A numerical study of the vorticity field generated by the baroclinic effect due to the propagation of a planar pressure wave through a cylindrical premixed laminar flame

Abstract

The importance of vorticity production in combustion systems has been highlighted previously by several authors (Markstein 1964; Picone et al. 1984). The consequent distortion and enlargement of flame surfaces can lead to substantial enhancement of the burning rate which may be beneficial or disastrous depending on the physical context. We describe the results of numerical simulations of an experimental configuration similar to that described by Scarinci & Thomas (1992), who examined the effect of initially planar pressure signals on two-dimensional flame balls. The flame ball is here set-up from ignition using a code, based on the second-order Godunov scheme described by Falle (1991). A simple Arrhenius reaction scheme is adopted in modelling a unimolecular decomposition. As in previous papers (Batley et al. 1993 a, b) the thermal conductivity is assumed to vary linearly with temperature, and the Lewis and Prandtl numbers are taken as unity. A short time after ignition, when the flame ball has reached a radius of approximately 2 cm, a very short-lengthscale pressure step disturbance is introduced, propagating towards the combustion region. As the signal crosses the flame, the interaction of the sharp, misaligned pressure and density gradients, creates a strong vorticity field. The resulting roll-up of the flame eventually divides it into two smaller rotating reacting regions. In order to gauge the effect of the chemical reaction and in particular the viscous diffusion on the evolution of the vorticity field, the results are compared with analogous solutions of the Euler equations.

Origins of the deflagration-to-detonation transition in gas-phase combustion

“…Again, emphasis was on the vortex structure and how this was affected by energy release. The vorticity field generated by a single planar pressure wave moving through a cylindrical laminar flame was also examined in [74]. The shock-flame interaction creates vortices, and there has been significant work in flame-vortex-acoustic interactions (for a review, see [75]; for more recent work, see, for example, [76]).…”

Baroclinic distortion of laminar flames

“…(Note th at the direction of this vector is normal to the plane of the flame.) It is clear that r x y = sin 772, (2.7) where the direction corresponding to 77 = 0 is defined in figure 1 As stated by R ottm an & Stansby (1993), Batley (1995) and Batley et al (1994), the time scale of the evolution of the vorticity field can be given in terms of the vortex sheet strength ( V(r] ), equal to the total vorticity per unit by the formula…”

“…Although this single passage is insufficient to cause such rapid transformation to turbulence and the same increase in overall burning rates, the experiments are useful in that they provide more convenient cases for theoretical and numerical modelling. A recent paper by the authors (Batley et al 1994) describes a numerical simulation of the same type of experiment, and the reader is referred to th at paper for any detail of the methodology not included here. The results were compared with those of the studies of Rottm an & Stansby (1993) who investigated the evolution of a cylinder of fluid released from rest in a cross flow.…”

Experimental and numerical studies on interactions of a spherical flame with incident and reflected shocks

“…On the basis of a one-step chemical reaction, Batley et al [3] studied numerically a two-dimensional interaction process between a planar incident and reflected shock wave and a cylindrical flame. The vorticity and flame distortion induced by the baroclinic effects were discussed.…”