Influência do fator de atrito com dependência da freqüência na simulação de transientes em oleodutos - Tepedino, Alexandre Figueira (2007)
Unsteady liquid flow in pipelines is usually described by using onedimensional models and, in a procedure referred to as quasi-steady approximation, friction losses are estimated by formulae derived for steady state flow conditions. The assumption is that the friction loss during transient flow conditions can be approximated by the friction loss obtained for steady flow, with an average velocity equal to the instantaneous transient velocity. However, during unsteady flow conditions the velocity profile can be considerably different from the steady flow. The shear stress at the pipe wall and the mean velocity are not in phase. Therefore, friction losses computed according to the quasi-steady approximation are inaccurate, especially in fast transients. To overcome this, the concept of frequency-dependent friction was proposed, including the time history of the mean flow velocity and acceleration, resulting in better correlation to experimental data. On-line and off-line transient simulations performed for liquid pipelines are traditionally carried out by employing the quasi-steady approximation. Therefore, questions arise as to the suitability of this simple friction model to some real world applications, such as the specification of surge relief valves and the performance of real-time transient model for leak detection and leak location systems. This work presents an investigation of situations in which the use of a frequency-dependent friction model could bring additional improvement for the petroleum and products pipeline simulation. To do so, through computer simulations, the predictions of both quasi-steady and unsteady friction models, for short and long lines, operating under a range of Reynolds numbers, are compared and the significance of the friction model is evaluated.