A dynamic multi-timescale method for combustion modeling with detailed and reduced chemical kinetic mechanisms

Gou, Xiaolong; Sun, Wenting; Chen, Zheng; Ju, Yiguang

doi:10.1016/j.combustflame.2010.02.020

Cited by 145 publications

(70 citation statements)

References 23 publications

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“…The stiffness of chemically reacting flows is generally believed to be due to the stiff source terms in the species transport equations, but not due to the temperature transport equation [27,74,75]. An estimate for the temperature time scale in a n-C 7 H 16 /air premixed flame (test case presented in Section 4.1) gives…”

Section: Overview Of the Numerical Solvermentioning

confidence: 99%

“…This can be accomplished using Quasi-SteadyState (QSS) assumptions and Partial-Equilibrium (PE) approximations [22,23], or more advanced methods such as Directed Relation Graph (DRG) [24] and DRG with Error Propagation (DRGEP) [25] before being applied to the simulation [23,26]. Even with these techniques, it has been pointed out in previous work that the size of reduced mechanisms for practical hydrocarbon fuel surrogates is still too large to be used directly in Direct Numerical Simulations (DNS) with finite-rate chemistry [27]. Alternative chemistry reduction techniques based on separation of chemical timescales could be applied.…”

Section: Introductionmentioning

confidence: 99%

“…n-heptane [6], iso-octane [8], and ethanol [9]). The application of explicit time-integration methods are commonly limited by prohibitively small time step sizes to resolve the smallest chemical timescales present in the system (challenge #4) [27,40]. This is the reason why the S3D code relies on "stiffness removal" techniques such as QSSA [22,49,23].…”

Section: Introductionmentioning

confidence: 99%

“…Such techniques include the Computational Singular Perturbation (CSP) method [28] and the Intrinsic Low Dimensional Manifold (ILDM) [4] method. However, these methods require significant computational efforts to conduct chemical Jacobian decomposition and mode separation [27], which makes them not suited for the DNS of multi-dimensional reacting flows.…”

Section: Introductionmentioning

confidence: 99%

“…Unfortunately, fully-implicit methods are generally prohibitively expensive [27], especially for unsteady problems [52], due to the large computational overhead for chemical Jacobian inversion within each time step. This makes fully-implicit time-integration methods prohibitive for simulations of reacting flows with large hydrocarbon fuels (e.g.…”

Section: Introductionmentioning

confidence: 99%

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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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Section: Overview Of the Numerical Solvermentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 3 more Smart Citations

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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A Time‐Space Dual Adaptive Uncoupled Method for Supersonic Combustion

Wu,

Xu,

Zhang

et al. 2024

Numerical Methods in Fluids

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High computational complexity due to rapidly increasing numerical stiffness is a difficult problem for simulating a supersonic reactive flow by using the uncoupled method. On the basis of our previous work, this paper proposes a dual adaptive method to ensure high calculation efficiency and good robustness in simulating stiff cases. The principle of this method is to realize adaptive coordination for the advection and reaction time steps in accordance with the non‐uniform feature of stiffness in the space and time dimensions. The proposed method can advance by a small time step in strong stiffness while with a large one in weak stiffness through the “prediction‐correction‐recovery” strategy. Some classical problems are chosen to verify the performance of the proposed method. The proposed method improved the computation efficiency by at least comparing with the previous method [1] and widened the error tolerance of the initial time step.

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A Genetic Algorithm–Based Method for the Optimization of Reduced Kinetics Mechanisms

Sikalo

Hasemann

Schulz

et al. 2015

Int J of Chemical Kinetics

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This paper describes an automatic method for the optimization of reaction rate constants of reduced reaction mechanisms. The optimization technique is based on a genetic algorithm that aims at finding new reaction rate coefficients that minimize the error introduced by the preceding reduction process. The error is defined by an objective function that covers regions of interest where the reduced mechanism may deviate from the original mechanism. The mechanism's performance is assessed for homogeneous reactor or laminar-flame simulations against the results obtained from a given reference-the original mechanism, another detailed mechanism, or experimental data, if available. The overall objective function directs the search towards more accurate reduced mechanisms that are valid for a given set of operating conditions. An optional feature to the objective function is a penalty term that permits to minimize the change to the reaction coefficients, keeping them as close as possible to the original value. This means that the penalty function can be used to constrain the reaction rates modifications during the optimization if needed. It is demonstrated that the penalty function is successful and can be combined with predefined uncertainty bounds for each reaction of the mechanism. In addition, the penalty function can be modified to achieve a further reduction of the mechanism. The algorithm is demonstrated for the optimization of a previously reduced variant of the GRI-Mech 3.0, a tert-butanol combustion mechanism by Sarathy et al. (Combust. Flame, 2012, 159, 2028-2055) and a hydrogen mechanism by Konnov (Combust. Flame, 2008, 152,

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A dynamic multi-timescale method for combustion modeling with detailed and reduced chemical kinetic mechanisms

Cited by 145 publications

References 23 publications

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

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

A Time‐Space Dual Adaptive Uncoupled Method for Supersonic Combustion

A Genetic Algorithm–Based Method for the Optimization of Reduced Kinetics Mechanisms

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