Search

At critical conditions, the effect of instability plays a prominent role in the gaseous detonation transmission from a tube into an unconfined space. This study aims to clarify such an effect by investigating the critical tube diameter of quasi-detonations, i.e., detonations under the influence of minor perturbations along the tube walls. The strategy is to conduct two-dimensional numerical simulations using the reactive Euler equations with a two-step induction-reaction kinetic model. The chemical kinetic parameters were adapted to model the detonation wave in the stoichiometric hydrogen-oxygen mixture at 20 kPa and 300 K. The quasi-detonations are obtained in channels with obstacles (attached to the boundaries) of different sizes to mimic wall roughness, σ , which is defined as the ratio between the obstacle size δ and half of the channel width D 1 / 2. Below a critical value of σ , the rough wall creates only minor perturbations to the intrinsic cellular detonation. Apart from the velocity deficit, the degree of instability and cellular irregularity increases with roughness, resulting in a broader spectrum in the probability density function of the pressure and induction rate. For σ ≳ 0.24, the intrinsic propagation dynamics are more significantly altered—the cellular structure vanishes locally or small cells re-appear from new re-initiation points. Detonations in these more significantly obstructed channels are not considered quasi-detonations subjected to minor boundary perturbations. The influence of small values of roughness on the critical tube diameter phenomenon is then examined. A shot-to-shot variation in cellular dynamics of quasi-detonations is considered by performing multiple simulations for each value of roughness to assess the probability of successful transmission into an unconfined space. For quasi-detonation diffraction at the sub-critical condition, despite a velocity deficit, increasingly higher instabilities resulting from a rough-walled geometry promote the re-initiation of a detonation in the open area. However, if the roughness increases beyond 0.24, both the velocity deficit and different propagation modes in a significantly obstructed channel lead to a lower probability of successful transmission. [ABSTRACT FROM AUTHOR]

The characteristics of the propagation of a detonation from a cylindrical tube of constant cross section into a diverging cone were experimentally investigated using the smoked-foil technique for three explosive gas mixtures: C2H2+2.5O2, 2H2+O2+4.5Ar, and C2H4+3O2+0.44N2. The initial pressure and the cone enlargement angle were varied as governing parameters. The results were summarized in terms of the ratio between the inner diameter of the cylindrical tube through which a detonation initially propagated and the detonation cell width d/λ and of the cone enlargement half angle θ. Four patterns of detonation propagation were observed in the diverging cone: continuous propagation, re-initiation on the cone wall, re-initiation apart from the cone wall, and failure. The obtained results were qualitatively consistent with past experimental results reported by other researchers. However, quantitatively, the obtained results were dependent on the explosive gas mixtures, particularly on the so-called critical tube diameter. Actually, when the critical values of d/λ against detonation failure were normalized by that corresponding to θ = 90°, a single curve unifying all data to some degree was obtained. In addition, some characteristics of the detonation behavior in the diverging cone were explained by simple models.

For stoichiometric C2H4–O2 and C2H2–O2 mixtures with or without argon dilution, the processes of detonation diffraction have been investigated in a two-dimensional setup through high-speed schlieren imaging, with the characteristic length and the stability of detonation varied by regulating the initial pressure and argon mole fraction of the mixture. In particular, a length relevant to the process of supercritical diffraction (i.e., distance from the channel end corner to reflection point of the transverse detonation on the channel end face, reflection point distance in short) was deduced from obtained sequential schlieren images and analyzed. The reflection point distance can be idealized for the infinitely wide donor channel, and thus, it can be a parameter in which properties intrinsic to each detonable mixture are manifested. Experimental results showed that the reflection point distance was roughly inversely proportional to the initial pressure for identical mixtures and independent of the width of the donor channel at high initial pressures. For a certain combination of the fuel and oxidizer, correlations between the reflection point distance and the initial partial pressure of fuel were very similar regardless of the argon mole fraction. Critical conditions of the diffraction problem could be given for the ratio of the reflection point distance to the channel width, and it was suggested that the critical value lies in a range of 3–5 and does not significantly depend on the stability of the mixture. [ABSTRACT FROM AUTHOR]

Abstract The transmission of detonation waves, propagating in a homogeneous, gaseous, reactive medium, from a tube into an unconfined space is well known to succeed or fail based on the tube diameter. Below a certain diameter, the detonation fails to transition into the unconfined space, while for a large enough geometry, the transition succeeds. This critical diameter is well correlated to the incoming detonation cell size. For common undiluted hydrocarbon mixtures with a strong degree of transverse instability, the ratio of critical tube diameter to cell size has been measured at D c = 13 λ. In this paper, stoichiometric acetylene-oxygen mixture at different initial pressures is detonated in a circular tube that transitions into an effectively unconfined space. The transition is observed with simultaneous schlieren photography and soot foil records to look at the role of transverse cellular instability. Three regimes of transition are observed: supercritical, where the cellular pattern is continuously connected from the donor tube to the larger space; subcritical, where the wave fails and the cellular pattern disappears; and a critical regime, where the wave initially fails, asymptoting to a weakly decoupled shock-reaction front regime, and exhibits a subsequent re-initiation in a critical zone of pre-shocked gas through the onset of an explosion bubble. A substantial amount of transverse instability remains even after the expansion wave reaches the central axis, sustaining the diffracted wave at a critical thermodynamic state for the re-initiation. The location of this critical zone is identified at about 22 λ and a small obstacle is used to promote the generation of transverse waves and a re-initiation kernel. The re-initiation is effected by placing an obstacle in the critical region. The role of the resulting instability is also illustrated through a simple numerical simulation using an obstacle in the sub-critical regime to perturb the flow and promote the re-initiation. [ABSTRACT FROM AUTHOR]

A new algorithm for obtaining the critical tube diameter and intercept factor of parabolic trough solar collectors (PTCs) under the condition of tube alignment error has been developed theoretically, which, compared with the Monte Carlo Ray Tracing (MCRT) method, reduces the computing time remarkably. The results produced by the proposed method comply very well with the results obtained by MCRT. The critical tube diameters for different alignment errors can be precisely calculated using the algorithm, which can also be used to explain well the variation of optical efficiency. Effects of structural parameters on the optical performance are also discussed comprehensively. It is revealed that the offset direction that is perpendicular to the focus-edge connection line is most likely to cause rays-escaping. There exists an aperture width range (and also focal length range) in which the optical efficiency decreases with increasing offset angle, which is contrary to the conclusion presented in previous literature that the effects of X-direction offset ( a  = 0°) is greater than that in Y-direction ( a  = 90°). The proposed algorithm establishes the foundation for further geometric study on the coupling effects of multi-errors on PTCs’ performance, and can also be used for quick calculation and analysis in practice. [ABSTRACT FROM AUTHOR]

Abstract: In this investigation, the dynamic detonation parameters for stoichiometric acetylene–oxygen mixtures diluted with varying amount of argon are measured and analyzed. The experimental results show that the critical tube diameter and the critical energy for direct initiation of spherical detonations increase with the increase of argon dilution. The scaling behavior between the critical tube diameter d c and the detonation cell size λ as well as the critical direct initiation energy E c is systematically studied with the effect of argon dilution. The present results again validate that the relation d c =13λ holds for 0–30% argon diluted mixtures and breaks down when argon dilution increases up to 40%. It is found that the explosion length scaling of R o ∼26λ becomes also invalid when the mixture contains approximately this same amount of argon dilution or more. This critical argon dilution is indeed close to that found from experiments in porous-walled tubes by Radulescu and Lee (2002) which exhibit a distinct transition in the failure mechanism. Cell size analysis in literature also indicates that the cellular detonation front starts to become more regular (or stable) when the argon dilution reaches more than 40–50%. Regardless of the degree of argon dilution or mixture sensitivity, the phenomenological model developed from the surface energy concept by Lee, which provides a relation that links the critical tube diameter and the critical energy remains valid. The present experimental results also follow qualitatively the observation from chemical kinetic and detonation instability analyses. [Copyright &y& Elsevier]

In this experimental study, the critical tube diameter phenomenon of gaseous detonations is investigated in both stable and unstable mixtures with focus on the failure mechanism. It was previously postulated that in unstable mixtures, where the cellular detonation front is highly irregular, the failure is caused by the suppression of local re-initiation centers linked to the dynamics of instabilities. In stable mixtures, typically with high argon dilution, the detonation structure is very regular and the failure mode is attributed to the excessive curvature of the global front. In order to differentiate between these two failure mechanisms, flow perturbations are introduced by placing an obstacle resulting in a minimal blockage ratio of approximately 8 %. The obstacle is placed at the tube exit, before the detonation diffraction. Results show that the perturbations caused by the obstacle only have an effect on undiluted (i.e., unstable) mixtures, causing a decrease in the minimum initial pressure required for successful detonation transmission. This thus demonstrates that local hydrodynamic instabilities play an important role for the critical tube diameter phenomenon in undiluted, unstable mixtures. In contrast, the results for the stable, argon-diluted mixture exhibit little variation in critical initial pressure between the perturbed and unperturbed cases. This can be attributed to the minimal effect of the perturbations on global curvature for the emergent detonation wave. The geometry of the perturbation is also tested, while holding the blockage area constant, by varying the number and position of the obstacle(s). The results demonstrate that the transmission of a detonation is independent of the blockage geometry and is only a function of its imposed blockage area. Consequently, the change in required minimum pressure for transmission shows an identical behavior in unstable mixtures for different perturbation geometries while the transmission characteristics of the stable mixture remain unaffected. [ABSTRACT FROM AUTHOR]

Abstract: In this study, the dynamic detonation parameters, namely, the critical tube diameter and critical energy for direct initiation, of C2H2/N2O/Ar mixtures were measured at various initial conditions. Using chemical kinetics with the Konnov mechanism and experimental measured data, a simple correlation to evaluate the critical tube diameter of C2H2/N2O/Ar detonation is developed, given by which is applicable for stoichiometric mixtures with initial pressures ranging from 50 to 130kPa, equivalence ratios from 0.625 to 2.5 and stoichiometric mixtures with maximum percentage of argon dilution up to 50% at the atmospheric pressure. By combining this correlation function with a theoretical model based on a simple work done concept, the critical energy for direct blast initiation can be predicted; and the theoretical predictions are found to be in good agreement with the critical energy measured experimentally. To assess the detonation sensitivity, the critical energy results for direct initiation of detonation in C2H2/N2O/Ar mixtures are compared with those in H2/N2O/Ar mixtures [Zhang et al., Int. J. Hydrogen Energy 39 (2011) 5707–5716]. The results indicate that C2H2/N2O/Ar is more sensitive than H2/N2O/Ar at the same initial conditions. This is also supported qualitatively by the chemical kinetic calculation which shows that the ZND induction length scale for C2H2/N2O/Ar is relatively smaller than that of H2/N2O/Ar mixture. Lastly, the effect of the oxidizer on the detonation sensitivity is studied by comparing the critical energy between C2H2/N2O/Ar and C2H2/O2/Ar mixture. It is found that a higher energy is required to successfully initiate a spherical detonation in C2H2/N2O/Ar than in C2H2/O2/Ar mixtures and equivalently, the results agree qualitatively with the ZND induction length analysis. [Copyright &y& Elsevier]

A critical tube diameter measurement system was established for C2H2-2.502-Ar mixtures detonation. Initiation of detonation was accomplished via a high voltage spark energy source. The critical tube diameters under different initial pressures of C2H2-2.502, C2H2-2.502- 50%Ar, C2H2-2.502-70%Ar mixtures were measured in experiments. The results show that, with the increasing of argon dilution for the same tube diameter, the critical pressure, at which the planar detonation can emerge from a tube into unconfined space to form a spherical detonation, increases as well, that indicates the sensitivity of the mixtures detonation decreases. In addition, the relationship between critical tube diameter and cell size for those mixtures were investigated. Finally, the correlation between critical tube diameter and critical energy of direct initiation was analyzed. Good agreement was found by comparing the experiment data with Lee's surface energy model. Therefore, the parametric function between critical tube diameter and the critical energy would be Due to image rights restrictions, multiple line equation(s) cannot be graphically displayed. [ABSTRACT FROM AUTHOR]