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

Technical Report · Tue Apr 01 04:00:00 EST 1997

OSTI ID:495694

Margolis, S B ^[1]

---

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

The classical Landau/Levich models of liquid-propellant combustion serves 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 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 parameters 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 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 long-wavenumber regime, thereby providing important modifications to previous analyses in which one or more of these effects were neglected.

• Research Organization: Sandia National Labs., Livermore, CA (United States)
• Sponsoring Organization: USDOE Assistant Secretary for Energy Efficiency and Renewable Energy, Washington, DC (United States); National Aeronautics and Space Administration, Washington, DC (United States)
• DOE Contract Number: AC04-94AL85000
• OSTI ID: 495694
• Report Number(s): SAND--97-8501; ON: DE97007009; CNN: Contract C-32031-E
• Country of Publication: United States
• Language: English

Related Subjects

40 CHEMISTRY
AMMONIUM NITRATES
COMBUSTION INSTABILITY
COMBUSTION KINETICS
GRAVITATION
MATHEMATICAL MODELS
SURFACE TENSION
VISCOSITY