On the Mean Flow Solutions of Related Rotating Disk Flows of the BEK System

Year 2020, Volume: 3 Issue: 2, 168 - 174, 15.12.2020

Burhan Alveroğlu

https://doi.org/10.33401/fujma.796886

Abstract

This paper investigates the effects of the YHP roughness model on the mean flow solutions of some flows belong to the family of the rotating BEK system flows. The governing mean flow equations are formulated in the rotating frame of reference, therefore, they include terms arising from the centrifugal force. These mean flow equations are solved using the method of lines and the backward difference method. Then, obtained results are compared for specifically selected value of roughness parameters with the results of a fundamentally different roughness model, the MW model. The results of the YHP model reveal that applying surface roughness changes the characteristics of the mean flow components. Moreover, the comparison of the YHP and MW models points that these changes are notably different for each model. Therefore, possible future researches can be conducted to investigate the stability characteristics of the flows due to the selection of the roughness model.

Keywords

Hydrodynamic Stability, BEK system flows, Rotating flows

References

• [1] W. E. Gray, The nature of the boundary layer flow at the nose of a swept wing, Roy. Aircraft Est. TM, 256 (1952).
• [2] D. Poll, Some observations of the transition process on the windward face of a long yawed cylinder, J. Fluid Mech., 150 (1985), 329–356.
• [3] P. Hall, An asymptotic investigation of the stationary modes of instability of the boundary layer on a rotating disc, Proc. R. Soc. Lond. Ser. A Math. Phys. Eng. Sci., 406 (1986).
• [4] R. J. Lingwood, Absolute instability of the ekman layer and related rotating flows, J. Fluid Mech., 331 (1997), 405–428.
• [5] P. Carpenter, The right sort of roughness, Nature, 388(6644) (1997), 713–714.
• [6] K. Choi, Fluid dynamics: The rough with the smooth, Nature, 440(7085) (2006), 754–754.
• [7] L. Sirovich, S. Karlsson, Turbulent drag reduction by passive mechanisms, Nature, 388(6644) (1997), 753–755.
• [8] B. Alveroglu, A. Segalini, S. J. Garrett, The effect of surface roughness on the convective instability of the BEK family of boundary-layer flows, Eur. J. Mech. B Fluids, 56 (2016), 178–187.
• [9] A. J. Colley, P. J. Thomas, P. W. Carpenter, A. J. Cooper, An experimental study of boundary-layer transition over a rotating, compliant disk, Phys. Fluids (1994-present), 11(11) (1999), 3340–3352.
• [10] S. J. Garrett, A. J. Cooper, J. H. Harris, M. Ozkan, A. Segalini, P. J. Thomas, On the stability of von karman rotating-disk boundary layers with radial anisotropic surface roughness, Phys. Fluids, 28(1) (2016), 014104.
• [11] M. Türkyılmazoğlu, Suspension of dust particles over a stretchable rotating disk and two-phase heat transfer. Int. J. Multiphase Flow, 127 (2020), 103260.
• [12] M. Türkyılmazoğlu, Single phase nanofluids in fluid mechanics and their hydrodynamic linear stability analysis, Comp. Meth. Prog. Biomedicine, 187 (2020), 105171.
• [13] T. Watanabe, H. M. Warui, N. Fujisawa, Effect of distributed roughness on laminar-turbulent transition in the boundary layer over a rotating cone, Experiments Fluids, 14(5) (1993), 390–392.
• [14] A. J. Cooper, J. H. Harris, S. J. Garrett, M. Ozkan, P. J. Thomas, The effect of anisotropic and isotropic roughness on the convective stability of the rotating disk boundary layer, Phys. Fluids, 27(1) (2015), 16.
• [15] A. J. Cooper, P. W. Carpenter, The stability of rotating-disc boundary-layer flow over a compliant wall. part 1. type I and II instabilities, J. Fluid Mech., 350 (1997), 231–259.
• [16] M. Miklavcic, C. Y. Wang, The flow due to a rough rotating disk, Z. Angew. Math. Phys., 55(2) (2004), 235–246.
• [17] M. S. Yoon, J. M. Hyun, P. Jun Sang, Flow and heat transfer over a rotating disk with surface roughness, Int. J. Heat Fluid Flow, 28(2) (2007), 262–267.