Periodically-forced density wave oscillations in boiling flow at low forcing frequencies: Nonlinear dynamics and control issues

•Nonlinear dynamics and frequency entrainments in a periodically forced boiling channel.•Performance of NMPC in controlling the oscillations at low forcing frequency.•Comparison of numerical simulations and harmonic solutions.

In this paper, we investigate the effect of a periodic perturbation of total pressure drop on density wave oscillations (DWOs) in a boiling channel (BC). The focus is on the nonlinear dynamics and control of the DWO at low forcing frequencies ff+ for a range of inlet subcooling number Nsub. At a relatively high Nsub  , the system exhibits frequency entrainment. Relying on the harmonic balance applied to the linearized model for DWOs, semi-analytical solutions can successfully explain the numerically-detected harmonic entrainment. The effect of ff+ and Nsub on the periodically-perturbed DWOs has been studied. We also propose a nonlinear model predictive controller (NMPC) to control the periodically-forced DWOs. The performance of NMPC was found to be improving on increasing Nsub   and on decreasing ff+ in 0≤ff+<2fn+ (fn+ is natural frequency), except the regions of entrainment. Both the numerical simulations and the semi-analytical solutions consistently predict the control effort that also varies with ff+ and Nsub.