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Research Papers: Fundamental Issues and Canonical Flows

# Theoretical Investigation on Inflow Between Two Rotating Disks

[+] Author and Article Information
Achhaibar Singh

Department of Mechanical Engineering,
Amity School of Engineering and Technology,
Amity University,
Sector-125,
Noida 201313, Uttar Pradesh, India
e-mail: drasingh@hotmail.com

Contributed by the Fluids Engineering Division of ASME for publication in the JOURNAL OF FLUIDS ENGINEERING. Manuscript received January 4, 2017; final manuscript received June 2, 2017; published online August 8, 2017. Assoc. Editor: Daniel Livescu.

J. Fluids Eng 139(11), 111202 (Aug 08, 2017) (7 pages) Paper No: FE-17-1008; doi: 10.1115/1.4037058 History: Received January 04, 2017; Revised June 02, 2017

## Abstract

Mathematical relations are obtained for velocities and pressure distribution for a fluid entering the peripheral clearance of a pair of rotating concentric disks that converges and discharges through an opening at the center. Both, the flows in the gap of corotating disks and in the gap of contrarotating disks can be predicted using the present analytical solutions. The prediction of instability of radial velocity for corotating disks at the speed ratio of unity is very important for practical applications. The radial velocity profile is similar to a parabolic profile exactly at speed ratio of unity. The profile drastically changes with the small difference of $±1%$ in the disks’ rotation. The radial convection was observed in the tangential velocity at a low radius. Centrifugal force caused by disk rotation highly influences the flow resulting in backflow on the disks. The pressure consists of friction losses and convective inertia. Therefore, the pressure decrease is high for increased speed ratio, throughflow Reynolds number, and rotational Reynolds number. The pressure decrease for the flow between contrarotating disks is lesser than that for the flow between corotating disks due to decreased viscous losses in the tangential direction. This study provides valuable guidance for the design of devices where disks are rotated independently by highlighting the instabilities in the radial velocity at the speed ratio of unity.

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## References

Lawn, M. J. , and Rice, W. , 1974, “ Calculated Design Data for the Multiple-Disk Turbine Using Incompressible Fluid,” ASME J. Fluids Eng., 96(3), pp. 252–258.
Djaoui, M. , Dyment, A. , and Debuchy, R. , 2001, “ Heat Transfer in a Rotor–Stator System With a Radial Inflow,” Eur. J. Mech. B, 20(3), pp. 371–398.
Owen, J. M. , and Rogers, R. H. , 1989, Flow and Heat Transfer in Rotating-Disc Systems: Rotor-Stator Systems, Wiley, New York, Chap. 1.
Molki, M. , and Nagalla, M. K. , 2005, “ Flow Characteristics of Rotating Disks Simulating a Computer Hard Drive,” Numer. Heat Transfer, Part A: Appl., 48(8), pp. 745–761.
Zueco, J. , and Beg, O. A. , 2010, “ Network Numerical Analysis of Hydromagnetic Squeeze Film Flow Dynamics Between Two Parallel Rotating Disks With Induced Magnetic Field Effects,” Tribol. Int., 43(3), pp. 532–543.
McGinn, J. H. , 1956, “ Observations on the Radial Flow of Water Between Fixed Parallel Plates,” Appl. Sci. Res., 5(4), pp. 255–264.
Garcia, C. E. , 1969, “ Unsteady Airflow Between Two Disks at Low Velocity,” Proc. Inst. Mech. Eng., 184(1969), pp. 913–923.
Murphy, H. D. , Coxon, M. , and McEligot, D. M. , 1978, “ Symmetric Sink Flow Between Parallel Plates,” ASME J. Fluids Eng., 100(4), pp. 477–484.
Murphy, H. D. , Chambers, F. W. , and McEligot, D. M. , 1983, “ Laterally Converging Flow, Part 1 Mean Flow,” J. Fluid Mech., 127, pp. 379–401.
Lee, P. M. , and Lin, S. , 1985, “ Pressure Distribution for Radially Inflow Between Narrowly Spaced Disks,” ASME J. Fluids Eng., 107(3), pp. 338–341.
Vatistas, G. H. , 1988, “ Radial Flow Between Two Closely Placed Flat Disks,” AIAA J., 26(7), pp. 887–890.
Vatistas, G. H. , 1990, “ Radial Inflow Within Two Flat Disks,” AIAA J., 28(7), pp. 1308–1311.
Rohtgi, V. , and Reshotko, E. , 1974, “ Analysis of Laminar Flow Between Stationary and Rotating Disks With Inflow,” Case Western Reserve University, Cleveland, OH, NASA Report No. NASA-CR-2356.
Adams, M. L. , and Szeri, A. Z. , 1982, “ Incompressible Flow Between Finite Disks,” ASME J. Appl. Mech., 49(1), pp. 1–9.
Soo, S. L. , 1958, “ Laminar Flow Over an Enclosed Rotating Disk,” Trans. ASME, 80, pp. 287–296.
Bayley, F. J. , and Owen, J. M. , 1969, “ Flow Between a Rotating and a Stationary Disk,” Aeronaut. Q., 20(4), pp. 333–341.
Conover, R. A. , 1968, “ Laminar Flow Between a Rotating Disk and a Parallel Stationary Wall With or Without Radial Inflow,” ASME J. Basic Eng., 90(3), pp. 325–331.
Senoo, Y. , and Hayami, H. , 1976, “ An Analysis on the Flow in a Casing Induced by Rotating Disk Using a Four-Layer Flow Model,” ASME J. Fluids Eng., 98(2), pp. 192–198.
Poncet, S. , Chauve, M. P. , and Le Gal, P. , 2005, “ Turbulent Rotating Disk Flow With Inward Throughflow,” J. Fluid Mech., 522, pp. 253–262.
Szeri, A. Z. , Schneider, S. J. , Labbe, F. , and Kaufman, H. N. , 1983, “ Flow Between Rotating Disks—Part 1: Basic Flow,” J. Fluid Mech., 134, pp. 103–131.
Truman, C. R. , Rice, W. , and Jankowski, D. F. , 1979, “ Laminar Throughflow of a Fluid Containing Particles Between Corotating Disks,” ASME J. Fluids Eng., 101(1), pp. 87–92.
Pater, L. L. , Crowther, E. , and Rice, W. , 1974, “ Flow Regime Definition for Flow Between Corotating Disks,” ASME J. Fluids Eng., 96(1), pp. 29–34.
Owen, J. M. , Pincombe, J. R. , and Rogers, R. H. , 1985, “ Source–Sink Flow Inside a Rotating Cylindrical Cavity,” J. Fluid Mech., 155, pp. 233–265.
Luoa, X. , Fenga, A. , Quana, Y. , Zhoub, Z. , and Liaob, N. , 2016, “ Experimental Analysis of Varied Vortex Reducers in Reducing the Pressure Drop in a Rotating Cavity With Radial Inflow,” Exp. Therm. Fluid Sci., 77, pp. 159–166.
Firouzian, M. , Owen, J. M. , Pincombe, J. R. , and Rogers, R. H. , 1985, “ Flow and Heat Transfer in a Rotating Cavity With a Radial Inflow of Fluid—Part 1: The Flow Structure,” Int. J. Heat Fluid Flow, 6(4), pp. 228–234.
Singh, A. , 2014, “ Inward Flow Between Stationary and Rotating Disks,” ASME J. Fluids Eng., 136(10), p. 101205.
Singh, A. , 2016, “ Closed Form Solution for Outflow Between Corotating Disks,” ASME J. Fluids Eng., 138(10), p. 051203.
Childs, P. R. N. , 2011, Rotating Flow, Butterworth Heinemann (Elsevier), Burlington, ON, Canada, Chap. 2.
Forsyth, A. R. , 1995, A Treatise on Differential Equations, CBS Publishers and Distributors, New Delhi, India, Chap. 3.
Wang, C. Y. , 2012, “ Discussion: Slip-Flow Pressure Drop in Microchannels of General Cross Section,” ASME J. Fluids Eng., 134(5), p. 055501.

## Figures

Fig. 1

Simplified flow domain

Fig. 2

Tangential velocity distribution: (a) Reø = 10,714, g = 0.05, s = −1.023 and (b) Req = 100, g = 0.01, r¯ = 1.0

Fig. 3

Tangential velocity distribution: (a) g = 0.01, r¯ = 0.2 and (b) Req = 100, r¯ = 0.2

Fig. 4

Radial velocity distribution: (a) Reø = 10714, g = 0.05, s = −1.023 and (b) Reø = 10,000, g = 0.01, s = 1.1, r¯ = 0.8

Fig. 5

Radial velocity distribution at various speed ratios for Req = 20, Reø = 50,000, g = 0.01, r¯ = 0.8: (a) corotating disks and (b) contrarotating disks

Fig. 6

Radial velocity distribution: (a) Req = 10, g = 0.01, s = 1.1, r¯ = 0.8 and (b) Req = 20, Reø = 10,000, s = 1.1, r¯ = 0.8

Fig. 7

Pressure distribution: (a) Reϕ = 38643, g = 0.0075, s = 1.0 and (b) Req = 1000, g = 0.01, s = 1.0

Fig. 8

Pressure distribution: (a) Req = 1000, Reø = 50,000, g = 0.002 and (b) Req = 1000, Reø = 50,000, s = 1.0

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