A Wall Friction Model for One-Dimensional Unsteady Turbulent Pipe Flows

A phenomenological model is proposed in this paper for simulating the effect of wall friction in turbulent pipe flows. The flow in this model is divided into two regions: wall region and core region. The turbulent flow in the core region obeys the law of the wake, while the flow in the wall region follows the law of the wall. In the overlapping region they interact and behave like a dynamic system of two degrees of freedom. The model can predict the variation of friction coefficient and phase shift.

The model is formulated in a simple form, and can be easily integrated into one-dimensional flow calculations. The model has been validated against published measured data, including a pulsating flow without flow reversal and a reciprocating flow with flow reversal. The model predictions have shown good agreement with measurements.

The model has been used to simulate the gas flows in the internal combustion engines, including a single-cylinder motored engine and a four-cylinder firing engine. The comparison shows that the model can predict the variation of wall friction with mean flow and that the pressure waveforms calculated from this dynamic model lead by 5 degrees in crank angle compared with the results calculated from constant friction coefficient. The model provides a useful predictive capability for analyzing turbulent pipe flows.