On numerical simulation of electromagnetic field effects in the combustion process
Abstract
This paper deals with a simplified model taking into account the interplay of compressible, laminar, axisymmetric flow and the electrodynamical effects due to Lorentz force’s action on the combustion process in a cylindrical pipe. The combustion process with Arrhenius kinetics is modelled by a single step exothermic chemical reaction of fuel and oxidant. We analyze non-stationary PDEs with 6 unknown functions: the 3 components of velocity, density, concentration of fuel and temperature. For pressure the ideal gas law is used. For the inviscid flow approximation ADI method is used. Some numerical results are presented.
Keyword : compressible, laminar, axisymmetric flow, Lorentz force, Arrhenius kinetics
How to Cite
Kalis, H., Marinaki, M., Strautins, U., & Zake, M. (2018). On numerical simulation of electromagnetic field effects in the combustion process. Mathematical Modelling and Analysis, 23(2), 327-343. https://doi.org/10.3846/mma.2018.020
This work is licensed under a Creative Commons Attribution 4.0 International License.
References
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[16] H. Kalis and M. Marinaki. Numerical study of 2D MHD convection around periodically placed cylinders. Int. Jour. of Pure and Applied Mathematics, 110(3):503–517, 2016. https://doi.org/10.12732/ijpam.v110i3.10
[17] H. Kalis, M. Marinaki, U. Strautins and Lietuvietis. On the numerical simulation of the combustion process with simple chemical reaction. In Dmitri Meshumayev and Bength Sunden(Eds.), Proc. of the 7-th Baltic Heat Transfer Conference , Tallinn, Estonia, Aug. 24-26, 2015, Baltic Heat Transfer Conference BHTC, pp. 175–180. Tallinn University of Technology, 2015. ISBN 978-9949-23-817-0.
[18] H. Kalis, M. Marinaki, U. Strautins and Lietuvietis. On the numerical simulation of the vortex breakdown in the combustion process with simple chemical reaction and axial magnetic field. Int. Jour. of Differential Equations and Applications, 14(3):235–250, 2015.
[19] V.M. Kovenya and N.N. Yanenko. The method of decomposition in gaz dynamical problems. Nauka Press, Novosibirsk, 1981, in Russian.
[20] D.G. Lilley. Swirl flows in combustion: A review. AIAA Journal, 15(8):1063–1078, 1977. https://doi.org/10.2514/3.60756
[21] D. Meeker. Finite Element Method Magnetics. Version 4.2, User’s Manual, 2015.
[22] V. Mittal, H. Pitsh and F. Egolfopoulos. Assessment of counterflow to measure laminar burning velocities using direct numerical simulation. Combustion Theory and Modelling, 16(3):419–433, 2012. https://doi.org/10.1080/13647830.2011.631033
[23] N. Syred and J.M. Beer. Combustion in swirling flows: A review. Combustion and Flame, 23(2):143–201, 1974. https://doi.org/10.1016/0010-2180(74)90057-1
[24] A.B. Watathin, G.A. Lyubimov and S.A. Regirer. Magnetohydrodynamical flows in the canalls. Nauka Press,Moscou, 1970, in Russian.
[25] A. Zlotnik and R. Ciegis. A converse stability condition is necessary for a compact higher order scheme on non-uniform meshes. Applied Mathematics Letters, 80:35–40, 2018. https://doi.org/10.1016/j.aml.2018.01.005
[26] A. Zlotnik and V. Gavrilin. On quasi-gasdynamic system of equations with general equations of state and its application. Mathematical Modelling ana Analysis, 16(4):509–526, 2011. https://doi.org/10.3846/13926292.2011.627382
[2] M. Abricka, I. Barmina, R. Valdmanis, M. Zake and H. Kalis. Experimental and numerical studies on integrated gasification and combustion of biomass. Chemical Engineering Transactions, 50:127–132, 2016.
[3] N. Ahmed and K.Kr. Das. Effects of heat absorption and chemical reaction on a three dimensional MHD convective flow past a porous plate. Int. J.of Phys. Sciences, 8(39):1907–1922, 2013.
[4] I. Barmina, A. Kolmickovs, R. Valdmanis, M. Zake and H. Kalis. Experimental and numerical studies of electric field effects on biomass thermo-chemical conversion. Chemical Engineering Transactions, 50:121–126, 2016.
[5] I. Barmina, A. Komickova, R. Valdmanis and M. Zake. Combustion dynamics of swirling flame at thermo chemical conversion of biomass. Chemical Engineering Transaction, 43:649–654, 2015.
[6] I. Barmina, R. Valdmanis, H. Kalis and M. Marinaki. Experimental and numerical study of the development of swirling flow and flame dynamics and combustion characteristics at biomass thermo-chemical conversion. In Latvia J. Palabinskis, Latvia University of Agriculture(Ed.), Proc. of of the 16-th Int. Conf. On Engineering for Rural Development (ERDev17), Jelgava, Latvia, May. 24-26, 2017, pp. 68–74, Latvia University of Agriculture, Faculty of Engineering, 2017. https://doi.org/10.22616/ERDev2017.16.N013
[7] I. Barmina, R. Valdmanis, M. Zake, H. Kalis, M. Marinaki and U. Strautins. Magnetic field control of the combustion dynamics. Latvian Jour. of Physics and Technical Sciences, 53(4):36–47, 2016. https://doi.org/10.1515/lpts-2016-0027
[8] I. Barmina, M. Zake, H. Kalis and M. Marinaki. Electic field effects on gasification / combustion at thermo-chemical conversion of biomass mixtures. In Latvia J. Palabinskis, Latvia University of Agriculture(Ed.), Proc. of of the 16-th Int. Conf. on Engineering for Rural Development (ERDev17), Jelgava, Latvia, May. 24-26, 2017, pp. 60–67, Latvia University of Agriculture, Faculty of Engineering, 2017. https://doi.org/10.22616/ERDev2017.16.N012
[9] F. Battaglija, K. McGrattan, R.G. Rehm and H.R. Baum. Simuling fire whirls. Combustion Theory and Modelling, 4(2):123–138, 2000. https://doi.org/10.1088/1364-7830/4/2/303
[10] V. Bayona and M. Kindelan. Propagation of premixed laminar flames in 3D narrow open ducts using PBF- generated finite-differences. Combustion Theory and Modelling, 17(5):789–803, 2013. https://doi.org/10.1080/13647830.2013.801519
[11] V.V. Boyarevitch, Y.Zh. Freiberg, E.I. Shilova and E.V. Therbinyn. Electro-vortexed flows. Zinatne Press,Riga, 1985, in Russian.
[12] J.J. Choi, Z. Rusak and A.K. Kapila. Numerical simulation of premixed chemical reactions with swirl. Combustion theorie and modelling, 6(11):863–887, 2007.
[13] J. Douglas and R. Rachford. On the numerical sulution of heat conduction problems in two and three space variables. Trans. Amer.Math.Soc., 82(2):421–439, 1956. https://doi.org/10.1090/S0002-9947-1956-0084194-4
[14] A.K. Gupta, D.G. Lilley and N. Syred. Swirl Flows. Abacus Press, 1984.
[15] H. Kalis, I. Barmina, M. Zake and A. Koliskins. Mathematical modelling and experimental study of electrodynamic control of swirling flame flows. In Latvia J. Palabinskis, Latvia University of Agriculture(Ed.), Proc. of of the 15-th Int. Conf. on Engineering for Rural Development (ERDev16), Jelgava, Latvia, May. 25-27, 2016, pp. 134–141, Latvia University of Agriculture, Faculty of Engineering, 2016.
[16] H. Kalis and M. Marinaki. Numerical study of 2D MHD convection around periodically placed cylinders. Int. Jour. of Pure and Applied Mathematics, 110(3):503–517, 2016. https://doi.org/10.12732/ijpam.v110i3.10
[17] H. Kalis, M. Marinaki, U. Strautins and Lietuvietis. On the numerical simulation of the combustion process with simple chemical reaction. In Dmitri Meshumayev and Bength Sunden(Eds.), Proc. of the 7-th Baltic Heat Transfer Conference , Tallinn, Estonia, Aug. 24-26, 2015, Baltic Heat Transfer Conference BHTC, pp. 175–180. Tallinn University of Technology, 2015. ISBN 978-9949-23-817-0.
[18] H. Kalis, M. Marinaki, U. Strautins and Lietuvietis. On the numerical simulation of the vortex breakdown in the combustion process with simple chemical reaction and axial magnetic field. Int. Jour. of Differential Equations and Applications, 14(3):235–250, 2015.
[19] V.M. Kovenya and N.N. Yanenko. The method of decomposition in gaz dynamical problems. Nauka Press, Novosibirsk, 1981, in Russian.
[20] D.G. Lilley. Swirl flows in combustion: A review. AIAA Journal, 15(8):1063–1078, 1977. https://doi.org/10.2514/3.60756
[21] D. Meeker. Finite Element Method Magnetics. Version 4.2, User’s Manual, 2015.
[22] V. Mittal, H. Pitsh and F. Egolfopoulos. Assessment of counterflow to measure laminar burning velocities using direct numerical simulation. Combustion Theory and Modelling, 16(3):419–433, 2012. https://doi.org/10.1080/13647830.2011.631033
[23] N. Syred and J.M. Beer. Combustion in swirling flows: A review. Combustion and Flame, 23(2):143–201, 1974. https://doi.org/10.1016/0010-2180(74)90057-1
[24] A.B. Watathin, G.A. Lyubimov and S.A. Regirer. Magnetohydrodynamical flows in the canalls. Nauka Press,Moscou, 1970, in Russian.
[25] A. Zlotnik and R. Ciegis. A converse stability condition is necessary for a compact higher order scheme on non-uniform meshes. Applied Mathematics Letters, 80:35–40, 2018. https://doi.org/10.1016/j.aml.2018.01.005
[26] A. Zlotnik and V. Gavrilin. On quasi-gasdynamic system of equations with general equations of state and its application. Mathematical Modelling ana Analysis, 16(4):509–526, 2011. https://doi.org/10.3846/13926292.2011.627382