Homogeneous explosion and shock initiation for a three-step chain-branching reaction model

The role of chain-branching cross-over temperatures in shock-induced ignition of reactive materials is studied by numerical simulation, using a three-step chainbranching reaction model. In order to provide insight into shock initiation, the simpler problem of a spatially homogeneous explosion is first considered. It is shown that for ratios of the cross-over temperature to the initial temperature, T-B, sufficiently less than unity, the homogeneous explosion can be quantitatively described by a widely used two-step model, while for T-B sufficiently above unity the homogeneous explosion can be effectively described by the standard one-step model. From the matchings between these homogeneous-explosion solutions, the parameters of the reduced models are identified in terms of those of the three-step model. When T-B is close to unity, all the reactions of the three-step model have a leading role, and hence in this case the model cannot be reduced further. In the case of shock initiation, for T-B (which is now the ratio of the cross-over temperature to the initial shock temperature) sufficiently below unity, the three-step solutions are qualitatively described by those of the matched two-step model, but there are quantitative differences due to the assumption in the reduced model that a purely chain-branching explosion occurs instantaneously. For T-B sufficiently above unity, the matched one-step model is found to effectively describe the way in which the heat release and fluid dynamics couple. For T-B close to unity, the competition between chain branching and chain termination is important from the outset. In these cases the speed at which the forward moving explosion wave that emerges from the piston is sensitive to T-B, and changes from supersonic to subsonic for a value of T-B just below unity

Linear and nonlinear dynamics of cylindrically and spherically expanding detonation waves

The nonlinear stability of cylindrically and spherically expanding detonation waves is investigated using numerical simulations for both directly (blast) initiated detonations and cases where the simulations are initialized by placing quasi-steady solutions corresponding to different initial shock radii onto the grid. First, high-resolution one-dimensional (axially or radially symmetric) simulations of pulsating detonations are performed. Emphasis is on comparing with the predictions of a recent one-dimensional linear stability analysis of weakly curved detonation waves. The simulations show that, in agreement with the linear analysis, increasing curvature has a rapid destabilizing effect on detonation waves. The initial size and growth rate of the pulsation amplitude decreases as the radius where the detonation first forms increases. The pulsations may reach a saturated nonlinear behaviour as the amplitude grows, such that the subsequent evolution is independent of the initial conditions. As the wave expands outwards towards higher (and hence more stable) radii, the nature of the saturated nonlinear dynamics evolves to that of more stable behaviour (e.g. the amplitude of the saturated nonlinear oscillation decreases, or for sufficiently unstable cases, the oscillations evolve from multi-mode to period-doubled to limit-cycle-type behaviour). For parameter regimes where the planar detonation is stable, the linear stability prediction of the neutrally stable curvature gives a good prediction of the location of the maximum amplitude (provided the stability boundary is reached before the oscillations saturate) and of the critical radius of formation above which no oscillations are seen. The linear analysis also predicts very well the dependence of the period on the radius, even in the saturated nonlinear regimes. Secondly, preliminary two-dimensional numerical simulations of expanding cellular detonations are performed, but it is shown that resolved and accurate calculations of the cellular dynamics are currently computationally prohibitive, even with a dynamically adaptive numerical scheme

Nonlinear cellular dynamics of the idealized detonation model: Regular cells

High-resolution numerical simulations of cellular detonations are performed using a parallelized adaptive grid solver, in the case where the channel width is very wide. In particular, the nonlinear response of a weakly unstable ZND detonation to two-dimensional perturbations is studied in the context of the idealized one-step chemistry model. For random perturbations, cells appear with a characteristic size in good agreement with that corresponding to the maximum growth rate from a linear stability analysis. However, the cells then grow and equilibrate at a larger size. It is also shown that the linear analysis predicts well the ratio of cell lengths to cell widths of the fully developed cells. The evolutionary dynamics of the growth are nonetheless quite slow, in that the detonation needs to run of the order of 1000 reaction lengths before the final size and equilibrium state is reached. For sinusoidal perturbations, it is found that there is a large band of wavelengths/cell sizes which can propagate over very long distances (~1000 reaction lengths). By perturbing the fully developed cells of each wavelength, it is found that smaller cells in this range are unstable to symmetry breaking, which again results in cellular growth to a larger final size. However, a range of larger cell sizes appear to be nonlinearly stable. As a result it is found that the final cell size of the model is non-unique, even for such a weakly unstable, regular cell case. Indeed, in the case studied, the equilibrium cell size varies by 100% with different initial conditions. Numerical dependencies of the cellular dynamics are also examined

One-dimensional nonlinear stability of pathological detonations

In this paper we perform high-resolution one-dimensional time-dependent numerical simulations of detonations for which the underlying steady planar waves are of the pathological type. Pathological detonations are possible when there are endothermic or dissipative effects in the system. We consider a system with two consecutive irreversible reactions A[rightward arrow]B[rightward arrow]C, with an Arrhenius form of the reaction rates and the second reaction endothermic. The self-sustaining steady planar detonation then travels at the minimum speed, which is faster than the Chapman–Jouguet speed, and has an internal frozen sonic point at which the thermicity vanishes. The flow downstream of this sonic point is supersonic if the detonation is unsupported or subsonic if the detonation is supported, the two cases having very different detonation wave structures. We compare and contrast the long-time nonlinear behaviour of the unsupported and supported pathological detonations. We show that the stability of the supported and unsupported steady waves can be quite different, even near the stability boundary. Indeed, the unsupported detonation can easily fail while the supported wave propagates as a pulsating detonation. We also consider overdriven detonations for the system. We show that, in agreement with a linear stability analysis, the stability of the steady wave is very sensitive to the degree of overdrive near the pathological detonation speed, and that increasing the overdrive can destabilize the wave, in contrast to systems where the self-sustaining wave is the Chapman–Jouguet detonation

Steady non-ideal detonations in cylindrical sticks of expolsives

Numerical simulations of detonations in cylindrical rate-sticks of highly non-ideal explosives are performed, using a simple model with a weakly pressure dependent rate law and a pseudo-polytropic equation of state. Some numerical issues with such simulations are investigated, and it is shown that very high resolution (hundreds of points in the reaction zone) are required for highly accurate (converged) solutions. High resolution simulations are then used to investigate the qualitative dependences of the detonation driving zone structure on the diameter and degree of confinement of the explosive charge. The simulation results are used to show that, given the radius of curvature of the shock at the charge axis, the steady detonation speed and the axial solution are accurately predicted by a quasi-one-dimensional theory, even for cases where the detonation propagates at speeds significantly below the Chapman-Jouguet speed. Given reaction rate and equation of state models, this quasi-one-dimensional theory offers a significant improvement to Wood-Kirkwood theories currently used in industry

Influence of spark ignition in the determination of Markstein lengths using spherically expanding flames

Constant pressure outwardly propagating flame experiments in a spherical bomb are performed to examine the duration and radius over which spark ignition effects persist. This is motivated by the need to properly account for such effects in the measurement of laminar burning velocity and Markstein length using the spark ignited expanding flame technique. Ignition energy was varied and its effects on flame propagation in methane-air and isooctane-air mixtures were studied. The Markstein length of the mixture proved critical in the ignition energy dependency of flame propagation. For relatively high values, an underlying common variation of self-sustaining flame speed with radius can be identified by the rapid convergence of curves for different ignition energies. As the Markstein length decreases, low energy spark ignition is found to give rise to a distorted and wrinkled flame kernel. For such mixtures, due to the weak effect of stretch, the kernel subsequently develops into a non-spherically propagating flame. In these cases the spark ignition effect persists up to large radius. It is shown that using low ignition energy leads to a flame speed, during the development phase, which is higher than that of a self-sustaining spherical flame. It is further shown that if this effect is not accounted for, measurements of Markstein length using standard fitting techniques results in a large error. This problem is found to worsen as the Markstein length decreases, such that its apparent measured value becomes increasingly influenced by any distortions of the flame kernel produced by the spark

PROTOCOL: What is the effect of intergenerational activities on the wellbeing and mental health of older people?

This is the protocol for a Campbell systematic review. The objectives are as follows: This systematic review will examine the impact of intergenerational interventions on the mental health and wellbeing of older people and will identify areas for future research as well as key messages for service commissioners

What is the effect of intergenerational activities on the wellbeing and mental health of older people?: A systematic review

Background Opportunities for social connection between generations have diminished over the last few decades around the world as a result of changes in the way that we live and work. The COVID-19 pandemic has exacerbated loneliness for many with young and old being kept apart for safety. The Public Health England prevention concordat for better mental health (Office for Health Improvement and Disparities) aims to bring a prevention-focused approach to improving public mental health. The concordat promotes evidence-based planning and commissioning to increase the impact on reducing health inequalities using sustainable and cost-effective interventions that impact on the wider determinants of mental health and wellbeing for children and young people and older people. Intergenerational activities could provide an opportunity to support both populations. In 2023, we produced an evidence and gap map to illustrate the amount and variety of research on intergenerational interventions and the gaps in research that still exist in this area. The review conducted here is based on the evidence in that map. Objectives This systematic review examines the impact of intergenerational interventions on the wellbeing and mental health of older people and identifies areas for future research as well as key messages for service commissioners. Search Methods We searched an evidence and gap map published in 2022 (comprehensive searches conducted July 2021 and updated June 2023) to identify randomised controlled trials of intergenerational interventions that report mental health and wellbeing outcomes for older people. Selection Criteria Randomised controlled trials of intergenerational interventions that involved unrelated younger and older people with at least one skipped generation between them and reported mental health or wellbeing outcomes for older people were included in this review. Data Collection and Analysis We used standard methodological procedures expected by The Campbell Collaboration. We conducted data extraction and Cochrane risk of bias assessments in EPPI reviewer. Where data allowed meta-analyses were conducted in STATA. Main Results This review includes 14 trials from six different countries. The trials had some important methodological weaknesses. Interventions were mainly delivered in-person and often in groups. They included visiting programmes, school volunteering programmes, music-based interventions and task-oriented interventions such as activities set in a multigenerational park, reminiscing activities, aggression management programmes, learning a language, making local environmental changes and in-school project work. Intergenerational interventions showed a small positive trend towards improving self-esteem (effect size [ES]: 0.33, 95% confidence interval [CI]: −0.35, 1.01) and depression (ES: 0.19, 95% CI: −0.23, 0.60) for older people participating. However, due to the small study sizes and low number of studies available, we cannot be confident about any effects. The results for other mental health and wellbeing outcomes are reported but due to little overlap in similar assessments across the studies, we could not combine them to assess the strength of evidence. There were no data about social isolation, spiritual health or sense of community. There are no long-term studies and no data on equity. We still know very little about what works and how or why. Whilst some interventions do use theories and logic to inform their development others do not. More exploration of this is needed. Authors’ Conclusions Commissioners and intervention developers should ensure interventions provide sufficient theoretical evidence for the logic behind the proposed intervention and should improve their consideration of equity within the interventions Research on intergenerational interventions need more consistent and agreed measures for reporting outcomes including community outcomes (core outcome sets). More understanding is needed on how best to measure ‘community’ outcomes. Research on intergenerational interventions should measure outcomes for BOTH the older and younger population engaged in the intervention—these may or may not be the same outcomes reflected in both populations. Further research is needed on the long-term impact of interventions on outcomes (whether participants need to keep being involved in an ‘intervention’ to continue to benefit) and sustainability of interventions beyond the initial funding of the research project. Supporting this our stakeholders highlighted that interventions that are initiated for research and then end (usually within a year) are not helpful

Effect of Initial Disturbance on The Detonation Front Structure of a Narrow Duct

The effect of an initial disturbance on the detonation front structure in a narrow duct is studied by three-dimensional numerical simulation. The numerical method used includes a high resolution fifth-order weighted essentially non-oscillatory scheme for spatial discretization, coupled with a third order total variation diminishing Runge-Kutta time stepping method. Two types of disturbances are used for the initial perturbation. One is a random disturbance which is imposed on the whole area of the detonation front, and the other is a symmetrical disturbance imposed within a band along the diagonal direction on the front. The results show that the two types of disturbances lead to different processes. For the random disturbance, the detonation front evolves into a stable spinning detonation. For the symmetrical diagonal disturbance, the detonation front displays a diagonal pattern at an early stage, but this pattern is unstable. It breaks down after a short while and it finally evolves into a spinning detonation. The spinning detonation structure ultimately formed due to the two types of disturbances is the same. This means that spinning detonation is the most stable mode for the simulated narrow duct. Therefore, in a narrow duct, triggering a spinning detonation can be an effective way to produce a stable detonation as well as to speed up the deflagration to detonation transition process.Comment: 30 pages and 11 figure

Models for Type Ia supernovae and related astrophysical transients

We give an overview of recent efforts to model Type Ia supernovae and related astrophysical transients resulting from thermonuclear explosions in white dwarfs. In particular we point out the challenges resulting from the multi-physics multi-scale nature of the problem and discuss possible numerical approaches to meet them in hydrodynamical explosion simulations and radiative transfer modeling. We give examples of how these methods are applied to several explosion scenarios that have been proposed to explain distinct subsets or, in some cases, the majority of the observed events. In case we comment on some of the successes and shortcoming of these scenarios and highlight important outstanding issues.Comment: 20 pages, 2 figures, review published in Space Science Reviews as part of the topical collection on supernovae, replacement corrects typos in the conclusions sectio