Numerical Simulation Study On Inversion Modeling Of Complex Pipeline Leakage Based On Adjoint Equation

With the development of society,the demand of water supply pipe network is increasing.In order to find,locate,repair the leakage and eliminate the potential danger caused by water leakage in time,this paper puts forward a direction finding method based on the adjoint equation in order to find,locate,repair and eliminate the potential danger caused by water leakage.In order to determine the leakage source of pipe network leakage,this paper modeling and numerical simulation of the pipeline leakage process,concretely subsoil the forward pressure transport model,introduce the objective function,and combine the adjoint theory with the sensitivity analysis method to deduce the forward adjoint equation.The sensitivity function is guided by the pressure function and the adjoint operator is introduced.The inverse adjoint equation of the transient flow field is derived,and the MATLAB software is used to verify the adjoint model,which proves that it can be used to detect the leakage of the pipe network.Based on the characteristics of the open source computational fluid dynamics software OpenFOAM and the flow characteristics of the pipe network,this paper establishes a numerical simulation model of a complex pipe network based on the adjoint equation,taking into account the different inlet pressure and the demand of the user,and the bubble caused by turbulence intensity or pressure drop.The effect of the phenomenon on the simulated parameters is simulated,and the pressure distribution near the whole pipe network and the leakage hole in different operating conditions is simulated,and the instantaneous pressure changes under different working conditions are monitored.Two new time delay processing is carried out on the pressure waveform diagram of different monitoring points,and the correlation analysis is carried out to judge the correlation and get the pressure.The time difference between force and wave transmitted to two measuring points is determined,and then several locations of leakage can be determined.On this basis,the exact location of leakage is determined by the way of global search.The simulated leak location accuracy is compared with different leak diameter and different inlet pressure.The result shows that the accuracy is between 92%-96%.In this paper,the iterative time needed for the single SIMPLE,PISO and the PISO algorithm added to the adjoint equation is compared in different calculation steps.The results show that the calculation speed of the PISO algorithm combined with the adjoint equation is obviously superior to the single SIMPLE and PISO algorithm,which proves the superiority of the adjoint square method.In practical application,the simulated model can be set up according to the actual layout of the pipe network,and the leakage detection and location of the complex pipe network with different layout can be completed by using the verified numerical simulation system.