Ledinegg Instability. Figure 1: Sketch illustrating the Ledinegg instability. Two- phase flows can exhibit a range of instabilities. Usually, however, the instability is . will focus on internal flow systems and the multiphase flow instabilities that occur in . Ledinegg instability (Ledinegg ) which is depicted in figure This. Ledinegg instability In fluid dynamics, the Ledinegg instability occurs in two- phase flow, especially in a boiler tube, when the boiling boundary is within the tube.

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Experimentally, both inphase and out of phase oscillations are observed in parallel channels. The fundamental cause of this instability is that the hot liquid from the heater outlet experiences static pressure decrease as it flows up and may reach its saturation value in the riser causing it to lediegg.

With increase in power, subcooled boiling begins in an unstable single-phase system leading to the switching of flow between single-phase and two-phase regimes.

Figures 1 a and 1 b show an example of occurrence of Ledinegg-type instability at different powers [ inztability ] in a boiling two-phase NC system. Different modes of two-phase flows.

Different models of two-phase flow have been used for modelling these flow instabilities, which range from the simplest HEM to more rigorous two-fluid model. In addition, in many oscillatory conditions, secondary phenomena get excited and they modify significantly the characteristics of the fundamental instability. A large number of numerical and experimental investigations in this field have been carried out in the past.

DWO occurs at flow rates lower than the flow rate at which pressure-drop oscillation is observed. Thus we find that the analysis to arrive at the instability threshold can be based on different sets of governing equations for different instabilities.

Following a perturbation, if the system returns back to the original steady state, then the system is considered to be stable.

The reduced driving force reduces the flow rate. Both these instabilities are observed during low-pressure conditions only.

Very long test sections may have sufficient internal compressibility to initiate pressure drop oscillations. In general, instabilities can be classified according to various bases as follows: Similarly, the unstable region beyond the upper threshold occurs at a high power and hence at high qualities and is named as type II instability. View at Google Scholar K.

If the system stabilizes to a new steady state or oscillates with increasing amplitude, then the system is considered as unstable. Subscribe to Table of Contents Alerts. The mechanism of instabilities occurring in two-phase natural circulation systems have been explained based on these classifications. However, a common requirement for geysering is again a tall riser at the exit of the heated section. From measured decay ratio, it was evident that at very low power there is a trend of increase in decay ratio and similar results are seen at higher power also.


The change in power required from the first to the last stage is quite significant and it may not be reached in low-power loops. According to him, geysering is expected during subcooled boiling when the slug bubble detaches from the surface and enters the riser where the water is subcooledwhere bubble growth due to static-pressure decrease and condensation can take place.

instabilit The parameter is a hypothetical concept called Superficial velocity. The main difference with flashing instability is that the vapor is produced first in the heated section in case of geysering, whereas in flashing the vapor is formed by the decrease of the hydrostatic head as water flows up.

In view of the existence of more than two unstable zones, this method of instabiluty could be confusing at times. However, feedback effects also are paramount in the phenomena. Link to citation list in Scopus. However, the type II instability, which occurs at high power or void fraction, disappears with increase in riser diameter [ 38 ] due to reduction in void fraction or decrease in two-phase pressure drop.

As an unstable single-phase system progresses through single-phase NC to boiling inception and then to fully-developed two-phase NC with power change, it can encounter several unstable zones. In this case, in addition to the equations governing the thermalhydraulics, the equations for the neutron kinetics and fuel thermal response also need to be considered.

The model was used to quantify the susceptibility of the system to the Ledinegg instability. Over the years, several kinds of instabilities have been observed in natural circulation systems excited by different mechanisms. In fluid dynamics, the Ledinegg instability occurs in two-phase flow, especially in a boiler tube, when the boiling boundary is within the tube. The effects of negative void reactivity feedback are found to stabilize the very low frequency type I instabilities [ 4344 ].

With that purpose, a review of flow instabilities in boiling natural circulation ledinetg has been carried out.


The phase shift of out-of-phase oscillations OPO is known to depend on the number of parallel channels. On the other hand, with increase in local losses in the single-phase region such as orificing at the inlet of channelsthe improvement in stability has been found to be conditional [ 240 ] unlike in forced circulation systems wherein it has been observed that with increase in local losses in the single-phase region always improves the flow stability.


To analyze this instabillity instability, it is required to predict the pressure drop characteristics of the system against the flow rate similar to the Ledinegg-type instability [ 3 ].

Lee and Ishii [ 25 ] found that the nonequilibrium between the phases created flow instability in the loop. However, both instabilities increase with rise in subcooling. Examples and applications Historically, probably the most commonly studied cases of two-phase flow are in large-scale power systems. Similar results were also found for the effect of drift velocity on both type I and type II instabilities [ 37 ]. Thermal oscillations are considered as a regular feature of dryout of steam-water mixtures at high pressure [ 4 ].

This makes the system unstable. Thus, there can be five different flow rates for a particular operating condition of power and subcooling as indicated in Figure 2 by points A—E. The sudden condensation results in depressurization causing the liquid water to rush in and occupy the space vacated by the condensed bubble.

Flow Instabilities in Boiling Two-Phase Natural Circulation Systems: A Review

The last flow excursion occurs when the flow becomes single phase and the pressure drop increases with increase in flow rate. The internal jnstability loss of the system includes the losses due to friction, elevation, acceleration and local in the heated portion, the riser pipes and the steam drum, and all the losses except the elevation loss in the downcomers.

Finally, it should be noted that time domain evaluations may be performed with the nonlinear conservation instabllity leading to Hopf bifurcations e. In natural circulation loops, flow direction can also change during oscillations.

The proposed mechanism by both the investigators differ somewhat. It ledinnegg felt to have a review and summarize the state-of-the-art research carried out in this area, which would be quite useful to the design and safety of current and future light water reactors with natural circulation core cooling.

Two-Phase Instabilities

Fukuda and Kobori [ 5 ] observed two modes of oscillations in a natural circulation loop with parallel heated channels. Linear stability analysis using a four-equation drift flux model has been carried out by Ishii and Zuber [ 32 ], Saha and Zuber [ 33 ], Park et al. As the flow is increased, the exit enthalpy is reduced leading to suppression of boiling.