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* the local kinematic relation defining the local front velocity (e.g. with respect to local curvature). | * the local kinematic relation defining the local front velocity (e.g. with respect to local curvature). | ||
when the density contrast between 'hot' and 'cold' fluids is asymptotically small. | when the density contrast between 'hot' and 'cold' fluids is asymptotically small. | ||
| + | == Main features== | ||
| + | * Solving first-order or second order EE in the Fourier or Fourier-Legendre basis. | ||
| + | * Time resolution using ETDRK1 and 4, using contour integrals to avoid cancelation errors (Trefethen et al. 2005) | ||
| + | * EEM for 2D or 3D planar, 3D expanding/converging fronts, acoustics, fast-transients.. | ||
| + | * Laminar or turbulent configurations (EE with additive noise, e.g. Passot-Pouquet, Kraichnan-Celik, Von Karman/Pao or 'DNS turbulence') | ||
{| class="wikitable" | {| class="wikitable" | ||
|+ Examples of first-order in time obtained EEM: for 2D planar, 3D planar, or 3D expanding fronts | |+ Examples of first-order in time obtained EEM: for 2D planar, 3D planar, or 3D expanding fronts | ||
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|[[File:OUIEqEEM_1D.png|400 px]] | |[[File:OUIEqEEM_1D.png|400 px]] | ||
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== Sample Results == | == Sample Results == | ||
We show below a short gallery of pictures obtained using the FLAMEX solver. | We show below a short gallery of pictures obtained using the FLAMEX solver. | ||
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{| class="wikitable" | {| class="wikitable" | ||
|+ Sample results for 3D planar fronts | |+ Sample results for 3D planar fronts | ||
|[[File:OUIImages_Luk.png|700 px]] | |[[File:OUIImages_Luk.png|700 px]] | ||
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{| class="wikitable" | {| class="wikitable" | ||
|+ Sample results for 3D expanding fronts with variable turbulence intensity, | |+ Sample results for 3D expanding fronts with variable turbulence intensity, | ||
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Notice the 'soccer-ball' and 'cauliflower' aspects of the front, as described by Zel'dovitch in the 40's. | Notice the 'soccer-ball' and 'cauliflower' aspects of the front, as described by Zel'dovitch in the 40's. | ||
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* See also some quantitative comparisons between FLAMEX and DNS (HALLEGRO) results at [http://www.coria-cfd.fr/index.php/H-Allegro#Direct_simulation_of_propagating_flames:_3D_expanding_front_.28Eric_Albin_.26_Yves_D.27Angelo.29] | * See also some quantitative comparisons between FLAMEX and DNS (HALLEGRO) results at [http://www.coria-cfd.fr/index.php/H-Allegro#Direct_simulation_of_propagating_flames:_3D_expanding_front_.28Eric_Albin_.26_Yves_D.27Angelo.29] | ||
* More details (and comparisons with experimental results) in [http://dx.doi.org/10.1016/j.ijnonlinmec.2011.05.018], [http://dx.doi.org/10.1016/j.combustflame.2011.12.019] | * More details (and comparisons with experimental results) in [http://dx.doi.org/10.1016/j.ijnonlinmec.2011.05.018], [http://dx.doi.org/10.1016/j.combustflame.2011.12.019] | ||
==Sub-module for asymptotic modeling of Flame-Balls== | ==Sub-module for asymptotic modeling of Flame-Balls== | ||
| − | + | A sub-module of FLAMEX has been devoted to the numerical solution to flame-balls (FB) dynamics. | |
| − | A sub-module of FLAMEX has | + | |
Using a Batchelor approximation for the surrounding Lagrangian flow and high activation energy asymptotics, we derived a nonlinear forced (stochastic) integrodifferential equation for the current FB radius. This gives access to the FB response to the ambiant Lagrangian rate-of-strain tensor g(t). | Using a Batchelor approximation for the surrounding Lagrangian flow and high activation energy asymptotics, we derived a nonlinear forced (stochastic) integrodifferential equation for the current FB radius. This gives access to the FB response to the ambiant Lagrangian rate-of-strain tensor g(t). | ||
For a diagonal g(t) deduced from random Markov processes of the Ornstein- Uhlenbeck type, | For a diagonal g(t) deduced from random Markov processes of the Ornstein- Uhlenbeck type, | ||
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* large enough values of t_life are compatible with Poisson statistics; | * large enough values of t_life are compatible with Poisson statistics; | ||
* the variations of with the characteristics of g(t) mirror the latter’s statistics, more precisely that of trace(g*g). | * the variations of with the characteristics of g(t) mirror the latter’s statistics, more precisely that of trace(g*g). | ||
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{| class="wikitable" | {| class="wikitable" | ||
|+ System of equations, EEM and sample results of FB radius dynamics | |+ System of equations, EEM and sample results of FB radius dynamics | ||
|[[File:Fbdynamics.png|600 px]] | |[[File:Fbdynamics.png|600 px]] | ||
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== Participants == | == Participants == | ||
Yves D'Angelo, Guy Joulin, Eric Albin, Rui Rego, Gaël Boury, Lancelot Boulet, Viphaphorn Srinavawongs, Yosifumi Tsuji. | Yves D'Angelo, Guy Joulin, Eric Albin, Rui Rego, Gaël Boury, Lancelot Boulet, Viphaphorn Srinavawongs, Yosifumi Tsuji. | ||
Revision as of 11:39, 1 April 2016
Contents
The FLAMEX Solver
FLAMEX is a suite of solvers able to compute high accuracy solutions to non-linear non-local asymptotics-based evolution equations (EE), of 1rt For propagatong fronts, the EEM (Evolution Equation Modeling) can be found by solving exactly the set of
- Euler equations
- Rankine-Hugoniot jump relations
- the local kinematic relation defining the local front velocity (e.g. with respect to local curvature).
when the density contrast between 'hot' and 'cold' fluids is asymptotically small.
Main features
- Solving first-order or second order EE in the Fourier or Fourier-Legendre basis.
- Time resolution using ETDRK1 and 4, using contour integrals to avoid cancelation errors (Trefethen et al. 2005)
- EEM for 2D or 3D planar, 3D expanding/converging fronts, acoustics, fast-transients..
- Laminar or turbulent configurations (EE with additive noise, e.g. Passot-Pouquet, Kraichnan-Celik, Von Karman/Pao or 'DNS turbulence')
|
|
Sample Results
We show below a short gallery of pictures obtained using the FLAMEX solver.
|
|
Notice the 'soccer-ball' and 'cauliflower' aspects of the front, as described by Zel'dovitch in the 40's.
- See also some quantitative comparisons between FLAMEX and DNS (HALLEGRO) results at [1]
- More details (and comparisons with experimental results) in [2], [3]
Sub-module for asymptotic modeling of Flame-Balls
A sub-module of FLAMEX has been devoted to the numerical solution to flame-balls (FB) dynamics. Using a Batchelor approximation for the surrounding Lagrangian flow and high activation energy asymptotics, we derived a nonlinear forced (stochastic) integrodifferential equation for the current FB radius. This gives access to the FB response to the ambiant Lagrangian rate-of-strain tensor g(t). For a diagonal g(t) deduced from random Markov processes of the Ornstein- Uhlenbeck type, or linearly filtered versions thereof, extensive numerical simulations and approximate theoretical analyses agree that
- flame balls can definitely live for much longer than their time of spontaneous expansion/collapse;
- large enough values of t_life are compatible with Poisson statistics;
- the variations of with the characteristics of g(t) mirror the latter’s statistics, more precisely that of trace(g*g).
|
Participants
Yves D'Angelo, Guy Joulin, Eric Albin, Rui Rego, Gaël Boury, Lancelot Boulet, Viphaphorn Srinavawongs, Yosifumi Tsuji.