Effects of structural-fluid coupling uncertainty on the dynamic behavior of nominally straight and uniform pipes conveying fluid: Modeling and numerical study

This investigation is focused on understanding and modeling the effects of specific structural uncertainties in nearly-straight and uniform pipes conveying fluid on the dynamic response and stability of these pipes. The structural uncertainties of interest here are those that affect directly the fluid flow and its feedback on the structural response, e.g., uncertainties on/variations of the inner cross-section and curvature of the pipe. Owing to the complexity of introducing such uncertainties directly in finite element models, it is desired to proceed directly at the level of modal models by randomizing simultaneously the appropriate mass, stiffness, and damping matrices. The maximum entropy framework is adopted to carry out the stochastic modeling of these matrices with appropriate symmetry constraints guaranteeing that the nature, e.g., divergence or flutter, of the bifurcation is preserved when introducing uncertainty. To support the formulation of this stochastic reduced order model (ROM), a series of finite element computations are first carried out for pipes with straight centerline but inner radius varying randomly along the pipe. The results of this numerical discovery effort demonstrate that the dominant effects originate from the variations of the exit flow velocity, induced by the change in inner cross-section at the pipe end, with the uncertainty on the cross-section at other locations playing a secondary role. Relying on these observations, the stochastic reduced order model is constructed to model separately the uncertainty in inner cross-section at the pipe end and at other locations. Then, the fluid related mass, damping, and stiffness matrices of this stochastic ROM are all determined from a single random matrix and one additional random variable. The predictions from this stochastic ROM are found to closely match the corresponding results obtained with the randomized finite element model. It is finally argued that this stochastic ROM also accounts for the small effects due to uncertainty in pipe curvature.