Density wave instability

The following parametric effects on density wave instability are summarized, as these effects have been often observed in the most common type of two-phase flow instability (Boure et al., 1973) ... 

The physical properties are independent of pressure. (This assumption is valid only for density wave instability at high pressures it is not valid for acoustic instability.)... 

Analysis of density wave instability Analyses have been made by using either simplified models or comprehensive computer codes. 

Computer codes Because of the computer s ability to handle the complicated mathematics, most of the compounded and feedback effects are built into computer codes for analyzing dynamic instabilities. Most of these codes can analyze one or more of the following instabilities density wave instability, compound dynamic instabilities such as BWR instability and parallel-channel instability, and pressure drop oscillations. 

Check the onset of density wave instability in a heated channel by using a simplified model or a nondimensional plot, if the geometry and boundary conditions of the equipment agree with that of the nondimensional plot analysis (e.g., Boure, Zuber, etc.). 

Finally, check the onset of density wave instability in a heated channel with specific boundary conditions by using a computer code, such as STABLE-5 (Jones and Dight, 1961-1964), RAMONA (Solverg and Bakstad, 1967), HYDNA (Currin et al., 1961) and SAT (Roy et al., 1988). 

If the r 4-dependent attractive interactions were unscreened, they would indeed give rise to mean-field criticality. On the other hand, an unscreened repulsive interaction would suppress the development of a critical point, giving rise instead to a charge-density wave instability in the neighborhood of where criticality would take place in the absence of the r-4 cavity term. The latter scenario was developed some time ago by Nabutovskii et al. [305] using a Ginzburg-type analysis. 

Correlations are important [73] in the ID chains and a charge density wave or spin density wave instability will open a gap in a natural way [74]. 

Flow Maldistribution in Heat Exchangers with Phase Change. Two-phase flow maldistribution may be caused and/or influenced by phase separation, oscillating flows, variable pressure drops (density-wave instability), flow reversals, and other flow instabilities. For a review of pertinent literature, refer to Ref. 131. 

Natural circulation systems may undergo thermal-hydraulic instabilities under low-power and low-pressure conditions, which occur during start-up. The void reactivity feedback and void fraction fluctuations in the reactor core would create power oscillations during start-up. Three kinds of thermal-hydraulic instabilities may occur during start-up in natural circulation BWRs, which are as follows (1) geysering induced by condensation, (2) natural circulation instability induced by hydrostatic head fluctuation in steam separators, and (3) density wave instabilities. 

As the heat input is increased, geysering is suppressed and another instability called natural circulation instability is induced due to hydrostatic head fluctuation (caused by PDO), which varies the natural circulation force. As the heat flux is further increased, density wave instabilities appear. The period of natural circulahon oscillations is much longer than that of density wave instabilities, and reduces with an increase in heat flux and with a decrease in inlet subcooling. 

NUREG/CR-6003 ORNL/TM-12130, Density wave instabilities in boiling water reactors, issued September 1992. 

Ambrosini, W., Ferreri, J.C., 2006. Analysis of basic phenomena in boiling channel instabilities with different flow models and numerical schemes. In Proceedings of on Density Wave Instability Phenomena — Modelling and Experimental Investigation, 14th International Conference on Nuclear Engineering (ICONE 14), Miami, Florida, USA, July 17—20, 2006. 

Papini, D., Colombo, M., Cammi, A., Rocotti, M.E., 2014. Experimental and theoretical studies on density wave instabilities in helically coiled tubes. Intemational Journal of Heat and Mass Transfer 68, 343—356. 

The results indicate that as the Froude number decreases, the flow becomes unstable, where zero Froude number is for horizontal flows, and negative Froude number is for downflow. On the other hand, the critical subcooling number decreases with the increase in the exit loss coefficient, implying that the stable region is smaller. Both these results have been also confirmed for density-wave instabilities. 

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