Abstract

Application of the Self-Similar Solutions for the Analysis of Nonlinear Fluctuations in the Thermoacoustic Devices

Y.M.Tichomirov (Krylov Shipbuilding Research Institute, St.Petersburg, Russia)

e-mail: ksri@pop3.rcom.ru

Theoretical and the experimental investigations of the thermoacoustic devices (prime movers and refrigerators) is carried out in many countries, since the appearance of the works Rott, Swif etc. The great attention last years is given to the calculations of nonlinear acoustic self- oscillations, which are established after the first modes of operations of these devices. Usually, the general solution is derived in the form of combining of the several solutions for the different areas inside the cases of the device. This approach essentially simplifies reception of the solutions, however does not enable correctly to estimate the tendencies of development of nonlinear oscillations with the large amplitudes. A good basis for elimination of these lacks is the one-dimensional model of the thermoacoustic oscillations, offered recently by Watanabe, Prosperetti etc. The authors of this theory have presented the solutions derived by numerical methods and a method of decomposition on small time scale parameter and have compared them to experimental data. It is possible also to show, that for one-dimensional model there is a class of the self-similar solutions, which can be used for deriving of the general solution. These aspects of the one-dimensional theory will be discussed in the paper.

Section : 7