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ROCKET PROPULSION | COMBUSTION INSTABILITY
Historic dif culties in modeling by Sigman and Zinn3 by solving the COMSOL nite element framework to
and predicting combustion instability acoustic velocity potential equation model the steady ow- eld parameters
have reduced most instances of rocket (AVPE) formulated by perturbing the of a generic liquid engine using the
systems experiencing instability to a Euler equations4. High Mach Number Laminar Flow
costly x through testing (see Figure 1), physics interface, which makes use of
or to scrapping of the system entirely. Determining eigenvalues of the the fully compressible Navier-Stokes
AVPE, where ψ is the complex acoustic equations for an ideal gas together
“A more complete potential, λ the complex eigenvalues, with conservation of energy and
c the speed of sound, and M the mass equations.
depiction of Mach vector,
combustion instability In order to account for the injection
oscillations is is considerably more complex than the of hot gas due to the burning
achieved when a traditionally used pressure-based propellant, the injector face plate is
global energy-based wave equation, modeled with a uniform inward ow of
assessment is used.” combusted propellant gas (see Figure 2).
and requires numerical approximations All other solid boundaries are modeled
During the early development of of the chamber ow eld and with the slip boundary condition, and
rocket propulsion technology scientists eigenvalues. the exit plane is modeled with the
and engineers were cued to the hybrid out ow condition, which means
underlying physics at play through the ð MODELING CHAMBER that both subsonic and supersonic ows
measurement of vibrating test stands, GAS DYNAMICS are supported.
observation of uctuating exhaust
plumes, and, most notably, the audible The latest theoretical models for Results from the mean ow analysis
tones accompanying instabilities. These oscillatory disturbances in high-speed are reviewed to ensure a valid and
observations lead the pioneers of converged solution. Mean ow
combustion instability research to focus ows require a precise determination parameters such as pressure, density,
their modeling efforts on the acoustic of the chamber acoustic eigenmodes. velocity, and speed of sound are needed
waves inside combustion chambers. But rst, a simulation of the mean ow to model the AVPE. The values of the
properties of the combustion chamber mean ow in the converging section of
This focus on acoustics is quite logical must be performed. the nozzle, near the sonic choke plane,
given that the measured frequency are of considerable interest. The sonic
of oscillation often closely matches COMSOL Multiphysics® software plane, where the Mach number is equal
the normal acoustic modes of the provides a numerical platform for to 1, creates an acoustic barrier in the
combustion chamber. But this narrow conveniently and accurately simulating
focus misses contributions made by ow. In order to create an accurate
rotational and thermal waves that are a FIGURE 1. Pressure trace of a stable (red) geometry for the acoustic analysis, the
direct result of, or closely coupled with, and unstable (blue) solid rocket motor1. sonic plane (pictured in magenta in
the acoustic wave. A more complete Figure 3) is extracted from the mean
depiction of combustion instability both the chamber gas dynamics and
oscillations is achieved when a global internal acoustics. This nite element ow analysis.
energy-based assessment is used. software package provides many
prede ned physics along with a ð MODELING CHAMBER
Recent advances in energy-based generalized mathematics interface. ACOUSTICS
modeling of combustion instabilities
require an accurate determination The present study employs the The Coef cient Form PDE (Partial
of acoustic frequencies and mode Differential Equation) mathematics
shapes. Of particular interest are the interface of COMSOL Multiphysics
acoustic mean ow interactions within is used to determine the complex
the converging section of a rocket eigenvalues of the AVPE. Mean ow
nozzle, where gradients of pressure, terms in the AVPE are supplied by the
density, and velocity become large. The solution from the mean ow analysis.
expulsion of unsteady energy through Gas dynamics within the combustion
the nozzle of a rocket is identi ed as chamber play a key role in de ning the
the predominate source of acoustic boundary conditions for the acoustic
damping for most rocket systems. analysis. Within the converging and
diverging section of the rocket nozzle,
Recently, an approach to address gradients of chamber pressure, velocity,
nozzle damping with mean ow effects and density grow theoretically in nite
was implemented by French2. This new at the sonic plane where the Mach
approach extends the work originated number is equal to 1. Downstream of
the sonic plane, acoustic disturbances
are convected with the mean ow at
speeds greater than the speed of sound.
Originally published in the December 2015 edition of NASA Tech Briefs magazine. COMSOL.COM 9
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