A note on damping in heat-exchanger tubes subjected to cross-flow

Desai, Ajinkya and Vourganti, Varun and Vyasarayani, Chandrika Prakash (2020) A note on damping in heat-exchanger tubes subjected to cross-flow. International Journal of Dynamics and Control. ISSN 2195-268X

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Abstract

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. The contour plots showing the damping in different regions of the stability chart has never been reported, due to the complexity in solving the infinite-dimensional nonlinear eigenvalue problem associated with characteristic roots of the governing DDE. In this work using Galerkin approximations, the spectrum (characteristic roots) of the DDE is obtained. The rightmost characteristic root, whose real part represents the damping in the heat-exchanger tube is included in the stability chart. Interestingly, it is found that the highest damping is present in localized areas of the stability charts, which are close to the stability boundaries. These stability charts can be used to determine the optimal cross-flow velocities for operating the heat-exchanger tube for achieving maximum damping. Explicit evaluation of the characteristic roots allows us to show that the roots cross the stability boundary with a non-zero velocity, clearly indicating the existence of Hopf bifurcation at the stability boundary.

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IITH Creators:

IITH Creators	ORCiD
Vyasarayani, Chandrika Prakash	http://orcid.org/0000-0002-3396-0484

Item Type:

Article

Additional Information:

Funding was provided to C.P. Vyasarayani by the Department of Science and Technology through the Inspire fellowship (Grant Number DST/INSPIRE/04/2014/000972). The funders had no role in designing the study, collecting or analyzing data, the decision to publish, or preparing the manuscript

Uncontrolled Keywords:

Damping contours; Delay differential equation; Heat-exchanger tube; Nonlinear eigenvalue problem; Stability chart

Subjects:

Physics > Mechanical and aerospace

Divisions:

Department of Mechanical & Aerospace Engineering

Depositing User:

Team Library

Date Deposited:

27 Nov 2019 06:07

Last Modified:

22 Oct 2022 08:05