Abstract
The dynamics of cross‐flow tubes were studied in consideration of initial axial load and distributed impacting constraints, modeled as cubic and trilinear spring constraints. The tubes were modeled as Euler–Bernoulli beams and supported at both ends, including the simply supported tube and clamped‐clamped tube. The analytical model involves a time‐delayed displacement term induced by the cross flow based on the quasi‐steady theory. For simplicity, a single flexible supported beam in a rigid square array of cylinders was studied by using the damping‐controlled mechanism. The mean extension of the tube was considered, and thus, it added another nonlinear term in the equation of motion. Results show that the tube loses stability by buckling and fluttering at various initial pressure loads and cross‐flow velocities. An increase was observed for critical velocities and initial pressure loads. Chaotic oscillations were observed for the trilinear spring model. The distribution of the impacting forces was also calculated. Some of the fresh results obtained in the impact system are expected to be helpful in understanding and controlling the dynamic responses of fluid‐conveying pipes.
Highlights
Cross-flow heat exchanger tubes are found in many power generating industries, such as in steam generators, boilers, and nuclear reactors [1,2,3,4]
Tube arrays exhibit fluid elastic instabilities at sufficiently high cross-flow velocities. ese instabilities are related to negative fluid damping caused by the flow-induced dynamic forces acting on the tubes
The nonlinear dynamics of cross-flow tubes subjected to initial axial load and distributed impacting constraints was analysed by considering the effect of axial extension of the tubes. e force of the distributed impact constraints was modeled as either a cubic spring or a smoothed trilinear spring, and the results were in good agreement with experiments [37]
Summary
Cross-flow heat exchanger tubes are found in many power generating industries, such as in steam generators, boilers, and nuclear reactors [1,2,3,4]. Studies on heat exchanger tube failures related to flow induced vibration began in the 1950s and have greatly progressed since the 1970s [5,6,7]. Tube arrays exhibit fluid elastic instabilities at sufficiently high cross-flow velocities. Ese instabilities are related to negative fluid damping caused by the flow-induced dynamic forces acting on the tubes. Many studies have focused on the dynamics of crossflow induced vibrations of heat exchanger tubes by using single degree of freedom models and complicated continuous models of flexible beams. E displacement of the tube may become large when the crossflow velocity increases after the onset of fluid-elastic instability. In this case, the nonlinear effects become important to some extent
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