Radial Grid Research Articles

Geometric decomposition and algorithmic model of main gate muqarnas of Ankara Cenabi Ahmet Pasha Mosque

Cenabi Ahmet Pasha Mosque (Cenab-ı Ahmet Paşa Mosque) is known to be the only work that resembles the style of Architect Sinan in Ankara. In this study, it is aimed to examine the two-dimensional muqarnas scheme of the mosque's main gate and to determine through algorithmic modeling the combination of muqarnas cells in the third dimension. By the photogrammetry method, the grid and star forms used in the muqarnas plan scheme are revealed. The geometric characteristic of the muqarnas in two dimensions is determined. Cell types of the muqarnas and their geometric configurations are obtained. It is demonstrated that there is a radial grid in the plan of the Cenabi Ahmet Pasha Mosque main gate muqarnas, and that the three-dimensional structure of the muqarnas consisting of six layers includes almond cell, triangle cell, deltoid cell, intermediate triangle cell, intermediate deltoid cell, biped cell and triped cell. Additionally, an algorithmic model based on the creation of cell unit system is proposed for the creation of the muqarnas geometry in 3D.

Non-steady flow decomposition behaviors of heat and mass transfer on intrinsic kinetics for methane hydrate particles transported in pipelines

The differential equations governing the decomposition rate and activation energy, convective mass transfer, methane diffusion and fugacity, as well as heat conduction and enthalpy change were derived by integrating thermal convection, heat conduction, mass transfer and intrinsic kinetics. Mathematical models for decomposition kinetics and thermodynamics in a non-steady field were solved using a radial logarithmic grid for node division and discretization of the equations. The study elucidated the heat and mass transfer processes as well as decomposition kinetics in pipelines by analyzing the impacts of particle size, temperature, pressure, flow rate and activation energy on decomposition rate. The results indicated that compared with the isothermal decomposition of the intrinsic kinetic model and static experimental decomposition, the complex non-steady multiphase flow model offers a more accurately simulation of hydrate decomposition as well as associated heat and mass transfer processes. Hydrate decomposition is characterized as a non-isothermal dynamic ablation process with heat transfer rate and intrinsic kinetics dominating during the preliminary stage and the stable stage, respectively. An increasing in the slurry temperature, temperature fluctuation and flow rate accelerated the heat transfer rate capacity, enhanced convective heat transfer capacity and facilitated hydrate decomposition, with the mass transfer rate exhibiting lesser influence. The particle surface area and slurry temperature exhibited the most significant influence on hydrate decomposition, which was followed by flow rate. Upon increasing particle size from 1 mm to 5 mm and the temperature from 293 K to 313 K, the decomposition rate increased by 20.7 times and 13.5 times, respectively. Furthermore, enhancing temperature and flow rate while decreasing particle size and pressure decreased both the decomposition time and the duration required for the decomposition rate to reach its peak. Additionally, the decomposition rate and its constant vary with the activation energy.

Efficient Time-Dependent Method for Strong-Field Ionization of Atoms with Smoothly Varying Radial Steps

We present an efficient numerical method to solve the time-dependent Schrödinger equation in the single-active electron picture for atoms interacting with intense optical laser fields. Our approach is based on a non-uniform radial grid with smoothly increasing steps for the electron distance from the residual ion. We study the accuracy and efficiency of the method, as well as its applicability to investigate strong-field ionization phenomena, the process of high-order harmonic generation, and the dynamics of highly excited Rydberg states.

Collaborative Planning and Comprehensive Evaluation Method for Energy Storage System and Flexible Interconnection in Distribution Networks Considering Island Operation

Introduction: When the superior power grid fails and loses power, due to the traditional single power supply radial grid structure of low-voltage substation areas, all loads in the lowvoltage substation area will lose power, causing a poor electricity consumption experience for low-voltage users. To enhance the resilience of low-voltage distribution areas against faults and power outages from higher-tier power grids, a collaborative planning and comprehensive evaluation method for grid-forming energy storage systems (GFM-ESS) and flexible interconnection in distribution networks, considering island operation, is proposed. Method: This method integrates GFM-ESS and flexible interconnections, taking islanding operations into account. Firstly, the structure of GFM-ESS and voltage source converters is analyzed. The control modes of GFM-ESS in parallel or off-grid scenarios are also scrutinized. Secondly, minimizing the annual comprehensive cost and the annual power outage load are the objective functions. A bilevel programming model for GFM-ESS and flexible interconnection of lowvoltage distribution networks, considering island operation, has been established. Moreover, a comprehensive evaluation method based on the analytic hierarchy process for proposed lowvoltage distribution network structural schemes is introduced. An evaluation index system is established to assess the rationality of these proposed network structural planning schemes. Finally, the superiority of the proposed collaborative planning method is verified through a comparative analysis of three planning methods. Result: The proposed collaborative planning method can effectively ensure the continuous power supply of low-voltage distribution networks under the fault scenario of the upper power network. Conclusion: Moreover, the rationality of the results obtained from the proposed collaborative planning method is verified through a comprehensive evaluation method of grid structure schemes based on the analytic hierarchy process. The proposed comprehensive evaluation method can determine which two areas are optimal for grid planning. result: The superiority of the proposed collaborative planning method was verified by comparative analysis of three planning methods. And the rationality of the proposed collaborative planning method results was verified by the comprehensive evaluation method of grid structure schemes based on analytic hierarchy process.

An ADP framework for flexibility and cost aggregation: Guarantees and open problems

With the increasing amount of Distributed Energy Resources (DERs), coordination of Distribution Grid Operators (DSOs) and Transmission Grid Operators (TSOs) is of paramount importance. Managing a large number of DERs at the TSO level is, however, challenging. To address this problem, flexibility aggregation is a topic of frequent research activities. Aggregation means to describe the combined flexibility of the DERs at the vertical grid coupling between DSO and TSO. Existing works are often limited with respect to guaranteeing feasibility, with respect to efficient numerical implementation, and in terms of quantification of the cost of DER usage. In the present paper, we investigate aggregation based on Approximate Dynamic Programming (ADP). We propose efficient numerical aggregation schemes using tools from computational geometry thus avoiding the need to solve multiple OPF problems. We rely on different variants of the DistFlow model for radial grids, which are computationally efficient. This allows to model of current and voltage limits and enables the consideration of voltage dependencies in the aggregation. Furthermore, we propose a method for cost aggregation and identify open problems of flexibility aggregation.

Admittance matrix estimation of radial distribution grids using power and voltage magnitude measurements

Accurate knowledge of the admittance matrix of distribution grids is essential for grid operation and control as more renewable energy sources and electric vehicles are integrated into distribution grids. Due to limited observability, measurement noise, topology assumptions, and partial data availability, the exact calculation of the admittance matrix of distribution grids is challenging. In this paper, we present a method for estimating the admittance matrix of radial distribution grids. The proposed method uses low-cost measurement devices that record ten-minute-based measurements of voltage magnitudes, active power, and reactive power at a single end of the lines or transformers instead of second-based phasor measurements. The impedance of lines or transformers is then estimated using a statistical optimization subject to the distribution flow (DistFlow) model. The effectiveness of proposed method is demonstrated by simulation, laboratory testing, and field measurements taken from a distribution grid in Switzerland.

Impact of disc magnetisation on MHD disc wind signature

Context. Observations of blue-shifted X-ray absorption lines indicate the presence of wind from the accretion disc in X-ray binaries. Magnetohydrodynamic (MHD) driving is one possible wind-launching mechanism. Recent theoretical developments have made self-similar magnetic accretion-ejection solutions much more generalised, showing that wind can be launched at a much lower magnetisation than the equipartition value, which had previously been the only possibility. Aims. In this work, we model the transmitted spectra through MHD-driven photoionised wind models with different levels of magnetisation. We investigate the possibility of detecting absorption lines by upcoming instruments, such as XRISM and Athena. We investigate the robustness of the method of fitting asymmetric line profiles by multiple Gaussians. Methods. We used the photoionisation code XSTAR to simulate the transmitted model spectra. To cover the extensive range of velocity and density of the wind spanned over a large distance (∼105 gravitational radii), we divided the wind into slabs following a logarithmic radial grid. Fake observed spectra are finally produced by convolving model spectra with instrument responses. Since the line asymmetries are apparent in the convolved spectra as well, this can be used in future XRISM and Athena spectra as an observable diagnostic to fit for. We applied some amount of rigor in assessing the equivalent widths of the major absorption lines, including the Fe XXVI Lyα doublets, which will be clearly distinguishable thanks to the superior quality of future high-resolution spectra. Results. Disc magnetisation stands as another crucial MHD variable that can significantly alter the absorption line profiles. Pure MHD outflow models at low magnetisation are dense enough to be observed by the existing or upcoming instruments. Therefore, these models can serve as simpler alternatives to MHD-thermal models. Fitting with multiple Gaussians is a promising method for handling asymmetric line profiles, as well as the Fe XXVI Lyα doublets.

Inter-array cabling optimization in offshore wind power plants, a new reliability indicator for radial grids

The inter-array grid relates to a significant share of the investments into an offshore wind power plant (OWPP). Optimizing the cable connections regarding costs and reliability is a mathematically complex task due to the high variety of possible wind and component (wind turbine or cable) failure scenarios. This paper presents a novel mixed integer linear programming approach to support investment decisions into OWPPs by trading off cabling purchase and installation costs with power capacity risk (PCR), which is defined as a length-weighed cumulative power flow summation that reflects the consequences of cable failures. Then, quasi-random Monte Carlo simulations assess the optimized collection grids (CGs) to quantify their levelized cost of energy (LCOE). To construct relevant case studies, this work investigates the real OWPPs Ormonde, Horns Rev 1, Thanet, and London Array, which contain 30, 80, 100, and 175 wind turbines. The results reveal Pearson correlation coefficients around 0.99 between the proposed PCR and the expected energy not supplied. Furthermore, this paper’s findings indicate that minimum-cost CGs do not necessarily present the lowest LCOE.

Quantum study of the CH3+ photodissociation in full-dimensional neural network potential energy surfaces.

C H 3 + , a cornerstone intermediate in interstellar chemistry, has recently been detected for the first time by using the James Webb Space Telescope. The photodissociation of this ion is studied here. Accurate explicitly correlated multi-reference configuration interaction abinitio calculations are done, and full-dimensional potential energy surfaces are developed for the three lower electronic states, with a fundamental invariant neural network method. The photodissociation cross section is calculated using a full-dimensional quantum wave packet method in heliocentric Radau coordinates. The wave packet is represented in angular and radial grids, allowing us to reduce the number of points physically accessible, requiring to push up the spurious states appearing when evaluating the angular kinetic terms, through projection technique. The photodissociation spectra, when employed in astrochemical models to simulate the conditions of the Orion bar, result in a lesser destruction of CH3+ compared to that obtained when utilizing the recommended values in the kinetic database for astrochemistry.

A numerical Poisson solver with improved radial solutions for a self-consistent locally scaled self-interaction correction method

The universal applicability of density functional approximations is limited by self-interaction error made by these functionals. Recently, a novel one-electron self-interaction-correction (SIC) method that uses an iso-orbital indicator to apply the SIC at each point in space by scaling the exchange-correlation and Coulomb energy densities was proposed. The locally scaled SIC (LSIC) method is exact for the one-electron densities, and unlike the well-known Perdew–Zunger SIC (PZSIC) method recovers the uniform electron gas limit of the uncorrected density functional approximation, and reduces to PZSIC method as a special case when isoorbital indicator is set to the unity. Here, we present a numerical scheme that we have adopted to evaluate the Coulomb potential of the electron density scaled by the iso-orbital indicator required for the self-consistent LSIC calculations. After analyzing the behavior of the finite difference method (FDM) and the green function solution to the radial part of the Poisson equation, we adopt a hybrid approach that uses the FDM for the Coulomb potential due to the monopole and the GF for all higher-order terms. The performance of the resultant hybrid method is assessed using a variety of systems. The results show improved accuracy than earlier numerical schemes. We also find that, even with a generic set of radial grid parameters, accurate energy differences can be obtained using a numerical Coulomb solver in standard density functional studies.

The effect of adaptive mesh refinement and grid stretching on the magnetized coronal mass ejection model in Icarus

Context. Coronal mass ejections (CMEs) are the main driver of solar wind disturbances near the Earth. When directed toward Earth, the internal magnetic field of the CME can interact with the Earth’s magnetic field and cause geomagnetic storms. In order to better predict and avoid damage coming from such events, the optimized heliospheric model Icarus has been implemented. Advanced numerical techniques, such as gradual radial grid stretching and solution adaptive mesh refinement (AMR) are implemented in the model to achieve better performance and more reliable results. Aims. The impact of a CME at Earth is greatly affected by its internal magnetic field structure. The aim of this work is to enable the modeling of the evolution of the magnetic field configuration of the CME throughout its propagation in Icarus. Thus, we used Icarus to implement a magnetized CME model that is more realistic than the already available simple hydrodynamics cone CME model, allowing us to study the evolution of the magnetized CME during its interactions with the solar wind. The focus of the study is on the global magnetic structure of the CME and its evolution and interaction with the solar wind. Methods. The magnetized CME model implemented in Icarus is the linear force-free spheromak (LFFS) solution that has been imported from EUHFORIA. Simulations with the spheromak model were performed for different effective resolutions of the computational domain. We applied advanced techniques such as grid stretching and AMR. Different AMR levels were applied in order to obtain high resolution locally, where needed. The original uniform medium- and high-resolution simulation results are also shown as a reference. The results of all the simulations are compared in detail and the wall-clock times of the simulations are provided. Results. We analyzed the results from the performed simulations. The co-latitudinal magnetic field component is plotted at 1 AU for both Icarus and EUHFORIA simulations. The time series at Earth (L1) of the radial velocity, density, and different magnetic field components are plotted and compared. The arrival time is better approximated by the EUHFORIA simulation, with the CME shock arriving 1.6 and 1.09 h later than in the AMR level 4 and 5 simulations, respectively. The profile features and variable strengths are best modeled by Icarus simulations with AMR level 4 and 5. The uniform, medium-resolution simulation with Icarus took 6.5 h wall-clock time, whereas with EUHFORIA, the most similar setup takes 18.5 h, when performed on 1 node with 2 Xeon Gold 6240 CPUs at 2.6 GHz (Cascadelake), 18 cores each, on the Genius cluster at KU Leuven. The Icarus simulation with AMR level 4 took only 2.5 h on the same computer infrastructure, while showing better resolved shocks and magnetic field features, when compared to the observational data and the referene uniform simulation results. Conclusions. The results from different Icarus simulations in Icarus are presented using results from the EUHFORIA heliospheric modeling tool as a reference. The arrival time is closer to the observed time in the EUHFORIA simulation, but the profiles of the different variables show more features and details in the Icarus simulations. The simulations with AMR levels 4 and 5 offered the most detailed results. Considering the small difference in the modeled results and the large difference in terms of computational resources, the AMR level 4 simulation is considered to have displayed the most optimal performance. The gradients in the AMR level 4 results are sharper than those in the uniform simulations with both EUHFORIA and Icarus, while the AMR level 4 effective resolution is the most comparable to the standard resolution runs. The AMR level 3 simulation is 15 and 41 times faster than the Icarus and EUHFORIA uniform simulations, respectively; while the AMR level 4 simulation is about three and seven times faster than the uniform simulations, respectively.

Optimal Design and Operation of Wind Turbines in Radial Distribution Power Grids for Power Loss Minimization

This research proposes a strategy to minimize the active power loss in the standard IEEE 85-node radial distribution power grid by optimizing the placement of wind turbines in the grid. The osprey optimization algorithm (OOA) and walrus optimization algorithm (WOA) are implemented to solve the problem. The two algorithms are validated in three study cases of placing two wind turbines (WTs) in the system for power loss reduction. Mainly, in Case 1, WTs can only produce active power, while in Case 2 and Case 3, WTs can supply both active and reactive power to the grid with different ranges of power factors. In Case 4, the best-applied methods between the two are reapplied to reach the minimum value of the total energy loss within one year. Notably, this case focuses on minimizing the total power loss for each hour in a day under load demand variations and dynamic power supply from WTs. On top of that, this case uses two different sets of actual wind power data acquired from the Global Wind Atlas for the two positions inherited from the previous case. Moreover, the utilization of wind power is also evaluated in the two scenarios: (1) wind power from WTs is fully used for all values of load demand, (2) and wind power from WTs is optimized for each load demand value. The results in the first three cases indicate that the WOA achieves better minimum, mean, and maximum power losses for the two cases than the OOA over fifty trial runs. Moreover, the WOA obtains an excellent loss reduction compared to the Base case without WTs. The loss of the base system is 224.3 kW, but that of Case 1, Case 2, and Case 3 is 115.6, 30.6 kW, and 0.097 kW. The placement of wind turbines in Case 1, Case 2, and Case 3 reached a loss reduction of 48.5%, 84.3%, and 99.96% compared to the Base case. The optimal placement of WTs in the selected distribution power grid has shown huge advantages in reducing active power loss, especially in Case 3. For the last study case, the energy loss in a year is calculated by WSO after reaching hourly power loss, the energy loss in a month, and the season. The results in this case also indicate that the optimization of wind power, as mentioned in Scenario 2, results in a better total energy loss value in a year than in Scenario 1. The total energy loss in Scenario 2 is reduced by approximately 95.98% compared to Scenario 1. So, WOA is an effective algorithm for optimizing the placement and determining the power output of wind turbines in distribution power grids to minimize the total energy loss in years.

Bayesian Entropy Methodology: A Novel Approach to Setting Anti-Islanding Protections with Enhanced Stability and Sensibility

The risk of unintentional islanding creation in distributed energy systems poses a significant security concern since unintentional islanding formation could lead to a supply of energy outside of the optimal quality limits. This constitutes a risk for users, maintenance personnel, infrastructure, and devices. To mitigate this problem, anti-islanding protections are widely used to prevent the distributed generator from feeding a portion of the radial distribution grid when a protection device trips upstream. However, the effectiveness of these protections heavily relies on properly tuning protection setting thresholds (such as time delay and pickup). This work proposes a novel approach that utilizes entropy as a model and metric of the uncertainty associated with a particular protection setting. By minimizing entropy, the proposed method aims to improve stability and sensitivity, consequently improving the overall performance of anti-islanding protection. Simulation results demonstrate that the Bayesian entropy methodology (BEM) approach achieves enhanced stability in various scenarios, including frequency transients, and demonstrates a notable reduction in the size of the dataset and computational burden, ranging between 91% and 98%, when compared to related works, with an improvement of the uncertainty achieved. The findings of this study contribute to the development of more robust and reliable anti-islanding protections.

A study of distribution grid topology and its optimization in planning and operation

Abstract This paper combines the characteristics of a distribution network grid, analyzes the topology and application scenarios of a typical grid, and puts forward the design requirements for the optimization of radial DC distribution network grid structure. Based on the constraints of grid optimization, a Pareto multi-objective planning method is selected, and a multi-objective genetic algorithm is designed to improve the grid reliability index of the distribution network grid planning steps. Analyze the parameters of the example, encode the initial 110kV distribution network frame, carry out the optimal solution of the multi-objective genetic algorithm, compare the iteration number and convergence of different genetic algorithms, and obtain the best economic effect of the optimization of the distribution network frame structure. Analyze the power supply reliability index of distribution networks with different grid switching schemes and explore the degree of reliability influence on grid switching and power supply capacity. The optimal solution is obtained in 10 iterations of the algorithm, that is, the objective function is 65.2421 million yuan, and the optimal solution is reached in the interval of the number of iterations [0,100], and the fitness value is in the range of 2 × 104 million yuan.

Inter-array cabling optimization in offshore wind power plants, a new reliability indicator for radial grids.

The inter-array grid relates to a significant share of the investments into an offshore wind power plant (OWPP). Optimizing the cable connections regarding costs and reliability is a mathematically complex task due to the high variety of possible wind and component (wind turbine or cable) failure scenarios. This paper presents a novel mixed integer linear programming approach to support investment decisions into OWPPs by trading off cabling purchase and installation costs with power capacity risk (PCR), which is defined as a length-weighed cumulative power flow summation that reflects the consequences of cable failures. Then, quasi-random Monte Carlo simulations assess the optimized collection grids (CGs) to quantify their levelized cost of energy (LCOE). To construct relevant case studies, this work investigates the real OWPPs Ormonde, Horns Rev 1, Thanet, and London Array, which contain 30, 80, 100, and 175 wind turbines. The results reveal Pearson correlation coefficients around 0.99 between the proposed PCR and the expected energy not supplied. Furthermore, this paper's findings indicate that minimum-cost CGs do not necessarily present the lowest LCOE.

An efficient operation strategy for dispersed generation sources in bipolar asymmetric DC distribution networks: a sequential quadratic approximation

AbstractThis paper proposes a sequential quadratic optimization of the optimal power flow (OPF) in bipolar direct current (DC) grids. This formulation is based on Taylor’s expansion applied to the non-convex constraints, thus transforming them into affine equations. This approach, suitable for both radial and meshed grids, considers that the neutral terminal is only grounded at the substation bus. Other groundings can be considered in the loads without a loss of generality. Two test feeders composed of 21 and 33 nodes are considered in order to validate the effectiveness of the proposed sequential quadratic convex approximation model. Since this approach is based on convex optimization, a fast convergence, the uniqueness of the solution, and the global optimum are ensured. Simulations were performed using Python with the CvxPy library, a modeling system specialized in convex programming, as well as the ECOS solver. The 21-bus grid was employed to validate the effectiveness of the proposed convex model regarding power losses minimization, and the 33-bus one was used to evaluate the effect of the efficient dispatch of renewable generators within day-ahead operation environments.

CoLinFlow: An Iterative Solution Approach for the Scenario-Based AC OPF in Active Meshed Distribution Grids With Batteries

Distribution grids are characterized by an increased installation of renewable energy sources (RESs) and of batteries. Both the uncertainty of RESs and the controllability of batteries should be considered when optimizing their operation. This leads to large-scale, non-convex Optimal Power Flow (OPF) problems. Existing solution approaches either refer to radial grids or do not work under uncertainty. However, many Distribution System Operators operate their grids in meshed topologies. In this paper, CoLinFlow, an efficient solution approach for a scenario-based AC OPF in meshed balanced three-phase distribution grids with intermittent RESs and controllable batteries is proposed. First, a particular power flow form in rectangular coordinates that is accurate for meshed grids is applied. Then, Generalized Linearized Power Flow (GLPF), a novel linearization of the power flow equations based on replacing non-linear terms with constants is developed. Based on GLPF, we design CoLinFlow, a heuristic iterative scheme that at each iteration solves a convex OPF and updates GLPF until convergence. The solution of CoLinFlow at convergence is proven to be feasible with respect to the original non-convex OPF and convergence is reached after very few iterations. Also, it is shown that CoLinFlow achieves almost the same optimal objective as Ipopt, while being faster.

Basis-Set-Error-Free Random-Phase Approximation Correlation Energies for Atoms Based on the Sternheimer Equation.

The finite basis set errors for all-electron random-phase approximation (RPA) correlation energy calculations are analyzed for isolated atomic systems. We show that, within the resolution-of-identity (RI) RPA framework, the major source of the basis set errors is the incompleteness of the single-particle atomic orbitals used to expand the Kohn-Sham eigenstates, instead of the auxiliary basis set (ABS) to represent the density response function χ0 and the bare Coulomb operator v. By solving the Sternheimer equation for the first-order wave function on a dense radial grid, we are able to eliminate the major error─the incompleteness error of the single-particle atomic basis set─for atomic RPA calculations. The error stemming from a finite ABS can be readily rendered vanishingly small by increasing the size of the ABS, or by iteratively determining the eigenmodes of the χ0v operator. The variational property of the RI-RPA correlation energy can be further exploited to optimize the ABS in order to achieve fast convergence of the RI-RPA correlation energy. These numerical techniques enable us to obtain basis-set-error-free RPA correlation energies for atoms, and in this work, such energies for atoms from H to Kr are presented. The implications of the numerical techniques developed in the present work for addressing the basis set issue for molecules and solids are discussed.

Radial grid reflectance correction for hyperspectral images of fruits with rounded surfaces

Over the last two decades, the viability of hyperspectral imaging (HSI) technology as a tool for determining food quality has been established. This technology has been successfully combined with chemometric tools and image-processing techniques to enhance its effectiveness. Despite the advances in imaging technology, significant challenges related to non-uniformity caused by object geometry still need to be addressed. The inappropriate processing of non-uniform food products can significantly affect subsequent calculations, including accurate measurements and precise analysis. A popular method used to face up non-uniformity is the Lambertian surface correction, which assumes spherical surfaces of food products; however, it presents some issues with non-spherical shapes. This work proposes a generalized reflectance correction method for HSI of rounded fruits that are not necessarily spherical. The method is based on the correlation between the pixel’s position and its reflectance. For proof of concept, a case study was designed considering the HSI of mango fruits (Mangifera indica L) Kent variety. For comparison, each image was corrected using both the Lambertian surface correction and the proposed method. Results show a strong correlation between the standard deviation of the spectral profiles of images and the roundness of the fruit, which is more evident in the case of the proposed radial grid correction method. Hence, the proposed radial correction method produced a more uniform texture in corrected hyperspectral images.

An efficient two-phase flow calculation method based on grid mergence and dimension transformation

Two-phase flow numerical methods are applied in internal ballistics widely, which has made higher fidelity analysis with minimal cost become an urgent demand. Current methods are based on independent dimension, and there is no definite conversion criterion and data transmission method, which have limited the application of efficient hybrid models applied to calculation. In this paper, we propose a hybrid method by linking a two dimensional (2D) model to a one dimensional (1D) model for two-phase flow. First, 1D and 2D two-phase flow models are established according to the flow field states in different phases. Next, the criterion of conversion between the two models is established, which is a quantitative index to judge the degree of radial effect and axial effect. Finally, dimension transformation in the radial direction and grid mergence in the axial direction are conducted to complete the whole computing model. The simulation results show that the hybrid method is more efficient in the interior ballistic process and maintains the level of trust in classical codes. Compared with the 2D method, the hybrid method significantly improves the computational efficiency by 86.5%. By analyzing the state in the chamber, the accuracy of the conversion criterion is confirmed. This criterion can be used as the transformation criterion of the hybrid model to form the standard multi-dimensional calculation transformation criterion of interior ballistics and may be promising for the rapid simulation of two-phase flow in interior ballistics.