8 Some Aspects on Pulsating Detonation Wave Numerical Simulation …
105
This tendency was confirmed with the results from [2]. In [6], the mechanism accompanying the process of detonation propagation in the channel with an array of circular
obstacles was studied. The mechanism was based on the formation of a temperature
gradient and spontaneous waves in the unburned gas adjacent to DW front. The
influence of chemical kinetics on the modeling of detonation initiation by a temperature gradient in the hydrogen–air mixture was discussed in [8]. The chemical model
that contains 19 reactions and 9 components was considered as the detailed kinetics
model. The model described correctly some parameters like ignition delay times
and laminar flames characteristics for a wide range of initial parameters. The global
Arrhenius kinetics [7] of hydrogen–air combustion was considered as the one-step
model. The model reproduced some characteristics like the flame speed and the width
of the laminar flame. The critical size of the “hot spots” capable to initiate detonation
was shown to be larger in the case of the detailed chemistry. The differences were
explained by the fact that the one-step kinetics model is exothermic for all temperatures, while chain branching reactions in complex kinetics start with endothermic
induction stage representing chain initiation and branching. Besides, the induction
times obtained using one-step kinetics were several orders of magnitude smaller than
the experimental results that are in good agreement with induction times obtained
using detailed kinetics. Thus, the complex kinetics is shown to provide a sufficiently
wide range of parameters, where the kinetics works correctly, and takes into account
a number of factors better than the one-step one, especially at the stage of detonation
initiation, although it significantly increases the calculation time. On the other hand,
the use of one-step kinetics with gasdynamics values from a vicinity of parameters that are used in the process of calibrating gives an opportunity to obtain some
adequate results and useful recommendations to study the dynamics of detonation
instability.
In [9], the detailed analysis of the nonlinear dynamics of detonation in the
hydrogen–air mixture was carried out using the detailed kinetics model. The mathematical model included the system of Euler equations written for the case of the multicomponent mixture. The chemical kinetics model included nine components and 38
elementary reactions. The numerical method of the high order of accuracy included
the fifth-order convergence rate monotonicity preserving scheme, the third-order
total variation diminishing the Runge–Kutta time integration scheme, Roe flux and
Gaussian elimination scheme for solving chemical kinetics implicitly. The authors
considered direct initiation of 1D detonation in the channel covered with computational grids with cell sizes of 2.5 and 12.5 µm. The transition from the overdriven
detonation regime to the self-sustaining one with the formation of two pulsating
modes was obtained. For both grid sizes, the HF pulsations mode was followed
by the high-amplitude (HA) pulsations mode with the time increase. The specific
features of each mode including the frequency values are described. The mechanism
of processes in the induction zone behind the front of LSW was described in terms of
acoustic and entropy waves in a manner similar to that of McVey and Toong [10] and
it seems to be a reasonable description of the mechanism of pulsating detonation. The
work demonstrated a sensitivity of the results to the values of the initial conditions
parameters, grid resolution, and properties of the numerical method.
105
This tendency was confirmed with the results from [2]. In [6], the mechanism accompanying the process of detonation propagation in the channel with an array of circular
obstacles was studied. The mechanism was based on the formation of a temperature
gradient and spontaneous waves in the unburned gas adjacent to DW front. The
influence of chemical kinetics on the modeling of detonation initiation by a temperature gradient in the hydrogen–air mixture was discussed in [8]. The chemical model
that contains 19 reactions and 9 components was considered as the detailed kinetics
model. The model described correctly some parameters like ignition delay times
and laminar flames characteristics for a wide range of initial parameters. The global
Arrhenius kinetics [7] of hydrogen–air combustion was considered as the one-step
model. The model reproduced some characteristics like the flame speed and the width
of the laminar flame. The critical size of the “hot spots” capable to initiate detonation
was shown to be larger in the case of the detailed chemistry. The differences were
explained by the fact that the one-step kinetics model is exothermic for all temperatures, while chain branching reactions in complex kinetics start with endothermic
induction stage representing chain initiation and branching. Besides, the induction
times obtained using one-step kinetics were several orders of magnitude smaller than
the experimental results that are in good agreement with induction times obtained
using detailed kinetics. Thus, the complex kinetics is shown to provide a sufficiently
wide range of parameters, where the kinetics works correctly, and takes into account
a number of factors better than the one-step one, especially at the stage of detonation
initiation, although it significantly increases the calculation time. On the other hand,
the use of one-step kinetics with gasdynamics values from a vicinity of parameters that are used in the process of calibrating gives an opportunity to obtain some
adequate results and useful recommendations to study the dynamics of detonation
instability.
In [9], the detailed analysis of the nonlinear dynamics of detonation in the
hydrogen–air mixture was carried out using the detailed kinetics model. The mathematical model included the system of Euler equations written for the case of the multicomponent mixture. The chemical kinetics model included nine components and 38
elementary reactions. The numerical method of the high order of accuracy included
the fifth-order convergence rate monotonicity preserving scheme, the third-order
total variation diminishing the Runge–Kutta time integration scheme, Roe flux and
Gaussian elimination scheme for solving chemical kinetics implicitly. The authors
considered direct initiation of 1D detonation in the channel covered with computational grids with cell sizes of 2.5 and 12.5 µm. The transition from the overdriven
detonation regime to the self-sustaining one with the formation of two pulsating
modes was obtained. For both grid sizes, the HF pulsations mode was followed
by the high-amplitude (HA) pulsations mode with the time increase. The specific
features of each mode including the frequency values are described. The mechanism
of processes in the induction zone behind the front of LSW was described in terms of
acoustic and entropy waves in a manner similar to that of McVey and Toong [10] and
it seems to be a reasonable description of the mechanism of pulsating detonation. The
work demonstrated a sensitivity of the results to the values of the initial conditions
parameters, grid resolution, and properties of the numerical method.