating bluff body, using a conditional averaging technique. J Fluid Mech 75(2):209–231
du Plessix P (2015) Low-order representations in the turbulent wake of a normal flat plate. Master’s thesis, University of Calgary
Fage A, Johansen FC (1927) On the flow of air behind an inclined flat plate of infinite span. Proc Royal Soc Lond Ser A 116:170–197
Fage A, Johansen FC (1928) The structure of vortex sheets. Lond Edinb Dublin Philos Mag J Sci 5(28):417–441
Holmes P, Lumley JL, Berkooz G, Rowley CW (2012) Turbulence, coherent structures, dynamical systems and symmetry, 2nd edn. Cambridge University Press, Cambridge
Hornung H, Perry AE (1984) Some aspects of three-dimensional separation. i-streamsurface bifurcations. Zeitschrift fur Flugwissenschaften und Weltraumforschung 8:77–87
Hosseini Z, Martinuzzi RJ, Noack BR (2016) Modal energy analysis of a highly modulated wake behind a wall-mounted pyramid. J Fluid Mech 798:171–750
Hussain AKMF (1983) Coherent structures—reality and myth. Phys Fluids 25(10):2816–2850
Hussain AKMF, Reynolds WC (1970) The mechanics of an organized wave in turbulent shear flow. J Fluid Mech 41(2):241–258
Knisely CW (1990) Strouhal numbers of rectangular cylinders at incidence: a review and new data. J Fluids Struct 4(4):371–393
Kogaki T, Matsumiya H, Iida M, Inaba T, Yoshimizu N, Kieda K (2002) Development and experimental verification of an airfoil for small wind turbines. Proceedings of 2002 global windpower conference and exhibition
Kuwahara K (1973) Numerical study of flow past an inclined flat plate by an inviscid model. J Phys Soc Japan 35(5):1545–1551
Lam KM (1996) Phase locked eduction of vortex shedding in flow past an inclined flat plate. Phys Fluids 8(5):1159–1168
Lam KM, Leung MYH (2005) Asymmetric vortex shedding flow past an inclined flat plate at high incidence. Eur J Mech B Fluids 24(1):33–48
Leder A (1991) Dynamics of fluid mixing in separated flows. Phys Fluids A Fluid Dyn (1989–1993) 3:1741–1748
Mimura Y (1958) The flow with wake past an oblique plate. J Phys Soc Japan 13(9):1048–1055
Najjar FM, Balachandar S (1998) Low-frequency unsteadiness in the wake of a normal flat plate. J Fluid Mech 370:101–147
Najjar FM, Vanka SP (1995) Simulations of the unsteady separated flow past a normal flat plate. Int J Numer Methods Fluids 21(7):525–547
Narasimhamurthy VD, Andersson HI (2009) Numerical simulation of the turbulent wake behind a normal flat plate. Int J Heat Fluid Flow 30(6):1037–1043
Noack BR, Afanasiev K, Morzynski M, Tadmor G, Thiele F (2003) A hierarchy of low-dimensional models for the transient and post-transient cylinder wake. J Fluid Mech 497:335–363
Norberg C (1993) Flow around rectangular cylinders: pressure forces and wake frequencies. J Wind Eng Indus Aerodyn 49(1–3):187–196
Novak J (1973) Strouhal number and flat plate oscillation in an air stream. Acta Technica Csav 18(4):372–386
Ota T, Okamoto Y, Yoshikawa H (1994) A correction formula for wall effects on unsteady forces of two-dimensional bluff bodies. J Fluid Eng 116:414–418
Perry AE, Steiner TR (1987) Large-scale vortex structures in turbulent wakes behind bluff bodies. Part 1. Vortex formation processes. J Fluid Mech 174:233–270
Prasad AK (2000) Steresocopic particle image velocimetry. Exp Fluids 29(2):103–116
Prasad AK, Adrian RJ (1993) Stereoscopic particle image velocimetry applied to liquid flows. Exp Fluids 15(1):49–60
Raffel M, Willert C, Wereley S, Kompenhans J (2013) Particle image velocimetry: a practical guide. Springer, Berlin
Roshko A (1954) A new hodograph for free-streamline theory. National Advisory Committee for Aeronautics Technical Note 3168
Roshko A (1955) On the wake and drag of bluff bodies. J Aeronaut Sci (Institute of the Aeronautical Sciences) 22(2):124–132
Sarpkaya T (1975) An inviscid model of two-dimensional vortex shedding for transient and asymptotically steady separated flow over an inclined plate. J Fluid Mech 68(01):109–128
Sinha SK, Kuhlman PS (1992) Investigating the use of stereoscopic particle streak velocimetry for estimating the three-dimensional vorticity field. Exp Fluids 12(6):377–384
Sirovich L (1987) Turbulence and the dynamics of coherent structures, parts i–iii. Quart Appl Math XLV(3):561–582
Soloff SM, Adrian RJ, Liu ZC (1997) Distortion compensation for generalized stereoscopic particle image velocimetry. Meas Sci Technol 8(12):1441
Thom A (1943) Blockage corrections in a closed high-speed tunnel. HM Stationery Office
Timmer WA (2010) Aerodynamic characteristics of wind turbine blade airfoils at high angles-of-attack. In: 3rd EWEA Conference-Torque 2010: The Science of making Torque from Wind, Heraklion, Crete, Greece
Vickery BJ (1966) Fluctuating lift and drag on a long cylinder of square cross-section in a smooth and in a turbulent stream. J Fluid Mech 25(03):481–494
Weygandt JA, Mehta RD (1992) Three-dimensional structure of straight and curved plane wakes. J Fluid Mech 282:279–311
Wheeler AJ, Ganji AR (2009) Introduction to engineering experimentation, 3rd edn. Prentice Hall, Upper Saddle River
Williamson CHK, Roshko A (1990) Measurements of base pressure in the wake of a cylinder at low reynolds numbers. Zeitschrift fur Flugwissenschaften und Weltraumforschung 14:38–46
Wu TY (1962) A wake model for free-streamline flow theory. J Fluid Mech 13:161
Zhou Y, d Mahbub Alam M, Yang HX, Guo H, Wood DH (2011) Fluid force on a very low Reynolds number airfoil and their prediction. Int J Heat 32:329–339
Acknowledgements
This work is supported by NSERC Discovery Grants to R. J. Martinuzzi and D. H. Wood.
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
About this article
Cite this article
Mohebi, M., Wood, D.H. & Martinuzzi, R.J. The turbulence structure of the wake of a thin flat plate at post-stall angles of attack. Exp Fluids 58, 67 (2017). https://doi.org/10.1007/s00348-017-2352-8
Received:
Revised:
Accepted:
Published:
DOI: https://doi.org/10.1007/s00348-017-2352-8