Dynamic frequency response of a single-phase natural circulation loop under an imposed sinusoidal excitation

Abstract

Natural circulation loops in industrial applications are always likely to experience both aperiodic and periodic variations in control parameters. Present work performs a comprehensive analyses to investigate the effect of periodic power supply on the nature of transient system response. Mathematical model of a rectangular single-phase loop is developed and a sinusoidal profile is imposed on the steady-state heater power. Cooling of the system is achieved in convective mode, whereas other sections are ideally insulated. Nature of temporal response is found to depend on the frequency of imposed sinusoid, showing both repetitive patterns and occasional irregular fluctuations. A natural frequency can be identified corresponding to each power level by performing Fast Fourier transform on the resultant transient dataset, which is found to be independent of the frequency of imposed profile. Magnitude of natural frequency increases continually with mean heater power within stable zone and corresponding critical time period exhibits a decreasing power-law profile. Both generally-stable and unstable system exhibits highly unstable oscillations and early flow reversal, when subjected to a profile with frequency analogous to the natural frequency of mean power level. Increase in amplitude of imposed sinusoid hardly affects the nature of the response, other than accelerating flow reversal and introducing phase lag in response. An active feedback control mechanism is also proposed by modulating additional pressure losses, which is able to suppress resonance behavior at both stable and unstable regime.