Semi-Analytical Bifurcation Analysis of Two-Phase Flow in a Heated Channel

Abstract

Using a drift flux representation for the two-phase flow, a new reduced order model has been developed to simulate density-wave oscillations (DWOs) in a heated channel. This model is then used to perform stability and semi-analytical bifurcation analysis, using the bifurcation code BIFDD, in which the stability boundary (SB) and the nature of Hopf bifurcation are determined in a suitable two-dimensional parameter space. A comparative study is carried out to investigate the effects of the parameters in the drift flux model (DFM) — the radially void distribution parameter C0 and the drift velocity Vgj — on the SB as well as on the nature of Hopf bifurcation. It is the first time that a systematic analysis has been carried out to investigate the effects of DFM parameters on the nature of Hopf bifurcation in a heated-channel two-phase flow. The results obtained show that both sub- and super-critical Hopf bifurcations are encountered. In addition, it has been found that, while the SB is sensitive to both C0 and Vgj, the nature of Hopf bifurcation for lower values of N sub is more sensitive to Vgj than to C0. Numerical integration of the set of ODEs is carried out to confirm the predictions of the semi-analytical bifurcation analysis.

A Novel Result in the Field of Nonlinear Stability Analysis of Boiling Water Reactors

“…In order to get information about the stability behavior beyond the local bifurcation findings, numerical integration (in the time domain) of the set of the ODEs is necessary. Besides, the predictions of the semi-analytical bifurcation analysis can be confirmed independently [Dokhane 2005;Lange, 2009]. …”

“…These are a neutron kinetic model, a fuel heat conduction model, and a two-channel thermal-hydraulic model [Dokhane et al, 2005]. The constitutive characteristics of the ROM are depicted in Fig.…”

“…This work is a continuation of the previous work at the Paul Scherrer Institute (PSI, Switzerland) and at the University of Illinois (USA) in this field [Dokhane, 2004;Dokhane et al, 2005;Hennig, 1999]. In the scope of a PhD work at the Technical University Dresden (Germany), the current ROM was extended to an advanced ROM and the RAM-ROM method was qualified for BWR stability analysis [Lange, 2009;Lange et al, 2011].…”

Analysis of a BWR Stability Behavior using Generalized Discrete Shannon Functions. Application to Ringhals and Forsmark Benchmarks Data

“…In this last case, the amplitude of the oscillation is growing, amplifying the non-linear behavior, which in some cases can induce the 1 Hz band of frequencies. 3,4) The fluctuations or oscillations of neutron signals can be described by stochastic nonlinear dynamics methods with a global-regional interaction. 1,23,31) In case of regional oscillations, we can directly observe the 0.5 Hz oscillation in the LPRM signals.…”

Linear stability analysis of flow instabilities with a nodalized reduced order model in heated channel

“…Clausse and Lahey [32] developed a simple model using approximations for spatial dependence of the single phase enthalpy and two-phase density. Followed by these developments Karve [33], Dokhane [34] and Dokhane et al [35] developed models for DWO by introducing quadratic profiles of single phase enthalpy and two-phase quality using HEM as well as drift flux model (DFM). However due to the presence of quadratic profiles, the system equations became highly complicated and even run for several pages.…”