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Small-size rotating detonation engine: scaling and minimum mass flow rate

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Abstract

Rotating detonation engines (RDEs) have been observed to exhibit several operating modes and instabilities under different operation conditions (reactant mixture, injection pressure, engine geometry, injection mass flow rate, etc.). We develop the simplest model possible describing the operation of an RDE. This model takes into account the dependence of detonation properties on engine conditions, the injection process, and the geometric constraints. Using this model, we predict the lowest allowable reactant injection rates that allow an RDE to operate with a single detonation wave propagating in the annular combustion chamber. This model is compared with experimental results of engines running on H\({}_2\)/O\({}_2\) and C\({}_2\)H\({}_4\)/O\({}_2\).

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Abbreviations

\(C_{L}\) :

Cell size scaling constant for \(L_\mathrm {cr}\)

D :

Nominal engine diameter

F :

Thrust

h :

Combustion chamber annulus thickness

\(I_\mathrm {sp}\) :

Specific impulse

\(K_{L}\) :

Annulus thickness scaling constant for \(L_\mathrm {cr}\)

\(L_\mathrm {cr}\) :

Length of detonating zone in the combustion chamber

\(\dot{m}\) :

Mass flow rate through the engine

P :

Pressure

\(R_\mathrm{sp}\) :

Specific gas constant

T :

Temperature

\(U_\mathrm {CJ}\) :

Chapman–Jouguet detonation wave speed

\(U_\mathrm {D}\) :

Detonation wave speed

\(V_\mathrm {inj}\) :

Reactant injection velocity

\(\theta \) :

Angle of reactant injection surface

\(\lambda \) :

Detonation cell width

\(\rho \) :

Density

\(\phi \) :

Equivalence ratio

\(\omega \) :

Wavenumber: number of co-rotating detonation waves within the combustion chamber

\(*\) :

Choking property

\(\mathrm {0}\) :

Stagnation property

\(\mathrm {ref}\) :

Reference state

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Acknowledgements

This work would not have been possible without the numerous discussions which took place with A.J. Higgins of McGill University and X. Mi currently at McGill University. This work was supported by a Discovery Grant from the National Science and Engineering Research Council of Canada.

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  1. V. Joseph

    Present address: Nagoya University, Nagoya, Japan

Authors and Affiliations

  1. Department of Mechanical, Industrial, and Aerospace Engineering, Concordia University, Montreal, QC, Canada

    S. Connolly-Boutin, V. Joseph, H. D. Ng & C. B. Kiyanda

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Correspondence to S. Connolly-Boutin.

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Communicated by E. Gutmark.

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Connolly-Boutin, S., Joseph, V., Ng, H.D. et al. Small-size rotating detonation engine: scaling and minimum mass flow rate. Shock Waves 31, 665–674 (2021). https://doi.org/10.1007/s00193-021-00991-2

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