Dynamics of Cross-Flow Heat Exchanger Tubes With Multiple Loose Supports

Dynamics of cross-flow heat exchanger tubes with two loose supports has been studied. An analytical model of a cantilever beam that includes time-delayed displacement term along with two restrained spring forces has been used to model the flexible tube. The model consists of one loose support placed at the free end of the tube and the other at the midspan of the tube. The critical fluid flow velocity at which the Hopf bifurcation occurs has been obtained after solving a free vibration problem. The beam equation is discretized to five second-order delay differential equations (DDEs) using Galerkin approximation and solved numerically. It has been found that for flow velocity less than the critical flow velocity, the system shows a positive damping leading to a stable response. Beyond the critical velocity, the system becomes unstable, but a further increase in the velocity leads to the formation of a positive damping which stabilizes the system at an amplified oscillatory state. For a sufficiently high flow velocity, the tube impacts on the loose supports and generates complex and chaotic vibrations. The impact loading on the loose support is modeled either as a cubic spring or a trilinear spring. The effect of spring constants and free-gap of the loose support on the dynamics of the tube has been studied