Hydrodynamic instability in an extended Landau/Levich model of liquid-propellant combustion at normal and reduced gravity

Journal Article · Fri May 01 04:00:00 EDT 1998 · Combustion and Flame

DOI:https://doi.org/10.1016/S0010-2180(97)00221-6· OSTI ID:619607

Margolis, S B ^[1]

---

1. Sandia National Labs., Livermore, CA (United States). Combustion Research Facility

The 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. 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.

• Research Organization: Sandia National Laboratory
• Sponsoring Organization: USDOE, Washington, DC (United States); National Aeronautics and Space Administration, Washington, DC (United States)
• DOE Contract Number: AC04-94AL85000
• OSTI ID: 619607
• Journal Information: Combustion and Flame, Journal Name: Combustion and Flame Journal Issue: 3 Vol. 113; ISSN CBFMAO; ISSN 0010-2180
• Country of Publication: United States
• Language: English

Related Subjects

40 CHEMISTRY
45 MILITARY TECHNOLOGY, WEAPONRY, AND NATIONAL DEFENSE
AMMONIUM NITRATES
COMBUSTION KINETICS
FLAME PROPAGATION
GRAVITATION
LIQUID FUELS
MATHEMATICAL MODELS
PARAMETRIC ANALYSIS
SURFACE TENSION
VISCOSITY