Hydrodynamic instability model

Models available to explain the CHF phenomenon are the hydrodynamic instability model and the macrolayer dryout model. The former postulates that the increase in vapor generation from the heater surface causes a limit of the steady-state vapor escape flow when CHF occurs. The latter postulates that a liquid sublayer (macrolayer) formed on the heating surface (see Secs. 2.2.5.5 and 2.4.1.2)... 

For the hydrodynamic instability model, Lienhard and Dhir (1973b) extended the Zuber model to the CHF on finite bodies of several kinds (see Sec. 2.3.1, Fig. 2.18). Lienhard and Hasan (1979) proposed a mechanical energy stability criterion The vapor-escape wake system in a boiling process remains stable as long as the net mechanical energy transfer to the system is negative. They concluded that there is no contradiction between this criterion and the hydrodynamic instability model. 

Macrolayer Consumption Model. Although the hydrodynamic instability model agrees well with much of the experimental data, the very extensive photographic studies that have been conducted on boiling (exemplified by those sketched in Fig. 15.48) indicate a quite different pattern of behavior as the critical heat flux is approached. Thus, vapor mushrooms are... 

Correlations for CHF in Pool Boiling. Most correlations for critical heat flux in pool boiling have been of the form indicated in Eq. 15.128. Although this equation was introduced in the context of the hydrodynamic instability model of Zuber [159,160], the form of the equation was derived some years earlier by Kutateladze [166], Thus, the use of the equation is not necessarily associated with any physical model. In the following text, equations will be given for the most usual practical cases of horizontal flat plates and horizontal cylinders relationships for other shapes are discussed by Lienhard and Dhir [155,161],... 

Reactors which generate vortex flows (VFs) are common in both planktonic cellular and biofilm reactor applications due to the mixing provided by the VF. The generation of Taylor vortices in Couette cells has been studied by MRM to characterize the dynamics of hydrodynamic instabilities [56], The presence of the coherent flow structures renders the mass transfer coefficient approaches of limited utility, as in the biofilm capillary reactor, due to the inability to incorporate microscale details of the advection field into the mass transfer coefficient model. 

The substantial effect of secondary breakup of droplets on the final droplet size distributions in sprays has been reported by many researchers, particularly for overheated hydrocarbon fuel sprays. 557 A quantitative analysis of the secondary breakup process must deal with the aerodynamic effects caused by the flow around each individual, moving droplet, introducing additional difficulty in theoretical treatment. Aslanov and Shamshev 557 presented an elementary mathematical model of this highly transient phenomenon, formulated on the basis of the theory of hydrodynamic instability on the droplet-gas interface. The model and approach may be used to make estimations of the range of droplet sizes and to calculate droplet breakup in high-speed flows behind shock waves, characteristic of detonation spray processes. 

The first simulations of the collapsar scenario have been performed using 2D Newtonian, hydrodynamics (MacFadyen Woosley 1999) exploring the collapse of helium cores of more than 10 M . In their 2D simulation MacFadyen Woosley found the jet to be collimated by the stellar material into opening angles of a few degrees and to transverse the star within 10 s. The accretion process was estimated to occur for a few tens of seconds. In such a model variability in the lightcurve could result for example from (magneto-) hydrodynamic instabilities in the accretion disk that would translate into a modulation of the neutrino emission/annihilation processes or via Kelvin-Helmholtz instabilities at the interface between the jet and the stellar mantle. 

As shown in Figure 26.1, the wide gap opens up between the particle and continuum paradigms. This gap cannot be spanned using statistical mechanical methods only. The existing theoretical models to be applied in the mesoscale are based on heuristics obtained via downscaling of macroscopic models and upscaling particle approach. Simphfied theoretical models of complex fluid flows, e.g., flows in porous media, non-Newtonian fluid dynamics, thin film behavior, flows in presence of chemical reactions, and hydrodynamic instabilities formation, involve not only vah-dation but should be supported by more accurate computational models as well. However, until now, there has not been any precisely defined computational model, which operates in the mesoscale, in the range from 10 A to tens of microns. 

In Figure 26.24 we display the snapshots from modeling of the R-T hydrodynamic instability using smoothed particle hydrodynamics in which 10 smoothed particles were modeled in about 3000 timesteps. 

Michelson, D. M., Sivashinsky, G. I. (1977) Nonlinear analysis of hydrodynamic instability in laminar flames - II. Numerical experiments. Acta Astronautica 4, 1207 Moon, H. T., Huerre, P., Redekopp, L. G. (1982) Three-frequency motion and chaos in the Ginzburg-Landau equation. Phys. Rev. Lett. 49, 458 Murray, J. D. (1976) On travelling wave solutions in a model for the Belousov-Zhabotinsky reaction. J. Theor. Biol. 56, 329... 

S.S. Minaev, E.A. Pirogov, O. V. Sharypov, A nonlinear model for hydrodynamic instability of an expanding flame. Combust. Explo. Shock Waves 32(5), 481 88 (1996)... 

The lumped parameter model of Example 13.9 takes no account of hydrodynamics and predicts stable operation in regions where the velocity profile is elongated to the point of instability. It also overestimates conversion in the stable regions. The next example illustrates the computations that are needed... 

An alternative description of membrane stability has been based on hydrodynamic models, originally developed for liquid films in various environments [54-56]. Rupture of the film was rationalized by the instability of symmetrical squeezing modes (SQM) related to the thickness fluctuations. In the simplest form it can be described by a condition [54] d Vdis/dh < where is the interaction contribution related to the dis-... 

Similar instability is caused by the electrostatic attraction due to the applied voltage [56]. Subsequently the hydrodynamic approach was extended to viscoelastic films apparently designed to imitate membranes (see Refs. 58-60, and references therein). A number of studies [58, 61-64] concluded that the SQM could be unstable in such models at small voltages with low associated thinning, consistent with the experimental results. However, as has been shown [60, 65-67], the viscoelastic models leading to instability of the SQM did not account for the elastic force normal to the membrane plane which opposes thickness... 

Throughout this chapter we focus on the extended hydrodynamic description for smectic A-type systems presented in [42,43], We discuss the possibility of an undulation instability of the layers under shear flow keeping the layer thickness and the total number of layers constant. In contrast to previous approaches, Auernhammer et al. derived the set of macroscopic dynamic equations within the framework of irreversible thermodynamics (which allows the inclusion of dissipative as well as reversible effects) and performed a linear stability analysis of these equations. The key point in this model is to take into account both the layer displacement u and the director field ft. The director ft is coupled elastically to the layer normal p = in such a way that ft and p are parallel in equilibrium z is the coordinate perpendicular to the plates. 

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