Fluid dynamic instability

In many applications involving nonequilibrium instabilities and dissipative structures, the sharp transitions corresponding to bifurcation rarely occur. Small impurities, imperfections, or external fields tend to distort these transitions. Many experiments, particularly in fluid dynamics, illustrate this fact and demonstrate, in addition, that small imperfections may have large or even qualitative effects. This very general phenomenon is at the basis of the enhanced sensitivity of systems operating near a bifurcation point discussed in the chapter by I. Prigogine. 

Combustion instability that leads to performance deterioration and excessive mechanical loads, which could result in reduced life and premature failure, is an important issue with modern gas turbine engines and ramjet and scramjet combustors. Various techniques of passive and active control to reduce combustion instabilities and improve performance are addressed. Since extensive, promising research is being carried out to develop sensors and actuators, these techniques can be used in practical combustors in the near future. The topics covered in Section 3 provide the required chemical, kinetic, and fluid dynamic understanding to help the designer who is involved in active feedback control for combustion systems. 

Later, the critical Re was further raised for pipe flows, establishing that there is perhaps no upper limit above which transition to turbulence can not be prevented. This example also suggests the importance of receptivity of flow to different types of input disturbances to the system. If there is no input to a fluid dynamical system of a particular kind that triggers instability, then the response will demonstrate the flow to be orderly, even if the fluid dynamical system is unstable to that kind of input. Thus, if the basic flow is receptive to a particular disturbance, then the equilibrium flow will not be observable in the presence of such disturbances. 

Here, we will investigate the stability property of mixed convection flow past a heated horizontal plate, to provide the threshold buoyancy parameter that alters the instability property qualitatively. Such a problem is of importance for many engineering applications and in geophysical fluid dynamics. We also note that Steinriick (1994) has shown, for mixed convection over a horizontal plate that is cooled to exhibit non-uniqueness and numerical instabilities for the corresponding boundary layer equation, that would not affect the analysis when the plate is heated. 

The following chapters present an overview of combustion and of CFD (Computational Fluid Dynamics) for combustion. The objective is not to repeat classical textbooks on these topics [379 306 288 334 340] but to focus on the place of instabilities in reacting flows and in CFD for reacting flows. These instabilities are found at many levels ... 

A rigorous mathematical treatment of mass-transfer instability is difficult and requires a detailed knowledge of fluid dynamics in the reactor, information hard to come by. The best way to proceed in process design therefore is to establish approximately where the limit of stability lies, and then keep away from it by a safe margin. No plant operates without excursions from design operating conditions, and the risk that it could stray into the region of instability must be minimized. 

Instabilities arise in combustion processes in many different ways a thorough classification is difficult to present because so many different phenomena may be involved. In one approach [1], a classification is based on the components of a system (such as a motor or an industrial boiler) that participate in the instability in an essential fashion. Three major categories are identified intrinsic instabilities, which may develop irrespective of whether the combustion occurs within a combustion chamber, chamber instabilities, which are specifically associated with the occurrence of combustion within a chamber, and system instabilities, which involve an interaction of processes occurring within a combustion chamber with processes operative in at least one other part of the system. Within each of the three major categories are several subcategories selected according to the nature of the physical processes that participate in the instability. Thus intrinsic instabilities may involve chemical-kinetic instabilities, diffusive-thermal instabilities, or hydrodynamic instabilities, for example. Chamber instabilities may be caused by acoustic instabilities, shock instabilities, or fluid-dynamic instabilities within chambers, and system instabilities may be associated with feed-system interactions or exhaust-system interactions, for example, and have been assigned different specific names in different contexts. 

In simulations for engineering problems involving turbulent combustion, a RANS description of the flow [1] and simplistic combustion models (e.g., [2]) are typically combined. This involves simulating only the mean flow-field features and modeling the effects of the entire range of turbulent scales. The restricted information provided by this approach, regarding the fluid dynamics, combustion, and their different interactions, precludes adequate prediction of the important phenomena required to achieve effective control of the combustion processes, such as combustion-induced flow instabilities, cycle-to-cycle variations, and combustion oscillations associated with unsteady vortex dynamics. 

For the MTBE process also oscillatory behavior was reported in the literature. Potential sources for such an oscillatory behavior are either unwanted periodic forcing (e. g., by badly tuned controllers), fluid dynamic instabilities, or instabilities of the concentration dynamics. 

Fluid dynamic instabilities were reported for the MTBE process by Sundmacher and Hoffmann [104]. The cycle times for fluid dynamic oscillations are typically in... 

At low values of the capillary number (typically Ca < 10 ), formation of droplets follows the squeezing model, at intermediate values of Ca the device operates in the dripping mode in which the viscous effects become more important and, at highest flow rates, the system develops a long jet and droplets are sheared off due to fluid dynamics instabilities effects. ... 

Abstract In an effort to characterize fuel sprays using Computational Fluid Dynamics (CFD) codes, a number of spray breakup models have been developed. The primary atomization of liquid jets and sheets is modeled considering growing wave instabilities on the liquid/gaseous interface or a combination of turbulence perturbations and instability theories. The most popular approaches for the secondary atomization are the Taylor Analogy Breakup (TAB) model, the Enhanced-TAB (E-TAB) model, and the WAVE model. Variations and improvements of these models have also been proposed by other researchers. In this chapter, an overview of the most representative models used nowadays is provided. 

Abstract Among the noncontinuum-based computational techniques, the lattice Boltzman method (LBM) has received considerable attention recently. In this chapter, we will briefly present the main elements of the LBM, which has evolved as a minimal kinetic method for fluid dynamics, focusing in particular, on multiphase flow modeling. We will then discuss some of its recent developments based on the multiple-relaxation-time formulation and consistent discretizatirai strategies for enhanced numerical stability, high viscosity contrasts, and density ratios for simulation of interfacial instabilities and multiphase flow problems. As examples, numerical investigations of drop collisions, jet break-up, and drop impact on walls will be presented. We will also outline some future directions for further development of the LBM for applications related to interfacial instabilities and sprays. 

G. A. BlaisdeU, Collicott, S. H., and Portillo J. E., Measurements of instability waves in a high-speed liquid jet, 61st Conference of the American Physical Society, Division of Fluid Dynamics, San Antonio TX, 2008. 

Even though the transition regime may offer a maximum for the gas holdup and interfacial area, it is not desired for industrial processes due to its unstable and erratic nature. The instability has made the exact identification of the transition point nearly impossible. Although computational fluid dynamics and other methods are capable of predicting the other flow regimes, these methods usually have a difficult time predicting the transition point or the hydrodynamic behavior near it (Olmos et al., 2003). Hence, even if the operator wanted to work with the transition regime, it would be nearly impossible to achieve consistent results. 

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. 

Linde, H., Schwartz, R, and Wilke, H., Dissipative structures and nonlinear kinetics of the Marangoni instability, in Dynamics and Instability of Fluid Interfaces, Sorensen, T.S. (ed.). Springer-Verlag, Berlin, 1979, p. 75. 

Mass-transport (i.e., diffusion or electromigration) effects are particularly acute in the cases of cracking, pitting, and crevice corrosion, whereby occlusion effects can create highly concentrated solutions that move an otherwise stable system into regions of thermodynamic instability at the local level [13,14,41 3, 79-82]. When porous films or particular solution flow conditions exist, mass-transport effects should also be taken into account [83, 84]. Molecular dynamics and Monte Carlo simulations of interfaces over the past few decades have provided some insight into the concentration gradients that occur close to the electrochemical interface [85-91], and these, coupled with computational fluid dynamics simulations, can indicate the extent to which mass-transport effects can dominate an overall corrosion scenario [92]. 

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