Article: Start-up of oscillating heat pipes via Hopf bifurcation Journal: International Journal of Mathematical Modelling and Numerical Optimisation (IJMMNO) 2024 Vol.14 No.1/2 pp.32 - 52 Abstract: Phase changes occur in oscillating heat pipes (OHPs) inside a tube partially filled with liquid that loops through the hot and cold zones of the device. Evaporation occurs in the hot zone, condensation in the cold zone. Their net effect would intuitively lead to accumulation of liquid slugs in the cold zone and flow stagnation. In recent work, however, self-oscillations observed in a single-branch heat pipe are explained as self-excited mechanical resonator motion. We extend their analysis to typical OHP geometry. Based on a model that combines slug dynamics with a phenomenological model of evaporation, linear stability of the equilibrium corresponding to liquid slugs filling up the cold zone of the heat exchanger is analysed. Our results reveal relations among the system parameters that determine stability and oscillatory behaviour via Hopf bifurcations. Thus, an explanation is proposed for successful start-up - one of the grand challenges for OHP design. Inderscience Publishers - linking academia, business and industry through research

Title: Start-up of oscillating heat pipes via Hopf bifurcation

Authors: Carmen Chicone; Z.C. Feng; Stephen J. Lombardo; David G. Retzloff

Addresses: Department of Mathematics, University of Missouri, MO 65211, Columbia ' Department of Mechanical and Aerospace Engineering, University of Missouri, MO 65211, Columbia ' Department of Mechanical and Aerospace Engineering, University of Missouri, MO 65211, Columbia; Department of Biomedical, Biological and Chemical Engineering, University of Missouri, MO 65211, Columbia ' Department of Biomedical, Biological and Chemical Engineering, University of Missouri, MO 65211, Columbia

Abstract: Phase changes occur in oscillating heat pipes (OHPs) inside a tube partially filled with liquid that loops through the hot and cold zones of the device. Evaporation occurs in the hot zone, condensation in the cold zone. Their net effect would intuitively lead to accumulation of liquid slugs in the cold zone and flow stagnation. In recent work, however, self-oscillations observed in a single-branch heat pipe are explained as self-excited mechanical resonator motion. We extend their analysis to typical OHP geometry. Based on a model that combines slug dynamics with a phenomenological model of evaporation, linear stability of the equilibrium corresponding to liquid slugs filling up the cold zone of the heat exchanger is analysed. Our results reveal relations among the system parameters that determine stability and oscillatory behaviour via Hopf bifurcations. Thus, an explanation is proposed for successful start-up - one of the grand challenges for OHP design.

Keywords: oscillating heat pipe; mathematical model; linearisation; Hopf bifurcation; start-up; model validation.

DOI: 10.1504/IJMMNO.2024.143238

International Journal of Mathematical Modelling and Numerical Optimisation, 2024 Vol.14 No.1/2, pp.32 - 52

Received: 22 Aug 2022
Accepted: 10 Jul 2023
Published online: 11 Dec 2024 *

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Title: Start-up of oscillating heat pipes via Hopf bifurcation

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