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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.

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References

Figures

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Fig. 1

Geometry and coordinate system

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Fig. 2

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

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Fig. 3

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

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Fig. 4

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

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Fig. 5

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

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Fig. 6

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

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Fig. 7

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

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Fig. 8

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

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Fig. 9

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

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Fig. 10

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

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Fig. 11

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

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Fig. 12

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

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Fig. 13

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

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Fig. 14

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

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