TY - JOUR
T1 - Simulation of reactive nanolaminates using reduced models
T2 - III. Ingredients for a general multidimensional formulation
AU - Salloum, Maher
AU - Knio, Omar M.
N1 - Funding Information:
The authors are grateful to Prof. Timothy Weihs and his research team for providing the average front velocity data at large bilayers. This work was supported by the Office of Naval Research through Award N00014-07-1-0740 .
PY - 2010/6
Y1 - 2010/6
N2 - A transient multidimensional reduced model is constructed for the simulation of reaction fronts in Ni/Al multilayers. The formulation is based on the generalization of earlier methodologies developed for quasi-1D axial and normal propagation, specifically by adapting the reduced formalism for atomic mixing and heat release. This approach enables us to focus on resolving the thermal front structure, whose evolution is governed by thermal diffusion and heat release. A mixed integration scheme is used for this purpose, combining an extended-stability, Runge-Kutta-Chebychev (RKC) integration of the diffusion term with exact treatment of the chemical source term. Thus, a detailed description of atomic mixing within individual layers is avoided, which enables transient modeling of the reduced equations of motion in multiple dimensions. Two-dimensional simulations are first conducted of front propagation in composites combining two bilayer periods. Results are compared with the experimental measurements of Knepper et al. [. 22], which reveal that the reaction velocity can depend significantly on layering frequency. The comparison indicates that, using a concentration-dependent conductivity model, the transient 2D computations can reasonably reproduce the experimental behavior. Additional tests are performed based on 3D computations of surface initiated reactions. Comparison of computed predictions with laser ignition measurements indicates that the computations provide reasonable estimates of ignition thresholds. A detailed discussion is finally provided of potential generalizations and associated hurdles.
AB - A transient multidimensional reduced model is constructed for the simulation of reaction fronts in Ni/Al multilayers. The formulation is based on the generalization of earlier methodologies developed for quasi-1D axial and normal propagation, specifically by adapting the reduced formalism for atomic mixing and heat release. This approach enables us to focus on resolving the thermal front structure, whose evolution is governed by thermal diffusion and heat release. A mixed integration scheme is used for this purpose, combining an extended-stability, Runge-Kutta-Chebychev (RKC) integration of the diffusion term with exact treatment of the chemical source term. Thus, a detailed description of atomic mixing within individual layers is avoided, which enables transient modeling of the reduced equations of motion in multiple dimensions. Two-dimensional simulations are first conducted of front propagation in composites combining two bilayer periods. Results are compared with the experimental measurements of Knepper et al. [. 22], which reveal that the reaction velocity can depend significantly on layering frequency. The comparison indicates that, using a concentration-dependent conductivity model, the transient 2D computations can reasonably reproduce the experimental behavior. Additional tests are performed based on 3D computations of surface initiated reactions. Comparison of computed predictions with laser ignition measurements indicates that the computations provide reasonable estimates of ignition thresholds. A detailed discussion is finally provided of potential generalizations and associated hurdles.
KW - Multidimensional simulation
KW - Reactive multilayers
KW - Reduced model
KW - Self-propagating reactions
UR - http://www.scopus.com/inward/record.url?scp=77950356015&partnerID=8YFLogxK
U2 - 10.1016/j.combustflame.2009.10.005
DO - 10.1016/j.combustflame.2009.10.005
M3 - Article
AN - SCOPUS:77950356015
SN - 0010-2180
VL - 157
SP - 1154
EP - 1166
JO - Combustion and Flame
JF - Combustion and Flame
IS - 6
ER -