Instability analysis

N. Noiray, D. Durox, T. Schuller, and S. Candel. A unified framework for nonlinear combustion instability analysis based on the flame describing function. /. Fluid Mech., 2008 (In press). 

Recently, Razumovskid441 studied the shape of drops, and satellite droplets formed by forced capillary breakup of a liquid jet. On the basis of an instability analysis, Teng et al.[442] derived a simple equation for the prediction of droplet size from the breakup of cylindrical liquid jets at low-velocities. The equation correlates droplet size to a modified Ohnesorge number, and is applicable to both liquid-in-liquid, and liquid-in-gas jets of Newtonian or non-Newtonian fluids. Yamane et al.[439] measured Sauter mean diameter, and air-entrainment characteristics of non-evaporating unsteady dense sprays by means of an image analysis technique which uses an instantaneous shadow picture of the spray and amount of injected fuel. Influences of injection pressure and ambient gas density on the Sauter mean diameter and air entrainment were investigated parametrically. An empirical equation for the Sauter mean diameter was proposed based on a dimensionless analysis of the experimental results. It was indicated that the Sauter mean diameter decreases with an increase in injection pressure and a decrease in ambient gas density. It was also shown that the air-entrainment characteristics can be predicted from the quasi-steady jet theory. 

Alternative methods of analysis have been examined and evaluated. Shokoohi and Elrod[533] solved the Navier-Stokes equations numerically in the axisymmetric form. Bogy15271 used the Cosserat theory developed by Green.[534] Ibrahim and Linl535 conducted a weakly nonlinear instability analysis. The method of strained coordinates was also examined. In spite of the mathematical or computational elegance, all of these methods suffer from inherent complexity. Lee15361 developed a 1 -D, nonlinear direct-simulation technique that proved to be a simple and practical method for investigating the nonlinear instability of a liquid j et. Lee s direct-simulation approach formed the... 

AN INSTABILITY ANALYSIS OF HETEROEPITAXIAL INTERLACES VIA A DISCRETE ATOM METHOD... 

An instability analysis of a multiphase flow is usually based on the continuum assumption and the equations of motion of the phases. Two different approaches are common. One approach is to study the wave propagation speed from the equations of motion using an analogy to the surface wave situation. The other approach is to study the growth rate of the perturbation wave when a small perturbation wave is introduced to the system. The criterion for stability can then be derived. A perturbation wave can be expressed by... 

Instability Analysis of a Batch-Solid Fluidization System The instability analysis of Eq. (6.182) for a can yield a stability criterion accounting for the conditions under which bubbles will form in a fluidized bed. In this analysis, when bubbles form, the bed is regarded as unstable. Thus, the instability analysis gives rise to the condition for minimum bubbling of the bed (also see 9.4). 

Bi, H. T. and Zhu, J. (1993). Static Instability Analysis of Circulating Fluidized Beds and Concept of High-Density Risers. AlChE J., 39,1272. 

C. D. Han and J. Y. Park, Studies on Blown Film Extrusion, III. Bubble Instability. Analysis of the Deformation and Heat Transfer Process, J. Appl. Polym. Sci., 19, 3291 (1975). 

Instability Analysis from Solntion of Orr-Sommerfeld Equation... 

Let us show a way of locating eigenvalues on the left-half of a— plane from instability analysis point of view. Let us explain the way eigenvalues are located for which Real a) < 0 and Real Q) > 0 and +... 

The quantities with the over-bar are related to the mean flow solutions of the previous section, via the appropriate transformations. The stability equations are obtained by making the additional parallel flow assumption, U = U y), V = 0 and T = T y) so that a normal mode spatial instability analysis is possible by looking for a solution of the linearized equations of the following form ... 

Instability Analysis from Solution of Orr-Sommerfeld Equation 43... 

In addition, sometimes a normal-phase HPLC method at subambient temperature must be applied for analytes that are extremely prone to hydrolysis. In the synthesis of leukotriene D4 antagonist, accurate quantitation of mesylate intermediate is essential for process optimization. Owing to its inherent instability, analysis of mesylate intermediate must be carried out under normal-phase conditions with nonprotic solvents however, significant cycliza-tion of mesylation was stiU observed in such condition at room temperature. The authors concluded that the on-column reaction of the mesylate was silica-catalyzed cyclization. By conducting the normal-phase HPLC analysis at -30 C, it was demonstrated that on-column cyclization was adequately inhibited [30]. 

Figure 1 shows schematically viscous fingering, which occurs because the injection fluid is less viscous, and gravity override, which occurs because the injection fluid is less dense. Chapter 2 of this book, by Chang and Slattery, describes a linear instability analysis for gas flooding and also introduces a nonlinear treatment of the flow instabilities. 

If attention is restricted to the vicinity of the bifurcation point, then a nonlinear perturbation analysis can be developed for describing analytically the nature of the pulsating mode [111]. In effect, the difference between A and its bifurcation value is treated as a small parameter, say e, and oscillatory solutions for temperature profiles are calculated as perturbations about the steady solution in the form of a power series in /e. The departure of the oscillation frequency from its value at bifurcation is expressed in the same type of series. The methods of analysis possess a qualitative similarity to those of the shock-instability analysis discussed at the end of the previous section. The results exhibit the same general behavior that was found from the numerical integrations [109] for conditions near bifurcation. 

Carson, J.M. 2001. Subharmonic and non-subharmonic pulsed control of thermoacoustic instabilities Analysis and experiment. M.S. Thesis. Blacksburg, VA Virginia Polytechnic Institute and State University. 

Baumann, W. T., W. R. Saunders, and J. M. Carson. 2005 (in press). Pulsed control of thermo-acoustic instabilities Analysis and experiment. ASME Transactions on Dynamic Systems, Measurement and Control. 

Rayleigh [5] used a periodic perturbation in both axial and angular direction of the following form R = a + cos kx cos mO, here, w = 1 is termed kink mode and m > 2 are termed flute modes. However, he showed that the linear instability analysis provides that the jet is stable for all angular disturbances, and it is only the axial disturbances that may be unstable. This is related to the fact that only the axisymmetric perturbations can reduce the surface energy. Therefore, we only consider the axial disturbances. 

The DPF method [5-7] assumes spray formation is a combination of random and nonrandom processes. An instability analysis is used to describe primary breakup, which is uniquely determined for a given set of initial conditions (fluid physical properties and atomizer parameters) and a model of the breakup mechanism. The drop size distribution arises from fluctuations in the initial conditions due to such factors as gas and liquid turbulence, atomizer passage surface roughness, vortex shedding, liquid mixture composition, etc. 

Inputs that can be computed now One representative diameter (from instability analysis) No experimental PDFs exist N/A... 

Dombrowski and John [36] provided a mean drop size d for an impinging jet based on sheet instability analysis (see Chapter 3) ... 

There has been some development in the numerical modeling of the sheet formation from swirl nozzles. A fully nonlinear model using an axisymmetric boundary element formulation has been developed for simulating the free surface shape and spray formed by simplex/pressure swirl atomizers [30, 32]. A linear instability analysis by Ponstein has been used to predict the number of droplets formed from each ring-shaped ligament shed from the parent surface. 

The limit equilibrium methods forming the framework of slope stability/instability analysis generally accept the Mohr-Coulomb failure criterion, which can be expressed in terms of effective or total stresses. The Mohr-Coulomb shear strength in terms of effective stresses is as follows ... 

Bi HT, Zhu JX. Static instability analysis of circulating fluidized beds and the concept of high-density risers. AIChE J 39 1272-1280, 1993. 

Analyzing the Laplace pressure difference in a film sinusoidally perturbed (given by the two principal radii of curvature) it results that the pressure in a valley is larger than in a crest if the wavelength of the perturbation (A.) is larger than Ina, where a is the fiber radius. In this case, the liquid flows from the valley to the crest and the perturbation is increased. A first order instability analysis shows that the fastest growing perturbation has a wavelength... 

The inability to obtain general analytical solution of the problem makes the linear instability analysis the most widely applied mathematical approach [487,537,538]. In Secs. Vni.B.l and VIII.B.2, we review the application of this approach to free and wetting thin liquid films. 

Chen K, Richter HJ (1997) Instability analysis of the transition from bubbhng to jetting in a gas injected into a liquid. Int J Multiphase How 23(4) 699-712... 

Tian, W., Tian, X., Feng, J., et al., 2013. Flow instability analysis of supercritical water-cooled reactor CSRIOOO based on frequency domain. Nuclear Power Engineering 1, 45—51. 

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