Application of the Polynomial Chaos Expansion to the simulation of chemical reactors with uncertainties

In this paper we consider the simulation of probabilistic chemical reactions in isothermal and adiabatic conditions. Models for reactions under isothermal conditions result in advection equations, adiabatic conditions yield the reactive Euler equations. In order to treat with scattering data, the equations are projected onto the polynomial chaos space. Scattering data can largely affect the estimation of quantities in the system, including variable optimization. This is demonstrated on a selective non-catalytic reduction of nitric oxide.

[1]  D. Xiu,et al.  Modeling uncertainty in flow simulations via generalized polynomial chaos , 2003 .

[2]  J. Marsden,et al.  A mathematical introduction to fluid mechanics , 1979 .

[3]  N. Wiener.  The Homogeneous Chaos , 1938 .

[4]  I. Dunn,et al.  Chemical Engineering Dynamics: An Introduction to Modelling and Computer Simulation , 2000 .

[5]  William L. Luyben,et al.  Chemical Reactor Design and Control , 2007 .

[6]  J. Brandts.  [Review of: W. Hundsdorfer, J.G. Verwer (2003) Numerical Solution of Time-Dependent Advection-Diffusion-Reaction Equations] , 2006 .

[7]  C. Hirsch,et al.  Numerical Computation of Internal and External Flows. By C. HIRSCH. Wiley. Vol. 1, Fundamentals of Numerical Discretization. 1988. 515 pp. £60. Vol. 2, Computational Methods for Inviscid and Viscous Flows. 1990, 691 pp. £65. , 1991, Journal of Fluid Mechanics.

[8]  R. LeVeque.  Finite Volume Methods for Hyperbolic Problems: Characteristics and Riemann Problems for Linear Hyperbolic Equations , 2002 .

[9]  J. Anderson,et al.  Hypersonic and High-Temperature Gas Dynamics , 2019 .

[10]  R. Caflisch,et al.  Quasi-Monte Carlo integration , 1995 .

[11]  Charles Hirsch,et al.  Numerical computation of internal & external flows: fundamentals of numerical discretization , 1988 .

[12]  Ishwar K. Puri,et al.  Combustion Science and Engineering , 2006 .

[13]  P. Rentrop,et al.  Polynomial chaos for the approximation of uncertainties: Chances and limits , 2008, European Journal of Applied Mathematics.

[14]  Roger Ghanem,et al.  Ingredients for a general purpose stochastic finite elements implementation , 1999 .

[15]  Dongbin Xiu,et al.  The Wiener-Askey Polynomial Chaos for Stochastic Differential Equations , 2002, SIAM J. Sci. Comput..

[16]  I. Dunn,et al.  Chemical Engineering Dynamics , 1994 .

[17]  Kim Dam-Johansen,et al.  Empirical modeling of the selective non-catalytic reduction of no: comparison with large-scale experiments and detailed kinetic modeling , 1994 .

[18]  Jun S. Liu,et al.  Monte Carlo strategies in scientific computing , 2001 .

[19]  O. L. Maître,et al.  Spectral Methods for Uncertainty Quantification: With Applications to Computational Fluid Dynamics , 2010 .

[20]  W. T. Martin,et al.  The Orthogonal Development of Non-Linear Functionals in Series of Fourier-Hermite Functionals , 1947 .

[21]  Black.  Power Plant Engineering , 2005 .

[22]  U. Wever,et al.  Adapted polynomial chaos expansion for failure detection , 2007, J. Comput. Phys..

[23]  G. Froment,et al.  Chemical Reactor Analysis and Design , 1979 .

[24]  J. Verwer,et al.  Numerical solution of time-dependent advection-diffusion-reaction equations , 2003 .

[25]  R. Ghanem,et al.  Quantifying uncertainty in chemical systems modeling , 2004 .

[26]  S. Janson.  Gaussian Hilbert Spaces , 1997 .

[27]  R. Ghanem,et al.  Stochastic Finite Elements: A Spectral Approach , 1990 .