0
Research Papers: Fundamental Issues and Canonical Flows

Closed Form Solution for Outflow Between Corotating Disks

[+] Author and Article Information
Achhaibar Singh

Department of Mechanical and
Automation 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 July 13, 2015; final manuscript received December 10, 2015; published online March 23, 2016. Assoc. Editor: Daniel Maynes.

J. Fluids Eng 138(5), 051203 (Mar 23, 2016) (8 pages) Paper No: FE-15-1476; doi: 10.1115/1.4032322 History: Received July 13, 2015; Revised December 10, 2015

Mathematical expressions are derived for flow velocities and pressure distributions for a laminar flow in the gap between two rotating concentric disks. Fluid enters the gap between disks at the center and diverges to the outer periphery. The Navier–Stokes equations are linearized in order to get closed-form solution. The present solution is applicable to the flow between corotating as well as contrarotating disks. The present results are in agreement with the published data of other investigators. The tangential velocity is less for contrarotating disks than for corotating disks in core region of the radial channel. The flow is influenced by rotational inertia and convective inertia both. Dominance of rotational inertia over convective inertia causes backflow. Pressure depends on viscous losses, convective inertia, and rotational inertias. Effect of viscous losses on pressure is high at small throughflow Reynolds number. The convective and rotational inertia influence pressure significantly at high throughflow and rotational Reynolds numbers. Both favorable and unfavorable pressure gradients can be found simultaneously depending on a combination of parameters.

FIGURES IN THIS ARTICLE
<>
Copyright © 2016 by ASME
Your Session has timed out. Please sign back in to continue.

References

Wang, B. , Okamoto, K. , Yamaguchi, K. , and Teramoto, S. , 2014, “ Loss Mechanisms in Shear-Force Pump With Multiple Corotating Disks,” ASME J. Fluids Eng., 136(8), p. 081101. [CrossRef]
Nicholas, R. A. , and Vasudevan, K. , 2014, “ Flow in a Rotating Cavity With Axial Throughflow at Engine Representative Conditions,” ASME Turbo Expo: Turbine Technical Conference and Exposition, pp. V05CT16A041–V05CT16A055.
Molki, M. , and Nagalla, M. K. , 2005, “ Flow Characteristics of Rotating Disks Simulating a Computer Hard Drive,” Numer. Heat Transfer, Part A, 48(8), pp. 745–761. [CrossRef]
Aphale, C. R. , Cho, J. , Schultz, W. W. , Ceccio, S. L. , Yoshioka, T. , and Hiraki, H. , 2006, “ Modeling and Parametric Study of Torque in Open Clutch Plates,” ASME J. Tribol., 128(2), pp. 422–430. [CrossRef]
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. [CrossRef]
Biswas, N. , Manna, N. K. , Mukhopadhyay, A. , and Sen, S. , 2012, “ Numerical Simulation of Laminar Confined Radial Flow Between Parallel Circular Discs,” ASME J. Fluids Eng., 134(1), p. 011205. [CrossRef]
Al-Shannag, M. , Herrero, J. , Humphrey, J. A. C. , and Giralt, F. , 2002, “ Effect of Radial Clearance on the Flow Between Corotating Disks in Fixed Cylindrical Enclosures,” ASME J. Fluids Eng., 124(3), pp. 719–727. [CrossRef]
Bogy, D. B. , Fromm, J. E. , and Talke, F. E. , 1977, “ Exit Region Central Source Flow Between Finite Closely Spaced Parallel Co-Rotating Disks,” Phys. Fluids, 20(2), pp. 176–186. [CrossRef]
Sim, Y. S. , and Wen-Jei, Y. , 1984, “ Numerical Study on Heat Transfer in Laminar Flow Through Co-Rotating Parallel Disks,” Int. J. Heat Mass Transfer, 27(11), pp. 1963–1970. [CrossRef]
Soong, C. Y. , and Yan, W. M. , 1994, “ Transport Phenomena in Non-Isothermal Flow Between Co-Rotating Asymmetrically-Heated Disks,” Int. J. Heat Mass Transfer, 37(15), pp. 2221–2230. [CrossRef]
Batista, M. , 2011, “ Steady Flow of Incompressible Fluid Between Two Corotating Disks,” Appl. Math. Modell., 35(10), pp. 5225–5233. [CrossRef]
Soong, C. Y. , Wu, C. , Liu, T.-P. , and Liu, T.-P. , 2003, “ Flow Structure Between Two Co-Axial Disks Rotating Independently,” Exp. Therm. Fluid Sci., 27(3), pp. 295–311. [CrossRef]
Gauthier, G. , Gondret, P. , Moisy, F. , and Rabaud, M. , 2002, “ Instabilities in the Flow Between Co-and Counter-Rotating Disks,” J. Fluid Mech., 473, pp. 1–21. [CrossRef]
Gan, X. , Kilic, M. , and Owen, J. M. , 1994, “ Superposed Flow Between Two Discs Contrarotating at Differential Speeds,” Int. J. Heat Fluid Flow, 15(6), pp. 438–446. [CrossRef]
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. [CrossRef]
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. [CrossRef]
Huang, R. F. , and Hsieh, M. K. , 2011, “ Turbulent Flow of Quadrangle Mode in Interdisk Midplane Between Two Shrouded Co-Rotating Disks,” Exp. Therm. Fluid Sci., 35(8), pp. 1608–1620. [CrossRef]
Nazir, A. , and Mahmood, T. , 2011, “ Analysis of Flow and Heat Transfer of Viscous Fluid Between Contracting Rotating Disks,” Appl. Math. Modell., 35(7), pp. 3154–3165. [CrossRef]
Bakket, E. , Kreider, J. F. , and Kreith, F. , 1973, “ Turbulent Source Flow Between Parallel Stationary and Co-Rotating Disks,” J. Fluid Mech., 58(2), pp. 209–231. [CrossRef]
Mazza, R. A. , and Rosa, E. S. , 2007, “ Corotating Disk Assembly With Turbulent Through Flow,” Numer. Heat Transfer, Part A, 53(2), pp. 157–177. [CrossRef]
Shirazi, S. A. , and Truman, C. R. , 1988, “ Prediction of Turbulent Source Flow Between Corotating Disks With an Anisotropic Two-Equation Turbulence Model,” ASME J. Turbomach., 110(2), pp. 187–194. [CrossRef]
Singh, A. , 2014, “ Inward Flow Between Stationary and Rotating Disks,” ASME J. Fluids Eng., 136(10), p. 101205. [CrossRef]
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. [CrossRef]

Figures

Grahic Jump Location
Fig. 1

Geometry and coordinate system

Grahic Jump Location
Fig. 2

Tangential velocity distribution at different radii for Req = 10,000, Reø = 90,000, g = 0.0167, s = 1.0

Grahic Jump Location
Fig. 3

Tangential velocity distribution at different speed ratio for Req = 10,000, g = 0.02, r¯  = 1.0

Grahic Jump Location
Fig. 4

Tangential velocity distribution at different throughflow Reynolds number for g = 0.02, s = 1.0, r¯  = 0.5

Grahic Jump Location
Fig. 5

Tangential velocity distribution at different gap ratio for Req = 100, s = 1.0, r¯  = 0.8

Grahic Jump Location
Fig. 6

Radial velocity distribution at different radii for Req = 10,000, Reø = 90,000, g = 0.0167, s = 1.0

Grahic Jump Location
Fig. 7

Radial velocity distribution at different speed ratio for Req = 500, Reø = 5000, g = 0.05, r¯  = 1.0

Grahic Jump Location
Fig. 8

Radial velocity distribution at different throughflow Reynolds number for Reø = 10,000, g = 0.05, s = 1.0, r¯  = 0.5

Grahic Jump Location
Fig. 9

Radial velocity distribution at different rotational Reynolds number for Req = 100, g = 0.05, s = 0.5, r¯  = 0.5

Grahic Jump Location
Fig. 10

Radial velocity distribution at different gap ratio for Req = 50, Reø = 1000, s = 1.0, r¯  = 0.8

Grahic Jump Location
Fig. 11

Pressure distribution at different rotational Reynolds number for Req = 1746, g = 0.0075, s = 1.0

Grahic Jump Location
Fig. 12

Pressure distribution at different throughflow Reynolds number for Reø = 1000, g = 0.02, s = 1.0

Grahic Jump Location
Fig. 13

Pressure distribution at different speed ratio for Req = 1000, Reø = 10,000, g = 0.02

Grahic Jump Location
Fig. 14

Pressure distribution at different gap ratio for Req = 100, Reø = 5000, s = 1.0

Tables

Errata

Discussions

Some tools below are only available to our subscribers or users with an online account.

Related Content

Customize your page view by dragging and repositioning the boxes below.

Related Journal Articles
Related eBook Content
Topic Collections

Sorry! You do not have access to this content. For assistance or to subscribe, please contact us:

  • TELEPHONE: 1-800-843-2763 (Toll-free in the USA)
  • EMAIL: asmedigitalcollection@asme.org
Sign In