Skip to main content

We use cookies to distinguish you from other users and to provide you with a better experience on our websites. Close this message to accept cookies or find out how to manage your cookie settings.

Close cookie message
Cancel
×
×
Home
  • Home
Article
  • Cited by 62
  • Cited by
    Crossref Citations
    Crossref logo
    This article has been cited by the following publications. This list is generated based on data provided by CrossRef.

    Mukherjee, Aryesh and Steinberg, Victor 2018. von Kármán swirling flow between a rotating and a stationary smooth disk: Experiment. Physical Review Fluids, Vol. 3, Issue. 1,

    Wang, Pengchuan Katopodes, Nikolaos and Fujii, Yuji 2017. Two-Phase MRF Model for Wet Clutch Drag Simulation. SAE International Journal of Engines, Vol. 10, Issue. 3,

    Dobryshman, E. M. Kochina, V. G. and Letunova, T. A. 2013. Dynamic parameters in models of atmospheric vortex structures. Izvestiya, Atmospheric and Oceanic Physics, Vol. 49, Issue. 5, p. 494.

    Nour, Fadi Abdel Rinaldi, Andrea Debuchy, Roger and Bois, Gerard 2012. Influence of a weak superposed centripetal flow in a rotor-stator system for several pre-swirl ratios. International Journal of Fluid Machinery and Systems, Vol. 5, Issue. 2, p. 49.

    Feng, Yu and Kleinstreuer, Clement 2012. Thermal Nanofluid Property Model With Application to Nanofluid Flow in a Parallel Disk System—Part II: Nanofluid Flow Between Parallel Disks. Journal of Heat Transfer, Vol. 134, Issue. 5, p. 051003.

    Pandya, Jigisha U. 2012. The Solution of a Coupled Nonlinear System Arising in a Three-Dimensional Rotating Flow Using Spline Method. International Journal of Mathematics and Mathematical Sciences, Vol. 2012, p. 1.

    Gherasim, Iulian Roy, Gilles Nguyen, Cong Tam and Vo-Ngoc, Dinh 2011. Heat transfer enhancement and pumping power in confined radial flows using nanoparticle suspensions (nanofluids). International Journal of Thermal Sciences, Vol. 50, Issue. 3, p. 369.

    Debuchy, Roger Abdel Nour, Fadi and Bois, Gérard 2010. An Analytical Modeling of the Central Core Flow in a Rotor-Stator System With Several Preswirl Conditions. Journal of Fluids Engineering, Vol. 132, Issue. 6, p. 061102.

    Jiji, Latif M. and Ganatos, Peter 2010. Microscale flow and heat transfer between rotating disks. International Journal of Heat and Fluid Flow, Vol. 31, Issue. 4, p. 702.

    Bataineh, Khaled M. Al-Nimr, Moh’d A. and Kiwan, Suhil M. 2010. Double-disk rotating viscous micro-pump with slip flow. Microsystem Technologies, Vol. 16, Issue. 10, p. 1811.

    Llerena-Chavez, Hugo and Larachi, Faïçal 2009. Analysis of flow in rotating packed beds via CFD simulations—Dry pressure drop and gas flow maldistribution. Chemical Engineering Science, Vol. 64, Issue. 9, p. 2113.

    Wu, Shen-Chun 2009. A PIV study of co-rotating disks flow in a fixed cylindrical enclosure. Experimental Thermal and Fluid Science, Vol. 33, Issue. 5, p. 875.

    Xu, Hang and Liao, Shijun 2007. A Series Solution of the Unsteady Von Kármán Swirling Viscous Flows. Acta Applicandae Mathematicae, Vol. 94, Issue. 3, p. 215.

    Palm, Samy Joseph Roy, Gilles and Nguyen, Cong Tam 2006. Heat transfer enhancement with the use of nanofluids in radial flow cooling systems considering temperature-dependent properties. Applied Thermal Engineering, Vol. 26, Issue. 17-18, p. 2209.

    Kang, Namcheol and Raman, Arvind 2006. Vibrations and stability of a flexible disk rotating in a gas-filled enclosure—Part 1: Theoretical study. Journal of Sound and Vibration, Vol. 296, Issue. 4-5, p. 651.

    Xu, Hang and Liao, Shi-Jun 2006. Series solutions of unsteady MHD flows above a rotating disk. Meccanica, Vol. 41, Issue. 6, p. 599.

    Maïga, Sidi El Bécaye Palm, Samy Joseph Nguyen, Cong Tam Roy, Gilles and Galanis, Nicolas 2005. Heat transfer enhancement by using nanofluids in forced convection flows. International Journal of Heat and Fluid Flow, Vol. 26, Issue. 4, p. 530.

    Roy, Gilles Nguyen, Cong Tam and Lajoie, Paul-René 2004. Numerical investigation of laminar flow and heat transfer in a radial flow cooling system with the use of nanofluids. Superlattices and Microstructures, Vol. 35, Issue. 3-6, p. 497.

    Usha, R. and Ravindran, R. 2004. Analysis of cooling of a conducting fluid film of non-uniform thickness on a rotating disk. International Journal of Non-Linear Mechanics, Vol. 39, Issue. 1, p. 153.

    Vajravelu, K. and Kumar, B.V.R. 2004. Analytical and numerical solutions of a coupled non-linear system arising in a three-dimensional rotating flow. International Journal of Non-Linear Mechanics, Vol. 39, Issue. 1, p. 13.

    Download full list
    ×
  • Get access
    Add to cart €30.00
    Check if you have access via personal or institutional login
    Log in Register Recommend to librarian

Flow between rotating disks. Part 1. Basic flow

  • A. Z. Szeri (a1), S. J. Schneider (a1), F. Labbe (a1) and H. N. Kaufman (a1) (a2)
Abstract

Laser-Doppler velocity measurements were obtained in water between finite rotating disks, with and without throughflow, in four cases: ω1 = ω2 = 0; ω2/ω1 = −1; ω2/ω1 = 0; ω2/ω1 = 1. The equilibrium flows are unique, and at mid-radius they show a high degree of independence from boundary conditions in r. With one disk rotating and the other stationary, this mid-radius ‘limiting flow’ is recognized as the Batchelor profile of infinite-disk theory. Other profiles, predicted by this theory to coexist with the Batchelor profile, were neither observed experimentally nor were they calculated numerically by the finite-disk solutions, obtained here via a Galerkin, B-spline formulation. Agreement on velocity between numerical results and experimental data is good at large values of the ratio RQ/Re, where RQ = Q/2πνs is the throughflow Reynolds number and Re = R22ω/ν is the rotational Reynolds number.

Copyright
© 1983 Cambridge University Press
References
Hide All
Adams, M. L. & Szeri, A. Z. 1982 Incompressible flow between finite disks. Trans. ASME E: J. Appl. Mech. 49, 1–14.
Batchelor, G. K. 1951 Note on a class of solutions of the Navier-Stokes equations representing rotationally symmetric flow Q. J. Mech. Appl. Maths 4, 29.
Deboor, C. 1978 A Practical Guide to Splines. Springer.
Dijkstra, D. 1980 On the relation between adjacent inviscid cell type solutions to the rotating-disk equations J. Engng Maths 14, 133–154.
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 disk Phil. Trans. R. Soc. Lond. A248, 155.
Hall, C. A. 1968 On error bounds for spline interpolation J. Approx. Theory 1, 209–218.
Holodniok, M., Kubicek, M. & Hlavacek, V. 1977 Computation of the flow between two rotating coaxial disks J. Fluid Mech. 81, 680–699.
Holodniok, M., Kubicek, M. & Hlavacek, V. 1981 Computation of the flow between two rotating coaxial disks: multiplicity of steady-state solutions. J. Fluid Mech. 108, 227–240.
Kármán, T. VON 1921 Laminar und turbulente Reibung Z. angew. Math. Mech. 1, 233.
Kreith, F. 1965 Reverse transition in radial source flow between two parallel plates Phys. Fluids 8, 1189–1190.
Labbe, F. 1981 Computation of stationary laminar solutions of flow between finite rotating disks. Ph.D. thesis, University of Pittsburgh.
Lance, G. N. & Rogers, M. H. 1961 The axially symmetric flow of viscous fluid between two infinite rotating disks Proc. R. Soc. Lond. A266, 109–121.
Lentini, M. & Keller, H. B. 1980 The von Kármán swirling flows SIAM J. Appl. Maths 38, 52–63.
Mellor, G. L., Chapple, P. J. & Stokes, V. K. 1968 On the flow between a rotating and a stationary disk J. Fluid Mech. 31, 95–112.
Nguyen, N. D., Ribault, J. P. & Florent, P. 1975 Multiple solutions for flow between coaxial disks J. Fluid Mech. 68, 369–388.
Rogers, M. H. & Lance, G. N. 1960 The rotationally symmetric flow of a viscous fluid in the presence of an infinite disk J. Fluid Mech. 7, 617–631.
Rudd, M. J. 1969 A new theoretical model for the laser Doppler-meter. J. Phys. E: Sci. Instr. 2, 55–63.
Schlichting, H. 1968 Boundary Layer Theory. McGraw-Hill.
Schneider, S. J. 1982 Flow between finite rotating disks: an experimental study of the basic motion and stability. Ph.D. thesis, University of Pittsburgh.
Stewartson, K. 1953 On the flow between two rotating co-axial disks Proc. Camb. Phil. Soc. 3, 333–341.
Szeri, A. Z. & Adams, M. L. 1978 Laminar throughflow between closely spaced rotating disks J. Fluid Mech. 86, 1–14.
Szeri, A. Z., Giron, A., Schneider, S. J. & Kaufman, H. N. 1983 Flow between rotating disks. Part 2. Stability J. Fluid Mech. 134, 133–154.
Weidman, P. D. & Redekopp, L. G. 1975 On the motion of a rotating fluid in the presence of an infinite rotating disk. In Proc. 12th Biennial Fluid Dyn. Symp., Bialowicza, Poland.
Wilson, L. O. & Schryer, N. L. 1978 Flow between a stationary and a rotating disk with suction J. Fluid Mech. 85, 479–496.
Yeh, Y. & Cummins, H. Z. 1964 Localized fluid flow measurements with an He-Ne laser spectometer Appl. Phys. Lett. 4, 176–184.
Zandbergen, P. J. & Dijkstra, D. 1977 Non-unique solutions of the Navier-Stokes equations for the Kármán swirling flow J. Engng Maths 11, 167–188.
Recommend this journal

Email your librarian or administrator to recommend adding this journal to your organisation's collection.

Journal of Fluid Mechanics
  • ISSN: 0022-1120
  • EISSN: 1469-7645
  • URL: /core/journals/journal-of-fluid-mechanics
Please enter your name
Please enter a valid email address
Who would you like to send this to? *

CAPTCHA *

Skip to the audio challenge
×
MathJax

Metrics

Full text views

Total number of HTML views: 0
Total number of PDF views: 53 *
Loading metrics...

Abstract views

Total abstract views: 275 *
Loading metrics...

* Views captured on Cambridge Core between September 2016 - 8th April 2018. This data will be updated every 24 hours.

Cancel
Confirm
×