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.

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.

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.

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.

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.

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.

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.

Grain size model for continuous dynamic recrystallization of titanium alloy in hot deformation

The continuous dynamic recrystallization(CDRX) through a progressive transformation of a subgrain structure into a grain structure with the increasing of misorientation occurred in the hot deformation of titanium alloy. A grain size model for CDRX of titanium alloy in hot deformation considering work hardening effect, dynamic softening effect and non-homogeneous deformation effect was established. The β grain size was described as functions of the deformation temperature, strain rate and strain by using the dislocation density as an internal state variable. The inside dislocation storage and dislocation annihilation,which respectively resulted from work hardening effect and dynamic softening effect, were described by the Kocks-Mecking and Picu-Majorell theories correspondingly. The dislocation density rate associated with non-homogeneous deformation effect was done in terms of the Ashby theory. The material constants in the present model were determined via genetic algorithm(GA)-based objective optimization technique. Applying the grain size model to the hot deformation of Ti-5Al-2Sn-2Zr-4Mo-4Cr, the maximum difference between the calculated and experimental β grain size was 8.2%. Moreover, the effect of deformation temperature and strain rate on the β grain size in the hot deformation of Ti-5Al-2Sn-2Zr-4Mo-4Cr was calculated, indicating that the β grain size increased with the increasing of deformation temperature and the decreasing of strain rate.

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.

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.

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.

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.

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.

基于近红外光谱技术苹果尺寸差异对糖度模型适用性的影响

为消除水果自身尺寸差异对其糖度预测模型的不利影响,进一步提高水果分选模型精度,应用近红外光谱在线检测装置采集不同果径苹果的近红外光谱,对光谱进行多种预处理后,分别建立苹果可溶性固形物的偏最小二乘法模型,再用苹果果径75~85mm组中的建模集预测苹果果径分别为65~75、85~95mm组中的预测集样品,最后用果径组65~75、75~85、85~95 mm中的建模集和预测集,分别作为混合苹果尺寸糖度预测模型的建模集和预测集,并利用特征光谱选择算法对模型进行简化,建立苹果糖度通用预测模型。结果显示:与建模集和预测集果径不同时所建立的苹果糖度预测模型最优组相比,其相关系数Rp由0.805提高至0.943,预测集均方根误差值RMSEP由0.778减小至0.480,RPD由0.96增加至3.05,再对建立的通用模型进行简化,可以降低苹果尺寸对苹果糖度模型的影响,提高模型预测性能。

Extension of the gurson model accounting for the void size effect

A continuum model of solids with cylindrical microvoids is proposed based on the Taylor dislocation model. The model is an extension of Gurson model in the sense that the void size effect is accounted for. Beside the void volume fraction f, the intrinsic material length l becomes a parameter representing voids since the void size comes into play in the Gurson model. Approximate yield functions in analytic forms are suggested for both solids with cylindrical microvoids and with spherical microvoids. The application to uniaxial tension curves shows a precise agreement between the approximate analytic yield function and the exact parametric form of integrals.

GEOMETRIC MODEL AND APPLIED METHOD FOR THE CALCULATION OF GRAIN SIZE DISTRIBUTIONS

Most of the available methods for the calculation of the three dimensional(3D)grain size dis- tribution functions(SDF)are based on the S model and lead a grave systematical error.The origin is the basic supposition of spherical grains in the S model,which does not correspond with the feature of real grains.A new model called A model is developed based on the hypothe- sis of polvhedral grains.The probability functions of the A model and the method to calculate the 3D SDFs using the A model are given in the present paper.The theoretical analyses and experimental tests have demonstrated that the A model reduces the systematical error radical- ly.It is nearly as simple as the so far used S model,but gives much better results in repro- ducing of 3D SDFs from the measured ID or 2D SDFs.

Precise large deviations for sums of random vectors in a multidimensional size-dependent renewal risk model

Consider a multidimensional renewal risk model, in which the claim sizes {Xk, k ≥1} form a sequence of independent and identically distributed random vectors with nonnegative components that are allowed to be dependent on each other. The univariate marginal distributions of these vectors have consistently varying tails and finite means. Suppose that the claim sizes and inter-arrival times correspondingly form a sequence of independent and identically distributed random pairs, with each pair obeying a dependence structure. A precise large deviation for the multidimensional renewal risk model is obtained.

Computational Optimization of Manufacturing Batch Size and Shipment for an Integrated EPQ Model with Scrap

This paper employs mathematical modeling and algebraic approach to derive the optimal manufacturing batch size and number of shipment for a vendor-buyer integrated economic production quantity (EPQ) model with scrap. Unlike the conventional method by using differential calculus to determine replenishment lot size and optimal number of shipments for such an integrated system, this paper proposes a straightforward algebraic approach to replace the use of calculus on the total cost function for solving the optimal production- shipment policies. A simpler form for computing long-run average cost for such a vendor- buyer integrated EPQ problem is also provided.

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.

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.