Hostname: page-component-cd9895bd7-dzt6s Total loading time: 0 Render date: 2024-12-27T13:39:09.801Z Has data issue: false hasContentIssue false
  • English
  • Français

Analysis of the melt phase of a rotating polymer disc supporting a diffusion flame

Published online by Cambridge University Press:  11 October 2011

Vedha Nayagam  and
F. A. Williams
Vedha Nayagam*
Affiliation:
National Center for Space Exploration Research, NASA Glenn Research Center, Cleveland, OH 44135, USA
F. A. Williams
Affiliation:
Department of Mechanical and Aerospace Engineering, University of California at San Diego, La Jolla, CA 92093, USA
*
†Email address for correspondence: [email protected]
Get access Rights & Permissions [Opens in a new window]

Abstract

When a laminar diffusion flame is established over a spinning, thermoplastic, polymer fuel disc in a quiescent, oxidizing environment, the polymer melts and flows radially outwards, causing some fuel to be lost and not transported to the diffusion flame. The viscosity of the liquid in the melt layer retards the radial flow, thereby determining the amount of fuel lost. The melt layer is analysed here for two limiting cases, namely one in which the liquid viscosity depends strongly on temperature, leading to an asymptotic analysis involving two zones in the liquid, and one in which the liquid viscosity is constant, independent of temperature, so that there is only one zone in the liquid. The utility of these two limits is assessed by comparing their predictions with those of full numerical integrations for poly(methyl methacrylate) (PMMA) discs burning in air at atmospheric pressure.

JFM classification

Reacting Flows: Laminar reacting flows Phase change: Solidification/melting
Type
Papers
Information
Journal of Fluid Mechanics , Volume 687 , 25 November 2011 , pp. 238 - 253
Copyright
Copyright © Cambridge University Press 2011

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

1. Asher, U., Christiansen, J. & Russell, R. D. 1981 Algorithm COLSYS: collocation software for boundary value ODE’s. ACM Trans. Math. Softw. 7, 223–229.CrossRefGoogle Scholar
2. Balakrishnan, M. 1992 An experimental analysis of the laminar burning characteristics of a rotating solid fuel disk. Master’s thesis, University of Alabama, Tascaloosa, Alabama.Google Scholar
3. Brydson, J. A. 1981 Flow Properties of Polymer Melts, 2nd edn. George Godwin.Google Scholar
4. Holcomb, J. M. & T’ien, J. S. 1996 Diffusion flame adjacent to rotating solid fuel disk in zero gravity. AIAA J. 35, 742–744.CrossRefGoogle Scholar
5. Hostler, S. R., Nayagam, V. & Williams, F. A. 2000 Melt-front instabilities during the combustion of a spinning polymer disk. In Procedings of the Technical Meeting of the Central State Section of the Combustion Institute.Google Scholar
6. von Kármán, Th. 1921 Über laminare und turbulente reibung. Z. Angew. Math. Mech. 1, 232–252.Google Scholar
7. Kashiwagi, T., Omori, A. & Nanbu, H. 1990 Effects of melt viscosity and thermal stability on polymer gasification. Combust. Flame 81, 188–201.CrossRefGoogle Scholar
8. Kim, J. S., Libby, P. A. & Williams, F. A. 1992 Influence of swirl on the structure and extinction of strained premixed flames. Part II. Strong rates of rotation. Phys. Fluids A 4 (2), 391–408.CrossRefGoogle Scholar
9. King, M. D., Nayagam, V. & Williams, F. A. 2000 Measurements of polymethyl methacrylate diffusion flames in von Karman swirling flows. Combust. Sci. Technol. 160, 151–163.CrossRefGoogle Scholar
10. Nayagam, V., Balasubramaniam, R. & Williams, F. A. 2009 Diffusion flames over a melting polymer disk in von Karman swirling flows. Combust. Flame 156, 1698–1704.CrossRefGoogle Scholar
11. Nayagam, V. & Williams, F. A. 2000a Diffusion-flame extinction for a spinning fuel disk in an oxidizing counterflow. Proc. Combust. Inst. 28, 2875–2881.Google Scholar
12. Nayagam, V. & Williams, F. A. 2000b Rotating spiral edge flames in von Kármán swirling flows. Phys. Rev. Lett. 84 (3), 479–482.CrossRefGoogle Scholar
13. Sparrow, E. M. & Gregg, J. L. 1960 Mass transfer, flow, and heat transfer about a rotating disk. ASME J. Heat Transfer 81, 294–302.CrossRefGoogle Scholar
14. Urzay, J., Nayagam, V. & Williams, F. A. 2011 Theory of the propagation dynamics of spiral edges of diffusion flames in von Kármán swirling flows. Combust. Flame 158 (2), 255–272.CrossRefGoogle Scholar
15. Wang, C. Y. 1989 Melting from a horizontal rotating disk. ASME J. Appl. Mech. 56, 47–50.CrossRefGoogle Scholar
16. Wang, C. Y. 2007 Condensation film on an inclined rotating disk. Appl. Math. Model. 31 (8), 1582–1593.CrossRefGoogle Scholar
17. Zandbergen, P. J. & Dijkstra, D. 1987 von Karman swirling flows. Annu. Rev. Fluid Mech. 19, 465–491.CrossRefGoogle Scholar