Advantages of the Adoption of a Generalized Flame Displacement Velocity as a Central Element of Flamelet Theory

In combustion theory, flames are usually described in terms of the dynamics of iso-surfaces of a specific scalar. The flame displacement speed is then introduced as a local variable quantifying the progression of these iso-surfaces relative to the flow field. While formally defined as a scalar, the physical meaning of this quantity allows relating it with a vector pointing along the normal direction of the scalar iso-surface. In this work, this one-dimensional concept is extended by the introduction of a generalized flame displacement velocity vector, which is associated with the dynamics of iso-surfaces of two generic scalars, \(\alpha \) and \(\beta \). It is then shown how a new flamelet paradigm can be built around this velocity vector, which leads to (i) an alternative procedure for the derivation of general flamelet equations, which is much simpler and more direct than the ones currently available in the literature, (ii) a very compact set of two-dimensional flamelet equations for the conditioning scalar gradients, \(g_{\alpha } = |\nabla \alpha |\) and \(g_{\beta } = |\nabla \beta |\), which comprise several effects in few terms directly related to the projections of the generalized flame displacement velocity, and (iii) the possibility of characterizing different composition space coordinate systems through the same generalized flame displacement velocity. The proposed framework is discussed in the context of partially premixed combustion, emphasizing how its adoption can contribute to both the further development of 2D flamelet theory and its coupling with CFD codes.