In reactive flows, combustion propagates mainly in two modes driven either by thermal and molecular diffusion or by thermal expansion due to adiabatic shock compression. These waves are known as deflagration and detonation, respectively. Their direct initiation is defined by the initial conditions, making these propagation modes to act as stable attractors. There exists also an indirect path from a deflagration to a detonation in a process described as Deflagration-to-Detonation Transition (DDT) or more specific for this thesis Shock-to-Detonation Transition (SDT). The low energy demands of DDT in starting detonation reflects in plenty of applications in the energy and transportation sectors. Apart from its use for energy production and vehicle propulsion, this phenomenon is also related to safety issues in mines, power stations, and nuclear power plants. As a part of the Collaborative Research Center 1029 TurbIn (SFB-1029), this work's motivation is to improve the thermal efficiency in gas turbines by replacing the conventional isobaric combustion with quasi-isochoric combustion. The pressure gain combustion is implemented in a new Pulse Detonation Engine (PDE). The physical-chemical processes leading to detonation initiation in the new design are investigated. The configuration consists of a circular pipe equipped with a pre-chamber and a single convergent-divergent axisymmetric nozzle. The latter obstructs the flow and acts as a shock-focusing geometry. The stoichiometric hydrogen mixture is injected through a circumferential aperture between the pipe and a hemispherical wave reflector. The study starts with a joined numerical and experimental approach to then apply exclusively numerical methods. The compressible reactive Navier-Stokes Equation (NSE) in the conservative skew-symmetric formulation is solved. The thermochemical methods are being updated as the investigation develops and more details of the processes inside the combustion chamber are needed. In that context, the global reaction is modeled with a one-step irreversible Arrhenius kinetics with pressure- and temperature-dependent parameters. These parameters are selected using the adjoint method to reproduce the induction time of a complex kinetics model (San Diego mechanism). A higher-order temperature-dependent polynomial describes the thermodynamics. The operating modes of the experimental facility are numerically described with data-based models. From intermediate results, a shock wave formation via an accelerating turbulent flame is identified previous to the detonation initiation. Subsequently, special attention is devoted to the reflection and focusing of the leading shock at the nozzle. Two different SDT initiation mechanisms (direct or mild) were distinguished depending on the strength of the incoming shock wave. A criteria for the prediction of the resulting combustion regime is derived from the velocity of the shock sequential focusing. This velocity is estimated from the spatial parametrization of the reflected shock wave at the nozzle. Once the influence of the obstacle's shape on the SDT initiation is determined, a geometrical optimization is carried out. For that purpose the adjoint approach is used to extract the sensitivity of the SDT initiation with respect to variations on the imploding shock wave just before the focusing. The proposed changes (adding a parabolic-like profile at the nozzle's corner and a slightly increase of the obstruction) show a reduction of 5 % in the detonation initiation threshold. Here, this threshold is defined by the incident shock strength, meaning that the geometrical modifications guarantee detonation initiation for weaker incoming shocks. As a consequence, the fuel consumption and the engine length can be reduced, further increasing the cycle thermal efficiency of the gas turbine.
Sergio Bengoechea Lozano (Thu,) studied this question.