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Diffusion and mixing effects in hot jet initiation and propagation of hydrogen detonations

Published online by Cambridge University Press:  11 December 2017

Xiaodong Cai Open the ORCID record for Xiaodong Cai [Opens in a new window] ,
Ralf Deiterding ,
Jianhan Liang ,
Mingbo Sun  and
Yasser Mahmoudi
Xiaodong Cai
Affiliation:
Science and Technology on Scramjet Laboratory, National University of Defense Technology, Changsha, 410073, China
Ralf Deiterding
Affiliation:
Aerodynamics and Flight Mechanics Research Group, University of Southampton, Highfield Campus, Southampton SO17 1BJ, UK
Jianhan Liang*
Affiliation:
Science and Technology on Scramjet Laboratory, National University of Defense Technology, Changsha, 410073, China
Mingbo Sun
Affiliation:
Science and Technology on Scramjet Laboratory, National University of Defense Technology, Changsha, 410073, China
Yasser Mahmoudi
Affiliation:
School of Mechanical and Aerospace Engineering, Queen’s University Belfast, Belfast BT9 5AH, UK
*
†Email address for correspondence: [email protected]
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Abstract

In the present work, the role of diffusion and mixing in hot jet initiation and detonation propagation in a supersonic combustible hydrogen–oxygen mixture is investigated in a two-dimensional channel. A second-order accurate finite volume method solver combined with an adaptive mesh refinement method is deployed for both the reactive Euler and Navier–Stokes equations in combination with a one-step and two-species reaction model. The results show that the small-scale vortices resulting from the Kelvin–Helmholtz instability enhance the reactant consumption in the inviscid result through the mixing. However, the suppression of the growth of the Kelvin–Helmholtz instability and the subsequent formation of small-scale vortices imposed by the diffusion in the viscous case can result in the reduction of the mixing rate, hence slowing the consumption of the reactant. After full initiation in the whole channel, the mixing becomes insufficient to facilitate the reactant consumption. This applies to both the inviscid and viscous cases and is due to the absence of the unburned reactant far away from the detonation front. Nonetheless, the stronger diffusion effect in the Navier–Stokes results can contribute more significantly to the reactant consumption closely behind the detonation front. However, further downstream the mixing is expected to be stronger, which eventually results in a stronger viscous detonation than the corresponding inviscid one. At high grid resolutions it is vital to correctly consider physical viscosity to suppress intrinsic instabilities in the detonation front, which can also result in the generation of less triple points even with a larger overdrive degree. Numerical viscosity was minimized to such an extent that inviscid results remained intrinsically unstable while asymptotically converged results were only obtained when the Navier–Stokes model was applied, indicating that solving the reactive Navier–Stokes equations is expected to give more correct descriptions of detonations.

JFM classification

Compressible Flows: Compressible Flows Compressible Flows: Detonation waves
Type
JFM Papers
Information
Journal of Fluid Mechanics , Volume 836 , 10 February 2018 , pp. 324 - 351
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Copyright
© 2017 Cambridge University Press 

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References

Arienti, M. & Shepherd, J. E. 2005 A numerical study of detonation diffraction. J. Fluid Mech. 529, 117–146.CrossRefGoogle Scholar
Berger, M.1982 Adaptive mesh refinement for hyperbolic differential equations. Report no. STAN-CS-82-924, Stanford University.CrossRefGoogle Scholar
Berger, M. & Olier, J. 1984 Adaptive mesh refinement for hyperbolic partial differential equations. J. Comput. Phys. 53, 484–512.CrossRefGoogle Scholar
Bhattacharjee, R. R., Lau-Chapdelaine, S. S. M., Maines, G., Maley, L. & Radulescu, M. I. 2013 Detonation re-initiation mechanism following the Mach reflection of a quenched detonation. Proc. Combust. Inst. 34, 1893–1901.CrossRefGoogle Scholar
Cai, X. D., Liang, J. H., Lin, Z. Y., Deiterding, R. & Liu, Y. 2014 Parametric study of detonation initiation using a hot jet in supersonic combustible mixtures. Aerosp. Sci. Technol. 39, 442–455.CrossRefGoogle Scholar
Cai, X. D., Liang, J. H., Lin, Z. Y., Deiterding, R. & Zhuang, F. C. 2015a Detonation initiation and propagation in nonuniform supersonic combustible mixtures. Combust. Sci. Technol. 187 (4), 525–536.CrossRefGoogle Scholar
Cai, X. D., Liang, J. H., Lin, Z. Y., Deiterding, R., Qin, H. & Han, X. 2015b Adaptive mesh refinement-based numerical simulation of detonation initiation in supersonic combustible mixtures using a hot jet. ASCE J. Aerosp. Engng 28 (1), 04014046.Google Scholar
Cai, X. D., Liang, J. H. & Deiterding, R. 2016 Numerical investigation on detonation control using a pulse hot jet in supersonic combustible mixture. Combust. Sci. Technol. 188, 1674–1690.CrossRefGoogle Scholar
Cai, X. D., Liang, J. H., Deiterding, R. & Lin, Z. Y. 2016a Adaptive simulations of cavity-based detonation in supersonic hydrogen–oxygen mixture. Intl J. Hydrogen Energy 41, 6917–6928.CrossRefGoogle Scholar
Cai, X. D., Liang, J. H., Deiterding, R. & Lin, Z. Y. 2016b Detonation simulations in supersonic combustible mixtures with nonuniform species. AIAA J. 54 (8), 2449–2462.CrossRefGoogle Scholar
Cai, X. D., Liang, J. H., Deiterding, R., Che, Y. G. & Lin, Z. Y. 2016c Adaptive mesh refinement based simulations of three-dimensional detonation combustion in supersonic combustible mixtures with a detailed reaction model. Intl J. Hydrogen Energy 41, 3222–3239.CrossRefGoogle Scholar
Cai, X. D., Deiterding, R., Liang, J. H. & Mahmoudi, Y. 2017 Adaptive simulations of viscous detonation using high-order hybrid WENO-CD scheme with a hot jet initiation. Proc. Combust. Inst. 36, 2725–2733.CrossRefGoogle Scholar
Deiterding, R.2003 Parallel adaptive simulation of multi-dimensional detonation structures. PhD thesis, Brandenburgische Technische Universität Cottbus, Cottbus.Google Scholar
Deiterding, R. 2009 A parallel adaptive method for simulating shock-induced combustion with detailed chemical kinetics in complex domains. Comput. Struct. 87, 769–783.CrossRefGoogle Scholar
Deiterding, R. 2011 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. J. Combust. 2011, 1–18.CrossRefGoogle Scholar
Gallier, S., Le Palud, F., Pintgen, F., Mével, R. & Shepherd, J. E. 2017 Detonation wave diffraction in H2–O2–Ar mixtures. Proc. Combust. Inst. 36 (2), 2781–2789.CrossRefGoogle Scholar
Gamezo, V. N., Desbordes, D. & Oran, E. S. 1999 Formation and evolution of two-dimensional cellular detonations. Combust. Flame 116, 154–165.CrossRefGoogle Scholar
Gamezo, V. N., Khokhlov, A. M. & Oran, E. S. 2001 The influence of shock bifurcation on shock flame interactions and DDT. Combust. Flame 126, 1810–1826.CrossRefGoogle Scholar
Gamezo, V. N., Ogawa, T. & Oran, E. S. 2007 Numerical simulations of flame propagation and DDT in obstructed channels filled with hydrogen–air mixture. Proc. Combust. Inst. 31, 2463–2471.CrossRefGoogle Scholar
Gamezo, V. N., Ogawa, T. & Oran, E. S. 2008 Flame acceleration and DDT in channels with obstacles: effect of obstacle spacing. Combust. Flame 155, 302–315.CrossRefGoogle Scholar
Goodwin, G. B., Houim, R. W. & Oran, E. S. 2016 Effect of decreasing blockage ratio on DDT in small channels with obstacles. Combust. Flame 173, 16–26.CrossRefGoogle Scholar
Goodwin, G. B., Houim, R. W. & Oran, E. S. 2017 Shock transition to detonation in channels with obstacles. Proc. Combust. Inst. 36 (2), 2717–2724.CrossRefGoogle Scholar
Grogan, K. P. & Ihme, M. 2015 Weak and strong ignition of hydrogen/oxygen mixtures in shock-tube systems. Proc. Combust. Inst. 35, 2181–2189.CrossRefGoogle Scholar
Hu, X. Y., Khoo, B. C., Zhang, D. L. & Jiang, Z. L. 2004 The cellular structure of a two-dimensional H2/O2/Ar detonation wave. Combust. Theor. Model. 8, 339–359.CrossRefGoogle Scholar
Hu, X. Y., Zhang, D. L., Khoo, B. C. & Jiang, Z. L. 2005 The structure and evolution of a two-dimensional H2/O2/Ar cellular detonation. Shock Waves 14, 37–44.CrossRefGoogle Scholar
Kaps, P. & Rentrop, P. 1979 Generalized Runge–Kutta methods of order four with step size control for stiff ordinary differential equations. Numer. Math. 33, 55–68.CrossRefGoogle Scholar
Kessler, D. A., Gamezo, V. N. & Oran, E. S. 2010 Simulations of flame acceleration and deflagration-to-detonation transitions in methane–air systems. Combust. Flame 157, 2063–2077.CrossRefGoogle Scholar
Kessler, D. A., Gamezo, V. N. & Oran, E. S. 2011 Multilevel detonation cell structures in methane–air mixtures. Proc. Combust. Inst. 33, 2211–2218.CrossRefGoogle Scholar
Lee, J. H. S. 1984 Dynamic parameters of gaseous detonation. Annu. Rev. Fluid Mech. 16, 311–336.CrossRefGoogle Scholar
Lee, J. H. S. 2008 The Detonation Phenomenon. Cambridge University Press.CrossRefGoogle Scholar
Liang, Z. & Bauwens, L. 2005 Detonation structure with pressure-dependent chain-branching kinetics. Proc. Combust. Inst. 30, 1879–1887.CrossRefGoogle Scholar
Liang, Z., Browne, S., Deiterding, R. & Shepherd, J. E. 2007 Detonation front structure and the competition for radicals. Proc. Combust. Inst. 31, 2445–2453.CrossRefGoogle Scholar
Liang, J. H., Cai, X. D., Lin, Z. Y. & Deiterding, R. 2014 Effects of a hot jet on detonation initiation and propagation in supersonic combustible mixtures. Acta Astronaut. 105 (1), 265–277.CrossRefGoogle Scholar
Lv, Y. & Ihme, M. 2015 Computational analysis of re-ignition and re-initiation mechanisms of quenched detonation waves behind a backward facing step. Proc. Combust. Inst. 35, 1963–1972.CrossRefGoogle Scholar
Mach, P. & Radulescu, M. I. 2011 Mach reflection bifurcations as a mechanism of cell multiplication in gaseous detonations. Proc. Combust. Inst. 33, 2279–2285.CrossRefGoogle Scholar
Mahmoudi, Y., Karimi, N., Deiterding, R. & Emami, S. 2014 Hydrodynamic instabilities in gaseous detonations: comparison of Euler, Navier–Stokes, and large-eddy simulation. J. Propul. Power 30, 384–396.CrossRefGoogle Scholar
Mahmoudi, Y. & Mazaheri, K. 2011 High resolution numerical simulation of the structure of 2-D gaseous detonations. Proc. Combust. Inst. 33, 2187–2194.CrossRefGoogle Scholar
Mahmoudi, Y. & Mazaheri, K. 2012 Triple point collision and hot spots in detonations with regular structure. Combust. Sci. Technol. 184, 1135–1151.CrossRefGoogle Scholar
Mahmoudi, Y. & Mazaheri, K. 2015 High resolution numerical simulation of triple point collision and origin of unburned gas pockets in turbulent detonations. Acta Astronaut. 115, 40–51.CrossRefGoogle Scholar
Maley, L., Bhattacharjee, R. R., Lau-Chapdelaine, S. S. M. & Radulescu, M. I. 2015 Influence of hydrodynamic instabilities on the propagation mechanism of fast flames. Proc. Combust. Inst. 35, 2117–2126.CrossRefGoogle Scholar
Maxwell, B. M., Bhattacharjee, R. R., Lau-Chapdelaine, S. S. M., Falle, S. A. E. G., Sharpe, G. J. & Radulescu, M. I. 2017 Influence of turbulent fluctuations on detonation propagation. J. Fluid Mech. 818, 646–696.CrossRefGoogle Scholar
Mazaheri, K., Mahmoudi, Y. & Radulescu, M. I. 2012 Diffusion and hydrodynamic instabilities in gaseous detonations. Combust. Flame 113, 2138–2154.CrossRefGoogle Scholar
Mazaheri, K., Mahmoudi, Y., Sabzpooshani, M. & Radulescu, M. I. 2015 Experimental and numerical investigation of propagation mechanism of gaseous detonations in channels with porous walls. Combust. Flame 162, 2638–2659.CrossRefGoogle Scholar
Melguizo-Gavilanes, J. & Bauwens, L. 2013 Shock initiated ignition for hydrogen mixtures of different concentrations. Intl J. Hydrogen Energy 38, 8061–8067.CrossRefGoogle Scholar
Melguizo-Gavilanes, J., Rezaeyan, N., Tian, M. & Bauwens, L. 2011 Shock-induced ignition with single step Arrhenius kinetics. Intl J. Hydrogen Energy 36, 2374–2380.CrossRefGoogle Scholar
Mével, R., Davidenko, D., Lafosse, F., Chaumeix, N., Dupré, G., Paillard, C. & Shepherd, J. E. 2015 Detonation in hydrogen–nitrous oxide-diluent mixtures: an experimental and numerical study. Combust. Flame 162, 1638–1649.CrossRefGoogle Scholar
Ng, H. D., Botros, B. B., Chao, J., Yang, J. M., Nikiforakis, N. & Lee, J. H. S. 2006 Head-on collision of a detonation with a planar shock wave. Shock Waves 15, 341–352.CrossRefGoogle Scholar
Ng, H. D. & Lee, J. H. S. 2003 Direct initiation of detonation with a multi-step reaction scheme. J. Fluid Mech. 476, 179–211.CrossRefGoogle Scholar
Oran, E. S. & Gamezo, V. N. 2007 Origins of the deflagration-to-detonation transition in gas-phase combustion. Combust. Flame 148, 4–47.CrossRefGoogle Scholar
Oran, E. S., Weber, J. W., Stefaniw, E. I., Lefebvre, M. H. & Anderson, J. D. 1998 A numerical study of two-dimensional H2–O2–Ar detonation using a detailed chemical reaction model. Combust. Flame 113, 147–163.CrossRefGoogle Scholar
Paolucci, S., Zikoski, Z. J. & Grenga, T. 2014b WAMR: an adaptive wavelet method for the simulation of compressible reacting flow. Part II. The parallel algorithm. J. Comput. Phys. 272, 842–864.CrossRefGoogle Scholar
Paolucci, S., Zikoski, Z. J. & Wirasaet, D. 2014a WAMR: an adaptive wavelet method for the simulation of compressible reacting flow. Part I. Accuracy and efficiency of algorithm. J. Comput. Phys. 272, 814–841.CrossRefGoogle Scholar
Pintgen, F., Eckett, C. A., Austin, J. M. & Shepherd, J. E. 2003 Direct observations of reaction zone structure in propagating detonations. Combust. Flame 133, 211–229.CrossRefGoogle Scholar
Radulescu, M. I. & Maxwell, B. McN. 2011 The mechanism of detonation attenuation by a porous medium and its subsequent re-initiation. J. Fluid Mech. 667, 96–134.CrossRefGoogle Scholar
Radulescu, M. I., Sharpe, G. J., Law, C. K. & Lee, J. H. S. 2007 The hydrodynamic structure of unstable cellular detonations. J. Fluid Mech. 580, 31–81.CrossRefGoogle Scholar
Radulescu, M. I., Sharpe, G. J., Lee, J. H. S., Kiyanda, C. B., Higgins, A. J. & Hanson, R. K. 2005 The ignition mechanism in irregular structure gaseous detonations. Proc. Combust. Inst. 30 (2), 1859–1867.CrossRefGoogle Scholar
Romick, C. M., Aslam, T. D. & Powers, J. M. 2012 The effect of diffusion on the dynamics of unsteady detonations. J. Fluid Mech. 699, 453–464.CrossRefGoogle Scholar
Romick, C. M., Aslam, T. D. & Powers, J. M. 2015 Verified and validated calculation of unsteady dynamics of viscous hydrogen–air detonations. J. Fluid Mech. 769, 154–181.CrossRefGoogle Scholar
Samtaney, R. & Pullin, D. I. 1996 On initial-value and self-similar solutions of the compressible Euler equations. Phys. Fluids 8, 2650–2655.CrossRefGoogle Scholar
Sharpe, G. J. 2001 Transverse wave in numerical simulations of cellular detonation. J. Fluid Mech. 447, 31–51.CrossRefGoogle Scholar
Shen, H. & Parsani, M. 2017 The role of multidimensional instabilities in direct initiation of gaseous detonations in free space. J. Fluid Mech. 813, R4.CrossRefGoogle Scholar
Shepherd, J. E. 2009 Detonation in gases. Proc. Combust. Inst. 32, 83–98.CrossRefGoogle Scholar
Singh, S., Rastigejev, Y., Paolucci, S. & Powers, J. M. 2001 Viscous detonation in H2–O2–Ar using intrinsic low-dimensional manifolds and wavelet adaptive multilevel representation. Combust. Theory Model. 5 (2), 163–184.CrossRefGoogle Scholar
Smirnov, N. N., Betelin, V. B., Shagaliev, R. M., Nikitin, V. F., Belyakov, I. M., Deryuguin, Y. N., Aksenov, S. V. & Korchazhkin, D. A. 2014 Hydrogen fuel rocket engines simulation using LOGOS code. Intl J. Hydrogen Energy 39, 10748–10756.CrossRefGoogle Scholar
Smirnov, N. N. & Nikitin, V. F. 2014 Modeling and simulation of hydrogen combustion in engines. Intl J. Hydrogen Energy 39, 1122–1136.CrossRefGoogle Scholar
Smirnov, N. N., Nikitin, V. F., Stamov, L. I. & Altoukhov, D. I. 2015 Supercomputing simulations of detonation of hydrogen–air mixtures. Intl J. Hydrogen Energy 40, 11059–11074.CrossRefGoogle Scholar
Taylor, B. D., Kessler, D. A., Gamezo, V. N. & Oran, E. S. 2013 Numerical simulations of hydrogen detonations with detailed chemical kinetics. Proc. Combust. Inst. 34, 2009–2016.CrossRefGoogle Scholar
Varatharajan, B. & Williams, F. A. 2001 Chemical-kinetic descriptions of high-temperature ignition and detonation of acetylene–oxygen-diluent systems. Combust. Flame 124, 624–645.CrossRefGoogle Scholar
Watt, S. D. & Sharpe, G. J. 2005 Linear and nonlinear dynamics of cylindrically and spherically expanding detonation waves. J. Fluid Mech. 522, 329–356.CrossRefGoogle Scholar
Williams, F. A. 1985 Combustion Theory. Addison-Wesley.Google Scholar
Ziegler, J. L.2011 Simulations of compressible, diffusive, reactive flows with detailed chemistry using a high-order hybrid WENO-CD scheme. PhD thesis, California Institute of Technology, Pasadena, CA.Google Scholar
Ziegler, J. L., Deiterding, R., Shepherd, J. E. & Pullin, D. I. 2011 An adaptive high-order hybrid scheme for compressive, viscous flows with detailed chemistry. J. Comput. Phys. 230, 7598–7630.CrossRefGoogle Scholar