The effect of velocity field forcing techniques on the Karman–Howarth equation

Carroll, Phares L.; Blanquart, Guillaume

doi:10.1080/14685248.2014.911876

Cited by 22 publications

(20 citation statements)

References 20 publications

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“…33 Even though some energy (albeit very small) is injected at the small scales, linear forcing has been found to maintain the correct dynamics of these small turbulent scales. 33 As shown by Carroll and Blanquart, 50 all forcing techniques (spectral or linear) produce the exact same small scales behavior as characterized by the second order structure function, namely,…”

Section: Turbulence Forcingmentioning

confidence: 99%

“…As a result, the decay rate of the energy spectrum, i.e., the n in E(κ) ∝ κ −n , was found to be smaller than 5/3 and to depend on the Reynolds number, a result consistent with a large body of experimental studies. 50,51 This is shown in Fig. 3 which presents the two-dimensional three component velocity spectra in the unburnt gas for each of the present cases, calculated in a single y-z plane (at x = 1.5L) and averaged over time.…”

Section: Turbulence Forcingmentioning

confidence: 99%

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Vorticity transformation in high Karlovitz number premixed flames

2016

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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, ω2 = 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, τη. As τη is a function only of the viscosity and dissipation rate, this work supports the validity of Kolmogorov’s first similarity hypothesis in premixed turbulent flames for sufficiently high Ka numbers. Results are unaffected by the transport model, chemical model, turbulent Reynolds number, and finally the physical configuration.

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Section: Turbulence Forcingmentioning

confidence: 99%

Section: Turbulence Forcingmentioning

confidence: 99%

Vorticity transformation in high Karlovitz number premixed flames

2016

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“…Linear velocity forcing [36,37] was chosen for its physical nature and good stability properties. Linearly forced turbulent fields under comparable Reynolds numbers were analyzed in Ref.…”

Section: Turbulence Forcingmentioning

confidence: 99%

Differential diffusion effects, distributed burning, and local extinctions in high Karlovitz premixed flames

Lapointe

Savard

Blanquart

2015

Combustion and Flame

118

108

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a b s t r a c tDirect numerical simulations of premixed n-heptane/air flames at different Karlovitz numbers are performed using detailed chemistry. Differential diffusion effects are systematically isolated by performing simulations with both non-unity and unity Lewis numbers. Different unburnt temperatures and turbulence intensities are used and their effects on the flame structure and chemical source terms are investigated. As the unburnt gases are preheated, the viscosity ratio across the flame is reduced and the Karlovitz number at the reaction zone is increased. The increase in turbulence intensity suppresses differential diffusion effects on the flame structure (i.e. species dependence on temperature). However, differential diffusion effects on the chemical source terms are still noticeable even at the highest Karlovitz number simulated. Simulations with differential diffusion effects exhibit lower mean fuel consumption and heat release rates than their unity Lewis number counterparts. However, the difference is reduced as the reaction zone Karlovitz number is increased. Transition to distributed burning is characterized by a broadening of the reaction zone resulting from enhanced turbulent mixing. Local extinctions in the burning rate are observed only in non-unity Lewis number simulations and their probability decreases at high Karlovitz numbers. These results highlight the importance of using the reaction zone Karlovitz number to investigate the effect of turbulence on the chemical source terms and to compare flames at different unburnt temperatures.

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“…The NGA code allows for accurate, robust, and flexible simulations of both laminar and turbulent reactive flows in complex geometries and has been applied in a wide range of test problems, including laminar and turbulent flows [10,66,67], constant and variable density flows [61,68,69], as well as Large-Eddy Simulations (LES) [66,70] and Direct Numerical Simulations (DNS) [12,69,71]. This numerical solver has been shown to conserve discretely mass, momentum, and kinetic energy, with arbitrarily high order spatial discretization [61].…”

Section: Overview Of the Numerical Solvermentioning

confidence: 99%

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

Savard

Xuan

Bobbitt

et al. 2015

Journal of Computational Physics

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Please cite this article in press as: B. Savard et al., A computationally-efficient, semi-implicit, iterative method for the time-integration of reacting flows with stiff chemistry, J. Comput. Phys. (2015), http://dx. Abstract 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.

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The effect of velocity field forcing techniques on the Karman–Howarth equation

Cited by 22 publications

References 20 publications

Vorticity transformation in high Karlovitz number premixed flames

Vorticity transformation in high Karlovitz number premixed flames

Differential diffusion effects, distributed burning, and local extinctions in high Karlovitz premixed flames

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

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