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Acoustic streaming in turbulent compressible channel flow for heat transfer enhancement

Published online by Cambridge University Press:  18 February 2020

Iman Rahbari Open the ORCID record for Iman Rahbari [Opens in a new window]  and
Guillermo Paniagua Open the ORCID record for Guillermo Paniagua [Opens in a new window]
Iman Rahbari*
Affiliation:
School of Mechanical Engineering, Purdue University, West Lafayette, IN47906, USA Zucrow Laboratories, Purdue University, West Lafayette, IN47907, USA
Guillermo Paniagua
Affiliation:
School of Mechanical Engineering, Purdue University, West Lafayette, IN47906, USA Zucrow Laboratories, Purdue University, West Lafayette, IN47907, USA
*
†Email address for correspondence: irahbari@purdue.edu
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Abstract

Acoustic streaming in high-speed compressible channel flow and its impact on heat and momentum transfer is analysed numerically at two different Mach numbers, $M_{b}=0.75$ and 1.5, and moderate Reynolds numbers, $Re_{b}=3000$ and 6000. An external time-periodic forcing function is implemented to model the effect of acoustic drivers placed on the sidewalls. The excitation frequency is chosen according to the linear stability analysis of the background (unexcited) flow. High-fidelity numerical simulations performed at the optimal resonant condition reveal an initially exponential growth of perturbations followed by a nonlinear regime leading to the limit-cycle oscillations. In the last stage, we observe an acoustic (steady) streaming appearing as a result of nonlinear interactions between the periodic external wave and the background flow. This causes a steady enhancement in heat transfer at a rate higher than the skin-friction augmentation. We also show that perturbations of similar amplitude, but at suboptimal frequencies, may not lead to such limit-cycle oscillations and cannot make any noticeable modifications to the time-averaged flow quantities. The present research is the first study to demonstrate the acoustic streaming in compressible turbulent flows, and it introduces a novel technique towards enhancing the heat transfer with minimal skin-friction production.

JFM classification

Compressible Flows: Compressible boundary layers Turbulent Flows: Turbulence control Boundary Layers: Boundary layer stability
Type
JFM Papers
Information
Journal of Fluid Mechanics , Volume 889 , 25 April 2020 , A2
Copyright
© The Author(s), 2020. Published by Cambridge University Press

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References

Aktas, M. K., Farouk, B. & Lin, Y. 2005 Heat transfer enhancement by acoustic streaming in an enclosure. J. Heat Transfer 127 (12), 1313–1321.CrossRefGoogle Scholar
Aktas, M. K. & Ozgumus, T. 2010 The effects of acoustic streaming on thermal convection in an enclosure with differentially heated horizontal walls. Intl J. Heat Mass Transfer 53 (23–24), 5289–5297.CrossRefGoogle Scholar
Bailliet, H., Gusev, V., Raspet, R. & Hiller, R. A. 2001 Acoustic streaming in closed thermoacoustic devices. J. Acoust. Soc. Am. 110 (4), 1808–1821.CrossRefGoogle ScholarPubMed
Boluriaan, S. & Morris, P. J. 2003 Acoustic streaming: from Rayleigh to today. Intl J. Aeroacoust. 2 (3), 255–292.CrossRefGoogle Scholar
Browne, O. M. F., Rubio, G., Ferrer, E. & Valero, E. 2014 Sensitivity analysis to unsteady perturbations of complex flows: a discrete approach. Intl J. Numer. Meth. Fluids 76 (12), 1088–1110.CrossRefGoogle Scholar
Coleman, G. N., Kim, J. & Moser, R. D. 1995 A numerical study of turbulent supersonic isothermal-wall channel flow. J. Fluid Mech. 305, 159–183.CrossRefGoogle Scholar
Del Alamo, J. C. & Jimenez, J. 2006 Linear energy amplification in turbulent channels. J. Fluid Mech. 559, 205–213.CrossRefGoogle Scholar
Friedrich, R. & Bertolotti, F. P. 1996 Compressibility effects due to turbulent fluctuations. Appl. Sci. Res. 57 (3–4), 165–194.CrossRefGoogle Scholar
Habib, M. A., Said, S. A. M., Al-Farayedhi, A. A., Al-Dini, S. A., Asghar, A. & Gbadebo, S. A. 1999 Heat transfer characteristics of pulsated turbulent pipe flow. Heat Mass Transfer 34 (5), 413–421.CrossRefGoogle Scholar
Havemann, H. A. & Narayan Rao, N. N. 1954 Heat transfer in pulsating flow. Nature 174 (4418), 41.CrossRefGoogle Scholar
Jiménez, J. 2013 How linear is wall-bounded turbulence? Phys. Fluids 25 (11), 110814.CrossRefGoogle Scholar
Jimenez, J., Uhlmann, M., Pinelli, A. & Kawahara, G. 2001 Turbulent shear flow over active and passive porous surfaces. J. Fluid Mech. 442, 89–117.CrossRefGoogle Scholar
Lee, M. J., Kim, J. & Moin, P. 1990 Structure of turbulence at high shear rate. J. Fluid Mech. 216, 561–583.CrossRefGoogle Scholar
Lévêque, E., Toschi, F., Shao, L. & Bertoglio, J.-P. 2007 Shear-improved Smagorinsky model for large-eddy simulation of wall-bounded turbulent flows. J. Fluid Mech. 570, 491–502.CrossRefGoogle Scholar
Lodahl, C. R., Sumer, B. M. & Fredse, J. 1998 Turbulent combined oscillatory flow and current in a pipe. J. Fluid Mech. 373, 313–348.CrossRefGoogle Scholar
Maffulli, R. & He, L. 2014 Wall temperature effects on heat transfer coefficient for high-pressure turbines. J. Propul. Power 30 (4), 1080–1090.CrossRefGoogle Scholar
Malik, M. R. 1990 Numerical methods for hypersonic boundary layer stability. J. Comput. Phys. 86 (2), 376–413.CrossRefGoogle Scholar
Menguy, L. & Gilbert, J. 2000 Non-linear acoustic streaming accompanying a plane stationary wave in a guide. Acoustica 86 (2), 249–259.Google Scholar
Mizushina, T., Maruyama, T. & Shiozaki, Y. 1974 Pulsating turbulent flow in a tube. J. Chem. Engng Japan 6 (6), 487–494.CrossRefGoogle Scholar
Nagarajan, S., Lele, S. K. & Ferziger, J. H. 2003 A robust high-order compact method for large eddy simulation. J. Comput. Phys. 191 (2), 392–419.CrossRefGoogle Scholar
Rahbari, I. & Scalo, C. 2017a Linear stability analysis of compressible channel flow over porous walls. In Whither Turbulence and Big Data in the 21st Century?, pp. 451–467. Springer.CrossRefGoogle Scholar
Rahbari, I. & Scalo, C. 2017b Quasi-spectral sparse bi-global stability analysis of compressible channel flow over complex impedance. In 55th AIAA Aerospace Sciences Meeting, p. 1879. American Institute of Aeronautics and Astronautics.Google Scholar
Rayleigh, Lord 1884 On the circulation of air observed in Kundt’s tubes, and on some allied acoustical problems. Phil. Trans. R. Soc. Lond. A 175, 1–21.Google Scholar
Reynolds, W. C. & Hussain, A. K. M. F. 1972 The mechanics of an organized wave in turbulent shear flow. Part 3. Theoretical models and comparisons with experiments. J. Fluid Mech. 54 (2), 263–288.CrossRefGoogle Scholar
Reynolds, W. C. & Tiederman, W. G. 1967 Stability of turbulent channel flow, with application to Malkus’s theory. J. Fluid Mech. 27 (2), 253–272.CrossRefGoogle Scholar
Riley, N. 2001 Steady streaming. Annu. Rev. Fluid Mech. 33 (1), 43–65.CrossRefGoogle Scholar
Said, S. A. M., Al-Farayedhi, A., Habib, M. A., Gbadebo, S. A., Asghar, A. & Al-Dini, S. 1998 Experimental investigation of heat transfer in pulsating turbulent pipe flow. In Proc Turbulent Heat Transfer Conference-2, Manchester, UK, vol. 2, pp. 54–62.Google Scholar
Scandura, P. 2007 Steady streaming in a turbulent oscillating boundary layer. J. Fluid Mech. 571, 265–280.CrossRefGoogle Scholar
Schlichting, H. 1932 Berechnung ebener periodischer Grenzschichtstromungen. Phys. Z. 33, 327–335.Google Scholar
Schmid, P. J. & Henningson, D. S. 2000 Stability and Transition in Shear Flows, vol. 142. Springer Science & Business Media.Google Scholar
Scotti, A. & Piomelli, U. 2001 Numerical simulation of pulsating turbulent channel flow. Phys. Fluids 13 (5), 1367–1384.CrossRefGoogle Scholar
Tardu, S. F., Binder, G. & Blackwelder, R. F. 1994 Turbulent channel flow with large-amplitude velocity oscillations. J. Fluid Mech. 267, 109–151.CrossRefGoogle Scholar
Tilton, N. & Cortelezzi, L. 2008 Linear stability analysis of pressure-driven flows in channels with porous walls. J. Fluid Mech. 604, 411–445.CrossRefGoogle Scholar
Trefethen, L. N. 2000 Spectral Methods in MATLAB, vol. 10. SIAM.CrossRefGoogle Scholar
Vainshtein, P., Fichman, M. & Gutfinger, C. 1995 Acoustic enhancement of heat transfer between two parallel plates. Intl J. Heat Mass Transfer 38 (10), 1893–1899.CrossRefGoogle Scholar
Weng, C., Boij, S. & Hanifi, A. 2016 Numerical and theoretical investigation of pulsatile turbulent channel flows. J. Fluid Mech. 792, 98–133.CrossRefGoogle Scholar
White, F. M. & Corfield, I. 2006 Viscous Fluid Flow, vol. 3. McGraw-Hill.Google Scholar
Wiklund, M., Green, R. & Ohlin, M. 2012 Acoustofluidics 14: applications of acoustic streaming in microfluidic devices. Lab on a Chip 12 (14), 2438–2451.CrossRefGoogle ScholarPubMed
Yano, T. 1999 Turbulent acoustic streaming excited by resonant gas oscillation with periodic shock waves in a closed tube. J. Acoust. Soc. Am. 106 (1), L7–L12.CrossRefGoogle Scholar