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Lagrangian dispersion and averaging behind a two-dimensional gaseous detonation front
- Hiroaki Watanabe, Akiko Matsuo, Ashwin Chinnayya, Noboru Itouyama, Akira Kawasaki, Ken Matsuoka, Jiro Kasahara
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- Journal:
- Journal of Fluid Mechanics / Volume 968 / 10 August 2023
- Published online by Cambridge University Press:
- 08 August 2023, A28
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Two-dimensional numerical simulations with the particle tracking method were conducted to analyse the dispersion behind the detonation front and its mean structure. The mixtures were 2H$_2$–O$_2$–7Ar and 2H$_2$–O$_2$ of increased irregularity in ambient conditions. The detonation could be described as a two-scale phenomenon, especially for the unstable case. The first scale is related to the main heat release zone, and the second where some classical laws of turbulence remain relevant. The dispersion of the particles was promoted by the fluctuations of the leading shock and its curvature, the presence of the reaction front, and to a lesser extent transverse waves, jets and vortex motion. Indeed, the dispersion and the relative dispersion could be scaled using the reduced activation energy and the $\chi$ parameter, respectively, suggesting that the main mechanism driving the dispersion came from the one-dimensional leading shock fluctuations and heat release. The dispersion within the induction time scale was closely related to the cellular structure, particles accumulating along the trajectory of the triple points. Then, after a transient where the fading transverse waves and the vortical motions coming from jets and slip lines were present, the relative dispersion relaxed towards a Richardson–Obukhov regime, especially for the unstable case. Two new Lagrangian Favre average procedures for the gaseous detonation in the instantaneous shock frame were proposed and the mean profiles were compared with those from Eulerian procedure. The characteristic lengths for the detonation were similar, meaning that the Eulerian procedure gave the mean structure with a reasonable accuracy.
Numerical analysis of the mean structure of gaseous detonation with dilute water spray
- Hiroaki Watanabe, Akiko Matsuo, Ashwin Chinnayya, Ken Matsuoka, Akira Kawasaki, Jiro Kasahara
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- Journal:
- Journal of Fluid Mechanics / Volume 887 / 25 March 2020
- Published online by Cambridge University Press:
- 17 January 2020, A4
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Two-dimensional (2-D) numerical simulations based on the Eulerian–Lagrangian method that take droplet break-up into account are conducted to clarify the mean structure of gaseous detonation laden with a dilute water spray. The premixed mixture is a slightly diluted stoichiometric hydrogen–oxygen mixture at low pressure. The simulated results are analysed via 2-D flow fields and statistical Favre spatiotemporal averaging techniques. Gaseous detonation with water droplets (WD) propagates stably with a velocity decrease compared with the dry Chapman–Jouguet speed. The mean structure of gaseous detonation with dilute water spray shares a similar structure as the one without water spray. However, the hydrodynamic thickness is changed due to the interaction with water spray. Overall interphase exchanges (mass, momentum and energy) that take place within the hydrodynamic thickness induce a decrease of the detonation velocity and lower the level of fluctuations downstream of the mean leading shock wave. Droplet break-up occurs downstream of the induction zone and in our case, the water vapour from the evaporation of water spray does not affect the reactivity of gaseous detonation. The laminar master equation for gaseous detonation laden with inert WD shows that the hydrodynamic thickness should rely on the gaseous sound speed, and works well as the working mixture is weakly unstable and its cellular structure is regular. The droplet flow regimes and break-up modes have also been determined. The characteristic lengths of detonation and interphase exchanges have been ordered under the present simulation conditions and have been shown to be intimately intertwined.
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- By Rose Teteki Abbey, K. C. Abraham, David Tuesday Adamo, LeRoy H. Aden, Efrain Agosto, Victor Aguilan, Gillian T. W. Ahlgren, Charanjit Kaur AjitSingh, Dorothy B E A Akoto, Giuseppe Alberigo, Daniel E. Albrecht, Ruth Albrecht, Daniel O. Aleshire, Urs Altermatt, Anand Amaladass, Michael Amaladoss, James N. Amanze, Lesley G. Anderson, Thomas C. Anderson, Victor Anderson, Hope S. Antone, María Pilar Aquino, Paula Arai, Victorio Araya Guillén, S. Wesley Ariarajah, Ellen T. Armour, Brett Gregory Armstrong, Atsuhiro Asano, Naim Stifan Ateek, Mahmoud Ayoub, John Alembillah Azumah, Mercedes L. García Bachmann, Irena Backus, J. Wayne Baker, Mieke Bal, Lewis V. Baldwin, William Barbieri, António Barbosa da Silva, David Basinger, Bolaji Olukemi Bateye, Oswald Bayer, Daniel H. Bays, Rosalie Beck, Nancy Elizabeth Bedford, Guy-Thomas Bedouelle, Chorbishop Seely Beggiani, Wolfgang Behringer, Christopher M. Bellitto, Byard Bennett, Harold V. Bennett, Teresa Berger, Miguel A. Bernad, Henley Bernard, Alan E. Bernstein, Jon L. Berquist, Johannes Beutler, Ana María Bidegain, Matthew P. Binkewicz, Jennifer Bird, Joseph Blenkinsopp, Dmytro Bondarenko, Paulo Bonfatti, Riet en Pim Bons-Storm, Jessica A. Boon, Marcus J. Borg, Mark Bosco, Peter C. Bouteneff, François Bovon, William D. Bowman, Paul S. Boyer, David Brakke, Richard E. Brantley, Marcus Braybrooke, Ian Breward, Ênio José da Costa Brito, Jewel Spears Brooker, Johannes Brosseder, Nicholas Canfield Read Brown, Robert F. Brown, Pamela K. Brubaker, Walter Brueggemann, Bishop Colin O. Buchanan, Stanley M. Burgess, Amy Nelson Burnett, J. Patout Burns, David B. Burrell, David Buttrick, James P. Byrd, Lavinia Byrne, Gerado Caetano, Marcos Caldas, Alkiviadis Calivas, William J. Callahan, Salvatore Calomino, Euan K. Cameron, William S. Campbell, Marcelo Ayres Camurça, Daniel F. Caner, Paul E. Capetz, Carlos F. Cardoza-Orlandi, Patrick W. Carey, Barbara Carvill, Hal Cauthron, Subhadra Mitra Channa, Mark D. Chapman, James H. Charlesworth, Kenneth R. Chase, Chen Zemin, Luciano Chianeque, Philip Chia Phin Yin, Francisca H. Chimhanda, Daniel Chiquete, John T. Chirban, Soobin Choi, Robert Choquette, Mita Choudhury, Gerald Christianson, John Chryssavgis, Sejong Chun, Esther Chung-Kim, Charles M. A. Clark, Elizabeth A. Clark, Sathianathan Clarke, Fred Cloud, John B. Cobb, W. Owen Cole, John A Coleman, John J. Collins, Sylvia Collins-Mayo, Paul K. Conkin, Beth A. Conklin, Sean Connolly, Demetrios J. Constantelos, Michael A. Conway, Paula M. Cooey, Austin Cooper, Michael L. Cooper-White, Pamela Cooper-White, L. William Countryman, Sérgio Coutinho, Pamela Couture, Shannon Craigo-Snell, James L. Crenshaw, David Crowner, Humberto Horacio Cucchetti, Lawrence S. Cunningham, Elizabeth Mason Currier, Emmanuel Cutrone, Mary L. Daniel, David D. Daniels, Robert Darden, Rolf Darge, Isaiah Dau, Jeffry C. Davis, Jane Dawson, Valentin Dedji, John W. de Gruchy, Paul DeHart, Wendy J. 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- The Cambridge Dictionary of Christianity
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- 05 August 2012
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- 20 September 2010, pp xi-xliv
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