Lumped Method Research Articles

東京湾における潮流発電ポテンシャル算定に対するカルマンフィルタFEMの適用

In recent years, tidal stream power generation is attracting attention as renewable energy. When a turbine submerged in the sea is rotated by a tidal current, kinetic energy is transformed to electric energy in this power generation method. In this paper, we present a flow field estimation analysis based on the Kalman filter FEM for locating the optimal positions for tidal stream power generation systems. We employed the shallow water equation as the governing equation. The Galerkin and the selective lumping methods are used as discretization techniques in space and time, respectively. The Kalman filter theory is applied to estimate the flow field. As a numerical example, we carried out a flow estimation analysis for Tokyo Bay and the electric power generation potential is calculated using the estimated flow field. It was confirmed that the estimation accuracy of the flow field estimation analysis by the Kalman filter FEM is higher than that by the conventional FEM.

Vapor-liquid phase boundaries and swelling factors of C3H8-n-C4H10-CO2-heavy oil systems under reservoir conditions

Techniques have been developed to determine vapor-liquid phase boundaries and swelling factors of CO2-heavy oil systems and C3H8-n-C4H10-CO2-heavy oil systems under reservoir conditions. Experimentally, a pure substance of CO2 and a gas mixture consisting of 27.7 mol% C3H8, 23.9 mol% n-C4H10, and 48.4 mol% CO2 are respectively introduced to dilute the highly viscous heavy oil. A pressure-volume-temperature (PVT) setup is used to measure vapor-liquid phase boundaries (i.e., saturation pressures) and swelling factors at high pressures up to 11.1 MPa and elevated temperatures up to 373.35 K. Theoretically, the volume-translated Peng-Robinson equation of state (PR EOS) coupled with a recently modified alpha function is applied as the primary thermodynamic model to reproduce the experimental measurements. The heavy oil which is a complex mixture with unknown molecular structure is characterized as six pseudocomponents by using an exponential distribution splitting function and a logarithm-type lumping method. The optimal exponents in binary interaction parameter (BIP) correlations are obtained by best matching the measured saturation pressures. Subsequently, the comparisons have been performed between this work and a commercial simulator in terms of the overall prediction accuracy of saturation pressures for the quaternary C3H8-n-C4H10-CO2-heavy oil systems. It is found that the minimum absolute average relative deviation (AARD) of 6.7% is obtained by the methodology developed in this work, compared to the AARD of 35.6% obtained by running the commercial simulator.

Second-order finite elements for Hex-Dominant explicit methods in nonlinear solid dynamics

Hexahedral-dominant modeling approaches strike a balance of meshing ease and accuracy/efficiency by exploiting wedge (and/or pyramid) elements to transition from hexahedral elements to volumes filled by other types. Unfortunately, first-order wedges are frequently very poor performers and are the only ones typically contained in explicit solid dynamic programs. The historic preference of first-order elements with explicit methods has frequently been for simplicity and cost, but has also been from the lack of both a satisfactory consistent nodal loading distribution and an acceptable mass lumping technique for serendipity elements. Row summation lumping, for example, produces negative and zero vertex node masses for the popular fifteen and eighteen node wedges, respectively, and zero vertex nodal loads from a uniform traction on the triangular faces. The paper first presents twenty-one node wedge element formulations that produce all positive nodal loads from uniform tractions and row summation mass lumping for this element is shown to produce all positive nodal masses. In addition, they are compatible with other second-order elements applicable to lumped mass explicit methods. Performance is assessed in standard benchmark problems and practical applications using various elastic and elastic-plastic material models and involving very large strains/deformations, severe distortions, and contact-impact. These wedge elements are evaluated on their own as well as part of hexahedral-dominant meshes that use wedges for fill regions and transition from hexahedral to tetrahedral elements. In all cases, these elements performed satisfactorily and thus demonstrate their viability and benefits for practical applications, especially for fill and transition regions of low interest.

Design and calibration of a novel transient radiative heat flux meter for a spacecraft thermal test.

Radiative heat flux measurement is significantly important for a spacecraft thermal test. To satisfy the requirements of both high accuracy and fast response, a novel transient radiative heat flux meter was developed. Its thermal receiver consists of a central thermal receiver and two thermal guarded annular plates, which ensure the temperature distribution of the central thermal receiver to be uniform enough for reasonably applying lumped heat capacity method in a transient radiative heat flux measurement. This novel transient radiative heat flux meter design can also take accurate measurements regardless of spacecraft surface temperature and incident radiation spectrum. The measurement principle was elaborated and the coefficients were calibrated. Experimental results from testing a blackbody furnace and an Xenon lamp show that this novel transient radiative heat flux meter can be used to measure transient radiative heat flux up to 1400 W/m(2) with high accuracy and the response time of less than 10 s.

Modeling and analysis of paste freezing in freeze-form extrusion fabrication of thin-wall parts via a lumped method

During the Freeze-form Extrusion Fabrication (FEF) process using aqueous-based pastes, the freezing environment solidifies the water content in the paste and thus aids the part in maintaining its shape. Because of the small temperature variation in the paste and the paste’s large latent heat introduced by the water contained in the paste, the paste typically freezes slowly during the FEF process. In this study, a lumped method was used to model the solidification process of thin-wall parts fabricated in a layer-by-layer manner. A non-dimensional analytical solution for the freezing time of parts with large numbers of layers was obtained using the lumped method, and its corresponding dimensional solution was compared with numerical simulation results. Based on the analytical solution, the effects of two non-dimensional factors (i.e., non-dimensional latent heat and effective Biot number) and six dimensional factors (i.e., convection coefficient, paste material, paste solids loading, ambient temperature, filament height, and filament width) on the freezing time were investigated. Experiments using different solids loadings pastes and extrusion parameters were conducted to validate the freezing time predictions generated by the lumped method. Possible error sources during the experiments were discussed and their effects were estimated. The results show that the lumped method can be used to accurately predict the freezing time of thin-wall parts within 17.9% differences from the measured results.

A combinational efficient algorithm for elliptic eigenvalue problems

In this paper, we present a combinational efficient algorithm for solving second-order elliptic ordinary differential equation eigenvalue problems on four kinds of meshes. Firstly, a combinational scheme is proposed by leveraging the linear finite element scheme and the second-order finite difference scheme based on mass lumping method. An efficient algorithm is constructed by using the combinational scheme with a constant combined parameter. Then, we improve the efficient algorithm by computing the quasi-optimal combined parameters for different eigenvalues. Finally, numerical experiments tested on both uniform and nonuniform meshes are shown to illustrate the efficiency of our algorithms.

Application of Biologically Based Lumping To Investigate the Toxicokinetic Interactions of a Complex Gasoline Mixture.

People are often exposed to complex mixtures of environmental chemicals such as gasoline, tobacco smoke, water contaminants, or food additives. We developed an approach that applies chemical lumping methods to complex mixtures, in this case gasoline, based on biologically relevant parameters used in physiologically based pharmacokinetic (PBPK) modeling. Inhalation exposures were performed with rats to evaluate the performance of our PBPK model and chemical lumping method. There were 109 chemicals identified and quantified in the vapor in the chamber. The time-course toxicokinetic profiles of 10 target chemicals were also determined from blood samples collected during and following the in vivo experiments. A general PBPK model was used to compare the experimental data to the simulated values of blood concentration for 10 target chemicals with various numbers of lumps, iteratively increasing from 0 to 99. Large reductions in simulation error were gained by incorporating enzymatic chemical interactions, in comparison to simulating the individual chemicals separately. The error was further reduced by lumping the 99 nontarget chemicals. The same biologically based lumping approach can be used to simplify any complex mixture with tens, hundreds, or thousands of constituents.

Application of an Investigated Lump Method to the Simulation of Ground Motion For Beichuan Town During the Wenchuan Earthquake

An investigated lump method based on the mixed mesh of triangle and quadrangle for simulating near-fault ground motion is presented by using finite-fault sources and a differential type of viscoelastic constitutive equations of the generalized zener body (GZB) with two mechanisms. One numerical test is performed to verify the validity and accuracy of the investigated lump method. The ground motion in Beichuan town during the Wenchuan earthquake is simulated, considering attenuation of real earth material and the effect of realistic topography. Numerical results of simulations demonstrated that the viscoelasticity of earth medium attenuates the PGAs noticeably and changes the frequency characteristics of the ground motion. The local topography influences greatly the PGAs in the area of Beichuan town.

カルマンフィルタ有限要素法による浅水域における流れ場の推定精度の検証（観測変数・観測点の数および位置が推定精度に与える影響）

In this study, the estimation of the flow field in open channel is carried out based on the finite element method and the Kalman filter theory. As the governing equation, the shallow water equation is employed, and the finite element and the selective lumping methods are applied to discretize the governing equation in space and time, respectively. The estimation of the distribution of the velosity vector and the water elevation is carried out by using the equations obtained by the Kalman filter theory. In the numerical experiments, the open channel flow is treated, and some examinations are carried out by changing the observation variables, number and posision of observation points.

305 カルマンフィルタ有限要素法による流れ場の推定解析における計測点配置に関する検討(OS4-2 次世代シミュレーション技術の開拓)

The Kalman filter developed by R. E. Kalman and R. S. Bucy is states estimation theory in the target domain and has been employed in various field of engineering. In general, observation data in any system include observation noise and the computational model include system noise. These noises can be eliminated by using a Kalman filter. The finite element equation is applied to derive the state transition matrix in the system equation of the Kalman filter. As the fundamental study, the estimation of the flow field in open channel is carried out based on the finite element method and the Kalman filter theory. In addition, as the governing equation, the shallow water equations are employed, and the finite element and the selective lumping methods are applied to discretize the governing equations in space and time, respectively. The open channel model is employed in the numerical experiment, and some examinations are carried out by changing the observation variables, number and position of observation points.

カルマンフィルタFEMによる浅水域の流れ場推定結果に対する境界条件の影響

In this study, we present numerical examples for estimation of shallow water flow based on the Kalman filter FEM. The shallow water equation is employed as the governing equation, and the Galerkin method using the triangular element and the selective lumping method are applied to discretize the governing equation in space and time, respectively. We investigated difference of numerical results by changing position of the observation points. It was found that high accurate flow field estimation result is obtained in case that the observation points are set to the upstream side in the open channel in comparison with the case that the observation points are set to the downstream side in the open channel. Therefore, inflow boundary condition is introduced to estimation analysis of shallow water flow based on Kalman filter FEM, and examinations of inflow boundary condition on the estimation accuracy are carried out.

Reduction of a Whole-Body Physiologically Based Pharmacokinetic Model to Stabilise the Bayesian Analysis of Clinical Data.

Whole-body physiologically based pharmacokinetic (PBPK) models are increasingly used in drug development for their ability to predict drug concentrations in clinically relevant tissues and to extrapolate across species, experimental conditions and sub-populations. A whole-body PBPK model can be fitted to clinical data using a Bayesian population approach. However, the analysis might be time consuming and numerically unstable if prior information on the model parameters is too vague given the complexity of the system. We suggest an approach where (i) a whole-body PBPK model is formally reduced using a Bayesian proper lumping method to retain the mechanistic interpretation of the system and account for parameter uncertainty, (ii) the simplified model is fitted to clinical data using Markov Chain Monte Carlo techniques and (iii) the optimised reduced PBPK model is used for extrapolation. A previously developed 16-compartment whole-body PBPK model for mavoglurant was reduced to 7 compartments while preserving plasma concentration-time profiles (median and variance) and giving emphasis to the brain (target site) and the liver (elimination site). The reduced model was numerically more stable than the whole-body model for the Bayesian analysis of mavoglurant pharmacokinetic data in healthy adult volunteers. Finally, the reduced yet mechanistic model could easily be scaled from adults to children and predict mavoglurant pharmacokinetics in children aged from 3 to 11years with similar performance compared with the whole-body model. This study is a first example of the practicality of formal reduction of complex mechanistic models for Bayesian inference in drug development.

Evaluating the spread plasticity model of IDARC for inelastic analysis of reinforced concrete frames

There are two types of nonlinear analysis methods for building frameworks depending on the method of modeling the plastification of members including lumped plasticity and distributed plasticity. The lumped plasticity method assumes that plasticity is concentrated at a zero-length plastic hinge section at the ends of the elements. The distributed plasticity method discretizes the structural members into many line segments, and further subdivides the cross-section of each segment into a number of finite elements. When a reinforced concrete member experiences inelastic deformations, cracks tend to spread form the joint interface resulting in a curvature distribution. The program IDARC includes a spread plasticity formulation to capture the variation of the section flexibility, and combine them to determine the element stiffness matrix. In this formulation, the flexibility distribution in the structural elements is assumed to be the linear. The main objective of this study is to evaluate the accuracy of linear flexibility distribution assumed in the spread inelasticity model. For this purpose, nonlinear analysis of two reinforced concrete frames is carried out and the linear flexibility models used in the elements are compared with the real ones. It is shown that the linear flexibility distribution is incorrect assumption in cases of significant gravity load effects and can be lead to incorrect nonlinear responses in some situations.

Feedstock molecular reconstruction for secondary reactions of fluid catalytic cracking gasoline by maximum information entropy method

A novel methodology of maximum information entropy theory combined with structure oriented lumping (SOL) and Monte Carlo (MC) method was developed to simulate the feedstock for secondary reactions of fluid catalytic cracking (FCC) gasoline at the molecular level. The SOL method was applied to represent the feedstock configuration framework; a molecular library consisting of a large ensemble of computational molecules was created by stochastically assembling structural increments using MC method; then, the maximum information entropy method (MIEM) was introduced to adjust the mole fractions of the structural increments in the molecular library to achieve a closer matching with the actual analytical characteristics. Three samples of catalytic cracking gasoline from the industrial FCC units of China were used to validate and evaluate the proposed method. The simulation results of the feedstock properties, such as the average molecular weight and the weight fractions of main components including paraffin, olefins, naphthenes and aromatics agreed well with the experimental data.

Analysis of the Land Surface Temperature Scaling Problem: A Case Study of Airborne and Satellite Data over the Heihe Basin

This study analyzed the scaling problem of land surface temperature (LST) data retrieved with the Temperature Emissivity Separation (TES) algorithm. We compiled a remotely sensed dataset that included Thermal Airborne Hyperspectral Imager (TASI) and satellite-based Advanced Spaceborne Thermal Emission Reflection (ASTER) data, which were acquired simultaneously. This dataset provided the range of spatial heterogeneities of land surface necessary for the study, which was quantified by the dispersion variance. The LST scaling problem was studied by comparing the remotely sensed LST products in two ways. First, the LST products calculated in the distributed method and the lumped method were compared. Second, the airborne and satellite-based LST products derived from the TES algorithm were compared. Four upscaling methods of LST were used in the process. A scaling correction methodology was developed based on the comparisons. The results showed that the scaling effect could be as large as 0.8 when the spatial resolution of the TASI LST data was coarse. The scaling effect increases quickly with the spatial resolution until it reaches the characteristic scale of the landscape and is positively correlated with the spatial heterogeneity. The first two upscaling methods denoted as Methods 1–2 can upscale the LST more effectively when compared with the other two scaling methods (Methods 3–4). The scaling effect for the ASTER data is not notable. The comparison between the TASI and ASTER data showed that they were highly consistent, with a root mean square error (RMSE) of approximately 0.88 K, when the pixels were relatively homogeneous. When the spatial heterogeneity was significant, the RMSE was as large as 2.68 K The scaling correction methodology provided resolution-invariant results with scaling effects of less than 0.5 K.

Aeroelastic behavior of a flag in ground effect

The aeroelastic behavior of a flexible plate subjected to a uniform axial flow is investigated in the presence of a rigid plane set parallel to the plate. It is shown that the ground effect reduces the flutter inflow velocity and strengthens the possibility of using the flag for extracting energy from winds and currents. The numerical analysis is carried out assuming that both the unsteady potential incompressible flow and the plate can be described with 2D models, i.e., a lumped vortex panel method and a nonlinear Euler–Bernoulli beam model, respectively, without losing the essential features of the fluid–structure interaction. Asymmetry of post-critical behavior (limit-cycle oscillations) and sensitivity of the results to the main flag parameters (distance from the ground, mass ratio and damping) are also considered, including also the energy distribution over the identified proper orthogonal modes. The investigated reduction of the flutter velocity in ground effect has been also confirmed with experimental tests relative to a polypropylene flag with and without the rigid panel mimicking the presence of the ground.

Generalised element load method for first- and second-order element solutions with element load effect

The finite element method in principle adaptively divides the continuous domain with complex geometry into discrete simple subdomain by using an approximate element function, and the continuous element loads are also converted into the nodal load by means of the traditional lumping and consistent load methods, which can standardise a plethora of element loads into a typical numerical procedure, but element load effect is restricted to the nodal solution. It in turn means the accurate continuous element solutions with the element load effects are merely restricted to element nodes discretely, and further limited to either displacement or force field depending on which type of approximate function is derived. On the other hand, the analytical stability functions can give the accurate continuous element solutions due to element loads. Unfortunately, the expressions of stability functions are very diverse and distinct when subjected to different element loads that deter the practical applications. To this end, this paper presents a displacement-based finite element function (generalised element load method) with a plethora of element load effects in the similar fashion that never be achieved by the stability function, as well as it can generate the continuous first- and second-order elastic displacement and force solutions along an element without loss of accuracy considerably as the analytical approach that never be achieved by neither the lumping nor consistent load methods. Hence, the salient and unique features of this paper (generalised element load method) embody its robustness, versatility and accuracy in continuous element solutions when subjected to the great diversity of transverse element loads.

Dynamics of Pb(II) adsorption on nanostructured γ-alumina: calculations of axial dispersion and overall mass transfer coefficients in the fixed-bed column.

In the present study, the removal of metal ions Pb(II) using nanostructured γ-alumina was investigated by tests on batch operations and fixed-bed columns. Optimization was determined for factors effective on adsorption such as pH, contact time of metal solution with adsorbent and initial solution concentration. The optimum pH level was determined at 4.5 and the maximum adsorption percentage was achieved at 150 minutes. pHpzc was measured 8.3 for nanostructured γ-Al2O3. The Langmuir, Freundlich and Temkin isotherms were used to analyze the experimental data. The Langmuir isotherm model showed the best agreement with the experimental data. The model showed evaluations for maximum adsorption capacity of adsorbent at 119.04 mg/g and adsorbent bed performance for different flow rates, bed heights and influent concentrations were also investigated. The lumped method was used to solve the bed equations, to predict the breakthrough curve and model overall mass transfer coefficient (Koverall) and axial dispersion coefficient (Dz) parameters to make comparisons with experimental results.

Olefin profile prediction of naphtha pyrolysis using a feeding-independent continuous lumping method with mechanism analysis

By avoiding the massive calculations of complicated reaction networks, the continuous lumping method has been welcomed as a means of describing hydrocarbon pyrolysis processes. In our work, with the introduction of a new distribution function representing different structure effects on kinetic parameters, a mechanism-oriented continuous lumping model is proposed to acquire the olefin profile of naphtha pyrolysis with experimentation independent of different feeding compositions. Meanwhile, micro-reactor pyrolysis experiments are conducted to analyze the structure mechanism and to obtain the pyrolysis parameters. The analytical results indicate that long-chain molecules with higher degrees of branching react faster, and long-chain alkanes with fewer side chains are more inclined to form ethylene product. The prediction results of the simulation method are consistent with the experimental results. The prediction performance is comparatively accurate and independent of feeding.

New kinetic model of coal tar hydrogenation process via carbon number component approach

Hydrogenation technology is an important chemical upgrading process for low quality oil such as coal tar. Kinetic modeling for hydrogenation process remains a challenging task because of the large amount of compounds and complex reactions involved. Therefore, a new systematic methodology is proposed in this study to characterize mixture streams for the kinetic modeling of coal tar hydrogenation. The methodology incorporates both lumped method based on boiling point to represent feedstock and a carbon number-based component approach in the form of a structural matrix to characterize products at a molecular level. A mathematical transformation model is built for interrelating the bulk properties and molecular composition of products. A detailed kinetic model for coal tar hydrogenation is constructed based on the reaction pathway networks between lumped feedstock and carbon number-based molecular product. Detailed molecular compositions of the products are obtained from experiments to provide a basis for estimating the parameters of the kinetic model. The proposed method is verified by experiment results, which are consistent with predicted values.