Lumped Method Research Articles

Application of a lumping method for fatigue design of monopile-based wind turbines using fully coupled and simplified models

The study presents different methods for fatigue assessment of monopile-based offshore wind turbines. Their accuracy and computational time is compared to full long-term time domain results. The damage-equivalent lumping method from Katsikogiannis et al. (2021) is further examined using nonlinear fully coupled time domain models as well as simplified, frequency domain, state–space models for three turbines (5 MW, 10 MW, 15 MW). The different dynamic characteristics of these turbines affect the resultant contour lines and lumped load cases for various wave conditions. The lumping method using fully coupled models had an accuracy of 92%–98% for the total fatigue damage along the support structure for all turbines, and decreased the computational time by 90%. The simplified models were able to accurately capture the dynamic characteristics of the turbines in the lumping process, resulting in similar lumped load cases and accuracy, with further reduction of the computational effort (96%). Long-term fatigue assessment in frequency domain generally resulted in discrepancies compared to time domain assessment (40%–80%), mainly due to the linear soil stiffness, sensitivity to damping (especially for parked conditions), and the simplified representation of the control system in the simplified models. Using the simplified models to select the lumped load cases, combined with time domain analyses of the lumped cases, resulted in the best combination of accuracy and computational effort.

Arbitrarily High-Order Maximum Bound Preserving Schemes with Cut-off Postprocessing for Allen–Cahn Equations

We develop and analyze a class of maximum bound preserving schemes for approximately solving Allen–Cahn equations. We apply a kth-order single-step scheme in time (where the nonlinear term is linearized by multi-step extrapolation), and a lumped mass finite element method in space with piecewise rth-order polynomials and Gauss–Lobatto quadrature. At each time level, a cut-off post-processing is proposed to eliminate extra values violating the maximum bound principle at the finite element nodal points. As a result, the numerical solution satisfies the maximum bound principle (at all nodal points), and the optimal error bound \(O(\tau ^k+h^{r+1})\) is theoretically proved for a certain class of schemes. These time stepping schemes include algebraically stable collocation-type methods, which could be arbitrarily high-order in both space and time. Moreover, combining the cut-off strategy with the scalar auxiliary value (SAV) technique, we develop a class of energy-stable and maximum bound preserving schemes, which is arbitrarily high-order in time. Numerical results are provided to illustrate the accuracy of the proposed method.

Calculation of reaction network and product properties of delayed coking process based on structural increments

The delayed coking reaction kinetic model based on the structure-oriented lumping method showed good accuracy in predicting the yield and composition of coking products at the molecular level. Based on the basic law that molecular structure determines molecular properties, the structural increment contribution method was constructed to expand the functions of established reaction kinetic model to predict the characteristic properties of coking gasoline and diesel products: distillation range, density, research octane number (RON) or cetane number (CN). The contributions of different structural increments of hydrocarbon molecules in gasoline to the RON and those in diesel to the CN could also be calculated by the model. The RONs of the hydrocarbon molecules decreased with the increase of R, and increased with the increase of br and me for the coking gasoline. The CNs of the paraffins molecules improved with the increase of R, but reduced with the increase of br and A6 for the coking diesel. The effects of all structural increments on the RON and CN could be quantitatively calculated through the established correlation formulas. The prediction of composition and properties of coking gasoline and diesel based on the model could guide the subsequent processing and process optimization of delayed coking plant.

Fast mass lumped multiscale wave propagation modelling

Abstract In this paper we investigate the use of a mass lumped fully explicit time-stepping scheme for the discretization of the wave equation with underlying material parameters that vary at arbitrarily fine scales. We combine the leapfrog scheme for the temporal discretization with the multiscale technique known as localized orthogonal decomposition (LOD) for the spatial discretization. To speed up the method and to make it fully explicit, a special mass lumping approach is introduced that relies on an appropriate interpolation operator. This operator is also employed in the construction of the LOD and is a key feature of the approach. We prove that the method converges with second order in the energy norm, with a leading constant that does not depend on the scales at which the material parameters vary. We also illustrate the performance of the mass lumped method in a set of numerical experiments.

Development and validation of a n‐butanol reduced chemical kinetic mechanism under engine relevant conditions

AbstractA n‐butanol reduced mechanism (60 species and 306 reactions) was developed using the direct relation graph with error propagation and isomer lumping methods. Sensitivity analysis (SA) was then performed to identify reactions that were sensitive to the ignition delay (ID) for the adjustments of the pre‐exponential factor to replicate the experimental ID times. As compared with the experimental measurements at initial temperatures of 343–1350 K, initial pressures of 0.02–80 bar, and equivalence ratios of 0.5–2.0, the maximum deviation for the predictions by the n‐butanol reduced mechanism was at 37.75% for the ID times, 8 cm/s for the laminar flame speed, and a factor of three for both the species concentration profiles under jet‐stirred reactor and premixed laminar flame. Furthermore, a maximum deviation of 2.5 crank angle degrees in combustion phasing was obtained when the reduced mechanism was benchmarked against the detailed mechanism under homogeneous charge compression ignition (HCCI) conditions at initial temperature of 413 K, initial pressure of 1 bar, and equivalence ratios of 0.5–2.0. Despite these deviations, the low temperature IDs and the laminar flame speed predicted by the present reduced mechanism were in better agreement to the experimental measurements than the existing n‐butanol reduced mechanisms of comparable sizes. Hence, this collectively indicates that improvements were made to the present reduced mechanism, particularly for the low‐temperature reactions. The n‐butanol reduced mechanism was also compared with gasoline and diesel surrogates under 0D HCCI simulations. The results indicate that the combustion characteristics of n‐butanol is closer to gasoline than to diesel. This suggests that n‐butanol could safely replace gasoline fuel in neat form while it is more suitable to be blended with diesel fuel to maintain engine performance and prevent any adverse effects on the engine.

Electro-Thermal Modeling of Power IGBT Module Cooled by A Heat Pipe Cooling System

This paper deals with the development of an electro-thermal model of an Insulated Gate Bipolar Transistor (IGBT) with a water-cooled heat pipe cooling system. Firstly, a thermal model of the heat pipe cooling system is proposed. Then, an electro-thermal model of the IGBT is developed to predict the junction temperature variations in transient operation. The thermal model of the IGBT is determined on the base of the thermal-capacitance lumped method. The electrical model of the IGBT is developed by considering the effect of the junction temperature on its static electrical parameters. Finally, the electro-thermal model is considered in a boost converter application. The model predictions show the effectiveness of the heat pipe cooling system for different commutation frequencies. It is proved that the heat pipe cooling system can keep the junction temperature of the IGBT at values allowing safe operation.

Molecular-level reaction network in delayed coking process based on structure-oriented lumping

Based on the structure-oriented lumping method, a molecular-level reaction kinetic model of the delayed coking process, which adopted 24 structural increments to construct the feed molecular matrix containing 2944 molecules, was established with a reaction network containing 74,581 reactions using MATLAB. The reliability of the model was verified by experimental results. According to the discriminant rules of structural increments, 173 structural vectors in gasoline and 1132 structural vectors in diesel were classified into different group compositions, respectively. The model could track the reaction path of any specific molecule in the complex thermal cracking reaction network. The influences of operation conditions such as recycle ratio on the product distribution could be discovered through the calculation of the molecular-level model, which is helpful for the process optimization and precise regulation of product composition for the delayed coking plants.

Construction of reduced oxidation mechanisms of polyoxymethylene dimethyl ethers (PODE1–6) with consistent structure using decoupling methodology and reaction rate rule

Due to high oxygen content and lack of CC bond, polyoxymethylene dimethyl ethers (PODEn) have become desired fuel additives to simultaneously reduce nitrogen oxides (NOx) and soot emissions. However, there is a vacancy of reduced reaction mechanisms to describe the long-chain PODEn (n>3) combustion for engine simulations. This study aims at the construction of reduced mechanisms for the series of PODE1–6 with a consistent structure based on the decoupling methodology and reaction rate rule. First, the reduced mechanisms of PODE1–2 are constructed using the reaction class-based global sensitivity analysis and the decoupling methodology. In the reduced mechanisms of PODE1–2, the skeletal fuel-related sub-mechanism is integrated with a detailed H2/CO/C1 sub-mechanism and a reliable reduced C2–C3 sub-mechanism. Then, due to the similar molecular structure, the skeletal fuel-specific sub-mechanisms of the long-chain PODE3–6 are constructed based on the benchmark fuel of PODE2. The kinetic parameters of the reactions in the skeletal fuel-specific sub-mechanism of PODE3–6 are obtained using the modified linear lumping method and the reaction rate rule assumption. Through the approach proposed in this study, the reduced mechanisms of long-chain PODEn can be effectively constructed based on the chemistry of short-chain PODEn, especially for PODE5–6 with no available detailed mechanisms so far. The final reduced mechanism for the complete series of PODE1–6 only consists of 92 species and 389 reactions. To validate the predictions of the reduced mechanism, extensive comparisons are carried out including ignition delay times in shock tubes, major species concentrations in jet-stirred reactors, and laminar flame speeds and flame species concentrations in premixed laminar flames. Moreover, the measurements of homogeneous charge compression ignition (HCCI) engines fueled with PODE2–4 and PODE3–6 are used for the validations of in-cylinder pressure, heat release rate, and emissions. The overall performance of the reduced mechanism of PODE1–6 is satisfactory under wide operating conditions. This present approach can also be extended to build compact-size reduced mechanisms for the fuels with similar molecular structures, even though no detailed mechanism is available.

Reaction network of sulfur compounds in delayed coking process

• A molecular-level model for delayed coking process was established. • The conversion behavior of sulfur in delayed coking process was investigated. • The sulfur compounds in gasoline were expressed as 57 structural vectors. • The sulfur compounds were classified according to the discriminant rules. In order to describe the reaction network and investigate the conversion behavior of sulfur compounds in delayed coking process, a molecular-level reaction kinetic model was established with a reaction network consisting of 81,081 reactions based on the structure-oriented lumping method. A feed molecular matrix containing 2,944 structural vectors was constructed with 24 structural increments based on the characteristics of the vacuum residue molecular composition. The reliability of the model was verified by industrial data. Through the calculation of the SOL model, the sulfur compounds in gasoline were expressed as 57 structural vectors, which were divided into thiophenes, mercaptans and thioethers according to the discriminant rules. The conversion law of sulfur compounds was investigated by tracking the reaction path of molecules in the reaction network. The SOL model could calculate the distribution of sulfur compounds in coking gasoline. The contents of thiophene molecules increased with the carbon numbers. Ethyl mercaptan and propyl mercaptan had higher content in mercaptans. The SOL model can reveal the influences of reaction conditions on sulfur compounds conversion in delayed coking process at the molecular level, which contributes to the accurate control of sulfur content in coking gasoline.

Exact maximal reduction of stochastic reaction networks by species lumping.

Stochastic reaction networks are a widespread model to describe biological systems where the presence of noise is relevant, such as in cell regulatory processes. Unfortunately, in all but simplest models the resulting discrete state-space representation hinders analytical tractability and makes numerical simulations expensive. Reduction methods can lower complexity by computing model projections that preserve dynamics of interest to the user. We present an exact lumping method for stochastic reaction networks with mass-action kinetics. It hinges on an equivalence relation between the species, resulting in a reduced network where the dynamics of each macro-species is stochastically equivalent to the sum of the original species in each equivalence class, for any choice of the initial state of the system. Furthermore, by an appropriate encoding of kinetic parameters as additional species, the method can establish equivalences that do not depend on specific values of the parameters. The method is supported by an efficient algorithm to compute the largest species equivalence, thus the maximal lumping. The effectiveness and scalability of our lumping technique, as well as the physical interpretability of resulting reductions, is demonstrated in several models of signaling pathways and epidemic processes on complex networks. The algorithms for species equivalence have been implemented in the software tool ERODE, freely available for download from https://www.erode.eu. Supplementary data are available at Bioinformatics online.

Residual Bearing Capabilities of Fire-Exposed Reinforced Concrete Beams

This work combines thermal and structural analyses to assessing the residual bearing capabilities, flexural and shear capacities of reinforced concrete beams after fire exposure. The thermal analysis uses the finite difference method to model the temperature distribution of a reinforced concrete beam maintained at high temperature. The structural analysis, using the lumped method, is utilized to calculate the residual bearing capabilities, flexural and shear capacities of reinforced concrete beams after fire exposure. The results of the thermal analysis are compared to the experimental results in the literature, and the analytically derived structural results are also compared with full-scale reinforced concrete beams in previous fire exposure experiments. The comparison results indicated that the calculation procedure in this study assessed the residual bearing capabilities of reinforced concrete beams exposed to fire with sufficient accuracy. As no two fires are the same, this novel scheme for predicting residual bearing capabilities of fire-exposed reinforced concrete beams is very promising in that is eliminates the extensive testing otherwise required when determining fire ratings for structural assemblies.

Dynamic Response Analyses of Plastic Greenhouse Structure considering Fluctuating Wind Load

Wind load is one of the main factors of plastic greenhouse collapse. To solve the dynamic response problem of greenhouses under wind load and determine the dangerous section of a skeleton structure, the investigated lump method is presented for the dynamic response analysis of a plastic greenhouse, considering pulsating wind on the basis of Timoshenko beam theory. First, the investigated lump is designed according to the Timoshenko beam microbody concept. On the basis of Timoshenko beam theory, the governing equations of the skeleton structure of the greenhouse are derived, and the realization process of the algorithm is also provided. Second, the accuracy and effectiveness of the proposed numerical method are verified by an example in which the bending wave of a variable cross section beam with free ends propagates. Finally, the dynamic response of the steel skeletons of plastic greenhouses is analyzed under the effect of the simulation wind speed, and the spatial distribution of the maximum node displacement and the section maximum stress of the steel skeleton are obtained. Computational results show that the displacement peak is near the top of the plastic greenhouse. The most dangerous section of the top chord in the steel skeleton is near the leeward bottom, which has a maximum stress of 219.4 MPa, and the most dangerous section of the bottom chord is near the 1 m height on the leeward side of the plastic greenhouse, which has a maximum stress of 248.5 MPa. Bending stress is the main factor of the rapid increase of stress at the bottom of the skeleton. The maximum node displacement and cross-sectional stress caused by fluctuating wind loads are higher than those caused by average wind loads. The fluctuating wind load should be considered in the wind-induced response analyses of plastic greenhouses.

Lumped Mass Finite Element Method of the Nonlinear BBM Equation

In this paper, the full-discrete approximation scheme of the lumped mass nonconforming finite element method for BBM equation is discussed. Without the Riesz projection used in the traditional finite element analysis, the optimal error estimations are derived based on interpolation technique and special properties of element.

Cyclic response of a reinforced concrete frame: Comparison of experimental results with different hysteretic models

<abstract> <p>An accurate hysteresis model is fundamental to well capture the non-linearity phenomena occurring in structural and non-structural elements in building structures, that are usually made of reinforced concrete or steel materials. In this sense, this paper aims to numerically estimate through simplified non-linear analyses, the cyclic response of a reinforced concrete frame using different hysteretic models present in the literature. A commercial Finite Element Method package is used to carry out most of the simulations using polygonal hysteretic models and a fiber model, and additionally, a MATLAB script is developed to use a smooth hysteresis model. The experimental data is based on the experiments carried out in the Laboratório Nacional de Engenharia Civil, Portugal. The numerical outcomes are further compared with the experimental result to evaluate the accuracy of the simplified analysis based on the lumped plasticity or plastic hinge method for the reinforced concrete bare frame. Results show that the tetralinear Takeda's model fits closely the experimental hysteresis loops. The fiber model can well capture the hysteresis behavior, though it requires knowledge and expertise on parameter calibration. Sivaselvan and Reinhorn's smooth hysteresis model was able to satisfactorily reproduce the actual non-linear cyclic behavior of the RC frame structure in a global way.</p> </abstract>

Asphaltene formation modeling using vapor-liquid-liquid equilibrium calculations by PC-SAFT for reservoir and surface conditions

Asphaltene precipitation can occur during the different stages of oil production, including an underground reservoir, wellbore, pipelines, and surface facilities. An accurate model to predict precipitation in these conditions is still a challenge, which is addressed in this work. In this study, we first utilize the lumped characterization method of Panuganti et al. 1 in a vapor-liquid-liquid equilibrium calculation approach using PC-SAFT, and by making use of a new parameter fitting method and genetic algorithm, we predict the Asphaltene instability conditions due to the pressure, composition and temperature variations in reservoir and surface. Titration experiments of the dead oils have indicated that Asphaltene is comprised of several sub-fractions with different molecular weights that precipitate under different thermodynamic conditions. Therefore, understanding the polydisperse nature of Asphaltene is crucial in order to better estimate the Asphaltene yield during the composition change. In the next step, Asphaltene is split into three sub-fractions according to the titration data of different precipitating agents. The parameters of Asphaltene sub-fraction are then adjusted with respect to the initial monodisperse Asphaltene parameters. In addition, the amount of precipitated Asphaltene at different solvent ratios of titrant to degassed oil is calculated. The results are compared with the model of Buenrostro‐Gonzalez et al. 2 and the experimental data of two Mexican crude oils (C1 and Y3). Regarding the outcomes, from a numerical perspective, this study's approach has resulted in accurate predictions for both the live and dead (degassed) oil. The average estimation error for sample C1 is equal to 3.46% for this study, while this number is 5.13% for the Buenrostro‐Gonzalez et al. 2. Regarding the sample Y3, the sum of errors are nearly at 3.60% and 5.10% for this study and Buenrostro‐Gonzalez et al. 2, respectively.

Lumped Kinetic Modeling Method for Fluid Catalytic Cracking

AbstractA new fluid catalytic cracking (FCC) lumped kinetic modeling method was put forward to improve the prediction accuracy of the FCC kinetic model. This model divided the feedstock into three lumps and the products into six lumps. The parameters of the kinetic model were obtained by combining the fourth‐order Runge‐Kutta integral method and the two‐swarm cooperative particle swarm optimization algorithm. Compared with dividing the feedstock according to the group composition and the distillation range, the average relative error between the experimental data and the calculated values proves the higher fitting accuracy of the new lumped method. The kinetic model established by the method exhibits better adaptability to different feedstock and fewer requirements for feedstock analysis data.

Lumped RC Thermal Network Method Applied to Transient Temperature Calculation of High Voltage Bushing and Its Insulation Life Assessment

To analyze how the internal transient temperature of the high voltage condenser bushing varies with its short-time current carrying capacity and long-aging properties, lumped RC thermal network model applicable to the structure of HV bushing is proposed. This model considers three heat transfer modes of the conduction, the convection and the radiation, and the changing relationship between material properties and temperature and the the thermal RC network topology is realized based on the MATLAB/SIMULINK. In the example of 550kV oil-SF6 bushing, the calculation results of transient temperature thermal network are in good agreement with the actual temperature rise test results which proves effectiveness and practicality of lumped RC thermal network. We used the thermal network to confirm the periodic transient variation at the hottest spot of HV bushing and analyze the shot-time current carrying capacity by step load curve fitting circadian cycle change load. Finite element method and thermal network method are used to get the electric and thermal stress respectively and HV bushing long-aging properties analysis was conducted based on classic ZHURKOV and CRINE electric and thermal combined aging model. This paper applies lumped RC thermal network method to transient temperature calculation and internal insulation life assessment of the HV bushing, reinforced classic bushing design method only considering rated steady-state operating conditions and has theoretical guidance on assessing short-time current-carrying capacity and long-aging properties in high voltage bushings.

Perturbation Observer-Based Robust Control Using a Multiple Sliding Surfaces for Nonlinear Systems with Influences of Matched and Unmatched Uncertainties

This paper presents a lumped perturbation observer-based robust control method using an extended multiple sliding surface for a system with matched and unmatched uncertainties. The fundamental methodology is to apply the multiple surfaces to approximate the unknown lumped perturbations simultaneously influencing on a nonlinear single input–single output (SISO) system. Subsequently, a robust controller, based on the proposed multi-surface and the approximated values, is designed to highly improve the control performance of the system. A general stability of the lumped perturbation observer and closed-loop control system is obtained through the Lyapunov theory. Results of a numerical simulation of an illustrative example demonstrate the soundness of the proposed algorithm.

A multi-component reaction mechanism of n-butanol, n-octanol, and di-n-buthylether for engine combustion

The purpose of this study is to develop a multi-component skeletal mechanism including renewable fuels of n-butanol, n-octanol, and DnBE (di-n-buthylether) for engine combustion. Mechanism reductions using the directed relation graph, directed relation graph with error propagation and sensitivity analysis, peak concentration analysis, and isomer lumping methods were first carried out on the detailed reaction mechanisms for each type of the fuels. Then, the obtained single-fuel skeletal mechanisms were combined to construct the multi-component skeletal mechanism. Finally, the developed reaction mechanism, which consisting of 117 species and 610 elementary reactions, was obtained. To validate the fuel model, calculations on ignition delay times for each component of the skeletal mechanism, species concentrations in JSR for n-octanol, laminar flame speeds for DnBE, and 3-D diesel engine combustion fueled with n-octanol and DnBE were carried out. Results demonstrated that the predicted ignition delay times can well match the data given by detailed mechanisms and experiments under the conditions covering a wide range of temperatures, pressures, and equivalence ratios. Also, the concentration profiles of important species in a jet stirred reactor were well reproduced by the skeletal mechanism with equivalence ratios of 0.5, 1.0, and 2.0. The laminar flame speeds of DnBE were also in good agreement with experimental data at 1 atm with a wide range of equivalence ratios. For diesel engine simulations fueled with n-octanol and DnBE, with different engine speeds and loads, both in-cylinder pressure traces and heat release rate profiles can be well represented by the present skeletal reaction mechanism.

Numerical simulations for the predator-prey model on surfaces with lumped mass method

The predator-prey model is powerful mathematical tool to describe the dynamics of biological systems and promote research on biological populations. In this paper, we present a lumped mass finite element method for solving the predator-prey models on surfaces. The main purpose of the proposed method is to overcome the difficulty of the positivity preservation of the solutions. Based on positivity preservation results, we investigate the stabilities of semi-discrete and fully discrete approximations. Besides, numerical simulations are considered to illustrate the feasibility of the numerical method by convergence tests. Two classical phenomena of the predator-prey model are simulated on three different implicit surfaces.