Boreskov Institute of Catalysis of the Siberian Branch of Russian ...

OP-III-9mass dispersion and to analyze transversal symmetry breaking of moving and stationaryfronts using the relation between the velocity (V f ) and the local curvature (K) of the front.AnalysisAs a first stage we derived for a planar front two algebraic equations with two unknowns(∆T m ,V f ), which and in the limiting case of Pe C →∞ can be reduced to the approximaterelations known for a 1-D «ideal» front in the case of negligible mass dispersion 5 . Numericalsimulations of a 1-D PBR show a good agreement between the simulated and approximatedvalues for moderate and large Pe C .At the next stage we considered a curvilinear front propagation in a local polar coordinatesystem and derived approximate relations for the propagation velocity (V C f ) and the maximaltemperature rise for the case of a finite curvature. Applying the condition dV C f /dK| K=0 =0 weobtained a necessary condition for symmetry breaking in the following form:C(α,∆T ad ,Da,Pe T ,Pe C ,∆T C m ,V C f ,γ)[1- α] 0and the planar 1-D front is stable. Analysis of simplified Eq. (2) with α >1-δ (δ>0, small)shows that C>0 at least for 1< α 1 coincides with the previously obtained criterion (1), while refinedcondition (2) can define the upper α boundary of transversal patterns to emerge.SimulationsThe derived criterion was verified by direct numericalsimulations of the 2-D cylindrical shell and a full 3-D PBRmodels showing various types of moving transversal patternsin upstream propagating fronts (Fig. 1).In conclusion we would like to point that transversalthree-dimensional patterns were predicted and simulated inPBR's with a first order activated kinetics within the feasibledomain of parameters for the first time.Fig. 1.Typical quasi-«frozen»spiral structure of a frontpropagating in a 3-D PBRshowing the temperature patternin a cross-section normal to theflow (behind the front).References1. V. Balakotaiah, E.L. Christaforatou, & D.H. West, Chem. Eng. Sci., 54, 1725–1734 (1999).2. G. Viswanathan, A. Bindal, J. Khinast, & D. Luss, D, AIChE J., 51, 3028-3038 (2005).3. V. Balakotaiah, N. Gupta, & D.H. West, Chem. Eng. Sci., 57, 435–448 (2002).4. O. Nekhamkina, & M. Sheintuch, Chem. Eng. Sci, submitted.5. O.V. Kiselev, & Yu.Sh. Matros, Combustion, Explos. And Shock Waves, 16, 152 (1980).108