Abstract
In this work, we revisit the application of the compressible linear eddy model for large eddy simulation (CLEM-LES) of calorically perfect gas detonations in an attempt to clarify if the Kolmogorov number can be treated as a constant instead of a tuning parameter when no-slip boundary conditions are included in three-dimensional simulations. In its early development, the CLEM-LES with a one-step combustion chemistry model was used to simulate two-dimensional methane-oxygen detonations to gain insight on the roles and impact of turbulent mixing rates on the presence of unburned pockets of reactive gas and cellular structure. In these past simulations, special treatment of the boundary conditions was not considered, and therefore wave speeds always recovered the Chapman-Jouguet (CJ)-velocity. Moreover, tuning of the Kolmogorov number was required in order to qualitatively capture the experimentally observed flow fields. In this work we carefully perform three-dimensional simulations of detonation propagation using the CLEM-LES, and include no-slip walls as boundary conditions. Also, instead of tuning the Kolmogorov number to obtain the correct cell size, as was done in the past, we instead use a standard value of 1.5. We found that by carefully specifying the boundary conditions, and treating the Kolmogorov as a constant (thus no model calibration), both the expected propagation velocity deficit and cellular structure are recovered. Finally, upon constructing the resulting energy spectrum, we found that the kinetic energy cascade follows the well-known −5/3 power law description of incompressible turbulence in the inertial subrange, but was not symmetric nor isotropic.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
Data availability
The data sets generated during and/or analysed during the current study are available from the corresponding author on reasonable request.
References
Abdel-Gayed, R.G., Al-Khishali, K.J., Bradley, D.: Turbulent burning velocities and flame straining in explosions. Proc. R. Soc. A: Math. Phys. Eng. Sci. 391, 393–414 (1984)
Bourlioux, A., Majda, A.J.: Theoretical and numerical structure for unstable two-dimensional detonations. Combust. Flame 90(3), 211–229 (1992). https://doi.org/10.1016/0010-2180(92)90084-3
Cael, G., Ng, H.D., Bates, K.R., et al.: Numerical simulation of detonation structures using a thermodynamically consistent and fully conservative reactive flow model for multi-component computations. Proc. R. Soc. A: Math. Phys. Eng. Sci. 465(2107), 2135–2153 (2009). https://doi.org/10.1098/rspa.2008.0371
Cai, X., Deiterding, R., Liang, J., et al.: Diffusion and mixing effects in hot jet initiation and propagation of hydrogen detonations. J. Fluid Mech. 836, 324–351 (2018). https://doi.org/10.1017/jfm.2017.770
Chasnov, J.R.: Simulation of the Kolmogorov inertial subrange using an improved subgrid model. Phys. Fluids A Fluid Dyn. 3(1), 188–200 (1991). https://doi.org/10.1063/1.857878
Choi, J.Y., Ma, F.H., Yang, V.: Some numerical issues on simulation of detonation cell structures. Combust. Explos. Shock Waves 44, 560–578 (2008). https://doi.org/10.1007/s10573-008-0086-x
Cooley, J.W., Tukey, J.W.: An algorithm for the machine calculation of complex fourier series. Math. Comput. 19, 297–301 (1965). https://doi.org/10.1090/S0025-5718-1965-0178586-1
Crane, J., Lipkowicz, J.T., Shi, X., et al.: Three-dimensional detonation structure and its response to confinement. Proc. Combust. Inst. 39(3), 2915–2923 (2023). https://doi.org/10.1016/j.proci.2022.10.019
Durran, D., Weyn, J.A., Menchaca, M.Q.: Practical considerations for computing dimensional spectra from gridded data. Mon. Weather Rev. 145(9), 3901–3910 (2017). https://doi.org/10.1175/MWR-D-17-0056.1
Falle, S.A.E.G., Giddings, J.R.: Body capturing using adaptive cartesian grids. In: Baines, M.J., Morton, K.W. (eds.) Numerical methods for fluid dynamics IV, pp. 337–343. Oxford University Press, Oxford (1993)
Floring, G., Peswani, M., Maxwell, B.: On the role of transverse detonation waves in the re-establishment of attenuated detonations in methane-oxygen. Combust. Flame 247, 112497 (2023). https://doi.org/10.1016/j.combustflame.2022.112497
Gamezo, V.N., Desbordes, D., Oran, E.S.: Two-dimensional reactive flow dynamics in cellular detonation waves. Shock Waves 9, 11–17 (1999). https://doi.org/10.1007/s001930050134
Gamezo, V.N., Vasil’ev, A.A., Khokhlov, A.M., et al.: Fine cellular structures produced by marginal detonations. Proc. Combust. Inst. 28, 611–617 (2000). https://doi.org/10.1016/s0082-0784(00)80261-1
Gavrikov, A., Efimenko, A., Dorofeev, S.: A model for detonation cell size prediction from chemical kinetics. Combust. Flame 120(1), 19–33 (2000). https://doi.org/10.1016/S0010-2180(99)00076-0
Hu, X.Y., Khoo, B.C., Zhang, D.L., et al.: The cellular structure of a two-dimensional \(\text{ H}_2/\text{O}_2\)/Ar detonation wave. Combust. Theory Model. 8(2), 339–359 (2004). https://doi.org/10.1088/1364-7830/8/2/008
Kailasanath, K., Oran, E., Boris, J., et al.: Determination of detonation cell size and the role of transverse waves in two-dimensional detonations. Combust. Flame 61(3), 199–209 (1985). https://doi.org/10.1016/0010-2180(85)90101-4
Kawai, S., Larson, J.: Wall-modeling in large eddy simulation: Length scales, grid resolution, and accuracy. Phys. Fluids 24, 015105 (2012). https://doi.org/10.1063/1.3678331
Kiyanda, C.B., Higgins, A.J.: Photographic investigation into the mechanism of combustion in irregular detonation waves. Shock Waves 23, 115–130 (2013). https://doi.org/10.1007/s00193-012-0413-8
Liang, Z., Bauwens, L.: Cell structure and stability of detonations with a pressure-dependent chain-branching reaction rate model. Combust. Theory Model. 9(1), 93–112 (2005). https://doi.org/10.1080/13647830500051885
Mahmoudi, Y., Karimi, N., Deiterding, R., et al.: Hydrodynamic instabilities in gaseous detonations: Comparison of Euler, Navier-Stokes, and large-eddy simulation. J. Propuls. Power 30(2), 384–396 (2014). https://doi.org/10.2514/1.B34986
Massa, L., Lu, F.K.: The role of the induction zone on the detonation-turbulence linear interaction. Combust. Theory Model. 15(3), 347–371 (2011). https://doi.org/10.1080/13647830.2010.540353
Maxwell, B., Pekalski, A., Radulescu, M.: Modelling of the transition of a turbulent shock-flame complex to detonation using the linear eddy model. Combust. Flame 192, 340–357 (2018). https://doi.org/10.1016/j.combustflame.2018.02.013
Maxwell, B.M., Falle, S.A.E.G., Sharpe, G., et al.: A compressible-LEM turbulent combustion subgrid model for assessing gaseous explosion hazards. J. Loss Prev. Process Ind. 36, 460–470 (2015). https://doi.org/10.1016/j.jlp.2015.01.014
Maxwell, B.M., Bhattacharjee, R.R., Lau-Chapdelaine, S.S.M., et al.: Influence of turbulent fluctuations on detonation propagation. J. Fluid Mech. 818, 646–696 (2017). https://doi.org/10.1017/jfm.2017.145
Mazaheri, K., Mahmoudi, Y., Radulescu, M.I.: Diffusion and hydrodynamic instabilities in gaseous detonations. Combust. Flame 159, 2138–2154 (2012)
Menon, S., Kerstein, A.R.: The linear-eddy model. In: Echekki, T., Mastorakos, E.I. (eds.) Turbulent combustion modeling: advances, new trends and perspectives, pp. 221–247. Springer, Berlin, Heidelberg (2011). https://doi.org/10.1007/978-94-007-0412-1_10
Oran, E., Boris, J., Young, T., et al.: Numerical simulations of detonations in hydrogen-air and methane-air mixtures. Symp. (Int.) Combust. 18(1), 1641–1649 (1981). https://doi.org/10.1016/S0082-0784(81)80168-3
Oran, E.S., Weber, J.W., Stefaniw, E.I., et al.: A numerical study of a two-dimensional \(\text{ H}_2\)-\(\text{ O}_2\)-Ar detonation using a detailed chemical reaction model. Combust. Flame 113(1), 147–163 (1998). https://doi.org/10.1016/S0010-2180(97)00218-6
Pope, S.: Turbulent Flows. Cambridge University Press, Cambridge (2000). https://doi.org/10.1017/CBO9780511840531
Pope, S.B.: Ten questions concerning the large-eddy simulation of turbulent flows. New J. Phys. 6, 35 (2004). https://doi.org/10.1088/1367-2630/6/1/035
Radulescu, M.I., Sharpe, G.J., Law, C.K., et al.: The hydrodynamic structure of unstable cellular detonations. J. Fluid Mech. 580, 31–81 (2007). https://doi.org/10.1017/s0022112007005046
Saddoughi, S.G., Veeravalli, S.V.: Local isotropy in turbulent boundary layers at high Reynolds number. J. Fluid Mech. 268, 333–372 (1994). https://doi.org/10.1017/S0022112094001370
Sankaran, V.: Sub-grid combustion modeling for compressible two-phase reacting flows. In: PhD thesis, school of aerospace engineering, georgia institute of technology, Atlanta, Georgia (2003). https://smartech.gatech.edu/handle/1853/5274?show=full
Sharpe, G.J.: Transverse waves in numerical simulations of cellular detonations. J. Fluid Mech. 447, 31–51 (2001). https://doi.org/10.1017/s0022112001005535
Singh, S., Powers, J.M., Paolucci, S.: Multidimensional detonation solutions from reactive navier-stokes equations. In: 17th intl colloquium on the dynamics of explosions and reactive systems, Heidelberg, Germany (1999)
Taileb, S., Melguizo-Gavilanes, J., Chinnayya, A.: Influence of the chemical modeling on the quenching limits of gaseous detonation waves confined by an inert layer. Combust. Flame 218, 247–259 (2020). https://doi.org/10.1016/j.combustflame.2020.04.018
Taki, S., Fujiwara, T.: Numerical simulation of triple shock behavior of gaseous detonation. Symp. (Int.) Combust. 18(1), 1671–1681 (1981). https://doi.org/10.1016/S0082-0784(81)80171-3
Taylor, B., Kessler, D., Gamezo, V., et al.: Numerical simulations of hydrogen detonations with detailed chemical kinetics. Proc. Combust. Inst. 34(2), 2009–2016 (2013). https://doi.org/10.1016/j.proci.2012.05.045
Vanella, M., Piomelli, U., Balaras, E.: Effect of grid discontinuities on large-eddy simulation statistics and flow fields. J. Turbul. 9(32), 1–23 (2008). https://doi.org/10.1080/14685240802446737
Vijayakumar, N., Munipalli, R., Wilson, D.: Reinitiation mode study of methane-oxygen detonation using reduced chemistry. In: AIAA Propulsion and Energy 2020 Forum (2020). https://doi.org/10.2514/6.2020-3862
Wang, C., Qian, C., Liu, J., et al.: Influence of chemical kinetics on detonation initiating by temperature gradients in methane/air. Combust. Flame 197, 400–415 (2018). https://doi.org/10.1016/j.combustflame.2018.08.017
Xiao, Q., Sow, A., Maxwell, B., et al.: Effect of boundary layer losses on 2D detonation cellular structures. Proc. Combust. Inst. 38(3), 3641–3649 (2021). https://doi.org/10.1016/j.proci.2020.07.068
Acknowledgements
This research was enabled in part by high performance computing resources provided the Core Facility for Advanced Research Computing at Case Western Reserve University and also through computing resources provided by the Digital Research Alliance of Canada.
Funding
BM acknowledges the support of the Natural Sciences and Engineering Research Council of Canada (NSERC), funding reference number RGPIN-2023-03691 (Towards detonation, explosion, and blast modelling at industrially relevant scales).
Author information
Authors and Affiliations
Corresponding author
Ethics declarations
Conflict of interest
The authors have no competing interests to declare that are relevant to the content of this article.
Rights and permissions
Springer Nature or its licensor (e.g. a society or other partner) holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law.
About this article
Cite this article
Maxwell, B., Wang, W.H. The Influence of Boundary Conditions on Three-Dimensional Large Eddy Simulations of Calorically Perfect Gas Detonations. Flow Turbulence Combust 111, 1279–1299 (2023). https://doi.org/10.1007/s10494-023-00491-6
Received:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s10494-023-00491-6