Stability of a Cross-Flow Heat-Exchanger Tube With Asymmetric Supports

Abstract

Heat-exchanger tubes subjected to cross-flow experience a fluid elastic instability (FEI) at a critical flow velocity. Baffle plates are often used to provide additional stiffness to long tubes. A cladding is provided between the baffle plates and the tubes to allow for thermal expansion, and the cladding acts like a soft spring. In this paper, we study the contact between the cladding and the tube when the stiffness of the cladding is asymmetric. The tube is modelled as a cantilever Euler-Bernoulli beam, and the fluid forces are represented using an added mass, added damping and a time-delayed displacement term. This results in a partial delay differential equation model for the tube vibration. Using the Galerkin approximation and considering only a single mode, a delay differential equation (DDE) model is developed. However, due to the presence of the delay the single mode model is also infinite-dimensional. This model contains sign function nonlinearity due to the asymmetry in the contact stiffness of the cladding. The DDE model is essentially nonlinear --- that is, no linear approximation exists. However, its solutions are scalable: if $q(t)$ is a solution, then $\alpha\, q(t)$ is also a solution for any $\alpha>0$. By exploiting this scalability property of solutions, we use Lyapunov-like exponents to probe the stability of the nonlinear DDE. Further, by numerical continuation, we numerically demonstrate the existence of periodic solutions on the stability boundary. Our stability charts will be beneficial to the designers of heat-exchangers.

Nonlinear vibrations and wear predictions of slender cylinders with loose support subjected to axial flows

“…It is noted that when the slender cylinder/pipe has loose supports, the flow-induced vibration behavior becomes complex because of impact and friction forces due to the loose support, which is one of the most important reasons causing wear failures of the cylinder [25]. Therefore, many studies have been performed to explore nonlinear dynamical behviors of cylinders with loose supports in heat exchangers over the past few decades [25][26][27][28][29][30][31][32][33][34]. Experimental investigations [1,12,31] and numerical simulations [26,27] are included.…”

“…Hassan et al [27] presented simulations of a loosely supported multi-span U-bend tube subjected to turbulence and fluid-elastic instability forces. Recently, Balaji et al [30] studied the contact between the loose support and the tube when the stiffness of loose support is asymmetric. Lai et al [31] presented a mathematical model of a single flexible tube in tube bundles subjected to turbulence random force and loose support.…”