Reaction diffusion transport model to predict precursor uptake and spatial distribution in vapor phase infiltration processes

2021 ◽  
Author(s):  
Yi Ren ◽  
Emily McGuinness ◽  
Chaofan Huang ◽  
Ryan Lively ◽  
Mark Losego ◽  
...  
Keyword(s):  
Spatial Distribution ◽  
Vapor Phase ◽  
Transport Model ◽  
Reaction Diffusion ◽  
Diffusion Transport ◽  
Infiltration Processes

scholarly journals Validation of an Eulerian Stochastic Fields Solver Coupled with Reaction–Diffusion Manifolds on LES of Methane/Air Non-premixed Flames

2020 ◽  
Author(s):  
Paola Breda ◽  
Chunkan Yu ◽  
Ulrich Maas ◽  
Michael Pfitzner
Keyword(s):  
Transport Model ◽  
Reaction Diffusion ◽  
Passive Scalar ◽  
Scalar Dissipation ◽  
Combustion Model ◽  
Filtered Density Function ◽  
Detailed Chemistry ◽  
Stochastic Fields ◽  
Reduced Chemistry ◽  
Flame Behavior

AbstractThe Eulerian stochastic fields (ESF) combustion model can be used in LES in order to evaluate the filtered density function to describe the process of turbulence–chemistry interaction. The method is typically computationally expensive, especially if detailed chemistry mechanisms involving hydrocarbons are used. In this work, expensive computations are avoided by coupling the ESF solver with a reduced chemistry model. The reaction–diffusion manifold (REDIM) is chosen for this purpose, consisting of a passive scalar and a suitable reaction progress variable. The latter allows the use of a constant parametrization matrix when projecting the ESF equations onto the manifold. The piloted flames Sandia D–E were selected for validation using a 2D-REDIM. The results show that the combined solver is able to correctly capture the flame behavior in the investigated sections, although local extinction is underestimated by the ESF close to the injection plate. Hydrogen concentrations are strongly influenced by the transport model selected within the REDIM tabulation. A total solver performance increase by a factor of 81% is observed, compared to a full chemistry ESF simulation with 19 species. An accurate prediction of flame F instead required the extension of the REDIM table to a third variable, the scalar dissipation rate.

scholarly journals Influences of hydroxyl radicals (OH) on top-down estimates of the global and regional methane budgets

2020 ◽  
Author(s):  
Yuanhong Zhao ◽  
Marielle Saunois ◽  
Philippe Bousquet ◽  
Xin Lin ◽  
Antoine Berchet ◽  
...  
Keyword(s):  
Spatial Distribution ◽  
Climate Models ◽  
Transport Model ◽  
Atmospheric Transport ◽  
Temporal Variations ◽  
Oh Radicals ◽  
Chemical Transport Model ◽  
Top Down ◽  
Ch4 Emissions ◽  
The Impact

Abstract. The hydroxyl radical (OH), which is the dominant sink of methane (CH4), plays a key role to close the global methane budget. Previous research that assessed the impact of OH changes on the CH4 budget mostly relied on box modeling inversions with a very simplified atmospheric transport and no representation of the heterogeneous spatial distribution of OH radicals. Here using a variational Bayesian inversion framework and a 3D chemical transport model, LMDz, combined with 10 different OH fields derived from chemistry-climate models (CCMI experiment), we evaluate the influence of OH burden, spatial distribution, and temporal variations on the global CH4 budget. The global tropospheric mean CH4-reaction-weighted [OH] ([OH]GM-CH4) ranges 10.3–16.3 × 105 molec cm−3 across 10 OH fields during the early 2000s, resulting in inversion-based global CH4 emissions between 518 and 757 Tg yr−1. The uncertainties in CH4 inversions induced by the different OH fields are comparable to, or even larger than the uncertainty typically given by bottom-up and top-down estimates. Based on the LMDz inversions, we estimate that a 1 %-increase in OH burden leads to an increase of 4 Tg yr−1 in the estimate of global methane emissions, which is about 25 % smaller than what is estimated by box-models. The uncertainties in emissions induced by OH are largest over South America, corresponding to large inter-model differences of [OH] in this region. From the early to the late 2000s, the optimized CH4 emissions increased by 21.9 ± 5.7 Tg yr−1 (16.6–30.0 Tg yr−1), of which ~ 25 % (on average) is contributed by −0.5 to +1.8 % increase in OH burden. If the CCMI models represent the OH trend properly over the 2000s, our results show that a higher increasing trend of CH4 emissions is needed to match the CH4 observations compared to the CH4 emission trend derived using constant OH. This study strengthens the importance to reach a better representation of OH burden and of OH spatial and temporal distributions to reduce the uncertainties on the global CH4 budget.

scholarly journals Nonlinear Dynamics of a Toxin-Phytoplankton-Zooplankton System with Self- and Cross-Diffusion

2016 ◽  
Vol 2016 ◽  
pp. 1-11
Author(s):  
Pengfei Wang ◽  
Min Zhao ◽  
Hengguo Yu ◽  
Chuanjun Dai ◽  
Nan Wang ◽  
...  
Keyword(s):  
Nonlinear Dynamics ◽  
Spatial Distribution ◽  
Theoretical Analysis ◽  
Numerical Simulations ◽  
Reaction Diffusion ◽  
Turing Instability ◽  
Reaction Diffusion Equations ◽  
Diffusion Equations ◽  
Cross Diffusion ◽  
The Rich

A nonlinear system describing the interaction between toxin-producing phytoplankton and zooplankton was investigated analytically and numerically, where the system was represented by a couple of reaction-diffusion equations. We analyzed the effect of self- and cross-diffusion on the system. Some conditions for the local and global stability of the equilibrium were obtained based on the theoretical analysis. Furthermore, we found that the equilibrium lost its stability via Turing instability and patterns formation then occurred. In particular, the analysis indicated that cross-diffusion can play an important role in pattern formation. Subsequently, we performed a series of numerical simulations to further study the dynamics of the system, which demonstrated the rich dynamics induced by diffusion in the system. In addition, the numerical simulations indicated that the direction of cross-diffusion can influence the spatial distribution of the population and the population density. The numerical results agreed with the theoretical analysis. We hope that these results will prove useful in the study of toxic plankton systems.

scholarly journals Multi-spike solutions of a hybrid reaction–transport model

2021 ◽  
Vol 477 (2247) ◽  
pp. 20200829
Author(s):  
P. C. Bressloff
Keyword(s):  
Transport Model ◽  
Reaction Diffusion ◽  
Reaction Diffusion Systems ◽  
Strongly Nonlinear ◽  
Diffusion Systems ◽  
Spike Solution ◽  
Classical Pattern ◽  
Final Steady State ◽  
Reaction Transport ◽  
Pattern Forming

Simulations of classical pattern-forming reaction–diffusion systems indicate that they often operate in the strongly nonlinear regime, with the final steady state consisting of a spatially repeating pattern of localized spikes. In activator–inhibitor systems such as the two-component Gierer–Meinhardt (GM) model, one can consider the singular limit D a  ≪  D h , where D a and D h are the diffusivities of the activator and inhibitor, respectively. Asymptotic analysis can then be used to analyse the existence and linear stability of multi-spike solutions. In this paper, we analyse multi-spike solutions in a hybrid reaction–transport model, consisting of a slowly diffusing activator and an actively transported inhibitor that switches at a rate α between right-moving and left-moving velocity states. Such a model was recently introduced to account for the formation and homeostatic regulation of synaptic puncta during larval development in Caenorhabditis elegans . We exploit the fact that the hybrid model can be mapped onto the classical GM model in the fast switching limit α  → ∞, which establishes the existence of multi-spike solutions. Linearization about the multi-spike solution yields a non-local eigenvalue problem that is used to investigate stability of the multi-spike solution by combining analytical results for α  → ∞ with a graphical construction for finite α .

scholarly journals Dynamic identification of boundary conditions for convection-diffusion transport model in the case of noisy measurements

2019 ◽  
Vol 21 (4) ◽  
pp. 469-479
Author(s):  
Anastasia N. Kuvshinova
Keyword(s):  
Boundary Conditions ◽  
Transport Model ◽  
Mixed Boundary ◽  
Mixed Boundary Conditions ◽  
Simultaneous Estimation ◽  
Dynamic Identification ◽  
Diffusion Transport ◽  
One Dimensional ◽  
Convection Diffusion ◽  
Noisy Measurements

The paper addresses the problem of dynamic identification of mixed boundary conditions for one-dimensional convection-diffusion transport model based on noisy measurements of the function of interest. Using finite difference method the original model with the partial differential equation is replaced with the discrete linear dynamic system with noisy multisensor measurements in which boundary conditions are included as unknown input vector. To solve the problem, the algorithm of simultaneous estimation of the state and input vectors is used. The results of numerical experiments are presented which confirm the practical applicability of the proposed method.

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