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Hydrodynamic Instability in an Extended Landau/Levich Model of Liquid-Propellant Combustion at Normal and Reduced GravityThe classical Landau/Levich models of liquid-propellant combustion, despite their relative simplicity, serve as seminal examples that correctly describe the onset of hydrodynamic instability in reactive systems. Recently, these two separate models have been combined and extended to account for a dynamic dependence, absent in the original formulations, of the local burning rate on the local pressure and temperature fields. The resulting model admits an extremely rich variety of both hydrodynamic and reactive/diffusive instabilities that can be analyzed either numerically or analytically in various limiting parameter regimes. In the present work, a formal asymptotic analysis, based on the realistic smallness of the gas-to-liquid density ratio, is developed to investigate the combined effects of gravity and other parameters on the hydrodynamic instability of the propagating liquid/gas interface. In particular, an analytical expression is derived for the neutral stability boundary A(sub p)(k), where A(sub p) is the pressure sensitivity of the burning rate and k is the wavenumber of the disturbance. The results demonstrate explicitly the stabilizing effect of gravity on long-wave disturbances, the stabilizing effect of viscosity (both liquid and gas) and surface tension on short-wave perturbations, and the instability associated with intermediate wavenumbers for critical negative values of A(sub p). In the limiting case of weak gravity, it is shown that hydrodynamic instability in liquid-propellant combustion is a long-wave instability phenomenon, whereas at normal gravity, this instability is first manifested through O(1) wavenumber disturbances. It is also demonstrated that, in general, surface tension and the viscosity of both the liquid and gas phases each produce comparable stabilizing effects in the large-wavenumber regime, thereby providing important modifications to previous analyses in which one or more of these effects were neglected.
Document ID
20020034902
Acquisition Source
Glenn Research Center
Document Type
Reprint (Version printed in journal)
Authors
Margolis, Stephen B.
(Sandia National Labs. Livermore, CA United States)
Date Acquired
August 20, 2013
Publication Date
May 1, 1998
Publication Information
Publication: Combustion and Flame
Publisher: Elsevier Science, Inc.
Volume: 113
Issue: 3
ISSN: 0010-2180
Subject Category
Propellants And Fuels
Funding Number(s)
CONTRACT_GRANT: NASA Order C-32031-E
CONTRACT_GRANT: RTOP 101-15-05
CONTRACT_GRANT: DE-AC04-94AL-85000
Distribution Limits
Public
Copyright
Other

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