Numerical simulation based on a weakly compressible model in the multi-elbow pipe

The negative pressure wave method is a more important method used for pipeline leak detection and location in practical engineering applications. In this paper, a new method based on a weakly compressible model and a standard k-e turbulence model is proposed, which is used to simulate the propagation of negative pressure waves in pipelines. The purpose of the study is to capture the negative pressure wave propagation phenomenon in multi-elbow pipe leaks based on the weakly compressible method and to investigate the negative pressure wave propagation law in multi-elbow pipes. The results show that the negative pressure wave transmission phenomenon inside the leaking pipeline can be calculated by using the weakly compressible model, and the transmission law is consistent with the actual one. It was found that the propagation velocity of the negative pressure wave in the elbow was 1.4% higher than that in the straight pipe, and there was backflow in each elbow, which affected the propagation distance of the negative pressure wave at different locations in the elbow. The vortex viscosity and turbulence frequency in the axis of the elbow were 12.2% and 5.4% higher than those in the straight pipe, respectively. In addition, the high viscous force and pulsation frequency in the elbow accelerate the volume compression and expansion of the flow elements, for which the equivalent length equation of the elbow in the negative pressure wave leakage localization method is proposed to verify the applicability of the weakly compressible model. The research in this paper reveals the internal effects of the negative pressure wave method in the bend as well as provides an innovative equivalence formula for the negative pressure wave leak location method. This work will provide a more accurate method for pipeline leak detection and localization.