Numerical Calculation Method Research Articles

Research on Pipeline Leakage Calculation and Correction Method Based on Numerical Calculation Method

The hazard coefficient for leakage diffusion of gas transmission pipeline is extremely high, which can easily lead to explosive accidents. The amount of gas leakage is an important factor in the safety assessment of pipeline leakage. Therefore, this paper considers the influence of gas interactions inside and outside the pipeline on pipeline leakage and establishes a three-dimensional leakage diffusion model that is coupled with the pipeline and air domain. Through the use of theoretical, experimental, and numerical simulation methods, this paper investigates the effects of leak hole diameter, leak hole shape, and changes in transport pressure on pipeline leakage. Finally, based on simulated leakage data, we analyze the sources of error and propose a high-precision formula for calculating leakage from small holes in pipelines. The results show that an increase in the diameter of the leak hole leads to a decrease in the central velocity of the leak hole and a sharp increase in leakage volume. The leakage volume of different leak hole shapes is ranked in the following order: rectangle > diamond > circle. When the leak holes are rectangle and diamond, the leakage velocity distribution range of the leak hole is larger and more regular than that of the circular leak hole. Also, the volume of gas leakage increases with the increase in delivery pressure, while the central velocity of the leak hole remains relatively unchanged. Based on the proposed pipeline leakage correction formula, it is calculated that under the same working condition, the relative error range between the numerical simulated leakage rate and the theoretically corrected leakage rate is significantly reduced from −8.40%~18.03% to −1.58%~2.60%, and the calculation accuracy is significantly improved.

Active learning modules for a numerical methods course

Education research has suggested that students who receive a wider variety of sensory inputs during the learning process will be able to make more connections and more deeply understand course content. To this end, three physical hands-on laboratory learning modules were designed for a computational numerical methods course to help students develop intuition for physical systems, to allow for a comparison of real data against numerical solutions of physics equations, and to increase student engagement. These modules were designed to reinforce specific topics covered in the numerical methods curriculum, including numerical differentiation and numerical solution of ordinary differential equations. Pre- and post-tests showed an increase in student knowledge after module completion. In addition, end-of-term surveys showed that a strong majority of students believed modules helped them visualize and understand key numerical methods concepts, and that most would be interested in learning new material with similar modules in the future.

Evaluation of friction calculation methods for rolling bearings

In gearboxes, rolling bearing power losses often make up a large amount of the total gearbox power losses. Therefore, an exact calculation of rolling bearing power losses is very important for resource and energy efficient gearbox design. The state of the art offers numerous friction calculation methods with different levels of detail to calculate power losses of rolling bearings. Bearing manufacturers like SKF and Schaeffler offer popular bearing-based/global calculation methods for standard rolling bearings. Contact-based/local calculation methods can consider a wider application field by generalization of tribological relations, which enables its application to e.g. hybrid bearings or non-standard bearings. The different methods may yield widely differing results. For its validation, measurement results are required. In this study, a broad comparison of calculation results with substantial measurement results is shown. Based on the validation a classification of the calculation methods is derived, which provides guidance for the design engineer to choose the appropriate method for the respective application. Contact-based/local calculation methods have the potential to predict friction in rolling bearings precisely.

Inverse kinematic analysis and agile control of a magnetically actuated catheter

In recent years, there has been a growing application of robotic-assisted magnetic actuation systems in the treatment of cardiovascular diseases because of the fast response and the miniaturization of medical tools. However, inverse kinematic (IK) modeling in permanent magnet systems is still a challenging task due to the complexity of the magneto-solid strong coupling field. In this paper, we present a magnetic actuation system that uses the rotation of a single permanent magnet to steer the intravascular catheter. The main contribution is the proposal of an IK modeling method that establishes a relationship between the catheter's deflection angle and the rotation angle of the driving magnet (DM). Our proposed method uses the constant curvature model (CCM) to decouple the catheter's deformation and the magnetic loads, thus enabling the efficient estimation of the position of the catheter's tip based on the desired deflection angle. After establishing the equilibrium equation, we employ a numerical computation method to optimize the rotation angle of the DM. To facilitate fast convergence, we propose an analytical solution to determine the optimal initial value. Our proposed IK modeling method has been proven to be effective in the model validation experiment, which achieves a good balance between accuracy and efficiency. The difference between the planned and actual deflection angle is 4.55±3.44° and the distal position error is 1.26±0.74 mm. The completion time of our IK method is 1–4 ms. The performance of our magnetic actuation system has been evaluated in the phantom experiment, in which the catheter can pass sequentially through the planned bifurcations and finally reach all the goals under the magnetic guidance.

Study on the effect of waveform film holes on film cooling efficiency

In order to improve the film cooling efficiency of the cooling gas on the hot side wall of the plate, the flow field, temperature field and the average film cooling efficiency of the cylindrical hole, rectangular hole and waveform hole near the wall were compared and analyzed by numerical calculation method. Compared with cylindrical holes, the average spanwise film cooling efficiency of rectangular hole is improved by 100%, and the average spanwise film cooling efficiency of waveform hole is improved by 130%. In addition, the effects of the amplitude A of the waveform hole and the initial phase ϕ on the cooling efficiency are compared and analyzed. The results show that: Within the scope of this study, when the blowing ratio M = 1, lifting the initial phase ϕ of the waveform hole can effectively improve the film cooling efficiency of the cooling gas on the wall. When the amplitude A of the waveform hole is raised, the film cooling efficiency of the cooling gas on the wall will first increase and then decrease, reaching the maximum at the amplitude A = 0.4D. At low blowing ratio, the geometric structure of waveform hole has little influence on the cooling effect of wall surface. Under high blowing ratio, when the geometric structure of waveform hole is changed, the influence of secondary flow on the average spanwise cooling efficiency of wall surface is great.

Analysis of contribution degree of vibration transmission of bolted structure

In practical engineering, the vibration transmission between bolted structures supported by cantilever beams involves many factors. The vibration transmission effect is the embodiment of the coupling of various factors, so it is impossible to accurately and quantitatively evaluate the influence degree of various factors. In this paper, the influence factors of vibration between bolted plates in the form of cantilever beam are studied by numerical calculation method. The effects of friction coefficient, bolt preload, temperature and pressure on vibration characteristics are studied. Finally, the contribution of different influencing factors to vibration transmission is given.

An improved time-varying mesh stiffness calculation method and dynamic characteristic analysis for helical gears under variable torque conditions

Based on the slice theory and numerical calculation methods, the time varying meshing stiffness (TVMS) calculation method of the gear pair was constructed for the helical gear pair of a electric continuously variable transmission (ECVT), and the TVMS of the helical gear were calculated under different constant and time-varying torque in this study. The obtained stiffness values were introduced into the established dynamics model of helical gear system, and the influence of changed TVMS, resulting from the variable speed and torque, on the nonlinear dynamic characteristics of gear pair was analyzed using the Runge-Kutta method. The results show that the proposed TVMS calculation method is very effective in computing the TVMS of helical gear pair under time-varying condition. The TVMS and dynamic transmission error (DTE) increase as the torque increase, and vice versa. Meanwhile, the system exhibits a diverse range of periodic, sub-harmonic, and chaotic behaviors at high speed and at low speed when torque is low, whereas not appear at steady high torque under low speed range. This study offers a method for gaining the TVMS of helical gear pair to analyze the dynamic characteristics of gear pair under actual working condition, and the influence of torque that change with the speed ratio on the dynamic performance of a gear system should be considered in the industrial applications.

Modeling and analysis of the equivalent convex mandrel of the three-dimensional braiding carbon fiber composite robotic arm

The third robotic arm (drive housing) of a six-axis industrial robot often has a vertical inwardly concave surface to facilitate the installation of spatially vertical drive motors. With the inwardly concave surface of the robotic arm it is difficult to realize three-dimensional (3D) braiding directly, and based on this problem, an equivalent convex mandrel is added to the concave mandrel. The mathematical model of the concave mandrel is established, and the mathematical expression of the concave mandrel is obtained. In any cross-section perpendicular to the x-axis, the equivalent outwardly convex cross-sectional line is obtained according to the condition that the length of the outwardly convex and concave mandrel cross-sectional line is equal. All outwardly convex cross-sectional lines form a smooth surface of the equivalent convex mandrel. By the numerical calculation method, the braiding trajectory and the downward pressure trajectory are predicted for various take-up speeds. The length error of the braiding trajectory and the downward pressure trajectory are within 5%, which verifies the accuracy of the convex mandrel. The variation pattern of the braiding angle is smooth, verifying the braidability of the convex mandrel. The experimental results show that the outwardly convex carbon fiber fabric can be pressed down to fit the surface of the concave mandrel. Therefore, a carbon fiber composite arm with an inwardly concave surface can be manufactured by 3D braiding with the addition of an equivalent convex mandrel.

Numerical calculation and experimental analysis of thermal environment in industrialized aquaculture facilities.

With the increasing market demand for high-quality aquatic products, the application of industrialized aquaculture facilities may get more attention. In order to improve the poor performance of thermal insulation, the accuracy of the numerical model was verified in this study through actual measured data. The model verification results shown that the average relative errors of the measured and calculated values of indoor air temperature, water temperature and roof inner surface temperature in the industrialized aquaculture workshop is within 2.5%, it suggested that the numerical calculation results are accurate. Furthermore, the thermal environment and thermal insulation performance of industrialized aquaculture facilities in winter were conducted based on the numerical calculations. After optimized the thermophysical parameters of the workshop enclosure structure, we found that the water body temperature could reach 21°C (which was close to the breeding temperature of grouper (Epinephelinae). Therefore, the numerical calculation method was further used to analyze the energy consumption of aquaculture water in January of a typical year in this area by heating to three constant temperatures (22, 25, and 28°C). When the aquaculture water was heated to the three constant temperature states, it needed to consume 8.56×105, 1.02×106 and 1.22×106 MJ of energy respectively, which were equal to the amount of energy released by the complete combustion of 29.3, 35.1 and 41.8 t standard coal. Moreover, it is concluded that the artificial temperature increase in winter maintains the temperature in the range of 22~25°C to provide the highest heating efficiency. This conclusion can provide theoretical basis and application reference for industrialized aquaculture in winter.

Survey on analytical and numerical methods for lightning-induced voltages calculations

Survey on analytical and numerical methods for lightning-induced voltages calculations

THE RESEARCH OF IMPLEMENTATION OF NUMERICAL RIGOROUS MATHEMATICAL METHODS WITH THE PARAMETER OF THE MEMBERS NUMBER IN THE TAYLOR SERIES

The current level of development of geoinformation technologies makes it possible to determine the cartometric properties of terrain objects with a user-defined accuracy. The author of this paper proposes a mathematical model that allows to implement the function of converting geodetic coordinates into rectangular flat Gauss-Kruger projections in a software environment based on the setting of the parameter of the number of members in the Taylor series, adjusting the accuracy of the coordinate transformation and their dimension. The purpose of this work is to implement a mathematical model of a numerical approximate computer method of converting geodetic coordinates into flat rectangular Gauss-Kruger projections. The results of this study will also be used to create functions for converting coordinates from rectangular flat Gauss-Kruger projections to geodetic coordinates and from one 6-degree zone of the Gauss-Kruger projection to another, taking into account the parameter of the number of members in the Taylor series. The proposed mathematical models are recommended to be implemented in the MATLAB or PhyCharm using the necessary libraries. The following studies will focus on determining the areas and lengths of objects located in two or more 6-degree zones of the Gauss-Kruger projection.

Identification of the effects of pathogenic genetic variations of human CYP2C9 and CYP2D6: an in silico approach

Genetic variations in the human cytochrome P450 family 2 subfamily C member 9 (CYP2C9) and cytochrome P450 family 2 subfamily D member 6 (CYP2D6) genes may affect drug metabolism and lead to alterations in phenotypes. Genetic variations are associated with toxicity, adverse drug reactions, inefficient treatment. Various in silico tools were combined to investigate the deleterious effects of missense non-synonymous single nucleotide polymorphisms (nsSNPs) of the human CYP2C9 and CYP2D6. The structural and functional effects of the high-risk non-synonymous SNPs in the human CYP2C9 and CYP2D6 were predicted by numerous computational mutation analysis methods. Out of 24 pathogenic missense SNPs in the CYP2C9, 22 nsSNPs had a decreasing effect on protein stability and 13 SNPs were showed to be located at conserved positions. Out of 27 high-risk deleterious non-synonymous SNPs in the human CYP2D6, 21 SNPs decreased protein stability and 16 nsSNPs were predicted to be positioned at conserved regions. Our present study suggests that the identified functional SNPs may affect drug metabolism associated with CYP2C9 and CYP2D6 enzymes.

Spatio-temporal characterization of tightly focused femtosecond laser fields formed by paraboloidal mirrors with different F-numbers.

The focusing spatiotemporal property of a femtosecond laser pulse is presented under tight focusing conditions by using the frequency-resolved incident electric field and vector diffraction formulas with the wavefront correction term. In the ideal case, the focused laser intensity reaches its maximum at the F-number of ∼0.35 due to the strong diffraction effect under extremely tight focusing conditions. In spatio-temporal coupling distortion cases, their spatiotemporal Strehl ratios show a trend of improvement as the F-number decreases and this phenomenon is mainly concentrated along the y-direction. Based on the numerical calculation method used in this work, the precise information of tightly focused ultra-intense femtosecond laser fields can be obtained, which is crucial for assessing a focused intensity and describing the motion of charged particles under an extremely strong electric field. Moreover, the evolution law of focal fields with spatiotemporal distortions found in this paper can offer some theoretical guidance for realizing ultrahigh laser intensity in the near future.

Mechanism of Cement Deep Mixing and Design Method Improving Soft Ground in Mekong Delta

Soil improvement technique for embankment fill is often needed to rapidly improve the strength of the soft ground. In recent years, the cement deep mixing (CDM) method has been commonly used as an alternative to improve the soft soil foundation of embankment. This method is a reasonable solution used for several applications as to treat the soft soil behind the bridge abutment, to minimize settlement and enhance the bearing capacity of soil foundation for a storage tank, to support segmental retaining walls, and to prevent differential settlement between a new embankment over soft soil and existing embankment where the settlement has ceased. The stability of cement column stabilized embankments can be analyzed either by a numerical calculation method such as the finite element method (FEM) or by a limit equilibrium method. The numerical calculation methods require reliable material parameters as determined by field and laboratory tests or in-situ on excavated columns and on the unstabilized soil. Another method considering simplified method is limit equilibrium method. In analysis of this method, the stability of cement column is analyzed by assuming that failure of the cement columns and the soil.

Refraction correction for deep-water three-dimensional visual measurement based on multi-objective optimization.

Refraction-induced errors affect the accuracy of three-dimensional visual measurements in deepwater environments. In this study, a binocular camera refractive imaging model was established, and a calibration method for the refraction parameters was proposed for high-accuracy shape and deformation measurements in deep-water environments. First, an initial estimate of the refractive axis was obtained using a three-dimensional calibration target. Then, the errors in the distance between the spatial point pairs and the reprojection errors are taken as the dual optimization objectives, and the Non-dominated Sorting Genetic Algorithm II is applied to optimize the refraction parameters. To efficiently calculate the reprojection error, an improved numerical computation method is proposed to accelerate the calculation of the analytical forward projection. Underwater experiments were conducted to verify the method's effectiveness. The results showed that the average error of the absolute position of the reconstructed points was less than 1.1 mm and the average error of the displacement was less than 0.04 mm. This study provides a sound solution for accurate three-dimensional visual measurement in deep-water environments.

Open-source Python library for modeling coupled thermo-hydro-mechanical (THM) processes

Abstract. The interactions between temperature, fluids, and mechanical properties in a repository system are essentially described scientifically by coupled thermo-hydro-mechanical (THM) processes. THM modeling, i.e., the prediction of the behavior of materials under different conditions, is the fundamental numerical tool here. The confident handling and deep understanding of numerical computation methods is thus the prerequisite for performing and evaluating preliminary safety analyses in the site selection process. At the Federal Office for the Safety of Nuclear Waste Management (BASE), a software library for the simulation of coupled THM processes is currently being developed. The main goal of the in-house development is an open-source toolbox in the scripting language Python and is motivated by several long-term sub-goals: targeted development of expertise within BASE regarding numerical modeling of safety-relevant aspects in the long-term safety analyses; diversification of the testing capabilities regarding the preliminary safety investigations by means of an in-house, independent modeling software; foundation of a library of known benchmarks and evaluation examples for the comparison of different software tools; documentation and processing of basic THM scenarios for internal or, if necessary, public technical training. The focus of this development is on creating a toolbox that is easy to use and at the same time highly flexible. The main methodical aspects are as follows: building a new library based on the pyGIMLi pre- and postprocessing framework (Rücker et al., 2017); creating a finite-element reference implementation in the Python scripting language for maximal transparency; creating an easy-to-use interface to the solution of the weak formulation for the finite-element theory with expressions of a symbolic manner allowing maximal flexibility; defining an interface to allow for the integration of alternative, third-party high-performance libraries; creating a collection of Jupyter notebooks of well-documented test cases and benchmarks. Choosing the open-source approach ensures the best possible transparency and, in the long term, also allows the provision of appropriately quality-assured and documented simulation tools to the public. The presented poster shows the current development status of the software library and the currently implemented quality assurance concepts and gives an outline of the potential applications of the library.

Parameter Calibration and System Design of Material Lifting System for Inclined Shaft Construction

As a key transportation equipment in the construction of long tunnels with large slope, the material hoisting system plays an important role in the transportation of materials in sloping shafts. This paper proposes a parameterized calibration scheme for the hoisting system based on the structure and working principle of the hoisting system, taking the wire rope, hoist, motor and overhead wheel as the research objects, and according to the relevant industry specifications and numerical calculation methods. Based on the structural design and functional analysis of the hoisting system, a reasonable control system, monitoring system and safety protection devices are designed, and the calibration scheme and the designed system are introduced into the Dianzhong water diversion project for verification. The parameters of each component of the hoisting system were calculated as follows: maximum breaking tension value of wire rope 490.29 KN, drum diameter 2000 mm, motor hoisting power 213.7 KW, and the system design was as follows: control system selects frequency conversion electric control method, safety protection device selects ZDC30-2.5 anti-running device. The results show that: the hoisting system components structure parameters meet the specification requirements—safety protection devices can effectively prevent the occurrence of sports car slippage and man-car jumping rail overturning accident—to meet the requirements of the construction period transport capacity and transport safety. The relevant experience can provide the basis for the design of a material hoisting system for a similar inclined shaft construction.

Numerical calculation method for the mean free path of single-mode semiconductor nanosheets with surface roughness

A numerical calculation method is proposed to compute the transport mean free path of single-mode semiconductor nanosheets with surface roughness, where the mean free path is extracted from the statistical average of the logarithm of the dimensionless resistance. The present method requires only a computationally less demanding coherent transmission probability, and is applicable to wider channel length ranges from the quasi-ballistic to the localization regime. The channel thickness, T w, dependence of the mean free path calculated by the proposed method within the effective mass approximation shows the well-known T W 6 dependence for thicker T w, while it becomes weaker for thinner T w.

Improving numerical methods for the steel yield strain calculation in reinforced concrete members with Machine Learning algorithms

Improving numerical methods for the steel yield strain calculation in reinforced concrete members with Machine Learning algorithms

Probability life calculation model of beam element application and study in welded structures reliability analysis

Statistical size and geometrical size are the main factors affecting the service life of mechanical structure calculation. To explore the reliability of the lifespan of beam structures, a probability lifespan numerical calculation method based on Vector Form Intrinsic Finite Element Method (VFIFEM) was proposed, and the method was verified through full lifespan experiments on I-beam welded structures. First, a fatigue fracture model that considers the coupling of residual stress (RS) and cyclic load variations was established. Based on this fatigue fracture model, a probability lifespan calculation model for beam elements was defined by proposing a cross-sectional shape correction coefficient and a position correction coefficient. The proposed probability lifespan model for beam elements was used to calculate the I-beam welded structure, and the calculated results were compared with the full lifespan experiment results, which were close in statistical results, with all experimental results falling within the [10%, 90%] interval except for one experiment. This method effectively couples the influence of statistical size and geometric size on probability lifespan, providing a new approach for the structure probability lifespan calculation in the future.