Density wave oscillations

The pressure spike introduces a disruption in the flow. Depending on the local conditions, the excess pressure inside the bubble may overcome the inertia of the incoming liquid and the pressure in the inlet manifold, and cause a reverse flow of varying intensity depending on the local conditions. There are two ways to reduce the flow instabilities reduce the local liquid superheat at the ONB and introduce a pressure drop element at the entrance of each channel, Kandlikar (2006). Kakac and Bon (2008) reported that density-wave oscillations were observed also in conventional size channels. Introduction of additional pressure drop at the inlet (small diameter orifices were employed for this purpose) stabilized the system. 

Density-wave oscillations Pressure drop oscillations Flow regime-induced instability... 

Lahey (1990) indicated the applications of fractal and chaos theory in the field of two-phase flow and heat transfer, especially during density wave oscillations in boiling flow. 

Yadigaroglu, G., and A. E. Bergles, 1969, An Experimental and Theoretical Study of Density-Wave Oscillation in Two-Phase Flow, M.I.T. Rep. DSR 74629-3 (HTL 74629-67), Massachusetts Institute of Technology, Cambridge, MA. (6)... 

A feature of peculiar importance in one dimension is that long wavelength charge or spin-density-wave oscillations constructed by the combination of electron-hole pair excitations at low energy form extremely stable excitations... 

Dynamic Density wave oscillation Low frequencies related to transmit time of a continuity wave -... 

Kinematic waves result from the existence of a functional dependency between some "flux" and the corresponding "density", otherwise related through a balance equation (Whitham, 1974, p. 27). In two-phase flows, the foregoing flux and density are respectively the drift flux (volumetric flow rate of one phase with respect to the mixture) and the void fraction (volumetric concentration of the same phase in the mixture). Kinematic waves convey information on the flow structure and the associated variables such as the void fraction and the drift flux. In particular, they control flow pattern changes and density wave oscillations. 

Fukuda, K. and T. Kobori. 1979. Classification of two-phase flow instability by density wave oscillation model. J. Nud. Sci. Technol. 16 95-108. 

Stability analyses of the coolant flow through the three-pass core of the HPLWR have been studied by Ortega Gomez (2008). As with BWRs, Ortega Gomez shows that the most effective measure to avoid density wave oscillations in the core is the installation of orifices at the inlet of fuel assemblies. These orifices need to be customized for a hot fuel assembly. 

In the case of a BWR, the operation point of the average heated fuel assembly should correspond to a decay ratio less than 0.5 for a single-channel density wave oscillation, and a decay ratio less than 0.25 should correspond to the coupled thermal-hydraulic/neutronic density wave oscillation. Furthermore, the whole operation range, also including hot fuel assemblies, should be in the linear stable region of the stability map. 

Although the first superheater is stable with respect to density wave oscillations, even without orifices, we have to expect flow reversal in some fuel assemblies of the first superheater of a three-pass core at low mass flow rates because of an unstable stratification... 

Density wave oscillation in parallel channels Coupled neutronic thermo-hydrauUc instabilities FlaSHing instabiUty (FSH)... 

The decay ratios are calculated in the average power channel at 25 MPa for 100% power and 100% flow conditions. The decay ratio is calculated as 0.185 by extrapolation in Fig. 5.50 to the zero mesh size. The oscillation frequency is about 0.3 Hz, which is t5q)ical for density wave oscillation. The stability criterion is satisfied. 

The physics of deterioration of heat transfer of the flow of supercritical water with low mass flux through a tube with high heat flux has been studied with CFD. A numerical study of turbulence enhancement by ribs on the heated wall indicated that this measure is appropriate to avoid deterioration of heat transfer. A first design proposal of a containment for the HPLWR has been worked out. First transient analyses of design basis accidents have been started. Stability analyses of coolant flow through the core have been completed like with BWRs, inlet orifices can avoid density wave oscillations in the core. 

NC experiments have also been performed in ITF that simulate the BWR system performance. Relevant NC data have also been recorded from the operation of BWR NPP and used for benchmarking system code performance. The flow map for the operation of BWR systems shows the core power as a function of the core flow rate. A parabola like curve in the considered plane is derived from experiments and confirmed from code applications. A steep power increase up to about 50% of nominal core power can be observed from the mentioned diagram when core flow rate achieves roughly 30% of the its nominal value (i.e. value at 100% core power). This implies that the BWR systems can operate at 50% power in NC. However, in these conditions the system is prone to instabilities, identified in the literature as density wave oscillations (DWO). A wide literature exists related to the DWO that can be considered as a NC phenomenon. A state-of-the-art report on this topic has been recently issued by OECD/CSNI, Ref [14]. 

Definitions for the experimental onset of instability are not universal, and were often reported as the onset of density wave oscillations, not static instability, obtained by usually raising the power until some unstable or oscillating flow was observed. Data review yielded over 300 data points, extracted from 30 years of the literature, covering a range of pressures from 0.1 to 19 MPa,(i.e. nearly 1-190 bars), for tubes, rod bundles and parallel channels. In Figure 3, the data and theory are shown, with the density wave data cluster at the lower subcoolings and powers. 

Because the core flow responds to changes in power the stability of a natural-circulation BWR is somewhat different from the stability of a forced-circulation BWR. Therefore, the stability of a natural-circulation BWR requires special attention. It has been shown that two different instability types exist for such a reactor, denoted by type-I and type-II [4]. Type-I oscillations are typical for natural-circulation BWRs and are driven by the gravitational pressure drop over the core and riser. Type-II oscillations are driven by the interplay between single-phase and two-phase friction in the core. This division in different types is not sharp. The transition from one type to the other occurs gradually. Although the character of both types of oscillations is different one could describe both of them as density-wave oscillations. 

FUKUDA, K. and KOBORI, T., "Classification of Two-Phase Flow Instability by Density-Wave Oscillation Model", J. Nucl. Sci. Technol., 16 (1979) 95-108. 

ZBORAY, R. et al, "Experiments on nonlinear density-wave oscillations in the DESIRE facility," Proceedings of the NURETH-9 Conference, October 3-8, 1999, San Francisco, California, USA (on CDROM). 

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