https://orcid.org/0000-0002-9805-2583
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ABSTRACT
Rotating detonation engines have been studied experimentally and numerically due to a higher thermal efficiency in theory. Numerical simulations of the flow field inside the engine cost more since the flow is unsteady and contains shock waves, detonation waves, and contact surfaces. Thus, a two-dimensional theoretical study with the method of pressure behind a shock wave or a rarefaction wave as a function of deflection angle of flow was carried out to predict the flow field and reduce the cost. Numerical simulations with a premixed inviscid model were also carried out to verify the theoretical results. The flow field at an equivalence ratio of 0.8 has a curved contact surface, whereas it has a plane contact surface at equivalence ratios of 0.9–1.2 because the RDW is stronger and more stable. Comparisons between the theoretical and numerical results show the theoretical method can be used to obtain a rough flow field inside the RDE, including the pressure and deflection angle of flow behind the shock wave and rarefaction wave. Most of the errors between the numerical and theoretical results are less than 10%.
Nomenclature
| A | = | Pre-exponential factor |
| CJ | = | Chapman–Jouguet |
| D | = | Speed of detonation relative to reactants |
| E | = | Total energy |
| Ea | = | Activation energy |
| Er | = | Global equivalence ratio |
| L | = | Length |
| M | = | Total species number |
| Ma | = | Mach number |
| OR | = | Reflected rarefaction wave |
| OT | = | Refracted shock wave |
| R | = | Gas constant |
| RDE | = | Rotating detonation engine |
| RDW | = | Rotating detonation wave |
| T | = | Temperature |
| T’ | = | Seven cycle time |
| U | = | Velocity vector |
| Ym | = | Mass fraction of the m-th species |
| b | = | Temperature exponent |
| c | = | Sound speed |
| h | = | Enthalpy |
| kf | = | Reaction rate constant |
| p | = | Pressure |
| q | = | Fluid velocity in the moving reference frame |
| r | = | Any physical quantity |
| t | = | Time |
| ud | = | Detonation velocity in the lab reference frame |
| u0’ | = | Fluid velocity in zone 0’ in the lab reference frame |
| u0 | = | Fluid velocity in zone 0 in the lab reference frame |
| θ | = | Deflection angle |
| α | = | Angle between the oblique shock wave and q0 |
| β | = | Angle between deflagration surface and inlet |
| δ | = | Angle between the flow velocity in zone 0’ and detonation velocity in the lab reference frame |
| γ | = | Specific heat ratio |
| ρ | = | Density |
| = | Heat release rate | |
| = | Formation or consumption rate of the m-th species | |
| Subscripts | = | |
| J | = | Chapman–Jouguet |
| d | = | Detonation |
| m | = | m-th species |
| min | = | Minimum |
| n | = | Numerical |
| t | = | Theoretical |
Disclosure statement
No potential conflict of interest was reported by the author(s).
Supplementary material
Supplemental data for this article can be accessed online at https://doi.org/10.1080/00102202.2024.2378493