Fluid instabilities

T.J. Poinsot, A.C. Trouv D.P. Veynante, S.M. Candel, and E.J. Esposito. Vortex driven acoustically coupled combustion instabilities. /. Fluid Mech., 177 265-292,1987. 

Figure 10.4.2 Photographs of liquid jet breakup in air (A) into spherical drops. [Courtesy of Prof. Richard K. Chang. From Qian, S-X. et al. 1986. Lasing droplets Highlighting the liquid-air interface by laser emission. Science 231, 486-488. Copyright 1986 by the AAAS. With permission.] (B) into spherical drops with satellite droplets. [Courtesy of Prof. M.C. Yuen. From Goedde, E.F. Yuen, M.C. 1970. Experiments on liquid jet instability. /. Fluid Mech. 40, 495-511. Cambridge University Press. With permission.]...

Sivashinsky G I 1983 Instabilities, pattern formation and turbulence in flames Ann. Rev. Fluid Mech. 15 179-99... 

A second case to be considered is that of mixtures witli a small size ratio, <0.2. For a long time it was believed tliat such mixtures would not show any instability in tire fluid phase, but such an instability was predicted by Biben and Flansen [109]. This can be understood to be as a result of depletion interactions, exerted on the large spheres by tire small spheres (see section C2.6.4.3). Experimentally, such mixtures were indeed found to display an instability [110]. The gas-liquid transition does, however, seem to be metastable witli respect to tire fluid-crystal transition [111, 112]. This was confinned by computer simulations [113]. 

Fig. 14. Shear instability in stably stratified fluid lower denser fluid is dyed.

Taylor instabilities involve effects of buoyancy or acceleration in fluids with variable density a light fluid beneath a heavy fluid is unstable by the Taylor mechanism. The upward propagation of premixed flames in tubes is subject to Taylor instability (11). 

Phase Diagram (Zenz and Othmer) Zenz and Othmer (op. cit.) have graphically represented (Fig. 17-2) all gas-solid svstems in which the gas is flowing counter to gravity as a function o pressure drop per unit of height versus velocity. Note that line OAB in Fig. 17-2 is the pressure-drop versus gas-velocity curve for a packed bed and BD the cui ve for a fluid bed. Zenz indicates an instability between D and H because with no sohds flow all the particles will be entrained from the bed however, if sohds are added to replace those entrained, system JJ prevails. The area DHJJ will be discussed further. 

Whirl from fluid trapped in the rotor. This type of whirl oeeurs when liquids are inadvertently trapped in an internal rotor eavity. The meehanism of this instability is shown in Figure 5-24. The fluid does not flow in a radial direetion but flows in a tangential direetion. The onset of instability oeeurs between the first and seeond eritieal speeds. Table 5-4 is a handy summary for both avoidanee and diagnosis of self-exeitation and instabilities in rotating shafts. 

Figure 5-24. Whirl from fluid trapped in the rotor. (Ehrich, F.F., Identification and Avoidance of Instabilities and Self-Excited Vibrations in Rotating Machinery, Adopted from ASME Paper 72-DE-21, General Electric Co., Aircraft Engine Group, Group Engineering Division, May 11, 1972.)...

T. Biben, J. P. Hansen. Spinodal instability of suspensions of large spheres in a fluid of small spheres. J Phys Condens Matter 2 F65-72, 1991. 

D. C. Morse. Topological instabilities and phase behavior of fluid membranes. Phys Rev E 50 R2419-R2422, 1994. 

The primary vibration frequency components associated with fluid-film bearings problems are in fact displays of turbulent or non-uniform oil film. Such instability problems are classified as either oil whirl or oil whip depending on the severity of the instability. 

Church s equations, 176-177 Combustion instability, 52-57 bulk-coupled, 56-57 pressure-coupled, 52-55 velocity-coupled, 55-56 steady-state, 29-51 prediction, 30 pressure plateaus, 34 propellants, 31-50 termination, 57-64 depressurization, 58-62 fluid-injection, 63-64 L, 62-63... 

When a bluff body is interspersed in a fluid stream, the flow is split into two parts. The boundary layer (see Chapter 11) which forms over the surface of the obstruction develops instabilities and vortices are formed and then shed successively from alternate sides of the body, giving rise to what is known as a von Karman vortex street. This process sets up regular pressure variations downstream from the obstruction whose frequency is proportional to the fluid velocity, as shown by Strouai. 9. Vortex flowmeters are very versatile and can be used with almost any fluid — gases, liquids and multi-phase fluids. The operation of the vortex meter, illustrated in Figure 6.27, is described in more detail in Volume 3, by Gjnesi(8) and in a publication by a commercial manufacturer, Endress and Hauser.10 ... 

The experimental investigations of boiling instability in parallel micro-channels have been carried out by simultaneous measurements of temporal variations of pressure drop, fluid and heater temperatures. The channel-to-channel interactions may affect pressure drop between the inlet and the outlet manifold as well as associated temperature of the fluid in the outlet manifold and heater temperature. Figure 6.37 illustrates this phenomenon for pressure drop in the heat sink that contains 13 micro-channels of d = 220 pm at mass flux G = 93.3kg/m s and heat flux q = 200kW/m. The temporal behavior of the pressure drop in the whole boiling system is shown in Fig. 6.37a. The considerable oscillations were caused by the flow pattern alternation, that is, by the liquid/two-phase alternating flow in the micro-channels. The pressure drop FFT is presented in Fig. 6.37b. Under... 

Wojtan L, Revellin R, Thome J (2006) Investigation of critical heat flux in single uniformly heated micro-channels. Exp. Therm, Fluid Sci. 30 765-774 Wu H Y, Cheng P (2004) Boiling instability in parallel silicon micro-channels at different heat flux. Int J Heat Mass Transfer 47 3631-3641... 

Kandlikar SG, Joshi S, Tian S (2003) Effect of surface roughness on heat transfer and fluid flow characteristics at low Reynolds numbers in small diameter tubes. Heat Transfer Eng 24 4-16 Kawahara A, Chung PM, Kawaji M (2002) Investigation of two-phase flow pattern, void fraction and pressure drop in a micro-channel. Int J Multiphase Flow 28 1411-1435 Kennedy JE, Roach GM, Dowling ME, Abdel-Khalik SI, Ghiaasiaan SM, Jeter SM, Quershi ZH (2000) The onset of flow instability in uniformly heated horizontal micro-channels. Trans ASME J Heat Transfer 122 118-125... 

The forced fluid flow in heated micro-channels with a distinct evaporation front is considered. The effect of a number of dimensionless parameters such as the Peclet, Jacob numbers, and dimensionless heat flux, on the velocity, temperature and pressure within the liquid and vapor domains has been studied, and the parameters corresponding to the steady flow regime, as well as the domains of flow instability are delineated. An experiment was conducted and demonstrated that the flow in microchannels appear to have to distinct phase domains one for the liquid and the other for the vapor, with a short section of two-phase mixture between them. 

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. 

Tube-to-tube interactions. The problems of velocity profile elongation and thermal runaway can be eliminated by using a multitubular reactor with many small-diameter tubes in parallel. Unfortunately, this introduces another form of instability. Tubes may plug with pol5nner that cannot be displaced using the low-viscosity inlet fluid. Imagine a 1000-tube reactor with 999 plugged tubes ... 

Short exposure image of growth of instability on a propane-air flame enriched with oxygen. The image has been rotated 90°. (From Searby, G., Truffaut, J.M., and Joulin, G., Phys. Fluids, 13, 3270, 2001. With permission.)... 

G. Searby, J.M. Truffaut, and G. Joulin. Comparison of experiments and a non-linear model for spatially developing flame instability. Physics of Fluids, 13 3270-3276, 2001. 

P. Clavin, P. Pelc and L. He. One-dimensional vibratory instability of planar flames propagating in tubes. Journal of Fluid Mechanics, 216 299-322, 1990. 

G. Searby and D. Rochwerger. A parametric acoustic instability in premixed flames. Journal of Fluid Mechanics, 231 529-543,1991. 

C. Clanet, G. Searby, and P. Clavin. Primary acoustic instability of flames propagating in tubes Cases of spray and premixed gas combustion. Journal of Fluid Mechanics, 385 157-197,1999. 

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