Nonlinear Pressure Wave Analysis by Concentrated Mass Model (4th Report, Modeling of Elastic Pipe Element)

Abstract

A pressure wave propagating in a tube often changes to a shock wave because of the nonlinear effects in the propagation medium. The purpose of this study is to establish a practical analytical model of this phenomenon. In previous reports, a concentrated mass model was proposed to analyze nonlinear pressure wave phenomena in a rigid straight cylindrical pipe. In this paper, we apply the model to an elastic pipe. The model of the elastic pipe consists of masses, nonlinear connecting springs, base support dampers, base support springs, and connecting dampers. The effect that the cross-sectional area of the elastic pipe changes is taken into account through the nonlinear connecting spring. To confirm the validity of the proposed elastic pipe model, we perform experiments on a silicone pipe, and the experimental results are compared with the numerical results obtained by the concentrated mass model. The numerical computational results agree well with the experimental results. Therefore, it is concluded that the proposed elastic pipe model is valid for the numerical analysis of nonlinear pressure wave problems in an elastic pipe.

Nonlinear Pressure Wave Analysis by Concentrated Mass Model

“…Figure 14 shows time series of the waveform of dp at the closed end of the main pipe at 85.3 Hz, which is the resonance frequency. A shock wave is generated in the experimental result, and this phenomenon is simulated by the concentrated mass model, as we have discussed in previous reports (3), (4) . Figure 15 shows the frequency responses at the closed ends of the main pipe and the branch pipe as the distance of the piston to the branch pipe, 0 l , is varied.…”

“…When the amplitude of the pressure boundary condition in Fig. 6 is large, a shock wave is generated because of nonlinear effects (3), (4) . We investigate the decrease of pressure amplitude due to the branch pipe when the shock wave appears.…”

“…We use the model shown in Fig.6 and the parameters in Table 3 is set to a large value to generate the shock wave. In addition, the viscosity b µ for the base support damper is the real value of air, but the viscosity c µ for the connecting damper is larger in order to suppress the generation of the numerical vibrations (3), (4) . The nonlinear damper in Section 2.3 is neglected to clarify the effect of the branch pipe on the pressure amplitude.…”

“…A pressure wave propagating in a tube often changes to a shock wave because of the nonlinear effect of fluid (1), (2) . In previous reports (3), (4) , we examined one-dimensional nonlinear pressure waves, and proposed a concentrated mass model to analyze this phenomenon. Pressure waves generated in a sound tube and in a plane-wave tube were analyzed numerically by the proposed model to confirm the validity of the model.…”