Bubble size modeling approach for the simulation of bubble columns

The constant bubble size modeling approach(CBSM)and variable bubble size modeling approach(VBSM)are frequently employed in Eulerian–Eulerian simulation of bubble columns.However,the accuracy of CBSM is limited while the computational efficiency of VBSM needs to be improved.This work aims to develop method for bubble size modeling which has high computational efficiency and accuracy in the simulation of bubble columns.The distribution of bubble sizes is represented by a series of discrete points,and the percentage of bubbles with various sizes at gas inlet is determined by the results of computational fluid dynamics(CFD)–population balance model(PBM)simulations,whereas the influence of bubble coalescence and breakup is neglected.The simulated results of a 0.15 m diameter bubble column suggest that the developed method has high computational speed and can achieve similar accuracy as CFD–PBM modeling.Furthermore,the convergence issues caused by solving population balance equations are addressed.

Applicability of Fractal Models in Estimating Soil Water Retention Characteristics from Particle-Size Distribution Data

Soil water retention characteristics are the key information required in hydrological modeling. Frac-tal models provide a practical alternative for indirectly estimating soil water retention characteristics fromparticle-size distribution data. Predictive capabilities of three fractal models, i.e, Tyler-Wheatcraft model,Rieu-Sposito model, and Brooks-Corey model, were fully evaluated in this work using experimental datafrom an international database and literature. Particle-size distribution data were firstly interpolated into20 classes using a van Genuchten-type equation. Fractal dimensions of the tortuous pore wall and the poresurface were then calculated from the detailed particle-size distribution and incorporated as a parameter infractal water retention models. Comparisons between measured and model-estimated water retention cha-racteristics indicated that these three models were applicable to relatively different soil textures and pressurehead ranges. Tyler-Wheatcraft and Brooks-Corey models led to reasonable agreements for both coarse- andmedium-textured soils, while the latter showed applicability to a broader texture range. In contrast, Rieu-Sposito model was more suitable for fine-textured soils. Fractal models produced a better estimation of watercontents at low pressure heads than at high pressure heads.

Modeling size-dependent thermo-mechanical behaviors of shape memory polymer Bernoulli-Euler microbeam

The objective of this paper is to model the size-dependent thermo-mechanical behaviors of a shape memory polymer (SMP) microbeam.Size-dependent constitutive equations,which can capture the size effect of the SMP,are proposed based on the modified couple stress theory (MCST).The deformation energy expression of the SMP microbeam is obtained by employing the proposed size-dependent constitutive equation and Bernoulli-Euler beam theory.An SMP microbeam model,which includes the formulations of deflection,strain,curvature,stress and couple stress,is developed by using the principle of minimum potential energy and the separation of variables together.The sizedependent thermo-mechanical and shape memory behaviors of the SMP microbeam and the influence of the Poisson ratio are numerically investigated according to the developed SMP microbeam model.Results show that the size effects of the SMP microbeam are significant when the dimensionless height is small enough.However,they are too slight to be necessarily considered when the dimensionless height is large enough.The bending flexibility and stress level of the SMP microbeam rise with the increasing dimensionless height,while the couple stress level declines with the increasing dimensionless height.The larger the dimensionless height is,the more obvious the viscous property and shape memory effect of the SMP microbeam are.The Poisson ratio has obvious influence on the size-dependent behaviors of the SMP microbeam.The paper provides a theoretical basis and a quantitatively analyzing tool for the design and analysis of SMP micro-structures in the field of biological medicine,microelectronic devices and micro-electro-mechanical system (MEMS) self-assembling.

THE VOID-SIZE EFFECT ON PLASTIC FLOW LOCALIZATION IN THE GURSON MODEL

Recent studies have shown that the size of microvoids has a significant effect on the void growth rate.The purpose of this paper is to explore whether the void size effect can influence the plastic flow localization in ductile materials.We have used the extended Gurson's dilatational plasticity theory,which accounts for the void size effect,to study the plastic flow localization in porous solids with long cylindrical voids.The localization model of Rice is adopted,in which the material inside the band may display a different response from that outside the band at the incipient plastic flow localization.The present study shows that it has little effect on the shear band angle.

Effects of model size and particle size on the response of sea-ice samples created with a hexagonal-close-packing pattern in discrete-element method simulations

We investigated the effects of model size and particle size on the simulated macroscopic mechanical properties, uniaxial compressive strength, Young＇s modulus, and flexural strength of sea-ice samples, using the discrete-element method （DEM） with a bonded-particle model. Many different samples with a hexagonal-close-packing pattern and a unique particle size were considered, and several ratios of particle size to sample dimension （D/L） were studied for each sample. The macroscopic mechanical properties simulated by the DEM decrease monotonously with an increase in D/L. For different samples with different particle sizes, the macroscopic mechanical properties will be identical when D/L is constant. The quanti- tative relationships between macroscopic mechanical properties and ratio of particle size to sample size are important aspects in engineering applications of the DEM method. The results provide guidance on the choice of a particle size in the DEM simulation for numerical samples with a hexagonal-close-packing pattern.

Effect of Time Step Size and Turbulence Model on the Open Water Hydrodynamic Performance Prediction of Contra-Rotating Propellers

A growing interest has been devoted to the contra-rotating propellers （CRPs） due to their high propulsive efficiency, torque balance, low fuel consumption, low cavitations, low noise performance and low hull vibration. Compared with the single-screw system, it is more difficult for the open water performance prediction because forward and aft propellers interact with each other and generate a more complicated flow field around the CRPs system. The current work focuses on the open water performance prediction of contra-rotating propellers by RANS and sliding mesh method considering the effect of computational time step size and turbulence model. The validation study has been performed on two sets of contra-rotating propellers developed by David W Taylor Naval Ship R ＆ D center. Compared with the experimental data, it shows that RANS with sliding mesh method and SST k-ω turbulence model has a good precision in the open water performance prediction of contra-rotating propellers, and small time step size can improve the level of accuracy for CRPs with the same blade number of forward and aft propellers, while a relatively large time step size is a better choice for CRPs with different blade numbers.

Modeling of the Relationship Between Pore Size Distribution and Thickness of Ceramic MF Membrane

The pore size distribution(PSD)measured by the gas bubble point(GBP)method ofceramic microfiltration(MF)membranes prepared by suspension technique was found to be signifi-cantly influenced by the membrane thickness.A culm-like model for pore structure was introduced tocharacterize the membrane pores instead of the conventional model which does not reflect the radiusvariation along the pore passages and is unable to explain the thickness effect on the membrane PSD.A laminate structure,taking the culm-like model for pore structure into consideration,was hypoth-esized for ceramic MF membranes.A mathematical model was then established to quantitativelydescribe the relationship between the membrane number PSD and the membrane thickness.Goodresults were obtained for the correlation of mean pore size and simulation of the PSD for ceramicMF membranes.

Model Optimization of Litter Size and Genetic Analyses of Model Parameters in Sows

According to two properties of the life cycle and to fluctuation with parities, four mathemati- cal models, the Poisson cycle model, the cubic polyno- mial model, the modified quadratic polynomial model- I artd the modified quadratic polynomial model-H, were used to fit the records of litter size in Jiangquhai sows. From the viewpoint of statistics and biological significance, the modified quadratic polynomial mod- el-I was found to be the optimum model. A single traitanimal model and DFREML procedures were further used to estimate the heritability values of optimum model parameters. The results show that the heritabili- ty values for the coefficients A and B and the herita- bility value for the acme of the model pure quadric curve are larger than the heritability value for the litter size. This suggests that selection for model parameters may be more effective than direct selection for litter size.

SIZE DISTRIBUTION OF DROPLETS ABOVE A ROTATING STREAM TRAY AND MODEL OF DROPLET MOTION THEREIN

Droplet size distributions have been investigated with a two-probe system above a rotatingstream tray of 300 mm diameter.The measured distributions are found to follow the upper limitedlognormal distribution with three parameters dependent primarily on gas hole F-factor.A probabilitymethod is used to describe the initial state of the droplet population above the tray,and a model fordroplet motion is presented.The results computed with model agree well with experimental data.

Micro-plasticity Constitutive Model Taking Account of Size Effects for Pure Aluminum by Microindentation

The macro-plasticity power function constitutive model （MPFCM）, the modified macro- plasticity power function constitutive model （MMPFCM） and the micro-plasticity constitutive model （MCM） taking the material intrinsic length were established to characterize the microindentation size effects of pure aluminum, respectively. The experimental results indicated MPFCM only determined precisely in the great indentation load. While a modified one named MMPFCM was subsequently established taking account of the parameters variation with the increase of indentation depth. The conventional dimensional analysis method was employed to determine the strength coefficient K and the strain hardening exponent n of this modified model. And then MCM taking account of size effects was proposed based on the Taylor dislocation model. The first- order steepest gradient descent method was adopted to obtain the material intrinsic length for the geometrically necessary dislocations. The parameters of MCM were identified by using the UMAT subroutine of ABAQUS software. The average absolute relative error of MCM is relatively lower than that of the macro-one. Although the precision of the modified one is also high, the applied scope is limited, only for the microindentation material. In addition, the intrinsic length 5.09 bun of pure aluminum is also obtained based on the strain gradient theory.

A Population Balance Model for Disperse Systems:Particle Size Distribution in Suspension Polymerization

On the basis of population balance a mathematical model is developed to describe the formation of polymer partlcle in styrene suspension polymerization. The characteristics of coalescence and breakage of droplets and the gel effect are analyzed in particular. Parameters of the models are esthnztted by experimental. on reaction conversion and particle size distributlon. The results show that the model is suitable for predicting polymerization processes.

Implementing a multispecies size-spectrum model in a datapoor ecosystem

Multispecies ecological models have been used for predicting the effects of fishing activity and evaluating the performance of management strategies. Size-spectrum models are one type of physiologically-structured ecological model that provide a feasible approach to describing fish communities in terms of individual dietary variation and ontogenetic niche shift. Despite the potential of ecological models in improving our understanding of ecosystems, their application is usually limited for data-poor fisheries. As a first step in implementing ecosystem-based fisheries management（EBFM）, this study built a size-spectrum model for the fish community in the Haizhou Bay, China. We describe data collection procedures and model parameterization to facilitate the implementation of such size-spectrum models for future studies of data-poor ecosystems. The effects of fishing on the ecosystem were exemplified with a range of fishing effort and were monitored with a set of ecological indicators. Total community biomass, biodiversity index, W-statistic, LFI（Large fish index）, Mean W（mean body weight） and Slope（slope of community size spectra） showed a strong non-linear pattern in response to fishing pressure, and largest fishing effort did not generate the most drastic responses in certain scenarios. We emphasize the value and feasibility of developing size-spectrum models to capture ecological dynamics and suggest limitations as well as potential for model improvement. This study aims to promote a wide use of this type of model in support of EBFM.

A Study on Modifying the Calculation Model of Valid Opening Size of Heat-bonded Nonwoven Fabrics

It has been found that there are marked errors in the value of valid opening size of heat-bonded nonwoven fabrics between theoretical calculations and engineering measurements. A new modified theoretical model is advanced in this paper. The equivalent diameter of the pore of a fibre web is used to calculate the valid opening size instead of the maximum diameter of inscribed circle used, because the fibres in practical fibre webs are flexible elastomers with definite diameters and the pore of fibre web may produce deformation in screening teat and engineering usage. The results show that the theoretical calculations coincide well with the engineering measurements. This method offers a theoretical basis for computer simulation to the performance of filters of heatbonded nonwoven fabrics.

A method of manufacturing process modeling based on activity network for large-sized and complex products

Simulation technique is an efficient approach to realize the planning and scheduling of manufacturing process of products. An appropriate and efficient manufacturing process model is the basis and key of manufacturing process simulation. By analyzing the features of large-sized and complex products, a method of manufacturing process modeling based on activity network is presented and a mapping algorithm of translating BOM/BOP into the manufacturing process model is designed in detail.

Sensitivity of Statistical Models for Extremes Rainfall Adjustment Regarding Data Size: Case of Ivory Coast

The objective of this study is to analyze the sensitivity of the statistical models regarding the size of samples. The study carried out in Ivory Coast is based on annual maximum daily rainfall data collected from 26 stations. The methodological approach is based on the statistical modeling of maximum daily rainfall. Adjustments were made on several sample sizes and several return periods (2, 5, 10, 20, 50 and 100 years). The main results have shown that the 30 years series (1931-1960;1961-1990;1991-2020) are better adjusted by the Gumbel (26.92% - 53.85%) and Inverse Gamma (26.92% - 46.15%). Concerning the 60-years series (1931-1990;1961-2020), they are better adjusted by the Inverse Gamma (30.77%), Gamma (15.38% - 46.15%) and Gumbel (15.38% - 42.31%). The full chronicle 1931-2020 (90 years) presents a notable supremacy of 50% of Gumbel model over the Gamma (34.62%) and Gamma Inverse (15.38%) model. It is noted that the Gumbel is the most dominant model overall and more particularly in wet periods. The data for periods with normal and dry trends were better fitted by Gamma and Inverse Gamma.

Ultrasonic attenuation model for measuring particle size and inverse calculation of particle size distribution in mineral slurries

Based on various ultrasonic loss mechanisms, the formula of the cumulative mass percentage of minerals with different particle sizes was given, with which the particle size distribution was integrated into an ultrasonic attenuation model. And then the correlations between the ultrasonic attenuation and the pulp density, and the particle size were obtained. The derived model was combined with the experiment and the analysis of experimental data to determine the inverse model relating ultrasonic attenuation coefficient with size distribution. Finally, an optimization method of inverse parameter, genetic algorithm was applied for particle size distribution. The results of inverse calculation show that the precision of measurement was high.

Simulation of size effects by a phase field model for fracture

In phase field fracture models the value of the order parameter distin- guishes between broken and undamaged material. At crack faces the order param- eter interpolates smoothly between these two states of the material, which can be regarded as phases. The crack evolution follows implicitly from the time inte- gration of an evolution equation of the order parameter, which is coupled to the mechanical field equations. Among other phenomena phase field fracture mod- els are able to reproduce crack nucleation in initially sound materials. For a 1D setting it has been shown that crack nucleation is triggered by the loss of stability of the unfractured, spatially homogeneous solution, and that the stability point depends on the size of the considered structure. This work numerically investi- gates to which extend size effects are reproduced by the 2D phase field model. Exemplarily, a finite element study of the hole size effect is performed and the simulation results are compared to exnerimental data.

Derivation of Hillert-type 3D grain growth rate model with topological considerations and discussion on its grain size parameter

A Hillert-type three-dimensional grain growth rate model was derived throughthe grain topology-size correlation model, combined with a topology-dependent grain growth rateequation in three dimensions. It shows clearly that the Hillert-type 3D grain growth rate model mayalso be described with topology considerations of microstructure. The size parameter bearing in themodel is further discussed both according to the derived model and in another approach with the aidof quantitative relationship between the grain size and the integral mean curvature over grainsurface. Both approaches successfully demonstrate that, if the concerned grains can be wellapproximated by a space-filling convex polyhedra in shape, the grain size parameter bearing in theHillert-type 3D grain growth model should be a parameter proportional to the mean grain tangentradius.

WRF Simulations of Extreme Rainfall over Uganda’s Lake Victoria Basin: Sensitivity to Parameterization, Model Resolution and Domain Size

Rainfall extremes have strong connotations to socio-economic activities and human well-being in Uganda’s Lake Victoria Basin (LVB). Reliable prediction and dissemination of extreme rainfall events are therefore of paramount importance to the region’s development agenda. The main objective of this study was to contribute to the prediction of rainfall extremes over this region using a numerical modelling approach. The Weather Research and Forecasting (WRF) model was used to simulate a 20-day period of extremely heavy rainfall that was observed in the March to May season of 2008. The underlying interest was to investigate the performance of different combinations of cumulus and microphysical parameterization along with the model grid resolution and domain size. The model output was validated against rainfall observations from the Tropical Rainfall Measuring Mission (TRMM) using 5 metrics;the rainfall distribution, root mean square error, mean error, probability of detection and false alarm ratio. The results showed that the model was able to simulate extreme rainfall and the most satisfactory skill was obtained with a model setup using the Grell 3D cumulus scheme combined with the SBU_YLin microphysical scheme. This study concludes that the WRF model can be used for simulating extreme rainfall over western LVB. In the other 2 regions, central and eastern LVB, its performance is limited by failure to simulate nocturnal rainfall. Furthermore, increasing the model grid resolution showed good potential for improving the model simulation especially when a large domain is used.

Proof of the Monotonicity of Grid Size and Its Application in Grid-Size Selection for Mesoscale Models

Terrain characteristics can be accurately represented in spectrum space. Terrain spectra can quantitatively reflect the effect of topographic dynamic forcing on the atmosphere. In wavelength space, topographic spectral energy decreases with decreasing wavelength, in spite of several departures. This relationship is approximated by an exponential function. A power law relationship between the terrain height spectra and wavelength is fitted by the least-squares method, and the fitting slope is associated with grid-size selection for mesoscale models. The monotonicity of grid size is investigated, and it is strictly proved that grid size increases with increasing fitting exponent, indicating that the universal grid size is determined by the minimum fitting exponent. An example of landslide-prone areas in western Sichuan is given, and the universal grid spacing of 4.1 km is shown to be a requirement to resolve 90% of terrain height variance for mesoscale models, without resorting to the parameterization of subgrid-scale terrain variance. Comparison among results of different simulations shows that the simulations estimate the observed precipitation well when using a resolution of 4.1 km or finer. Although the main flow patterns are similar, finer grids produce more complex patterns that show divergence zones, convergence zones and vortices. Horizontal grid size significantly affects the vertical structure of the convective boundary layer. Stronger vertical wind components are simulated for finer grid resolutions. In particular, noticeable sinking airflows over mountains are captured for those model configurations.