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 v0* 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 Nsub and the phase change number Npch. 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 - Nsub - Npch. The effects of the void distribution parameter C0 and the drift velocity Vgj on the MSB are examined. The MSB is shown to be sensitive to the value of C0 and comparison with experimental data shows that the drift flux model with C0 > 1 predicts the experimental MSB and the neighboring region of stable oscillations (limit cycles) considerably better than do the homogeneous equilibrium model (C0 = 1, Vgj = 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 Nsub and/or Npch.
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