Pulsating hydrodynamic instability and thermal coupling in an extended Landau/Levich model of liquid-propellant combustion. 2. Viscous analysis Page: 4 of 35
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Printed January 2000
PULSATING HYDRODYNAMIC INSTABILITY AND THERMAL COUPLING
IN AN EXTENDED LANDAU/LEVICH MODEL OF
LIQUID-PROPELLANT COMBUSTION - II. VISCOUS ANALYSIS
STEPHEN B. MARGOLIS*t
Sandia National Laboratories, Livermore, California 94551-0969
A pulsating form of hydrodynamic instability has recently been shown to arise during liquid-
propellant deflagration in those parameter regimes where the pressure-dependent burning rate
is characterized by a negative pressure sensitivity. This type of instability can coexist with the
classical cellular, or Landau, form of hydrodynamic instability, with the occurrence of either de-
pendent on whether the pressure sensitivity is sufficiently large or small in magnitude. For the
inviscid problem, it has been shown that when the burning rate is realistically allowed to depend
on temperature as well as pressure, that sufficiently large values of the temperature sensitivity rel-
ative to the pressure sensitivity causes the pulsating form of hydrodynamic instability to become
dominant. In that regime, steady, planar burning becomes intrinsically unstable to pulsating dis-
turbances whose wavenumbers are sufficiently small. In the present work, this analysis is extended
to the fully viscous case, where it is shown that although viscosity is stabilizing for intermediate
and larger wavenumber perturbations, the intrinsic pulsating instability for small wavenumbers
remains. Under these conditions, liquid-propellant combustion is predicted to be characterized by
large unsteady cells along the liquid/gas interface.
*Principal Member of Technical Staff, Combustion Research Facility/MS email@example.com.
tThis work was supported by the U.S. Department of Energy under contract DE-AC04-94AL85000
and by the NASA Microgravity Science Research Program under contract C-32031-E.
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Margolis, Stephen B. Pulsating hydrodynamic instability and thermal coupling in an extended Landau/Levich model of liquid-propellant combustion. 2. Viscous analysis, report, January 1, 2000; Albuquerque, New Mexico. (https://digital.library.unt.edu/ark:/67531/metadc709733/m1/4/: accessed April 19, 2019), University of North Texas Libraries, Digital Library, https://digital.library.unt.edu; crediting UNT Libraries Government Documents Department.