MATHEMATICAL MODELING OF FLUID SPRAY CURTAINS FOR MITIGATION OF ACCIDENTAL RELEASES

In this article experimental and theoretical investigations on liquid spray curtains are presented, in the context of absorbing and dispersing accidental releases of chlorine in air. A mathematical model of a two-phase jet is developed to evaluate the entrained air rate in connection with the liquid flow rate. The model was successfully compared by means of replicated wind tunnel experimental runs adopting spray nozzles suitable to create a two-blade barrier. The experimental work demonstrated that it is possible to distinguish two regions in the barrier. One region is dominated by the liquid inertia and is comparable to an airplane jet. The other region is dominated by gravitational effects, and its dimensions do not vary appreciably. An analytical solution to the problem is obtained, taking into account the instantaneous and nonreversible chemical reactions, i.e., chlorine absorption in alkaline solutions, in the case of still air. The developed methodology could be applied to more complex situations, allowing the attainment of a more generalized approach for the design of a curtain given the release parameters, the site layout, and vulnerable target specifications.     

MATHEMATICAL MODELING OF HEAT AND MASS TRANSFER IN HOT GAS SPRAY SYSTEMS

A mathematical model is developed to study simultaneous heat and mass transfer in hot gas spray systems. The model is obtained by writing mass, energy, and momentum balances for both continuous and discontinuous phases. Governing equations along with suitable correlations for heat and mass transfer coefficients have been solved numerically. In order to develop a realistic model for such complicated systems, a droplet size distribution was implemented in the model instead of using an average size. A steady state spray-cooling problem is analyzed to illustrate the applicability of the model. To validate the mathematical model for this case, necessary data was collected and measured in commercial cement plants. A good agreement between plant data and the model was noticed in general, and results obtained from the model indicate that size distribution of water droplets and physical dimensions of the spray-cooling system are important parameters. This model is very useful in determining the so-called "critical operation condition" at which sludge formation at the bottom of spray-cooling systems will happen. The predicted parameters in spray-cooling systems both for droplet phase and gas phase aptly illustrate the ability of the model to treat the complex phenomena associated with two-phase flows.     

A MECHANISTICALLY BASED MATHEMATICAL MODEL OF SULFUR DIOXIDE ABSORPTION INTO A CALCIUM HYDROXIDE SLURRY IN A SPRAY DRYER

A mathematical model has been developed to predict So₂ absorption and removal during the constant rate drying period of a spray dryer. The model, based on film theory, treats the atomized slurry droplets as spheres containing discrete sorbent particles of slaked lime with the fluid uniformly distributed around the individual particles. The model includes gas and liquid phase mass transfer coefficients as well as resistance to Ca(OH)₂ dissolution. A sensitivity analysis has been conducted and a comparison was made between pilot-scale experimental data and model-predicted values of S0₂ removal efficiency.     

MATHEMATICAL MODELING OF DIFFUSION-CONTROLLED PNEUMATIC-CONVEYING DRYERS

A mathematical model for a continuous pneumatic-conveying dryer has been developed for removing internally bound moisture from solid particulates. The dryer relies on a recirculating carrier gas stream for entrainment. Drying is carried out by injecting into the gas loop a fresh stream of conditioned drying gas while an equal amount of wet gas is vented out. Because pneumatic-conveying dryers usually employ huge gas velocities, the particulates are well dispersed in the gas. Therefore, for solids absent of surface moisture, the drying kinetics is controlled by intraparticle diffusion. The mode! developed based on the diffusion mechanism relates the moisture reduction in the solids to various process parameters (diffusiv-ity, partition coefficient, particle size, residence time, solids loading, drying gas usage, and carrier gas recirculating rate), and is fully predictive. Therefore, it can be used to study the effects of these variables. The model was compared with the plant data and found to match the data within ± 15%.     

USE OF COMPUTATIONAL FLUID DYNAMICS TECHNIQUES TO ASSESS DESIGN ALTERNATIVES FOR THE PLENUM CHAMBER OF A SMALL SPRAY DRYER

The inlet region of a pilot-scale, co-current spray dryer was simulated using the proprietary Computational Fluid Dynamics (CFD) codes, CFX4 and CFX5. Several design alternatives were considered for correcting uneven inlet air distribution, which is known to influence spray dryer performance and airflow patterns. The simulations were used to assess each alternative prior to construction, assuming isothermal and incompressible flow conditions. Experimental measurements were compared with the simulation results for the original and one modified design.

Drying air is supplied to this dryer via an overhead pipe feeding an annular plenum chamber, of diameter 400 mm, surrounding the atomiser. A distributor plate with two concentric rings of 50 holes, each of 5 mm diameter, forms the base of the plenum chamber. A three-dimensional grid was required to model each of the 100 holes separately and to consider the asymmetric flow behaviour. The resulting grid consisted of about 532,000 cells. The CFD simulations proved useful in predicting the trends in flow distributions in each of the designs.     

USE OF COMPUTATIONAL FLUID DYNAMICS TECHNIQUES TO ASSESS DESIGN ALTERNATIVES FOR THE PLENUM CHAMBER OF A SMALL SPRAY DRYER

The inlet region of a pilot-scale, co-current spray dryer was simulated using the proprietary Computational Fluid Dynamics (CFD) codes, CFX4 and CFX5. Several design alternatives were considered for correcting uneven inlet air distribution, which is known to influence spray dryer performance and airflow patterns. The simulations were used to assess each alternative prior to construction, assuming isothermal and incompressible flow conditions. Experimental measurements were compared with the simulation results for the original and one modified design.

Drying air is supplied to this dryer via an overhead pipe feeding an annular plenum chamber, of diameter 400 mm, surrounding the atomiser. A distributor plate with two concentric rings of 50 holes, each of 5 mm diameter, forms the base of the plenum chamber. A three-dimensional grid was required to model each of the 100 holes separately and to consider the asymmetric flow behaviour. The resulting grid consisted of about 532,000 cells. The CFD simulations proved useful in predicting the trends in flow distributions in each of the designs.     

MATHEMATICAL MODELING OF FLUIDIZED BED HEAT REGENERATORS

Based on the two-phase theory of fluidization, a fairly rigorous model is developed to describe the dynamic behavior of fluidized-bed heat regenerators. This model takes into account the major hydrodynamic aspects of bubbling fluid beds. Based on the assumption that the gas leaves the bed in thermal equilibrium with the solids, a rather simplified model is presented. Exact analytical solutions are obtained for both models. The predictions of the more rigorous model are found to be in good agreement with many experimental observations. On the other hand, the simplified model gives satisfactory results only when the value of the parameter m₁is relatively large. Using the rigorous model, it has been shown that the bed thermal efficiency can be improved by reducing the time of operation, increasing the mass of solids or decreasing the bed aspect ratio. Also it has been found that when the gas flow-rate is increased, the amount of heat transferred to the solids displays a non-monotonic behavior and passes through a maximum.     

MATHEMATICAL MODELING OF MULTISTAGE DIFFUSION-CONTROLLED PNEUMATIC-CONVEYING DRYER TRAIN

Based on the single stage dryer model (Qi, 1996), a model for a multi-stage diffusion-controlled pneumatic-conveying dryer train was developed. The model consisted of a set of algebraic equations describing the relationship between the moisture level in solids and major process parameters (i.e., diffusivity, partition coefficient, particle size, number of stages, solids loading, residence time, etc.rpar;. The effects of these parameters on drying were studied using the model. Equilibrium and other special or asymptotical conditions (e.g., infinitesimal injection of drying gas, uniform partition coefficient and Fourier numbers, etc.rpar; were analyzed. Model calculations have been shown to compare very well with data from an actual plant HOPE drying process.     

PERFORMANCE OF SPRAY DRYER WITH INTEGRATED FILTER AND FLUID BED

Spray dryers featuring a fluid bed integrated into the base of a spray drying chamber have proved one of the most significant developments introduced into industry during the last decade, producing dust-free particulates under low product temperature conditions. The latest design development involves all particulate collection and exhaust air cleaning within the drying chamber with the use of integrated metallic filter elements (with CIP capability). This eliminates handling of fines outside the drying chamber and simplifies the exhaust air system contributing to lower pressure drop losses and lower overall energy consumption. This paper describes the performance of a pilot plant sized spray dryer featuring a drying chamber with both integrated particulate filters and fluid bed. Various products were tested. The results showed that the placing of particulate filters inside the drying chamber does not adversely affect the agglomeration process and that the powder quality compared with that achieved in a standard Fluidized Spray Dryer can be reproduced in this new design concept, with every possibility for improved quality due to no powder handling outside the drying chamber. The work also showed that by containing the powder within the drying chamber, notable operational advantages are apparent and that scale-up of the design concept represents no apparent difficulties.     

MODELING MASS TRANSFER OF FITC-LABELED DEXTRAN FROM POLYELECTROLYTE MICROCAPSULES

Layer-by-layer adsorption of oppositely charged polyelectrolytes has been used for the manufacturing of hollow microspheres or capsules for controlled release studies. Using this self-assembly technique, microsphere core material was encapsulated with poly styrenesulfonate (PSS) and poly allylamine (PAH) multilayers or PAH and polyvinyl sulfate (PVS) multilayers and the core dissolved to produce hollow microcapsules. The microspheres were loaded with fluorescein-isothiocyanate (FITC)-labeled dextran of different molecular weights for different lengths of time to quantify the release properties. After loading, the capsules were immersed in water and the FITC-dextran was allowed to diffuse into the mother liquor. The FITC-dextran concentration of the mother liquor was measured over a period of hours and days. In this study, one- and two-compartment models were developed, based on a species mass balance, to predict the concentration of dextran release from the microcapsules over time. The two-compartment model was found to be superior to the one-compartment model in its fit to the observed data. The model was applied to experimental data in order to characterize the release properties of microcapsules with different numbers of layers and constituent architectures.     

熔融挤压快速成型系统的喷头结构分析

分别从进料装置、塑化装置、喷嘴和双喷头等方面对目前市场上熔融挤压快速成型系统的喷头结构进行详细剖析,找出它们的特点及存在的问题。通过对不同啧头结构进行研究和分析,不但可以改进和完善熔融挤压快速成型工艺,同时能推进该工艺的商业化与应用。     

固体氧化物燃料电池中的阳极电化学过程数学模拟研究

在质量守恒、动量守恒和能量守恒定律及Butler-Voulmer方程组的基础上,加上边界条件和初始条件,通过数学模型对SOFC中的阳极催化层内部的燃料反应气体的气相扩散及产物的气相扩散的基本动态规律进行了描述。其偏微分方程只能通过数值计算求解,而无法得到解析解。增大阳极孔隙率ε可提高多孔电极中的有效气体扩散系数。当阳极较薄时,阳极的总极化电阻与单位体积内的电化学活性区的面积A成反比,增大阳极的电化学活性区的面积有利于降低其总极化电阻。该数学推演结论对阳极的优化制备具有重要的参考价值。     

MODELING ANALYTICAL TESTS OF SUPERCRITICAL FLUID EXTRACTION FROM SOLIDS WITH LANGMUIR KINETICS

A model for the analytical supercritical fluid extraction (SFE) tests from solid samples in which desorption of the solute from the surface of the solid is the rate determining step is presented. The desorption process is described by the Langmuir kinetics. The two stages of the test (static and dynamic) are modeled, where each of the two phases (solid and supercritical fluid) are considered well mixed. The resulting ordinary differential equations are solved analytically for the static stage and numerically for the dynamic stage. Dimensionless curves of concentrations of the two phases and fractional recovery during the two stages of the tests are predicted. These curves are characterized by two dimensionless parameters for the static stage, the equilibrium constant and the fractional initial capacity, in addition to one parameter for the dynamic stage, the desorption coefficient. The model provides a good fit to experimental results for SFE from solids. The trends in the fitted parameters with respect to pressure and temperature are in agreement with theory.     

APPLICATION OF LASER DIAGNOSTIC TECHNIQUES FOR THE EXAMINATION OF LIQUID FUEL SPRAY STRUCTURE

Results are presented on the spatial distribution of droplet mean size and number density obtained from a hollow-cone kerosene spray, introduced into nonswirling and swirling flow fields. An ensemble light scattering technique, based on measurement of the polarization ratio, has been employed to determine local droplet characteristics in both dense and dilute regions of the spray. The measurements are complemented with Lorenz-Mie calculations of the scattering characteristics for a polydispersion of droplets; the calculations were carried out for different mean sizes and refractive indices. The results reveal that the degree of swirl imparted to the surrounding air flow has a strong influence on spray structure. For all conditions examined the droplet mean size is found lo be larger on the spray boundary than towards the centerline. Droplet mean size is also found to increase with axial distance at all radial positions of the spray; this trend is attributed to the vaporization of smaller droplets and/or possible coalescence between the droplets.

In addition to the ensemble technique, measurements have also been obtained with the phase/Doppler interferometry and light intensity deconvolution techniques under identical experimental conditions. The droplet mean sizes obtained with the ensemble approach are in general smaller than those measured with the phase/Doppler technique; however, general features of the radial profiles obtained with both techniques are similar. The deconvolution technique also indicates the presence of smaller size droplets and supports the results obtained with the ensemble technique. The selective sensitivity of these sizing techniques to different ranges of droplet size and number density is discussed.     

FREE-RADICAL RETROGRADE-PRECIPITATION POLYMERIZATION: A MATHEMATICAL MODELING STUDY OF POLYMERIZATION OF STYRENE IN DIETHYL ETHER

Polymerizing a monomer above the lower critical solution temperature (LCST) of its polymer-monomer-(non)solvent mixture has demonstrated better control characteristics than conventional free-radical polymerization kinetics. Reaction kinetics of polymerization in a poor solvent are strongly influenced by heat and mass transfer properties, as understood from modeling the transport phenomena in our earlier work. The study has now been extended to model the reaction kinetics in a styrene-diethyl ether system. The model was based on the CCS model for free radical polymerization, with the modification proposed by Achilias-Kiparissides. Computer simulation results agree well with those obtained from experiments carried under similar conditions, with the onset of phase separation as the only adjustable parameter. Drawbacks of the model are lack of analysis for the effect of monomer concentration and the absence of an appropriate radical trapping mechanism.     

STACK-WIDE EFFECTS IN THE MODELING OF SOLAR KILNS FOR DRYING TIMBER

This study examines the stack-wide effects due to the humidification and cooling of air as it passes through a 6 m wide stack of Australian ironbark timber for conditions that are representative of those for solar drying (dry and wet-bulb temperatures of 60 and 50°C, respectively). A solar kiln model for a greenhouse-type design has been modified to account for the drying of timber boards and the possibility of stack-wide effects, in terms of moisture-content differences in the streamwise direction of air flow through the stack. The maximum difference between the moisture contents of the leading and trailing boards is predicted to be 0.011 kg kg^-1 for these conditions, compared with timber moisture contents of 0.15-0.35 kg kg^-1. Hence, the stack-wide effect is insignificant for these conditions in this greenhouse kiln design and may be ignored, reducing the simulation time by over 50%. In addition, 14 elements within a finite-difference model for the drying of the timber boards (25 mm thick) gives predictions of the drying time that are acceptably accurate, while minimizing the computational time.     

THE EFFECT OF DRUG DISSOLUTION ON DRUG RELEASE FROM SWELLING POLYMERIC MATRICES: MATHEMATICAL MODELING

A mathematical model of simultaneous dissolution and diffusion controlled drug release from swellable, non-erodible viscoelastic polymer matrices is developed. The model assumes that the drug is loaded into the dry matrix as a solid phase. Two unsteady-state mass balances are required for both the drug and the incoming external penetrant. The Camera-Roda and Sarti equation is considered for the determination of the penetrant uptake, while Ficlc's equation accounting for the density gradient developing in the matrix is considered for the drug diffusion. Assuming that upon dissolution a drug phase transition may occur which affects the drug solubility without altering the diffusion coefficient. This analysis revealed that the features of the drug release kinetics are sensibly affected by the viscoelastic properties of the swollen matrices and by the drug dissolution and phase transition rates.     

SINGLE-LAYER DRYING BEHAVIOR OF MEXICAN TEA LEAVES (CHENOPODIUM AMBROSIOIDES) IN A CONVECTIVE SOLAR DRYER AND MATHEMATICAL MODELING

Single-layer solar drying experiments were conducted for Mexican tea leaves (Chenopodium ambrosioides) grown in Marrakech. An indirect forced convection solar dryer was used in drying the Mexican tea leaves at different conditions such as ambient air temperature (21° to 35°C), drying air temperature (45° to 60°C) with relative humidity (29 to 53%), airflow rate (0.0277 to 0.0556 m ³/s), and solar radiation (150–920 W/m²). The experimental drying curves showed only a falling rate period. In order to select the suitable form of drying curves, 14 mathematical models were applied to the experimental data and compared according to their statistical parameters. The main factor in controlling the drying rate was found to be the temperature. The drying rate equation was determined empirically from the characteristic drying curve. The diffusion coefficient of the Chenopodium ambrosioides leaves was estimated and varied between 1.0209 × 10^?9 and 1.0440 × 10^?8 m ²·s^?1.The activation energy was found to be 89.1486 kJ·mol^?1.