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Turbulent flow on a planar moving belt and a rotating disk: modelling and comparisons

Published online by Cambridge University Press:  31 August 2007

JOHN M. McDARBY  and
FRANK T. SMITH
JOHN M. McDARBY
Affiliation:
Dept. of Mathematics, University College London, Gower Street, London, WC1E 6BT, UK
FRANK T. SMITH
Affiliation:
Dept. of Mathematics, University College London, Gower Street, London, WC1E 6BT, UK
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Abstract

Modelling of the fully turbulent flow produced on a moving belt and of that induced ona rotating disk is described, for each of which a more analytical approach is adopted than previously seen. The analysis for the two-dimensional moving belt indicates novel structures and these are found to carry over directly to the rotating disk flow which, ignoring the transitional regime, is three-componential but two-dimensional due to axisymmetry. This is based on addressing the Reynolds-averaged Navier–Stokes equations together with an eddy viscosity model, with the flow structure being analysed for high Reynolds numbers. A classical (von Kármán) constant within the model plays an important and surprising role, indicating that each of the belt and the disk flows has quite a massive thickness. Comparisons made with previous work show varying degrees of agreement. The approach, including the new prediction of massive thicknesses independent of the Reynoldsnumber, is expected to extend to flows induced by rotary blades, by related rotary devices and by other configurations of industrial interest.

Type
Papers
Information
Journal of Fluid Mechanics , Volume 587 , 25 September 2007 , pp. 255 - 270
Copyright
Copyright © Cambridge University Press 2007

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References

REFERENCES

Afzal, N. 1996 Turbulent boundary layer on a moving continuous plate. Fluid Dyn. Res. 17, 181–194.CrossRefGoogle Scholar
Bhattacharrya, S. & Smith, F. T. 2003 Comparisons of direct simulations and analytical predictions for multi-plate flows. Computers Fluid. 33, 257–265.CrossRefGoogle Scholar
Bowles, R. G. A. & Smith, F. T. 2000a Interactive flow past multiple blades and wakes. Q. J. Mech. Appl. Maths 53 (2), 207–251.CrossRefGoogle Scholar
Bowles, R. G. A. & Smith, F. T. 2000b Lifting multi-blade flows with interaction. J. Fluid Mech. 415, 203–226.CrossRefGoogle Scholar
Bush, W. B. & Fendell, F. E. 1972 Asymptotic analysis of turbulent channel and boundary-layer flow. J. Fluid Mech. 56, 657–681.CrossRefGoogle Scholar
Cebeci, T. & Abbott, D. E. 1975 Boundary layers on a rotating disc. AIAA J. 13, 829–832.CrossRefGoogle Scholar
Clauser, F. H. 1956 The turbulent boundary layer. Adv. Appl. Mech. IV, 1–51.Google Scholar
Cooper, P. 1971 Turbulent boundary layer on a rotating disc calculated with an effective viscosity. AIAA J. 9, 255–261.CrossRefGoogle Scholar
Davies, C. & Carpenter, P. W. 2003 Global behaviour corresponding to the absolute instability of the rotating-disc boundary layer. J. Fluid Mech. 486, 287–329.CrossRefGoogle Scholar
Davies, C., Thomas, C. & Carpenter, P. W. 2007 Global stability of the rotating-disc boundary ayer. J. Engng Maths (in press).Google Scholar
Erian, F. F. & Tong, Y. H. 1971 Turbulent flow due to a rotating disc. Phys. Fluid. 14, 2588–2591.CrossRefGoogle Scholar
Gregory, N., Stuart, J. T. & Walker, W. S. 1955 On the stability of three-dimensional boundary layers with application to the flow due to a rotating disc. Phil. Trans. R. Soc. Lond. A 248, 155–199.Google Scholar
Jones, M. A. & Smith, F. T. 2003 Fluid motion for car undertrays in ground effect. J. Engng Math. 45, 309–334.CrossRefGoogle Scholar
vonKarman, Th. Karman, Th. 1921 Laminare und Turbulente Reibung. Z. Angew. Math. Mech. 1, Part 4, 233–252.Google Scholar
Launder, B. E. & Sharma, X. 1974 Application of the energy-dissipation model of turbulence to the calculation of flow near a spinning disc. Lett. Heat Mass Transfe. 1, 131–138.CrossRefGoogle Scholar
Lingwood, R. J. 1995 Absolute instability of the boundary layer on a rotating disc. J. Fluid Mech. 29, 17–33.CrossRefGoogle Scholar
Lingwood, R. J. 1996 An experimental study of absolute instability of the rotating-disc boundary-layer flow. J. Fluid Mech. 314, 373–405.CrossRefGoogle Scholar
Littell, H. S. & Eaton, J. K. 1994 Turbulence characteristics of the boundary layer on a rotating disk. J. Fluid Mech. 266, 175–207.CrossRefGoogle Scholar
McDarby, J. M. 2004 Modelling of turbulent rotor-blade flow and ground effect. PhD thesis, University of London.Google Scholar
Mellor, G. L. 1972 The large Reynolds number, asymptotic theory of turbulent boundary layers. Intl J. Engng Sci. 10, 851–873.CrossRefGoogle Scholar
Neish, A. & Smith, F. T. 1988 The turbulent boundary layer and wake of an aligned flat plate. J. Engng Math. 22, 15–42.CrossRefGoogle Scholar
Prandtl, L. 1952 Essentials of Fluid Dynamics. Blackie & Son.Google Scholar
Purvis, R. & Smith, F. T. 2004 Planar flow past two or more blades in ground effect. Q. J. Mech. Appl. Math. 57, 137–160.CrossRefGoogle Scholar
Sakiadis, B. 1961a Boundary layer on continuous solid surface. I Boundary-layer equations for two-dimensional and axisymmetric flow. AIChE J. 7, 26–27.CrossRefGoogle Scholar
Sakiadis, B. 1961b Boundary layer on continuous solid surface. II The Boundary layer on a continuous flat surface. AIChE J. 7, 221–225.CrossRefGoogle Scholar
Scheichl, B. 2001 Asymptotic theory of marginal turbulent separation. PhD thesis, Vienna University of Technology.Google Scholar
Scheichl, B. & Kluwick, A. 2007a Turbulent marginal separation and the turbulent Goldstein problem. AIAA J. 45, 20–36.CrossRefGoogle Scholar
Scheichl, B. & Kluwick, A. 2007b A novel triple-deck problem for turbulent flows. Progress in Turbulence II. Proc. iTi Conference on Turbulence 2005. Proceedings in Physics, Vol. 109. Springer.Google Scholar
Schlichting, H. 1960 Boundary Layer Theory, 4th Edn. McGraw-Hill.Google Scholar
Smith, F. T. & Timoshin, S. N. 1996a Blade-wake interaction and rotary boundary layers. Proc. R. Soc. Lond. 452, 1301–1329.Google Scholar
Smith, F. T. & Timoshin, S. N. 1996b Planar flows past thin multi-blade configurations. J. Fluid Mech. 324, 355–377.CrossRefGoogle Scholar
Speziale, C. G. & So, R. M. C. 1998 Turbulence modelling and simulation. In The Handbook of Fluid Dynamics (ed. Johnson, R. W.). CRC Press.Google Scholar
Tsou, F. K., Sparrow, E. M. & Goldstein, R. J. 1967 Flow and heat transfer in the boundary layer on a continuous moving surface. Intl J. Heat Mass Transfe. 10, 219–235.CrossRefGoogle Scholar
Wilcox, D. C. 1998 Turbulence Modelling for CFD, 2nd Edn. DCW Industries, Inc.Google Scholar
Wu, X. & Squires, K. D. 2000 Prediction and investigation of the turbulent flow over a rotating disk. J. Fluid Mech. 418, 231–264.CrossRefGoogle Scholar
Zandbergen, P. J. & Dijkstra, D. 1987 Von Karman swirling flows. Annu. Rev. Fluid Mech. 19, 465–491.CrossRefGoogle Scholar