On de-coupling of Shvab-Zel'dovich variables in the presence of diffusion

Lam, S. H.; Bellan, Josette

doi:10.1016/s0010-2180(02)00519-9

Cited by 10 publications

(4 citation statements)

References 13 publications

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“…Note that each individual Y i (x) need not be spatially homogeneous, only the values of the constraints defined in Eq. (14). Each row vector of ϕ li can be correlated to a physical constraint on our system (i.e.…”

Section: Iic Model Reductionmentioning

confidence: 99%

Model Reduction for Reaction-Diffusion Systems: Bifurcations in Slow Invariant Manifolds

Mengers

Powers

2012

50th AIAA Aerospace Sciences Meeting Including the New Horizons Forum and Aerospace Exposition

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Slow invariant manifolds (SIM) are calculated for spatially inhomogeneous closed reactive systems to obtain a model reduction. A simple oxygen dissociation reaction-diffusion system is evaluated. SIMs are calculated using a robust method of finding the system's equilibria and integrating to find heteroclinic orbits. Diffusion effects are obtained by using a Galerkin method to project the infinite dimensional dynamical system onto a low dimensional approximate inertial manifold. This projection rigorously accounts for the coupling of reaction and diffusion processes. An analytic coupling between reaction and diffusion time scales is shown to be a function of length scale. A critical length scale is identified where reaction and diffusion time scales are equal. At this critical length scale, a supercritical pitchfork bifurcation occurs which changes the SIM.

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Section: Iic Model Reductionmentioning

confidence: 99%

Model Reduction for Reaction-Diffusion Systems: Bifurcations in Slow Invariant Manifolds

Mengers

Powers

2012

50th AIAA Aerospace Sciences Meeting Including the New Horizons Forum and Aerospace Exposition

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“…We can further simplify the system using reductions similar to those in Lam and Bellan, 13 who label them as generalized Shvab-Zel'dovich relations. We construct a matrix ϕ li of dimension L × N , where the L row vectors span the left null space of matrix ν ij :…”

Section: Iic1 Generalized Shvab-zel'dovichmentioning

confidence: 99%

Application of the Slow Invariant Manifold Correction for Diffusion

Mengers

Powers

2011

49th AIAA Aerospace Sciences Meeting Including the New Horizons Forum and Aerospace Exposition

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Slow invariant manifolds (SIM) are calculated for spatially inhomogeneous closed reactive systems to obtain a model reduction. A robust method of constructing a onedimensional SIM by calculating equilibria and then integrating along heteroclinic orbits is extended to two new cases: i) adiabatic systems, and ii) spatially inhomogeneous systems with simple diffusion. The adiabatic condition can be modeled as a new algebraic constraint in the limit of unity Lewis number. Diffusion effects on the SIM are examined for systems with small characteristic lengths. A diffusion correction is obtained by using a Galerkin method to project the infinite dimensional dynamical system onto a low dimensional approximate inertial manifold. This projection rigorously accounts for the coupling of reaction and diffusion processes, and an analytic length and time scale coupling is shown. An example is demonstrated on a system of N O production which highlights the correlation between an established isothermal spatially homogeneous technique and the new techniques.

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“…Because mass diffusion is reduced and thermal conductivity is enhanced in supercritical situations, the Lewis number is considerably larger than in subcritical situations (Harstad and Bellan, 1999). Therefore, it is foreseen that supercritical reacting flow modeling will not benefit from the simplifications associated with Shvab-Zel'dovich variables, which decouple the conservation equations, and that perhaps alternative means for simplifying the conservation equations should be considered (Lam and Bellan, 2003).…”

Section: Supercritical Turbulence and Mixing: Species-system Dependenmentioning

confidence: 99%

Theory, Modeling and Analysis of Turbulent Supercritical Mixing

Bellan

2006

Combustion Science and Technology

103

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Previous studies of supercritical three-dimensional mixing layers are reviewed to derive a unified understanding of supercritical turbulence and mixing. These studies consisted of Direct Numerical Simulations of mixing layers having initially a single chemical species in each of the two free streams. Each mixing layer was initially perturbed, which led to a double pairing of four initial spanwise vortices. These pairings yielded in each case an ultimate vortex within which small scales proliferated, resulting in a state having turbulence characteristics, called a transitional state. The evolution of the layer to this transitional state and the state itself were previously analyzed to elucidate the features of supercritical turbulence and mixing. This analysis is here used to classify those supercritical turbulent mixing characteristics that are species-system independent or speciessystem dependent. Finally, comments are offered on future prospects of developing small-scale models particularly suited for Large Eddy Simulations of supercritical turbulent mixing.

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On de-coupling of Shvab-Zel'dovich variables in the presence of diffusion

Cited by 10 publications

References 13 publications

Model Reduction for Reaction-Diffusion Systems: Bifurcations in Slow Invariant Manifolds

Model Reduction for Reaction-Diffusion Systems: Bifurcations in Slow Invariant Manifolds

Application of the Slow Invariant Manifold Correction for Diffusion

Theory, Modeling and Analysis of Turbulent Supercritical Mixing

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