Abstract :
Regenerative gas cycles, including the Stirling
engine, are sealed machines using pistons within cylinders
to transfer energy from a heat source to a colder reservoir
using a gas as working substance. For the optimal design of
these cycles, we need a detailed description of gas dynamic
behavior. This contribution deals with the simulation of
cylinder spaces without internal combustion (as we find for
regenerative gas cycles). For the simulation, we suggested
a symbolic mathematics-based strategy to describe the
dynamic system behavior based on partial non-linear differential
equations for the conserved quantity. The renunciation
of numerical approximation gives the advantage
that the underlying physical mechanisms are characterized
by exact expressions and parameters. Using some
assumptions, the dynamic behavior of the gas within the
cylinder is already described by ordinary non-linear differential
equations. Depending on the selected boundary
conditions analytical solutions can be obtained for some
cases. Finally, the developed solution is based on it and
will be received as a series expansion. Additionally, for the
simulation-based optimization of the processes it is possible
to calculate directly the periodical-steady state of the
system with the help of the symbolic solution. The simulation
is suitable for fundamental theoretical investigations,
as well as for the implementation in simulation software for
different regenerative gas cycles.
