Instability premixed-flame

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). 

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). 

Real-life premixed flame fronts are rarely planar. Of course, if the flow is turbulent, gas motion will continuously deform and modify the geometry of the flame front, see Chapter 7. However, even when a flame propagates in a quiescent mixture, the front rapidly becomes structured. In this chapter, we will discuss hydrodynamic flame instability, thermo-diffusive instability, and thermo-acoushc 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. 

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. 

G. Searby. Acoustic instability in premixed flames. Combustion Science and Technology, 81 221-231, 1992. 

N. Noiray, D. Durox, T. Schuller, and S. Candel. Self-induced instabilities of premixed flames in a multiple self-induced instabilities of premixed flames in a multiple injection configuration. Combust. Flame, 145 435 46, 2006. 

Kadowaki, S. and Hasegawa, T, Numerical simulation of d)mamics of premixed flames Flame instability and vortex-flame interaction. Progress in Energy and Combustion Science, 31, 193-241, 2005. 

This section emphasizes on flame quenching by stretch, as well as highlights and separately discusses the four aspects of counterflow premixed flame extinction limits, including (1) effect of nonequidiffusion, (2) influence of different boundary conditions, (3) effect of pulsating instability, and (4) relahonship of the fundamental limit of flammability. 

Nevertheless, despite all these remarkable achievements, some open questions still remain. Among them is the influence of the molecular transport properties, in particular Lewis number effects, on the structure of turbulent premixed flames. Additional work is also needed to quantify the flame-generated turbulence phenomena and its relationship with the Darrieus-Landau instability. Another question is what are exactly the conditions for turbulent scalar transport to occur in a coimter-gradient mode Finally, is it realistic to expect that a turbulent premixed flame reaches an asymptotic steady-state of propagation, and if so, is it possible, in the future, to devise an experiment demonstrating it ... 

In Chapter 5.3, D. Dunn-Rankin discusses the shape of deflagrations in closed tubes and the conditions under which it assumes the form of a tulip. The propagation of a premixed flame in closed vessels has been studied from the nineteenth century. The tulip flame is an interesting example of flame-flow interaction originating from the Landau-Darrieus instability. 

Heitor, M., A.M. K.P. Taylor, and J.H. Whitelaw. 1984. Influence of confinement on combustion instabilities of premixed flames stabilized on axisymmetric baflfles. Combustion Flame 57 109-21. 

Theoretical Studies of Liquid-Propellant Rocket Instability , Ibid, pp 1101-28 Pj) G.A. McD. Cummings A.R. Hall, "Perchloric Acid Flames Premixed Flames With Methane and Other Fuels , Ibid, 1365-72 P2) D.J. Carlson, Emittance of Condensed Oxides in Solid Propellants Combustion Products , Ibid, 1413-24 Qj) Ibid, "Perchloric Acid Flames Some Flame Temperatures and Burning Velocities , Ministry of Aviation,... 

The first example is a small-scale laboratory combustor using an aeroengine gas turbine burner (power 30 kW) while the second one corresponds to a laboratory-scale staged burner in which self-excited instabilities can be easily triggered by changing the outlet acoustic boundary conditions. In staged combustors, fuel and air are premixed but they are introduced into the chamber at different locations and different equivalence ratios so that partially premixed flames are found inside the burner. All combustors are operated at atmospheric pressure. 

C. Angelberger, D. Veynante, F. Egolfopoulos, and T. Poinsot. Large eddy simulations of combustion instabilities in premixed flames. In Proc. of the Summer Program, pages 61-82. Center for Turbulence Research, NASA Ames/Stanford Univ., 1998. 

Among the areas not covered here is that of intrinsic instabilities associated with chemical-kinetic mechanisms, as exhibited in cool-flame phenomena, for example these subjects are touched briefly in Section B.2.5.3. Intrinsic instabilities of detonations were considered in Section 6.3.1 and will not be revisited. Certain aspects of intrinsic instabilities of diffusion flames were mentioned briefly in Section 3.4.4 diffusion flames appear to exhibit fewer intrinsic instabilities than premixed flames, although under appropriate experimental conditions their effects can be observed, as indicated at the end of Section 9.5.2. Certain chamber instabilities that are not related to acoustic instabilities (such as Coanda effects—oscillatory attachment of flows to different walls) will not be discussed here, but reviews are available [1]. 

There are three basic distinct types of phenomena that may be responsible for intrinsic instabilities of premixed flames with one-step chemistry body-force effects, hydrodynamic effects and diffusive-thermal effects. Cellular flames—flames that spontaneously take on a nonplanar shape—often have structures affected most strongly by diffusive-thermal... 

In the early investigations of hydrodynamic instability [9], [190], it was presumed that the instability evolves to a chaotic state characteristic of turbulence. Thus self-turbulization of premixed flames was attributed to hydrodynamic instability (analogous, in a sense, to the development of turbulence in shear flows). This viewpoint must be revised if the instability evolves to stable nonplanar structures, as suggested above. From numerical experiments with equations describing the self-evolution of flame surfaces in the limit of small values of the density change across the flame, it has been inferred [152], [198]-[200] that the hydrodynamic instability evolves... 

Chapter 9 represents an effort to provide a unified and tutorial presentation of the broad field of the theory of combustion instabilities. The length of the chapter attests to the vastness of the field and to the progress that has been made therein in recent years. The final section of this chapter, on the theory of instabilities of premixed flames, is basic to analyses of premixed turbulent flame propagation and also has a bearing on aspects of flammability limits. 

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