Steady Propagation Research Articles

Effects of thermal expansion, strain rate, and gravity force on the steady propagation of a premixed flame in semi-closed channels

The flame dynamics of steady propagation of a premixed flame in semi-closed channels is investigated. The hydrodynamic model takes into account impacts of channel width, thermal expansion, straining effect, and downward gravity force on the flame front. The steady flame shape and its velocity field could be determined by numerical iteration of a weakly nonlinear front equation and linearized governing equations with Fourier transform, respectively. Results reveal that the introduction of thermal expansion and gravity force enhance the flame curvature and increase the burning velocity, while the straining effect suppresses the flame bending processes. In addition, a non-monotonic dependence of the burning velocity on the Peclet number is further demonstrated. It reveals that the thermal expansion and strain effect would have impacts on the burning velocity as well.

Numerical investigation of the effects of fracturing fluid parameters on hydraulic fracture propagation in jointed rock mass based on peridynamics

In this study, we develop a coupled hydraulic fracturing model based on peridynamics, propose a contact-friction constitutive model, and establish a bond breaking criterion based on bond stress to explore hydraulic fracture propagation in jointed rock. Subsequently, we study the effects of fracturing fluid parameters (viscosity and pumping rate) on the fracture propagation behavior. Our results show that the viscosity of fracturing fluid can significantly affect the fracture morphology and propagation pattern. Fracturing fluid with higher viscosity is beneficial for the hydraulic fracture to cross natural fractures and continue to propagate in the original direction. The pumping rate mainly affects the fracture propagation speed and fracturing fluid pressure, but has limited influence on the fracture shape. Furthermore, the pumping rate has limited effect on the interaction between the hydraulic fracture and the natural fracture, but in general, lower pumping rate is conducive to the steady fracture propagation in jointed rock.

Insight into the fracture evolution behavior of pre‐flawed hollow‐cylinder granite under multi‐stage increasing‐amplitude cyclic loads: A lab‐scale testing

AbstractThe structural deterioration and associated fracture evolution behavior of pre‐flawed hollow‐cylinder granite subjected to multi‐stage increasing‐amplitude (MSIA) cyclic loads are studied herein. The influences of rock structure on volumetric deformation, damage accumulation, energy dissipation, and failure pattern were investigated. It is shown that the volumetric deformation is relatively large for rock having high flaw angle, and it is the minimum and maximum for rock having a 10° and 70° flaw angle. A damage evolution model that can describe a first fast and then steady damage propagation was proposed based on the irreversible axial strain. Much energy needs to be consumed to drive crack propagation and hole collapse for rock having high angle flaws. A series of 2D computed tomography (CT) images reveal the different crack network pattern and how it is affected by the rock structure. A more complicated crack network is found for rock having a high flaw angle.

STUDY ON EVOLUTION MODEL OF GASEOUS DETONATION WAVE IN PERIODIC INHOMOGENEOUS MEDIUM

The initiation, steady propagation and failure mechanism of gaseous detonation wave in periodic inhomogeneous media are very complex, and many physical mechanisms are still unclear, which is an active topic in detonation physics. Numerical simulation of propagation of gaseous detonations in the inhomogeneous medium is studied by using the reactive Euler equations coupled with a two-step chemical reaction model. The inhomogeneity is generated by placing artificial temperature perturbations with different wavelengths and amplitudes. The influence of temperature disturbance with different wavelength and amplitude on the structure of wave front is analyzed. The results show that, the transition of ZND detonation to cellular detonation under artificial temperature disturbance is mainly controlled by two competitive factors: one is the intrinsic instability of detonation wave, the other is the wavelength and amplitude of artificial disturbance, the former is the internal factor, the latter is the external factor. The existence of artificial temperature disturbance delays the evolution of ZND detonation to cellular detonation by suppressing the development of shear wave, and the increase of internal instability can slow down this delay phenomenon. This shows that the artificial temperature disturbance can restrain the development of cell instability in a certain range, but it cannot stop the process. The discontinuity of temperature makes the detonation wave front more distorted, which leads to the existence of a weak triple-wave structure near the shear wave, which is, the artificial disturbance increases the inherent instability of detonation wave and changes the propagation mechanism of detonation wave front. The propagation of detonation and the instability of detonation are restrained by the artificial temperature disturbance with large amplitude. The formation of detonation front cellular structure depends on the artificial temperature disturbance and its own instability.

Experimental investigation of immersed granular collapse in viscous and inertial regimes

This paper presents an experimental investigation of immersed granular collapse with an initially dense packing, mainly focusing on the collapse characteristics of different flow regimes and the influence of the initial aspect ratio. A novel experimental setup and imaging method are introduced to simultaneously observe the motion of the particles and the fluid. The collapse dynamics, including the collapse acceleration, steady propagation velocity, and collapse duration, are analyzed based on the front propagation. It is found that the collapse procedures in the inertial and viscous regimes differ significantly, with the transitional regime possessing some unique characteristics of both. The inertial regime exhibits a faster collapse process, sharper final deposition, and a depression near the right wall in the case of high columns. The viscous regime collapses from the upper-left corner, from where particles drop to the bottom and form the flow front in advance of the particles initially at the bottom, and exhibits a triangular final deposition. The inertial regime exhibits swirling fluid motion, which helps the granular transport, whereas the fluid flow in the viscous regime mainly follows the granular flow. The collapse regime characteristics are more pronounced in higher columns.

Investigation of crack growth in CFRP-concrete interface under fatigue loading

In this paper, the fatigue crack growth behavior along the interface between carbon fiber reinforced polymer (CFRP) sheets and concrete induced by intermediate flexural crack in CFRP-sheet strengthened concrete beams was studied, both experimentally and theoretically. The fatigue crack growth behavior of the intermediate crack-induced debonding was investigated by modified beam tests. The major variables considered in the test were loading amplitude, concrete strength, and the width ratio of CFRP-sheet to concrete. Test results indicated that three stages were observed in the evolution of CFRP-concrete interfacial crack propagation under cyclic loading, including debonding initiation, steady propagation, and instability propagation. Furthermore, the fatigue crack propagation rate grew with the increase of the load level, concrete strength, or the width ratio of CFRP-sheet to concrete, and was reduced as load cycles increased in the steady propagation stage due to the interfacial friction existed in the debonding zone. Based on the test results and fracture mechanic method, a crack growth prediction model, which considered the effects of concrete strength and width ratio of CFRP-sheet to concrete, was proposed for predicting the whole crack growth process and fatigue life of intermediate crack-induced debonding of CFRP-concrete interface under cyclic loading. The predicting results using this proposed model agreed well with test results.

Shear fracture performance of the interface between ultra-high toughness cementitious composites and reactive powder concrete

This study used unnotched compression tests and digital image correlation technology to analyze the influence of two different casting intervals and three different roughness conditions on the fracture toughness of the interfaces between ultra-high toughness cementitious composite (UHTCC) and reactive powder concrete (RPC). UHTCC exhibits pseudo-strain-hardening responses and multi-cracking behaviors, and the most notable characteristic of RPC is its dense microstructure. The results show that the complete interfacial shear fracture process included three stages: crack initiation, steady crack propagation and unsteady crack propagation. A double-K crack propagation criterion for interfacial shear fracture of composite structures was proposed by introducing two parameters: initial and unstable fracture toughness. After introducing interfacial roughness via the scratch method, the unstable fracture toughness decreased. The 24-h casting interval group had a lower initial fracture toughness and higher unstable fracture toughness than the 2-h group. The unstable fracture toughness of all the composite specimens exceeded that of C60 concrete, indicating that they had excellent resistance to interfacial shear fracture.

Bifurcations of drops and bubbles propagating in variable-depth Hele-Shaw channels

The steady propagation of air bubbles through a Hele-Shaw channel with either a rectangular or partially occluded cross section is known to exhibit solution multiplicity for steadily propagating bubbles, along with complicated transient behaviour where the bubble may visit several edge states or even change topology several times, before typically reaching its final propagation mode. Many of these phenomena can be observed both in experimental realisations and in numerical simulations based on simple Darcy models of flow and bubble propagation in a Hele-Shaw cell. In this paper, we investigate the corresponding problem for the propagation of a viscous drop (with viscosity nu relative to the surrounding fluid) using a Darcy model. We explore the effect of drop viscosity on the steady solution structure for drops in rectangular channels or with imposed height variations. Under the Darcy model in a uniform channel, steady solutions for bubbles map directly on to those for drops with any internal viscosity nu ne 1. Hence, the solution multiplicity predicted for bubbles also occurs for drops, although for nu >1, the interface shape is reversed with inflection points appearing at the rear rather than the front of the drop. The equivalence between bubbles and drops breaks down for transient behaviour, at the introduction of any height variation, for multiple bodies of different viscosity ratios and for more detailed models which produce a more complicated flow in the interior of the drop. We show that the introduction of topography variations affects bubbles and drops differently, with very viscous drops preferentially moving towards more constricted regions of the channel. Both bubbles and drops can undergo transient behaviour which involves breakup into two almost equal bodies, which then symmetry break before either recombining or separating indefinitely.

Combustion/decomposition characteristics of 3D-printed Al/CuO, Al/Fe2O3, Al/Bi2O3 and Al/PTFE hollow filaments

In recent decades, the preparation of various metastable intermolecular composites (MICs) has been widely reported in pursuit of excellent reactivity and safety. However, there is still relatively little research on structural energetic materials (EMs) through 3D printing of MICs inks. In this work, the hollow filaments with different MICs formulas were prepared by 3D printing using a core-shell nozzle. The morphology, thermal decomposition and gas-generation performance of the filaments were characterized, and the different combustion stages of the filaments were analyzed. The results show that the hollow filaments exhibit shorter unsteady combustion time and significantly increased steady flame propagation rate compared with solid filaments. For the hollow filaments of Al/CuO/F2311 formula (15 wt % of F2311), the unsteady combustion time is as low as 0.65 ms, and the steady flame propagation rate reaches 206.936 g/s. Thermal analysis and constant-volume combustion tests show that Al/CuO/F2311 formula provides the lowest thermal decomposition onset temperature (288 °C) and the best gas-generation performance (peak pressure: 0.191 MPa, pressurization rate: 12.337 MPa/s) compared with other composites.

Application of Smooth Particle Hydrodynamics to Particular Flow Cases Solved by Saint-Venant Equations

Smoothed particle hydrodynamics (SPH) is a Lagrangian mesh free particle method which has been developed and widely applied to different areas in engineering. Recently, the SPH method has also been used to solve the shallow water equations, resulting in (SPH-SWEs) formulations. With the significant developments made, SPH-SWEs provide an accurate computational tool for solving problems of wave propagation, flood inundation, and wet-dry interfaces. Capabilities of the SPH method to solve Saint-Venant equations have been tested using a SPH-SWE code to simulate different hydraulic test cases. Results were compared to other established and commercial hydraulic modelling packages that use Eulerian approaches. The test cases cover non-uniform steady state profiles, wave propagation, and flood inundation cases. The SPH-SWEs simulations provided results that compared well with other established and commercial hydraulic modeling packages. Nevertheless, SPH-SWEs simulations experienced some drawbacks such as loss of inflow water volume of up to 2%, for 2D flood propagation. Simulations were carried out using an open source solver, named SWE-SPHysics.

Strange wave formation and detonation onset in narrow channels

Experiments are conducted in a smooth 10 × 10 mm square cross-section, 1-m long channel, closed at the ignition end and open at the other end. Simultaneous two-direction schlieren visualization is used to investigate the three-dimensional dynamics of transition to detonation for a stoichiometric H2–O2 mixture. Results show the existence of two distinct structures before detonation onset: (i) asymmetric, composed of an oblique shock trailed by a flame, that runs preferentially along the wall, and seems to get ignited inside the boundary layer developed by the precursor shock; (ii) symmetric, referred to as strange wave in literature, propagating roughly at the speed of sound in combustion products. The combined effect of shock induced preheating and viscous heating near walls seem to be responsible for the formation of the complex flame-shock interactions observed. A simple thermodynamic analysis applied to the strange wave using the experimentally measured wave speed yield a pressure ratio of ~ 15 during its steady propagation; furthermore, an estimate of the total energy losses required to thermodynamically realize such propagation regime revealed that approximately half of the energy released by combustion should be dissipated (i.e. momentum and heat losses). Finally, simultaneous two-direction optical access allows to map the exact location of detonation onset, showing that 78 % of cases exploded in corners, highlighting the role of corner flows and boundary layers in transition to detonation at this scale.

Numerical Study on the Fracture Properties of Concrete Shield Tunnel Lining Segments

Shield tunnel lining structure is usually under very complex loading conditions in the underground space. As a kind of the common concrete structures, any defect in the tunnel lining segment may deteriorate its bearing capacity and even cause severe disasters. Three-dimensional numerical models of shield tunnel lining segments with initial cracks are built using the Symmetric Galerkin Boundary Element Method- (SGBEM-) Finite Element Method (FEM) Alternating Method. The cracking load and ultimate load of the tunnel segments are obtained, and crack propagation under fatigue load is also simulated by employing the Paris Fatigue Law. Results show that loading eccentricity has a very large influence on the bearing capacity of the cracked lining segment; the larger the loading eccentricity, the smaller the bearing capacity. Deformation and damage of the lining segment show obvious phases, which consist of the initial crack, cracking stage, steady crack propagation, unsteady crack propagation, and eventual failure.

Eliminating injection and memory effects in bubble rise experiments within yield stress fluids

Bubbles rising steadily in Carbopol often have an inverted teardrop shape with pointed tail, in contrast to steady bubble rise computations using simple yield stress fluid models. The cause of the pointed tail is suspected to be viscoelasticity, but another possibility is that the tail arises during the bubble formation and the shape is retained via some form of fluid memory effect (elastic, thixotropic or yield stress). Here we present results of a study in which we eliminate all possibility of memory effects using a multi-layered experimental design, but still find the pointed tail in steady bubble propagation. Thus, the tail shape can only result from a combination of the rheology and steady fluid deformation around the rising bubble. Further experiments show that the same steady shapes are found for quite different initial bubble shapes. • Removing the effect of the injection method on the steady-state propagation of bubbles in Carbopol. • Effect of the initial shape of bubbles on their steady propagation in Carbopol. • Controlling the size of bubbles by changing the yield stress of the host fluid. • Bubble rise through a three-layered yield stress–Newtonian-yield stress fluid system.

A Study on the Mechanical Properties and Bursting Liability of Coal-Rock Composites with Seam Partings

Geological tectonic movements, as well as complex and varying coal-forming conditions, have led to the formation of rock partings in most coal seams. Consequently, the coal in coal-rock composites is characterised by different mechanical properties than those of pure coal. Uniaxial compression tests were performed in this study to determine the mechanical properties and bursting liability of specimens of coal-rock composites (hereinafter referred to as “composites”) with rock partings with different dip angles θ and thicknesses D. The results showed that as θ increased, the failure mode of the composite changed from tensile and splitting failure to slip and shear failure, which was accompanied by a decrease in the brittleness of the composite and an increase in its ductility as well as a decrease in the extent of fragmentation of the coal in the composite. Additionally, as θ increased, the uniaxial compressive strength σu, elastic modulus E, and bursting energy index Ke of the composite decreased. The rock parting in the composite was the key area in which elastic energy accumulated. As D increased, σu, E, and Ke of the composite increased. In addition, as D increased, the ductility of the composite decreased, and the brittleness and extent of coal fragmentation in the composite increased. Notably, the curve for the cumulative acoustic emission (AE) counts of the composite corresponding to the stress-strain curve could be divided into four regimes: pore compaction and closure, a slowly ascending linear elastic section, prepeak steady crack propagation, and peak unsteady crack propagation. The experimental results were used to propose two technologies for controlling the stability of coal-rock composites to effectively ensure safe and efficient production at working faces.

Modelling finger propagation in elasto-rigid channels

Abstract

Modeling interaction of ultrashort pulses with ENZ materials

In this work, the split-step Fourier method for beam propagation is used to investigate the interaction of ultra-short pulses with epsilon-near-zero materials. The propagation of pulses is governed by the nonlinear Schrödinger equation (NLSE) containing dispersion, gain-bandwidth, self-phase modulation, self-steepening, and absorption parameters. It is found that the intensity profile of the pulse is broadened and the phase of the pulse is shifted by dispersion phenomena. The gain/loss related to the imaginary part of the refractive index causes an increase or decrease in intensity and pulse edge effects. These effects do not favor the steady propagation of the pulse. The self-phase modulation is not noted to appreciably affect the intensity pulse profile. The self-steepening modifies the phase and energy of the pulse during propagation, as well as absorption, which influences the losses by both the linear and nonlinear effects.

Bending fatigue behavior of thin Zr61Ti2Cu25Al12 bulk metallic glass beams for compliant mechanisms application

In this work, bending fatigue behavior of thinner Zr61Ti2Cu25Al12 (ZT1) BMG beams with thicknesses of 500 μm and 100 μm were investigated with three-point bending (3PB), to evaluate the reliability and safety of this potentially material used in compliant mechanisms under cyclic bending load. Fatigue endurance limits (FELs) of ZT1 beams with thicknesses of 500 μm and 100 μm were determined to be 470 MPa, and ∼0.3 of its tensile strength. Fatigue life and FEL of ZT1 beams in bending are substantially independent of the beam thickness, in the scale from 500 μm down to 100 μm. Fatigue cracks of all ZT1 beams initiated at the extrinsic microvoids, either indirectly derived from surface scratches during mechanical polishing or originated from as-cast process. However, fatigue crack propagation behavior is highly related to the magnitude of cyclic stress level. By interrupted fatigue tests, larger proportion about 60–70% of fatigue life was spent on crack propagation under high stress level, while crack initiation occupied larger proportion about 80–85% under low stress level. The medium stress level of about 590 MPa almost shared the crack-initiation life and crack-propagation life. In addition, there are two crack deflection mechanisms during cracks steady propagation stage. One mechanism is crack deflection along the interacted shear bands ahead of crack-tip, the other one is crack “jump” from one shear band to another shear band at a certain angle. These two mechanisms alternate dominate the crack propagation process, generating typical staircase-like crack propagation trajectory. Fatigue endurance limits of ZT1 beams in the form of either stress amplitude or strain amplitude are superior to traditional candidate materials in the field of compliant mechanisms, showing that the better reliability and larger deflection deformation can be achieved for flexible members made by ZT1 BMG even under cyclic loading.

An analytical solution for the inverted four-point bending test in orthotropic specimens

Analytical solutions are derived for interfacial energy release rate and mode mixity angle in the inverted four-point bending test. In the test, the loads applied in the classical four-point bending test are inverted so that the crack faces come into contact at the midspan and mode mixity with an important mode II component is produced. The contact forces are evaluated by employing a beam model and imposing that the two delaminated arms undergo the same deflection at the contact point. Friction is accounted for within an approximate Coulomb model. Both Timoshenko and Euler-Bernoulli beam theories are applied and local 2D effects due to near tip deformations are introduced through suitable analytically derived crack tip root rotations and displacements. The results are verified by comparison with finite element results. The model accurately estimates energy release rate and mode mixity angle in orthotropic specimens, also for short/intermediate delaminations, and defines the minimum length of the crack ensuring a steady state propagation under a constant value of energy release rate and mode mixity. Steady state propagation under different mode mixity conditions is demonstrated by varying the relative thickness of the delaminated arms.

Steady dynamic buckle propagation simulation of confined pipelines under external pressure by user defined elements in ABAQUS

This paper simulates steady dynamic buckle propagation of confined linearly elastic pipelines under external pressure by developing a user-defined-element in Abaqus allowing the simulation of dynamic propagation through conventional static step. The simulation is separated into two parts: the static indenting step to deform a pipeline locally and the steady dynamic propagation step to obtain the relationship between the deformation profile and propagation speed.

Anisotropy of crack initiation strength and damage strength of coal reservoirs

Abstract The crack volume strain method and acoustic emission (AE) method are used to analyze the anisotropy of the crack initiation strength, damage strength, the failure mode and the AE characteristics of coal reservoir. The results show that coal reservoirs show obvious anisotropic characteristics in compressive strength, cracking initiation strength and damage strength. The compressive strength of coal reservoirs decreases with the increase of bedding angle, but the reservoirs with bedding angles of 45° and 90° differ little in compressive strength. The crack initiation strength and damage strength decrease first and then increase with the increase of bedding angle. The crack initiation strength and damage strength are the highest, at the bedding angle of 0°, moderate at the bedding angle of 90°, and lowest at the bedding angle of 45°. When the bedding angle is 0°, the failure of the coal reservoirs is mainly steady propagation of large-scale fractures. When the bedding angle is 45°, one type of failure is caused by steady propagation of small-scale fractures, and the other type of failure is due to a sudden instability of large-scale fractures. When the bedding angle is 90°, the failure is mainly demonstrated by a sudden-instability of small-scale fractures. Compared with the cumulative count method of the AE, the cumulative energy method is more suitable for determining crack initiation strength and damage strength of coal reservoirs.