Abstract
An optimisation study of a shock-wave-focusing geometry is presented in this work. The configuration serves as a reliable and deterministic detonation initiator in a pulsed detonation engine. The combustion chamber consists of a circular pipe with one convergent–divergent axisymmetric nozzle, acting as a focusing device for an incoming shock wave. Geometrical changes are proposed to reduce the minimum shock wave strength necessary for a successful detonation initiation. For that purpose, the adjoint approach is applied. The sensitivity of the initiation to flow variations delivered by this method is used to reshape the obstacle’s form. The thermodynamics is described by a higher-order temperature-dependent polynomial, avoiding the large errors of the constant adiabatic exponent assumption. The chemical reaction of stoichiometric premixed hydrogen-air is modelled by means of a one-step kinetics with a variable pre-exponential factor. This factor is adapted to reproduce the induction time of a complex kinetics model. The optimisation results in a 5% decrease of the incident shock wave threshold for the successful detonation initiation.
Highlights
The predictions for constant-pressure gas turbines foresee a convergence in terms of thermodynamic efficiency [1]
The results describe a highly inhomogenous flow where the detonation initiation is located on contact surfaces originating from shock wave interactions
This geometry parameters replicate the optimal Shock-to-detonation transition (SDT) geometry with a minimum in the incoming shock wave strength proposed by Semenov et al [14,15]
Summary
The predictions for constant-pressure gas turbines foresee a convergence in terms of thermodynamic efficiency [1]. The temporal rate of these sequential focusing events is defined by the curvature of the imploding shock wave, resulting from the reflection at the nozzle. This curvature is determined by the geometry, proving the existence of a complex relation between the obstacle’s shape and the final combustion regime. This geometry parameters replicate the optimal SDT geometry with a minimum in the incoming shock wave strength proposed by Semenov et al [14,15]. The validation and verification of the in-house code is presented in these appendices
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