Abstract
Turbulent energy dissipation in the turbulent boundary layer has been estimated experimentally. Dissipation has been derived from dynamics of two-component instantaneous velocity vector fields measured by an optical method. Smoke Image Velocimetry technique based on digital processing of smoke visualization of flow and adapted to relatively large smoke displacement between two consecutive video frames has been employed. The obtained dissipation profiles have been compared with measurements by multi-sensor hot-wire anemometers, stereo PIV, Tomo-3D-PTV with VIC+, and DNS results.
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Abbreviations
- I :
-
Pixel intensity
- k :
-
Frame number
- L :
-
Distance between the channel inlet and the measurement area (m)
- N x :
-
Interrogation window length (pixel)
- N y :
-
Interrogation window height (pixel)
- S ii :
-
Strain-rate tensor components
- U :
-
Velocity (m/s)
- U ∞ :
-
Free-stream velocity (m/s)
- U 99 :
-
0.99 U ∞
- \( \bar{U}_{99} \) :
-
Average velocity in the boundary layer (m/s)
- u′ :
-
Fluctuating component of velocity vector (m/s)
- u τ :
-
Dynamic velocity (m/s)
- Δi :
-
Window displacement along x coordinate
- Δj :
-
Window displacement along y coordinate
- Δx :
-
Distance between the points at which U is measured (m)
- δ :
-
Boundary layer thickness at 0.99 U ∞ (m)
- δ x :
-
Distance between the points at which U is measured allowing for the approximation scheme (m)
- ε :
-
Turbulent energy dissipation
- θ :
-
Momentum thickness (m)
- λ K :
-
Kolmogorov length scale (m)
- υ :
-
Kinematic viscosity coefficient (m2/s)
- Φ :
-
Functional of window similarity
- Re :
-
Reynolds number based on 2δ and \( \bar{U}_{99} \)
- Re τ :
-
Reynolds number based on δ and u τ
- Re θ :
-
Reynolds number based on θ and U θ
References
Adrian RJ, Westerweel J (2011) Particle image velocimetry. Cambridge University Press, Cambridge
Atkinson C, Coudert S, Foucaut JM, Stanislas M, Soria J (2011) The accuracy of tomographic particle image velocimetry for measurements of a turbulent boundary layer. Exp Fluids 50:1031. doi:10.1007/s00348-010-1004-z
Baldi S, Yianneskis M (2003) On the direct measurement of turbulence energy dissipation in stirred vessels with PIV. Ind Eng Chem Res 42(26):7006–7016. doi:10.1021/ie0208265
Balint JL, Wallace JM, Vukolavcevic P (1991) The velocity and vorticity vector fields of a turbulent boundary layer. Part 2. Statistical properties. J Fluid Mech 228:53–86. doi:10.1017/S002211209100263X
Belov IA, Isaev SA (2001) Simulation of turbulent flows: Textbook. Baltiyskiy Gosudarstvenniy Tekhnicheskiy Universitet, S.Petersburg (in Russian)
Bizjan B, Orbanic A, Sirok B, Bajcar T, Novak L, Kovac B (2014) Flow image velocimetry method based on advection-diffusion equation. Strojniski vestnik J Mech Eng 60(7–8):483–494. doi:10.5545/sv-jme.2013.1614
Buxton O R H (2011) Fine scale features of turbulent shear flows. PhD thesis, Imperial College, Prince Consort Road, London, United Kingdom
Charonko J, Prestridge K (2016) Error and uncertainty for dissipation estimates using particle image velocimetry. 18th International Symposium on the Application of Laser and Imaging Techniques to Fluid Mechanics, 04–10 July 2016, Lisbon, Portugal (ISBN 978-989-98777-8-8)
Elsinga GE, Scarano F, Wieneke B, van Oudheusden BW (2006) Tomographic particle image velocimetry. Exp Fluids 41(6):933–947. doi:10.1007/s00348-006-0212-z
Elsinga GE, Westerweel J, Scarano F, Novara M (2011) On the velocity of ghost particles and the bias errors in Tomographic-PIV. Exp Fluids 50:825–838. doi:10.1007/s00348-010-0930-0
Etebari A, Vlachos P (2005) Improvements on the accuracy of derivative estimation from DPIV velocity measurements. Exp Fluids 39:1040–1050. doi:10.1007/s00348-005-0037-1
Foucaut JM, Carlier J, Stanislas M (2004) PIV optimization for the study of turbulent flow using spectral analysis. Meas Sci Technol 15:1046. doi:10.1088/0957-0233/15/6/003
Foucaut JM, Cuvier C, Stanislas M, George WK (2016) Quantification of the full dissipation tensor from an L-shaped SPIV experiment in the near wall region. Progress in wall turbulence 2. Ercoftac series 23. Springer International Publishing, Switzerland. doi:10.1007/978-3-319-20388-1_38
George WK, Hussein HJ (1991) Locally axisymmetric turbulence. J Fluid Mech 233:1–23. doi:10.1017/S0022112091000368
Hearst RJ, Buxton ORH, Ganapathisubramani B, Lavoie P (2012) Experimental estimation of fluctuating velocity and scalar gradients in turbulence. Exp Fluids 53:925–942. doi:10.1007/s00348-012-1318-0
Hinze JO (1975) Turbulence, 2nd edn. McGraw-Hill, New York
Honkan A, Andreopoulos Y (1997) Vorticity, strain-rate and dissipation characteristics in the near-wall region of turbulent boundary layers. J Fluid Mech 350:29–96. doi:10.1017/S0022112097006770
Huser A, Biringen S (1993) Direct numerical simulation of turbulent flow in a square duct. Fluid Mech. 257:65–95. doi:10.2514/6.1993-198
Kähler CJ, Scharnowski S, Cierpka C (2012) On the uncertainty of digital PIV and PTV near walls. Exp Fluids 52(6):1641–1656. doi:10.1007/s00348-012-1307-3
Klebanoff PS (1955) Characteristics of turbulence in a boundary layer with zero pressure gradient. Rep. 1247, Natl. Adv. Comm. For Aeronaut. Washington, D.C
Lavoie P, Djenidi L, Antonia RA (2007a) Effects of initial conditions in decaying turbulence generated by passive grids. J Fluid Mech 585:395–420. doi:10.1017/S0022112007006763
Lavoie P, Avallone G, De Gregorio F, Romano GP, Antonia RA (2007b) Spatial resolution of PIV for the measurement of turbulence. Exp Fluids 43(1):39–51. doi:10.1007/s00348-007-0319-x
Maas HG, Gruen A, Papantoniou D (1993) Particle tracking velocimetry in three-dimensional flows. Exp Fluids 15(2):133–146. doi:10.1007/BF00190953
Martinuzzi RJ, Hussein HJ (1995) Measurement of the turbulence dissipation rate in the wake of a bluff body. In: Symposium on Turbulent Shear Flows, 10th, Pennsylvania State Univ, University Park, pp 13–18
Mikheev NI, Dushin NS (2016) A method for measuring the dynamics of velocity vector fields in a turbulent flow using smoke image-visualization vide. Instr Exp Tech 59(6):880–887. doi:10.1134/S0020441216060063
Novara M, Scarano F (2013) A particle-tracking approach for accurate material derivative measurements with tomographic PIV. Exp Fluids 54:1–12. doi:10.1007/s00348-013-1584-5
Racina A, Kind M (2006) Specific power input and local micromixing times in turbulent Taylor-Couette flow. Exp Fluids 41(3):513–522. doi:10.1007/s00348-006-0178-x
Raffel M, Willert CE, Kompenhans J (1998) Particle Image Velocimetry: a practical guide. Springer, Berlin Heidelberg New York
Roach PE, Brierley DH (1989) The influence of a turbulent freestream on zero pressure gradient transitional boundary layer development including the condition test cases T3A and T3B. In: Pironneau O et al (eds) Numerical simulation of unsteady flows and transition to turbulence. Cambridge University Press, Cambridge
Saarenrinne P, Piirto M (2000) Turbulent kinetic energy dissipation rate estimation from PIV velocity vector fields. Exp Fluids 29:300–307. doi:10.1007/s003480070032
Schanz D, Gesemann S, Schröder A (2016) Shake-The-Box: Lagrangian particle tracking at high particle image densities. Exp Fluids 57:70. doi:10.1007/s00348-016-2157-1
Schlatter P, Örlü R (2010) Assessment of direct numerical simulation data of turbulent boundary layers. J Fluid Mech 659:116–126. doi:10.1017/S0022112010003113
Schlatter P, Örlü R, Li Q, Brethouwer G, Fransson JHM, Johansson AV, Alfredsson PH, Henningson DS (2009) Turbulent boundary layers up to Re- = 2500 studied through simulation and experiment. Phys Fluids 21(5):051702. doi:10.1063/1.3139294
Schneiders JFG, Scarano F, Elsinga G (2016) On the Resolved Scales in a Turbulent Boundary Layer by Tomographic PIV and PTV aided by VIC+. In: 18th International Symposium on the Application of Laser and Imaging Techniques to Fluid Mechanics, 04–10 July 2016, Lisbon, Portugal (ISBN 978-989-98777-8-8)
Schröder A, Schanz D, Geisler R, Gesemann S (2016) Investigations of coherent structures in near-wall turbulence and large wall-shear stress events using Shake-The-Box. In: 18th International Symposium on the Application of Laser and Imaging Techniques to Fluid Mechanics, 04–10 July 2016, Lisbon, Portugal (ISBN 978-989-98777-8-8)
Sharp KV, Adrian RJ (2001) PIV study of small-scale flow structure around a Rushton turbine. AIChE J 47(4):766–778. doi:10.1002/aic.690470403
Sheng J, Meng H, Fox RO (2000) A large eddy PIV method for turbulence dissipation rate estimation. Chem Eng Sci 55(20):4423–4434. doi:10.1016/S0009-2509(00)00039-7
Tanaka T, Eaton JK (2007) A correction method for measuring turbulence kinetic energy dissipation rate by PIV. Exp Fluids 42(6):893–902. doi:10.1007/s00348-007-0298-y
Tokgoz S, Elsinga G, Delfos R, Westerweel J (2012) Spatial resolution and dissipation rate estimation in Taylor–Couette flow for tomographic PIV. Exp Fluids 53(3):561–583. doi:10.1007/s00348-012-1311-7
Wernersson ESW, Tragardh C (1999) Scale-up of Rushton turbine agitated tanks. Chem Eng Sci 54:4245. doi:10.1016/S0009-2509(99)00127-X
Wieneke B (2013) Iterative reconstruction of volumetric particle distribution. Meas Sci Technol 24:024008. doi:10.1088/0957-0233/24/2/024008
Wilcox DC (1994) Turbulence modeling for CFD. DCW Industries Inc, La Canada, California
Willert CE (2015) High-speed particle image velocimetry for the efficient measurement of turbulence statistics. Exp Fluids 56:17. doi:10.1007/s00348-014-1892-4
Zaripov DI, Aslaev AK, Mikheev NI, Dushin NS (2016) Estimation of accuracy of new optical method of instantaneous flow velocity field measurement. Trudi Academenergo 1:42–52 (in Russian)
Acknowledgements
This study was supported by the Russian Science Foundation (Project no. 16-19-10336). The authors would like to thank the anonymous reviewers for their insightful comments on the manuscript.
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Mikheev, N.I., Goltsman, A.E., Saushin, I.I. et al. Estimation of turbulent energy dissipation in the boundary layer using Smoke Image Velocimetry. Exp Fluids 58, 97 (2017). https://doi.org/10.1007/s00348-017-2379-x
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DOI: https://doi.org/10.1007/s00348-017-2379-x