Flow pattern transition instability

Analysis of flow-pattern transition instability The boundary of flow pattern transitions is not sharply defined, but is usually an operational band. As discussed in Chapter 3, analytical methods for predicting the stability of flow patterns are quite limited and require further development. The same is true for analyses of nonequilibrium state instability. 

Static Flow pattern transition instability Cyclic flow pattern transition and flow rate variations [8]... 

Check the static instabilities by steady-state correlations, to avoid or alleviate the primary phenomenon of a potential static instability, namely, boiling crisis, vapor burst, flow pattern transition, and the physical conditions that extend the static instability into repetitive oscillations. 

Characteristic pressure drop vs. flow rate instabilities Ledinegg instability Flow distribution instabrbty Flow pattern transition Pressure Drop Oscillation (PDO)... 

Prediction of the heat-transfer coefficient in the transition flow regime is uncertain due to the strong effects of entrance conditions and instability of the flow pattern. Gnielinski [18] modified the Petukhov-Popov equation to accommodate the transition region and extend it into the turbulent flow range ... 

This equation has been derived as a model amplitude equation in several contexts, from the flow of thin fluid films down an inclined plane to the development of instabilities on flame fronts and pattern formation in reaction-diffusion systems we will not discuss here the validity of the K-S as a model of the above physicochemical processes (see (5) and references therein). Extensive theoretical and numerical work on several versions of the K-S has been performed by many researchers (2). One of the main reasons is the rich patterns of dynamic behavior and transitions that this model exhibits even in one spatial dimension. This makes it a testing ground for methods and algorithms for the study and analysis of complex dynamics. Another reason is the recent theory of Inertial Manifolds, through which it can be shown that the K-S is strictly equivalent to a low dimensional dynamical system (a set of Ordinary Differentia Equations) (6). The dimension of this set of course varies as the parameter a varies. This implies that the various bifurcations of the solutions of the K-S as well as the chaotic dynamics associated with them can be predicted by low-dimensional sets of ODEs. It is interesting that the Inertial Manifold Theory provides an algorithmic approach for the construction of this set of ODEs. 

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