Abstract
Thermal engines based on pressure gain combustion offer new opportunities to generate thrust with enhanced efficiency and relatively simple machinery. The sudden expansion of detonation products from a single-opening tube yields thrust, although this is suboptimal. In this article, we present the complete design optimization strategy for nozzles exposed to detonation pulses, combining unsteady Reynolds-averaged Navier–Stokes solvers with the accurate modeling of the combustion process. The parameterized shape of the nozzle is optimized using a differential evolution algorithm to maximize the force at the nozzle exhaust. The design of experiments begins with a first optimization considering steady-flow conditions, subsequently followed by a refined optimization for transient supersonic flow pulse. Finally, the optimized nozzle performance is assessed in three dimensions with unsteady Reynolds-averaged Navier–Stokes capturing the deflagration-to-detonation transition of a stoichiometric, premixed hydrogen–air mixture. The optimized nozzle can deliver 80% more thrust than a standard detonation tube and about 2% more than the optimized results assuming steady-flow operation. This study proposes a new multi-fidelity approach to optimize the design of nozzles exposed to transient operation, instead of the traditional methods proposed for steady-flow operation.
Highlights
Pressure gain combustion, and in particular detonationbased thermal engines, offers increased thermal efficiency compared to the traditional Joule–Brayton cycle.[1,2] In a pulsed detonation combustor, the combustion process evolves from deflagration to detonation along a tube, resulting in a very energetic detonation front moving at supersonic velocities toward the open end of the tube
This article addresses the void of optimization tools for nozzles exposed to transient supersonic flows
In the first step, using inexpensive 2D steady Navier–Stokes evaluations, we explored a broad design of experiments, from converging–diverging nozzles to diverging–converging, to select optimal geometries in terms of delivered axial force
Summary
In particular detonationbased thermal engines, offers increased thermal efficiency compared to the traditional Joule–Brayton cycle.[1,2] In a pulsed detonation combustor, the combustion process evolves from deflagration to detonation along a tube, resulting in a very energetic detonation front moving at supersonic velocities toward the open end of the tube. Already in 1998, Cambier[3] had identified the importance of optimizing the nozzle geometry to maximize the potential engine thrust. Because the detonation process is characterized by supersonic flows, one would conclude that divergent nozzles would outperform other types of nozzles, allowing the further expansion of the supersonic combustion gas. Ruhul et al.[5] investigated numerically three nozzle geometries including straight, converging/diverging, and diverging and concluded that for all of them, long nozzles should be selected to sustain detonation for a longer duration, allowing longer periods with positive thrust. Kailasanath[6] noted that an increase in the impulse is achievable by reshaping the nozzle, without penalizing the detonation tube refilling frequency. Based on the experimental comparisons of several supersonic nozzles, Falempin et al.[7] concluded that a bell-shaped nozzle delivers the maximum thrust
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