Destabilization of a laminar flow in a rectangular channel by transversely-oriented wall corrugation

• Autorzy: Szumbarski J. , Błoński S.
• Języki publikacji: EN

Abstrakty

EN

Linear stability of the flow through the transversely corrugated channel with flat sidewalls is investigated numerically. Two variants of the wall corrugation are considered: symmetric sinusoidal waviness of the top and bottom walls and onesided corrugation, i.e., one of the walls remains flat. Spectrally accurate Galerkin method formulated in a transformed domain is used for the solution of the main flow and linear stability equations. Unstable normal modes have been identified and their parametric variation has been determined. The results show that for sufficiently large aspect ratios, the influence of the sidewalls is weak and the stability properties resemble those of the spanwise-periodic channel (investigated recently by the first author). It means that an appropriately designed transversal corrugation may be regarded as a promising method for passive enhancement of mixing in laminar regime.

Słowa kluczowe

EN

hydrodynamic stability; wavy channel; wall corrugation; laminar mixing

• Wydawca: Instytut Podstawowych Problemów Techniki PAN
• Czasopismo: Archives of Mechanics
• Rocznik: 2011
• Tom: Vol. 63, nr 4
• Strony: 393--428
• Opis fizyczny: Bibliogr. 27 poz.

Twórcy

autor

Szumbarski J.

autor

Błoński S.

• Institute of Aeronautics and Applied Mechanics Warsaw University of Technology Nowowiejska 24 00-665 Warszawa, Poland,

Bibliografia

• 1. J.L. Goldstein, E.M. Sparrow, Heat-mass transfer characteristics for flow in a corrugated wall channel, Journal of Heat Transfer, 99, 187–195, 1977.
• 2. I.J. Sobey, On flow through furrowed channels. Part 1: Calculated flow patterns, Journal of Fluid Mechanics, 96, 1–26, 1980.
• 3. K.D. Stephanoff, I.J. Sobey, B.J. Bellhouse, On flow through furrowed channels. Part 2: Observed flow patterns, Journal of Fluid Mechanics, 96, 27–32, 1980.
• 4. T. Nishimura, S. Murakami, S. Arakawa, Y. Kawamura, Flow observations and mass transfer characteristics in symmetrical wavy-walled channels at moderate Reynolds number for steady flow, Int. J. Heat and Mass Transfer, 33, 835–844, 1990.
• 5. T. Nishimura, S. Arakawa, S. Murakami, Y. Kawamura, Oscillatory viscous flow in symmetric wavy-wall channels, Chemical Engineering Science, 44, 2211–2224, 1989.
• 6. T. Nishimura, Y. Kawamura, Three-dimensionality of Oscillatory Flow in a Twodimensional Symmetric Sinusoidal Wavy-Walled Channel, Exp. Therm. Fluid Sci., 10, 62–73, 1995.
• 7. T. Nishimura, T. Yoshino, Y. Kawamura, Numerical flow analysis of pulsatile flow in a channel with symmetric wavy walls at moderate Reynolds numbers, J. Chem. Eng. J pn., 20, 479–485, 1987.
• 8. T. Nishimura, N. Kojima, Mass transfer enhancement in a sinusoidal wavy-walled channel for pulsatile flow, International Journal of Heat and Mass Transfer, 38, 1719–1731, 1995.
• 9. G. Wang, S.P. Vanka, Convective heat transfer in periodic wavy passages, International Journal of Heat and Mass Transfer, 38, 3219–3230, 1995.
• 10. N. Ghaddar, A. El-Hajj, Numerical Study of Heat Transfer Augmentation of Viscous Flow in Corrugated Channels, Heat Transfer Engineering, 21, 35–46, 2000.
• 11. B. Niceno, E. Nobile, Numerical analysis of fluid flow and heat transfer in periodic wavy channel, International Journal of Heat and Fluid Flow, 22, 156–167, 2001.
• 12. K.J. Cho, M. Kim, H.D. Shin, Linear stability of two-dimensional steady flow in wavywalled channel, Fluid Dynamic Research, 23, 349–370, 1998.
• 13. S. Blancher, R. Creff, P. Le Quere, Effect of Tollmien-Schlichting wave on convective heat transfer in a wavy channel. Part I: Linear Analysis, International Journal of Heat and Fluid Flow, 19, 39–48, 1998.
• 14. S. Blancher, R. Creff, P. Le Quere, Analysis of convective hydrodynamic instabilities in a symmetric wavy channel, Physics of Fluids, 16, 3726–3737, 2004.
• 15. J. Szumbarski, Immersed boundary approach to stability equations for a spatially periodic viscous flow, Archives of Mechanics, 54, 199–222, 2002.
• 16. A. Cabal, J. Szumbarski, J.M. Floryan, Stability of flow in a wavy channel, Journal of Fluid Mechanics, 457, 191–212, 2002.
• 17. J.M. Floryan, Vortex instability in a diverging-converging channel, J. Fluid. Mech., 482, 17–50, 2003.
• 18. P.R. Viswanath, Aircraft viscous drag reduction using riblets, Progress in Aerospace Sciences, 38, 571–600, 2002.
• 19. A.V. Boiko, G.R. Grek, A.V. Dovgal, V.V. Kozlov, The Origin of Turbulence In Near-Wall Flows. Springer–Verlag, 2002.
• 20. U. Ehrenstein, On the linear stability of channel flow over riblets, Physics of Fluids, 8, 3194–3196, 1996.
• 21. J. Szumbarski, Instability of a viscous liquid flow in a corrugated channel [in Polish, the habilitation thesis], Published by Warsaw University of Technology, Warszawa, 2007.
• 22. J. Szumbarski, Instability of viscous incompressible flow in a channel with transversely corrugated walls, Journal of Theoretical and Applied Mechanics, 45, 659–683, 2007.
• 23. S. Blonski, J. Szumbarski, T.A. Kowalewski, Low-Reynolds-number instability of the laminar flow between wavy walls, Proceedings of the Sixth International ASME Conference on Nanochannels, Microchannels and Minichannels (ICNMM2008), Darmstadt, Germany, June 23–25, 2008.
• 24. T. Tatsumi, T. Yoshimura, Stability of the laminar flow in a rectangular duct, Journal of Fluid Mechanics, 212, 437–449, 1990.
• 25. J. Szumbarski, Stability analysis of a laminar viscous flow in the finite-span wavy channel, European Fluid Mechanics Conference EFMC-8, Bad Reichenhall, Germany, September 13–16, 2010.
• 26. Y. Saad, Numerical methods for large eigenvalue problems, Manchester University Press, 1992.
• 27. J. Szumbarski, S. Blonski, T.A. Kowalewski, On the impact of transversely-oriented wall corrugation on hydraulic resistance of a laminar channel flow, to be submitted to Archives of Mechanical Engineering, 2011.