Influence of Frequency-Dependent Friction Modeling on the Simulation of Transient Flows in High-Pressure Flow Pipelines

Frequency-dependent friction can be an important dissipative factor for unsteady flows. In this research investigation, various popular models have been reviewed thoroughly and then applied to evaluate frequency-dependent friction in high-pressure transient flows. Three piezoresistive transducers were used to measure pressure signals along a 2 m high-pressure pipe: the first and the third signal were assumed as boundary conditions in a homemade code that is able to solve the velocity and pressure fields along the pipe. The simulation pressure data have been compared with the pressure signal measured by means of the transducer installed in the middle of the pipe. In addition, an injector model has been applied to a 2 m pipe in order to perform additional simulations in which the rail pressure time distribution and the electrical current time history to the injector are provided as boundary conditions. It has been observed that when frequency-dependent friction is taken into account, more accurate pressure results are generally obtained along the injector supply line than in the case in which the viscous stress is calculated by only taking into account the steady-state Darcy–Weisbach contribution. On the other hand, on the basis of a comparison between the obtained numerical results and experimental traces, the improvement is not related to the method by which the unsteady friction is evaluated. Therefore, the simplest frequency-dependent friction model is recommended to simulate high-pressure transient flows in pipes with a shorter aspect ratio than 800 and lower Reynolds numbers than 10⁴.