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The Eckert–Weise effect and energy separation under the flow interference behind side-by-side cylinders

Published online by Cambridge University Press:  25 March 2021

Andrey I. Aleksyuk Open the ORCID record for Andrey I. Aleksyuk [Opens in a new window]
Andrey I. Aleksyuk*
Affiliation:
Faculty of Mechanics and Mathematics, Lomonosov Moscow State University, Moscow119991, Russian Federation Institute of Mechanics, Lomonosov Moscow State University, Moscow119192, Russian Federation Water Problems Institute, Russian Academy of Sciences, Moscow119333, Russian Federation
*
†Email address for correspondence: aleksyuk@mech.math.msu.su
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Abstract

The total enthalpy of a uniform flow is redistributed behind a thermally insulated body such that a considerable cooling of fluid in terms of total temperature occurs near the wake centreline. This energy separation phenomenon is also observed after time averaging and can lead to the recovery temperature at the rear part of the body becoming lower than the static temperature of the incoming flow (the Eckert–Weise effect). By the numerical solution of the Navier–Stokes equations, the present work studies energy separation in the wake, the Eckert–Weise effect and their sensitivity on the flow interference behind side-by-side cylinders. The considered distances between the cylinders cover the key regimes of interference: single, bistable and coupled vortex streets. The first and second regimes amplify the efficiency of energy separation in the wake and the intensity of the Eckert–Weise effect, respectively. In the developed wake, a clear relation between the vortex structure and the total enthalpy redistribution is demonstrated as well as a limitation on the intensity of this redistribution imposed by the deficit of velocity. The connection of the Eckert–Weise effect with the vortex formation process is clarified. Among the mechanisms changing the total enthalpy in fluid particles, the non-stationarity of pressure defines the averaged distribution: the decrease of pressure in forming vortices is mainly responsible for the cooling of fluid behind the body. The balance with the heating of the rear surface by the involvement of fluid from the sides defines the intensity of the effect.

JFM classification

Vortex Flows: Vortex shedding Wakes/Jets: Wakes
Type
JFM Papers
Information
Journal of Fluid Mechanics , Volume 915 , 25 May 2021 , A95
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Copyright
© The Author(s), 2021. Published by Cambridge University Press

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References

REFERENCES

Aleksyuk, A.I. 2019 Influence of vortex street structure on the efficiency of energy separation. Intl J. Heat Mass Transfer 135, 284–293.CrossRefGoogle Scholar
Aleksyuk, A.I. & Osiptsov, A.N. 2018 Direct numerical simulation of energy separation effect in the near wake behind a circular cylinder. Intl J. Heat Mass Transfer 119, 665–677.CrossRefGoogle Scholar
Aleksyuk, A.I. & Shkadov, V.Y.. 2018 Analysis of three-dimensional transition mechanisms in the near wake behind a circular cylinder. Eur. J. Mech. B/Fluids 72, 456–466.CrossRefGoogle Scholar
Azanov, G.M. & Osiptsov, A.N. 2017 The efficiency of one method of machineless gasdynamic temperature stratification in a gas flow. Intl J. Heat Mass Transfer 106, 1125–1133.CrossRefGoogle Scholar
Barkley, D. & Henderson, R.D. 1996 Three-dimensional Floquet stability analysis of the wake of a circular cylinder. J. Fluid Mech. 322, 215–241.CrossRefGoogle Scholar
Burazer, J. 2018 Energy separation in transient and steady-state flow across the cylinder. Theor. Appl. Mech. 45 (1), 83–94.CrossRefGoogle Scholar
Canuto, D. & Taira, K. 2015 Two-dimensional compressible viscous flow around a circular cylinder. J. Fluid Mech. 785, 349–371.CrossRefGoogle Scholar
Chaitanya, N.S.K. & Dhiman, A.K. 2012 Non-Newtonian power-law flow and heat transfer across a pair of side-by-side circular cylinders. Intl J. Heat Mass Transfer 55 (21–22), 5941–5958.CrossRefGoogle Scholar
Dynnikova, G.Y.. 2008 Calculation of flow around a circular cylinder on the basis of two-dimensional Navier–Stokes equations at large Reynolds numbers with high resolution in a boundary layer. Dokl. Phys. 53 (10), 544–547.CrossRefGoogle Scholar
Eckert, E. & Weise, W. 1942 Messungen der Temperaturverteilung auf der Oberfläche schnell angeströmter unbeheizter Körper. Forsch. Ing. Wes. 13 (6), 246–254.CrossRefGoogle Scholar
Eckert, E.R.G. 1984 Experiments on energy separation in fluid streams. Mech. Engng 106 (10), 58–65.Google Scholar
Eckert, E.R.G. 1987 Cross transport of energy in fluid streams. Wärme-Stoffübertrag. 21, 73–81.CrossRefGoogle Scholar
Eiamsa-ard, S. & Promvonge, P. 2008 Review of Ranque–Hilsch effects in vortex tubes. Renew. Sust. Energ. Rev. 12 (7), 1822–1842.CrossRefGoogle Scholar
Goldstein, R.J. & Kulkarni, K.S. 2008 Energy separation in the wake of a cylinder. Trans. ASME: J. Heat Transfer 130 (6), 061703.CrossRefGoogle Scholar
Gu, X.-J., Barber, R.W., John, B. & Emerson, D.R. 2019 Non-equilibrium effects on flow past a circular cylinder in the slip and early transition regime. J. Fluid Mech. 860, 654–681.CrossRefGoogle Scholar
Henderson, R.D. 1995 Details of the drag curve near the onset of vortex shedding. Phys. Fluids 7 (9), 2102–2104.CrossRefGoogle Scholar
Hu, J.C. & Zhou, Y. 2008 Flow structure behind two staggered circular cylinders. Part 2. Heat and momentum transport. J. Fluid Mech. 607, 81–107.CrossRefGoogle Scholar
Jester, W. & Kallinderis, Y. 2003 Numerical study of incompressible flow about fixed cylinder pairs. J. Fluids Struct. 17 (4), 561–577.CrossRefGoogle Scholar
Kiselev, N.A., Leontiev, A.I., Vinogradov, Y..A., Zditovets, A.G. & Strongin, M.M. 2019 Effect of large-scale vortex induced by a cylinder on the drag and heat transfer coefficients of smooth and dimpled surfaces. Intl J. Therm. Sci. 136, 396–409.CrossRefGoogle Scholar
Kulkarni, K.S. & Goldstein, R.J. 2009 Energy separation in the wake of a cylinder: effect of Reynolds number and acoustic resonance. Intl J. Heat Mass Transfer 52 (17–18), 3994–4000.CrossRefGoogle Scholar
Kurosaka, M., Gertz, J.B., Graham, J.E., Goodman, J.R., Sundaram, P., Riner, W.C., Kuroda, H. & Hankey, W.L. 1987 Energy separation in a vortex street. J. Fluid Mech. 178, 1–29.CrossRefGoogle Scholar
Leont'ev, A.I. 1997 Gas-dynamic method of energy separation of gas flows. High Temp. 35 (1), 155–157.Google Scholar
Leontiev, A.I., Zditovets, A.G., Kiselev, N.A., Vinogradov, Y..A. & Strongin, M.M. 2019 Experimental investigation of energy (temperature) separation of a high-velocity air flow in a cylindrical channel with a permeable wall. Exp. Therm. Fluid Sci. 105, 206–215.CrossRefGoogle Scholar
Leontiev, A.I., Zditovets, A.G., Vinogradov, Y.A., Strongin, M.M. & Kiselev, N.A. 2017 Experimental investigation of the machine-free method of temperature separation of air flows based on the energy separation effect in a compressible boundary layer. Exp. Therm. Fluid Sci. 88, 202–219.CrossRefGoogle Scholar
Meliga, P., Sipp, D. & Chomaz, J.-M. 2010 Effect of compressibility on the global stability of axisymmetric wake flows. J. Fluid Mech. 660, 499–526.CrossRefGoogle Scholar
Meneghini, J.R., Saltara, F., Siqueira, C.L.R. & Ferrari, J.A. 2001 Numerical simulation of flow interference between two circular cylinders in tandem and side-by-side arrangements. J. Fluids Struct. 15 (2), 327–350.CrossRefGoogle Scholar
Munday, P.M., Taira, K., Suwa, T., Numata, D. & Asai, K. 2015 Nonlinear lift on a triangular airfoil in low-Reynolds-number compressible flow. J. Aircraft 52 (3), 924–931.CrossRefGoogle Scholar
Nagata, T., Noguchi, A., Kusama, K., Nonomura, T., Komuro, A., Ando, A. & Asai, K. 2020 a Experimental investigation on compressible flow over a circular cylinder at Reynolds number of between 1000 and 5000. J. Fluid Mech. 893, A13.CrossRefGoogle Scholar
Nagata, T., Nonomura, T., Takahashi, S. & Fukuda, K. 2020 b Direct numerical simulation of subsonic, transonic and supersonic flow over an isolated sphere up to a Reynolds number of 1000. J. Fluid Mech. 904, A36.CrossRefGoogle Scholar
Nagata, T., Nonomura, T., Takahashi, S., Mizuno, Y. & Fukuda, K. 2016 Investigation on subsonic to supersonic flow around a sphere at low Reynolds number of between 50 and 300 by direct numerical simulation. Phys. Fluids 28 (5), 056101.CrossRefGoogle Scholar
Ng, W.F., Chakroun, W.M. & Kurosaka, M. 1990 Time-resolved measurements of total temperature and pressure in the vortex street behind a cylinder. Phys. Fluids A 2 (6), 971–978.CrossRefGoogle Scholar
Roshko, A. 1961 Experiments on the flow past a circular cylinder at very high Reynolds number. J. Fluid Mech. 10 (3), 345–356.CrossRefGoogle Scholar
Roshko, A. 1993 Perspectives on bluff body aerodynamics. J. Wind Engng Ind. Aerodyn. 49 (1–3), 79–100.CrossRefGoogle Scholar
Ryan, L.F. 1951 Experiments on aerodynamic cooling. PhD thesis, Swiss Federal Institute of Technology, Zurich.Google Scholar
Schlichting, H. & Gersten, K. 2017 Boundary-Layer Theory. Springer.CrossRefGoogle Scholar
Sieverding, C. & Manna, M. 2020 A review on turbine trailing edge flow. Intl J. Turbomach. Propul. Power 5 (2), 1–58.CrossRefGoogle Scholar
Singh, S.P. & Mittal, S. 2005 Flow past a cylinder: shear layer instability and drag crisis. Intl J. Numer. Meth. Fluids 47 (1), 75–98.CrossRefGoogle Scholar
Sumner, D. 2010 Two circular cylinders in cross-flow: a review. J. Fluids Struct. 26 (6), 849–899.CrossRefGoogle Scholar
Thomann, H. 1959 Measurements of the recovery temperature in the wake of a cylinder and of a wedge at Mach numbers between 0.5 and 3. Tech. Rep. 84. National Aeronautical Research Institute (FFA), Sweden.Google Scholar
Wen, C.-Y. & Lin, C.-Y. 2001 Two-dimensional vortex shedding of a circular cylinder. Phys. Fluids 13 (3), 557–560.CrossRefGoogle Scholar
Williamson, C.H.K. 1988 The existence of two stages in the transition to three-dimensionality of a cylinder wake. Phys. Fluids 31 (11), 3165–3168.CrossRefGoogle Scholar
Williamson, C.H.K. 1996 Vortex dynamics in the cylinder wake. Annu. Rev. Fluid Mech. 28, 477–539.CrossRefGoogle Scholar
Xu, S.J., Zhou, Y. & So, R.M.C. 2003 Reynolds number effects on the flow structure behind two side-by-side cylinders. Phys. Fluids 15 (5), 1214–1219.CrossRefGoogle Scholar
Yoon, H.S., Seo, J.H. & Kim, J.H. 2010 Laminar forced convection heat transfer around two rotating side-by-side circular cylinder. Intl J. Heat Mass Transfer 53 (21–22), 4525–4535.CrossRefGoogle Scholar
Zdravkovich, M.M 1987 The effects of interference between circular cylinders in cross flow. J. Fluids Struct. 1 (2), 239–261.CrossRefGoogle Scholar
Zdravkovich, M.M. 1997 Flow Around Circular Cylinders. Volume 1. Fundamentals. Oxford University Press.Google Scholar
Zhou, Y. & Mahbub Alam, M.. 2016 Wake of two interacting circular cylinders: a review. Intl J. Heat Fluid Flow 62, 510–537.CrossRefGoogle Scholar
Zhou, Y., Zhang, H.J. & Yiu, M.W. 2002 The turbulent wake of two side-by-side circular cylinders. J. Fluid Mech. 458, 303–332.CrossRefGoogle Scholar