Simulation of nonlinear liquid oscillations in the pulsation apparatus of variable cross section using a one-dimensional model

摘要

The theoretical description of nonlinear liquid oscillations in pulsation bulk-capacity apparatuses has been considered. A mathematical model of liquid oscillations in a pulsation apparatus of generalized shape with elbows of variable cross sections has been constructed, and the obtained differential equations have been solved by the harmonic balance method and the Fourier expansion of the amplitude of oscillations in the levels of liquid in apparatus elbows. It has been shown that it is necessary to take into account at least four expansion term including the constant one and the phase shift at least of the first-order harmonic to obtain a satisfactory description of liquid oscillations in the considered system. Pronounced fundamental, second- and third-order superharmonic, and 1/2- and 1/3-order subharmonic system oscillations and the possibility of 2/3- and 3/2-order combined-frequency system oscillations have been revealed. The constructed model enables one to calculate the frequency of natural oscillations in pulsation apparatuses, including oscillations with greats amplitude at which their nonlinearity produced by a nonlinear character of the Mendeleev-Clapeyron equation in resilient members cannot be neglected. In combination with the calculated amplitudes of oscillations, this will provide the possibility of determining liquid velocities and passing to the calculations of other hydrodynamic parameters.