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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Several decades have been spent on the study of flow instabilities in boiling two-phase natural circulation systems. It is 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.
With that purpose, a review of flow instabilities in boiling natural circulation systems has been carried out.
An attempt has been made to classify the instabilities occurring in natural circulation systems similar to that in forced convection boiling systems. The mechanism of instabilities occurring in two-phase natural circulation systems have been explained based on these classifications.
The characteristics of different instabilities as well as the effects of different operating and geometric parameters on them have been reviewed. Natural circulation NC systems are susceptible to several kinds of instabilities. Although instabilities are common to both forced and natural circulation systems, the latter is inherently more unstable than forced circulation systems due to more nonlinearity of the NC process and its low driving force.
Because of this, any disturbance in the driving force affects the flow which in turn influences the driving force leading to an oscillatory behavior even in cases where eventually a steady state is expected. In other words, a regenerative feedback is inherent in the mechanism causing NC flow due to the strong coupling between the flow and the driving force.
Even among two-phase systems, the NC systems are more unstable than forced circulation systems due to the above reasons. Following a perturbation, if the system returns back to the original steady state, then the system is considered to be stable. If on the other hand, the system continues to oscillate with the same amplitude, then the system is neutrally stable.
If the system stabilizes to a new steady state or oscillates with increasing amplitude, then the system is considered as unstable. It may be noted that the amplitude of oscillations cannot go on increasing indefinitely even for unstable flow.
Instead for almost all cases of instability, the amplitude is limited by nonlinearities of the system and limit cycle oscillations which may be chaotic or periodic are eventually established.
The time series of the limit cycle oscillations may exhibit characteristics similar to the neutrally stable condition.
Ledinegg instability | Revolvy
Further, even in steady state case, especially for two-phase systems with slug flow, small amplitude oscillations are visible. Thus, for identification purposes especially during experiments, often it becomes necessary to quantify the amplitude of oscillations as a certain percentage of the steady state value.
Instability is undesirable as sustained flow oscillations may cause forced mechanical vibration of components. Further, premature CHF critical heat flux occurrence can be induced by flow oscillations as well instabillity other undesirable secondary effects like power oscillations in BWRs. Instability can also disturb control systems and cause operational problems in nuclear reactors.
Over the years, several kinds of instabilities have been observed in natural circulation systems excited by different mechanisms. Differences also exist in their transport mechanism, oscillatory mode, and analysis methods. In addition,effects of loop geometry and secondary parameters also cause complications in the observed instabilities. Under the circumstances, it looks relevant to classify instabilities into various categories which will help in improving our understanding and hence control of these instabilities.
Mathematically, the fundamental cause of all instabilities is due to instagility existence of competing multiple solutions so that the system is not able to settle down to anyone of them permanently. Instead, the system swings from one solution to the other.
An essential characteristic of the unstable oscillating NC systems is that as it tries to settle down to one of the solutions, a self-generated feedback appears making another solution more attractive causing the system to swing toward it. Again, during the process of settling down on this solution, another feedback of opposite sign inztability the original solution is self-generated and the system ledniegg back to it.
The process repeats itself resulting in perpetual oscillatory behavior if the operating conditions are maintained constant. Although this is a instaility characteristic it hardly distinguishes the different types of instabilities found to occur in various systems. In general, instabilities can be instabjlity according to various bases as follows:. In some cases, the occurrence of multiple solutions and the instability threshold itself can be predicted from the steady-state equations governing the process pure or fundamental static instability.
The Ledinegg-type instability is one such example occurring in boiling two-phase NC systems. The occurrence of this type of instability can be ascertained by investigating the steady-state behavior alone. The criterion for this type of instability is given by where is the internal pressure loss in the system and is the driving head due to buoyancy.
The internal pressure 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. The driving head is basically the gravitational head available from the steam drum to the bottom of the heated section.
Figures 1 a and 1 b show an example of occurrence of Ledinegg-type instability at different powers [ 2 ] in a boiling two-phase NC system. When the power is in between the above specified range, the internal pressure loss curve intersects the driving buoyancy curve at three points i. Like the Ledinegg instability, the flow pattern transition instability is another static instability caused by the excursion of flow due to differences in the pressure drop characteristics of different flow patterns.
To analyze this type instability, it is required to predict the pressure drop characteristics of the system against the flow rate similar to the Ledinegg-type instability [ 3 ]. Figure 2 shows an example of the steady-state pressure drop characteristics of the system for analysis of flow pattern transition instability. The gravitational head, which depends on the density of the single-phase fluid, remains constant at a particular core inlet temperature.
The different flow patterns in the vertical and horizontal portions of the riser pipes are shown in the two-phase region at the operating conditions. It can be observed from Figure 3 that there can be multiple steady-state flow rates point at which the driving head intersects the internal loss curve at this operating condition.
The number of flow excursions is seen to be five, unlike that of the Ledinegg-type instability. The type of flow excursion in different flow regimes are observed to be as follows: The next flow excursion occurs due to rise in pressure drop when the flow pattern changes from annular to slug flow in the vertical portion of the riser pipes.
The other flow excursion occurs when the flow pattern changes from the annular to dispersed bubbly flow in the horizontal portion of riser pipes due to reduction of pressure drop with flow rate.
The last flow excursion occurs when the flow becomes single phase and the pressure drop increases with increase in flow rate. 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 existence of multiple flow rates as a particular operating power and subcooling makes the system unstable. For example, if the system is initially operating at point C, any slight disturbance causing the flow to increase will shift the flow rate to point D and the to point E.
Similarly, any slight disturbance causing the flow rate to decrease will shift the operating point to B and then to point A. Thus, the flow rate can jump from one value to the other even ledineyg the operating power and pressure are constant. This makes the system unstable. However, there are many situations with multiple steady-state solutions where the threshold of instability cannot be predicted from the steady-state laws alone or the predicted threshold is modified by other effects.
In this case, feedback effects are important in predicting the threshold compound static instability. Besides, many NCSs with only a unique steady-state solution can also become unstable during the approach to the steady state due to the appearance ldinegg competing multiple solutions due to the inertia and feedback effects pure dynamic instability.
Neither the cause nor the threshold of instability of such systems can be predicted purely from the steady state equations alone.
Instead, it requires the full transient governing equations to be considered for explaining the cause and predicting the threshold. In addition, in many oscillatory conditions, secondary phenomena get excited and they modify significantly the instabiliy of the fundamental instability. In such cases, even the prediction of the instability threshold may require consideration of the secondary effect compound dynamic instability.
A typical case is the neutronic feedback responding to the void fluctuations resulting in both flow and power oscillations in a BWR. 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.
Ledinegg instability in microchannels
Thus we find that the analysis ledineg arrive at the instability threshold can be based on different sets of governing equations for different instabilities. This classification is actually restricted to only the dynamic instabilities. According to Boure et al. In two-phase flow, the disturbances can be transported by two different kinds of waves: In any two-phase system, both types inztability waves are present, however, their velocities differ by one or two orders of magnitude allowing us to distinguish between the two.
Acoustic instability is considered to be caused by the resonance of pressure waves. Acoustic oscillations are also observed during blowdown experiments with pressurized hot-water systems possibly due to multiple wave reflections. Acoustic oscillations have been observed in subcooled boiling, bulk boiling, and film boiling. The thermal response of the vapor film to passing pressure wave is suggested as a mechanism for the oscillations during film boiling. For example, when a compression pressure wave consists of compression and rarefaction wave passes, the vapor film is compressed enhancing its thermal conductance resulting in increased vapor generation.
On the other hand when a rarefaction wave passes, the vapor film expands reducing its thermal conductance resulting in decreased vapor generation. The process repeats itself.
A density-wave instability is the typical dynamic instability which may occur due to the multiple regenerative feedback between the flow rate, enthalpy, density, and pressure drop in the boiling system. The occurrence of the instability depends on the perturbed pressure drop in the two-phase and single-phase regions of the system and the propagation time delay of the void fraction or density in the system. Such an instability can occur at very low-power and intsability high-power conditions.
This depends on the relative importance of instabi,ity respective components of pressure drop such as gravity or frictional losses in the system. Fukuda and Kobori [ 5 ] have classified the density-wave instability as type I and type II for the low power and high-power instabilities, respectively.
The mechanisms can be explained as follows [ 6 ]. Type I Instability For this type of instability to occur, the presence of a long riser plays an important role such as in a boiling two-phase natural circulation loop. Under low quality conditions, a slight change in quality due to any disturbance can cause a large change in void fraction and consequently in the driving head.
Therefore, the flow can oscillate at such low-power conditions. But as the power increases, the flow quality increases where the slope of the void fraction versus quality reduces. This can suppress the fluctuation of the driving head for a small change in quality. Hence, the flow stabilises at higher power Figures 3 a and 3 b. This instability is driven by the interaction between the single and two-phase frictional component of pressure losses, mass flow, void formation, and propagation in the two-phase region.
At high power, the flow quality or void fraction in the system is very large. Hence, the two-phase frictional pressure loss may be high owing to the smaller two-phase mixture density. Having a large void fraction will increase the void propagation time delay in the two-phase region of the system. Under these conditions, any small fluctuation in flow can cause a larger fluctuation of the two-phase frictional pressure loss due to fluctuation of density and flow, which propagates slowly in the two-phase region.
On the other hand, the fluctuation of the pressure drop in the single-phase region occurs due to fluctuation of flow alone since the fluctuation of the density is negligible.