Implementation of Linear Stability Theory on Hollow Cone-shaped Liquid Sheet

  • Hadiseh Karimaei
    Affiliation

    Department of Astronautics Systems, Aerospace Research Institute, Ministry of Science, Research and Technology, Mahestan street, 14668-834 Tehran, Iran

  • Ramin Ghorbani
    Affiliation

    Energy, Water and Environment Research Lab, Department of Mechanical engineering, Iran University of Science and Technology, P. O. B. 16765-163, 16846-13114 Tehran, Narmak, Iran

  • Seyed Mostafa Hosseinalipour
    Affiliation

    Energy, Water and Environment Research Lab, Department of Mechanical engineering, Iran University of Science and Technology, P. O. B. 16765-163, 16846-13114 Tehran, Narmak, Iran

Abstract

Surface instability of a swirling liquid sheet emanating from a centrifugal injector in presence of external and internal gas flows is studied in this paper. A three-dimensional flow for the liquid sheet and two-dimensional flows for external and internal gas flows are considered. The set of equations involved in this analysis differs from the earlier analyzes. In previous studies, a cylindrical liquid sheet has been considered to implement the linear theory but in this study, the linear stability theory is implemented on a cone-shaped liquid sheet for different cone angles. Actually more over than axial and tangential movements, the radial movements of liquid sheet and gas flows are considered in the present model. Due to complexity of the derived governing equations, semi-analytical and numerical methods were applied to solve them. The case study is oxidizer injector of rocket engines. Implementation of linear stability theory on a hollow cone-shaped liquid sheet better can predict instability phenomenon than the general linear stability analysis for this type of liquid sheets. The results show very close agreement with available experimental data.

Keywords: cone-shaped liquid sheet, linear stability theory, primary breakup, wave growing rate, wave number
Published online
2020-07-07
How to Cite
Karimaei, H., Ghorbani, R., Hosseinalipour, S. M. “Implementation of Linear Stability Theory on Hollow Cone-shaped Liquid Sheet”, Periodica Polytechnica Mechanical Engineering, 64(3), pp. 179-188, 2020. https://doi.org/10.3311/PPme.11727
Section
Articles