Run-up Distance Research Articles

Effect of composition gradient on detonation initiation in fuel-rich hydrogen-air mixtures in an obstructed channel

Numerical simulations were performed to study the effect of composition gradient and obstacle arrangement on detonation initiation in fuel-rich hydrogen-air mixtures. A third-order WENO method with adaptive mesh refinement (AMR) was used to solve the unsteady, fully-compressible, reactive Navier-Stokes equations coupled to a calibrated chemical-diffusive model (CDM). An obstructed channel at a blockage ratio of 0.3 filled with non-uniform hydrogen-air mixtures of an average H2 concentration 50 vol% was considered. The results show that unilateral obstacle arrangement is more conducive to flame acceleration (FA) and DDT than bilateral obstacle arrangement for both homogeneous and inhomogeneous mixtures. For inhomogeneous mixtures, the flame accelerates faster, and the detonation onset time is shorter when obstacles are placed on the sidewall with a hydrogen concentration closer to the stoichiometric ratio than the those when obstacles are placed on the other sidewall. However, the placement of unilateral obstacles on either the upper or lower sidewall does not significantly affect the DDT run-up distance. Besides, for fuel-rich inhomogeneous hydrogen-air mixtures, detonation tends to be initiated in the regions of high H2 concentration. Idealized models were introduced to simplify the intricate interactions of the reaction waves and flow fields to better understand the connection between H2 concentration distribution and detonation initiation. The analysis suggests that the minimum shock strength required for detonation initiation decreases with increasing equivalence ratio. This is supported by a kinetics analysis with detailed reaction model, which shows that ignition delay increases with decreasing equivalence ratio when detonation is about to be initiated.

Study on inhomogeneous hydrogen–air mixture flame acceleration and deflagration-to-detonation transition

This paper discusses the effect of obstacle spacing on flame acceleration (FA) and deflagration-to-detonation transition (DDT) in inhomogeneous hydrogen–air mixture using the OpenFOAM open-source code and large eddy simulation technology based on the unsteady compressible reacting flow Navier–Stokes equation and the detailed chemical reaction mechanism of 9 species and 21 steps. The results show that the obstacle spacing has a more significant impact on the rapid deflagration state, manifested as an inverse relationship between the flame propagation speed and the obstacle spacing due to the negative correlation between the interference intensity of obstacles to the flow within a unit channel length and the obstacle spacing. In addition, under all conditions considered in this paper, the main mechanisms of FA and DDT are the same. Further analysis reveals that the detonation initiation dynamics portrayed in this study seem more aligned with the mechanisms proposed by Liberman and akin to the shock wave amplification mechanism of coherent energy release models. As the obstacle spacing increases, the run-up distance and the acceleration time of supersonic flames and DDT also increase. This paper also observes that the flame structure during explosion flame propagation has typical self-similarity, and the turbulence level in the obstacle area is higher, resulting in a larger fractal dimension. During flame acceleration, there is a mode transition from the “thin reaction zone” to the “broken reaction zone.”

Run-up speed and jumping ground reaction force of male elite gymnasts on vault in China

BackgroundA high run-up speed and a big jumping ground reaction force are crucial to perform difficult movements and improving the quality of movement performance in the competition vault. However, the relationship between performance in the competition vault and run-up speeds, as well as jumping ground reaction force, still needs to be discovered in detail. ObjectiveWe aimed to investigate the interrelations between different run-up speeds and jumping ground reaction force, and to explore the different requirements of performing different vault styles as well as difficult movements on run-up speed and jumping ground reaction force. MethodsThe data, including vaulting run-up speed and jumping ground reaction force of 30 Chinese male elite gymnasts of performance testing, were analyzed. Descriptive statistics and Binary logistic regression analysis were used for statistical analysis. ResultsThere was no significant difference in the pedaling run-up speed between the Front handspring types and Cartwheel types (p > 0.05). The comparison between interval run-up speeds revealed that the last 5 m run-up speeds were faster during the 25 m run-up distance, and 30 m sprint speed was strongly associated with the 25 m vaulting run-up speed of Handspring and Cartwheel (r = 0.81, p < 0.01). There are significant differences in the jumping ground reaction force of different types and difficult movements (p < 0.01). When the D-score is greater than 4.6, the jumping ground reaction force will increase significantly. Jumping ground reaction force was strongly correlated with 25 m run-up speed (r = 0.715, p < 0.01), last 5 m run-up speed (r = 0.718, p < 0.01), and 30 m sprint speed (r = 0.704, p < 0.01) respectively, but not significantly associated with last 10-5 m run-up speed as well as before the last 10 m run-up speed (p > 0.05). ConclusionsThe special requirement for run-up speed and jumping ground reaction force may vary as the difficult vault. Moreover, the optimization of interval run-up speeds and improvement of the 25 m run-up speed may contribute to the bigger jumping ground reaction force and increase the potential to perform more difficult Handspring/Cartwheel vaults. The topic may merit an interventional study to optimize run-up rhythm and improve lower limb strength for achieving higher run-up speeds and bigger jumping ground reaction force within the limited run-up distance to perform more difficult vaults for male elite gymnasts in China.

Computational Study of Deflagration-to-Detonation Transition in a Semi-Confined Slit Combustor

Systematic three-dimensional numerical simulations of flame acceleration and deflagration-to-detonation transition (DDT) in a semi-confined flat slit combustor are performed. The combustor is assumed to be partly filled with the stoichiometric ethylene–oxygen mixture at normal pressure and temperature conditions. The objective of the study is to reveal the conditions for DDT in terms of the minimum height of the combustible mixture layer in the slit, the maximum dilution of the mixture with nitrogen and the maximum slit width. The results of the calculations are compared with the available experimental data. The calculation results are shown to agree satisfactorily with the experimental data on the slit-filling dynamics, flame structure, the occurrence of the preflame self-ignition center, DDT, and detonation propagation. DDT occurs in the layer at a time instant when the flame accelerates to a velocity close to 750 m/s. DDT occurs near the slit bottom due to the formation of the self-ignition center ahead of the leading edge of the flame as a result of shock wave reflections from the walls of injector holes at the slit bottom and from the corners of the conjugation of the slit bottom and side walls. The decrease in the height of the mixture layer, the dilution of the mixture with nitrogen, and the increase in the slit width are shown to slow down flame acceleration in the slit and increase the DDT run-up distance and time until DDT failure. The obtained results are important for determining the conditions for mild initiation of detonation via DDT in semi-confined annular RDE combustors.

A study of the occurrence of DDT in an array of obstacles: Combined effects of longitudinal and transverse obstacle spacings

Combustion wave propagation in a channel containing a stoichiometric hydrogen-air mixture and an array of obstacles was investigated, aiming to explore the effects of longitudinal (ls) and transverse (ts) spacings of the obstacles on the occurrence of deflagration-to-detonation transition (DDT). A high-order numerical algorithm and adaptive mesh refinement were adopted to solve reactive Navier-Stokes equations. The spacings, ls and ts, are varied from 1.2 to 6 times the obstacle diameter (do = 12.7 mm). The results show that the occurrence of DDT is largely dependent on ts. The DDT is likely to occur when the ratio of transverse obstacle gap to detonation cell size d/λ ≥ 0.64. The DDT run-up distance and time are closely related to ls and ts. For large ts, the DDT occurrence time increases with ls. However, the DDT distance may decrease significantly as ls increases when ls is relatively small, due to frequent local explosions in the isolated pockets of unreacted material. A requirement for the generation of these isolated explosions can be quantified as (ls/ts)2(12–4br) < 1, where br is the blockage ratio of the channel. For small ts, the increase of DDT distance with ls/ts slows down notably when ls/ts exceeds a threshold, because there is a mechanism characterized by large fluctuations in flame surface area that promotes the occurrence of DDT in the case with a large enough ls/ts.

TSUNAMI RUN-UP CONSIDERING TIME VARIATION OF DENSITY OF INUNDATION WATER

Aiming for the advancement of tsunami load, historical and/or prospective tsunami scale evaluations, practical empirical formulas for evaluating friction factor K of inundation flow and density ρ of inundation water over a movable bed, which can be applied to a tsunami run-up theory, are proposed using experimental data whose amount (range) is increased (expanded) by carrying out additional experiments on ρ and run-up of inundation flow with sediment, and verification data of the above theory under a uniformly sloping movable bed condition are provided. Series solutions with a higher universality to the run-up of tsunami inundation flow with sediment over a uniformly sloping movable bed, in which both K and ρ depend on time, are derived under the conditions depending on an incident bore height h1 at shoreline (or an initial stored water depth), bed slope i, median particle diameter d50 of initial bed material, and examples of the solutions are shown. The solutions are applicable to the case that ρ is independent on time, i.e., the case of inundation flow without sediment over a movable bed or fixed bed. Including the case of inundation flow without sediment, validity of one of the solutions is also verified through a comparison with the verification data on run-up distance.

Experimental study of DDT run-up distance and detonation wave velocity deficit for stoichiometric hydrogen-oxygen mixture in micro spiral channels

The determination of the deflagration-to-detonation transition (DDT) run-up distance LDDT is crucial in both the design of pulse detonation engines (PDEs) and safety protection. In this paper, the LDDT of stoichiometric hydrogen–oxygen premixed mixtures in millimeter-scale spiral channels were studied experimentally and high-speed photography was employed to capture the flame propagation process. The mixtures in three different rectangular cross-sectional channel widths and various initial pressures were tested. The present results show that the LDDT decreases with increasing the initial pressure, and with increasing the channel width, the larger LDDT is observed. When fitted with the LDDT ∝ P0−m relationship, the values of m obtained in this study ranged from 0.997 to 4.222. The critical value of 0.1 for the equivalent area divergence induced by the boundary layer ξ is proposed to distinguish the behaviors between micro and macro channels, regardless of the type of mixture and channel configuration. Additionally, an empirical formula considering the influence of the boundary layer is obtained, which allows for the quantitative prediction of LDDT. Because of the influence of curvature effect, the smaller the channel width, the greater the prediction deviation. Due to the boundary layer effect, the momentum and heat dissipation are more pronounced in smaller tubes, resulting in a loss of velocity for the detonation wave. It is suggested that the detonation wave velocity increases as the channel width and initial pressure increase. Fay's model was employed to estimate the theoretical velocity deficit, and the experimental results were in good agreement with the theoretical predictions. The current findings are valuable for the field of micro PDE and may help the assessment of the potential risk of hydrogen detonation in micro systems.

DDT run-up distance in an obstructed tube

Self-luminous high-speed photography was used to study flame acceleration and deflagration-to-detonation transition (DDT) in a clear polycarbonate round tube equipped with orifice plates. The 288 cm long, 7.6 cm inner-diameter tube was equipped with equally spaced 50% and 75% area-blockage orifice plates. The primary test mixture was stoichiometric ethylene–oxygen diluted with varying amounts of nitrogen, and the initial pressure was varied between 5 and 90 kPa. Tests were also performed with stoichiometric hydrogen–oxygen with large argon dilution to study the effect of detonation cell structure regularity. High-speed video showed that the initial DDT always occurred following shock reflection off an obstacle, allowing an accurate determination of the DDT run-up distance. Soot foils were used to measure cell size at the end of the obstacle-free tube. A correlation for flame acceleration to one-half the Chapman–Jouguet detonation velocity (VCJ) predicted the measured DDT run-up distance successfully for the most reactive mixture conditions. However, the measured DDT run-up distance increasingly deviated from the correlation with decreasing initial pressure, significantly under predicting the run-up distance at the DDT limit. A correlation for the DDT run-up distance was proposed based on the concept of flame acceleration to one-half VCJ followed by an induction phase that ends with the transition to detonation. For a given tube and obstacle configuration, the flame acceleration distance depends on the flame properties, and the DDT induction distance depends on the properties that quantify the detonation length-scale and stability.

Characteristics of flame acceleration and deflagration-to-detonation transition enhanced by SF6 jet-in-cross-flow/flame interaction

Jet-in-crossflow (JICF), as a turbulence generator, is proposed to promote the flame acceleration and deflagration-to-detonation transition (DDT) process. Previous work has suggested that JICF using CO2 or Ar was in favor of flame acceleration under optimal conditions. The competition mechanism between the positive combustion-enhancement effect caused by jet-induced turbulence and the negative combustion-inhibition caused by non-reactive gas has been demonstrated. It is worth noting that the difference in molar weight between the medium of JICF and the combustible mixture may significantly impact deflagration propagation prior to DDT. Thus, in this work, to investigate the flame propagation perturbed by the enhancement on the difference in molar weight between the JICF medium and combustible mixture, an experimental study of the flame propagation perturbed by SF6 JICF is carried out. By adjusting the injection pressure (Pj) of the SF6 JICF, the characteristics of flame propagation and DDT are analyzed. The results showed that the flame can accelerate to the onset of detonation within a short run-up distance in the cases with SF6 JICF. Schlieren images of flame evolution show that the flame disturbed by SF6 JICF rapidly transitions to a wrinkled flame. It is suggested that the SF6 JICF-enhanced turbulence promotes flame acceleration and DDT. The effect of SF6 JICF on the flame characteristics can be concluded in two aspects: one is that the inhomogeneously distributed vortices that are induced by JICF cause a nonuniform diffusion of SF6 in the tube, resulting in a nonuniform dilution of the combustible mixture near the jet; another one is that the vortices induced by JICF stretch the flame surface to increase the flame area. Increasing the injection pressure could promote the formation of complex wrinkles in the flame, however, it shows few further improvements in promoting DDT. Different jet mediums are also tested, and the results show that SF6 JICF can shorten the run-up distance significantly compared with helium and nitrogen JICF. The small and densely distributed wrinkles significantly increase the flame area to enhance heat release. The flame disturbed by SF6 JICF could accelerate to the local sound speed of the unburnt mixture, which results in the facilitation of the precursor shock wave formation. After the flame passes through the SF6 JICF, it remains a larger acceleration rate and then transitions to quasi-detonation rapidly. The conclusion of this work could help to qualitatively understand the positive effect of JICF-induced turbulence on flame acceleration and DDT. It also provides a relatively efficient and safe technology to promote detonation initiation in the design of detonation engines.

Influence of longitudinal obstacle spacing on the deflagration-to-detonation transition through a bank of obstacles in a hydrogen-air mixture

Flame acceleration and deflagration-to-detonation transition (DDT) in a channel containing an array of staggered cylindrical obstacles and a stoichiometric hydrogen-air mixture were studied by solving the fully-compressible reactive Navier-Stokes equations using a high-order numerical algorithm and adaptive mesh refinement. Four different longitudinal spacings (ls) of the neighboring obstacle rows (i.e., ls = 15.28, 19.1, 25.4, and 38.2 mm, corresponding to 1.2, 1.5, 2 and 3 times of obstacle diameter, respectively) were used to examine the effect of obstacle spacing on flame acceleration and DDT. The results show that the main mechanisms of flame acceleration and transition to detonation in all the cases studied are consistent. While the flame acceleration is caused by the growth of flame surface area in the initial stage, it is governed by shock-flame interactions in the later stage when shock waves are generated. The focusing of strong shocks at flame front is responsible for the initiation of detonation. It was found that the flame propagation speed and the DDT run-up distance and time are highly dependent on ls. Specifically, the flame acceleration declines as ls increases, since a larger ls leads to less disturbance of flow by obstacles per unit channel length. For detonation initiation, both the run-up distance and time increase with the increase of ls. It is interesting to note that the DDT distance and time increase significantly as ls increases from 19.1 mm to 25.4 mm. This is related to the slowdown of the increase rate of energy release over a period before DDT occurs under large ls condition, because every time the flame passes over an obstacle row the shock-flame interaction is delayed and numerous isolated pockets of unburned gas material are formed.

Experimental investigation on the DDT run-up distance and propagation characteristics of detonation wave in a millimeter-scale spiral channel filled with hydrogen-air mixture

An experimental study on flame acceleration (FA) of hydrogen–air premixed gas in a millimeter-scale Archimedean spiral channel is presented in this paper. Experiments were performed in a transparent rectangular cross-section channel and the flames were recorded by high-speed photography. The flame propagation characteristics under different equivalent ratios and different initial pressures was compared. Results show that the minimum LDDT (DDT run-up distance) are obtained at stoichiometric ratio. With increasing the initial pressure, the smaller LDDT is observed. Moreover, Due to the combined effects of the chemical reaction, wall dissipation, and geometric curvature effects, the flame velocity showed a significant oscillation pattern. Decreasing initial pressure and keeping away from the stoichiometric ratio increasingly favour the low velocity mode. The current conclusions of this study are helpful to the development of new pre-detonator and evaluate the danger of hydrogen detonation in micro systems.

Effects of low-temperature chemistry on direct detonation initiation by a hot spot under engine conditions

This study investigates the effect of low-temperature chemistry (LTC) on the minimum runup distance, lm, of direct detonation initiation by an autoignitive hot spot under engine conditions. A newly predictive model is proposed to determine an a priorilm. The temperature and pressure increase and the radical build-up prior to the main ignition resulting from LTC are incorporated in the model that allows a better prediction of ignition modes. A series of 1D simulations are performed by varying the initial temperature, the hot spot size and its temperature difference at constant-volume and engine conditions. DME (ethanol) is used to represent a two (single) stage ignition fuel. It was found that taking the transient evolution of the mixture state as an initial condition to the ZND model results in a better representative exothermic characteristic length scale, which exhibits a strong linear correlation with lm regardless of fuel types over a wide range of conditions. The LTC oxidation is found to reduce lm by approximately a factor of two for the low-temperature cases, leading to a comparable value of lm to that of the high-temperature cases. It was also found that the ignition modes are better predicted by identifying an alternative characteristic length scale based on the variation of ignition delay time τig within its range of monotonic distribution. For a hot spot that has temperature variation spanning across the NTC regime, the runup distance was found to be shortened by approximately a factor of two, such that a longer hot-spot size is required to form detonation. In addition, a better prediction of ignition modes was achieved by defining the normalized front speed as a statistical mean for each runup-distance element than that determined at the midpoint of a hot spot.

Tsunami Numerical Modelling in Ujung Kulon National Park with the Earthquake Magnitude Scenario of 6.5 and 6.9 Mw

Tsunami modelling was conducted to simulate tsunami events based on earthquake data previously occurring around Ujung Kulon National Park (TNUK), Banten Province using TUNAMI-F1 and TUNAMI-N3. TUNAMI-F1 is a modelling method to get the wave height and tsunami arrival time with a grid spacing of 0.00167°. While the TUNAMI-N3 is a model that applies the theory of wave propagation linearly in a grid variation to get a high output of tsunami inundation. The tsunami source data was used from historical earthquake generation on January 14, 2022 (6.5 Mw) and August 2, 2019 (6,9 Mw). The reverse fault type scenario from Wells & Coppersmith (1994) is used to calculate the scaling law with length, width, and the focal mechanism value obtained from the United States Geological Survey (USGS) to generate initial waves based on the multideform model. The TUNAMI-N3 model applies a nested model with variations in grid spacing and the most detailed value is 68,556 m. The tsunami wave height based on the magnitude 6.5 Mw scenario is around 0.001 m to 0.05 m with the highest wave height found on the southern coast of TNUK and the southern coastal area of Peucang Island (0.03-0.05m). The inundation produced is only visible in the E1 domain reaching 96-192 m in areas A, B, C. Then, the maximum inundation area is the south coast of TNUK (0.01-0.03m). Based on the second scenario, the height of the tsunami waves generated is in the range of 0.001 − 0.3 m. The maximum tsunami height was in the Rancecet Beach area, south of Tinjil Island, the south, east, and north coasts of TNUK (0.03-0.3m). The run-up distance resulting from scenario 1 is less than 1 km. Based on TUNAMI-F1 model results, wave height maximum caused by 6.5 Mw magnitude is higher than 6.9 Mw.

Prediction of the developing detonation regime in a NTC-fuel/air mixture with temperature inhomogeneities under engine conditions

The developing detonation process resulting in superknock development under realistic engine conditions in the presence of low-temperature chemistry (LTC) is investigated using two-dimensional direct numerical simulations (DNS). A new model is proposed to predict the developing detonation regime under engine conditions. The prediction is validated against the DNS results. Dimethyl ether (DME) exhibiting a typical negative temperature coefficient (NTC) behavior is used as a fuel. In the presence of the NTC regime, the mean distance of dissipation elements of the ignition delay field, l¯DE, is considered as the characteristic length scale of hot spots to improve the predictive accuracy of the model. The model also accounts for the multi-dimensional effect resulting from the interaction and collision of multiple ignition kernels that is found to promote the onset of detonation and reduce the runup distance of detonation initiation as compared to that of 1D laminar detonation cases. The trasient mixture state is also incorporated in the model development. The model is demonstrated to accurately capture the developing detonation boundary that is consistent with the knock intensity level obtained from the statistical analysis of DNS dataset.

Transition to detonation in inhomogeneous hydrogen-air mixtures: The importance of gradients in detonation cell size

This paper presents a numerical study of flame acceleration and deflagration-to-detonation transition (DDT) of hydrogen-air mixtures in a channel with obstacles, where the mixture composition has a spatial gradient perpendicular to the wave propagation direction. The mixture composition gradient corresponds to a detonation cell size gradient, which characterizes the detonability or the detonation sensitivity. We use a recently developed chemical-diffusive model (CDM) to investigate the influence of the cell size gradient on the detonability of an inhomogeneous mixture and examine characteristic behaviors of flame acceleration and DDT. The CDM is a parametric model for chemical reaction and diffusive transport processes in compressible Navier-Stokes simulations. When optimized, the CDM can reproduce the correct flame and detonation properties, particularly the detonation cell size. The simulation results show that the ease with which an inhomogeneous mixture can detonate is bounded by the detonation limits of the most and least detonable homogeneous mixture. That is, the run-up distance to DDT of inhomogeneous mixtures with 0.8<ϕ<1.0 is found to be greater and less than the most and the least detonable mixtures with ϕ=1.0 and ϕ=0.8, respectively. Other macroscopic observables in the inhomogeneous mixture such as the average combustion wave speed and the total flame surface area are also in between those in these two homogeneous mixtures. The simulation data showed that pressure waves generated by a deflagration play an important role to re-distribute the prescribed mixture composition. The combustion process occurs preferentially in mixtures that initially concentrate along the unobstructed channel centerline. The numerical results agree with prior experimental findings that the averaged equivalence ratio cannot adequately estimate the detonability of an inhomogeneous mixture.

Flame–turbulence interactions during flame acceleration using solid and fluid obstacles

A combination of solid and transverse jet obstacles is proposed to trigger flame acceleration and deflagration-to-detonation transition (DDT). A numerical study of this approach is performed by solving the reactive Navier–Stokes equations deploying an adaptive mesh refinement technique. A detailed hydrogen–air reaction mechanism with 12 species and 42 steps is employed. The efficiency and mechanisms of the combined obstacles on the flame acceleration are investigated comprehensively. The effects of multiple jets, jet start time, and jet stagnation pressure on the DDT process are studied. Results show that there is a 22.26% improvement in the DDT run-up time and a 33.36% reduction in the DDT run-up distance for the combined obstacles compared to that having only solid obstacles. The jet acts as an obstruction by producing a suitable blockage ratio and introducing an intense turbulent region due to the Kelvin–Helmholtz instability. This leads to dramatic flame–turbulence interactions, increasing the flame surface area dramatically. The dual jet produces mushroom-like vortices, leading to a significantly stretched flame front and intensive Kelvin–Helmholtz instabilities, and therefore, these features produce a high flame acceleration. As the jet operation time decreases, the jet obstacle almost changes its role from both physical blockage ratio and turbulence and vorticity generator to a physical blockage ratio. There is a moderate jet stagnation pressure that reduces the run-up time to detonation and run-up distance to detonation in the obstacle-laden chamber. While further increasing the jet stagnation pressure, it does not have a positive effect on shortening the detonation transition.

An integrated approach for coastal cliff susceptibility: The case study of Procida Island (southern Italy)

Procida Island, located in the Gulf of Naples (southern Italy), is characterized by steep cliffed coasts, articulated in a succession of headlands and small embayments with narrow pocket beaches, such as Ciraccio and Chiaia, often characterized by instability.In this study, a methodology for coastal cliff susceptibility assessment has been conceived based on hydraulic and geomorphological characteristics, which supported the construction of a Cliff Stability Index (CSI). The geomorphological characteristics are related to the whole cliff face, the cliff material resistance, and the cliff failure mechanisms. The hydraulic actions on the cliff are related to the wave impact which is exerted by the breaking waves once the wave run-up distance exceeds the beach width. The index takes into account the slope of the cliff, the rock strength, the wave energy at the cliff base produced by the broken wave and the presence of defence structures at the cliff base. The resulting index classification, obtained by addition of the partial sub-indices, has been compared with the observed coastal cliff evolution from 1954 to 2021.

Maximum Run-Up and Alongshore Mass Transport Due to Edge Waves

The edge wave on a uniform-sloped seabed was described by the velocity-potential function by Mok and Yeh in 1999. Edge waves cannot be extended above a certain level from the still-water level, and the upper limit of the run-up of the edge waves for given conditions is found here. In this study, quantitative mass transport by the edge waves of the beach is introduced. The maximum run-up height is decided from the wave’s amplitude at shoreline, and the maximum run-up distance from the shoreline is proportional to the wavelength of the edge waves. The fluid alongshore-mass-transport profile shows that the strongest mass transport rate corresponds to the position offshoreward multiplied by 0.0362 times the wavelength, and its magnitude is 1.23 times the mass-transport rate at the shoreline. The maximum cross-sectional total mass-transport rate is 0.214 times the mass transport at the shoreline, multiplied by the wavelength for the maximum run-up condition. This study suggests that edge waves cannot be increased infinitely and that there is a maximum run-up on the coast.

Effects of jet/flame interaction on deflagration-to-detonation transition by non-reactive gas jet in a methane-oxygen mixture

Jet-in-crossflow (JICF) is a potential and reliable technique that can promote flame acceleration and deflagration-to-detonation transition (DDT). Most of the previous researches utilized combustible mixture or oxygen as the medium of JICF, therefore the detonation enhancement effect may be partly attributed to the chemical properties of the jet, and the purely turbulent effect induced by JICF on DDT has not been fully understood. In our previous work, the non-reactive gas jet affected flame propagation indirectly by separating the injection and ignition in the control sequence. A competing mechanism between the positive combustion-enhancement effect caused by jet-induced turbulence and the negative non-reactive gas-inhibition effect on combustion has not been found, the non-reactive gas jet with high pressure and short duration time was also verified to be beneficial for precursor shock wave formation and flame acceleration. However, no detonation was observed in the work. In this paper, the non-reactive jet interacts with the flame propagation directly by overlapping the working time of the jet and ignitor partly, and the effect of jet parameters including injection pressure and time delay on DDT is investigated systematically. The results show that the flame affected by the non-reactive gas jet with a high-pressure ratio and a short time delay can transit to detonation in a short run-up distance successfully. The schlieren images of the flame evolution process illustrate that the flame interacted by the jet experiences four states: layered flame, wrinkled flame, cellular flamelets, and turbulent flame. Kelvin–Helmholtz (K-H) instability and Rayleigh-Taylor (R-T) instability dominate in the flame distortion. The characteristic timescales of the flow and reaction are computed in the four flame states, turning out that as the flame evolving, the turbulent intensity of the flame is enhanced. Damköhler number (Da) on the flame front eventually converges to [1,2] demonstrates the characteristic timescales of the turbulence and reaction are on the same order, and the turbulence dominates the flame evolution.

Effects of a significant boundary layer on the flame acceleration and transition to detonation in millimeter-scale tubes

Experiments using three different mixtures (ethylene–oxygen, methane–oxygen, and acetylene–oxygen–argon) and four different tube diameters (0.5, 1, 2, and 4 mm) were carried out to investigate the entire process of flame propagation in narrow tubes. Flame propagation in the four sizes of tubes was recorded synchronously by a high-speed camera. The results show that the deflagration-to-detonation transition (DDT) process goes through four stages according to velocity evolution, in the sequence of (i) exponential acceleration, (ii) “hesitation” period, (iii) linear acceleration, and (iv) velocity jump. The DDT run-up distance decreases with decreasing tube diameter, which arises from the effect of the significant boundary layer during flame acceleration. The area divergence is introduced by analyzing how tube diameter and initial pressure affect the DDT run-up distance. The critical value of 0.1 for the area divergence can be used to distinguish the variation characteristics of the normalized DDT run-up distance between millimeter-scale tubes and the large tubes (centimeter-scale). Moreover, an empirical formula with a unified form is obtained, which describes the DDT run-up distance as a function of tube diameter and initial pressure. It allows a good prediction of the experimental results regardless of the tube size as well as the type of mixture.