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Lumped parameterization of boiling channel—Bifurcations during density wave oscillations

Chemical Engineering Science
Publication Date
DOI: 10.1016/j.ces.2012.02.039
  • Bifurcation
  • Boiling Channel
  • Chaos
  • Nonlinear Dynamics
  • Phase Change
  • Stability
  • Computer Science


Abstract The research on density wave oscillation (DWO) in boiling channels during the last few decades has been reviewed. Model reductions through lumped parameterization of the distributed channels have been exercised to compute nonlinear DWOs. In the present article, we attempt to analyze DWOs in several boiling channels with varying lengths (Froude number) adopting moving node scheme (MNS) and fixed node scheme (FNS). Relative performances of MNS and FNS have been analyzed to evaluate the capability of the methods. The analysis suggests that MNS is highly computationally efficient and has excellent convergence compared to FNS and finite difference method. Extended numerical oscillations have been observed in FNS. The analysis also suggests that DWOs are strongly coupled with the extent of inlet subcooling (boiling boundary), pressure drop and vapor quality. At high inlet subcooling, the ratio of time period to transit time is significantly higher than 2.0 (2.5–6.0) whereas at low inlet subcooling the ratio remains around 2.0. Numerical experiments on long boiling channels (low Froude number) and short ones (high Froude number) derives a clear difference that the short channels with high Froude number has “islands of instability” in Npch–Nsub plane and undergoes both supercritical and subcritical bifurcations, whereas the boiling channel with low Froude number undergoes only supercritical bifurcations. The effect of node numbers on marginal stability boundary (MSB) has been discussed. Increased speed of convergence is observed with higher number of nodes. With finer nodalizations, the region of instability extends. Extensive validations of the nonlinear models with reference experimental data and numerical results confirm that MNS satisfactorily predicts MSB, supercritical and subcritical bifurcations. Quasi-periodic en route to chaos has been detected in the boiling channel as a result of periodic perturbation of pressure drop (Eu). The same has been confirmed by the analysis of power spectrum density (PSD) and computation of Lyapunov exponents.

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