### ASA 128th Meeting - Austin, Texas - 1994 Nov 28 .. Dec 02

## 1aPA3. A nonlinear analysis of a simple thermoacoustic system.

**Ronald E. Kumon
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*Appl. Res. Labs., Univ. Texas at Austin, 10000 Burnet Rd., Austin, TX
78713
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A simple thermoacoustic system was studied to try to better understand the
interaction between the temperature, pressure, and velocity modes of the
system. The system considered was a one-dimensional ``tube,'' closed and
isothermal at both ends and filled with a helium gas. Initially, the gas is
static but with a sinusoidal temperature distribution. To obtain a simplified
model of the system, a Galerkin-type method was applied to the full
hydrodynamic equations in one spatial dimension and the ideal gas law equation
of state. By substituting highly truncated sine and cosine series in the
spatial variable with time-dependent amplitudes into the aforementioned PDEs,
the model was reduced to a set of coupled nonlinear ODEs. First, these
equations were linearized and examined for series expansions with different
number of terms. Next, the nonlinear ODEs were studied. Finally, these results
were compared with direct finite-difference calculations using MacCormack's
method to integrate the full hydrodynamic equations.