Cellular detonation diffraction in gas–particle mixtures

Diffraction of cellular heterogeneous detonation out of a channel into open half-space in a mixture of aluminum particles and oxygen is investigated numerically. The flow is found to be very similar to gas detonation diffraction. The detonation weakening behind the step results in combustion front deceleration and decoupling from the leading shock wave. Subsequent re-initiation takes place in a transverse wave. New transverse waves are generated along the expanding front. The computations that were performed show that the critical number of cells is several times less than that for gases. This is confirmed by theoretical estimates based upon the Mitrofanov–Soloukhin approach.     

Oil–water flows through sudden contraction and expansion in a horizontal pipe – Phase distribution and pressure drop

In this paper, change of flow patterns during the simultaneous flow of high viscous oil and water through the sudden contraction and expansion in a horizontal conduit has been studied. It is noted that these sudden changes in cross-section have a significant influence on the downstream phase distribution of lube oil–water flow. The observation suggests a simple technique to establish core flow as well as a way to prevent pipe wall fouling during the transportation of such oil. A number of interesting differences have been noted during low viscous oil–water flow through the same test rigs. While several types of core annular flow are observed for the former case, a wider variety of interfacial distribution characterizes kerosene–water systems. The pressure profiles during the simultaneous flow of lube oil and water through the sudden contraction and expansion are also studied and compared with low viscous oil–water flows. The pressure profiles are found to be independent of liquid viscosity and the loss coefficients are observed to be independent of flow patterns in both the cases.     

Measurement and chemical kinetic model predictions of detonation cell size in methanol–oxygen mixtures

In this study, detonation cell sizes of methanol–oxygen mixtures are experimentally measured at different initial pressures and compositions. Good agreement is found between the experiment data and predictions based on the chemical length scales obtained from a detailed chemical kinetic model. To assess the detonation sensitivity in methanol–oxygen mixtures, the results are compared with those of hydrogen–oxygen and methane–oxygen mixtures. Based on the cell size comparison, it is shown that methanol–oxygen is more detonation sensitive than methane–oxygen but less sensitive than hydrogen–oxygen.     

Transient phenomena in one-dimensional compressible gas–particle flows

The transient behavior of compressible gas– particle flows produced in shock tubes with particle-laden driver section is studied. Particular attention is focused on the time scales with which the solution approaches the equilibrium state. Theoretical estimates indicate that the gas and particle contact surfaces equilibrate first, followed by the shock wave, and finally by the expansion fan. The estimates are in good agreement with numerical simulations. The simulations also show that the approach to equilibrium condition of the shock speed is non-monotonic (monotonic) if the mass fraction of particles initially located in the driver section is below (above) a particle-diameter dependent critical value. For the speed of the particle contact surface, the reverse trends are observed.      

Order and disorder in particle–liquid flows in a pipe

The spherical expanded polystyrene particle–oil two-phase flow in a vertical pipe was used to simulate the dispersed phase distribution in laminar bubbly flows. A three-dimensional particle image tracking technique was used to track the particles in the flow to study the ordered structure of dispersed phase distribution and its transition to disorder. The ordered structures behaved as particle strings aligned in the flow direction as induced by the flow shear. The structures were quite durable in high liquid velocity flows and dispersed gradually as the liquid velocity decreased. In lower velocity flows, the particles tended to form clusters in the horizontal direction, as predicted by potential theory for spherical bubbles rising in a quiescent inviscid liquid and as observed in experiments on non-shear bubbly water flows.     

Shock–vortex interactions in a soap film

This work experimentally visualizes the interaction of a quasi-one-dimensional moving shock wave with a two-dimensional vortex in a soap film for the first time. A vertical soap film shock tube was used to generate a quasi-one-dimensional moving shock wave and a NACA-0012 airfoil intruded into the soap film was towed to shed the starting vortex. The interesting interaction phenomena were then visualized using a traditional high-speed flash photography. The concentration of sodium dodecyl sulfate (SDS) used was 0.5 CMC (critical micelle concentration) to keep the surfactant molecules behave as two-dimensional gases. A sequence of pictures shows that the shock is distorted non-symmetrically as it passes through the spiral vortex flow field and the vortex structure is compressed in the direction normal to the shock. These flow features observed in soap films are qualitatively similar to their counterparts in gases. In addition, the visualization of the interactions of a quasi-one-dimensional moving shock wave with a Kármán vortex street are presented.      

Shock wave bifurcation in convergent–divergent channels of rectangular cross section

This work addresses two- and three-dimensional turbulent flow in simple channels, modeling the air intakes of rectangular cross section. Flow regimes with a supersonic free stream and supersonic velocities at the throat or immediately downstream of the throat are considered. Bifurcations of the shock wave arising ahead of the cowl are studied numerically. Solutions of the Reynolds-averaged Navier–Stokes equations are obtained with a finite-volume solver of second-order accuracy on fine computational meshes. The solutions reveal jumps of the shock leg position with variations of the free-stream Mach number. The dependence of the shock position on the cowl slope and streamwise location of the throat is examined.     

Roll waves in a gas–liquid medium

The onevelocity motion of a gas–liquid medium with a variable mass fraction of the gas phase, which is equilibrium in terms of phase pressures, is considered. The existence conditions of nonlinear periodic wave packets similar in structure to roll waves in open inclined channels are found. The structure of travelling waves in the medium with continuous addition of energy to the gas phase is studied.     

Specific features of unsteady exhaustion of a gas–particle medium into vacuum

Results of an analysis of two-dimensional unsteady exhaustion of a one-velocity gas–particle medium into vacuum for limiting equilibrium cases of heat transfer between the phases are reported. Domains of existence of a one-dimensional Riemann wave and a lateral expansion wave, as well as boundaries of the flow expansion region are determined. Under thermal equilibrium conditions, the reverse flow is found to occupy a large domain extending beyond the boundaries defined by angles of expansion for an ideal gas and for a gas–particle mixture with thermally insulated phases. Exhaustion of a nonequilibrium (in terms of velocities and temperatures) two-phase medium into vacuum is numerically simulated. It is demonstrated that a barrel-shaped structure with wave expansion of the gas and a combined discontinuity in the expanding gas–particle mixture is formed.     

Effect of coal particle swarm properties on the fluidization characteristics and coal beneficiation in a dense-phase gas–solid fluidized bed

This paper analyzes the influence of different coal mass fraction in an air dense medium fluidized bed (ADMFB). The effect of the low density particles layer on heavy sedimentation increased with increasing material layer thickness. The thickness of the low density particles layer also affected the final settling time of the high density particles. Increasing the thickness of the low density particles layer by Δh provoked an increase in the settling of high density particles that was related to their diameter (Δh/D). The pressure gradient across the bed was lower than that observed for the control experiment, which had only the dense material, owing to a decrease in the pressure gradient in Zones 1 and 5 (at the top and bottom of the bed, respectively). Introducing different coal sizes resulted in different fluidization environments, particle accumulation layers, and changes to the surrounding zone. However, the influence of the coal particles on the local bed characteristics was related to its concentration. The feeding mass fraction of 6–13 mm size and 13–25 mm size coal should be limited to10% and 13%, respectively. The ranges of possible deviation were found to be 0.08–0.15 and 0.07–0.10 for the respective samples.     

Multi-scale particle dynamics of low air velocity in a horizontal self-excited gas–solid two-phase pipe flow

The particle fluctuation velocities of a horizontal self-excited gas–solid two-phase pipe flow with soft fins near MPD (minimum pressure drop) air velocity are first measured by high-speed PIV in the acceleration and fully-developed regimes. Then orthogonal wavelet multi-resolution analysis and power spectrum are used to reveal multi-scale characteristics of particle fluctuation velocity. It is observed that the pronounced peaks of the spectra of axial and vertical fluctuation velocities appear in the range of low frequency near the bottom of pipe. These peaks of spectra become larger and their frequencies decrease by using fins. In the range of low frequencies (3–25 Hz), the wavelet components of the fluctuating energy of axial particle velocity make the main contribution accounting for 87% and 93% respectively for non-fin and using fins near the bottom of pipe. In the range of relatively high frequency (50–400 Hz), however, the wavelet components of using fins, accounting for about 49%, become smaller than that of non-fin, accounting for about 72%, in the suspension flow regime near the top of pipe. The skewness factor of axial particle fluctuation velocity indicates that the wavelet components follow the Gaussian probability distribution as the central frequency decreases.     

Measurement on particle rotation speed in gas–solid flow based on identification of particle rotation axis

When a two-dimensional (2D) imaging system is used to visualize particle motion in a 3D gas–solid flow, the particle rotation speed was found extremely difficult to be accurately measured due to the fact that the direction of rotation axis was usually random and hard to be distinguished. The paper presents a method to calculate the particle rotation speed from particle images based on the identification of its rotation axis using two or more characteristic points on its surface. The idea was analyzed and realized in a mathematical way and based on which a calculation program was given. The measurement method was verified with an experiment using a small sphere with known rotation axis and rotation speed. The effects of several factors, including the direction of the particle rotation axis, the particle image resolution, the types and positions of characteristic points, etc., on the measurement error are discussed. The error is found to be acceptable for most cases. The measurement method was finally applied to those small glass beads in a real 3D gas–solid flow inside a cold circulating fluidized bed (CFB) riser, which indicates that the problems of 2D imaging system applying to 3D particulate system could be solved by using this mathematical method.     

Apparent viscosity of mixed particle system in pulsed gas–solid separation fluidized bed

The apparent viscosity reflects the resistance of the fluidized medium in the bed to the beneficiation particles, which directly affects the separation time and mismatch content. So, the falling-ball method was used to measure the apparent viscosity of a binary medium in a pulsed fluidized bed by varying the gas velocity, pulsation frequency, and fine particle content. The results show that with increasing gas velocity and fine particle content, the apparent viscosity of the bed gradually decreased, whereas it first decreased and then increased with pulsation frequency increasing and achieved a minimum value in the range of 4–6 Hz. Within limits, the adjustment of gas velocity and fine content can effectively reduce the apparent viscosity and improve the separation process. A model for predicting the apparent viscosity in a pulsation separation fluidized bed was established with good accuracy.     

Numerical study of gas–solid two-phase flow and erosion in a cavity with a slope

Gate valve is mainly used to turn on or turn off the pipeline in pneumatic conveying. When the gate valve is fully open, the particles are easy to collide with the cavity rear wall and enter into the cavity, resulting in particles’ accumulation in the cavity. The particles in cavity will accumulate between the cavity bottom and the flashboard bottom wall and prevent the gate from turning off normally. Meanwhile, the particles’ collision with cavity rear wall will cause serious erosion. Both the particles’ accumulation and erosion will cause the poor sealing of the gate valve, further resulting in the leakage of the pipeline system. To reduce the particles’ accumulation in cavity and erosion on cavity when the gate valve is fully open, we simplify the gate valve into a cavity structure and study it. We find that adding a slope upstream the cavity can effectively reduce the particles’ accumulation in the cavity and the erosion on the cavity rear wall. In this work, Eulerian–Lagrangian method in commercial code (FLUENT) was used to study the gas–solid two-phase flow and erosion characteristics of a cavity with a slope. The particle distribution shows that the particles with Stokes number St = 1.3 and St = 13 cannot enter the cavity due to the slope, but the particles with St = 0.13 enter the cavity following the gas. For St = 13, the particles collide with the wall many times in the ideal cavity. Erosion results show that the slope can transfer the erosion on cavity rear wall to the slope and reduce the maximum erosion rate of the wall near the cavity to some degrees.     

Two-cell detonation: losses effects on cellular structure and propagation in rich H2–NO2/N2O4–Ar mixtures

Detonation experiments in H₂–NO₂/N₂O₄–Ar mixtures (Equivalence ratio 1.2 and initial pressure lower than 0.1 MPa) confined in a tube of internal diameter 52 mm reveal two propagation regimes depending on initial pressure: (1) a quasi-CJ regime is observed along with a double cellular structure at high pressures; (2) at lower pressures, a low velocity detonation regime is observed with a single structure. Transition between this two regimes happens when the spinning detonation of the larger cell vanishes. Each detonation regime is characterized by velocity and pressure measurements and cellular structure records. Coherence between all experimental data for each experiment leads in assumption that losses are responsible for the transition between one regime to another. In a second part, we study such behaviour for a two-step mixture through numerical simulations using a global two-step chemical kinetics and a simple losses model. Numerical simulations qualitatively agree with experiments. Both detonation regimes with their own cellular structures are reproduced.     

Squeeze-flow and vane rheometry of a gas–liquid foam

The rheology and slip of a dry shaving foam are investigated using squeeze-flow and rotating-vane methods. Constant-force squeeze flow between planar surfaces is used to study the effect of surface roughness on slip and to obtain the yield stress. Non-slip vane measurements are used to obtain the linear shear viscosity and elasticity at small strains, and the yield stress and strain at large strains. Data are compared with the small-strain Maxwell and Kelvin–Voigt linear-viscoelastic models. An apparent dependence of the yield stress and elasticity on the rotational speed of the vane is shown to result from time-dependent rheological parameters as the foam ages. The effect of viscosity in the pre-yield region may give an erroneous identification of yield.     

Differentially weighted direct simulation Monte Carlo method for particle collision in gas–solid flows

In gas–solid flows, particle–particle interaction (typical, particle collision) is highly significant, despite the small particles fractional volume. Widely distributed polydisperse particle population is a typical characteristic during dynamic evolution of particles (e.g., agglomeration and fragmentation) in spite of their initial monodisperse particle distribution. The conventional direct simulation Monte Carlo (DSMC) method for particle collision tracks equally weighted simulation particles, which results in high statistical noise for particle fields if there are insufficient simulation particles in less-populated regions. In this study, a new differentially weighted DSMC (DW-DSMC) method for collisions of particles with different number weight is proposed within the framework of the general Eulerian–Lagrangian models for hydrodynamics. Three schemes (mass, momentum and energy conservation) were developed to restore the numbers of simulation particle while keeping total mass, momentum or energy of the whole system unchanged respectively. A limiting case of high-inertia particle flow was numerically simulated to validate the DW-DSMC method in terms of computational precision and efficiency. The momentum conservation scheme which leads to little fluctuation around the mass and energy of the whole system performed best. Improved resolution in particle fields and dynamic behavior could be attained simultaneously using DW-DSMC, compared with the equally weighted DSMC. Meanwhile, computational cost can be largely reduced in contrast with direct numerical simulation.     

Wavelet analysis on particle dynamics in a horizontal air–solid two-phase pipe flow at low air velocity

High-speed particle image velocimetry (PIV) is first used to measure two components of the fluctuating particle velocities for different particle sizes and solid mass flow rates at low air velocity in a horizontal pipe. Then, the continuous wavelet transform and orthogonal wavelet multi-resolution techniques are employed to analyze and decompose the fluctuating particle velocities to provide both quantitative and qualitative information on the particle fluctuation velocity of various frequencies. It is revealed that the fluctuating energy of axial particle velocity is mainly contributed from the wavelet components of low frequency, accounting for about 84%, near the bottom part of the pipe cross-section. However, the contribution to the fluctuating energy of vertical particle velocity accounts for about 82% from the wavelet components of high frequency. The auto-correlation analysis suggests a quasi-periodical large-scale axial particle fluctuating velocity. On the other hand, the spatial correlation analysis indicates that the low-frequency components of the axial particle velocity exhibit a large correlation near the bottom part of the pipe cross-section. From the probability density function (PDF) distribution, it is found that the low-frequency components of the axial particle velocity exhibit larger fluctuation, and this fluctuation reduces as the frequencies increase near the bottom part of the pipe cross-section. Near the top part of the pipe cross-section, however, a larger fluctuating axial particle velocity appears in the high-frequency range.