Numerical Technique Research Articles

Enhanced meshfree method with nodal integration for analysis of functionally graded material sandwich curved shells

This paper presents a nodal integration technique, the sub-domain stabilized conforming integration (SSCI), for the meshfree radial point interpolation method (RPIM) applied to the static and modal analysis of functionally graded material (FGM) sandwich curved shells. FGM sandwich shells with different kinds of core and face sheets are considered in this work while the interested curved shell is formulated by the first-order shear deformation theory. The numerical integration technique to compute the stiffness and mass matrices in the equilibrium equation is the SSCI, which is a stabilized nodal integration with strain smoothing to preserve the accuracy and stability of the numerical results. The RPIM shape functions are utilized in this study for interpolating both the field variables and the geometry of the curved shell due to their ability to satisfy the Kronecker delta property, a rare advantage among meshfree methods. The static and modal analysis of different geometry curved shells with various sandwich FGMs are conducted. Through several numerical examples, the accuracy and efficiency of the SSCI technique in the meshfree RPIM are demonstrated and discussed.

Numerical Investigation on Cathodic Protection of X80 Pipeline Steel in Marine Environment

Abstract Submarine pipelines are usually buried in sea mud, but part of the pipes will be exposed to seawater directly because of the change of seabed, the differences between sea mud and seawater result in different corrosion states. Generally, due to its large geometric size, complex medium, difficult to detect and other reasons, corrosion defects will cause greater harm to pipeline materials. A numerical analysis model of the outer surface corrosion of submarine pipelines was developed to simulate status of cathodic protection, furthermore, potential distribution and local density of current inside the defects was also analyzed and evaluated. The results indicates that: (1)The CP potential distributes more evenly in sea mud when the same sacrificial anode is used, and the cathodic protection current density needed to meet the anti-corrosion requirements is much larger in seawater than in sea mud.(2)Compared with sea mud, the polarization potential of the sacrificial anode in seawater is more negative, and the CP potential at the edge of anodes is the most positive in both sea mud and seawater. Furthermore, in seawater, the dissolution rate of sacrificial anodes closer to the seabed is lower, and anodes dissolve much faster at the inner surface, while it is just the opposite in sea mud.(3)Cathodic protection cannot ensure complete and effective protection at defect points. At defect bottom, the cathodic protection current is partially shielded, reducing the effectiveness of CP system on corrosion protection of pipelines. Moreover, the shielding effect of defect point on cathodic protection current has a great deal with the geometric shape of defect points, with decreasing width and increasing depth, the shielding phenomenon becomes more obvious.(4) Numerical simulation technique based on the finite element model provides a new method to solve this problem and plays a positive role in assessing anti-corrosion status and the service life of anodes.

Turbulent models of shallow-water equations-based smoothed particle hydrodynamics

The depth-averaged models such as those based on the shallow water equations (SWEs) are commonly used to simulate the large-scale flows with engineering importance. The smoothed particle hydrodynamics (SPH) approach has been documented to solve the SWEs due to its mesh-free superiority in treating the free surfaces and wet-dry boundaries. However, nearly all SWE-SPH models were developed without a turbulent model, which seriously limited the model applications where the flows are complex and where the turbulent parameters are explicitly needed. For the first time, this paper includes a depth-averaged turbulent k̂-ε̂ model in the SWE-SPH solver, making the model more capable of treating the turbulent flows in the practical field. For comparison purpose, a sub-particle-scale turbulent model widely adopted in three-dimensional (3D) SPH was also included in the present SWE-SPH scheme. To evaluate the performance of the two proposed turbulent SWE-SPH models, various open channel flows of increasing complexity were simulated, and the SPH computations were compared with the reported data in the literature. Through the analysis of results for a rough riverbed, L-shaped and sudden expansion channels, it is demonstrated that the present turbulent SWE-SPH models are equipped with good robustness and accuracy in capturing the shallow water turbulent dynamics, with the potential to be used in practical river and coastal flows. In summary, there are two distinct novelties in the proposed work. First, the mesh-free numerical modeling technique SPH is used to solve the shallow water equations, which enable the model to work in large engineering field through simple and effective tracking of free surfaces and wet-dry boundaries. Second, the proposed research expands the shallow water SPH modeling technique by including robust turbulence simulation capacity. The newly developed model can address more challenging engineering scenarios such as the sediment and pollutant transports when the flow turbulence plays an important role and where the turbulent parameters are explicitly required in the relevant transport equations.

Simulating the Universe from the cosmological horizon to halo scales

Ultra-large scales close to the cosmological horizon will be probed by the upcoming observational campaigns. They hold the promise to constrain single-field inflation as well as general relativity, but in order to include them in the forthcoming analyses, their modelling has to be robust. In particular, general relativistic effects may be mistaken for primordial signals, and no consensus has emerged either from analytical modelling nor from the numerical route, obstructed by the large dynamical range to be simulated. In this work, we present a numerical technique to overcome the latter limitation: we compute the general relativistic displacement field with the N-body relativistic code gevolution and combine it with the accurate Newtonian simulation Gadget-4. This combination leads to an effective simulation reproducing the desired behaviour at the level of the matter power spectrum and bispectrum. We then measure, for the first time in a simulation, the relativistic scale-dependent bias in Poisson gauge; at redshift z = 0, we find b 1 GR = -8.1 ± 2.8. Our results at the field level are only valid in the Poisson gauge and need to be complemented with a relativistic ray tracing algorithm to compute the number count observable.

Study the effect of solar power on the efficiency of desalinating saline water: Case studies Al-Khafji and Gulf of Aqaba areas

The desalination of salty water has become a necessary industrial process to overcome the next global shortage in freshwater. In this study, adding a Reheat Solar Collector Cycle (RSCC) to a multi-stage flash plant is used to increase the optimization of the desalination process, improving efficiencies, reducing energy, and increasing the production of freshwater demands to overcome the global crisis of shortage in freshwater. Two projects employ this numerical technique. The first project is conducted in the Al-Khafji multi-stage flash plant in Saudi Arabia with an input mass flow rate of 1 Mkg/h (277.78 kg/s), TDS of 35,000 ppm, and wind velocity of 1 m/s. The second project is conducted in the Gulf of Aqaba in Jordan with an input mass flow rate of 1 Mkg/h (277.78 kg/s), TDS of 40,000 ppm, and wind velocity of 1 m/s. The module of the LS-2 Parabolic Trough Collector (PTC) is used to gain the required energy to heat seawater. The results show that in the Al-Khafji project, an increase of 7.1% in the plant capacity per day and an increase in efficiency from 7.8 to 8.4 were observed. While, in the Gulf of Aqaba, an increase of 7.7% in the plant capacity per day and an increase in efficiency from 7.8 to 8.4 are observed.

Iterative Numerical Approximation Technique for 3D Eddy Current Models in Harmonic Regime Based on the Electromagnetic T-Formulation and the Finite Element Method

In this paper, an iterative numerical approximation technique is used for analyzing the distribution of eddy currents density in conductive materials plates by using the electromagnetic T-formulation and the Biot-Savart law, solved by the finite element method. The proposed approach allows for the meshing of the different parts of the studied system separately, including the sensor and the conductive plate, without the need for an air region. Firstly, this approach reduces the number of unknown variables by avoiding the air region of the system's mesh. Secondly, it simplifies the consideration of the sensor's motion without the need to remesh the system. For this purpose, a calculation code has been developed for solving an electromagnetic three-dimensional non-destructive testing model. This latter permits the resolution of JSEAM # 6 Benchmark problem to validate the proposed method. The impedance variation due to the presence of a defect are evaluated. The obtained results are compared with the experimental ones found in the literature. These results reveal a good agreement, which proves the validity of the proposed method.

Development and testing of hybrid (PNM–CFD) mathematical model and numerical algorithm for description of fluid flows in three-dimensional digital core models

Numerical simulation of fluid flow in porous and fractured rocks is an important task for many industrial applications. The most common approaches to constructing such models are direct (CFD or lattice Boltzmann) and porous network (PNM) modeling. Each approach has its own advantages and disadvantages. This paper presents a hybrid mathematical PNM–CFD model for describing fluid flows in three-dimensional digital core models, which has the high speed performance of PNM approaches and high accuracy of CFD models. Numerical technique has been developed for describing fluid flows in three-dimensional digital core models using a hybrid PNM–CFD model. The numerical technique links a one-dimensional pore network solver and a three-dimensional CFD solver into a combined model in original way by constructing a single pressure field for the entire computation domain. To validate the model, several tests were performed, including flow in straight channels and numerical simulation of fluid flow in a microfluidic chip. The test results have shown the adequacy of the hybrid model performance. The hybrid model for determining pressure drop in a branched network with three-dimensional chambers has an error of no more than 5 % when compared to experimental data. Similarly, the error in calculating velocity does not exceed 7 % when compared to the full three-dimensional calculation. The hybrid model has shown an almost twofold increase in calculation speed compared to the full three-dimensional model.

An artificial neural network approach to characterizing the behavior of bioconvective nanofluid model using backpropagation of Levenberg–Marquardt algorithm

The study of the behavior of bioconvective nanofluid model (BC-NFM) was explored using bioconvection properties in the computational analysis of magnetized nanofluid flow that was convectively heated, which is critical for applications in energy systems and biomedical devices. We implemented a backpropagated Levenberg–Marquardt neural network approach (BLMNNA) to enhance the analysis and prediction accuracy of such fluid flows. Using the Adams numerical technique, we generated a comprehensive dataset for eight distinct scenarios by variation of thermophoresis parameter, Rayleigh number, Deborah parameter, Hartman number, Prandtl number, bioconvection Lewis number, and Schmidt number to train and test our model. The results demonstrate significant improvements in prediction accuracy and computational efficiency compared to traditional numerical solvers. The steps of training, testing, and validating the developed BLMNNA are used to get the desired numerical solutions of BC-NFM for various instances. The worth and accuracy of the stochastic numerical solutions of BC-NFM are established and authenticated by the outputs of the designed methodology BLMNNA through Adaptation graphs of Mean Square Error, regression studies, plots of error histogram and index of state transition. Excellent measurements of performance in terms of MEAN SQUARE ERROR are achieved at level 9.76E[Formula: see text], 1.41E[Formula: see text], 1.79E[Formula: see text], 1.22E[Formula: see text], 8.49E[Formula: see text], 7.19E[Formula: see text], 9.72E[Formula: see text], and 9.35E[Formula: see text] against 69, 73, 96, 76, 237, 86, 120, and 33 epochs. The significant connection between the proposed and reference findings demonstrates the validity of the BLMNNA based on error analysis, which ranges from E[Formula: see text] to E[Formula: see text] for all situations. The results show that the proposed neural network approach achieves a high level of accuracy, closely matching the outcomes obtained from the numerical solver. The method provides an efficient and precise solution for the analysis of complex fluid flow problems, representing a significant advancement over traditional numerical techniques.

Numerical Investigation of Bionic Axial Fan used in Split Air Conditioner

Abstract: Bionic axial fan is the main component in the outdoor unit split type room air-conditioner (AC) which impact the cooling and comfort. The present work aims to improve the aerodynamic performances of bionic axial fan by numerical technique. The detailed simulation has been carried out to investigate the aerodynamic performance of bionic axial fan with various design proposals for a detailed investigation and development of a prospective fan design prior to the manufacture and testing of costly prototypes. According to the biological fact that the serrations at the wing improve the acoustics as well the aerodynamic performances, various design modifications performed on the bionic axial fan blade. As the serrations at the trailing edge help to improve the aerodynamic performance, the fan blade design modified to investigate the change in mass flow rate. The flow field is simulated with the finite element Computational Fluid Dynamics (CFD) solver Altair-AcuSolve to analyse the influence of trailing edge serrations on the air flow rate of fan. The three-dimensional (3D) computational domain with SpalartAllmaras (SA) turbulence model is considered to predict the air flow rate. The present computation is carried out for the axial fan speed of 820 rpm. The flow rate is correlated with the test results to validate the CFD modeling approach. The result shows that the trailing edge serrations at the tip of the fan has predicted improvement in flow rate since it alter the length of separation bubble near the trailing edge which also helps to reduce the noise level.

Interplay between endothelial glycocalyx layer and red blood cell in microvascular blood flow: A numerical study.

The endothelial glycocalyx layer (EGL) plays a crucial role in regulating blood flow in microvessels. Experimental evidence suggests that there is greater blood flow resistance in vivo compared to in vitro, partially due to the presence of the EGL. However, the complex relationship between EGL deformation and blood cell behavior in shear flow and its quantification remains incompletely understood. To address this gap, we employ a particle-based numerical simulation technique to examine the interaction of the EGL with flowing red blood cells (RBCs) in microtubes. We examine changes in EGL deformation in response to variations in shear rate, EGL graft density, and contour height. Our results indicate that the alterations in EGL height are influenced by the mechanical properties of the EGL, flow conditions, and the RBC-EGL interaction. The flowing RBC compresses the EGL, causing a notable reduction in EGL height near the RBC flow. Additionally, we find that the presence of the EGL in the microtube results in increased RBC deformation and a wider gap between the RBC and tube wall due to spatial occupancy. The significant impact of the EGL on RBC flow is particularly evident in microtubes with diameters ranging from 7 to 10µm, a range consistent with notable differences in vascular flow resistance observed between in vivo and in vitro experiments. The simulation results shed insight on the dynamic interplay between RBC and the EGL in microvascular blood flow.

New alpha power transformed beta distribution with its properties and applications

The main purpose of this paper is to introduce a new alpha power transformed beta probability distribution that reveals interesting properties. The studuy provide a comprehensive explanation of the statistical characteristics of this innovative model. Various properties of the new distribution were derived, using the baseline beta distribution, statistical techniques, and probabilistic axioms. These include the probability density, cumulative distribution, survival function, hazard function, moments about the origin, moment generating function, and order statistics. For parameter estimation, the maximum likelihood estimation method using Newton Raphson numerical technique is employed. To evaluate the performance of our estimation method, the mean squared errors of the estimated parameters for different simulated sample sizes are used. In addition simulation studies of the new distribution are conducted to demonstrate the behavior of the probability model. To demonstrate the practical utility and flexibility of the alpha power transformed beta distribution, it is fitted to two real-life datasets and compared to commonly known probability distributions such as the Weibull, exponential Weibull, Beta, and Kumaraswamy beta distributions. It offers a superior fit to the data considered. The distribution reviales of the microbes reveald a wide range of shapes of probability density functions and flexible hazard rates. The distribution is a new contribution to the field of statistical and probability theory. The findings of the study can be used as a basis for future research in the area of statistical science and health.

Impact of thermal conductivity of a Williamson’s nanofluid flow due to a stretching sheet

This paper intends to build a mathematical model of a two-dimensional Williamson nanofluid flow due to the stretching of a sheet linearly. The flow geometry is influenced by the magnetic field that is applied externally to the system. The induced magnetic field is infinitesimal and hence neglected. However, the flow structure is incorporated with the Brownian motion and thermophoresis effects as it alter the physics of the flow. The equations that model the flow comprise the highly nonlinear coupled simultaneous system. Thus, a numerical technique namely finite difference accompanied with the Thomas algorithm is adopted to approach the flow system. The motion, temperature, and concentration of the Williamson nanofluid flow are studied for the different flow controlling parameters. The co-efficient of skin-friction, heat, and mass transfer rates is also computed. The streamlines, isotherms, and iso-concentration are plotted to picturise the flow phenomena in the complete domain. The study reveals that the temperature of the flow raises with the Brownian motion of the nanoparticles and the trend is opposite with the concentration. The strength of the streamlines, isotherms, and the concentration contour is identified to be high for the least magnitude of Weissenberg number. The Brownian motion raises the heat transfer rate and slows down the mass transfer rate.

An efficient product design tool for aftertreatment system

A numerical simulation technique based on the conservation of mass and energy in the gas phase has been developed to optimize the aftertreatment system with the lowest costs. Both oxygen storage capacity model and catalyst deterioration model have been integrated into the three-way catalyst performance model. Applications have been discussed, including XY-L 1.5L I3 gasoline turbocharged direct injection (GTDI) production hybrid vehicle, BY-L 1.5L I4 GTDI hybrid vehicle, XY-L (overseas version) 1.5L I4 GTDI hybrid vehicle, and G-L7 1.5L I4 GTDI hybrid vehicle. Vehicle tests in support of the proposed model have been described. The developed model covers the complete range of the cold start, high temperature and volume flow conditions. To optimize a three-way catalyst performance, this work simulated the effect of air fuel ratio, space velocity, temperature, biasing adjustment on the catalyst efficiency. The simulations presented the technique’s capability of well predicting emissions on fresh and full useful life aged aftertreatment systems, respectively, and carried out under transient conditions. The investigation indicated that excess fueling was used upon engine start to heat the catalyst up to its full operating temperature of greater than 350°C. The model results prompted a redesign of the I3 and I4 1.5L GTDI China 6b, Euro VId and Tier 3/SULEV30 exhaust systems over the world light vehicle test procedure (WLTP) and federal test procedure (FTP) cycles, respectively, for example, the model suggested that the latest design for the SULEV30 aftertreatment system on XY-L (overseas version) 1.5L I4 GTDI hybrid vehicle with the revised calibrations in the areas of cold-start and closed-loop fuel treated emissions of NMOG, NOx, and CO to the 70% of the SULEV30 standards with a $64 cost reduction relative to the baseline.

Stability Analysis of Hermite Collocation Method for Pulp Washing Models

Pulp washing is concerned with detaching cellulose fibres from black liquor with the use of a minimal amount of wash liquor. An efficient numerical technique of hermite collocation method is used for the solution of mathematical models related to pulp washing. The linear and non-linear models are solved using Quintic Hermite collocation method with Dirichlet’s and mixed Robin’s boundary conditions. Numerical solution of the models are derived using MATLAB ode15s. This study deals with the justification of accuracy of the method with stability analysis. The present method is more convenient, simple and elegant for solving the two point boundary value problems and the results found are very much stable from numerical point of view

Improved Parameter Estimation of Three-Phase Squirrel-Cage Induction Motors Using the Nelder-Mead Simplex Algorithm

This work presents a technique for precisely determining the characteristics of a squirrel-cage three-phase induction motor using the Nelder-Mead simplex algorithm. This approach is a frequently employed numerical optimization technique for determining the minimal value of a multi-dimensional objective function. An advantageous feature of the Nelder-Mead simplex algorithm is its independence from the need to calculate partial derivatives of the objective function. Nevertheless, similar to several optimization techniques, the Nelder-Mead simplex approach can also exhibit sensitivity to the initial conditions. Thus, the initial estimation of the parameters of the approximated equivalent circuit of the induction motor was used as the starting point for the Nelder-Mead optimization approach. The experiment's results are compared to those obtained using the polynomial regression approach to demonstrate the efficacy of the proposed method.

A novel approach for solving weakly singular fractional integro-differential equations

In this essay, we introduce a novel idea to tackle the challenges of fractional integro-differential equations (FIDEs) featuring weakly singular kernels (WSKs). New idea leverages B-splines for solving such equations, offering a robust numerical solution technique. We delve into the operational matrices integral to this method, providing comprehensive insights into their functionality. Furthermore, we establish the convergence of our approach and substantiate its effectiveness through various numerical examples.

A novel approach for fractional pharmacokinetics modeling and integrating stochastic simulation techniques using Sibuya distribution

Fractional compartment models are widely used to simulate pharmacokinetics with power-law behavior. In this work, we study an approach, previously mainly used in Epidemiology for the age model, employing the Sibuya distribution, a discrete-time, non-Markov probability distribution, to effectively emulate Mittag-Leffler functions. We demonstrate the validity of our method by applying it to various pharmacokinetic datasets and comparing the results with traditional methods like the Numerical Inverse Laplace Transform (NILT) algorithm. Additionally, we propose two stochastic simulation algorithms, where the Monte Carlo SSA allows us to capture the randomness of data and the Gillespie-like stochastic numerical simulation technique can optimize computational resources in fractional analysis.

Performance Properties and Finite Element Modelling of Forest-Based Bionanomaterials/Activated Carbon Composite Film for Sustainable Future

Thanks to its highly crystalline structure and excellent thermal, optical, electrical and mechanical properties, carbon and its derivatives are considered the preferred reinforcement material in composites used in many industrial applications, especially in the forest and forest products sector, including oil, gas and aviation. Since hydroxyethyl cellulose (HEC) is a biopolymer, it has poor mechanical and thermal properties. These properties need to be strengthened with various additives. This study aims to improve the thermal and mechanical properties of hydroxyethyl cellulose by preparing hydroxyethyl cellulose/activated carbon (HEC/AC) composite materials. With this study, composites were obtained for the first time and their mechanical properties were examined using a 3D numerical modeling technique. The thermal stability of the prepared composite materials was investigated via thermal gravimetric analysis (TGA). The samples were heated from 30 °C to 750 °C with a heating rate of 10 °C/min under a nitrogen atmosphere and their masses were measured subsequently. The mechanical properties of the composites were investigated via the tensile test. The viscoelastic properties of the composite films were determined with dynamic mechanical thermal analyses (DMTA) and their morphologies were examined with scanning electron microscopy (SEM) images. According to the results, the best F3 sample (films containing 3 wt.% activated carbon) had an elastic modulus of 168.3 MPa, a thermal conductivity value of 0.068 W/mK, the maximum mass loss was at 328.20 °C and the initial storage modulus at 30 °C was 206.13 MPa. It was determined that the hydroxyethyl cellulose composite films containing 3 wt.% activated carbon revealed the optimum results in terms of both thermal conductivity and viscoelastic response and showed that the obtained composite films could be used in industrial applications where thermal conductivity was required.

Computational Fluid Dynamics Study on Bottom-Hole Multiphase Flow Fields Formed by Polycrystalline Diamond Compact Drill Bits in Foam Drilling

High-temperature geothermal wells frequently employ foam drilling fluids and Polycrystalline Diamond Compact (PDC) drill bits. Understanding the bottom-hole flow field of PDC drill bits in foam drilling is essential for accurately analyzing their hydraulic structure design. Based on computational fluid dynamics (CFD) and multiphase flow theory, this paper establishes a numerical simulation technique for gas-liquid-solid multiphase flow in foam drilling with PDC drill bits, combined with a qualitative and quantitative hydraulic structure evaluation method. This method is applied to simulate the bottom-hole flow field of a six-blade PDC drill bit. The results show that the flow velocity of the air phase in foam drilling fluid is generally higher than that of the water phase. Some blades’ cutting teeth exhibit poor cleaning and cooling effects, with individual cutting teeth showing signs of erosion damage and cuttings cross-flow between channels. To address these issues, optimizing the nozzle spray angle and channel design is necessary to improve hydraulic energy distribution, enhance drilling efficiency, and extend drill bit life. This study provides new ideas and methods for developing geothermal drilling technology in the numerical simulation of a gas-liquid-solid three-phase flow field. Additionally, the combined qualitative and quantitative evaluation method offers new insights and approaches for research and practice in drilling engineering.

Global buckling behaviour and design of cold-formed steel octagonal hollow section columns under compression

This paper experimentally and numerically investigated the global buckling behaviour of cold-formed steel octagonal hollow section columns. A test programme was first conducted on 10 OctHS steel columns made of Q460 and Q690 high strength steels. Each steel grade comprised five specimens with distinct geometric dimensions. Material properties and initial global imperfection were measured and are reported herein. Axial load versus mid-height lateral deflection curves, axial load versus axial strain curves, and failure modes of OctHS specimens are presented and discussed. In conjunction with laboratory works, finite element models were subsequently developed to replicate the load-deformation responses and failure modes of OctHS columns against the experimental results. Following the validation of proposed numerical modelling technique, extensive parametric studies were performed to evaluate the effects of steel grade, cross-section slenderness, member slenderness, and initial global imperfection. Furthermore, results from 10 test specimens and 608 numerical models were used to comprehensively assess the applicability of current codes of practice on the design of OctHS long columns. Modifications and design recommendations were proposed based on the assessment results. Corresponding reliability analyses were also performed for each design method.