Hopf Bifurcation and Optimal Control of Thermo-Hydraulic Instabilities in a Microchannel

Abstract

Lakshmi. N. Sridhar

The growing demand for high-performance thermal management systems in data centers, power electronics, artificial intelligence hardware, and advanced manufacturing has increased industrial interest in two-phase microchannel cooling technologies. Companies such as 3M Corporation have played an important role in developing advanced cooling solutions based on phase-change heat transfer, where thermo-hydraulic instabilities can significantly affect performance and reliability. In this work, a reduced-order nonlinear dynamic model of a boiling microchannel system is developed and analyzed to investigate the onset of oscillatory behavior and its implications for system operation. The model consists of four ordinary differential equations that describe the evolution of the void fraction, pressure drop, wall temperature, and mass flow rate. Bifurcation analysis using MATCONT reveals the existence of a Hopf bifurcation, indicating a transition from stable steady-state operation to self-sustained limit-cycle oscillations. To facilitate real- time stability assessment, a neural-network surrogate model is trained using bifurcation-generated data and embedded within a dynamic optimization framework. An optimal control problem is subsequently formulated in PYOMO.DAE with the heat-input parameter as the manipulated variable. Results demonstrate that incorporating bifurcation-awareness into the optimization process enables the controller to avoid unstable operating regions while maintaining desirable thermal-fluid performance.

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