Mixing of two binary nonequilibrium phases in one dimension

The mixing of nonequilibrium phases has important applications in improved oil recovery and geological CO₂‐storage. The rate of mixing is often controlled by diffusion and modeling requires diffusion coefficients at subsurface temperature and pressure. High‐pressure diffusion coefficients are commonly inferred from changes in bulk properties as two phases equilibrate in a PVT cell. However, models relating measured quantities to diffusion coefficients usually ignore convective mass transport. This work presents a comprehensive model of mixing of two nonequilibrium binary phases in one‐dimension. Mass transport due to bulk velocity triggered by compressibility and nonideality is taken into account. Ignoring this phenomenon violates local mass balance and does not allow for changes in phase volumes. Simulations of two PVT cell experiments show that models ignoring bulk velocity may significantly overestimate the diffusion coefficients. © 2009 American Institute of Chemical Engineers AIChE J, 2009     

Counter‐current gas‐liquid wavy film flow between the vertical plates analyzed using the Navier‐Stokes equations

The article is devoted to a theoretical analysis of counter‐current gas‐liquid wavy film flow between vertical plates. We consider two‐dimensional nonlinear waves on the interface over a wide variation of parameters. The main interest is to analyse the wave structure at the parameter values corresponding to the onset of flooding observed in experiments. We use the Navier‐Stokes equations in their full statement to describe the liquid phase hydrodynamics. For the gas phase equations, we use two models: (1) the Navier‐Stokes system and (2) the simplified Benjamin‐Miles approach where the liquid phase is a small disturbance for the laminar or turbulent gas flow. With the superficial gas velocity increasing and starting from some value of the velocity, the waves demonstrate a rapid decreasing of both the minimal film thickness and the phase wave velocity. We obtain a region of the gas velocity where we have two solutions at one set of the problem parameters and where the flooding takes place. Both the phase wave velocity and the minimal film thickness are positive numbers at such values of the velocity. We calculate the flooding point dependences on the liquid Reynolds number for two different liquids. The wave regime corresponding to the flooding point demonstrates negative u‐velocities in the neighbourhood of the interface near the film thickness maximum. At smaller values of the superficial gas velocity, the negative u‐velocities take place in the neighbourhood of the film thickness minimum. © 2009 American Institute of Chemical Engineers AIChE J, 2010     

Volume‐of‐fluid‐based model for multiphase flow in high‐pressure trickle‐bed reactor: Optimization of numerical parameters

Aiming to understand the effect of various parameters such as liquid velocity, surface tension, and wetting phenomena, a Volume‐of‐Fluid (VOF) model was developed to simulate the multiphase flow in high‐pressure trickle‐bed reactor (TBR). As the accuracy of the simulation is largely dependent on mesh density, different mesh sizes were compared for the hydrodynamic validation of the multiphase flow model. Several model solution parameters comprising different time steps, convergence criteria and discretization schemes were examined to establish model parametric independency results. High‐order differencing schemes were found to agree better with the experimental data from the literature given that its formulation includes inherently the minimization of artificial numerical dissipation. The optimum values for the numerical solution parameters were then used to evaluate the hydrodynamic predictions at high‐pressure demonstrating the significant influence of the gas flow rate mainly on liquid holdup rather than on two‐phase pressure drop and exhibiting hysteresis in both hydrodynamic parameters. Afterwards, the VOF model was applied to evaluate successive radial planes of liquid volume fraction at different packed bed cross‐sections. © 2009 American Institute of Chemical Engineers AIChE J, 2009     

Development of a Structure for Blast Wave Mitigation

The internal structure of a blast containment container has been developed and examined by experiments involving the explosion of a high explosive. A steel pipe was selected as an effective structure for blast mitigation, because it dramatically reduces the blast wave in the radial direction near the explosion source. To also reduce the blast wave in the axial direction, two types of model structures consisting of a steel pipe as the main part were examined by both high‐speed photography and pressure measurements of the blast waves. A 0.34‐scale internal structure was constructed by combining these structures. To induce a powerful mitigation effect, the internal structure was filled with a shock‐absorbing material. The peak pressures of C4 explosions in free air were obtained on the basis of the published blast wave data for TNT explosions in free air using an equivalent weight of 1.37. The peak pressures of the blast waves from the structures for all cases were compared with the blast wave data for C4 explosions in free air to estimate the blast mitigation effect. As a result it was estimated that the internal structure not only eliminates the blast pressure in the radial direction but also reduces the blast wave in the axial direction by 36 %. By combining the effects of the internal structure and the shock‐absorbing material, the structure can reduce the peak pressure by 75 %.     

Comparison of decoupling methods for analyzing pressure fluctuations in gas‐fluidized beds

Two methods of decoupling pressure fluctuations in fluidized beds by using the incoherent part (IOP) of absolute pressure (AP) and differential pressure (DP) fluctuations are evaluated in this study. Analysis is conducted first to demonstrate their similarities, differences, and drawbacks. Then, amplitudes, power spectral densities, mean frequencies, coherence functions, and filtering indices of the IOP of AP and DP fluctuations are calculated and compared based on experimental data from a two‐dimensional fluidized column of FCC particles. Derived bubble sizes are also compared with the sizes of bubbles viewed in the two‐dimensional bed. The results demonstrate the similarity of these two methods in filtering out global compression wave components from absolute pressure fluctuations, especially those generated from oscillations of fluidized particles and gas flow rate fluctuations. However, both methods are imperfect. Neither can filter out all the compression wave components and retain all the useful bubble‐related wave components. Their amplitudes can be used to characterize global bubble property and quality of gas–solids contacting in bed, but they do not give accurate measurement of bubble sizes. © 2009 American Institute of Chemical Engineers AIChE J, 2010     

Prediction of Axial Mixing for a Structured Packed Column Using a Two‐equation Model

A theoretical model based on the recently developed two‐equation method is proposed to predict the axial mixing behavior in a structured packed column. By solving the proposed model, the process of tracer injection experiments for determining the axial back‐mixing coefficient of structured packing can be simulated. Consequently, the axial Bodenstein number and dispersion coefficient under liquid single‐phase or gas‐liquid two‐phase flow conditions can be calculated. The validation of the proposed method is tested by simulating the two‐phase fluid flow behavior in Flexipac 2 structured packing. The simulated results are compared with the experimental data and satisfactory agreement is found between the simulation and the experiments.     

A mathematical model of the calendered exiting thickness of micropolar sheet

A theoretical analysis based on the lubrication theory is presented to study the calendering mechanism. The material to be calendered is described by the constitutive relationship of a micropolar fluid. An exact solution and numerical solution of the problem is calculated. The roll‐separating force, power function and exiting sheet thickness are computed numerically using Runge‐Kutta method. The influence of the material parameters on the pressure distribution, pressure gradient and related quantities of engineering interest in calendering process is analyzed through graphs. POLYM. ENG. SCI., 58:327–334, 2018. © 2017 Society of Plastics Engineers     

New development in flow‐through pressure‐swing frequency response method for mass‐transfer study: Ethane in ZIF‐8

A new pressure‐swing frequency response (PSFR) method has been developed to study mass transfer in adsorption systems as a function of temperature and pressure, from ?70 to 180°C, and up to 7 bar. New in‐phase and out‐of‐phase functions have been derived for the PSFR in a general way to allow information extracted from it independent of whether the system is operated in a batch volume swing or a flow‐through pressure swing mode. A new mathematical model that considers distribution of diffusion rates has been introduced to account for diffusive transport in heterogeneous samples. Numerical simulation results have shown that a single rate diffusion model works well when heterogeneity can be described by a normal distribution, but not for asymmetrically bimodal distributions. As a test reference system, the transport of ethane in ZIF‐8 was investigated at different pressures and temperatures using the new PSFR method. The mass transfer was found to be dominated by micropore diffusion. Diffusivity was found to be weakly dependent on pressure or loading, but quite strongly dependent on temperature. The results agree very well with our independent batch volume frequency response technique experiments. © 2016 American Institute of Chemical Engineers AIChE J, 63: 1077–1090, 2017     

Burning Phenomena of the Gun Propellant JA2

The combustion phenomena of the standard gun propellant JA2 are investigated in experiments and analyzed by a simplified theoretical model. Hereby energy transfer from the gas phase governs ignition and combustion of solid rocket and gun propellants. In addition to the heat conduction and convection, the radiation of the flame contributes to the heat feedback which controls the burning rate in dependence on pressure. The dependence on the initial temperature is given by physical parameters of the conversion from the solid to the gaseous state. Burning rates are measured in dependence on pressure and initial temperature confirming a simplified law for the burning rate. The evaluation yields that the pressure exponent can be directly assigned to the heat feedback and that the temperature of the conversion from the condensed to the gas phase lies at about 675 K. The experiments also comprise spectroscopic measurements at low pressures in the wavelength ranges from 300 nm to 14000 nm which are resolved spatially along the vertical flame profile. The analysis of the spectra delivers the profiles of species in the flames including di‐atomic radicals and tri‐atomic molecules of the final combustion products. In addition, gas phase temperatures are derived by application of the Single‐Line‐Group model which gives approximately 2800 K closely below the adiabatic flame temperature of 2900 K at low pressures. They are compared to temperatures assigned to soot particle emission. In summary, these data enable an estimation of the heat feedback from the flame to the burning surface.     

Experimental modeling of colour harmony

This study investigates colour harmony in visual experiments in order to develop a new quantitative colour harmony model. On the basis of new experimental results, colour harmony formulae were developed to predict colour harmony from the CIECAM02 hue, chroma, and lightness correlates of the members of two‐ or three‐colour combinations. In the experiments, observers were presented two‐ and three‐colour combinations displayed on a well‐characterized CRT monitor in a dark room. Colour harmony was estimated visually on an 11 category scale from ?5 (meaning completely disharmonious) to +5 (meaning completely harmonious), including 0 as the neutral colour harmony impression. From these results, mathematical models of colour harmony were developed. The visual results were also compared with classical colour harmony theories. Two supplementary experiments were also carried out: one of them tested the main principles of colour harmony with real Munsell colour chips, and another one compared the visual rating of the new models with existing colour harmony theories. © 2009 Wiley Periodicals, Inc. Col Res Appl, 2010.     

筒辊磨粉磨过程数学模型的建立及其计算机模拟

本文利用φ２５０ｍｍ筒辊磨——新型卧式挤压磨进行了分批水泥熟料的层压实验，提出了两个碎裂参数的数学表达式，建立了筒辊磨粉磨过程数学模型，并对筒辊磨产物的粒度分布进行了计算机模拟，模拟结果表明，建立的数学模型是合理的     

Modeling thermomechanical behaviors of shape memory polymer

The thermomechanical constitutive equations are critical for shape memory polymers (SMPs) in analyzing their shape, memory, and recovery responses under different constraints. In this study, a new physical‐based, temperature and time‐dependent constitutive model was proposed. The deformation mechanisms of this class of functional materials were explained, and the theoretical predicting values by different models were compared with available experimental results. © 2009 Wiley Periodicals, Inc. J Appl Polym Sci, 2009     

Laboratory‐Scale Method for Estimating Explosive Performance from Laser‐Induced Shock Waves

A new laboratory‐scale method for predicting explosive performance (e.g., detonation velocity and pressure) based on milligram quantities of material is demonstrated. This technique is based on schlieren imaging of the shock wave generated in air by the formation of a laser‐induced plasma on the surface of an energetic material residue. The shock wave from each laser ablation event is tracked for more than 100 μs using a high‐speed camera. A suite of conventional energetic materials including DNAN, TNT, HNS, TATB, NTO, PETN, RDX, HMX, and CL‐20 was used to develop calibration curves relating the characteristic shock velocity for each energetic material to several detonation parameters. A strong linear correlation between the laser‐induced shock velocity and the measured performance from full‐scale detonation testing has been observed. The Laser‐induced Air Shock from Energetic Materials (LASEM) method was validated using nitrocellulose, FOX‐7, nano‐RDX, three military formulations, and three novel high‐nitrogen explosives currently under development. This method is a potential screening tool for the development of new energetic materials and formulations prior to larger‐scale detonative testing. The main advantages are the small quantity of material required (a few milligrams or less per laser shot), the ease with which hundreds of measurements per day can be obtained, and the ability to estimate explosive performance without detonating the material (reducing cost and safety requirements).     

Theoretical Prediction of Pressure and Temperature of an Aluminized High Explosive in Underwater Explosion

The blast wave propagation in underwater explosion was studied. The shock propagation in water medium was different from that in air. The blast effect in water lasted longer and offered resistance to the expansion of hot gases and release of energy. A theoretical analysis of the expansion of blast wave in water was carried out and numerical results for pressures and temperatures were obtained as functions of distance and time by analytically solving the governing equations. The initial peak pressures of blast waves, which were required for theoretical analysis were calculated using the blast wave theory. Underwater blasts with different weights (0.045, 0.5, and 1.0 kg) of the aluminized high explosive HBX‐3 were conducted to record pressure as a function of distance and time from the blast point. Theoretical results were compared with experimental data and empirical data for HBX‐3 from literature. Since the measurement of pressure and temperature at close proximity of point of detonation is difficult, theoretical modeling of underwater blast is of significant importance.     

Using NSGA‐II and TOPSIS Methods for Interior Ballistic Optimization Based on One‐Dimensional Two‐Phase Flow Model

In order to meet the design demands of new gun systems or new types of projectiles, the interior ballistic charge design seems especially important. In this paper, a one‐dimensional two‐phase flow model is presented. The model describes the transient combustion of granular propellants in a gun, and pressure waves are considered as an objective. This study adopts a hybrid method to solve the problem. In the first stage, the non‐dominated sorting genetic algorithm (NSGA‐II) with “a “filter” is employed to approximate a set of Pareto‐optimal solutions. In the subsequent stage, a multi‐attribute decision‐making (MADM) approach is adopted to rank these solutions from the best to the worst. The ranking of Pareto‐optimal solutions is based on the technique ordered preference by similarity to ideal solution (TOPSIS) method. In TOPSIS method each objective needs a corresponding weight coefficient, and a practical problem is introduced. Both the entropy method and linear analysis method are adopted to get two sets of weights for the objectives, respectively. The two pairs of final, best compromise solutions are compared for satisfying the designer’s aim. For the analysis of the results, a two‐phase flow interior ballistic model for design optimization is established, and the hybrid approach could get a reasonable design scenario.     

A constitutive model for large multiaxial deformations of solid polypropylene at high temperature

Experiments on a blow‐molding grade of polypropylene have been performed at 135°C using a biaxial testing machine. Both simultaneous and sequential equibiaxial tests were performed at strain rates relevant to solid phase processing regimes. A constitutive model has been developed that includes a single Eyring process and two Edwards‐Vilgis networks. The effectiveness of this model for predicting the observed stress‐strain behavior is explored. Predictions of simultaneous stretching and the first stretch in sequential experiments are excellent. The second stretch in sequential experiments is less well predicted, but the model's performance is useful overall. The model is incorporated into a commercial finite element code and its practicality is demonstrated. POLYM. ENG. SCI., 2009. © 2009 Society of Plastics Engineers     

Granular pressure in a liquid‐fluidized bed as revealed by diffusing wave spectroscopy

The granular pressure and granular temperature underpin various models of granular flows while they are playing an increasing role in modeling of other phenomena in granular systems such as heat transfer, segregation, erosion, attrition, and aggregation. The development and validation of these theories demand experimental determination of these two quantities. Diffusing wave spectroscopy (DWS) is now an accepted technique for measurement of granular temperature in dense granular systems. Using granular temperature data obtained from DWS with the kinetic theory of granular flow, we have derived the granular pressure data for a liquid‐fluidized bed. The determined variation of the mean bed granular pressure with mean bed solid volume fraction compares favorably with previously published experimental data and theoretical models of others. Where discrepancies do occur, they may be attributed to differences in particle inertia, suggesting further work on granular pressure models is required. Finally, we report the variation of the granular pressure with height above the distributor for several mean solids volume fractions. © 2011 American Institute of Chemical Engineers AIChE J, 2012     

Low Inclination Oil‐water Flows

Two‐phase liquid flows at +5° inclination from the horizontal were studied experimentally for mixture velocities between 0.7 and 2.5 m/s and input oil fractions between 10% and 90%. The results were compared with a two‐fluid model that includes entrainment. The investigations were performed in a 38‐mm ID stainless steel test section, with water and oil as test fluids. Dual continuous flow (both phases remain continuous with inter‐dispersion) prevailed, while the two‐phase pressure gradient was found lower than the single‐phase oil or water. At low mixture velocities the velocity ratio increased with oil fraction while at high ones it decreased. Compared to horizontal flow, water holdup was higher and frictional pressure gradient lower.     

Experimental characterization and modeling of twin‐screw extruder elements for pharmaceutical hot melt extrusion

In this study we characterized various screw elements of a co‐rotating twin‐screw extruder used for pharmaceutical hot melt extrusion (HME) and measured the pressure characteristic, i.e., the correlation between the axial pressure gradient and the material throughput in a completely filled screw section at different screw speeds. A typical HME matrix material, Soluplus, was used for the experiments and its required rheological properties were determined. A three‐parameter model based on a dimensionless formulation of the measured quantities was used. These parameters could not be determined uniquely by fitting to experimental data. Therefore we developed an approach to approximate one empirical parameter based on the mechanistic consideration of a pressure‐driven channel flow. The model was extended to account for the variable melt temperature. The results confirmed the expected tendencies and established an essential input parameter set for one‐dimensional simulations of co‐rotating twin‐screw extruders. © 2013 American Institute of Chemical Engineers AIChE J, 59: 4440–4450, 2013