The use of slow manifolds in reactive flows

This work presents an analysis of the response of laminar, stretched, premixed CH 4 -air counterflow flames subject to periodical perturbations of the inflow mixture composition and the flow field in the context of ILDM and REDIM. Investigations of the perturbation propagation show, that the perturbation reaches the flame under certain conditions only; changes of the perturbation due to dissipative processes are investigated. Different methods are applied to gain an in-depth view of the influence of the perturbation on the chemical kinetics, namely correlation analyses of species in state space and timescale and element composition analyses. For the timescale analyses, two methods are applied, the ILDM method and a new concept for timescale analysis within the REDIM method. It is shown, that the perturbation does not change the global behaviour of the chemical kinetics and it is suggested to apply REDIMs for a low-dimensional description of perturbed flames.

mentioning

confidence: 99%

Investigation of the Dynamical Response of Methane/Air Counterflow Flames to Inflow Mixture Composition and Flow Field Perturbations

König

Bykov

Maas

2008

“…Recently, there has been much research activity in the field of reduced chemistry, in combination with chemistry-transport coupling. A comprehensive review is provided by Ren and Pope [18,19], which argues in favor of the 'close-parallel' assumption for chemistry-based slow manifolds. This basically reduces to the assumption that the system evolves on a manifold, close and parallel to a manifold that is solely based on chemistry.…”

Section: Introductionmentioning

confidence: 99%

Joint Scalar versus Joint Velocity-Scalar PDF Simulations of Bluff-Body Stabilized Flames with REDIM

Merci

Naud

Roekaerts

et al. 2008

Two transported PDF strategies, joint velocity-scalar PDF (JVSPDF) and joint scalar PDF (JSPDF), are investigated for bluff-body stabilized jet-type turbulent diffusion flames with a variable degree of turbulence-chemistry interaction. Chemistry is modeled by means of the novel reaction-diffusion manifold (REDIM) technique. A detailed chemistry mechanism is reduced, including diffusion effects, with N 2 and CO 2 mass fractions as reduced coordinates. The second-moment closure RANS turbulence model and the modified Curl's micro-mixing model are not varied. Radiative heat loss effects are ignored. The results for mean velocity and velocity fluctuations in physical space are very similar for both PDF methods. They agree well with experimental data up to the neck zone. Each of the two PDF approaches implies a different closure for the velocity-scalar correlation. This leads to differences in the radial profiles in physical space of mean scalars and mixture fraction variance, due to different scalar flux modeling. Differences are visible in mean mixture fraction and mean temperature, as well as in mixture fraction variance. In principle, the JVSPDF simulations can be closer to physical reality, as a differential model is implied for the scalar fluxes, whereas the gradient diffusion hypothesis is implied in JSPDF simulations. Yet, in JSPDF simulations, turbulent diffusion can be tuned by means of the turbulent Schmidt number. In the neck zone, where the turbulent flow field results deteriorate, the joint scalar PDF results are in somewhat better agreement with experimental data, for the test cases considered. In composition space, where results are reported as scatter plots, differences between the two PDF strategies are small in the calculations at hand, with a little more local extinction in the joint scalar PDF results.

“…For example, Fig. 3 shows the numerical errors of the proposed splitting schemes against the time step when applied for the reduced description of the extended Davis-Skodjie model system [51,52]. As shown in the plot, for the proposed splitting schemes, over a wide range of t, the error decreases with t, essentially as t 2 , thus illustrating their second-order accuracy in time.…”

Section: Splitting Schemesmentioning

confidence: 90%

“…For each time step t, schemes based on Strang splitting require two reaction sub-steps of length t/2 and one transport sub-step of length t. Schemes based on staggered time steps require a single reaction fractional step of length t and a single transport sub-step of length t. For the reaction substeps, efficient solutions can be obtained using ISAT. The computationally efficient solution to the transport sub-step is achieved through predictor-corrector methods [51,52]. The governing equations are dr 1 /dt = −r 1 u exp(−r 2 ) + (r in 1 − r 1 )/t res and dr 2 /dt = 0 + (r in 2 − r 2 )/t res + r 1 u 2 , with r ≡ [r 1 ; r 2 ] being the primary variables, u (a function of r) being the secondary variable, t res being the specified residence time, and r in being the specified inflow condition.…”

Section: Splitting Schemesmentioning

confidence: 99%

Efficient Implementation of Chemistry in Computational Combustion

Pope

Ren

2008

Self Cite

For hydrocarbon fuels, detailed chemical kinetics typically involve a large number of chemical species and reactions. In a high-fidelity combustion calculation, it is essential, though challenging, to incorporate sufficiently detailed chemical kinetics to enable reliable predictions of thermo-chemical quantities, especially for pollutants such as NO x and CO. In this paper, we review the recent work on efficient implementation of chemistry at Cornell, specifically: the invariant constrained equilibriumedge pre-image curve dimension-reduction method for the reduced description of reactive flows; the transport-chemistry coupling in the reduced description; the computationally efficient operator-splitting schemes for reactive flows; and, recent developments in the storage/retrieval algorithm in situ adaptive tabulation.