Impact Simulation of Process Equipment Tubes and Support Plates—A Numerical Algorithm

The occurrence of flow-induced vibration fretting wear in process equipment such as heat exchangers and steam generators accounts for the majority of the failures due to vibration. One of the parameters which plays a vital role in the prediction of tube wear rate is the impact force which occurs when the free displacements of the tube exceed the clearance in the support plates, resulting in a collision. To date the determination of these impact forces reported in the literature has been restricted to simplified mathematical models which consider only straight spans of tube with gaps. The need to consider more generalized configurations has led to the development of an analytical method which simulates the nonlinear dynamic-impact response of multi-supported tubes including U-bends and the effect of nonuniform gap clearances at the supports. The approach is incorporated into a computer code based on the finite element and displacement methods using an unconditionally stable numerical integration scheme to solve the nonlinear equations of motion. The algorithm developed includes equilibrium iteration and variable time stepping based on convergence criteria, which ensures that temporal solution errors are minimized. The direct integration of the equations enables all the frequencies (subject to the finite element mesh) to be included. This is necessary since the high-frequency response at impacting may be significant. At present, the method is being used to simulate impact between tubes and support plates in steam generators and heat exchangers in order to determine tube bundle susceptibility to fretting wear failure at the design stage or operational phase. The paper describes the analytical development of the method, verification cases, and applications to the problem of tube/support plate impacting.