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Russia Moscow; Novosibirsk; Saransk
Year
2017
Volume
27
Issue
4
Pages
608-617
 Section Mechanics Title Modeling the flow of a multicomponent reactive gas using high accuracy algorithms Author(-s) Zhalnin R.V.a, Peskova E.E.a, Stadnichenko O.A.b, Tishkin V.F.c Affiliations Ogarev Mordovia State Universitya, Boreskov Institute of Catalysis, Siberian Branch of the Russian Academy of Sciencesb, Keldysh Institute of Applied Mathematics, Russian Academy of Sciencesc Abstract The article considers a high-order accuracy algorithm for modelling the dynamics of multicomponent reactive gas taking into account the processes of diffusion, thermal conductivity and chemical reactions, based on WENO schemes. Computations for gas flow in a flowing reactor for thermal ethane pyrolysis with external heating of the reaction zone are carried out. The velocity of gas motion in explored flows is much less then sound velocity in gas mixture, which motivates using the Navier-Stokes equations in approximation of low Mach numbers for describing the processes under study. Computation of chemical kinetics equations is singled out as a separate step. The velocity of chemical reactions is defined by Arrhenius expressions. The ethane pyrolysis kinetic scheme is used for constructing the model, which is a branched radical mechanism. Computations of subsonic gas flow taking into account the processes of diffusion, chemical reactions and their thermal effects for different temperature of heating elements are carried out. Comparison with experimental data shows that $1.97\,\%$ conversion of ethane is reached at $648^{\circ}$C at the outflow of metal reactor. This result is close to $2.1\,\%$, which is obtained by experiment. Comparison of experimental data of thermal ethane pyrolysis with numerical experimental data shows a high level of reliability of the results obtained. Keywords Navier-Stokes equations, WENO scheme, pyrolysis of ethane UDC 519.63 MSC 35Q30, 76N15 DOI 10.20537/vm170410 Received 18 October 2017 Language Russian Citation Zhalnin R.V., Peskova E.E., Stadnichenko O.A., Tishkin V.F. Modeling the flow of a multicomponent reactive gas using high accuracy algorithms, Vestnik Udmurtskogo Universiteta. Matematika. Mekhanika. Komp'yuternye Nauki, 2017, vol. 27, issue 4, pp. 608-617. References Stadnichenko O.A., Snytnikov V.N., Snytnikov Vl.N. Mathematical modeling of multicomponent gas flows with energy intensive chemical processes by the example of ethane pyrolysis, Vychislitel'nye Metody i Programmirovanie, 2014, vol. 15, no. 4, pp. 658-668 (in Russian). Snytnikov V.N., Mishchenko T.I., Snytnikov V.N., Malykhin S.E., Avdeev V.I., Parmon V.N. Autocatalytic gas-phase dehydrogenation of ethane, Research on Chemical Intermediates, 2012, vol. 38, no. 3-5, pp. 1133-1147. DOI: 10.1007/s11164-011-0449-x Stadnichenko O.A., Snytnikov V.N., Snytnikov Vl.N., Masyuk N.S. Mathematical modeling of ethane pyrolysis in a flow reactor with allowance for laser radiation effects, Chemical Engineering Research and Design, 2016, vol. 109, pp. 405-413. DOI: 10.1016/j.cherd.2016.02.008 Ladonkina M.E., Neklyudova O.A., Tishkin V.F., Chevanin V.S. A version of essentially nonoscillatory high-order accurate difference schemes for systems of conservation laws, Mathematical Models and Computer Simulations, 2010, vol. 2, no. 3, pp. 304-316. DOI: 10.1134/S207004821003004X Ladonkina M.E., Neklyudova O.A., Tishkin V.F. Impact of different limiting functions on the order of solution obtained by RKDG, Mathematical Models and Computer Simulations, 2013, vol. 5, no. 4, pp. 346-349. DOI: 10.1134/S2070048213040091 Rodionov A.V. Correlation between the discontinuous Galerkin method and MUSCL-type schemes, Mathematical Models and Computer Simulations, 2016, vol. 8, no. 3, pp. 285-300. DOI: 10.1134/S207004821603008X Tishkin V.F., Zhukov V.T., Myshetskaya E.E. Justification of Godunov’s scheme in the multidimensional case, Mathematical Models and Computer Simulations, 2016, vol. 8, no. 5, pp. 548-556. DOI: 10.1134/S2070048216050124 Shumikhin A.A., Koroleva M.R., Dadikina S.Yu., Karpov A.I. Application of WENO scheme for simulation of turbulent flow in a channel with backward-facing step, Vestnik Udmurtskogo Universiteta. Matematika. Mekhanika. Komp'yuternye Nauki, 2017, vol. 27, issue 3, pp. 460-469. DOI: 10.20537/vm170313 Shu C.W. Essentially non-oscillatory and weighted essentially non-oscillatory schemes for hyperbolic conservation laws, ICASE Report No. 97-65, NASA-CR/97-206253, 1997, 83 p. https://ntrs.nasa.gov/archive/nasa/casi.ntrs.nasa.gov/19980007543.pdf Zhalnin R.V., Zmitrenko N.V., Ladonkina M.Ye., Tishkin V.F. Numerical simulation Richtmyer-Meshkov instability development using difference schemes of high order of accuracy, Matematicheskoe Modelirovanie, 2007, vol. 19, no. 10, pp. 61-66 (in Russian). Borisov V.E., Yakush S.E. Application of adaptive hierarchical grids to simulation of reacting gas flows, Physical-Chemical Kinetics in Gas Dynamics, 2015, vol. 16, issue 2 (in Russian). http://chemphys.edu.ru/issues/2015-16-2/articles/544/ Almgren A.S., Bell J.B., Colella P., Howell L.H., Welcome M.L. A conservative adaptive projection method for the variable density incompressible Navier-Stokes equations, Journal of Computational Physics, 1998, vol. 142, issue 1, pp. 1-46. DOI: 10.1006/jcph.1998.5890 Day M.S., Bell J.B. Numerical simulation of laminar reacting flows with complex chemistry, Combustion Theory and Modelling, 2000, vol. 4, issue 4, pp. 535-556. DOI: 10.1088/1364-7830/4/4/309 Nurislamova L.F., Stoyanovskaya O.P., Stadnichenko O.A., Gubaidullin I.M., Snytnikov V.N., Novichkova A.V. Few-step kinetic model of gaseous autocatalytic ethane pyrolysis and its evaluation by means of uncertainty and sensitivity analysis, Chemical Product and Process Modeling, 2014, vol. 9, issue 2, pp. 143-154. DOI: 10.1515/cppm-2014-0008 Belov A.A., Kalitkin N.N., Kuzmina L.V. Modeling of chemical kinetics in gases, Mathematical Models and Computer Simulations, 2017, vol. 9, no. 1, pp. 24-39. DOI: 10.1134/S2070048217010057 Rusanov V.V. The calculation of the interaction of non-stationary shock waves and obstacles, USSR Computational Mathematics and Mathematical Physics, 1962, vol. 1, issue 2, pp. 304-320. DOI: 10.1016/0041-5553(62)90062-9 Lax P.D. Weak solutions of nonlinear hyperbolic equations and their numerical computation, Communications on Pure and Applied Mathematics, 1954, vol. 7, issue 1, pp. 159-193. DOI: 10.1002/cpa.3160070112 Zhalnin R.V., Peskova E.E., Stadnichenko O.A., Tishkin V.F. Modeling the flow of multicomponent reactive gas by the example of hydrocarbons pyrolysis, Keldysh Institute Preprints, 2017, no. 101, pp. 1-16. DOI: 10.20948/prepr-2017-101 Zhalnin R.V., Peskova E.E., Stadnichenko O.A., Tishkin V.F. Using WENO schemes in mathematical modeling of gas mixture's dynamics by the example of ethane pyrolysis, Zhurnal Srednevolzhskogo Matematicheskogo Obshchestva, 2016, vol. 18, no. 3, pp. 98-106 (in Russian). Full text