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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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