Rainer Haas, Helmut Kogler, Bernhard Manhartsgruber,
"Simulation of a Periodically Excited Nonlinear Transmission Line"
, in Andrzej Sobczyk: 5th FPNI PhD Symposium, Cracow, Poland, 1-5 July 2008, Seite(n) 418-428, 7-2008, ISBN: 978-83-7242-474-7
Simulation of a Periodically Excited Nonlinear Transmission Line
Sprache des Titels:
5th FPNI PhD Symposium, Cracow, Poland, 1-5 July 2008
In many periodically excited applications there is the problem of pressure and flow-rate oscillations, e.g. in suction pipes of pumps or in more recent applications like common-rail diesel injection systems.
These physical problems are discussed in many recent papers and books. Most of these problems can be modelled as a
linear wave propagation equation which is solved for common boundary conditions in a lot of different ways e.g.
analytical (time and frequency domain), with the method of characteristics or some combined time and frequency
domain method for nonlinear boundary conditions.
However, the linear wave propagation equation only holds for the case of a linear fluid law. In many cases this is not
true e.g. in applications where the absolute pressure is near or deeper than the atmospheric pressure or if there are
large pressure oscillations at a low pressure range.
This problem can be treated in two different ways. The first one is to perform a numerical computation of the
conservation of mass and the momentum balance combined with a staggered grid – like many authors did before.
Another approach, discussed in this paper, is to formulate one nonlinear wave equation and compute a numerical
solution of this problem.
First the nonlinear wave equation is derived from a nonlinear fluid law, the conservation of mass and the momentum balance. For numerical computation a Galerkin discretisation is performed. To ensure an efficient calculation the solution is parameterised by a Fourier series. This approach results in a large scale, nonlinear system of equations.
From these equations we obtain the solution of the periodically excited nonlinear transmission line problem.