Accumulation of errors in numerical simulations of chemically reacting gas dynamics

Смирнов, Н.Н.; Бетелин, В. Б.; Никитин, В. Ф.; Стамов, Л.И.; Altoukhov, D.I.

doi:10.1016/j.actaastro.2015.08.013

Cited by 484 publications

(50 citation statements)

References 21 publications

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“…For a more quantitative comparison, the pressure and temperature profiles along the line y = 5 are shown in Figure 4. Overall, the curves are overlapped together so the effects of different grids Besides effects of numerical resolution, studies have shown that it is also important to take into consideration the accumulation of errors from each time-integration step for reactive flow simulations [71,72]. In other words, the effect of time-step size needs also to be verified on the reliability of the results.…”

Section: Resultsmentioning

confidence: 99%

The Effect of Chemical Reactivity on the Formation of Gaseous Oblique Detonation Waves

Yan

Teng

et al. 2019

Aerospace

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High-fidelity numerical simulations using a Graphics Processing Unit (GPU)-based solver are performed to investigate oblique detonations induced by a two-dimensional, semi-infinite wedge using an idealized model with the reactive Euler equations coupled with one-step Arrhenius or two-step induction-reaction kinetics. The novelty of this work lies in the analysis of chemical reaction sensitivity (characterized by the activation energy E a and heat release rate constant k R ) on the two types of oblique detonation formation, namely, the abrupt onset with a multi-wave point and a smooth transition with a curved shock. Scenarios with various inflow Mach number regimes M 0 and wedge angles θ are considered. The conditions for these two formation types are described quantitatively by the obtained boundary curves in M 0 -E a and M 0 -k R spaces. At a low M 0 , the critical E a,cr and k R,cr for the transition are essentially independent of the wedge angle. At a high flow Mach number regime with M 0 above approximately 9.0, the boundary curves for the three wedge angles deviate substantially from each other. The overdrive effect induced by the wedge becomes the dominant factor on the transition type. In the limit of large E a , the flow in the vicinity of the initiation region exhibits more complex features. The effects of the features on the unstable oblique detonation surface are discussed.Aerospace 2019, 6, 62 2 of 17 the conditions and interpret the observed flow field regimes in terms of competing reactions and flow-quenching effects.Alternatively, an oblique detonation wave can be induced by a wedge in an incoming reactive flow [20][21][22]. A standing oblique detonation wave attached to the wedge tip presents a more practical configuration for engine operation [23][24][25]. There has been indeed a remarkable progress in understanding the fundamental aspects of oblique detonation waves induced by a semi-infinite, two-dimensional wedge. Analytical solutions such as wave angles and steady structures as the basic foundation were sought in a number of pioneering works using detonation polar analysis by approximating the ODW as an oblique shock wave (OSW) coupled with an instantaneous post-shock heat release [26][27][28][29]. In later studies, it has been demonstrated that the ODW formation structure induced by the wedge is more complex. In many cases, an oblique shock wave first forms upon the flow interaction with the wedge igniting the combustible flow mixture, and subsequently transits into an oblique detonation wave [30]. Due to the strong coupling sensitivity between fluid dynamics and chemical reactions, as well as the inherent unstable nature of detonation waves [31], it remains technically challenging to establish steady oblique detonations in high-speed combustible mixtures for practical propulsion applications, and such success requires fundamental understanding of the initiation structure of oblique detonation waves. To this end, the dynamics of ODW formation has recently drawn significant research attention...

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Section: Resultsmentioning

confidence: 99%

The Effect of Chemical Reactivity on the Formation of Gaseous Oblique Detonation Waves

Yan

Teng

et al. 2019

Aerospace

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“…It is also demonstrated that reliability of results increases on increasing grid resolution and scheme accuracy [57] .…”

Section: Numerical Schemementioning

confidence: 94%

Adaptive simulations of cavity-based detonation in supersonic hydrogen–oxygen mixture

Cai

Liang

Deiterding

et al. 2016

International Journal of Hydrogen Energy

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Two-dimensional reactive Euler equations with a detailed reaction modelwhere the molar ratio of the combustible mixture H2/O2/Ar is 2:1:7 under the condition of pressure 6.67 kPa and temperature 298 K, are solved numerically with adaptive mesh refinement method to investigate detonation combustion using a hot jet initiation in cavity-based channels filled with the supersonic combustible mixture.Results show that from the comparison between the simulations in a cavity-based channel and a straight channel without any cavity embedded, it is indicated that the cavity can help realize detonation initiation in the combustible mixture with a hot jet.It is suggested that detonation initiation can be realized using a relatively weaker hot jet in cavity-based channels filled with the supersonic combustible mixture compared with that in straight channels without a cavity embedded. The cavity also plays a significant role in detonation propagation in the supersonic combustible mixture.After the hot jet is shut down, the acoustic wave generated by the subsonic combustion in the cavity can accelerate detonation propagation through a subsonic Corresponding author. Email addresses: cai-chonger@hotmail.com, jhleon@vip.sina.com, r.deiterding@soton.ac.uk, linzy96@nudt.edu.cn, channel and result in the formation of a slightly overdriven detonation eventually. For a given flow with a shadow cavity embedded, there should exist a minimum cavity width Lmin. When the width is below Lmin, only some pressure oscillations in the cavity can make some impacts on detonation initiation and propagation. Otherwise, cavity oscillations can be generated which can greatly accelerate detonation initiation and propagation in the supersonic combustible mixture. For the shadow cavity, purely increasing the cavity depth does not have any more influence on detonation combustion. However, if the cavity is a deep one, it can play an important role in accelerating detonation initiation and propagation in the supersonic combustible mixture due to resonant oscillations.

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“…The error estimates of the simulation For unsteady problems, the accumulated error should be considered. For the given allowable value of total error S max , the allowable number of time steps can be estimated by the following equation [30][31] :…”

Section: Grid Convergence Studymentioning

confidence: 99%

The influence of the elastic vibration of the carrier to the aerodynamics of the external store in air-launch-to-orbit process

Yang

2016

Acta Astronautica

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The separation between the carrier and store is one of the most important and difficult phases in Air-launch-to-orbit technology. Based on the previous researches, the interference aerodynamic forces of the store caused by the carrier are obvious in the earlier time during the separation. And the interference aerodynamics will be more complex when considering the elastic deformation of the carrier. Focusing on the conditions that in the earlier time during the separation, the steady and unsteady interference aerodynamic forces of the store are calculated at different angle of attacks and relative distances between the carrier and store. During the calculation, the elastic vibrations of the carrier are considered. According to the cause of formations of the interference aerodynamics, the interference aerodynamic forces of the store are divided into several components. The relative magnitude, change rule, sphere of influence and mechanism of interference aerodynamic forces components of the store are analyzed quantitatively. When the relative distance between the carrier and store is small, the interference aerodynamic forces caused by the elastic vibration of the carrier is about half of the total aerodynamic forces of the store. And as the relative distance increases, the value of interference aerodynamic forces decrease. When the relative distance is larger than twice the mean aerodynamic chord of the carrier, the values of interference aerodynamic forces of the store can be ignored. Besides, under the influence of the steady interference aerodynamic forces, the lift characteristics of the store are worse and the static stability margin is poorer.

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Accumulation of errors in numerical simulations of chemically reacting gas dynamics

Cited by 484 publications

References 21 publications

The Effect of Chemical Reactivity on the Formation of Gaseous Oblique Detonation Waves

The Effect of Chemical Reactivity on the Formation of Gaseous Oblique Detonation Waves

Adaptive simulations of cavity-based detonation in supersonic hydrogen–oxygen mixture

The influence of the elastic vibration of the carrier to the aerodynamics of the external store in air-launch-to-orbit process

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