A direct numerical simulation study of vorticity transformation in weakly turbulent premixed flames

Abstract

Database obtained earlier in 3D Direct Numerical Simulations (DNS) of statistically stationary, 1D, planar turbulent flames characterized by three different density ratios σ is processed in order to investigate vorticity transformation in premixed combustion under conditions of moderately weak turbulence (rms turbulent velocity and laminar flame speed are roughly equal to one another). In cases H and M characterized by σ = 7.53 and 5.0, respectively, anisotropic generation of vorticity within the flame brush is reported. In order to study physical mechanisms that control this phenomenon, various terms in vorticity and enstrophy balance equations are analyzed, with both mean terms and terms conditioned on a particular value c of the combustion progress variable being addressed. Results indicate an important role played by baroclinic torque and dilatation in transformation of average vorticity and enstrophy within both flamelets and flame brush. Besides these widely recognized physical mechanisms, two other effects are documented. First, viscous stresses redistribute enstrophy within flamelets, but play a minor role in the balance of the mean enstrophy within turbulent flame brush. Second, negative correlation u · ∇ between fluctuations in velocity u and enstrophy gradient contributes substantially to an increase in the mean within turbulent flame brush. This negative correlation is mainly controlled by the positive correlation between fluctuations in the enstrophy and dilatation and, therefore, dilatation fluctuations substantially reduce the damping effect of the mean dilatation on the vorticity and enstrophy fields. In case L characterized by σ = 2.5, these effects are weakly pronounced and is reduced mainly due to viscosity. Under conditions of the present DNS, vortex stretching plays a minor role in the balance of vorticity and enstrophy within turbulent flame brush in all three cases. C 2014 AIP Publishing LLC. [http://dx

Letter: Does flame-generated vorticity increase turbulent burning velocity?

“…In the present letter, we will restrict ourselves to results obtained in a single case H, characterized by the largest σ = 7.53 because significant amount of flamegenerated vorticity was documented in this case. 17 As shown elsewhere, 18 premixed turbulent flame H [the laminar flame speed S L = 0.6 m/s and thickness δ L = (T b − T u )/max{|∇T |} = 0.217 mm] is well associated with the flamelet combustion regime. 27 The rate A −1 F dA F /dt of an increase in an infinitesimal area A F of a flame surface is well known 28 to be equal to the local stretch rateṡ = ∇ · u − nn : u + S d ∇n.…”

“…Since the data were comprehensively discussed by various research groups, [10][11][12][13][14][15][16][17][18][19][20][21][22][23][24][25][26] we will restrict ourselves to a brief summary of those compressible simulations. They dealt with statistically 1D, planar, adiabatic flames modeled by unsteady 3D continuity, Navier-Stokes, and energy equations, as well as the ideal gas state equation.…”

“…Here, u is the velocity vector, n = −∇c/|∇c| is the unit vector normal to an iso-scalar surface of c(x, t) = const., S d = [∇ · (ρD∇c) + W ]/(ρ|∇c|) is the displacement speed, D is the molecular diffusivity of c, and W is the mass rate of product creation. Accordingly, probabilities of positive and negativeṡ, conditioned on the local enstrophy Ω = ω · ω or baroclinic torque term B = ω · (∇ρ × ∇p)/ρ 2 in the Ω-transport equation, 17 were extracted from the DNS data. Here, ω = ∇ × u is the vorticity vector and p is the pressure.…”

Vorticity isotropy in high Karlovitz number premixed flames

“…Previous relevant studies on small scale isotropy within premixed flames include those of Hamlington et al, 15,16 Poludnenko, 22 and Lipatnikov et al 23 Lipatnikov et al 23 considered direct numerical simulations (DNSs) at low unburnt Karlovitz numbers (Ka * u = 0.2-0.3, where Ka * u = (l F /l) 1/2 (u o /S L ) 3/2 and l and u o are the integral length and velocity scales, respectively). They found anisotropy in vorticity and related this primarily to the effects of baroclinic torque.…”

“…These goals are accomplished by analyzing a series of DNS with varying Karlovitz numbers, Reynolds numbers, and flame density ratios previously performed by Bobbitt et al 6 The simulations are of statistically one-dimensional, slightly lean n-heptane/air flames using either finite-rate chemistry or tabulated chemistry. Simplified chemical and transport models are often used in numerical simulations of premixed turbulent combustion to reduce the computation cost, 15,16,18,22,23,25 but their impact on vorticity isotropy is not known. By analyzing DNS with different models, their impact on vorticity may be tested.…”