Hydrodynamics in a jet bubbling reactor: Experimental research and mathematical modeling

The radial distribution of liquid velocity in the axial direction of a jet bubbling reactor has been measured by experimentation. Three different typical flow structures controlled by liquid jet, gas bubbling, and liquid jet coupled with bubbling are observed. A tank in series model is established on this basis. Calculated values in each region are in good agreement with measured values in jet, bubbling, and wall effect controlled areas. Axial flow rate, radial exchange rate, and jet controlled volume η are analyzed from energy input aspect under different u_g and u_j. Simulation results indicate that under the synergetic action of the liquid jet and gas bubbling effect, jet controlled area exhibits a “spindle” structure, and its size decreases with the increase of u_g. When gas input power occupies about 67% of total energy consumption, the best synergy of liquid jet and gas bubbling is obtained. © 2017 American Institute of Chemical Engineers AIChE J, 64: 1814–1827, 2018     

On the Break-Up of Shaped Charge Jets

It is shown from dimensional arguments that the semi-empirical jet break-up formula of Hirsch⁽¹⁾ is consistent with physical models characterized by ideal plasticity (yield stress σ₀), the material initial density (ϱ₀), strain rate (η₀), and jet radius (r₀). Similar arguments applied to a one-dimensional jet stretching model yields the existence of a maximum unstable perturbation wavelength, and fixes its value to within a numerical constant. Within the class of physical models considered the plastic velocity appearing in the Hirsch formula, the incremental velocity between successive fragments of a particulated jet, and the velocity (σ₀/ϱ₀)^1/2 are all related, as originally conjectured by Hirsch.     

Influence of Drift Velocity and Distance Between Jet Particles on the Penetration Depth of Shaped Charges

The penetration depth of shaped charge jet into target is strongly affected by the stand‐off. The penetration process terminates even when the jet velocity is still high, and the penetration capability of jet particles degrades after jet breakup at a large stand‐off. This work presents an analytical model to describe the radial drift velocity and distance between jet particles, which leads to decreased penetration depth. The results show that jet particles with low drift velocity impact the crater wall easily. Furthermore, the jet particles cannot reach the crater bottom to increase depth because the crater diameter generated by the jet is quite small. Moreover, the distances between jet particles also play an important role in penetration depth under the influences of strain hardening of target, as well as tumbling and dispersion of jet particles. The radial drift velocity and distance between jet particles are investigated by applying the model to non‐precision charge and precision charge penetrations into target at different stand‐offs. The cutoff jet velocity and cutoff penetration velocity also are determined based on the analytical model. With increased stand‐off, the cutoff jet velocity increases, and the cutoff penetration velocity is almost constant. This result is proven by a number of experiments. The stand‐off curves of two charges are also calculated, and results are in good agreement with experiments. The stand‐off curve can be determined with only two or three experiments using the proposed method. Notably, jet particles should have a slow drift velocity and great penetration capability after breakup for suitable shaped charge.     

Flame length scaling in a non-premixed turbulent diluted hydrogen jet with coaxial air

The effect of fuel composition on flame length was studied in a non-premixed turbulent diluted hydrogen jet with coaxial air. Because coaxial air entrained in a fuel stream enhances the mixing rate of fuel and air, it substantially reduces flame length. The observed flame length was expressed as a function of the ratio of coaxial air to fuel jet velocity and compared with a theoretical prediction based on the velocity ratio. Four cases of fuel mixed by volume were determined: 100% H₂, 80% H₂/20% N₂, 80% H₂/20% CO₂, and 80% H₂/20% CH₄. In addition, fuel jet air velocity and coaxial air velocity were varied in an attached flame region as u_F = 86-309 m/s and u_A = 7-14 m/s. In this study, we derived a scaling correlation for predicting the flame length in a simple jet with coaxial air using the effective jet diameter in a near-field concept. The experimental results showed that the visible flame length was in good relation to the theoretical prediction. The scaling analysis is also valid for diluted hydrogen jet flames with varied fuel composition, which affects flame length by varying the density of the fuel.     

Solid hold-up measurement in a jet-impactor assisted fluidized bed using gamma-ray densitometry

A jet-impactor assisted-fluidized bed (JIAFB) for continuous de-agglomeration of nanopowder agglomerates was presented in previous work. Therein, a jet caused agglomerates to impinge up an impactor, where they would break. However, efficient impactor positioning will be dictated by particle momentum: the product of solid concentration and velocity must be highest. Herein, the variation of solid hold-up was measured in a fluidized bed of Fe₂O₃ nanoparticles using gamma-ray densitometry. Behaviour was compared under minimum fluidization and bubbling regimes, over a wide range of jet velocities (0–200 m s⁻¹). A new line-decomposition approach allowed mapping local solid distribution across seven axial and five radial positions, tangibly demonstrating how increasing the gas velocity enhanced the fluidization quality by increasing axial solid diffusivity. Conversely, increasing jet velocity locally decreased solid hold-up in the jet-affected zone, and brought about inhomogeneities. With this information in hand, jet-to-impactor distance was optimized and validated experimentally.     

Hydrodynamic characteristics of jet-spouted beds

Jet-spouted beds characterised by high velocity gas jets (above 1.7 U_msl), and shallow bed depths H₀ of around 2 D₁ were investigated on laboratory scale beds and industrial scale beds and the results obtained thereof are correlated and presented in this work. Compared with the classical spouted beds, important differences in bed structure, solid movements and basic hydrodynamic characteristics were observed. The minimum spouting velocity, bed voidage and pressure drop during stabilized spouting are described in terms of dimensionless equations. Bed expansion was used as the basis for the classification of different jet-spouting regimes (incoherent spouting, fast spouting, pneumatic conveying) and changes in the slope of the bed expansion curve are correlated with regime changes. This classification could be useful in the optimization of industrial scale jet-spouted beds. A typically applicable regime of fast spouting was identified.     

Triggering of Detonation upon Flame Interaction with an Expansion Wave

The transition of a deflagration wave into an abruptly expanding part of a plane channel, where a quasisteady supersonic underexpanded jet of an unburned gas is formed, is studied for a propane–oxygen mixture using schlieren pictures. Two explosioninitiation modes (weak and strong) are registered. In the first case, almost instantaneous onset of the detonation wave occurs when the flame front enters the expanding section; the initial velocity of this wave is approximately 1.5 times the Chapman–Jouguet detonation velocity (D_CJ) and then decreases to a value corresponding to selfsustaining detonation. In the second case, the front velocity gradually increases from 0.4D _CJ to 1.0D _CJ. It is established that the starting pulse triggering the transformation of turbulent combustion to explosion and detonation regimes is generated by interaction of the flame front with expansion waves, which are elements of the structure of the initial section of the jet.     

Regimes of Unstable Expansion and Diffusion Combustion of a Hydrocarbon Fuel Jet

Results of an experimental study of hydrodynamics and diffusion combustion of hydrocarbon jets are presented. Various regimes of instability development both in the jet flame proper and inside the source of the fuel jet are considered. The experiments are performed for the case of subsonic gas jet expansion into the air from a long tube 3.2 mm in diameter in the range of Reynolds numbers from 200 to 13 500. The fuel is the propane–butane mixture in experiments with a cold jet (without combustion) and pure propane or propane mixed with an inert dilutant (CO₂ or He) for the jet flame. The mean velocity and velocity fluctuations in the near field of the jet without combustion are measured. Among four possible regimes of cold jet expansion (dissipative, laminar, transitional, and turbulent), three last regimes are investigated. The Hilbert visualization of the reacting flow is performed. The temperature profiles in the near field of the jet are measured by a Pt/Pt–Rh thermocouple. An attached laminar flame is observed in the transitional regime of propane jet expansion from the tube. In the case of combustion of C₃H₈ mixtures with CO₂ or with He in the range of Reynolds numbers from 1900 to 3500, the transitional regime is detected in the lifted flame. Turbulent spots formed in the tube in the transitional regime exert a significant effect on the flame front position: they can either initiate a transition to a turbulent flame or lead to its laminarization.     

Study of Jet Interaction with Interlayer Material of Bulging Armor

The paper presents an analytical approach for determining the effects of different properties of inert material of bulging armor sandwich on its efficiency against a shaped charge jet. The crater and shock wave parameters have been investigated. A theoretical relation for calculating the energy of the shock wave, produced by the jet impact, in the inert material has been derived on the basis of continuity of pressure and particle velocity at the interface of jet and inert material. This relation reveals that the higher the velocity of the jet the greater is the amount of energy in the shock wave. The energy of the shock wave also increases with increase of density and decrease of strength of the inert material. The shock energy has been found to further depend on the constants of equation of state of the inert material, (u_s=a+b u).     

Spray Characteristics of Two‐phase Feed Nozzles

The present study focuses on understanding the spray characteristics of a turbulent gas‐liquid jet (Re_liq = 24,000). Air and water are used as the test fluids. The angles of injection of the two phases upstream of the nozzle are varied (θ = 20°, 45° and 90°) and the effect of carrier gas on the droplet characteristics is are also investigated. The droplet size and velocity are non‐intrusively measured using a Phase‐Doppler Particle Analyzer (PDPA). In some respects, the characteristics of the present two‐phase jet are similar to those noticed in previous studies, while revealing some important differences. The centreline mean droplet velocities (15 ～ 20 m/s) increase in the initial region of the jet, attain a maximum and then decrease at larger distances from the nozzle exit. Most of the entrainment occurs at the tip of the nozzle and the jet expansion rate decreases significantly at distances where the spray velocity profiles become self‐similar. A Lorentz‐type fit has been used to model the normalized radial velocity profiles. The results indicate that the test configuration with θ = 45° may be beneficial for the scenario discussed.     

Numerical investigation of spinneret geometric effect on spinning dynamics of dry‐jet wet‐spinning of cellulose/[BMIM]Cl solution

In this study, the effect of spinneret geometry, including the entrance angle α of the entrance channel, the length L_s, and the diameter D₀ of the exit channel, on the spinning dynamics of dry‐jet wet‐spinning of cellulose/1‐butyl‐3‐methylimidazolium chloride ([BMIM]Cl) solution was simulated by using finite element method. Based on the mathematical model of dry‐jet wet‐spinning established in our previous work (Xia et al., Cellulose 2015, 22, 1963) the radial and axial profiles of velocity, pressure, and shear rate in the spinneret and the profiles of diameter, temperature, and tensile stress in the air‐gap region were obtained. From the simulated profiles, the effect of spinneret geometric parameters on the flow behavior and the pressure drop of polymer solution in the spinneret and the die‐swell ratio near the spinneret was discussed. The entrance angle α of the entrance channel mainly influences the flow behavior of polymer solution in the spinneret and the die‐swell effect near the spinneret. As the decrease of the entrance angle α of the entrance channel, the vortices in the spinneret could be removed and the die‐swell ratio decreases. The increase of the length L_s of the exit channel results in the increase of pressure drop in the spinneret and the decrease of the die‐swell ratio. It is also found that the increase of the diameter D₀ of the exit channel reduces the flow velocity of polymer solution and decreases the pressure drop in the spinneret at a constant mass flow rate. © 2016 Wiley Periodicals, Inc. J. Appl. Polym. Sci. 2016 , 133, 43962.     

The effect of CO2 dissolved in a diesel fuel on the jet flame characteristics

This paper is concerned with an experimental study of the jet diffusion flame characteristics of fuel containing CO₂. Using diesel fuel containing dissolved CO₂ gas, experiments were performed under atmospheric conditions with a diesel hole-type nozzle of 0.19 mm orifice diameter at constant injection pressure. In this study, four different CO₂ mass fraction in diesel fuel such as 3.13%, 7.18%, 12.33% and 17.82% were used to study the effect of CO₂ concentration on the jet flame characteristics. Jet flame characteristics were measured by direct photography, meanwhile the image colorimetry is used to assess the qualitative features of jet flame temperature. Experimental results show that the CO₂ gas dilution effect and the atomization effect have a great influence on the flame structure and average temperature. When the injection pressure of diesel fuel increased from 4 MPa to 6 MPa, the low temperature flame length increased from 18.4 cm to 21.7 cm and the full temperature flame length decreased from 147.6 cm to 134.7 cm. With the increase of CO₂ gas dissolved in the diesel fuel, the jet flame full length decreased for the jet atomization being improved greatly meanwhile the low temperature flame length increased for the CO₂ gas dilution effect; with the increase of CO₂ gas dissolved in the diesel fuel, the average temperature of flame increases firstly and then falls. Experimental results validate that higher injection pressure will improve jet atomization and then increased the flame average temperature.     

Turbulent flow study of an isothermal diesel spray injected by a common rail system

The flow characteristics of the intermittent spray of a single-hole diesel nozzle (d_o=0.11 mm) having a 1-spring holder, used in the injection system of heavy-duty diesel engines, were experimentally investigated. The hole belongs to a mini-sac 5-hole nozzle where only on hole is drilled. The mean velocity and turbulent characteristics of the diesel spray injected intermittently by a Common-Rail (CR) system into a pressurized vessel at room temperature were measured by using a 1-D PDPA (phase Doppler particle analyzer). The injection duration was a little stretched out (3 ms) to increase the quasi-steady part of the spray. The axial velocity of the droplets was studied in the main parts of the single-hole nozzle spray, i.e. the leading edge; the central part and the trailing edge. Temporal distributions of the mean axial velocity and its rms were constant in the central spray part, and they showed peaks in the leading edge of the spray. The radial distribution of the normalized axial mean velocity was similar to that of the free gas jet within r/r0.5=1.0−1.5 regardless of time, which is consistent with the theoretical velocity distributions suggested by Hinze. However, in the leading edge near the centreline axis, the normalized axial mean velocity displayed higher values. The turbulence intensity of the axial velocity measured along the radial direction was similar to the free gas jet within r/r0.5=0.5 and higher beyond. However, the turbulence intensity in the leading edge was higher than in the leading edge and the central part within r/r0.5=0.7 where it showed values of the 40–60% of the local mean velocity. The factors of skewness and flatness approached to those of the free gas jet in the central part and the trailing edge. In the leading edge, the flatness factor has presented dispersed values, and the skewness factor was always higher than were those of the two other parts of the spray. The gradient of the half-width exhibited a linear decrease with time since the beginning of the injection to reach the value of 0.106 at the end of the injection. The virtual origin value was within 10–13 mm independently of the injection pressure, and the spray cone angle, determined in comparison to the virtual origin, was close to 30°. The axial decrease of the mean axial velocity showed a great similarity with that of the free gas jet in the central spray part. However, the axial decrease of the rms-velocity was faster than that of the free gas jet.     

Jet breakup and droplet formation in near-critical regime of carbon dioxide-dichloromethane system

The jet breakup and droplet formation mechanism of a liquid in the near-critical conditions of a solvent-antisolvent system is examined with high-speed visualization experiments and simulated using a front tracking/finite volume method. The size of droplets formed under varying system pressure at various jet breakup regimes is measured with a Global Sizing Velocimetry, using the shadow sizing method. A stainless steel nozzle with 0.25 mm I.D and 1.6 mm O.D was used in this study. Experiments were performed at fixed temperature of 35 °C and system pressure in the range from 61 to 76 bar in the near-critical regime of the DCM-CO₂. At the near mixture critical regime for DCM-CO₂ mixture, the miscibility between the two fluid phases increases and the interfacial tension diminishes. This phase behavior has important applications in particle formation using gas antisolvent (GAS) and supercritical antisolvent (SAS) processes. The jet breakup and droplet formation in the near-critical regime is strongly dependent on the changes in interface tension and velocity of the liquid phase. An understanding of the droplet formation and jet breakup behavior of DCM-CO₂ in this regime is useful in experimental design for particle fabrication using SAS method.     

新型催化裂化提升管进料段内原料射流浓度分布的大型冷模实验研究

通过大型冷模实验研究了喷嘴射流与催化剂逆向接触的新型提升管进料段内喷嘴射流浓度沿径向的分布,考察了喷嘴气速、预提升气速的影响. 结果表明,喷嘴气速Uj=78.5 m/s和预提升气速Ur=4.1 m/s条件下可获得较好的油剂混合效果. 与传统形式相比,新型结构可促进油剂混合,在轴向距离H<0.7 m内完成油剂混合,油剂初始接触区域内喷嘴射流相浓度分布更均匀. 给出了新型进料段中不同区域喷嘴射流浓度沿径向分布的经验模型,计算值与实验值吻合较好.     

Radial Crater Growing Process in Different Materials with Shaped Charge Jets

The equations of Szendrei/Held for the radial crater growing process as a function of time can also be inverted to get the target strength R_t if the maximum crater radius r_cm is known. With this method the strength was calculated for an aluminum target to 300 N/mm² and for glass fiber reinforced plastic to 405 N/mm², which are at least very reasonable values. By using these values for R_t, the comparison of the radial crater growth process with carefully arranged and analysed experiments by the Ioffe Institute is showing good agreements.     

The influence of system scale on impinging jet sediment erosion: Observed using novel and standard measurement techniques

Jet impingement as a method for eroding particulate beds and maintaining sediment in suspension is an important process for a host of industries, particularly in nuclear waste processing, where such systems to disperse and mix particulate beds have a number of advantages over other approaches. Existing work has utilised fairly rudimentary techniques for the measurement of erosion depths and here we demonstrate a new technique for measuring both static and dynamic erosion of cohesionless particulates under an impinging jet, using ultrasonic Doppler velocimetry. This approach is tested on both quartz sands and on a range of Mg(OH)₂ particulates that are key simulants for nuclear waste facilities, such as the Highly Active Storage Tanks at Sellafield, U.K. A critical jet height was found to exist that balanced the impingement velocities and total entrained jet volume to maximise erosion. The effect of system scale was also considered by normalising steady-state crater depths and sizes, with erosion being enhanced in the small scale, possibly due to increased turbulent recirculation. Additionally, velocity profiles and acoustic backscatter were used to determine both steady-state crater profiles and kinetic changes in bed-depths with time, and highlighted important differences between static and dynamic measurements of erosion depth.     

Simulation of Homogeneous Particle Nucleation in a Free Turbulent Jet

The homogeneous particle nucleation in a free turbulent jet is simulated at Reynolds numbers of 3400 and 34,000 by using large eddy simulation (LES) coupled with our newly developed equivalent mean nucleation method (EMNM) for the present study. The simulated velocity field, passive scalar concentration, and nucleated particle concentration are compared with various available measurements in the literature. Both the simulated mean velocity and mean scalar concentration show self-similarity properties and agree well with the experimental measurements quantitatively in the literature. Using the EMNM, it is found that the nucleation primarily occurs in a very narrow region around the jet centerline. It is also found that the position of maximum nucleation is a function of the vapor temperature and concentration at the jet exit and its surrounding background (i.e., T ₀, T _∞, c ₀, and c _∞), and the function varies monotonically with respect to these four parameters. Present numerical simulation and analysis also show that the group, (where is the mean particle number concentration, u ₀ is the jet velocity, and d is the jet exit diameter), is constant along the axial direction of the jet, which was first observed in the experiment of Lesniewski, T. K., and Friedlander, S. K. (1998). Particle Nucleation and Growth in a Free Turbulent Jet. Proc. R. Soc. Lond. A, 454:2477–2504. However, a different physical explanation of the fact is provided. In this study, it is found that the maximum nucleation occurs around 20d away from the jet exit, other than in the shear layer (less than 5d), which was supposed by Lesniewski, T. K., and Friedlander, S. K. (1998). On the basis of the additional simulated results, more comprehensive and reasonable explanations of their measurement data are provided. In this study, an efficient and rigorous numerical method is presented to simulate the homogeneous particle nucleation in a free turbulent jet, and this has provided a deeper and thorough understanding of the process.     

Flow behaviors of a large spout-fluid bed at high pressure and temperature by 3D simulation with kinetic theory of granular flow

Flow behaviors of a large spout-fluid bed (I.D. 1.0 m) at high pressure and temperature were investigated by Eulerian simulation. The gas phase was modeled with k − ε turbulent model and the particle phase was modeled with kinetic theory of granular flow. The development of an internal jet, gas-solid flow patterns, particle concentrations, particle velocities and jet penetration depths at high pressure and temperature at different operating conditions were simulated. The results show that the bed operated at an initial bed height larger than the maximum spoutable bed height resembles the flow patterns of jetting fluidized beds. The radial profiles of particle velocities and concentrations at high temperature and pressure have the similar characteristic shapes to those at ambient pressure and temperature. The particle concentrations and velocities appear to depend on the bed heights when increasing pressure while keeping the gas velocities and temperature constant. The particle velocities in the lower region of the bed increase with increasing pressure, while they tend to decrease in the middle and upper regions of the bed. The particle concentrations have an opposite dependency with increasing pressure. They decrease in the lower region of the bed but increase in the middle and upper regions of the bed. Besides, the jet penetration depths are found to increase with increasing pressure.     

Effect of initial disturbance amplitude in gravity affected jet break-up

The initial disturbance amplitude has an effect on stretching jets that is not observed for capillary jet instability where gravitational acceleration is not significant. For inviscid and viscous fluids, gravity diminishes the effect that the initial amplitude has on jet length and its ability to prevent satellite formation. In stretching jets, not only the dimensionless frequency of the disturbance but also its initial amplitude must be known to properly study their satellite forming nature. Indirect methods of relating the applied disturbance energy to an initial velocity perturbation are not simple when the gravity parameter G is changing. When G≠0, the optimum disturbance frequency Ω_opt and the initial disturbance amplitude are related, with Ω_opt∝f(G)×ln(1/ε_v). Results from numerical simulations and experiments are presented here.