On pulsating and cellular forms of hydrodynamic instability in liquid-propellant combustion

Technical Report · Sat Nov 01 04:00:00 EST 1997

DOI:https://doi.org/10.2172/563184· OSTI ID:563184

Margolis, S B ^[1]

---

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

An extended Landau/Levich model of liquid-propellant combustion, one that allows for a local dependence of the burning rate on the (gas) pressure at the liquid/gas interface, exhibits not only the classical hydrodynamic cellular instability attributed to Landau, but also a pulsating hydrodynamic instability associated with sufficiently negative pressure sensitivities. Exploiting the realistic limit of small values of the gas-to-liquid density ratio {rho}, analytical formulas for both neutral stability boundaries may be obtained by expanding all quantities in appropriate powers of {rho} in each of three distinguished wavenumber regimes. In particular, composite analytical expressions are derived for the neutral stability boundaries A{sub p}(k), where A{sub p} is the pressure sensitivity of the burning rate and k is the wavenumber of the disturbance. For the cellular boundary, the results demonstrate explicitly the stabilizing effect of gravity on long-wave disturbances, the stabilizing effect of viscosity and surface tension on short-wave perturbations, and the instability associated with intermediate wavenumbers for negative values of A{sub p}, which is characteristic of many hydroxylammonium nitrate-based liquid propellants over certain pressure ranges. In contrast, the pulsating hydrodynamic stability boundary is insensitive to gravitational and surface-tension effects, but is more sensitive to the effects of liquid viscosity since, for typical nonzero values of the latter, the pulsating boundary decreases to larger negative values of A{sub p} as k increases through O(1) values.

• 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: 563184
• Report Number(s): SAND--98-8403; ON: DE98050978; CNN: Contract C-32031-E
• Country of Publication: United States
• Language: English

Related Subjects

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