Analytical modeling and validation of electrostatic sensors in metallic pipelines

Electrostatic sensors have been verified and applied in various industrial scenarios as a key means to detect the flow parameters of materials in pneumatic conveying pipes. However, the signal response information of electrostatic sensors caused by charged particles has long relied on numerical simulations with finite element tools, and there is a lack of analytical models that can quantitatively characterize them. In this paper, the electrostatic sensor and the metal pipe are considered as a whole to simplify the boundary conditions, and Poisson’s equation is solved based on the separation of variables method. The analytical expression of the three-dimensional potential distribution in the pipe is derived, and then the mathematical model between the charged particles and the sensor signal response is established. In order to verify the validity of the model, the finite element simulation results were used as a control to investigate the influence trend of the electrode width and angle on the accuracy of the model, and the results show that the maximum relative error between the analytical model and the simulated values is 4.05 %. In addition, the analytical model is experimentally verified by building a particle charge measurement system, which shows that the maximum relative error between the analytical model and the actual sensor is 14.64 %. The research content of this paper provides important theoretical support for the design and optimization of electrostatic sensors.