### Abstract

Linear and nonlinear mathematical stability analyses of parallel channel density wave oscillations are reported. The two phase flow is represented by the drift flux model. A constant characteristic velocity v_{0}^{*} is used to make the set of equations dimensionless to ensure the mutual independence of the dimensionless variables and parameters: the steady-state inlet velocity v, the inlet subcooling number N_{sub} and the phase change number N_{pch}. The exact equation for the total channel pressure drop is perturbed about the steady-state for the linear and nonlinear analyses. The surface defining the marginal stability boundary (MSB) is determined in the three-dimensional equilibrium-solution/operating-parameter space v - N_{sub} - N_{pch}. The effects of the void distribution parameter C_{0} and the drift velocity V_{gj} on the MSB are examined. The MSB is shown to be sensitive to the value of C_{0} and comparison with experimental data shows that the drift flux model with C_{0} > 1 predicts the experimental MSB and the neighboring region of stable oscillations (limit cycles) considerably better than do the homogeneous equilibrium model (C_{0} = 1, V_{gj} = 0) or a slip flow model. The nonlinear analysis shows that supercritical Hopf bifurcation occurs for the regions of parameter space studied; hence stable oscillatory solutions exist in the linearly unstable region in the vicinity of the MSB. That is, the stable fixed point v becomes unstable and bifurcates to a stable limit cycle as the MSB is crossed by varying N_{sub} and/or N_{pch}.

Original language | English (US) |
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Pages (from-to) | 1-14 |

Number of pages | 14 |

Journal | Nuclear Engineering and Design |

Volume | 93 |

Issue number | 1 |

DOIs | |

State | Published - May 1 1986 |

Externally published | Yes |

### ASJC Scopus subject areas

- Nuclear and High Energy Physics
- Nuclear Energy and Engineering
- Materials Science(all)
- Safety, Risk, Reliability and Quality
- Waste Management and Disposal
- Mechanical Engineering

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## Cite this

*Nuclear Engineering and Design*,

*93*(1), 1-14. https://doi.org/10.1016/0029-5493(86)90190-1