192 / 2021-03-31 20:42:01

Vibration characteristics of the pipe-in-pipe system subjected to two-phase internal flow by means of Green’s function

Pipe-in-pipe system;,Two-phase internal flow,The Green's functions;,The Closed-form solutions;

This paper studies the vibration characteristics of a spinning pipe-in-pipe system subjected to two-phase internal flow by using the Green's functions method, and affected by the combined effects of several parameters including the spinning motion, gas volume fraction and two-phase flow velocity. On the base of the Hamilton's variation principle, the dynamic equations of the spinning pipe-in-pipe system subjected to two-phase internal flow are established, which contain the spring-damping coupling parameters, the spinning angular velocity, the gyroscope coupling term and the two- phase flow velocity coupling term. The classic Green's function method is applied to the spinning PIP system, and four Green's function solutions for the transverse forces vibration of the inner and outer pipes are obtained. With the help of these four Green's function solutions and the first, second, and third derivatives, the closed-form frequency equation of the spinning PIP system is creatively obtained. Substituting the boundary conditions into the frequency equation of the spinning PIP system, and corresponding simplifications, the frequency equation of the model corresponding to the boundary conditions is obtained. The frequency equation of the PIP system can be decoupled to obtain the frequency equation of the single-pipe model, the spinning single-pipe model, and the non-spinning PIP system. The decoupled single-pipe model and spinning single-pipe model are used to calculate the corresponding frequency, which verifies the accuracy of the method in this paper by comparison with other literature. In the numerical results discussion part, taking cantilever pipes and simply supported pipes as examples, the effects of spring stiffness, damping coefficient, and gas volume fraction on the frequency characteristics of the non-spinning PIP system are studied. Next, the influence of gas volume fraction, flow velocity, and axial force on the frequency characteristics of the spinning single-pipe model is analyzed. In addition, the relationship between the first-order and second-order natural frequencies and spinning speed of the spinning PIP system under several simple boundary conditions are calculated and analyzed. The research in this paper clearly shows the influence of various parameters on the frequency characteristics of the system model, and the obtained closed-form frequency equation can be directly adopted by researchers.