Pressure Surge Load Estimation on Pipes With Dimensional Reduction and Rayleigh Energy Method

Abstract

The pressure surge in pipes due to change in operating conditions exerts an axial load on elbows proportional to the change in momentum of fluid and unbalanced pressure forces. The response of piping structure to such load needs the full time history analysis in three dimensional spaces which is cumbersome process due to high computing memory requirements and long simulation time. In present work it has been shown that using Rayleigh energy balance for each elbow-load configuration, the system can be reduced to equivalent 1D spring mass system and the response can be estimated by solving 1D equation of motion. Then it has been recommended to simulate the response of each elbow which gives good approximation of dynamic amplification of displacement also called as Dynamic Load Factor (DLF). These dynamic load factors for each elbow can be used for the interaction of forces using static equivalent response in 3D space. This approach is pseudo static equivalent analysis where the load amplifications factors DLF are estimated from the dynamic force profile and system response in one-dimensional space. An algorithm is developed for the above explained process. Most of the engineers are using the DLF = 2 for the load estimation due to absence of method to estimate the dynamic load factor. The approach was proposed by Goodling in 1989 and still widely followed in the industry. The present paper discusses uncertainty and inaccuracy involved in performing approximate analysis and shows the significance and need of performing full force time history analysis. The proposed method shows very good agreement with the time consuming 3D full force time history results. There are also limitations for the proposed method. As the spring mass system is simulated with dimensional reduction to single frequency domain, the pipe supports and guides should be properly placed before applying the present approach. It has been shown that with proper support configuration, this simplified approach yields very good approximation of surge load on pipes with reduced time.