PL EN


Preferencje help
Widoczny [Schowaj] Abstrakt
Liczba wyników
2014 | 35 | 1 | 3-18
Tytuł artykułu

Analysis of the Liquid Flow in a Vessel with a Rotating Disk at the Liquid Surface

Autorzy
Treść / Zawartość
Warianty tytułu
Języki publikacji
EN
Abstrakty
EN
This study is concerned with liquid flow induced by a disk which rotates steadily around its axis and touches the free surface of liquid contained in a cylindrical vessel. It is a simplified model of the flow in the inlet part of a vertical cooling crystallizer where a rotary distributor of inflowing solution is situated above the free surface of solution contained in the crystalliser. Numerical simulations of flow phenomena were conducted and the simulation results were interpreted assuming an analogy with Kármán’s theoretical equations. In a cylindrical coordinate system, the components of flow velocity were identified as functions of distance from the surface of the rotating disk. The experimental setup was developed to measure velocity fields, using digital particle velocimetry and optical flow. Conclusions concerning the influence of disc rotation on liquid velocity fields were presented and the experimental results were found to confirm the results of numerical simulation. On the basis of simulation data, an approximation function was determined to describe the relationship between the circumferential component of flow velocity and the distance from the disk.
Wydawca

Rocznik
Tom
35
Numer
1
Strony
3-18
Opis fizyczny
Daty
wydano
2014-03-01
otrzymano
2012-09-29
zaakceptowano
2013-11-29
online
2014-04-25
Twórcy
  • Warsaw University of Technology, Płock Campus, Institute of Mechanical Engineering, Department of Process Equipment, Jachowicza 2/4, Płock, Poland, suchecki@pw.plock.pl
Bibliografia
  • Carruthers J.R., Nassau K., 1968. Nonmixing cells due to crucible rotating during Czochralski crystal growth. J. Appl. Phys., 39, 5205-5214. DOI: 10.1063/1.1655943.[Crossref]
  • Escudier M.P., 1984. Observation of the flow produced in a cylindrical container by a rotating endwall. Exp. Fluids, 2, 189-196. DOI: 10.1007/BF00571864.[Crossref]
  • Hyun J.M., Leslie F., Fowlis W.W., Warn-Varnas A., 1983. Numerical solutions for spin-up from rest in cylinder. J. Fluid Mech., 127, 263-281. DOI: 10.1017/S0022112083002712.[Crossref]
  • Inamuro T., Yamaguchi A., Ogino F., 1997. Fluid flow in a rotating cylindrical container with a rotating disk at the fluid surface. Fluid Dyn. Res., 21, 417-430. DOI: 10.1016/S0169-5983(97)00020-8.[Crossref]
  • Jasmine H.A., Gajjar J.S.B., 2005. Absolute instability of the von Kármán, Bödewadt and Ekman flows between a rotating disc and a stationary lid. Phil. Trans. R. Soc. A, 363, 1131-1144. DOI: 10.1098/rsta.2005.1555.[Crossref]
  • Jones A.D.W., 1983. An experimental model of the flow in Czochralski growth. J. Cryst. Growth, 61, 235-244. DOI: 10.1016/0022-0248(83)90360-3.[Crossref]
  • Landau L.D., Lifshitz J.M., 2000. Fluid Mechanics, Volume 6 of course of theoretical physics. Butterworth- Heinemann, New Delhi.
  • Langlois W.E., 1977. Digital simulation of Czochralski bulk flow in a parameter range appropriate for liquid semiconductors. J. Cryst. Growth, 42, 386-399. DOI: 10.1016/0022-0248(77)90222-6.[Crossref]
  • Lingwood R.J., 1997. Absolute instability of the Ekman layer and related rotating flows. J. Fluid Mech., 331, 405-428. DOI: 10.1017/S0022112096004144.[Crossref]
  • Lugt H., Abboud M., 1987. Axisymmetric vortex breakdown with and without temperature effects in a container with a rotating lid. J. Fluid Mech., 179, 179-200. DOI: 10.1017/S0022112087001484.[Crossref]
  • Mihelčić M., Schroeck-Pauli C., Wingerath K., Wenzl H., Uelhoff W., Van Der Hart A., 1981. Numerical simulation of forced convection in the classical Czochralski method in ACRT and CACRT. J. Cryst. Growth, 53, 337-354. DOI: 10.1016/0022-0248(81)90083-X.[Crossref]
  • Ogino F., Kawai K., Mayumi K., 1993. Turbulent flow of liquid in a rotating vertical cylindrical container with a stationary solid cylinder at the liquid surface. 9th Symp. on Turbulent Shear Flows, Kyoto, Japan, August 16-18, 1993. Conference paper 3, 30-1.
  • Patankar S.V., 1980. Numerical Heat Transfer and Fluid Flow. McGraw-Hill, New York.
  • Quénot G.M., Pakleza J., Kowalewski T.A., 1998. Particle image velocimetry with optical flow. Exp. Fluids, 25, 177-189. DOI: 10.1007/s003480050222.[Crossref]
  • Raffel M., Willert Ch. E., Kompenhans J., 1998. Particle Image Velocimetry. A Practical Guide. Springer-Verlag, Berlin.[WoS]
  • Ruiz X., Aguilo M., Massons J., Daiz F., 1991. Influence of dynamic boundary condition on the computed flow patterns inside a coaxial rotating disk-cylinder system. Comp. Fluids, 20, 387-398. DOI: 10.1016/0045-7930(91)90080-2.[Crossref]
  • Schouveiler L., Le Gal P., Chauve M.P., 2001. Instabilities of the flow between a rotating and a stationary disk. J. Fluid Mech., 443, 329-350. DOI: 10.1017/S0022112001005328.[Crossref]
  • Sørensen J.N., Christensen E.A., 1995. Direct numerical simulation of rotating fluid flow in a closed cylinder. Phys. Fluids, 7, 764-778. DOI: 10.1063/1.868600.[Crossref]
  • Suchecki W., 2000. The application of digital velocimetry to the visualisation of particle-laden flows. Zeszyty Naukowe Politechniki Opolskiej, 60, Mech. 254/2000, Opole, 319-326 (in Polish).
  • Suchecki W., 2001. Using the methods of optical flow analysis to verify numerical CFD models. Chem. Eng. Equip., 40, 8-12 (in Polish).
  • Suchecki W., Alabrudziński S., 2003. A metod of correcting flow velocity maps in digital particle image velocimetry, Chem. Eng. Equip., 42 (34), 14-20 (in Polish).
  • Suchecki W., 2006. Study of fluid motion in the tank apparatus equipped with a rotating disc, Chem. Eng. Equip. 45, 228-229 (in Polish).
  • Suchecki W., 2007. Visualisation of rotary liquid flows using optical tomography. Zeszyt Monograficzny Politechniki Gdańskiej, 4, Gdańsk, 23-32 (in Polish).
  • Suchecki W., 2008. Study of suspension flow by segment crystallizer model, In: Suchecki W. (Ed.), Wybrane zagadnienia przepływu płynów i wymiany ciepła. Oficyna Wydawnicza Politechniki Warszawskiej, Warsaw, 23-57 (in Polish).
  • Von Kármán T., 1921. Über laminare und turbulente Reibung. J. Appl. Math. Mech., 1, 233-252. DOI: 10.1002/zamm.19210010401.[Crossref]
  • Warn-Varnas A., Fowlis W.W., Piasek S., Lee S.M., 1978. Numerical solutions and laser-Doppler measurements of spin-up. J. Fluid Mech., 85, 609-639. DOI: 10.1017/S0022112078000828.[Crossref]
  • Westerweel J. 1993. Digital particle image velocimetry - theory and application, Delft, Delft University Press.
Typ dokumentu
Bibliografia
Identyfikatory
Identyfikator YADDA
bwmeta1.element.-psjd-doi-10_2478_cpe-2014-0001
JavaScript jest wyłączony w Twojej przeglądarce internetowej. Włącz go, a następnie odśwież stronę, aby móc w pełni z niej korzystać.