Bluff-body stabilization theories

Dally, B. B., D. F. Fletcher, and A. R. Masri (1998). Measurements and modeling of a bluff-body stabilized flame. Combustion Theory and Modelling 2, 193-219. 

Stirred reactor theory was initially applied to stabilization in gas turbine combustor cans in which the primary zone was treated as a completely stirred region. This theory has sometimes been extended to bluff-body stabilization, even though aspects of the theory appear inconsistent with experimental measurements made in the wake of a flame holder. Nevertheless, it would appear that stirred reactor theory gives the same functional dependence as the other correlations developed. In the previous section, it was found from stirred reactor considerations that... 

Theoretical studies are primarily concentrated on the treatment of flame blow-off phenomenon and the prediction of flame spreading rates. Dunskii [12] is apparently the first to put forward the phenomenological theory of flame stabilization. The theory is based on the characteristic residence and combustion times in adjoining elementary volumes of fresh mixture and combustion products in the recirculation zone. It was shown in [13] that the criteria of [1, 2, 5] reduce to Dunskii s criterion. Longwell et al. [14] suggested the theory of bluff-body stabilized flames assuming that the recirculation zone in the wake of the baffle is so intensely mixed that it becomes homogeneous. The combustion is described by a second-order rate equation for the reaction of fuel and air. 

Early theoretical treatments of bluff-body stabilized flame spreading have been based, in general, on the assumption that the flame is a discontinuous surface separating gas streams of different densities and temperatures [1, 15-17]. These theories neglect the finite thickness of turbulent flame zone and predict the increase of the spreading rate both with the density ratio across the flame, and with the increase in the laminar flame velocity of fuel-air mixture. This does not correspond to experimental observations (e.g., [8, 10]). 

Thus, theoretical modeling of bluff-body flame stabilization cannot yet compete with the experimental approaches. Partially, it is due to the fundamental problems relevant to the turbulent combustion theory. The underestimation of the role of theory is also due to the lack of systematic studies based on existing models. 

As mentioned in section 12.1, Dunskii [12] was the first who put forward the phenomenological theory of flame stabilization. The theory is based on the characteristic residence time, L, and combustion time, tc, in adjoining elementary volumes of fresh mixture and combustion products in the recirculation zone behind the bluff body. Dunskii s condition for flame blow-off is U/tc = Mi, where Mi is the Mikhelson number close to unity (for example, for cone flame holder the measurements give Mi = 0.45 [36]). Residence time L is taken proportional to the flame holder size, H, and inversely proportional to the approach flow velocity, U, i.e., L = H/U. Combustion time is estimated as tc = at/Si, where... 

Boundary-layer theory finds wide application in analyses of flame stabilization. The simplest configuration is the stagnation-point boundary layer, studies of which provide information concerning stabilization of a flame ahead of a bluff body placed in the flow some analyses and ideas... 

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