Symmetry-Guided Numerical Simulation of Viscoelastic Pipe Leakage Based on Transient Inverse Problem Analysis

In this study, numerical simulations were performed, and leaks in viscoelastic pipelines were detected. Based on the transient flow equations derived from the continuity and momentum equations, the Kelvin–Voigt model was used to describe the viscoelastic constitutive relationship and derive the strain equation, further establishing a one-dimensional transient flow model for viscoelastic pipelines. A frequency-domain analysis of the transient flow was performed by deriving the Fourier transform and transfer matrix. An inverse problem analysis method for transient flow leak detection was proposed to identify the leak location and rate by minimizing the objective function. To verify the effectiveness of the proposed model, an experimental platform was built, and the pressure head frequency-domain data under working conditions of no leak, experimental leak, and simulated leak were compared. The results showed that the experimental data were consistent with the simulated data under leakage conditions, thus proving that the model was accurate and reliable. Under leak-free conditions, the frequency-domain characteristics of transient pressure waves exhibit significant symmetrical features, whereas when a leak exists in the pipeline, the leak point acts as a localized non-uniform disturbance source, disrupting the symmetry of the frequency-domain characteristics. Moreover, the leak point can be determined by the difference in the peak heights between the no-leak and leak conditions, and the leak parameters can be accurately identified using the inverse problem method.