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A complete set of ordinary differential equations, based on modifications of existing models, is used to investigate bubble growth and collapse under microgravity conditions in this paper. As in previous work, effects of inertia, surface tension and viscosity are taken into consideration in the momentum equation of the liquid phase outside of vapor bubble, while effects of “moving interface”, interface curvature and thermal resistance of surrounding liquid are considered in the evaporation of the vapor bubble. A dimensionless fitting constant b is introduced to account for area change of the moving vapor/liquid interface and the diffusive nature of the interface layer. The values of these fitting constants for bubble growth and bubble collapse in water and ethanol are obtained by matching predicted temporal variations of bubble radii with experimental data. The predicted interfacial dynamics during bubble growth and bubble collapse is analyzed. Different stages during the bubble growth process are characterized. During the early stage of bubble collapse, the simulated bubble radii show some “fluctuations”, which can be attributed to the “rebound effect” of pressure balance in the bubble owing to the initial condition of a sudden drop in temperature.

Bubble growth in superheated liquid is a fundamental process in vapor-liquid phase change which occurs widely in thermal and chemical engineering. The strong coupling of heat, mass and momentum transfer at the interface brings difficulties to accurately predict the dynamics of bubble growth. At present, bubble growth under three extreme conditions, i.e. the very early growth stage, low superheats and low pressures, cannot be well described by traditional asymptotic solutions. In this work, a mathematical model was presented for better prediction of bubble growth in a superheated liquid. The model was derived from the equations of motion for a bubble and took account of the heat and mass balances at the interface. The model was validated with a series of experiments from the literature, covering a wide range of operating conditions. The newly proposed model can well predict the features of bubble growth at the very early stage (less than 10 −6 s), for superheats varying from 0.8 K to 36 K and for system pressures reduced from 1.0 atm to 0.0124 atm. Analyses on the thermodynamics and hydrodynamics manifested that the bubble growth was characterized by three typical stages, i.e. a thermal delay stage, a fast expansion stage and a steady growth stage. The time lengths of these stages were related to the levels of superheat or system pressure. Characteristics of these stages were further discussed and the roles of interfacial forces under the different operating conditions were demonstrated.

One important phenomenon in coal beneficiation fluidized bed (CBFB) is the accumulation of fine coal particles in beneficiation due to poor screening efficiency and attrition of coal samples. The effect of fine coal accumulation is numerically studied in this work using a TFM–DEM hybrid model. The gas phase and medium solid phase are modeled by a two-fluid model (TFM), while the fine coal particles are modeled by the discrete element method (DEM). Particles with a diameter of 0.9 mm are used as the fine coal sample in the simulation. The gas–solid flow pattern and particle dynamics are investigated with different concentrations of fine coal particles accumulated in the bed. For model validation purpose, the mean bed density distributions are compared with the experimental reports from He et al. (2013). The results show that a critical particle concentration exists in the fine coal accumulation process in CBFB. When the fine coal particles are less than 11 wt% in the bed, the flow pattern of medium phase is little affected and the coal particles are well mixed in the bed. However, when the particle concentration exceeds this threshold, the uniformity of bed density distribution is destroyed and particle stratification occurs along the bed height according to their density difference. Flow dynamics of the dense bed and main forces acting on the fine coal particles are analyzed to explain the underlying mechanism. With a large number of particles accumulated in the bed, the mixing effect of medium flow is suppressed. Motion of the fine coal particles is less dependent on the bed disturbance, instead, the particle gravity plays a decisive role in the particle distribution and results in the particle segregation in the fine coal accumulation process.

A TFM–DEM hybrid model is introduced for modeling of the complex gas–solid flows in a pilot scale Coal Beneficiation Fluidized Bed (CBFB). The gas and the dense solid phases are modeled using an Eulerian-Eulerian or two fluid model (TFM), while the beneficiated coal particles are modeled as a dilute phase by the discrete element method (DEM). In this work, the influence of some key operation parameters on particle segregation behavior is studied, including fluidized air velocity, bed depth, and coal feed ratio and bed medium properties. Their effects are evaluated using a single coal sample of diameter 4.3 mm. Particles are divided into five different density fractions to represent the wide density range of raw coal samples. The simulation results demonstrate that by increasing the fluidizing air velocity from 1.2 u mf to 1.8 u mf of the dense medium solids, the segregation degree of beneficiated coal particles is significantly reduced, but the segregation time is only slightly decreased. Increasing the particle feed mass or decreasing the bed depth has a similar influence on CBFB operation. Both help to improve particle segregation, but a shallower bed is demonstrated to be more effective for coal beneficiation. A decrease in the medium density can reduce the bed cut density as well as the beneficiation limit for lighter samples, while a decrease in the medium size will increase the back-mixing effects, resulting in reduced beneficiation quality. Hydrodynamic forces acting on the beneficiated particles are also quantified from the simulation results. By analyzing the magnitude and direction of each force acting on discrete particles, the mechanisms influencing particle segregation under different operation conditions are explained at the particle scale.

Particle segregation behavior in a coal beneficiation fluidized bed (CBFB) is numerically studied using a TFM–DEM hybrid model, in which the gas and the dense solid phases are modeled using a Eulerian–Eulerian or two fluid model (TFM), while the beneficiated coal particles are modeled as a dilute phase by the discrete element method (DEM). For validation purpose, the numerical model was setup using geometric and operating conditions similar to a laboratory experimental model with the bed thickness set to one particle diameter to save computational cost. For a fixed gas injection velocity, the influence of particle size and density of the beneficiated samples was studied. It was found that the particles would segregate along the bed height due to the density differences with the degree of segregation being strongly influenced by particle size. Obvious segregation occurs for the coarse samples (6.7 mm and 4.3 mm) and little segregation occurs for the particles smaller than 3 mm. The flow patterns and segregation kinetics were qualitatively comparable with those observed in physical experiments conducted under similar conditions. On this basis, the underlying mechanisms governing particle segregation have been explained in terms of the hydrodynamic forces acting on individual particles. It was demonstrated that the segregation of coarse particles was mainly controlled by the balance between gravity and the local pressure force, while fine particles were more strongly affected by the direct drag forces from the gas phase and the continuum solid phase, thus making them difficult to separate.

The segregation behaviors of fine coal particles in a coal beneficiation fluidized bed (CBFB) were investigated in this work. The size range of 1–8 mm was taken into account and three separate size fractions were studied comparatively in the experiments, e.g. 1–2 mm, 3–5.5 mm and 5.5–8 mm. Both a clean coal sample and a gangue sample were used as the processed material to study the segregation behaviors of both light particles and heavy particles. The dense bed was divided as seven layers from bottom to top and the particle distribution in each layer for each sample was fully demonstrated. The influences of the particle density, particle size and the fluidized air velocity were revealed, the segregation patterns under different conditions were compared and the segregation mechanism was carefully analyzed. The results showed that the flotation and sedimentation of the particles in CBFB were still largely influenced by the particle density for the fine size range particles, and density stratification occurred even within each size fraction sample. The weight fraction in each layer showed a quadratic increase along the bed height for the coal particles. For gangue particles, a large fraction deposited in the bottom while the mass proportions in the middle layers also showed an increased tendency. With a decrease of the particle size, both the particle segregation and the density stratification phenomena deteriorated seriously. It was proved that particle feed size should be above 3 mm as the separation effect was quite inefficient for finer particles. By increasing the fluidized air velocity, the bed density slightly decreased but the bed turbulence was largely strengthened by the increasing bubble boiling effect. The flotation and sedimentation of the particles in 5.5–8 mm were obviously affected while no clear influence occurred to the rest of the two size fractions. Moreover, the results in this work provide a group of data that are quite suitable for CBFB numerical modeling studies.

The oscillatory regime for liquid rise in vertical capillaries has been observed but the analytical solution that can be applied for this regime is still in shortage. Some lack terms in the existing analytical solutions make them show deviations when predicting the oscillatory behavior of liquid rise. An improved dynamic model is built in this work for the oscillatory regime. Two main contributions are made, concerning the non-equal pressure losses at the entrance for liquid rise and fall, and the receding dynamic contact angle for the regions with negative capillary numbers. Experiments are performed to correlate the empirical parameters in the submodels and to validate the combined dynamic model. Good accuracies of the present model are obtained by comparing with the experimental data both in literature and from the present study. Inclusion of the non-equal pressure loss equations for the end effect makes the model well capture the high asymmetry of oscillations, while the two-stage dynamic contact angle models correct the local bouncing of the meniscus. The dynamics of liquid in the oscillatory regime is discussed by comparing the contribution of each pressure force. Occurrence criteria of the oscillatory regime is obtained through a non-dimensional analysis. It is shown that the oscillatory regime is affected not only by the combined parameter (ω), but also by the immersed height of tube (H0) and the pressure head loss coefficients (ξ).

Concentrated salt solutions are used as working fluids in heat exchangers for heavy oil drilling to meet the requirements of environmental protection. Deep understanding the nucleate flow boiling heat transfer mechanism of salt solutions is of great importance for the design and safe operation of modern steam power equipment. In this work, the nucleate flow boiling for NaCl solution and pure water was experimentally studied within the concentration (C) range of 0%–6% in a vertical heated tube. To simultaneously obtain the heat transfer coefficient (HTC) and bubble parameters, the test section was built to be transparent and the energy for boiling was provided by a transparent ITO heater. The bubble parameters, including bubble departure diameter (Dw), bubble departure frequency (f), bubble growth time (tg) and waiting time (tw), were measured in the experiments. A wide range of operating conditions is considered in this study, covering the inlet fluid temperature (Tinlet) between 337 and 365 K, the mass flux (G) between 200 and 600 kg/m2s and the heat flux between 10 and 180 kW/m2. Based on the experimental results, the difference of nucleate flow boiling heat transfer performance between pure water and solutions was compared. It was found that the HTC of pure water was higher than that of salt solutions under the operating conditions of Tinlet 351 K and q > 180 kW/m2, in some cases, it was lower than that of solutions. Dw in the solution is bigger than that in pure water while f in the solution is lower. The corresponding reasons for those heat transfer differences between pure water and solutions were revealed by considering the differences in bubble behaviors, physical properties and mass transfer rate. In addition, the influences of operating parameters on the heat transfer characteristics and bubble behaviors of salt solution during nucleate flow boiling were demonstrated.

The Computational Particle Fluid Dynamics (CPFD) numerical method was used to study the gas solid flow characteristics in a circulating fluidized bed (CFB) with a loop seal in this work. The influences of operating parameters, including loop seal aeration rate (Ql), fluidized air velocity in the riser (Ur) and total bed inventory (Mp) on the solid circulation characteristics were mainly investigated in this part. The solid circulating rate (Gs), total pressure drop in the riser (ΔPr), particle packed height (Hs), pressure gradient (ΔPs/Hs) and gas flow rate (Gg) in the standpipe, as well as the particle concentration and pressure distributions in the loop were carefully analyzed under different operating conditions. The simulation results were compared with the experimental results also reported in this work and good agreements were obtained. The results showed that the increase of Ql resulted in a decrease of Hs and increases of Gs, ΔPr and ΔPs/Hs. By increasing Ur, the increase of Gs was limited and the maximum value was approaching. An increase of Mp also had a positive effect on Gs while an elevated Hs was obtained as a result of mass and pressure balance. No gas bypass flow phenomenon occurred in the operating cases of this work from the simulation results. The pressure drop in the riser could be properly predicted while the gas–solid interactions in the standpipe and loop seal were slightly underestimated by the CPFD method, where a relatively lower ΔPs/Hs was obtained for CFB modeling.

The Computational Particle Fluid Dynamics (CPFD) method was applied in the simulation of the gas solid flow in a circulating fluidized bed (CFB) with a loop seal in this work, and the modeling parameters were mainly investigated in this part. The influences of some crucial modeling parameters in CPFD simulation, such as mesh size, particle close pack volume fraction, interphase drag model and particle size distribution (PSD) on the flow behaviors in the whole loop of CFB were carefully analyzed with the help of experimental data conducted on the same CFB test rig. A medium mesh size was proved to be appropriate and used for the CFB modeling in this work. The particle close pack volume fraction largely affected the particle packed condition in the dense loop seal and standpipe. A value of 0.58 was proved to be suitable to describe the particle circulation and pressure distribution characteristics. Different gas–solid drag models showed certain influence on the particle circulation behaviors, and the combination of Wen-Yu and standard Ergun model was determined as the optimum choice. The consideration of the real PSD in CPFD scheme would better predict the overall flow characteristics for CFB system than the mono-size simplifications. The determination of modeling parameters in this work provides the base for simulating the gas–solid flow in the whole loop of CFB reactors by CPFD method, especially for the dense flow behavior in the standpipe and loop seal.

Modeling the dynamic behavior of gas -solid flow in a pilot scale coal beneficiation fluidized bed (CBFB) model was performed in this work, a transient two-dimensional simulation was done based on the Eulerian model together with the kinetic theory of granular flows. Three steps were conducted to testify the choices of sub-models in CBFB modeling, including gas -solid exchange drag models, gas phase turbulence models, granular temperature models and wall boundary condition models for solid phase. Instantaneous and time-averaged results of particle volume fraction, bubble number and size, particle velocity distributions and vortices, as well as bed density distributions were obtained. The impacts of the sub-models on the flow characteristics in the dense CBFB were illustrated in detail and suitable models with better predictions of CBFB flow pattern were then demonstrated. The Syamlal -O'Brien drag model predicted better results in bed characteristics. The dispersed k-e turbulence model should be used to describe the gas turbulence in the dense CBFB flow regime. The partial slip wall condition for particles had a slight influence in the small model. The partial differential equation granular temperature model could predict the inter-phase surfaces more clearly and the flow pattern more accurately.

A computational particle fluid dynamics (CPFD) numerical method to model gas–solid flows in a circulating fluidized bed (CFB) riser was used to assess the effects of particle size distribution (PSD) on solids distribution and flow. We investigated a binary PSD and a polydisperse PSD case. Our simulations were compared with measured solids concentrations and velocity profiles from experiments, as well as with a published Eulerian-Eulerian simulation. Overall flow patterns were similar for both simulation cases, as confirmed by experimental measurements. However, our fine-mesh CPFD simulations failed to predict a dense bottom region in the riser, as seen in other numerical studies. Above this bottom region, distributions of particle volume fraction and particle vertical velocity were consistent with our experiments, and the simulated average particle diameter decreased as a power function with riser height. Interactions between particles and walls also were successfully modeled, with accurate predictions for the lateral profiles of particle vertical velocity. It was easy to implement PSD into the CPFD numerical model, and it required fewer computational resources compared with other models, especially when particles with a polydisperse PSD were present in the heterogeneous flow.