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The analysis of nonlinear density-wave oscillations in boiling channels. (English) Zbl 0585.76064
Summary: Thermally induced flow instabilities in uniformly heated boiling channels have been studied analytically. The classical homogeneous equilibrium model was used. This distributed model was transformed into an integrodifferential equation for inlet velocity. A linear analysis showed interesting features (i.e. islands of instability) of the marginal stability boundary which appear when the effects of gravity and friction were systematically considered. A quasilinear Hopf-bifurcation analysis, valid near the marginal-stability boundaries, gives the amplitude and frequency of limit-cycle oscillations that can appear on the unstable side of the boundary. The analysis also shows cases where a finite- amplitude perturbation can cause a divergent instability on the stable side of the linear-stability boundary.

76E30 Nonlinear effects in hydrodynamic stability
76T99 Multiphase and multicomponent flows
Full Text: DOI
[1] Krishnan, AIChE Symp. Ser. 76 pp 461– (1980)
[2] Kazarinoff, J. Inst. Maths Applics 21 pp 461– (1978)
[3] Hopf, Ber. Math. Phys. Kl. Sächs Acad. Wiss. Leipzig 94 pp 1– (1942)
[4] Achard, Chem. Engng Commun. 11 pp 59– (1981)
[5] Yadigaroglu, J. Heat Transfer 94 pp 189– (1972)
[6] Serov, Trudy, Moscow Energ. Inst. 11 pp 461– (1953)
[7] DOI: 10.1017/S0022112081003509 · Zbl 0493.76024
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