Numerical simulation of fuel combustion in stationary detonation wave in variable cross-section channel with supersonic flow at the inlet and outlet


DOI: 10.34759/trd-2019-109-6

Аuthors

Gidaspov V. Y.*, Kononov D. S.**

Moscow Aviation Institute (National Research University), 4, Volokolamskoe shosse, Moscow, А-80, GSP-3, 125993, Russia

*e-mail: gidaspov@mai.ru
**e-mail: dr.kononoff@yandex.r

Abstract

The authors studied the case of (H2 + 0.5O2 + 1.881N2) hydrogen-air mixture combustion in the stationary detonation wave. Analysis of possible flow patterns with stationary detonation wave was performed in chemically equilibrium quasi-single dimensional problem statement according to the technique [8] for a channel in the form of two successively arranged Laval nozzles. In case [8], solution depends exclusively on the radii ratio in the current, initial and minimum channel cross-sections. Passage modelling of a chemically non-equilibrium flow rate through the speed of sound was being realized employing “adjustment of fire” method (algorithm for a singular point passing) [10] using equilibrium solution as an initial approximation. This algorithm allows obtaining a quasi-one-dimensional non-equilibrium stationary solution with a detonation wave in the longitudinal x-coordinate of the l with the given mixture and basic thermodynamic parameters by varying setting coordinate of the detonation wave. Positions of detonation wave are close enough in both equilibrium and non-equilibrium cases. The range of mixture with detonation wave flow rates can be predicted with equilibrium analysis. As in the equilibrium case, three possible solutions with detonation waves in non-equilibrium flow exist in the loop.

Only one solution with detonation wave in the expanding section is stable. This fact was proved by Godunov’s method. The presented quasi-one-dimensional formulation of the problem can be employed for the initial analysis of flows. At the same time, the indisputable advantage of this technique is the high speed of calculations.

Keywords:

numerical modeling, variable cross-section channels, quasi-one-dimensional stationary flow model, direct problem of nozzle theory, non-equilibrium chemical transformations

References

  1. Chernyi G.G. Gazovaya dinamika (Gas dynamics), Moskow, Nauka, 1988, 424 p

  2. Kraiko A.N., Shironosov V.A. Prikladnaya matematika i mekhanika, 1976, vol. 40, pp. 579 – 586.

  3. Grin’ V.T., Kraiko A.N., Tillyaeva N.I., Shironosov V.A. Prikladnaya matematika i mekhanika, 1977, vol. 41, pp. 637 – 645.

  4. Borisov A.D. Trudy MAI, 2017, no. 90, available at: http://trudymai.ru/eng/published.php?ID=74721

  5. Anan’ev A.V., Borisov D.M., Vasyutichev A.S. Gidaspov V.Yu., Degtyarev S.A., Laptev I.V., Rudenko A.M. Aerospace MAI Journal, 2009, vol. 16, no. 2, pp. 131 – 140.

  6. Rebrov S.G., Golikov A.N., Golubev V.A., Molchanov A.M., Yakhina G.R. Trudy MAI, 2013, no. 69, available at: http://trudymai.ru/eng/published.php?ID=43154

  7. Liu J.-J. A thermodynamic analysis of quasi–one–dimensional self–sustaining gaseous detonation waves, Proceedings of the Royal Society A. Mathematical, physical & engineering sciences, 1999, available at: https://royalsocietypublishing.org/doi/abs/10.1098/rspa.1999.0426

  8. Gidaspov V.Yu., Kononov D.S. XXI mezhdunarodnaya konferentsiya po vychislitel’noi mekhanike i sovremennym prikladnym programmnym sistemam (VMSPPS’2019): materialy konferentsii, Moscow, Izd-vo MAI, 2019, pp. 438 – 440.

  9. Gidaspov V.Yu. Trudy MAI, 2015, no. 83, available at: http://trudymai.ru/eng/published.php?ID=61826

  10. Gidaspov V.Yu. Aerospace MAI Journal, 2013, vol. 20, no. 2, pp. 90 – 97.

  11. Sharpe G. J. The effect of curvature on detonation waves in Type Ia supernovae, Monthly Notices of the Royal Astronomical Society, 2001, vol. 322, pp. 614 – 624.

  12. Kryukov V.G., Abdullin A.L., Demin A.V., Safiullin I.I. Trudy MAI, 2017, no. 92, available at: http://trudymai.ru/eng/published.php?ID=76848

  13. Kryukov V.G., Abdullin A.L., Nikandrova M.V., Iskhakova R.L. Trudy MAI, 2019, no. 105, available at: http://trudymai.ru/eng/published.php?ID=104166

  14. Radenac E. Fluctuating energy balance method for postprocessing multiphase flow computations, Journal of propulsion and power, 2013, vol. 29, no. 3, pp. 699 – 708.

  15. Gurvich L.V., Veits I.V., Medvedev V.A. et at. Termodinamicheskie svoistva individual’nykh veshchestv. Spravochnoe izdanie (Thermodynamic properties of individual substances. Reference edition), Moscow, Nauka, 1978, vol. 1, 328 p.

  16. Sardeshmukh S., Heister S., Xia G., Merkle C., Sankaran V. Kinetic Modeling of Hypergolic Propellants Using Impinging Element Injectors, 48th AIAA/ASME/SAE/ASEE Joint Propulsion Conference & Exhibit, 2012, https://doi.org/10.2514/6.2012-3760

  17. Gardiner U., Dikson-L’yuis G. et al. Combustion chemistry, New York, Springer Verlag, 1984, 509 p.

  18. Godunov S.K., Zabrodin A.V., Ivanov M.Ya., Kraiko A.N., Prokopov G.P. Chislennoe reshenie mnogomernykh zadach gazovoi dinamiki (Numerical solution of multi-dimensional problems of gas dynamics), Moscow, Nauka, 1976, 400 p.

  19. Levin V.A., Manuilovich I.S., Markov V.V. Vestnik Moskovskogo universiteta. Seriya 1: Matematika. Mekhanika, 2011, no. 4, pp. 28 – 33.

  20. Deiterding R. High-resolution numerical simulation and analysis of Mach reflection structures in detonation waves in low-pressure H2–O2–Ar mixtures: a summary of results obtained with the adaptive mesh refinement framework AMROC, Journal of Combustion, 2011, doi:10.1155/2011/738969


Download

mai.ru — informational site MAI

Copyright © 2000-2024 by MAI

 Вход