Predicting Fluidelastic Instability in Tube Array With Potential Theory

This paper studies the possibility to use potential theory to predict fluidelastic instability critical velocity in tube bundles. Potential flow is calculated semi analytically using Laurent expansions with the addition of discrete vortices behind the tube. The only experimental criterion used in this approach is the location of vortices behind the tubes. Using the linearized unsteady Bernoulli theorem we are able to model fluid forces as added mass, damping and stiffness effects. Fluid forces include coupling terms; that is the force on another tube induced by tube acceleration, velocity and location. The tube array is then described by a mass, damping and stiffness. The fluidelastic instability critical velocity becomes the solution of a linear eigenvalue problem. This approach has been compared with several experimental values of mass, damping and stiffness measurements, as well as the critical velocity. Mass matrix is in a very good agreement with experimental values, however damping and stiffness models still need some improvement. In the end, the model is able to predict the critical velocity within 20% of experimental values. This approach does not need stiffness experimental values (stability derivative) nor time delay as the stiffness, damping and mass matrices are calculated independently. The main purpose of this work is to understand the effect of induced forces involved in the fluidelastic instability.