Attenuation analysis of hydraulic transients with laminar-turbulent flow alternations

An improved compound mathematical model is established to simulate the attenuation of hydraulic transients with laminar-turbulent alternations, which usually occur when the pipeline flow velocity fluctuates near the critical velocity. The laminar friction resistance and the turbulent friction resistance are considered respectively in this model by applying different resistance schemes to the characteristics method of fluid transient analysis. The hydraulic transients of the valve closing process are simulated using the model. A more reasonable attenuation of hydraulic transients is obtained. The accurate attenuation is more distinct than that obtained from the traditional mathematical model. The research shows that the hydraulic transient is a type of energy waves, and its attenuation is caused by the friction resistance. The laminar friction resistance is more important than the turbulent friction resistance if the flow velocity is smaller than the critical velocity. Otherwise the turbulent friction resistance is more important. The laminar friction resistance is important in the attenuation of hydraulic transients for the closing process. Thus, it is significant to consider the different resistances separately to obtain more accurate attenuation of hydraulic transients.