Vourganti, Varun and Vyasarayani, C P
(2020)
Nonlinear Dynamics of Heat-Exchanger Tubes Under Crossflow: A Time-Delay Approach.
PhD thesis, Indian Institute of Technology Hyderabad.
Abstract
Fluid-conveying heat-exchanger tubes in nuclear power plants are subjected to a secondary cross-flow to facilitate heat exchange. Beyond a critical value of the secondary flow velocity, the tube loses stability and vibrates with large amplitude. The equation governing the dynamics of a heat-exchanger tube is a delay differential equation (DDE). In all the earlier studies, only the stability boundaries in the parametric space of mass-damping parameter and reduced flow-velocity were reported. In this work using Galerkin approximations, the spectrum (characteristic roots) of the DDE is also obtained. The rightmost characteristic root, whose real part represents the damping in the heat-exchanger tube is included in the stability chart for the first time. The highest damping is found to be present in localized areas of the stability charts, which are close to the stability boundaries. These charts can be used to determine the optimal cross-flow velocities for operating the system for achieving maximum damping. Next, the interaction between the tube and the surrounding cladding at the baffle-plate makes it vital to determine the optimal design parameters for the baffle plates. The linear stability of a heat-exchanger tube modeled as a single-span Euler-Bernoulli cantilever beam subjected to cross-flow is studied with two parameters: (i) varying stiffness of the baffle-cladding at the free end and (ii) varying flow velocity. The partial delay differential equation governing the dynamics of the continuous system is discretized to a set of finite, nonlinear DDEs through a Galerkin method in which a single mode is considered. Unstable regions in the parametric space of cladding stiffness and flow velocity are identified, along with the magnitude of damping in the stable region. This information can be used to determine the design cladding stiffness to achieve maximum damping at a known operational flow velocity. Moreover, the system is found to lose stability by Hopf bifurcation and the method of multiple scales is used to analyze its post-instability behavior. Stable and unstable limit cycles are observed for different values of the linear component of the dimensionless cladding stiffness. An optimal range for the linear cladding stiffness is recommended where tube vibrations would either diminish to zero or assume a relatively low amplitude associated with a stable limit cycle. Furthermore, heat-exchanger tubes undergo thermal expansion, and are consequently subject to thermal loads acting along the axial direction, apart from design-induced external tensile loads. Nonlinear vibrations of a heat-exchanger tube modeled as a simply-supported EulerBernoulli beam under axial load and cross-flow have been studied. The fixed points (zero and buckled equilibria) of the nonlinear DDE are found, and their linear stability is analyzed. The stability of the DDE is investigated in the parametric space of fluid velocity and axial load. The method of multiple scales is used to study the post-instability behavior for both zero and buckled equilibria. Multiple limit-cycles coexist in the parametric space, which has implications on the fatigue life calculations of the heat-exchanger tubes.
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