Flow excursive instability

Ledinegg instability or flow excursive instability is characterized by a sudden change in the flow rate to a lower value or a flow reversal. This happens when the slope of the channel demand pressure drop versus flow rate curve (internal characteristics of the channel) becomes algebraically smaller than that of the loop supply pressure drop vs. flow rate curve (external characteristics of the channel). Physically, this behavior exists when the pressure drop decreases with increasing flow. The criterion or condition for Ledinegg instability to occur is expressed by the inequality (Boure et al., 1973)... 

Analysis of flow excursion The threshold of flow excursion can be predicted by evaluating the Ledinegg instability criterion in a flow system or a loop, Eq. (6-1),... 

Two-phase fluid flows are susceptible to instability and this is often a very important parameter in design. The variation of total pressure drop as a function of flow rate may take the form illustrated in Figure 10-6. For imposed pressure drop APi or AP4 there is only one possible value of flow. However, at AP3 there are two possible values and at APj, three values. Cases with more than one flow rate for a given pressure drop are susceptible to flow excursion from one operating condition to another. Similar excursions are possible when the imposed pressure drop is not constant but follows a pump characteristic such as shown by line PQ. 

Oscillatory instability is the most important form and occurs because of feed-back effects due to time lags in the system. If the inlet flow is oscillated at a given frequency, all components of pressure drop may be additive, but as the frequency increases, lag occurs In the various components. Oscillatory instabilities can be present even in the absence of excursive instability and can occur between parallel tubes forming part of a flow circuit. System instabiiity of the completed circuit can aiso occur. 

Compound dynamic instability as Pressure drop Flow excursion initiates dynamic interaction Very-low—frequency periodic... 

The requirement for both dynamic and static instabilities is that the increase in the two-phase pressure drop should be either equal to or greater than the decrease in the single-phase pressure drop as the inlet flow decreases. The relevant limit is actually the static (non-linear) instability boundary, which may lead to CHF, has been called the "zeroth mode" of dynamic instability. Thus, in dynamic dispersion-type analysis, it corresponds to the time-independent, zero-frequency (or infinite wave number), real wave number case which, corresponds precisely to the homogeneous equilibrium limit for the flow. In non-linear (called excursive instability ), the channels could switch from one flow rate to another while maintaining the same total pressure drop. When non-linearly unstable, the channel flow fluctuates, or reverses, and dryout can ensue. ... 

We review here the viscosity of the most common mobile phases, the factors that influence this viscosity, the temperature, the pressure, and the mobile phase composition, and we discuss two phenomena of practical importance in the preparative applications of chromatography (i) the dependence of the mobile phase viscosity on the concentration in feed components and the pressure excursion generated by the elution of high concentration bands of viscous feed and (ii) the occurrence of flow instabilities and fingerings due to the rapidly varying viscosity of the eluent. 

Bergles and Kandlikar [5] reviewed the existing studies on critical heat flux in microchannels. They concluded by saying that few single-tube CHF data were available for microchannels at the time of their review. For the case of parallel multi-microchannels, they noted that all the available CHF data at that time were taken under unstable conditions, where the critical condition was reached as the result of a compressible volume instability upstream or the excursive Ledinegg instability. As a result, the unstable CHF values reported in the literature were expected to be lower than they would be if the channel flow were kept stable by an inlet restriction. 

Static Ledinegg instability Flow undergoes sudden, large-amplitude excursion to a new stable operating condition [3,7]... 

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