Wrinkled laminar flames

To analy2e premixed turbulent flames theoretically, two processes should be considered (/) the effects of combustion on the turbulence, and (2) the effects of turbulence on the average chemical reaction rates. In a turbulent flame, the peak time-averaged reaction rate can be orders of magnitude smaller than the corresponding rates in a laminar flame. The reason for this is the existence of turbulence-induced fluctuations in composition, temperature, density, and heat release rate within the flame, which are caused by large eddy stmctures and wrinkled laminar flame fronts. 

What are the mechanisms by which slow, laminar combustion can be transformed into an intense, blast-generating process This transformation is most strongly influenced by turbulence, and secondarily by combustion instabilities. A laminar-flame front propagating into a turbulent mixture is strongly affected by the turbulence. Low-intensity turbulence will only wrinkle the flame front and enlarge its surface area. With increasing turbulence intensity, the flame front loses its more-or-less smooth, laminar character and breaks up into a combustion zone. In an intensely turbulent mixture, combustion takes place in an extended zone in which... 

In the so-called "wrinkled flame regime," the "turbulent flame speed" was expected to be controlled by a characteristic value of the turbulent fluctuations of velocity u rather than by chemistry and molecular diffusivities. Shchelkin [2] was the first to propose the law St/Sl= (1 + A u /Si) ), where A is a universal constant and Sl the laminar flame velocity of propagation. For the other limiting regime, called "distributed combustion," Summerfield [4] inferred that if the turbulent diffusivity simply replaces the molecular one, then the turbulent flame speed is proportional to the laminar flame speed but multiplied by the square root of the turbulence Reynolds number Re. ... 

Wrinkled laminar flamelet regime. The well-known ideal regime where the laminar flame structure is only wrinkled by turbulence without any modification of ifs internal structure. 

Consider initially the hydrodynamic instability—that is, the one due to the flow—first described by Darrieus [52], Landau [53], and Markstein [54], If no wrinkle occurs in a laminar flame, the flame speed SL is equal to the upstream unbumed gas velocity U0. But if a minor wrinkle occurs in a laminar flame, the approach flow streamlines will either diverge or converge as shown in Fig. 4.45. Considering the two middle streamlines, one notes that, because of the curvature due to the wrinkle, the normal component of the velocity, with respect to the flame, is less than U(). Thus, the streamlines diverge as they enter the wrinkled flame front. Since there must be continuity of mass between... 

FIGURE 4.45 Convergence-divergence of the flow streamlines due to a wrinkle in a laminar flame. 

Below and to the right of this line, the Klimov-Williams criterion is satisfied and wrinkled laminar flames may occur. The figure shows that this region includes both large and small values of turbulence Reynolds numbers and velocity ratios (VISA) both greater and less than 1, but predominantly large Da. 

In his attempts to analyze the early experimental data, Damkohler [55] considered that large-scale, low-intensity turbulence simply distorts the laminar flame while the transport properties remain the same thus, the laminar flame structure would not be affected. Essentially, his concept covered the range of the wrinkled and severely wrinkled flame cases defined earlier. Whereas a planar laminar flame would appear as a simple Bunsen cone, that cone is distorted by turbulence as shown in Fig. 4.43. It is apparent then, that the area of the laminar flame will increase due to a turbulent field. Thus, Damkohler [55] proposed for large-scale, small-intensity turbulence that... 

The classical view is that a turbulent flame is equivalent to a distorted and wrinkled laminar flame. The turbulent flame brush is thus supposed to be an integrated picture of a rapidly fluctuating surface, and instantaneous schlieren pictures seem to support this interpretation 50). Grumer, however, has shown that schlieren snapshots of turbulent hot gas issuing from a Bunsen burner look very much like the flame pictures (34) the implication is that one sees, not the instantaneous flame surface, but the boundary of the hot gas. 

Although strain and curvature effects can be combined as in equation (55), it cannot be concluded that they are of equal importance for wrinkled laminar flames in turbulent flows. If it is assumed that the flame shape is affected mainly by the large eddies, then in terms of the flame thickness 3 and the integral scale /, the nondimensional curvature is of order 3/i This may be compared with the corresponding relevant nondimensional strain... 

In the reaction-sheet regime, the structure of the turbulent flame is determined by the dynamics of wrinkled laminar flames. Thus the thickness of the turbulent flame (if it is large compared with that of the laminar flame) is controlled by the distance to which fluctuations in the laminar-flame position may extend. Statistical aspects of distributions of temperature and of species concentrations in the turbulent flame can be expressed entirely in terms of statistics of the laminar-flame position (through /), orientation (through V //1V / ), and structure (through k). The simplest example is... 

FIGURE 10.8. Schematic illustration of the relationship between the turbulent flame speed and the wrinkled flame area for a premixed turbulent flame consisting of a wrinkled laminar flame. 

When disruptions of flame sheets become sufficiently extensive, there is appreciable nonreactive mixing of reactants and products at molecular scales. The extent of disruption increases as IJS decreases certainly if l/S becomes small compared with unity, then the turbulent flame no longer can be composed of wrinkled laminar flames. The true structures of turbulent flames in the limit of small values of l/S are unknown. 

When the Lewis number is nonunity, the mass diffusivity can be greater than the thermal diffusivity. This discrepancy in diffusivities is important with respect to the reactant that limits the reaction. Ignoring the hydrodynamic instability, consider again the condition between a pair of streamlines entering a wrinkle in a laminar flame. This time, however, look more closely at the flame stmcture that these streamlines encompass, noting that the limiting reactant will diffuse into the flame zone faster than heat can diffuse from the flame zone into the unbumed mixture. Thus, the flame temperature rises, the flame speed increases, and the flame wrinkles bow further in the downstream direction. The result is a flame that looks very much like the flame depicted for the hydrodynamic instability in Fig. 45. The flame surface breaks up continuously into new cells in a chaotic... 

---