Application of meshfree methods to numerically simulate microscale deformations of different plant food materials during drying

Plant food materials have a very high demand in the consumer market and therefore, improved food products and efficient processing techniques are concurrently being researched in food engineering. In this context, numerical modelling and simulation techniques have a very high potential to reveal fundamentals of the underlying mechanisms involved. However, numerical modelling of plant food materials during drying becomes quite challenging, mainly due to the complexity of the multiphase microstructure of the material, which undergoes excessive deformations during drying. In this regard, conventional grid-based modelling techniques have limited applicability due to their inflexible grid-based fundamental limitations. As a result, meshfree methods have recently been developed which offer a more adaptable approach to problem domains of this nature, due to their fundamental grid-free advantages. In this work, a recently developed meshfree based two-dimensional plant tissue model is used for a comparative study of microscale morphological changes of several food materials during drying. The model involves Smoothed Particle Hydrodynamics (SPH) and Discrete Element Method (DEM) to represent fluid and solid phases of the cellular structure. Simulation are conducted on apple, potato, carrot and grape tissues and the results are qualitatively and quantitatively compared and related with experimental findings obtained from the literature. The study revealed that cellular deformations are highly sensitive to cell dimensions, cell wall physical and mechanical properties, middle lamella properties and turgor pressure. In particular, the meshfree model is well capable of simulating critically dried tissues at lower moisture content and turgor pressure, which lead to cell wall wrinkling. The findings further highlighted the potential applicability of the meshfree approach to model large deformations of the plant tissue microstructure during drying, providing a distinct advantage over the state of the art grid-based approaches.

An explicit scheme for coupling temperature and concentration fields in solidification models

A numerical scheme for coupling temperature and concentration fields in a general solidification model is presented. A key feature of this scheme is an explicit time stepping used in solving the governing thermal and solute conservation equations. This explicit approach results in a local point-by-point coupling scheme for the temperature and concentration and avoids the multi-level iteration required by implicit time stepping schemes. The proposed scheme is validated by predicting the concentration field in a benchmark solidification problem. Results compare well with an available similarity solution. The simplicity of the proposed explicit scheme allows for the incorporation of complex microscale models into a general solidification model. This is demonstrated by investigating the role of dendrite coarsening on the concentration field in the solidification benchmark problem.

Numerical investigation of case hardening of plant tissue during dying and its influence on the cellular level shrinkage

Dried plant food materials are one of the major contributors to the global food industry. Widening the fundamental understanding on different mechanisms of food material alterations during drying assists the development of novel dried food products and processing techniques. In this regard, case hardening is an important phenomenon, commonly observed during the drying processes of plant food materials, which significantly influences the product quality and process performance. In this work, a recent meshfree-based numerical model of the authors is further improved and used to simulate the influence of case hardening on shrinkage characteristics of plant tissues during drying. In order to model fluid and wall mechanisms in each cell, Smoothed Particle Hydrodynamics (SPH) and the Discrete Element Method (DEM) are used. The model is fundamentally more capable of simulating large deformation of multiphase materials, when compared with conventional grid-based modelling techniques such as Finite Element Methods (FEM) or Finite Difference Methods (FDM). Case hardening is implemented by maintaining distinct moisture levels in the different cell layers of a given tissue. In order to compare and investigate different factors influencing tissue deformations under case hardening, four different plant tissue varieties (apple, potato, carrot and grape) are studied. The simulation results indicate that the inner cells of any given tissue undergo limited shrinkage and cell wall wrinkling compared to the case hardened outer cell layers of the tissues. When comparing unique deformation characteristics of the different tissues, irrespective of the normalised moisture content, the cell size, cell fluid turgor pressure and cell wall characteristics influence the tissue response to case hardening.

Wind resource modelling in complex terrain using different mesoscale–microscale coupling techniques

Wind resource evaluation in two sites located in Portugal was performed using the mesoscale modelling system Weather Research and Forecasting (WRF) and the wind resource analysis tool commonly used within the wind power industry, the Wind Atlas Analysis and Application Program (WAsP) microscale model. Wind measurement campaigns were conducted in the selected sites, allowing for a comparison between in situ measurements and simulated wind, in terms of flow characteristics and energy yields estimates. Three different methodologies were tested, aiming to provide an overview of the benefits and limitations of these methodologies for wind resource estimation. In the first methodology the mesoscale model acts like “virtual” wind measuring stations, where wind data was computed by WRF for both sites and inserted directly as input in WAsP. In the second approach, the same procedure was followed but here the terrain influences induced by the mesoscale model low resolution terrain data were removed from the simulated wind data. In the third methodology, the simulated wind data is extracted at the top of the planetary boundary layer height for both sites, aiming to assess if the use of geostrophic winds (which, by definition, are not influenced by the local terrain) can bring any improvement in the models performance. The obtained results for the abovementioned methodologies were compared with those resulting from in situ measurements, in terms of mean wind speed, Weibull probability density function parameters and production estimates, considering the installation of one wind turbine in each site. Results showed that the second tested approach is the one that produces values closest to the measured ones, and fairly acceptable deviations were found using this coupling technique in terms of estimated annual production. However, mesoscale output should not be used directly in wind farm sitting projects, mainly due to the mesoscale model terrain data poor resolution. Instead, the use of mesoscale output in microscale models should be seen as a valid alternative to in situ data mainly for preliminary wind resource assessments, although the application of mesoscale and microscale coupling in areas with complex topography should be done with extreme caution.

Modeling of advanced high strength steels with the realistic microstructure–strength relationships

The objective of the work is to consider the first-order effects of the realistic microstructure morphology in the macroscale modeling of the multiphase Advanced High Strength Steels (AHSS). Instead of using constitutive equations at macroscale, the strength–microstructure relationship is studied in the forms of micromechanical and multiscale models that do not make considerable simplifications with regard to the microscale geometry and topology. The trade-off between the higher computational time and the higher accuracy has been offset with a stochastic approach in the construction of the microscale models. The multiphase composite effects of AHSS microstructure is considered in realistic microstructural models that are stochastically built from AHSS micrographs. Computational homogenization routines are used to couple micro and macroscale and resultant stress–strain relations are compared for models built with the simplified and idealized geometries of the microstructure. The results from this study show that using a realistic representation of the microstructure, either for DP or TRIP steel, could improve the accuracy of the predicted stress and strain distribution. The resultant globally averaged effective stress and strain fields from realistic microstructure model were able to accurately capture the onset of the plastic instability in the DP steel. It is shown that the macroscale mechanical behavior is directly affected by the level of complexities in the microscale models. Therefore, greater accuracy could be achieved if these stochastic realistic microstructures are used at the microscale models.

Building macroscale models from microscale probabilistic models : a general probabilistic approach for nonlinear diffusion and multispecies phenomena

A discrete agent-based model on a periodic lattice of arbitrary dimension is considered. Agents move to nearest-neighbor sites by a motility mechanism accounting for general interactions, which may include volume exclusion. The partial differential equation describing the average occupancy of the agent population is derived systematically. A diffusion equation arises for all types of interactions and is nonlinear except for the simplest interactions. In addition, multiple species of interacting subpopulations give rise to an advection-diffusion equation for each subpopulation. This work extends and generalizes previous specific results, providing a construction method for determining the transport coefficients in terms of a single conditional transition probability, which depends on the occupancy of sites in an influence region. These coefficients characterize the diffusion of agents in a crowded environment in biological and physical processes.

A compact difference scheme for numerical solutions of second order dual-phase-lagging models of microscale heat transfer

Dual-phase-lagging (DPL) models constitute a family of non-Fourier models of heat conduction that allow for the presence of time lags in the heat flux and the temperature gradient. These lags may need to be considered when modeling microscale heat transfer, and thus DPL models have found application in the last years in a wide range of theoretical and technical heat transfer problems. Consequently, analytical solutions and methods for computing numerical approximations have been proposed for particular DPL models in different settings. In this work, a compact difference scheme for second order DPL models is developed, providing higher order precision than a previously proposed method. The scheme is shown to be unconditionally stable and convergent, and its accuracy is illustrated with numerical examples.

Incorporating weather into regionwide safety planning prediction models

Predicting safety on roadways is standard practice for road safety professionals and has a corresponding extensive literature. The majority of safety prediction models are estimated using roadway segment and intersection (microscale) data, while more recently efforts have been undertaken to predict safety at the planning level (macroscale). Safety prediction models typically include roadway, operations, and exposure variables—factors known to affect safety in fundamental ways. Environmental variables, in particular variables attempting to capture the effect of rain on road safety, are difficult to obtain and have rarely been considered. In the few cases weather variables have been included, historical averages rather than actual weather conditions during which crashes are observed have been used. Without the inclusion of weather related variables researchers have had difficulty explaining regional differences in the safety performance of various entities (e.g. intersections, road segments, highways, etc.) As part of the NCHRP 8-44 research effort, researchers developed PLANSAFE, or planning level safety prediction models. These models make use of socio-economic, demographic, and roadway variables for predicting planning level safety. Accounting for regional differences - similar to the experience for microscale safety models - has been problematic during the development of planning level safety prediction models. More specifically, without weather related variables there is an insufficient set of variables for explaining safety differences across regions and states. Furthermore, omitted variable bias resulting from excluding these important variables may adversely impact the coefficients of included variables, thus contributing to difficulty in model interpretation and accuracy. This paper summarizes the results of an effort to include weather related variables, particularly various measures of rainfall, into accident frequency prediction and the prediction of the frequency of fatal and/or injury degree of severity crash models. The purpose of the study was to determine whether these variables do in fact improve overall goodness of fit of the models, whether these variables may explain some or all of observed regional differences, and identifying the estimated effects of rainfall on safety. The models are based on Traffic Analysis Zone level datasets from Michigan, and Pima and Maricopa Counties in Arizona. Numerous rain-related variables were found to be statistically significant, selected rain related variables improved the overall goodness of fit, and inclusion of these variables reduced the portion of the model explained by the constant in the base models without weather variables. Rain tends to diminish safety, as expected, in fairly complex ways, depending on rain frequency and intensity.

A particle based model to simulate microscale morphological changes of plant tissues during drying

Fundamental understanding on microscopic physical changes of plant materials is vital to optimize product quality and processing techniques, particularly in food engineering. Although grid-based numerical modelling can assist in this regard, it becomes quite challenging to overcome the inherited complexities of these biological materials especially when such materials undergo critical processing conditions such as drying, where the cellular structure undergoes extreme deformations. In this context, a meshfree particle based model was developed which is fundamentally capable of handling extreme deformations of plant tissues during drying. The model is built by coupling a particle based meshfree technique: Smoothed Particle Hydrodynamics (SPH) and a Discrete Element Method (DEM). Plant cells were initiated as hexagons and aggregated to form a tissue which also accounts for the characteristics of the middle lamella. In each cell, SPH was used to model cell protoplasm and DEM was used to model the cell wall. Drying was incorporated by varying the moisture content, the turgor pressure, and cell wall contraction effects. Compared to the state of the art grid-based microscale plant tissue drying models, the proposed model can be used to simulate tissues under excessive moisture content reductions incorporating cell wall wrinkling. Also, compared to the state of the art SPH-DEM tissue models, the proposed model better replicates real tissues and the cell-cell interactions used ensure efficient computations. Model predictions showed good agreement both qualitatively and quantitatively with experimental findings on dried plant tissues. The proposed modelling approach is fundamentally flexible to study different cellular structures for their microscale morphological changes at dehydration.

A meshfree particle based model for microscale shrinkage mechanisms of food materials in drying conditions

Cells are the fundamental building block of plant based food materials and many of the food processing born structural changes can fundamentally be derived as a function of the deformations of the cellular structure. In food dehydration the bulk level changes in porosity, density and shrinkage can be better explained using cellular level deformations initiated by the moisture removal from the cellular fluid. A novel approach is used in this research to model the cell fluid with Smoothed Particle Hydrodynamics (SPH) and cell walls with Discrete Element Methods (DEM), that are fundamentally known to be robust in treating complex fluid and solid mechanics. High Performance Computing (HPC) is used for the computations due to its computing advantages. Comparing with the deficiencies of the state of the art drying models, the current model is found to be robust in replicating drying mechanics of plant based food materials in microscale.

Microscale consolidation analysis of relaxation behavior of single living chondrocytes subjected to varying strain-rates

Besides the elastic stiffness, the relaxation behavior of single living cells is also of interest of various researchers when studying cell mechanics. It is hypothesized that the relaxation response of the cells is governed by both intrinsic viscoelasticity of the solid phase and fluid-solid interactions mechanisms. There are a number of mechanical models have been developed to investigate the relaxation behavior of single cells. However, there is lack of model enable to accurately capture both of the mechanisms. Therefore, in this study, the porohyperelastic (PHE) model, which is an extension of the consolidation theory, combined with inverse Finite Element Analysis (FEA) technique was used at the first time to investigate the relaxation response of living chondrocytes. This model was also utilized to study the dependence of relaxation behavior of the cells on strain-rates. The stress-relaxation experiments under the various strain-rates were conducted with the Atomic Force Microscopy (AFM). The results have demonstrated that the PHE model could effectively capture the stress-relaxation behavior of the living chondrocytes, especially at intermediate to high strain-rates. Although this model gave some errors at lower strain-rates, its performance was acceptable. Therefore, the PHE model is properly a promising model for single cell mechanics studies. Moreover, it has been found that the hydraulic permeability of living chondrocytes reduced with decreasing of strain-rates. It might be due to the intracellular fluid volume fraction and the fluid pore pressure gradients of chondrocytes were higher when higher strain-rates applied.