The deflagration-to-detonation transition (DDT) downstream of a 76 C_3H_8+5O_2 mixture, there was little difference in the DDT limit for the round and square channels, indicating that detonation initiation driven by hot-spot formation following transverse wave collisions is dominant, i.e., as effective as shock focusing in the corner.
In this work, we extended a global four-step combustion modelling approach to include the combustion of fuel blends involving hydrogen and methane. We were able to address key difficulties in the calibration process as the fuel blend ratio approached that of pure hydrogen–oxygen combustion. The first challenge involved solving the system of equations that determines the equilibrium state of the global species, while enforcing appropriate physical bounds on the solution. The second challenge was to develop a strategy to prevent endothermic reactions from occurring during the production of one of the product groups. Upon addressing these challenges, a model was developed that matched the ignition delay times and induction to reaction time ratios when compared to detailed chemistry. Moreover, the detonation velocities were recovered across the entire range of fuel blend ratios. Finally, two-dimensional simulations were carried out for stoichiometric hydrogen–oxygen, diluted with argon, and undiluted blended hydrogen–methane–oxygen. For the hydrogen–oxygen mixture, we found that the four-step combustion modelling approach was more than six times as fast to compute and captured the same cellular structure as its detailed chemistry counterpart. However, the real savings were achieved for the blended mixture, where the four-step combustion modelling approach was found to be more than forty times faster compared to using a detailed chemical mechanism that included hydrocarbon combustion. The proposed strategy thus presents a novel approach to simulate the combustion of blended fuels, where the application of detailed chemistry models may be too prohibitive.
In this work, the attenuation behaviour of naturally available river sand subjected to blast waves created using a vertical shock tube in a laboratory setting using compressed helium gas is studied. Among the number of granular media, river sand is commonly used to protect critical installations against devastating ground vibrations caused due to blast waves. It is crucial to note that the attenuation behaviour of soil in general is site specific and that full-scale field experiments are conventionally carried out to obtain the ground shock parameters like peak pressure and their attenuation along propagation distance, which are time-consuming, are expensive, and have significant environmental impact. In comparison, the vertical shock tube used here not only reduces the experimental time, costs, and risks involved but also ensures the repeatability of tests and reduction in sensor damage. The attenuation behaviour of the peak pressure in a sand column in a test chamber, at low, medium, and high relative density values, subjected to blast waves of varying intensities and decay times is studied presently. It is observed that the peak pressures measured at various locations in the sand column and peak overpressure in the air just above the free surface of the sand sample attenuate exponentially. It is also observed that the attenuation of blast wave is more pronounced for sand samples with medium relative density (43
Energetic materials (EMs) are multi-phase, multi-material mixtures in which reactive breakdown can occur with large heat release over short time scales. Eulerian frameworks for the simulation of compressible flow in heterogeneous EM must handle fast transients, and severe interfacial deformations that can occur as a shock wave traverse the material. The shock may also transition to a detonation wave, further exacerbating the complexity and challenges for simulation techniques. Previous simulation approaches have employed low-order numerical methods or diffuse interfaces to handle the high gradients and large material deformations. In this work, high-order numerical discretization and sharp interface treatments are combined to produce a high-fidelity modeling and simulation capability to accurately capture the reactive flow physics of EM at micro-, meso-, and macro-scales. Issues of stability and computational cost of the high-order scheme when implemented in concert with sharp interface treatments are addressed. The methodology is then applied to demonstrate the impact of high-accuracy simulations at the micro-scale: to calculate the hotspot ignition and growth due to the collapse of a micron-sized pore. Meso-scale simulations of shock-induced hotspot evolution in microstructures of neat-pressed (two-phase) EM show that the accuracy of the techniques significantly impacts the calculation of energy localization rates, which are used as closure models at the macro-scale. Finally, we show the ability of the methods to produce accurate simulations of macro-scale systems where shock-to-detonation transition occurs, requiring high accuracy in capturing the dynamics of curved detonation fronts interacting with embedded boundaries. This work establishes approaches toward solving a wide range of thermophysics problems that will be needed for the accurate design of systems operating on EM.
Shock tubes are highly valuable for elucidating chemical kinetic phenomena in combustion and hypersonic events because they can generate quasi-stagnant, high-enthalpy flow conditions. However, facility-dependent effects, such as shock wave bifurcation, can hamper their usability by perturbing the flow, leaving hot zones, or creating density gradients that disrupt optical diagnostics. Previous literature has investigated shock wave bifurcation as a function of many parameters, excluding the location at which the diagnostics were taken. To that end, shock tube experiments were performed to take reflected-shock bifurcation measurements at varying axial locations (2 cm and 6 cm) from the endwall using a laser schlieren technique and a pressure transducer. Mixture compositions with a wide range of molecular weights ( 10.0
Experiments were conducted to improve the thermal performance of a tapered Hartmann–Sprenger tube of length-to-diameter ratio 11 by replacing its tapered end section with a cylindrical section. Three modified tapered cavities with cylindrical end sections, having length-to-diameter ratios of 4.1, 6, and 6.85, are studied along with the reference cavity for jet–cavity spacings of 2.19 and 2.58, and nozzle pressure ratios ranging from 8 to 20. Cavities are made of zirconium dioxide ( ZrO_2 ), which allows the local heat release location to be observed distinctly as a glowing spot. Results indicate that varying the end configuration of the tapered cavity primarily increases the amplitude of pressure pulsations, which helps to enhance their thermal performance. The best configuration is the one in which a cylindrical section is added immediately downstream of the heat release location of the original reference tapered cavity. A threefold increase in (i) the maximum end wall temperature and (ii) the rate of heat generation is achieved relative to the reference cavity. The latter is critical in designing a resonator ignitor with the enhanced response time. The jet–cavity resonance phenomenon is studied using a K-type thermocouple and a 1/4" (6.35-mm) microphone placed at 50 diameters from the jet nozzle exit plane.
A simple formulation to model deflagrative burning behind a detonation front was proposed to determine the dynamics near criticality for stoichiometric hydrogen–oxygen mixture. Two different combustion mechanisms, auto-ignition and deflagrative burning, were separately activated based on local temperature. When the temperature was below the crossover temperature of the chain-branching reaction T_ B , deflagration was selected. Conversely, an auto-ignition source term was utilized when the local temperature was above T_ B . This study examined the significance of deflagrative burning on the quenching limit for gaseous detonation in a layer of stoichiometric hydrogen–oxygen semi-confined by nitrogen. With the inclusion of the deflagrative burning model, the propagation limit was significantly extended and the dynamics of a marginal detonation, i.e., higher velocity deficit compared to that given by Zel’dovich, von Neumann, and Döring model with curvature, was reproduced. The proper mass flux for deflagrative burning to reproduce the quenching limit ranged from one to two times the laminar value at post-shock state relevant to the lowest velocity at the near-limit condition, i.e., near the end of the cell. The contribution of deflagrative burning became more important near the limit (peaks of 30
This paper presents the application of background-oriented schlieren (BOS) to obtain a quantitative characterization of shock waves from a free-field outdoor pressure relief system. A BOS setup was constructed, and an investigation was carried out to examine the influence of the background. Although critical locations in the natural background were identified, they could not be eliminated due to their large number, so an optimized random dot pattern was used instead. The evaluation method also took into account the intense radiation from the high-enthalpy gas flow. The aim was to visualize the shock wave front and reconstruct the shock wave front overpressure field. To this end, a linear calibration was performed between the optical results and those of the subsidiary pressure sensors. The estimated peak overpressures showed a good agreement with the measured values, with the BOS-based estimates slightly underpredicting the measurements. The maximum observed deviation was 8
Gas explosions are a major hazard in coal mines, resulting in casualties and economic losses. To investigate the coupled effects of suppressor concentration and particle size on methane explosions, medium-scale explosion tube experiments were conducted using calcium carbonate powders with different particle sizes and concentrations. The effects on flame propagation velocity, explosion pressure, and pressure rise rate were systematically examined. Particle size analysis, scanning electron microscopy, and thermogravimetric analysis were employed to characterize the particle size distribution, microstructure, and thermochemical behavior of the powders. The results demonstrate that calcium carbonate powder exhibits a pronounced suppression effect on methane explosions. The suppression performance does not increase monotonically with decreasing particle size or increasing concentration, but instead shows a clear particle size–concentration coupling effect. Optimal suppression was achieved at a particle size of 23 m and a concentration of 125 g/m^3 , with a maximum suppression efficiency of 60.7 CO_2 -induced inerting, and physical interference with flame propagation. This study provides experimental evidence and theoretical guidance for the optimized design of calcium carbonate-based explosion suppressants and enhanced mine safety protection.
An asymptotic analysis was performed for direct detonation initiation in unsteady flow at elevated pressure, which extends our previous work for planar wave front. The reaction zone temperature-gradient equation was established and then solved asymptotically by assuming large activation energy and a one-step irreversible reaction model. The Noble-Abel and van der Waals gas models were adopted to study the impact of real-gas (RG) behavior. While the attractive intermolecular force makes initiation more difficult by increasing the critical shock decay time, the repulsive force promotes initiation. The effective range of divergence time is extended/limited by the attraction/repulsion force. Except for mixtures with large heat capacity ratio of the perfect gas ( γ ^∘ ) and small reduced activation energy with respect to the initial state ( ε ) and satisfying the blast wave model of Korobeinikov, the impact of the divergence time on the critical decay time is insignificant because the critical state is reached at large blast wave radius, indicating that the curvature effect is limited. The RG effects are enhanced when increasing the reduced activation energy or/and decreasing the perfect gas heat capacity ratio. For the ease of applying the present findings, the asymptotic solutions were firstly validated with quasi-unsteady simulation using detailed reaction models. It was then further simplified to obtain fully analytical solutions based on the strong-shock assumption. Qualitative or quantitative agreements were obtained for all these cases.
Boron (B) is considered as a high-energy additive for solid propellants owing to its high mass and volumetric calorific values. DAP-4, a novel solid energetic material, exhibits excellent detonation performance and strong oxidizing properties, making it a promising high-energy oxidizer for solid propellants. To explore the ignition and combustion characteristics of DAP-4-based boron-containing high-energy materials, mixed powders of DAP-4 and nanometric boron (nano-B) materials with varying mass ratios were prepared through mechanical blending. X-ray diffraction (XRD) analysis confirmed the crystalline structure of the DAP-4/nano-B mixed powder and the absence of additional compounds or phases. Scanning electron microscope (SEM) observations revealed that nano-B particles effectively adhered to the surface of the DAP-4 particles, with the density of attached nanometric boron increasing as its content in the samples increased. Elemental mapping and Energy Dispersive X-ray Spectroscopy (EDS) further validated this surface modification. TG-Differential Scanning Calorimetry (DSC) analysis indicated good compatibility between DAP-4 and nano-B, with minimal mutual influence during thermal decomposition under heating. The ignition and combustion characteristics of the DAP-4/nano-B mixed powders were investigated using a shock tube at temperatures of 2200–3100 K and pressures of 0.1 MPa and 0.5 MPa. Results showed that both ignition delay time and burn time decreased with increasing temperature, whereas pressure had a negligible effect. As the boron content increased from 0 to 30
Experimental measurement of explosive blast wave overpressures is demanding, requiring specialist instrumentation that can survive extreme pressures (> 1 MPa) over short durations (< 5 ms), yet sensitive enough to resolve spatial and temporal features that vary in the mm and s range, respectively. Distributed acoustic sensing (DAS) is an alternative approach that measures dynamic strain histories at multiple locations along a single optical fibre. This study investigates the capability of a high-resolution DAS (HR-DAS) system to capture strain responses induced by side-on (incident) blast overpressures, compared to a reference piezoelectric pressure sensor. While explosive events can produce overpressures exceeding 1 MPa, lower overpressure regimes (40–72 kPa) were adopted in this study for proof-of-concept demonstration of the HR-DAS methodology. Strain histories measured by the HR-DAS displayed reasonable qualitative agreement with overpressure histories measured using piezoelectric sensors, with the blast wave positive phase durations showing close quantitative agreement. Better correlation was observed between the measurements when HR-DAS sensors were mounted perpendicular to the blast wave propagation, validating the system’s efficacy under uniform loading conditions. However, discrepancies were observed for sensors aligned parallel to the wave direction, highlighting the limitations of the spatial resolution of the HR-DAS and fibre orientation when subjected to a dynamic, spatially varying loading scenario. Findings emphasise the importance of sensor placement and configuration for distributed pressure analysis. Proof of concept results and recommendations from this study highlight an interesting opportunity for developing a novel blast pressure metrology, enabling multiple measurement points from a single optical fibre, that is small, flexible, and relatively low cost, addressing several limitations with conventional pressure instrumentation methods.
Mesoscale simulations of energy localization at hotspots provide closure models for multiscale frameworks of shock-to-detonation transition (SDT). Validation of such mesoscale calculations is challenging as direct comparison with experiments is constrained both by limitations of data acquisition in the experiments (e.g., of temperature fields) and modeling over-simplifications in the simulations. To address the latter problem and bring modeling closer to experiments, we advance a high-fidelity mesoscale computational framework for interface-resolved reactive calculations of shock initiation in plastic-bonded explosives (PBXs). Accurate resolution of shock and interfacial dynamics is achieved through higher-order (fifth-order WENO) schemes, and sharp-interface treatments are implemented for physically accurate material–material interactions. Recently obtained atomistics-consistent material models are used for HMX, with the grid resolution taken down to atomistic scale (O(nm)). The crystal geometries are obtained directly from experiments via nano-CT imaging. The impacting flyer plate, energetic crystal, and binder are tracked as distinct phases, and flyer–binder impact and separation are simulated, capturing the flyer deformation and the effects of relief waves from the flyer surface. By integrating these high-fidelity modeling components, we evaluate how closely simulations can approach experimental data, identify the modeling aspects that most significantly influence mesoscale metrics of interest, and highlight areas for further improvement. We show that the treatment of boundary conditions for flyer impact plays an important role in producing physically correct shock wave and hotspot characteristics, which are not obtained by imposing phenomenological boundary conditions, which mimic impact conditions. Another key finding of this study is that the atomistics-consistent material model and temperature-dependent relation for specific heat together play a pivotal role in accurately capturing the elastoplastic response of HMX—demonstrating consistency with molecular dynamics by resolving shear dislocations under weak shock conditions and with experimental data through well-matched hotspot temperatures during strong shock initiation.
This paper introduces an innovative fifth-order monotonicity-preserving (MP) scheme that not only achieves remarkable resolution but also preserves monotonicity by skilfully integrating the strengths of the MP and weighted essentially non-oscillatory (WENO) schemes. A novel MP limiter that accommodates a broader range of numerical solutions is proposed, along with several innovative optimization and hybrid techniques designed to enhance the MP scheme’s resolution and robustness. In the context of efficient filtering, the hybrid limiter incorporates a flexible selection process. The proposed scheme switches between the MP5 and WENO5 methods depending on whether the interface values fall within the parameters of the MP limiter. Therefore, the final interface values are derived either from the MP5 scheme or through rigorous post-processing of the WENO5 method and further an optimization procedure by a convex combination technique. This approach maintains both consistency and accuracy in data processing, thereby ensuring more reliable and trustworthy outcomes. The results of one- and two-dimensional numerical experiments indicate that the new scheme outperforms WENO-JS/Z, TENO, MP-R, and MPWENO, delivering superior resolution and exceptional robustness.
The internal flow field of the rotating detonation engine is unique and complex due to the curvature of the annular combustion channel and pressure relief at the exit of the combustor. Despite this complexity, there are several prominent flow field features: the detonation wave front, the refill zone, the trailing oblique shock, and the shear layer. This paper studies the detonation wave structure, developing a model that can predict the wave structure and the wave mode based solely on the dimensions of the engine and the inlet flow conditions. The results from this model are compared to a combination of experimental and computational data in the literature. Further analysis is made with various propellants to extrapolate the effects of engine operation on the wave structure. Further work on the wave structure could lead to predicting engine performance.
Shock tubes have been widely used to obtain a uniform flow and/or a gas with high pressure and high temperature for aerodynamic, chemical, and combustion studies. Under the ideal condition, the flow properties, such as pressure and temperature, are kept constant during the test time, but in the real world, this may not happen due to the viscous effect, such as the boundary layer development, which depends on the unit Reynolds number. To investigate the effect of the unit Reynolds number on the pressure growth at the end-wall during the test time, experiments were conducted under a range of unit Reynolds numbers from 1.7× 10^6 to 8.1 × 10^6 1/m at the incident shock Mach numbers from 2.0 to 2.3. The schlieren visualization showed that the Shock-Wave/Boundary-Layer Interaction (SWBLI) occurred in the test section and that the structure under bifurcated shock waves varied with the unit Reynolds number. The pressure growth was observed for all the test conditions conducted, and the growth rate of pressure was also varied with both the unit Reynolds number and the incident shock Mach number. The growth rate of pressure at the end-wall decreased from 34 to 9.3
A novel combustion driver is designed and tested to replace conventional helium drivers for the hypersonic shock wind tunnels. Stoichiometric acetylene and oxygen were chosen to minimize the production of water to prevent major corrosion in facilities not made of stainless steel. A single-burst diaphragm mechanism was employed, which was found to generate a reproducible shock tube process even in the presence of small variations in diaphragm scribe depth. The driver gas mixture was proven to burn entirely deflagrative for a single spark plug configuration. This is a major advantage compared to other combustion-driven shock tube designs found in the literature using oxyhydrogen diluted with helium, which requires a carefully designed ignition system in order to avoid the formation of pressure oscillations induced by local autoignition or detonation in the driver. High levels of dilution using argon were shown to maximize the available test time to approximately 5.5 ms for low-enthalpy conditions (h0 = 1.12 MJ kg-1). Inhomogeneities in the driver temperature caused by the combustion in a closed vessel were correlated to the observed post-reflected-shock pressure traces in the experiments. However, the negative effects can be compensated for the given experimental setup by ignition at a single location near the diaphragm and conducting experiments at slightly undertailored interface conditions. The result of the present study is a novel, functioning combustion driver capable of replacing conventional helium drivers for low-enthalpy conditions with minimal modifications on the existing facility, which enables an experimentation at a fraction of the gas costs.
Blast wave mitigation is a critical issue whenever the protection of occupants and content within a structure is considered to avoid the destructive effects of explosive events at the structure exterior vicinity. This research focuses on louver systems mounted at the exterior window openings, aiming at evaluating their effectiveness in attenuating blast wave parameters, such as peak pressure and impulse, at the exterior building façade. A comprehensive numerical methodology was developed using an advanced CFD code to simulate blast propagation through louvers with specific geometric configurations under varying conditions of charge weight and scaled distance. The study focuses on the blast characteristics behind the louver and identifies significant spatial variability in attenuation effectiveness, emphasizing the importance of continuous spatial analysis rather than focusing on discrete point measurements. Symmetrical louver configurations demonstrated superior performance compared to asymmetrical designs, providing critical insights that may assist in optimizing mitigation solutions through further studies. Additionally, preliminary evaluations of the effect of the opening size within which the louver is installed revealed its impact on attenuation factors, warranting further dedicated research. A methodology for interpolation and extrapolation was proposed, enabling the estimation of attenuation factors for unexplored parameter combinations, significantly reducing computational effort. These findings contribute to significantly advancing the state of the art, enhancing the understanding of blast wave mitigation mechanisms, and illuminating the effectiveness of the examined louver-based protective solutions.
This study aims to contribute to the understanding of imploding detonations from a numerical perspective, focusing primarily on the detailed transient and wave structures during implosion that are challenging to capture experimentally. An inviscid perfect gas model with a single-step Arrhenius reaction is employed. Imploding detonations are initiated by collisions of multiple small hot spots, and both two-dimensional circular and polygonal implosions are examined, with attention to the effects of obstacles and varying ignition pressures. For circular implosions, a slight acceleration of detonation velocity is observed at ignition, with significant acceleration occurring only in the final stages. Near the implosion center, local wave velocities exceed twice the Chapman–Jouguet velocity, yet the wave front maintains cellular instabilities until the collapse is complete. Additionally, the merging of transverse waves is observed during the implosion. In polygonal cases, a small number of “ignition edges” allows regular reflection, preserving the initial wave front geometry, while increasing the number of ignition lines leads to Mach reflection and the formation of a circular wave front. When obstacles are introduced, the detonation reflects off the obstacle, causing localized delays in the wave front that cannot be fully compensated, as transverse waves are unable to propagate sufficiently in the circumferential direction to smooth out disturbances. Similar effects are noted for implosions with non-uniform ignition pressures. It should be noted that the findings are based on a simplified model and do not account for real gas effects or additional physical processes present in actual detonation implosions.
