Page 10 - COMSOL_News_2016

P. 10

```
COMBUSTION INSTABILITY | ROCKET PROPULSION
FIGURE 2. Simulated liquid engine geometry with boundary conditions.
Mach 1 surface FIGURE 5. Comparison of the rst
tangential eigenmode calculated using the
FIGURE 3. Velocity streamlines plotted over chamber pressure. The Mach 1 surface is classic homogeneous wave equation (left),
plotted in magenta. and the AVPE (right) of a half period (T)
of oscillation.
mode, with the imaginary
conditions, can now be more accurately
part de ning the frequency modeled before testing.
of oscillation. The complex ð CONTINUED WORK
eigenvectors represent the A more complete depiction of
combustion instability includes
spatial amplitude and phasing rotational oscillations and thermal
oscillations in conjunction with chamber
of the acoustic wave. acoustics. Rotational oscillations
occur as a direct result of the acoustic
Comparing the acoustic oscillation, where thermal waves can
also be present in the absence of
mode shapes derived using acoustic uctuation. Continued work
using COMSOL Multiphysics will focus
the classic homogeneous on solving the viscous rotational wave
that accompanies all
FIGURE 4. Acoustic analysis geometry with boundary wave equation (Helmholtz
conditions. equation) to those derived acoustic oscillations. v
using the AVPE demonstrates
This article was written by Sean R.
the bene ts of higher- Fischbach, Marshall Space Flight Center/
Jacobs ESSSA Group, MSFC, Huntsville, AL.
delity models that correctly
REFERENCES
This condition prevents disturbances represent the underlying physics (see
1. F. S. Bloomshield, Lessons Learned in Solid
downstream of the sonic plane from Figure 5). Inclusion of mean ow terms Rocket Combustion Instability, 43rd AIAA
Joint Propulsion Conference, AIAA-2007-
propagating back upstream. The in the AVPE accurately models the phase 5803, Cincinnati, OH, July 2007.
2. J. C. French, Nozzle Acoustic Dynamics
diverging section of the nozzle is shift caused by the steady gas ow. and Stability Modeling, Vol. 27, Journal of
Propulsion and Power, 2011.
acoustically silent and does not affect Phasing is extremely important since 3. R. K. Sigman and B. T. Zinn, A Finite
Element Approach for Predicting Nozzle
the chamber acoustics. The simulation combustion instability models make use Admittances, Vol. 88, Journal of Sound and
Vibration, 1983, pp. 117-131.
geometry is truncated at the nozzle of temporal and spatial integration of 4. L. M. B. C. Campos, On 36 Forms of the
Acoustic Wave Equation in Potential Flows
sonic line, where a zero ux boundary the acoustic eigenvectors. and Inhomogeneous Media, Vol. 60, Applied
Mechanics Reviews, 2007, pp. 149-171.
condition is self-satisfying (see Figure 4). Utilizing COMSOL Multiphysics to
The remaining boundaries are modeled simulate the rocket gas dynamics and
with a zero ux boundary condition, acoustic eigenmodes provides a more
assuming zero acoustic absorption on accurate mode shape over previous
all surfaces. techniques. The higher- delity acoustic
The eigenvalue analysis produces representation is easily incorporated
complex eigenmodes and eigenvalues into combustion instability models to
representing each acoustic mode and give rocket designers and engineers
its complex conjugate. The real part greater predictive capabilities. The
of the complex eigenvalue represents inclusion of damping devices, such
the temporal damping of the acoustic as baf es, or changes in operating
10 COMSOL NEWS 2016
```