Instability hydrodynamic

A startling discovery in flame theory was made independently by Darrieus and Landau [190] a stability analysis that neglects body forces and that treats the entire flame simply as a discontinuity in density that 

Since Rq , equation (100) gives a 0 and hence implies instability. 

FIGURE 9.8. Schematic illustration of the mechanism of hydrodynamic instability. 

In dimensional variables, equation (100) states that the growth rate of the disturbance is proportional to the product of the transverse wave number with the geometric-mean flame speed v Vq the factor of proportionality, which depends only on the density ratio, may be written as 

For stationary, planar flames in a vertically upward flow, buoyancy must be a significant contributor to stability. It can be shown [137], [178] that if the hydrodynamic stability problem is addressed as before [190] but with the body-force terms in equations (89) and (90) retained in the differential equations, then equation (100) becomes 

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Since the drop volume method involves creation of surface, it is frequently used as a dynamic technique to study adsorption processes occurring over intervals of seconds to minutes. A commercial instrument delivers computer-controlled drops over intervals from 0.5 sec to several hours [38, 39]. Accurate determination of the surface tension is limited to drop times of a second or greater due to hydrodynamic instabilities on the liquid bridge between the detaching and residing drops [40],... 

Interesting pattern formations also occur in surfactants spreading on water due to a hydrodynamic instability [52]. The spreading velocity from a crystal may vary with direction, depending on the contour and crystal facet. There may be sufficient imbalance to cause the solid particle to move around rapidly, as does camphor when placed on a clean water surface. The many such effects have been reviewed by Stemling and Scriven [53]. 

Landau instabilities are the hydrodynamic instabilities of flame sheets that are associated neither with acoustics nor with buoyancy but instead involve only the density decrease produced by combustion in incompressible flow. The mechanism of Landau instability is purely hydrodynamic. In principle, Landau instabilities should always be present in premixed flames, but in practice they are seldom observed (26,27). 

The frequencies of a spectrum can be divided into two parts subharmonic and harmonic (i.e., frequencies below and above the running speed). The subharmonic part of the spectrum may contain oil whirl in the journal bearings. Oil whirl is identifiable at about one-half the running speed (as are several components) due to structural resonances of the machine with the rest of the system in which it is operating and hydrodynamic instabilities in its journal bearings. Almost all subharmonic components are independent of the running speed. 

In all of these tests, flame acceleration was minimal or absent. Acceleration, when it occurred, was entirely due to intrinsic flame instability, for example, hydrodynamic instability (Istratov and Librovich 1969) or instability due to selective diffusion (Markstein 1964). To investigate whether the flame would accelerate when allowed to propagate over greater distances, tests were carried out in an open-sided test apparatus 45 m long (Harris and Wickens 1989). Flame acceleration was found to be no greater than in the balloon experiments (Table 4.1a). 

B20. Biancone, F., Companile, A., Galimi, G., and Goffi, M., Forced convection burn-out and hydrodynamic instability experiments for water at high pressure. 1. Presentation of data for round tubes with uniform and nonuniform power distribution, EUR 2490e (1965). 

Velocity profile elongation. Low fluid velocities near the tube wall give rise to high extents of pol5merization, high viscosities, and yet lower velocities. The velocity profile elongates, possibly to the point of hydrodynamic instability. 

All premixed flames are xmconditionally unstable to a hydrodynamic instability that has its origin in the expansion of the gas through the flame (but the flame may remain planar for other reasons). This phenomenon was first recognized by George Darrieus [1] and independently by Lev Landau [2], and is usually referred to as the Darrieus-Landau instability. The full derivation of the instability is arduous here we will give a simple heuristic explanation. 

Swinney, H.L. Gollub, J.P., Hydrodynamic Instabilities and the Transition to Turbulencef Springer-Verlag, New York, 1981. 

Figure 2.62 VOF-based simulation of a water cylinder decaying into droplets by a hydrodynamic instability [182],...

For axial capillary flow in the z direction the Reynolds number, Re = vzmaxI/v = inertial force/viscous force , characterizes the flow in terms of the kinematic viscosity v the average axial velocity, vzmax, and capillary cross sectional length scale l by indicating the magnitude of the inertial terms on the left-hand side of Eq. (5.1.5). In capillary systems for Re < 2000, flow is laminar, only the axial component of the velocity vector is present and the velocity is rectilinear, i.e., depends only on the cross sectional coordinates not the axial position, v= [0,0, vz(x,y). In turbulent flow with Re > 2000 or flows which exhibit hydrodynamic instabilities, the non-linear inertial term generates complexity in the flow such that in a steady state v= [vx(x,y,z), vy(x,y,z), vz(x,y,z). ... 

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. 

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. 

Figure 6.5 Effect of pressure on the power density at hydrodynamic instability. (From Mathisen, 1967. Copyright 1967 by Office for Official Publications of the European Community, Luxembourg. Reprinted with permission.)... 

Biancone, F., A. Campanile, G. Galimi, and M. Goffi, 1965, Forced Convection Burnout and Hydrodynamic Instability. Experiments for Water at High Pressure. I. Presentation of Data for Round Tubes with Uniform and Non-Uniform Power Distribution, Italian Rep. EUR-2490 e, European Atomic Energy Community, Brussels, Belgium. (5)... 

Collins, D. B., and M. Gacesa, 1969, Hydrodynamic Instability in a Full-Scale Simulated Reactor Channel, Proc. Inst. Mech. Eng. 184. (6)... 

Macbeth, R. V., 1963b, Forced Convection Burnout in Simple, Uniformly Heated Channels A Detailed Analysis of World Data, European Atomic Energy Community Symp. on Two Phase Flow, Steady State Burnout and Hydrodynamic Instability, Stockholm, Sweden. (5)... 

Neal, L. G., S. M. Zivi, and R. W. Wright, 1967, The Mechanisms of Hydrodynamic Instabilities in Boiling Channel, Euratom Rep., Proc. Symp. on Two-Phase Flow Dynamics, Eindhoven, The Netherlands. (6)... 

Waters, E. D., J. K. Anderson, W. L. Thorne, and J. M. Batch, 1965, Experimental Observations of Upstream Boiling Burnout, AIChE Chem. Eng. Prog. Symp. Ser. 67(57) 230 237. (5) Weatherhead, R. J., 1962, Hydrodynamic Instability and the Critical Heat Flux Occurrence in Forced Convection Vertical Boiling Channels, USAEC Rep. TID-16539, Washington, DC USAEC Rep. ANL-6675, Argonne National Lab, Argonne, IL. (5)... 

Pulsation in a spray is generated by hydrodynamic instabilities and waves on liquid surfaces, even for continuous supply of liquid and air to the atomizer. Dense clusters of droplets are projected into spray chamber at frequencies very similar to those of the liquid surface waves. The clusters interact with small-scale turbulent structures of the air in the core of the spray, and with large-scale structures of the air in the shear and entrainment layers of outer regions of the spray. The phenomenon of cluster formation accounts for the observation of many flame surfaces rather than a single flame in spray combustion. Each flame surrounds a cluster of droplets, and ignition and combustion appear to occur in configurations of flames surrounding droplet clusters rather than individual droplets. 

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. 

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