Predicting phase shift effects for vibrating fluid-conveying pipes due to Coriolis forces and fluid pulsation

Knowing the influence of fluid flow perturbations on the dynamic behavior of fluid-conveying pipes is of relevance, e.g., when exploiting flow-induced oscillations of pipes to determine the fluids mass flow or density, as done with Coriolis flow meters (CFM). This could be used in the attempts to improve accuracy, precision, and robustness of CFMs. A simple mathematical model of a fluid-conveying pipe is formulated and the effect of pulsating fluid flow is analyzed using a multiple time scaling perturbation analysis. The results are simple analytical predictions for the transverse pipe displacement and approximate axial shift in vibration phase. The analytical predictions are tested against pure numerical solution using representative examples, showing good agreement. Fluid pulsations are predicted not to influence CFM accuracy, since proper signal filtering is seen to allow the determination of the correct mean phase shift. Large amplitude motions, which could influence CFM robustness, do not appear to be induced by the investigated fluid pulsation. Pulsating fluid of the combination resonance type could, however, influence CFMs robustness, if induced pipe motions go unnoticed and uncontrolled during CFM operation by feedback control. The analytical predictions offer an immediate insight into how fluid pulsation affects phase shift, which is a quantity measured by CFMs to estimate the mass flow, and lead to hypotheses for more complex geometries, i.e. industrial CFMs. The validity of these hypotheses is suggested to be tested using laboratory experiments, or detailed computational models taking fluid-structure interaction into account.