Critical Velocity Research Articles

Influence of incident angle on spalling damage of underground tunnels subjected to explosion waves

Tensile waves formed by the reflection of explosive stress waves at the free surface of a tunnel can lead to the destruction of the surrounding rock in the form of spalling. The incident angle of stress waves is an important factor affecting the characteristics of spalling. Theoretical calculations were conducted on the spalling thickness, spalling range, ejection velocity of rock fragments, and the furthest spalling distance in cases of normal incidence and oblique incidence, respectively. The variations of the spalling with the incident angle along the axial direction of the tunnel are presented. The results show that when the Poisson’s ratio of the medium is less than 0.26, the reflected longitudinal wave transforms from a tensile wave to a compressive wave within a certain range of the incident angle. As the incident angle increases, the thickness of the first spalling layer increases monotonically, while the total spalling thickness decreases monotonically. The critical condition of spalling is reached when the first spalling thickness equals the total spalling thickness. For an explosion 6 m away from the tunnel, the critical spalling distance obtained by oblique incidence is 1.67 m/kg1/3, and the peak particle velocity is 3.11 m/s. The critical spalling distance obtained by normal incidence is 5.64 m/kg1/3, and the peak particle velocity is 0.42 m/s. The theoretical results agree well with the on-site experimental data, indicating that the results of oblique incidence overestimated the critical peak particle velocity for spalling.

A new experimental and numerical simulation method for measuring ash slag fluidity using VOF based on OpenFOAM

A numerical computational model of heated ash flow is proposed using the Volume of Fluid (VOF) method based on OpenFOAM. Established numerical model can accurately calculate the critical flow temperature (Tc) and critical flow velocity (Vc) of ash slag with the error of 1.5 % and 19 % from the experiment, respectively. Forty-five types of ash slag with widely varied properties in China were calculated based on the established model. Results show that high levels (>30 wt%) of Fe2O3 and CaO improve the flowability of the ash slag, and low levels of Al2O3 (10 wt%) also contribute to the flowability of the ash slag. Tc and Vc of the ash were distributed in the range of 1150 ∼ 1400 °C and 0.1 ∼ 1.0 mm/min, respectively. Tc and Vc change in opposite trends with the component content increases, indicating that a higher Tc corresponds to a lower Vc and fluidity reduction. Mathematical models for calculating the Tc and Vc of ash were obtained based on non-linear multiple regression and correlation coefficient, and prediction accuracy was within 10 % and 30 % for Tc and Vc, respectively. The proposed numerical simulation method and prediction model can provide an accurate reference for a wide range of ash fluidity. Also, it was demonstrated that elemental Na has a positive effect on ash flowability based on the model, which is important for measuring slag flowability in slag-tap furnaces.

Establishment of Critical Non-Depositing Velocity Prediction Model for Sediment in Drip Irrigation Laterals Based on PSO-SVM

Establishment of Critical Non-Depositing Velocity Prediction Model for Sediment in Drip Irrigation Laterals Based on PSO-SVM

Modelling of Fly Ash Viscous Deposition and Slagging Prediction of Biomass-fired Boiler

In addressing the ash melting-induced slagging on the high-temperature heating surfaces of biomass-fired boiler, a combined experimental and modelling study of biomass ash viscous deposition has been conducted. A comprehensive ash viscous deposition model based on ash fusion and viscosity characteristics and the critical velocity criterion has been proposed. The deposits of the top furnace and high-temperature superheater of a 130 t/h biomass-fired boiler have been sampled for validation, and a modelling study using ANSYS FLUENT with a user defined function (UDF) and dynamic mesh has been performed. The results show that small particles with diameter of 20 μm lead to less viscous adhesion because of faster response to temperature decrease before reaching the heating surfaces. Deposition efficiency and growth rate of deposits are positively correlated with temperature. Slagging in the top furnace area is dominated by the viscous deposition of molten ash. However, the amount of viscous deposition accounts for a low proportion (20.1%) in the high-temperature superheater, suggesting a change of dominant slagging mechanism from viscous deposition to gaseous condensation and the subsequent capture of fly ash. The model is suitable for predicting ash melting-induced slagging in high-temperature areas of biomass boilers.

Stability of boulders on cobble streambeds

The placement of boulders in streams enhances aquatic habitat by increasing the heterogeneity of flow conditions.  Practical design must ensure the stability of individual boulders, requiring calculation of their incipient movement conditions.  The stability of a boulder on a cobble bed is shown experimentally to depend on its size, the bed material size, the degree of embedment of the boulder, the slope of the bed and the flow velocity and depth.  An equation is derived through a pivoting analysis for predicting the relationship between the critical ambient depth-averaged velocity and the critical flow depth; this, together with a resistance equation, can be used to predict the flow conditions for boulder stability.  The equation is used to develop a simpler form for unsubmerged spherical boulders and cobbles.  The stability equation is tested against the experimental data, using an experimentally determined drag coefficient relationship.

Flexural-Gravity Waves in a Channel with a Compressed Ice Cover

The characteristics of linear hydroelastic waves propagating in a channel covered with compressed ice are investigated. The channel has a rectangular cross-section and is assumed to be infinite in length. The fluid in the channel is non-viscous and incompressible; its flow is potential. The ice cover is modelled by an elastic plate of constant thickness frozen to the channel walls. Principal attention is paid to the investigation of the influence of ice compression on the parameters of hydroelastic waves. The problem is solved in a coupled hydroelastic formulation. The profiles of propagating waves in the channel are sought in the form of series on the normal modes of a dry plate. The modes are defined analytically through trigonometric and hyperbolic functions. It is shown that compression in the longitudinal and transverse directions has different effects on the dispersion relations of these hydroelastic waves, their shape and phase, as well as on the critical velocities and strains distribution.

Enhancing gas film stability by alternating superhydrophobic and hydrophobic surfaces for stable drag reduction

Superhydrophobic surfaces can significantly reduce the resistance of underwater vehicles, but as the speed increases, the gas film is prone to be destroyed, leading to a decrease in the drag reduction effect or even an increase in the drag. Therefore, enhancing the stability of the gas film is crucial for maintaining the drag reduction effect. Inspired by the honeycomb array pit structures, the high adhesion hydrophobic properties of rose petals, and the wetting gradient surface of Namib desert beetles, an alternating superhydrophobic and hydrophobic surface (ASHHs) was constructed by femtosecond laser to enhance the stability of the gas film. The high adhesion hydrophobic surface (HAHs) provides greater adhesive force, allowing the gas film to firmly pin at the junction of a low-adhesion superhydrophobic surface (LASHs) and HAHs, thereby enhancing the stability of the gas film. The critical failure velocity of ASHHs can reach 2.3 m/s, which is significantly greater than that of low-adhesion superhydrophobic surface samples (LASH-S) (1.7 m/s). ASHHs maintains a stable drag reduction effect of 37% at a velocity of 2.3 m/s, while that of LASH-S is only 6%. It is envisioned that such superhydrophobic surfaces that enhance gas film stability should find widespread applications in minimizing resistance and reducing energy consumption in the marine engineering field.

Experimental Study: Effects of Pier Position and Critical Velocity Ratio on Scour Pattern in Two Consecutive Bends Under Clear Water Condition

Experimental Study: Effects of Pier Position and Critical Velocity Ratio on Scour Pattern in Two Consecutive Bends Under Clear Water Condition

Surface State Dissipation in Confined ^{3}He-A.

We have studied the power dependence of superfluid Helmholtz resonators in flat (750 and 1800nm) rectangular channels. In the A phase of superfluid ^{3}He, we observe a nonlinear response for velocities larger than a critical value. The small size of the channels stabilizes a static uniform texture that eliminates dissipative processes produced by changes in the texture. For such a static texture, the lowest velocity dissipative process is due to the pumping of surface bound states into the bulk liquid. We show that the temperature dependence of the critical velocity observed in our devices is consistent with this surface-state dissipation. Characterization of the force-velocity curves of our devices may provide a platform for studying the physics of exotic surface bound states in superfluid ^{3}He.

Spatio-temporal characterisation of local scour around a circular bridge pier in cohesive soil with different clay/silt ratio

This paper presents new data on scour around a vertical pier in cohesive soils. It specifically focuses on the temporal evolution of local scour hole around the pier with increasing the clay/silt ratio content. Series of flume tests were performed using soil mixtures made with 85% fine sand and 15% fines. The fines fraction used in the soil mixtures includes silt, kaolinite clay, and various combinations of both with different proportions. The water velocity during the tests was kept constant and slightly above the erosion critical velocity of the fine sand used in the mixtures. A 3D laser scanner was employed to continuously record the geometry of the scour hole. Results show that increasing the Kaolinite clay in the fine fraction reduces significantly the scour. The mixture with a range around 7.5–10% of kaolinite clay fines content provides the threshold composition for cohesive soil behaviour effect in scouring process, recognized through scour pattern change. As the clay content increases, notable reductions are observed in the dimensions of the scour hole. Furthermore, the temporal evolution of maximum scour depth measured in flume was in agreement with the results from SRICOS-EFA (Scour Rate in COhesive Soil - Erosion Function Apparatus) method.

Particle Bounce Stick Behaviour in the Rotating Frame of Reference

Abstract Particle deposition is a major damage mechanism for gas turbine components, especially in the secondary air system. Predicting the transport and deposition of ingested atmospheric contaminants is of great interest in component-level simulations during the design process. Bounce stick models predict deposition upon collision with a wall during Lagrangian particle tracking. The effect of collisions in the rotating frame of reference, considering centrifugal forces, has thus far been neglected in the literature. That is despite the significant centrifugal loads experienced by many components of interest for deposition studies, for example turbine blades. The collision physics of the rotating frame are discussed here using low-order models and Monte Carlo-style simulations. The centrifugal (CF) forces experienced by the particle are shown to have a primary dependence on friction with the rotating surface. No significant effect was found on the rebound velocities of particles experiencing “worst-case” CF forces. However, differences were observed in the sticking probability between concave and convex rotating surfaces, where the CF forces act in opposing directions to either push the particle into the surface or detach it. The variation of critical sticking velocity due to CF forces was likely to bias deposition towards concave surfaces in the rotating frame. The collision physics of the rotating frame were found to be unintuitive, with complex implications for modelling deposition in gas turbine components. However, they were consequential in determining the distribution of deposition through the system, hence should be included in particle deposition simulations in CFD.

Advancements in smoke control strategies for metro tunnel cross-passage: A theoretical and numerical study on critical velocity and driving force

Cross-passage is a commonly encountered structure within metro tunnels, providing a swift route for evacuating personnel from the accident tunnel to the safe tunnel opposite. Ventilation in the cross-passage of metro tunnels is established through the collaborative operation of ventilation systems on both sides of the tunnel. Concurrently, smoke movement within the metro tunnel is impacted by factors such as train blockage and the accumulation of heat within the train carriages. The former correlations need further refinement to predict the critical velocity and driving force required to prevent smoke from spreading into a metro tunnel cross-passage. One-dimensional theoretical analysis and full-scale cold smoke experiments were performed to investigate the relationship between the air supply parameters of tunnel fans on both sides and the ventilation velocity in the cross-passage. A calculation model of fan type selection in the opposite side safe tunnel for smoke control in the tunnel cross-passage is proposed. The influence of train location, fire heat release rate, and main tunnel ventilation velocity on critical velocity in the cross-passage was quantified by numerical simulations. The results show that the critical velocity in the cross-passage under unobstructed conditions surpasses that under blocked conditions. Meanwhile, the critical velocity exhibits relative stability under both unobstructed and blocked conditions. On the basis of the dimensionless analysis, a piecewise function was proposed to predict the critical velocity in tunnel cross-passage. The outcomes of this study provide valuable guidance for the implementation of fire prevention and smoke control measures in tunnels with similar structures.

A design model of multi-layer modified aramid fabrics against fragment simulating projectiles and full metal jacketed bullets

Soft body armor is required to meet threats of both bullets and explosion fragments in battlefield. However, designing body armor that can protect against these two types of projectiles considering both critical velocity and back face deformation (BFD) is often based on experience and extensive ballistic experiments. This paper proposes a quick design model for determining the layers of aramid fabrics modified by polyethylene (PE) to protect against fragment simulating projectiles (FSP) and full metal jacketed bullets (FMJ). Firstly, ballistic experiments are conducted discovering the optimal concentration of PE modification against the sphere and FSP is 10%. Secondly, finite element model is adapted to explore the protection capabilities of modified aramid fabrics against FSP and FMJ and a linear relationship between the BFD and the critical velocity has been observed. Thirdly, an analytical model is established to uncover the reason of this relationship. Finally, a design model is proposed to configure the improved outer tactical vest (IOTV) generation III based on the derived formulae of critical velocity and BFD for different layers of modified aramid fabrics against FSP and FMJ. The model indicates that the objectives of intercepting FSP or FMJ and reducing blunt trauma are usually not simultaneously attainable. 38 layers of modified aramid fabrics are sufficient to meet the protection requirements for both FSP and FMJ, regardless of critical velocity and BFD. Besides, 498m/s is the threshold of FMJ impact velocity to determine the priority of intercepting bullets or reducing blunt trauma. The design model can serve for the development of lightweight and effective body armor.

Filamentary velocity scaling validation and spin dynamics in the DIII-D tokamak

Measured filament velocities in the DIII-D tokamak are compared against theoretical scalings, finding that the latter often represents an upper limit on experimental velocity distributions with most filaments possessing lower velocity. Filament spin from internal E × B drift is experimentally demonstrated to alter filament radial velocity. A critical spin velocity, where filament radial velocity peaks, is observed and corresponds to approximately 5 km/s. This transition is corroborated using a less direct measure of filament spin in the form of a temperature ratio. These techniques are combined to find that the critical spin velocity closely aligns with transport times along and across filaments becoming comparable. The normalized filament size distribution is consistent with the most stable size as dictated by Kelvin–Helmholtz and curvature-driven instabilities. Overall, the findings suggest filament stability and spin alter filamentary transport that may threaten the integrity of first walls in fusion devices.

Migration trajectories and blocking effect of the fine particles in porous media based on particle flow simulation

The particle flow code method based on the discrete element method was used to establish the seepage migration model of fine particles [fine particles (FPs), i.e., suspended particles] in a porous medium. A series of numerical simulations were carried out by changing the particle size, seepage velocity, particle injection number, and wide particle size gradation. The research showed that large FPs play a major role in blocking porous medium channels when the injected FPs have a wide size gradation. Due to the blocking effect, small FPs that would not otherwise have deposited also deposit. Moreover, by increasing the number of large FPs in the mixed particles, the total number of particles deposited and the number of smaller FPs deposited will also increase. The distribution of FPs in porous mediums can be divided into three types: surface deposition, internal deposition, and non-deposition. When the seepage velocity increases and reaches a seepage threshold, which is the critical seepage velocity, the deposited FPs will once again be in a suspended state and undergo migration. On the contrary, the FPs will continue to maintain their sedimentary state, and the critical seepage velocity will also increase correspondingly with increasing particle size.

Flow-induced Vibrations of Dual-cylinders in Axial Flow via LES Simulations

The axial-flow-induced vibration (AFIV) of fuel rods in the nuclear power plant is closely related to nuclear safety. In this article, a numerical study is performed on vibration of two elastic cylinders arranged side-by-side in axial flow. Large eddy simulation (LES) is employed to predict the turbulent flow. The numerical method has been verified using the experimental root-mean-square vibration amplitude of a single cylinder. A wide range of inflow velocities u*, incident turbulence intensity Tu and space ratio P/D have been examined, where D and P are the diameter and centre-to-centre distance of the cylinders, respectively. The results show that the vibration amplitudes increase with an increasing u*, comparable to the case of a single cylinder in axial flow. However, the two cylinders could bend outwards during a relatively high u* and low Tu. Although Tu significantly affects the amplitudes of the cylinders, it does not change the vibration frequency and the critical velocity at which buckling instability occurs. As the gap between the two cylinders is sufficiently small, the vibration amplitude enhances significantly due to the pronounced hydrodynamic interaction between the two elastic cylinders and surrounding fluid. The direction of buckling is no longer random but fixed.

Effect of urban street canyon aspect ratio on fire-induced air pollutants dispersion under cross wind

The incidence of vehicle fires in urban street canyons has continuously increased with the process of urban modernization. The dispersion and accumulation of fire-induced air pollutants seriously affect residents’ safety. The effects of the street canyon aspect ratio and fire source location on fire-induced air pollutants dispersion under cross wind were numerically investigated in the paper. The results show that the street canyon aspect ratio can affect flow patterns and vortex structure and then lead to different accumulation states of air pollutants. Smoke development can be divided into four different regimes according to cross wind velocity. The re-entrainment phenomenon occurs when the fire source is close to the windward building or in the center of the street, but it does not occur when the fire source is close to the leeward building. Smoke tends to accumulate in street canyons when the aspect ratio is smaller and the fire source is closer to the leeward building. The variation of critical velocity with the aspect ratio can be divided into three regions, i.e., initial linear growth region (0.5 ≤ < 1), constant region (1 ≤ ≤ 1.5), and second linear growth region (1.5 < ≤ 2). The dimensionless critical velocity and critical Froude number are used to quantify the re-entrainment phenomenon in different fire scenarios, and prediction models are finally proposed. The main findings can provide a more detailed reference for urban layout and air pollution control to reduce fire-induced air pollutants.

Deposition mechanism of ceramic reinforced metal matrix composites via cold spraying

Understanding the mechanism underlying metal matrix composites (MMCs) in cold spraying is critical to fabricating innovative MMC coatings and deposits with tailored microstructures and excellent mechanical performance. In this work, we propose a systematic numerical simulation framework combined with experimental observations to reveal the co-deposition mechanism of cold-sprayed metal/ceramic MMCs. The finite element modeling results and experimental validation found some critical conclusions regarding the deposition mechanism. The modeling results show that most of alumina particles are significantly fractured in Inconel718/alumina coating in contrast to aluminum/alumina coating. This fact suggests that the critical fragmentation velocity (CFV) of ceramic particles is dependent on the hardness of the metal substrate/matrix. Ceramic particles are more prone to fracture when co-deposited with metals having high hardness. Moreover, the simulation results also indicate that the rebounded alumina particles or fragments are possibly captured by incoming metal particles and trapped into MMCs. Since intact alumina particles are barely seen in composites, especially when co-deposited with hard metals, it can be concluded that direct ceramic particle deposition significantly relies on fragmentation. In addition, secondary fragmentation plays a key role in the metal-ceramic co-deposition process. The particles that have completed the impact process may be subjected to secondary fragmentation in the form of new cracks and fragmentation due to the impact by following metal and ceramic particles.

Controlling Splat Boundary Network Evolution Towards the Development of Strong and Ductile Cold Sprayed Refractory Metals: The Role of Powder Characteristics

Feedstock powder characteristics such as composition (specific alloying elements and concentrations and impurity levels), microstructure, thickness/composition of surface oxide layers, and particle size distribution play a crucial role in determining the overall mechanical properties of cold sprayed deposits. Herein, we report on two deposits consolidated via cold spray processing from differently-sourced batches of nominally identical elemental refractory powders under identical spraying conditions, which exhibit bending strength and ductility values that differ by more than a factor of two – and with the weakest sample displaying negligible effective ductility. Through chemical, microstructural and micromechanical characterization of both the feedstock powders and cold sprayed deposits, we consider the possible influences of feedstock characteristics on the mechanical performance of cold spray consolidated deposits. It is shown that while differences in interstitial oxygen and hydrogen content may result in differences in the intrinsic yield characteristics of the feedstock material, both feedstocks maintain the ductile behavior required to induce good metallurgical bonding upon impact of optimally sized powder particles. We conclude that the deposits formed from the two feedstock powders are indistinguishable and exhibit high ductility when characterized locally within the relatively undeformed bulk of a single particle or splat. However, the two sprayed deposits show extremely low ductility or brittle behavior when loaded in tension across intersplat boundary domains comprising material that has undergone extensive deformation. In addition, one feedstock incorporates a broader particle size distribution, with a long tail of larger-than-optimal particles. These larger particles are accelerated below the critical impact velocity, resulting in observed imperfect metallurgical bonding at splat interfaces and higher porosity at such intersplat boundaries. This result, combined with the overall differences in the morphology of the intersplat boundary network between the two deposits, explains the difference in macroscopic mechanical behavior. We conclude that accurate control of the powder feedstock particle size distribution is essential for optimizing the mechanical integrity of cold sprayed refractory elements and alloys.

Stacking effects on dynamic mechanical behavior of bilayer hexagonal boron nitride under impact

Hexagonal boron nitride (h-BN) is a promising material for ballistic armor due to its excellent mechanical properties, enriched by different bilayer stacking arrangements. Molecular dynamics methods are used to study the stacking effects on the static and dynamic mechanical properties of bilayer h-BN. The AB (nitrogen) stacked bilayer structure attracts our attention because of its superior interlayer synergistic ability to resist projectile indentation up to a maximum force of 152.89 nN, which is about 22.9% higher than the average value of other stacked bilayers. The impact response of bilayer h-BN with AB (nitrogen) stacking arrangement is then investigated at velocities of 2-4 km/s, which has the highest critical perforation velocity of 3.075 km/s, increased by 36.7% compared to monolayer h-BN. At a low impact velocity of 2.5km/s, the AB (nitrogen) stacked h-BN bilayer spends the shortest time to dissipate the impact energy of projectile and remains intact, while the top layers of other stacked bilayers are penetrated. At high impact velocities, a perforation event occurs, accompanied by multiple deflections of crack tips from zigzag to armchair to zigzag again, which intrinsically enhances the toughness of material. This study provides more understanding of the dynamic mechanical behavior of bilayer h-BN, as well as the design of armor structures based on stacking arrangements of 2D materials.