Reactive flow

R. M. C. So, H. C. Mongia, and J. H. Whitelaw, Turbulent Reactive Flow Calculations, special issue of Combustion Science and Technology, Gordon and Breach Science Pubhshers, Inc., Montreux, Swit2erland, 1988. 

Pope, S.B., 1985. PDF methods for turbulent reactive flows. Progress in Energy and Combustion Science, 11, 119-192. 

The availability of large and fast computers, in combination with numerical techniques to compute transient, turbulent flow, has made it possible to simulate the process of turbulent, premixed combustion in a gas explosion in more detail. Hjertager (1982) was the first to develop a code for the computation of transient, compressible, turbulent, reactive flow. Its basic concept can be described as follows A gas explosion is a reactive fluid which expands under the influence of energy addition. Energy is supplied by combustion, which is modeled as a one-step conversion process of reactants into combustion products. The conversion (combustion)... 

Hjertager, B. H. 1982a. Simulation of transient compressible turbulent reactive flows. Comb. Sci. Tech. 41 159-170. 

Rivard, W. C., Farmar, O. A., and Butler, T. D., RICE A computer program for multicomponent chemically reactive flows at all speeds. National Technical Information Service, LA-5812,1975. 

V. Robin, A. Mura, M. Champion, and P. Plion 2006, A multi Dirac presumed PDF model for turbulent reactive flows. Combust. Sci. Technol. 178 1843-1870. 

Another particularly important topic in the modeling of strongly nonlinear phenomena is the occurrence of multiple fronts. For instance, in a supersonic reactive flow problem the position and speed of propagation of the shock wave and reaction front are different. 

Steefel, C. I. and A.C. Lasaga, 1994, A coupled model for transport of multiple chemical species and kinetic precipitation/dissolution reactions with application to reactive flow in single phase hydrothermal systems. American Journal of Science 294, 529-592. 

Anand, M. S., S. B. Pope, and H. C. Mongia (1989). A PDF method for turbulent recirculating flows. In Turbulent Reactive Flows, Lecture Notes in Engineering, pp. 672-693. Berlin Springer-Verlag. 

Jenny, P., S. B. Pope, M. Muradoglu, and D. A. Caughey (2001b). A hybrid algorithm for the joint PDF equation of turbulent reactive flows. Journal of Computational Physics 166, 218-252. 

Subramaniam, S. and S. B. Pope (1998). A mixing model for turbulent reactive flows based on Euclidean minimum spanning trees. Combustion and Flame 115,487-514. 

Comparison of mixing model performance for nonpremixed turbulent reactive flow. Combustion and Flame 117, 732-754. 

In turbulent reactive flows, the chemical species and temperature fluctuate in time and space. As a result, any variable can be decomposed in its mean and fluctuation. In Reynolds-averaged Navier-Stokes (RANS) simulations, only the means of the variables are computed. Therefore, a method to obtain a turbulent database (containing the means of species, temperature, etc.) from the laminar data is needed. In this work, the mean variables are calculated by PDF-averaging their laminar values with an assumed shape PDF function. For details the reader is referred to Refs. [16, 17]. In the combustion model, transport equations for the mean and variances of the mixture fraction and the progress variable and the mean mass fraction of NO are solved. More details about this turbulent implementation of the flamelet combustion model can also be found in Ref. [20],... 

Oran, E. S. Boris, J. P. Numerical Simulation of Reactive Flow, Cambridge University Press Cambridge, 2001. 

Mechanism reduction, nevertheless, may be necessary in some applications — for example, to model multidimensional reactive flows. Even the fastest computers today cannot handle such problems using detailed mechanisms in a reasonable time frame. It must be recognized, however, that models that utilize reduced mechanisms would have a far narrower range of applicability than the ones that use comprehensive reaction mechanisms. Furthermore, models that are based on reduced mechanisms cannot be expected to be valid outside the limits set in the mechanism reduction step. 

Kailasanath, K., J.H. Gardner, E. S. Oran, and J. P. Boris. 1991. Nnmerical simulations of unsteady reactive flows in a combustion chamber. Combustion Flame 86 115-34. 

Givi, P. 1989. Model free simulations of turbulent reactive flows. Progress Energy Combustion Science 15 1-107. 

Mathey, F., and J. P. Chollet. 1997. Large-eddy simulation of turbulent reactive flows. 11th Symposium on Turbulent Shear Flows Proceedings. Grenoble, France. 16.19-24. 

Kaplan, C. R., S. W. Back, E. S. Oran, and J. L. Ellzey. 1994. Dynamics of strongly radiating unsteady ethylene jet diffusion flame. Combustion Flame 96 1-22. Kennedy, C.A., and M. H. Carpenter. 1994. Several new numerical methods for compressible shear-layer simulations. Applied Numerical Methods 14 397-433. Baum, M., T. Poinsot, and D. Thevenin. 1994. Accurate boundary conditions for multicomponent reactive flows. J. Comput. Phys. 116 247-61. 

One can describe these phenomena through the Reynolds number (forced convection) and Rayleigh number (natural convection), but the reader can see immediately that the situations are so complicated that correlations in elementary texts on fluid flow are not easily applicable to predicting flame behavior. Reactive flows are among the most complex problems in modem engineering. 

Effective Dispersion Equations for Reactive Flows with Dominant Peclet and Damkohler Numbers... 

In many processes involving reactive flows different phenomena are present at different order of magnitude. It is fairly common that transport dominates diffusion and that chemical reaction happen at different timescales than convection/diffusion. Such processes are of importance in chemical engineering, pollution studies, etc. 

In bringing the models to a non-dimensional form, the presence of dominant Peclet and Damkohler numbers in reactive flows is observed. The problems of interest arise in complex geometries-like porous media or systems of capillary tubes. 

In the first flow regime, the velocity is small and Peclet number is of order one or smaller. Molecular diffusion plays the dominant role in solute dispersion. This case is well-understood even for reactive flows (see e.g. Conca et al., 2004, 2003 van Duijn and Knabner, 1997 van Duijn and Pop, 2004 van Duijn et al., 1998 Hornung and Jager, 1991 Knabner et al., 1995 Mikelic and Primicerio, 2006 and references therein). 

Our goal is the study of reactive flows through slit channels in the regime of Taylor dispersion-mediated mixing and in this chapter we will develop new effective models using the technique of anisotropic singular perturbations. 

Even with this enormous number of scientific papers on the subject, mathematically rigorous results on the subject are rare. Let us mention just ones aiming toward a rigorous justification of Taylor s dispersion model and its generalization to reactive flows. We could distinguish them by their approach... 

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