FORTRAN Research Articles

Numerical Simulation of Weak Shock Wave Reflection in Water Media

Abstract Shock wave reflection (SWR) is an interesting physical phenomenon that plays an important role in the ocean engineering. The existing research mainly focused on the gas SWR. Compared with the gas SWR, the water SWR has distinctive features. This article uses numerical methods to study the reflection mode and regularity inside a gas-filled and water-filled wedge. Specifically, we use the fifth-order weighted essentially nonoscillatory method in space and the third-order Runge–Kutta (RK) method in time to solve the compressible Euler equations. The ideal gas equation of state and water equation of state are also considered in the simulations. We developed a numerical solver using the Fortran language based on these equations and numerical methods. The reliability and accuracy of the developed program were validated by the existing theoretical solution and experiment data. Results show that the reflections are different in gas and water media. Regular reflection (RR) and Mach reflection are observed in a gas-filled wedge. However, only the RR is observed in a water-filled wedge for the weak water shock. Besides, it is found that the reflected shock (RS) wave in water is straighter than that in gas medium. Under the same pressure condition, the curvature of the RS wave is larger in a gas medium. The difference in SWR mode can be attributed to the difference in compressibility between the gas and water. It is found that there is a significant increase in temperature behind the incidence shock in the gas due to its high compressibility, which causes the change of local wave speed especially near the reflected wave. However, the temperature and wave speed are approximately constant during the SWR process in water. These distinctions can well explain the difference in SWR modes between gas and water.

Analysis of curing deformation for resin matrix composite T-shaped stiffened panel

In this work, a multi-field coupled finite element simulation method involving thermochemistry and mechanics was devised to predict the curing deformation (C-DE) of a T-shaped stiffened panel (T-SSPL), a typical aircraft structural component, during the autoclave forming process. A more comprehensive and detailed analysis of the factors affecting the C-DE of T-SSPL is also carried out. The methodology uses the Fortran language to write different user subroutines and establish corresponding mathematical models to simulate the different mechanical states of components, and ultimately simulate the entire molding process of the product in the autoclave. And investigates the effects of process parameters, including heating rate, cooling rate, curing pressure, and structural parameters, including the number of bars and height of stringer on the C-DE of T-SSPL, and obtains the following conclusions: the heating rate and curing pressure are positively correlated with the C-DE, and the cooling rate has little influence on the C-DE, and C-DE hardly changes with the change of cooling rate; C-DE increases with the ribs count; however, it decreases and then increases with the stringer height, and these conclusions provides a theoretical basis for the manufacturing of T-SSPL.

Determining the Suction Capacity of Compacted Clays with Fuzzy-Set Theory

Water suction capacity is an important parameter affecting the swelling properties and volumetric change of soil. Determination of the water suction capacity is made by the experiments which are needed long time in laboratory. However, this has random errors due to the heterogeneous and anisotropic structure of soil sample together with the error caused by the operator made the experiment. Such an estimation problem, included the errors, may be easily solved with the fuzzy-set theory. In this study, the suction capacity of compacted clayey soils is predicted with the fuzzy-set theory. For this reason, the engineering properties of clayey soil (plasticity index, dry density, initial water content and suction capacity) are partitioned into fuzzy subsets, and fuzzy rules are formed. Later, a computer program in the Fortran language is written to estimate the suction capacity of compacted clayey soil from these properties. It is shown that there is a good similarity between the results of the tests and proposed fuzzy logic model.

OPTIMIZATION OF INCIDENT FLOWS ON THE WALLS OF A HABITAT FOR A TYPICAL CLIMATE IN THE UPPER REGION IN REPUBLIC OF GUINEA

The aim of this work is to develop a mathematical model of the solar radiation incident on the walls of an inclined roof habitat for a typical climate of Guinea and to highlight the influence of the variation in the angle of inclination of the roof. Thereafter, we set up a program for the determination of all its parameters under the Fortran Language and plot our curves through the Origin software. This work allowed us to know, the amount of solar flux that each wall of a habitat receives, the importance of the orientation of the main facade of the habitat to the south, how often the roof is exposed to radiation solar and the influence of the variation of the angle of inclination of the roof compared to the horizontal. For example, for an angle of 15 ° the maximum value of the solar flux received is 547 W / m2 and for that of 75 ° is 995 W / m2. Thus, the optimal angle obtained from analyzes of the variation of solar radiation with respect to the inclination of the roof through Figure 7 is 60 °.

Transient study on heat transfer and flow performance of alkali metal heat pipe in space nuclear powered heat pipe radiator

The non-direct contact radiator has a simple structure and high reliability, making it more suitable for long-life nuclear powered spacecraft. This article is based on Fortran language and innovatively combines molecular dynamics models to establish a two-dimensional transient analysis program for thermo-hydraulic performance of rubidium heat pipes. The unsteady Navier Stokes control equation, heat conduction equation, and continuity equation is calculated by the finite difference method. This study adopt molecular dynamics theory for the first time to deal with condensation/ evaporation at the interface of alkali metal heat pipes under the background of space nuclear power. The delay method and multi grid method are used to ensure convergence and accelerate calculation speed. The transient thermo-hydraulic performance of different positions of heat pipes in non-direct contact radiators during start-up are analyzed. Current research can provide scientific reference for the upgradation of heat pipe radiators for nuclear powered spacecraft.

MHD Stagnation Point Flow of Micropolar Fluid over a Stretching/ Shrinking Sheet

In this article, the stagnation point flow of a micropolar fluid on a stretching/shrinking sheet has been discussed subject to the assumption of velocity slip. Similarity transformation is used to transform the modelled Partial Differential Equations (PDEs) into a system of Ordinary Differential Equations (ODEs). The numerical results have been found by the shooting technique along with Adams Moulton method of order four. The obtained numerical results are compared with the help of Fortran Language program and compared with the earlier published results and excellent validation of the present numerical results has been achieved for the local Nusselt number. Finally, the numerical results are presented with discussion of the effects of different physical parameters.

Impact and Technical Solutions of Hydrodynamic and Thermodynamic Processes in Liquefied Natural Gas Regasification Process

Transporting natural gas in liquid form increases opportunities for storage and export worldwide, thus making transportation more sustainable. However, liquefied natural gas (LNG) is in an unsteady state, leading to LNG conversion to the gas state occurring throughout the storage, loading, unloading, and transportation processes. To observe the transition of LNG to natural gas, mathematical models are developed to monitor technical parameters. This research analyses a floating storage and regasification unit for and adopts a mathematical model of the LNG regasification system, aiming for improved observation of hydrodynamic, dynamic, and thermo-physical properties. The complex mathematical model of the system was implemented using the Fortran programming language and MATLAB R28a. From the investigation of the total LNG regasification system, it could be concluded that increasing the outlet pressure of the system results in a decrease in the velocity of LNG. It was found that the total hydraulic energy losses of the total LNG regasification system were approximately 41.3 kW (with outlet pressure of 2 MPa), 12.75 kW (with outlet pressure of 5 MPa), and 4.24 kW (with outlet pressure of 7 MPa).

2D numerical modeling of crack propagation using SFEMD method of a LEHI material

Numerical methods today play a useful and important role in solving various problems related to fracture mechanics including modeling crack propagation, fretting fatigue and cohesion... Furthermore, these methods have been widely used to solve problems in linear and nonlinear fracture mechanics in cases of elastic, plastic fracture problems. The evaluation of stress intensity factor in 2D and 3D geometries, thus these techniques widely used for non-standard crack configurations. The objective of this work is study the effects of the crack length and the number of structural elements on the two crack parameters such as the stress intensity factor KI and KII and the contour integral (J). As well as presenting a numerical modeling of crack propagation, for a LEHIM (Linear Elastic Homogeneous Isotopic Material) with mechanical characteristics by the method SFEMD (Stretching Finite Element Method Developed), the model chosen with quadratic elements with 4 nodes (CPE4). However, this method is based on the effect of the number of contours and the number of elements around the crack tip on the variation of the stress intensity factors. In addition, the crack propagation criterion (MCSC) was used, a computer program was created in FORTRAN language to develop and evaluate the stress intensity factors and the contour integral (J). Several examples of crack lengths a = 0.7, 1.4, 2.1, 2.8 and 3.5 mm were used. Additionally, the number of items has been changed several times. The stress intensity factors of modes I and II and direction angles (α) are calculated to solve the problem using the ABAQUS finite element code. The results obtained by the SFEMD method and the results of the analytical method are very close.

A new strategy to produce calcium carbide-acetylene from integrated multi-level low carbon construction driven by biomass

A highly efficient and clean biomass energy-based calcium carbide-acetylene production system, including low-carbon energy supply, solid waste recycling and cascade utilization of waste heat, has been developed for the conventional energy-intensive and highly polluting fossil fuel-dependent calcium carbide industry. This system supplies the carbide-acetylene production plant with energy from the gasification of biomass and converts the plant's solid waste carbide slag into the calcium feedstock required by the plant. The waste heat from the plant's high-temperature exhaust gases is recycled and used via the multi-stage heat exchange, so that the energy cascade conversion and utilization is achieved. A simulation model of the plant is created in Aspen Plus, and a mathematical model for the biomass gasification process and cycle compensation of the calcium source through the Fortran language is written and embedded. When calculating the carbon consumption and CO2e emissions of the system, it was found that the carbon consumption and CO2e emissions of the conventional process were 5.43 t Coal·t−1C2H2 and 2.25 t CO2e·t−1C2H2, respectively. However, the carbon consumption of the new process was reduced by 65.19%, and carbon emissions by 27.24% in comparison. The energy analysis shows that the energy efficiency of the system is 36.21% for the conventional process and 44.82% for the new processes. The exergy analysis of the effective energy shows that the exergy efficiency of the new process is 73.20%, which is 52.98% better than that of the conventional process. Introduction of an index, the levelized income of acetylene product (LIOA), to characterize the product income of the system. When the price of acetylene is between 2.23 $/kg and 4.19 $/kg, the LIOA for the conventional and the new processes are 1.41 $/kg to 3.38 $/kg and − 1.28 $/kg to 0.68 $/kg, respectively. It is worth noting that the critical price (PCC2H2) for products generating net revenue from the new process is 3.17 $/kg. This study is of great importance for the development of a low-carbon biomass-coupled calcium carbide-acetylene process.

Numerical investigation of squeezing flow with mass and heat exchange between parallel plates: a study of velocity, temperature, and concentration distributions

The numerical study of squeezing flow with mass and heat exchange of an incompressible, 2-D viscous fluid between 2 plates held parallel to each other has been taken under consideration. The governing Partial Differential Equations (PDE) are reduced to the dimensionless Ordinary Differential Equations (ODEs) by an appropriate transformation. To solve ODEs, we used the shooting technique along with Adam’s Moulton method implemented in Fortran programming language. The results obtained are compared to the articles previously published. By changing the values of different physical parameters, we observed the nature of velocity, energy and the concentration distributions. At the end, the graphs and tables are shown which are obtained under this investigation.

Ultimate strength of light-rail hybrid cable-stayed bridge including concrete tension softening effect

This paper presents an analysis of the ultimate strength of a light-rail hybrid cable-stayed bridge (CSB) and discusses the influences of the concrete tension softening effect (CTSE), which is defined as the tensile strength of concrete being much less than its compressive strength. Both geometrical and material non-linearities are considered. A finite-element model of the bridge was established using Ansys software, with material non-linearity considered through the fibre beam element Beam189. An algorithm was written using Fortran language for the uniaxial concrete constitutive model to consider the CTSE (i.e. the concrete smeared crack model). The results showed that the CTSE significantly influenced the ultimate strength of the investigated bridge when the side-span concrete girder dominates the failure of the bridge as estimated by calculations. It is essential to consider the CTSE for the evaluation of the ultimate strength of a light-rail hybrid CSB.

Computational analysis of microgravity and viscous dissipation impact on periodical heat transfer of MHD fluid along porous radiative surface with thermal slip effects

The current thermal slip and Magnetohydrodynamic analysis plays prominent importance in heat insulation materials, polishing of artificial heart valves, heat exchangers, magnetic resonance imaging and nanoburning processes. The main objective of the existing article is to deliberate the impact of thermal slip, thermal radiation and viscous dissipation on magnetized cone embedded in a porous medium under reduced gravitational pressure. Convective heating characteristics are used to increase the rate of heating throughout the porous cone. For viscous flow along a heated and magnetized cone, the conclusions are drawn. The simulated nonlinear partial differential equations are transformed into a dimensionless state by means of suitable non-dimensional variables. The technique of finite differences is implemented to solve the given model with Gaussian elimination approach. The FORTRAN language is used to make uniform algorithm for asymptotic results according to the boundary conditions. The influence of controlling parameters, such as thermal radiation parameter Rd, Prandtl number Pr, porosity parameter Ω, viscous dissipation parameter Ec, δ thermal slip parameter, Rg reduced gravity parameter and mixed convection parameter λ is applied. Graphical representations were created to show the consequences of various parameters on velocity, temperature and magnetic field profiles along with fluctuating skin friction, fluctuating heat and oscillatory current density. It is found that velocity and temperature profile enhances as radiation parameter enhances. It is noted that the amplitude and oscillations in heat transfer and electromagnetic waves enhances as magnetic Prandtl factor increases.

Nonlinear inelastic behaviors of concrete-filled steel tubular beam-column structures

A new advanced method combining stability function and distributed plasticity model has been developed using Fortran programming language to predict the nonlinear inelastic behavior of concrete-filled steel tubalar (CFST) under static loading. The advantage of this method is the ability to accurately study the nonlinear behavior using only one or two beam-column elements per member instead of using solid and shell elements as traditional methods, thereby improving the model analysis time. The Generalized Displacement Control (GDC) algorithm, capable of analyzing beyond the limit point, will be used to solve the nonlinear equilibrium equations instead of the traditional Newton-Raphson algorithm. The element stiffness matrix is integrated through the Gauss-Lobatto numerical integration framework, while the nonlinear geometric effects P-Δ and P-δ are considered using stability functions and a corresponding geometric matrix. The reliability and accuracy of the proposed method are verified by comparing the analysis results with experimental data. The obtained results have demonstrated that using beam-column elements for simulation, the proposed method still provides accurate results while significantly reducing computational resources. Therefore, this new method holds promise as a useful tool for practical design and analysis of statically loaded CFST structures.

Thermal radiation and soret/dufour effects on amplitude and oscillating frequency of darcian mixed convective heat and mass rate of nanofluid along porous plate

The influence of thermal radiations and Soret/Dufour significantly increases the mass and heat transport in material science, geothermal process, chemical rectors and heat exchangers due to temperature and concentration variation of nanoparticles. Main objective is to enhance the amplitude, oscillation and frequency of heat transfer using the Soret and Dufour characteristics in Darcian radiating flow of thermophoretic nanoparticles along vertical porous surface. The dimensionless analysis is performed to develop the convenient form of governing thermodynamic Darcian nanofluid formulation. To develop the programming algorithm in FORTRAN language, the primitive variable formulation is used for both time-dependent and steady models. The numerical and graphical outcomes of primitive type equations under boundary conditions are explored by using implicit finite difference approach with Gaussian elimination scheme. Various pertinent parameters are used to elaborate the steady fluid velocity, surface temperature and steady concentrated nanoparticle volume fraction. Valuable novelty of current research is to use steady results for fluctuating shear stress, fluctuation heating rate and fluctuating mass rate. It is found that the influence of Soret and Dufour parameter enhances the fluid velocity and temperature distribution with maximum variations. It is noticed that the temperature distribution enhances as thermal radiation parameter increases. The oscillation and transient stability of heating rate enhances with prominent variations as thermal radiation and Soret/Dufour parameter increases. It is depicted that amplitude in shear stress and mass rate enhances as Soret and Dufour parameter enhances.

Seismic vulnerability analysis of a high‐rise steel frame structure equipped with novel displacement‐amplified viscoelastic dampers

SummaryThe energy dissipation capacity of conventional viscoelastic dampers (VEDs) cannot be fully exerted due to the relatively small inter‐story displacement of building structures. Thus, a novel VED with a displacement amplification mechanism based on the lever principle is developed in this study to achieve small displacement but high energy dissipation ability. First, the structural layout of an amplified viscoelastic damper (AVED) system is briefly introduced, and then the displacement amplification effect is described in detail. According to the working principle of the AVED and the relationship of force and geometric displacement in an actual frame structure, the restoring force theoretical formula of the corresponding amplified damper is derived. Based on the restoring force of the AVED and in combination with the secondary development function of the ABAQUS unit, a VUEL subroutine suitable for the explicit algorithm is programmed with the FORTRAN language. Then, the correctness of the subroutine is verified through a comparative analysis of the ABAQUS simulation and theoretically calculated results. Consequently, the vulnerability analysis of a high‐rise steel frame structure is conducted by using the incremental dynamic analysis (IDA) method, and the influence of the AVED on the seismic performance of the steel frame structure is quantitatively analyzed from the perspective of probability statistics. The analysis results show that compared with the VED structure, the failure probability of the AVED‐2 and AVED‐3 structures reaching the ultimate failure state at all levels is reduced by approximately 43% and 57%, respectively, and the collapse margin ratio (CMR) of structures under large earthquakes is increased by approximately 35% and 68%, respectively. This indicates that the AVED structures with displacement‐amplified dampers have a better effect on the seismic stability of tall steel frame structures under random seismic excitations. This study aims to provide comprehensive information for the seismic‐resistant design of tall buildings in earthquake‐prone regions.

Interaction between microcapsules and crack using XFEM and data-driven fracture toughness predictive model

The interaction mechanism between microstructures of materials, including microcrack, inclusion and interface defect, is crucial for studying the microscopic damage of materials. The interaction between microcapsules and cracks in self-healing material is examined using a combination of the extended finite element method (XFEM) and the interaction integral method, which is implemented by a program written in Fortran language. The non-dimensional stress intensity factors (SIFs) of a crack with a single microcapsule, a pair of microcapsules and a cluster of microcapsules are investigated. Moreover, the data-driven fracture toughness predictive model using a genetic programming-based symbolic regression (SR) technique is proposed by training the data from the XFEM program. Results reveal that the non-dimensional SIFs are related to the mechanical property, geometry and interface defect of microcapsule. The influence of microcapsule on the SIF is limited within a distance of five times the microcapsule radius. The predictive model quantifies the contribution of microscopic structures on the macroscopic fracture parameter, highlighting the potential of machine learning in guiding the quantitative design and discovery of high-performance smart materials.

Metric Temporal Equilibrium Logic over Timed Traces

AbstractIn temporal extensions of answer set programming (ASP) based on linear time, the behavior of dynamic systems is captured by sequences of states. While this representation reflects their relative order, it abstracts away the specific times associated with each state. However, timing constraints are important in many applications like, for instance, when planning and scheduling go hand in hand. We address this by developing a metric extension of linear-time temporal equilibrium logic, in which temporal operators are constrained by intervals over natural numbers. The resulting Metric Equilibrium Logic (MEL) provides the foundation of an ASP-based approach for specifying qualitative and quantitative dynamic constraints. To this end, we define a translation of metric formulas into monadic first-order formulas and give a correspondence between their models in MEL and Monadic Quantified Equilibrium Logic, respectively. Interestingly, our translation provides a blue print for implementation in terms of ASP modulo difference constraints.

Prediction of heavy metal lead contamination accident in Three Gorges Reservoir Area.

Water contamination incidents have become a significant ecological and environmental threat, particularly concerning the security of drinking water source areas (DWSAs). This research aimed to address this issue by integrating Geographic Information System (GIS) into bidimensional hydrodynamic water quality mathematical model developed using C + + and FORTRAN programming languages. The focus was on the Heshangshan drinking water source area (HDWSA), and the TECPLOT360 software was utilized for visualizing pollutant migration and dispersion processes. The study specifically considered a hypothetical lead (Pb) contamination accident, which is situated in the Three Gorges Reservoir Area (TGRA). The spatio-temporal variations in Pb concentration throughout the entire DWSA were analyzed, along with a comparison of Pb concentration changes during different water seasons. The results indicate that, during the accident, the Pb concentration at the water intake in the drought season, decline season, flood season, and impounding season reached the standard limits at 76, 58, 44, and 48 min, respectively. Moreover, the entire DWSA achieved standard levels of Pb concentration at 124, 89, 71, and 74 min during the respective seasons. The study also observed an expansion and subsequent contraction of the Pb contamination area in the DWSA, with the transfer rate of Pb concentration ranked as flood season > impounding season > decline season > drought season.

PyIRI: Whole‐Globe Approach to the International Reference Ionosphere Modeling Implemented in Python

AbstractThe International Reference Ionosphere (IRI) model is widely used in the ionospheric community and considered the gold standard for empirical ionospheric models. The development of this model was initiated in the late 1960s using the FORTRAN language; for its programming approach, the model outputs were calculated separately for each given geographic location and time stamp. The Consultative Committee on International Radio (CCIR) and International Union of Radio Science (URSI) coefficients provide the skeleton of the IRI model, as they define the global distribution of the maximum useable ionospheric frequency foF2 and the propagation factor M(3,000)F2. At the U.S. Naval Research Laboratory, a novel Python tool was developed that enables global runs of the IRI model with significantly lower computational overhead. This was made possible through the Python rebuild of the core IRI component (which calculates ionospheric critical frequency using the CCIR or URSI coefficients), taking advantage of NumPy matrix multiplication instead of using cyclic addition. This paper explains in detail this new approach and introduces all components of the PyIRI package.

Numerical simulation of the dynamic problem of a generalized system with distributed parameters

Introduction. Questions of mathematical modeling of the dynamic problem in the form of a generalized system with one degree of freedom are discussed. Such systems include high-rise tower-type structures. Seismic stability of unique tower-type objects represents a relevant research problem.Aim. To determine the stress-strain state of a studied object under the action of external factors in the form of an earthquake accelerogram.Materials and methods. The methods of structural mechanics, dynamics of structures, and numerical simulation were used. The Lagrange equation was used as a basis for obtaining the motion equation of a generalized system with distributed parameters. The research methodology also included mathematical modeling of the considered systems, their numerical analysis, comparison of the obtained results with literature data.Results. A mathematical model was developed to investigate the stress-strain state of engineering structures under various external, including seismic, effects. The differential equation of the generalized system is solved directly using the method of successive approximations and the Duhamel integral at each time step. The developed algorithm was used to compile a software application in the FORTRAN language followed by obtaining the kinematic and static data of the investigated object. Using the example of a tower-type structure, free vibrations from the action of an instantaneous impulse were investigated. The results from a given earthquake accelerogram are presented.Conclusions. The results obtained on the free vibrations of the object under study agree well with those obtained by numerical simulation. The results obtained by numerical differentiation are effectively identical with those obtained by numerical integration, under the action of various effects. The validity of the results is confirmed by comparing the results obtained by the two methods. The developed software applications can be used for monitoring the state of unique tower-type objects.