Simultaneous Solution Research Articles

Improvements in the mixed elastohydrodynamic lubrication and in the efficiency of hypoid gears

In this paper, the influence of the manufacturing parameters on the conditions of mixed elastohydrodynamic lubrication is investigated. On the basis of the obtained results, recommendations are formulated to improve the mixed EHL and the efficiency of face-milled hypoid gears. A full numerical analysis of the mixed EHL in hypoid gears is applied. The equation system and the numerical procedure are unified for a full coverage of all the lubrication regions, including the full film, mixed, and boundary lubrication. In the hydrodynamically lubricated areas, the calculation method employed is based on the simultaneous solution of the Reynolds, elasticity, energy, and Laplace's equations. In the asperity contact areas, the Reynolds equation is reduced to an expression equivalent to the mathematical description of dry contact problem. The real geometry and kinematics of the gear pair based on the manufacturing procedure are applied; thus, the exact geometrical separation of the mating tooth surfaces is included in the oil film shape, and the real velocities of these surfaces are used in the Reynolds and energy equations. The transient nature of gear tooth mesh is included. The oil viscosity variation with respect to pressure and temperature and the density variation with respect to pressure are included. The non-Newtonian behaviour of the lubricant is considered. Using this model, the pressures, film thickness, temperatures, and power losses in the mixed lubrication regime are predicted. The effectiveness of the presented method is demonstrated by using hypoid gear examples.

System Identification Under Relay and PI Control

This brief presents a symmetrical relay-based identification scheme for a class of linear time-invariant systems with time delay. During off-line identification, the adverse effect of static load disturbance may lead to erroneous system model parameters. Therefore, on-line identification scheme is proposed where the system characteristics is extracted with respect to proportional-integral (PI) controller dynamics in terms of sustained oscillatory responses broadly known as limit cycle at the system output. Utilizing the relay settings (amplitude and hysteresis width), controller parameters and limit cycle information, an explicit set of mathematical expressions for on-line parameter estimation of system dynamics in terms of a stable first order plus time delay (FOPTD) model is deduced from frequency domain and state space analyses. As compared to recent relay-based identification methods, the proposed set of explicit expressions does not require any prior guess of initial values of the system model parameters for the simultaneous solution of a nonlinear set of mathematical equations. Simulation of a benchmark example from literature and experimental results from the coupled tanks system are included for validation of the proposed identification algorithms using the deduced set of mathematical expressions.

Shadow economy and income inequality: new empirical evidence from Asian developing countries

This paper examines the impact of shadow economy on income inequality by using a panel data set of 19 Asian countries in the period 1990–2015. In contrast to previous studies, the results from estimations of fixed effect, random effect, and SGMM surprisingly show that the shadow economy reduces income inequality in the research region. Specifically, the shadow economy significantly increases the income share held by lowest quintile and decreases the income share held by highest quintile. The result can be explained by combining the three schools of thought on informal economy including Dualism, Legalism, and Volutarism. The finding contributes to the idea that the shadow economy is not always bad, especially to the poor, out of its negative effects. Therefore, policies to deal with the shadow economy should take the poor into close consideration with other simultaneous solutions for poverty eradication and income inequality reduction in developing countries.

Heat transfer in flow around a rotary oscillating cylinder at a high subcritical Reynolds number: A computational study

We studied numerically the heat transfer in flow over a rotationally oscillating cylinder at a subcritical Reynolds number (Re=1.4×105) that is an order of magnitude higher than previously reported in the literature. This paper is a follow-up of the earlier study of hydrodynamics and drag force in a range of forcing frequencies and amplitudes (Palkin et al., 2018). This time we focus on heat transfer and its correlation with the observed flow field and vortical patterns. Four forcing frequencies f=fe/f0=0,1,2.5,4 for two forcing amplitudes Ω=ΩeD/2U∞=1 and 2 are considered, where f0 is the natural vortex-shedding frequency, U∞ the free-stream velocity and D the cylinder diameter. The parametric study was performed by solving three-dimensional unsteady Reynolds-averaged Navier–Stokes (URANS) equations closed by a wall-integrated second-moment (Re-stress) model, verified earlier by Large-eddy simulations and experiments in several reference cases including flows over a stagnant, as well as rotary oscillating cylinders at the same Re number. The thermal field, treated as a passive scalar, was obtained from the simultaneous solution of the energy equation, closed by the standard (GGDH) anisotropic eddy-diffusivity model. The computations showed that for the unforced cylinder heat transfer is characterized by very high local rates due to a strong thinning of the thermal boundary layer as a result of the impact and interactions of large coherent structures with the wall. The overall average Nusselt number does not change much for the forced cylinder but its time-averaged, phase-averaged and instantaneous circumferential profiles show some profound differences compared to the stationary cylinder. The distribution of Nu on the back surface becomes more uniform with less frequent occurrence of high values, especially for the higher frequencies f=2.5 and f=4. This is attributed to diminishing of the mean-recirculation zone as well as to the overall suppression of turbulent fluctuations. The rotary oscillation of the cylinder appears potentially efficient in achieving a more uniform circumferential distribution of Nu and avoiding local overheats and hot spots.

Optimal estimation of spectral surface reflectance in challenging atmospheres

Optimal Estimation (OE) methods can simultaneously estimate surface and atmospheric properties from remote Visible/Shortwave imaging spectroscopy. Simultaneous solutions can improve retrieval accuracy with principled uncertainty quantification for hypothesis testing. While OE has been validated under benign atmospheric conditions, future global missions will observe environments with high aerosol and water vapor loadings. This work addresses the gap with diverse scenes from NASA's Next Generation Airborne Visible Infrared Imaging Spectrometer (AVIRIS-NG) India campaign. We refine atmospheric models to represent variable aerosol optical depths and properties. We quantify retrieval accuracy and information content for both reflectance and aerosols over different surface types, comparing results to in situ and remote references. Additionally, we assess uncertainty of maximum a posteriori solutions using linearized estimates as well as sampling-based inversions that more completely characterize posterior uncertainties. Principled uncertainty quantification can combine multiple spacecraft data products while preventing local environmental biases in future global investigations.

Prestrike modeling in SF6 circuit breakers

Prestrike is a common phenomenon in Circuit Breakers (CB) when the moving contact approaching to the fixed contact during the closing operation. This paper focuses on prestrike modeling in SF6 circuit breakers. A multi-physics method is developed to accurately modeling the prestrikes in SF6 circuit breakers. In this study, a model is developed for a simultaneous solution of the MHD equations and the governing equations of the circuit feeding the plasma in order to consider mutual effects of the circuit and the plasma. Navier-Stoke equations, turbulent flow equations, and the equation of heat transfer in fluids, coupled with Maxwell's equations are physical equations governing the circuit breakers. Kirchhoff's voltage and current laws equations are governing equations of the external electric circuit. The Electric-Circuit-Constrained Magnetohydrodynamic (ECC-MHD) model developed in this paper is able to study the electromagnetic properties of conducting fluids fed by electrical circuits. Motion of moving contact and temperature dependency of SF6 gas properties are considered during the solving of this multi-physics problem. Finite Element Method (FEM) is used to solve the multi-physics equations governing the circuit breaker. Finally a 72 kV single pressure puffer type SF6 circuit breaker is used for numerical studies. To investigate the mutual effects of the feeding circuit parameters and generated plasma in the circuit breaker, numerical studies are performed for different values of resistance and inductance in the arc current path.

Bending and Shear Stiffness of Cross-Laminated Timber Using a Variable Span Bending Test

Abstract Cross-laminated timber (CLT) is a novel wood product composed of lumber layers adhered orthogonally to create a two-way composite plate. The orthogonal orientation of the layers creates bending stiffness in both in-plane directions. However, compared to a solid wood beam, the orthogonal orientation of CLT reduces the shear stiffness in the longitudinal direction. Compared to a solid wood beam of the same material, shear deformation in CLT increases by approximately 30 %. Test methods to evaluate the shear stiffness terms of CLT beams are needed. This article examined two possible methods to obtain the bending and shear stiffness terms of CLT beams: (1) a simultaneous solution of the beam formulas currently tested in the product standard for CLT and (2) a regression method for variable span beams. Both methods produced similar bending and shear stiffness results. The use of a wide range of length-to-depth (L/d) ratios is recommended, with a minimum L/d value less than 10:1. Different loading configurations can be incorporated into the regression method provided that the regression terms are kept consistent. The simultaneous solution is of particular interest since no additional testing is needed beyond the current beam configurations in the CLT product standard.

Stress behaviours of viscoelastic flow around square cylinder

In this study, it is aimed the numerically investigation of the flow of liner PTT (Phan-Thien-Tanner) fluid, which is a viscoelastic fluid model over limited square obstacle by finite volume method. The finite volume method has been used for simultaneous solution of continuity, momentum and fluid model equations with appropriate boundary conditions. The effects of the inertia in terms of Reynolds number, Re, (0 < Re < 20) and the of elasticity in terms of Weissenberg number, We, (1 < We < 15) of PTT flow on vertical and shear stress areas are examined in detail.

Semi-Analytical Method for g-Function Calculation of bore fields with series- and parallel-connected boreholes

A semi-analytical method for the calculation of g-functions of bore fields with mixed arrangements of series- and parallel-connected boreholes is presented. Borehole wall temperature variations are obtained from the temporal and spatial superposition of the finite line source (FLS) solution. The FLS solution is coupled to a quasi-steady-state solution of the fluid temperature profiles in the boreholes, considering the piping connections between the boreholes. The dimensionless borehole wall temperatures in the bore field and the inlet fluid temperature are obtained from the simultaneous solution of the heat transfer inside and outside the boreholes. The effective borehole wall temperature (i.e., the g-function) is defined based on the dimensionless inlet fluid temperature and a newly introduced effective bore field thermal resistance. The g-function evaluation method is validated against the DST model and its use is demonstrated in a sample simulation of a seasonal thermal energy storage system.

Element balance formulation in reactive compositional flow and transport with parameterization technique

We present a novel nonlinear formulation for modeling reactive-compositional flow and transport in the presence of complex phase behavior due to a combination of thermodynamic and chemical equilibria in multi-phase systems. We apply this formulation to model precipitation/dissolution of minerals in reactive multiphase flow in subsurface reservoirs. The proposed formulation is based on the consistent element balance reduction of the molar (overall composition) formulation. To predict the complex phase behavior in such systems, we include the chemical equilibrium constraints to the multiphase multicomponent negative flash calculations and solve the thermodynamic phase and chemical phase equilibria simultaneously. In this solution, the phase equilibrium is represented by the partition coefficients, whereas the chemical equilibrium reaction is represented by the activity coefficients model. This provides a generic treatment of chemical and thermodynamic equilibrium within the successive substitution loop of mulmultiphase flash to accommodate chemical equilibrium reactions (precipitation and dissolution reactions). Equilibrium Rate Annihilation matrix allows us to reduce the governing component conservation equations to element conservation equations, while the coupling between chemical and thermodynamic equilibrium is captured by a simultaneous solution of modified multiphase flash equations. The element balance equation written in terms of overall component mole fractions is modified and defined in terms of element mole fractions. Therefore, the primary set of governing equations are the element balance equations and the kinetic equations. This element composition of the mixture serves as an input to the modified multiphase flash computations, whereas the output is fractions of components in each phase, including solids. The nonlinear element–based governing equations are solved with the modified version of the operator-based linearization (OBL) approach where the governing equations are formulated in terms of space- and state-dependent parameters constrained by the solution of the extended multiphase flash. The element balance molar formulation along with the modified multiphase flash has been tested in a simple transport model with dissolution and precipitation reactions. The simulation of multidimensional problems of practical interest has been performed using the adaptive OBL technique. This is the first time when a robust multiphase multicomponent flash based on element fractions is coupled with an element balance–based compositional formulation and tested for multidimensional problems of practical interest. The proposed technique improves both robustness and performance of complex chemical models.

Lagrangian simulation of three-dimensional macro-scale melting based on enthalpy method

Melting and solidification are encountered or utilized in industrial applications. Based on the moving particle semi-implicit (MPS) method a robust numerical approach is developed for simulation of macroscopic melting. In the approach the passively moving solid model, which accounts for liquid-solid interaction force, is introduced to facilitate simultaneous solution in the liquid and solid part for all the governing equations. An enthalpy-based viscosity model is utilized to realize smooth transition of viscosity on the liquid-solid interface. The potential-force surface tension and contact angle model are also employed to ensure realistic simulation of free surface motion during melting. To suppress possible numerical instability and ensure robustness of numerical solution, the viscosity term in the momentum equation is solved implicitly. In the meanwhile, the blended source term is utilized in the pressure Poisson equation. Verification of the developed simulation approach is carried out with a one-dimensional conduction-induced melting problem. The liquid-solid interface can be sharply predicted in the simulation. And the interface position and temperature profile are accurately calculated. The approach is further validated with the three-dimensional cube melting. Pressure oscillation is observed in the simulation when the melt starts. The oscillation can be dampened when enough liquid exists under the solid cube. Comparison with experimental data shows that the simulation can properly capture the motion of solid cube and spreading of liquid film during melting.

Simultaneous Solutions of Three Dimensional MHD Rotating Flow of Non-Newtonian Fluid over an Elongated Surface

Simultaneous Solutions of Three Dimensional MHD Rotating Flow of Non-Newtonian Fluid over an Elongated Surface

Strategic bidding of virtual power plant in energy markets: A bi-level multi-objective approach

This paper represents a model for finding the strategic bidding equilibrium of a virtual power plant in a joint energy and regulation market in the presence of rivals. A bi-level mathematical program with equilibrium constraints (MPEC) is represented for modeling the behavior of each producer. The upper level deals with profit maximization of each strategic unit and the lower level encompasses social welfare maximization. This is the first objective of the presented model. Power transfer distribution factors (PTDFs) are employed to model transmission constraints. The proposed bi-level problem is converted to a traceable mixed integer linear programming problem using duality theory and Karush-Kahn-Tucker (KKT) optimization conditions. Simultaneous solution of all MPECs forms an equilibrium problem with equilibrium constraints (EPEC). Solving the resulting EPEC using diagonalization algorithm and game theory, a market Nash equilibrium is obtained. Another goal is to solve the bi-level problem in a bi-objective way using the augmented epsilon constraint method, which maximizes the profit and minimizes the emissions of virtual power plant units. The proposed model is tested on a standard IEEE-24 bus system and the results indicate that, at the equilibrium point, the profit of a virtual power plant and GenCo will be less than in the initial state.

A Simultaneous Solution for Reserve Capacity Maximization and Delay Minimization Problems in Signalized Road Networks

In this study, we present a bilevel programming model in which upper level is defined as a biobjective problem and the lower level is considered as a stochastic user equilibrium assignment problem. It is clear that the biobjective problem has two objectives: the first maximizes the reserve capacity whereas the second minimizes performance index of a road network. We use a weighted-sum method to determine the Pareto optimal solutions of the biobjective problem by applying normalization approach for making the objective functions dimensionless. Following, a differential evolution based heuristic solution algorithm is introduced to overcome the problem presented by use of biobjective bilevel programming model. The first numerical test is conducted on two-junction network in order to represent the effect of the weighting on the solution of combined reserve capacity maximization and delay minimization problem. Allsop & Charlesworth’s network, which is a widely preferred road network in the literature, is selected for the second numerical application in order to present the applicability of the proposed model on a medium-sized signalized road network. Results support authorities who should usually make a choice between two conflicting issues, namely, reserve capacity maximization and delay minimization.

New modelling technique for improving crop model performance - Application to the GLAM model

Crop models simulate growth and development and they are often used for climate change applications. However, they have a variable skill in the simulation of crop responses to extreme climatic events. Here, we present a new dynamic crop modelling method for simulating the impact of abiotic stresses. The Simultaneous Equation Modelling for Annual Crops (SEMAC) uses simultaneous solution of the model equations to ensure internal model consistency within daily time steps; something that is not always guaranteed in the usual sequential method. The SEMAC approach is implemented in GLAM, resulting in a new model version (GLAM-Parti). The new model shows a clear improvement in skill under water stress conditions and it successfully simulates the acceleration of leaf senescence in response to drought. We conclude that SEMAC is a promising crop modelling technique that might be applied to a range of models.

The role of particle, energy and momentum losses in 1D simulations of divertor detachment

A new 1D divertor plasma code, SD1D, has been used to examine the role of recombination, radiation, and momentum exchange in detachment. Neither momentum or power losses by themselves are found to be sufficient to produce a reduction in target ion flux in detachment (flux rollover); radiative power losses are required to (a) limit and reduce the ionisation source and (b) access low-target temperature, Ttarget, conditions for volumetric momentum losses. Recombination is found to play a small role at flux rollover, but as Ttarget drops to temperatures around 1 eV, it becomes a strong ion sink. In the case where radiative losses are dominated by hydrogen, the detachment threshold is identified as a minimum gradient of the energy cost per ionisation with respect to Ttarget. This is also linked to thresholds in Ttarget and in the ratio of upstream pressure to power flux. A system of determining the detached condition is developed such that the divertor solution at a given Ttarget (or lack of one) is determined by the simultaneous solution of two equations for target ion current—one dependent on power losses and the other on momentum. Depending on the detailed momentum and power loss dependence on temperature there are regions of Ttarget where there is no solution and the plasma ‘jumps’ from high to low Ttarget states. The novel analysis methods developed here provide an intuitive way to understand complex detachment phenomena, and can potentially be used to predict how changes in the seeding impurity used or recycling aspects of the divertor can be utilised to modify the development of detachment.

A 3-D Weakly Conditionally Stable Single-Field Finite-Difference Time-Domain Method

A novel finite-difference solution of the time-domain three-dimensional wave equation with a stability criterion relaxed from the discretization space steps in two directions is presented. This method is particularly useful and efficient for electromagnetic simulation of structures having fine details in two Cartesian directions. During the algorithm iteration process, updating of only the electric field is required. In comparison to other weakly conditional finite-difference time-domain (WCS-FDTD) algorithms, the proposed method is shown to be computationally more efficient in terms of runtime because the implicit updating equations can be solved simultaneously (in parallel) by applying multithreading, while in the earlier WCS-FDTD methods, a simultaneous solution of the implicit updating equations was not feasible. The high computational efficiency and accuracy of the proposed method is demonstrated by producing several numerical examples and providing comparison to the results obtained using methods available in the literature.

Consistent dust and gas models for protoplanetary disks

Context. Consistent modeling of protoplanetary disks requires the simultaneous solution of both continuum and line radiative transfer, heating and cooling balance between dust and gas and, of course, chemistry. Such models depend on panchromatic observations that can provide a complete description of the physical and chemical properties and energy balance of protoplanetary systems. Along these lines, we present a homogeneous, panchromatic collection of data on a sample of 85 T Tauri and Herbig Ae objects for which data cover a range from X-rays to centimeter wavelengths. Datasets consist of photometric measurements, spectra, along with results from the data analysis such as line fluxes from atomic and molecular transitions. Additional properties resulting from modeling of the sources such as disk mass and shape parameters, dust size, and polycyclic aromatic hydrocarbon (PAH) properties are also provided for completeness. Aim. The purpose of this data collection is to provide a solid base that can enable consistent modeling of the properties of protoplanetary disks. To this end, we performed an unbiased collection of publicly available data that were combined to homogeneous datasets adopting consistent criteria. Targets were selected based on both their properties and the availability of data. Methods. Data from more than 50 different telescopes and facilities were retrieved and combined in homogeneous datasets directly from public data archives or after being extracted from more than 100 published articles. X-ray data for a subset of 56 sources represent an exception as they were reduced from scratch and are presented here for the first time. Results. Compiled datasets, along with a subset of continuum and emission-line models are stored in a dedicated database and distributed through a publicly accessible online system. All datasets contain metadata descriptors that allow us to track them back to their original resources. The graphical user interface of the online system allows the user to visually inspect individual objects but also compare between datasets and models. It also offers to the user the possibility to download any of the stored data and metadata for further processing.

Модель отказов цилиндрических зубчатых передач по критерию износостойкости рабочих поверхностей

Cylindrical gear failure due to tooth wear is one of the most common reasons for the decreased technical and economic indicators of various units resulting from the forced downtime for gear replacement or repair. Nowadays, the linear wear rate, an indicator that is found experimentally, is used to determine gear service life based on the statistical linear dependence of the wear on the friction forces. The determination of this indicator requires a large amount of data on the wear obtained with real transmissions or relevant laboratory samples that increases time and financial costs. Therefore, an analytical model of wear failures has been developed for project estimation of gear service life and the search for effective and lasting design solutions. The model represents a system of constitutive equations, which includes an energy equation describing the change in the current state of a pair of wear gear wheels and the conditions for their transition to the limiting state, a basic kinetic dependence of the energy-mechanical theory of stationary tribocoupling wear, and an equation for determining the transmission’s expected service life. The simultaneous solution of this system of equations taking into account the dependencies that describe the initial and boundary conditions of the gear element interaction resulted in the formulation of the algorithm for calculating their average expected service life. This allowed the authors to perform a comparative analysis of the effectiveness of various design options for improving gear durability and select the most appropriate ones. A distinctive feature of the proposed calculation algorithm is that it does not involve searching for experimental parameters similar to the linear wear rate.

SAT-376 Dynamic Modeling of the 1 mg Overnight Dexamethasone Suppression Test: Sources of Variability and Strategies to Improve Diagnostic Accuracy for Detection of Autonomous Cortisol Secretion in Adrenal Adenoma Patients

Among patients with adrenal adenoma, the 1 mg overnight dexamethasone suppression test (DST) is commonly used to help identify patients with biochemical evidence of autonomous cortisol secretion (ACS). The diagnostic accuracy of the DST in this setting is only fair, as illustrated by the application of different cut-scores for DEX-suppressed cortisol concentrations (e.g. 50 vs. 138 nM) favoring sensitivity or specificity, respectively (1). In the present study we sought to model the predictors of the DST to better characterize sources of variation and error in the diagnostic test. Forward solutions for DEX-suppressed total and free cortisol concentrations from midnight to 8 AM were obtained using simultaneous solution of differential equations in a dynamic 3-compartment model of free cortisol appearance, elimination, and reversible binding to serum proteins (2). Monte Carlo simulation was performed based on published distributional data for controls (n=1000) and ACS patients (n=1000). Predictor variables were assessed using standardized beta (STB) coefficients, which represent change in the standard deviation (SD) of the outcome (numerator, i.e. DEX-suppressed cortisol concentration) for each SD change in a predictor (denominator) in a multivariable context (2). The analysis confirmed diagnostic accuracy of the DST consistent with published guidelines (1). Significant predictors of DEX-suppressed cortisol included ACTH-independent cortisol secretion rate (CSRmin), free cortisol half-life, and the concentration of midnight serum total cortisol, corticosteroid binding globulin (CBG), and albumin (all P<0.01). The predictor variables having STB coefficients >0.4 included CSRmin (STB=0.67), free cortisol half-life (STB=0.53), and CBG (STB=0.44), with smaller influence of midnight total serum cortisol (STB=0.14), and albumin (STB=0.04) concentrations. STBs for DEX-suppressed free cortisol concentration were like those observed for total cortisol except that the influence of CBG was eliminated. Using a DEX-suppressed free cortisol cut-score of 2.5 nM improved sensitivity and specificity compared to DEX-suppressed total cortisol (P<0.001). We conclude that our model for DST agrees with experimental literature demonstrating limited diagnostic accuracy of the test and we have identified multiple factors that affect the DEX-suppressed cortisol concentration in both control and ACS populations. In addition, strategies to adjust for confounding variables, such as use of DEX-suppressed free cortisol, might improve diagnostic accuracy of the DST.