Brock Bobbitt

A computationally-efficient, semi-implicit, iterative method for the time-integration of reacting flows with stiff chemistry

A semi-implicit preconditioned iterative method is proposed for the time-integration of the stiff chemistry in simulations of unsteady reacting flows, such as turbulent flames, using detailed chemical kinetic mechanisms. Emphasis is placed on the simultaneous treatment of convection, diffusion, and chemistry, without using operator splitting techniques. The preconditioner corresponds to an approximation of the diagonal of the chemical Jacobian. Upon convergence of the sub-iterations, the fully-implicit, second-order time-accurate, Crank-Nicolson formulation is recovered. Performance of the proposed method is tested theoretically and numerically on one-dimensional laminar and three-dimensional high Karlovitz turbulent premixed n-heptane/air flames. The species lifetimes contained in the diagonal preconditioner are found to capture all critical small chemical timescales, such that the largest stable time step size for the simulation of the turbulent flame with the proposed method is limited by the convective CFL, rather than chemistry. The theoretical and numerical stability limits are in good agreement and are independent of the number of sub-iterations. The results indicate that the overall procedure is second-order accurate in time, free of lagging errors, and the cost per iteration is similar to that of an explicit time integration. The theoretical analysis is extended to a wide range of flames (premixed and non-premixed), unburnt conditions, fuels, and chemical mechanisms. In all cases, the proposed method is found (theoretically) to be stable and to provide good convergence rate for the sub-iterations up to a time step size larger than 1 µs. This makes the proposed method ideal for the simulation of turbulent flames.

Vorticity transformation in high Karlovitz number premixed flames

To better understand the two-way coupling between turbulence and chemistry, the changes in turbulence characteristics through a premixed flame are investigated. Specifically, this study focuses on vorticity, ω, which is characteristic of the smallest length and time scales of turbulence, analyzing its behavior within and across high Karlovitz number (Ka) premixed flames. This is accomplished through a series of direct numerical simulations (DNS) of premixed n-heptane/air flames, modeled with a 35-species finite-rate chemical mechanism, whose conditions span a wide range of unburnt Karlovitz numbers and flame density ratios. The behavior of the terms in the enstrophy, ω^2 = ω ⋅ ω, transport equation is analyzed, and a scaling is proposed for each term. The resulting normalized enstrophy transport equation involves only a small set of parameters. Specifically, the theoretical analysis and DNS results support that, at high Karlovitz number, enstrophy transport obtains a balance of the viscous dissipation and production/vortex stretching terms. It is shown that, as a result, vorticity scales in the same manner as in homogeneous, isotropic turbulence within and across the flame, namely, scaling with the inverse of the Kolmogorov time scale, τ_η. As τ_η is a function only of the viscosity and dissipation rate, this work supports the validity of Kolmogorov’s first similarity hypothesis in premixed turbulentflames for sufficiently high Ka numbers. Results are unaffected by the transport model, chemical model, turbulent Reynolds number, and finally the physical configuration.

Assessment of the constant non-unity Lewis number assumption in chemically-reacting flows

Accurate computation of molecular diffusion coefficients in chemically reacting flows can be an expensive procedure, and the use of constant non-unity Lewis numbers has been adopted often as a cheaper alternative. The goal of the current work is to explore the validity and the limitations of the constant non-unity Lewis number approach in the description of molecular mixing in laminar and turbulent flames. To carry out this analysis, three test cases have been selected, including a lean, highly unstable, premixed hydrogen/air flame, a lean turbulent premixed n-heptane/air flame, and a laminar ethylene/air coflow diffusion flame. For the hydrogen flame, both a laminar and a turbulent configuration have been considered. The three flames are characterised by Lewis numbers which are less than unity, greater than unity, and close to unity, respectively. For each flame, mixture-averaged transport simulations are carried out and used as reference data. The current analysis suggests that, for numerous combustion configurations, the constant non-unity Lewis number approximation leads to small errors when the set of Lewis numbers is chosen properly. For the selected test cases and our numerical framework, the reduction of computational cost is found to be minimal.

Vorticity isotropy in high Karlovitz number premixed flames

The isotropy of the smallest turbulent scales is investigated in premixed turbulent combustion by analyzing the vorticity vector in a series of high Karlovitz number premixed flame direct numerical simulations. It is found that increasing the Karlovitz number and the ratio of the integral length scale to the flame thickness both reduce the level of anisotropy. By analyzing the vorticity transport equation, it is determined that the vortex stretching term is primarily responsible for the development of any anisotropy. The local dynamics of the vortex stretching term and vorticity resemble that of homogeneous isotropic turbulence to a greater extent at higher Karlovitz numbers. This results in small scale isotropy at sufficiently high Karlovitz numbers and supports a fundamental similarity of the behavior of the smallest turbulent scales throughout the flame and in homogeneous isotropic turbulence. At lower Karlovitz numbers, the vortex stretching term and the vorticity alignment in the strain-rate tensor eigenframe are altered by the flame. The integral length scale has minimal impact on these local dynamics but promotes the effects of the flame to be equal in all directions. The resulting isotropy in vorticity does not reflect a fundamental similarity between the smallest turbulent scales in the flame and in homogeneous isotropic turbulence.