FORTRAN Program Research Articles

Thermodynamic analysis of absorption refrigeration cycles by parabolic trough collectors

The purpose of this study is to numerically investigate the performance of a solar physical surface absorption cooling system, in which activated carbon/methanol is used as a working pair, which is placed inside a parabolic-shaped solar collector. The governing mathematical model of this issue is based on the equations of conservation of mass, conservation of energy, and thermodynamics of the physical surface absorption process. The equations are discretized using the fully implicit finite difference method, and the Fortran computer program was simulated. A comparison with the results of previous laboratory and numerical studies validated this model. At each point in the bed, the temperature, pressure, and mass of the refrigerant absorbed during the physical surface absorption/discharge process were calculated. In addition, the effects of the bed diameter, amount of solar radiation, source temperature, temperature, and pressure of the evaporator and condenser were investigated on the solar performance coefficient and the specific cooling power of the system. According to the built laboratory model and the working conditions of the system, the solar performance coefficient and the specific cooling capacity of the system are equal to 0.12 and 45.6 W/kg, respectively.

Robust Transformations for Multiple Regression via Additivity and Variance Stabilization

ABSTRACT Outliers can have a major effect on the estimated transformation of the response in linear regression models, as they can on the estimates of the coefficients of the fitted model. The effect is more extreme in the Generalized Additive Models (GAMs) that are the subject of this article, as the forms of terms in the model can also be affected. We develop, describe and illustrate robust methods for the nonparametric transformation of the response and estimation of the terms in the model. Numerical integration is used to calculate the estimated variance stabilizing transformation. Robust regression provides outlier free input to the polynomial smoothers used in the calculation of the response transformation and in the backfitting algorithm for estimation of the functions of the GAM. Our starting point was the AVAS (Additivity and VAriance Stabilization) algorithm of Tibshirani. Even if robustness is not required, we have made four further general optional improvements to AVAS which greatly improve the performance of Tibshirani’s original Fortran program. We provide a publicly available and fully documented interactive program for our procedure which is a robust form of Tibshirani’s AVAS that allows many forms of robust regression. We illustrate the efficacy of our procedure through data analyses. A refinement of the backfitting algorithm has interesting implications for robust model selection. Supplementary materials for this article are available online.

Multibody Dynamics Model of the Cycloidal Gearbox, Implemented in Fortran for Analysis of Dynamic Parameters Influenced by the Backlash as a Design Tolerance

Abstract In this study, dynamical parameters of the cycloidal gearbox working at the constant angular velocity of the input shaft were investigated in the multibody dynamics 2D model implemented in the Fortran programming language. Time courses of input and output torques and forces acting on the internal and external sleeves have been shown as a function of the contact modelling parameters and backlash. The analysis results in the model implemented in Fortran were compared with the results in the 3D model designed using MSC Adams software. The values of contact forces are similar in both models. However, in the time courses obtained in MSC Adams there are numerical singularities in the form of peaks reaching 500 N for the forces at external sleeves and 400 N for the forces acting at internal sleeves, whereas in the Fortran model, there are fewer singularities and the maximum values of contact forces at internal and external sleeves do not exceed 200 N. The contact damping and discretisation level (the number of discrete contact points on the cycloidal wheels) significantly affect the accuracy of the results. The accuracy of computations improves when contact damping and discretisation are high. The disadvantage of the high discretization is the extended analysis time. High backlash values lead to a rise in contact forces and a decrease in the force acting time. The model implemented in Fortran gives a fast solution and performs well in the gearbox optimisation process. A reduction of cycloidal wheel discretisation to 600 points, which still allows satisfactory analysis, could reduce the solution time to 4 min, corresponding to an analysis time of 0.6 s with an angular velocity of the input shaft of 52.34 rad/s (500 RPM).

Estimation of yield strength due to neutron irradiation in a pressure vessel of WWER-1000 reactor based on the correction of the secondary displacement model

Due to neutron radiation, atomic displacement has a significant effect on material in nuclear reactors. A range of secondary displacement models, including the Kinchin-Pease (K–P), Lindhard, Norgett-Robinson-Torrens (NRT), and athermal recombination-corrected displacement per atom (arc-dpa) have been suggested to calculate the number of displacement per atom (dpa). As neutron elastic interaction is the main cause of displacement damage, the focus of the current study is to calculate the atomic displacement caused by the neutron elastic interaction in order to estimate the exact amount of yield strength in a WWER-1000 reactor pressure vessel. To achieve this purpose, the reactor core is simulated by MCNPX code. In addition, a program is developed to calculate the elastic radiation damage induced by the incident neutron flux (RADIX) based on different models using Fortran programming language. Also, due to non-elastic interaction, the displacement damage is calculated by the HEATR module of the NJOY code. ASME E-693-01 standard, SPECTER, NJOY codes, and other pervious findings have been used to validate RADIX results. The results showed that the RADIX(arc-dpa)/HEATR outputs have appropriate accuracy. The relative error of the calculated dpa resulting from RADIX(arc-dpa)/HEATR is about 8% and 46% less than NJOY code, respectively in the ¼ and ¾ vessel wall.

Parallel Algorithm for Solving Overdetermined Systems of Linear Equations, Taking into Account Round-Off Errors

The paper proposes a parallel algorithm for solving large overdetermined systems of linear algebraic equations with a dense matrix. This algorithm is based on the use of a modification of the conjugate gradient method, which is able to take into account rounding errors accumulated during calculations when making a decision to terminate the iterative process. The parallel algorithm is constructed in such a way that it takes into account the capabilities of the message passing interface (MPI) parallel programming technology, which is used for the software implementation of the proposed algorithm. The programming examples are shown using the Python programming language and the mpi4py package, but all programs are built in such a way that they can be easily rewritten using the C/C++/Fortran programming languages. The advantage of using the modern MPI-4.0 standard is demonstrated.

A Three-Dimensional Elastoplastic Constitutive Model for Geomaterials

The Mohr-Coulomb (M-C) failure criterion has been a popular choice for geotechnical analysis because of its simplicity and ease of use. The fact that the M-C criterion disregards the intermediate principal stress’s impact is a significant drawback. As a result, the M-C criterion is only applied to materials under biaxial stress. This paper presents a three-dimensional version of the M-C criterion. The proposed criterion, called the Generalized Mohr-Coulomb (GMC) criterion, considers the intermediate principal stress’s effect, in addition to inheriting the original M-C criterion’s benefits. We obtained the conditions that the strength parameters must satisfy when the GMC criterion fulfills the π plane’s convexity. The GMC criterion can better describe geotechnical materials’ strengths under general stress conditions. Based on an implicit algorithm, the user material subroutine (UMAT) of the three-dimensional GMC model was developed in ABAQUS using the Fortran programming language. The established elastoplastic model’s validity and the program’s accuracy were examined using numerical simulation. Finally, a numerical simulation of a three-dimensional tunnel excavation under various working conditions was performed. The calculation results from the GMC model are precise and have some engineering-related practical significance.

Analysis of fluctuating heat and current density of mixed convection flow with viscosity and thermal conductivity effects along horizontal nonconducting cylinder

Due to excessive heating, various physical mechanisms are less interested in engineering and modern technologies. To reduce excessive heating, the aligned magnetic field acts like a coating material to insulate the heat which is a very important mechanism in modern technologies. To solve this problem, the primary goal of the current analysis is to utilize magnetization normal to the surface. Numerical simulations have been made of the magnetohydrodynamic convective heat-transfer phenomena of electrically conductive fluid flow down the horizontally non-magnetized heated cylinder. The associated non-linear PDEs that control fluid motion can be conveniently represented by using the finite-difference algorithm and primitive element substitution. The numerical outcomes are deduced in graphs and tabular form with the help of FORTRAN program. The distinct parameters in the flow model are affected by physical features such skin friction, heat transfer, and current density for velocity profile, magnetic field profile, and temperature profile together with their slopes. The current magnetohydrodynamics and thermal problem is very important in the fields of MRI resonance sequences, artificial heart wolves, internal heart cavities, and nanoburning technologies. Additionally, the increase in Prandtl Pr leads to a reduction in skin friction and heat transmission, which is physically consistent, due to frictional forces between viscous layers with lesser magnitude.

Integration of the athena vortex lattice aerodynamic analysis software into the multivariate design synthesis of a blended wing body aircraft

This paper describes the process of integrating the Athena Vortex Lattice aerodynamics solver into a conceptual design environment for the multivariate design synthesis and optimisation of a Blended Wing Body (BWB) Aircraft. The work is derived from a PhD study, by one of the authors, which developed a design methodology for the conceptual design synthesis, analysis and optimisation of a BWB aircraft. This research was driven by the desire to utilise proven aerodynamic solvers, written in legacy codes, in modern computational design environments in order to improve the accuracy and fidelity in the design of novel aircraft configurations. The Athena Vortex Lattice code is a legacy code written in the FORTRAN programming language and developed at the Massachusetts Institute of Technology by Mark Drela while the multivariate conceptual design synthesis and optimisation was implemented in JAVA object oriented programming tool. The result from this study is the successful integration of the AVL software into the JAVA programming environment for the multivariate design synthesis optimisation of the BWB without loss of accuracy. The successful integration of these codes permit a more accurate design synthesis, analysis and optimisation of the novel aircraft configuration in the absence of a tailor-made and realistic empirical aerodynamic analysis model for the BWB Aircraft. Additionally, this research enables the automation of the design process and the accomplishment of the multivariate optimisation.

SBETHE: Stopping powers of materials for swift charged particles from the corrected Bethe formula

The Fortran program sbethe calculates the stopping power of materials for swift charged particles with small charges (electrons, muons, protons, their antiparticles, and alphas). The electronic stopping power is computed from the corrected Bethe formula, with the shell correction derived from numerical calculations with the plane-wave Born approximation (PWBA) for atoms, which were based on an independent-electron model with the Dirac–Hartree–Fock–Slater self-consistent potential for the ground-state configuration of the target atom. The density effect correction is evaluated from an empirical optical oscillator strength (OOS) model based on atomic subshell contributions obtained from PWBA calculations. For projectiles heavier than the electron, the Barkas correction is evaluated from the OOS model, and the Lindhard–Sørensen correction is estimated from an accurate parameterization of its numerical values. The calculated electronic stopping power is completely determined by a single empirical parameter, the mean excitation energy or I value of the material. The radiative stopping power for electrons, and positrons, is evaluated by means of Seltzer and Berger's cross section tables for bremsstrahlung emission. The program yields reliable stopping powers and particle ranges for arbitrary materials and projectiles with kinetic energy larger than a certain cutoff value Ecut, which is specific of each projectile kind. The program is accompanied by an extensive database that contains tables of relevant energy-dependent atomic quantities for all the elements from hydrogen to einsteinium. sbethe may be used to generate basic information for dosimetry calculations and Monte Carlo simulations of radiation transport, and as a pedagogical tool. Program summaryProgram title:sbetheCPC Library link to program files:https://doi.org/10.17632/7zw25f428t.1Licensing provisions: CC by NC 3.0Programming language: Fortran 90/95Nature of problem: The program calculates the stopping power of arbitrary materials for swift charged projectiles with small charges. The material is characterized by its chemical composition, mass density, and the empirical I value. The considered projectiles are electrons, positrons, negative muons, antimuons, protons, antiprotons, and alphas, which are described as point particles characterized by their mass and charge. If the actual I value of the material is known, the results from the program are expected to be reliable for projectiles with kinetic energy higher than a value Ecut, of the order of 1 keV for electrons and positrons, 150 keV for muons and antimuons, 0.75 MeV for protons and antiprotons, and 5 MeV for alpha particles.Solution method: The electronic stopping power is calculated by means of a corrected Bethe formula [1], which combines the conventional Bethe logarithm with the following corrections,1) the shell correction obtained from calculations based on the plane-wave Born approximation with the self-consistent Dirac–Hartree–Fock–Slater (DHFS) potential of neutral atoms in their ground-state configuration [2],2) the density effect correction, which accounts for the reduction of the stopping power caused by the dielectric polarization of the medium,3) a parameterization of the Lindhard–Sørensen correction, which generalizes the Bloch correction for relativistic projectiles, and4) the Barkas correction, which accounts for differences between the stopping powers of particles and their antiparticles.The density-effect and the Barkas corrections are calculated from a model of the optical oscillator strength (OOS) of the material, which combines the contributions of inner atomic subshells calculated with the DHFS potential, with a classical oscillator model for the contribution of valence electrons,A simple extrapolation formula is used to extend the calculated electronic stopping power to energies less than Ecut to allow the calculation of particle ranges.For electrons and positrons, the radiative stopping power is calculated from numerical tables prepared by Seltzer and Berger [3].Additional comments including restrictions and unusual features: The calculated stopping power is determined by a single parameter, the mean excitation energy or I value. The program assigns to each material a default I value, derived from the recommendations in the ICRU Report 37, which can be changed by the user. The distribution package includes text files with tables of atomic energy-dependent quantities (subshell optical oscillator strengths, shell corrections, scaled cross sections for bremsstrahlung emission) that are used in the calculations.

Nonlinear dynamic thermal-mechanical behaviors of framed structures under temperature variations

An abnormal change in dynamic characteristics is considered an indicator of structural damage and can help the optimal design of structures suffering from dynamic loads, but these characteristics are also affected by ambient temperature. Therefore, a novel advanced computational method based on the fiber-based approach is proposed for the first time to predict the nonlinear dynamic behaviors of frames under environmental temperature changes with linear and nonlinear profiles by using Fortran programming language. The cross-section will be divided into a matrix of fibers, and by assigning the different temperatures to each fiber, all linear and nonlinear temperature gradients in both vertical and horizontal directions will be operated. The material nonlinearity is traced by the distributed plasticity model using the same mesh as the fiber-based approach whereas the effects of geometric nonlinearity due to member curvature and member chord rotation are considered by using the stability functions and a geometric matrix, respectively. A sequential nonlinear thermal incremental-iterative solution scheme based on the Newton-Raphson algorithm and Newmark-β method is also developed to address the nonlinear dynamic problems due to temperature variations. The accuracy and computational performance of the proposed method are validated by comparing the obtained results with those from experiments and the Abaqus. Results obtained show that the proposed method is exact for the nonlinear inelastic dynamic thermo-mechanical analysis of framed structures. It would offer a tool for thermal-structural design practice instead of using time and cost-consuming commercial software.

To solve one problem of magnetostatics for a pipe with a defect on the inner surface

An algorithm has been developed and implemented for the numerical solution of a direct linear magnetostatics problem by calculating the resulting field of a pipe with a surface defect on its inner wall under the assumption that the perpendicular section of the pipe and the vector of the intensity of the external magnetizing field remain unchanged along the axis of the length of the pipe - this made it possible to take as a basis the two-dimensional integro-differential equation of magnetostatics. The algorithm is implemented in the FORTRAN programming language. The results are tested for reliability using precisely solved problems. Illustrative curves are constructed. The possibilities of applying the obtained calculation methodology for a class of problems that differ in some way in formulation are indicated.

OpenMP Fortran programs for solving the time-dependent dipolar Gross-Pitaevskii equation

OpenMP Fortran programs for solving the time-dependent dipolar Gross-Pitaevskii equation

PESPIP: Software to fit complex molecular and many-body potential energy surfaces with permutationally invariant polynomials.

We wish to describe a potential energy surface by using a basis of permutationally invariant polynomials whose coefficients will be determined by numerical regression so as to smoothly fit a dataset of electronic energies as well as, perhaps, gradients. The polynomials will be powers of transformed internuclear distances, usually either Morse variables, exp(-ri,j/λ), where λ is a constant range hyperparameter, or reciprocals of the distances, 1/ri,j. The question we address is how to create the most efficient basis, including (a) which polynomials to keep or discard, (b) how many polynomials will be needed, (c) how to make sure the polynomials correctly reproduce the zero interaction at a large distance, (d) how to ensure special symmetries, and (e) how to calculate gradients efficiently. This article discusses how these questions can be answered by using a set of programs to choose and manipulate the polynomials as well as to write efficient Fortran programs for the calculation of energies and gradients. A user-friendly interface for access to monomial symmetrization approach results is also described. The software for these programs is now publicly available.

Effects of Double-Diffusive Convection on Calculation Time and Accuracy Results of a Salt Gradient Solar Pond: Numerical Investigation and Experimental Validation

The main aim of this study is to investigate numerically and experimentally the effects of double-diffusive convection on calculation time and accuracy results of a Salt Gradient Solar Pond (SGSP). To this end, two-numerical models are developed based on the Fortran programming language. The first one is based on energy balance neglecting the development of double-diffusive convection, while the second is two-dimensional and is based on Navier-Stokes, heat, and mass transfer equations considering the development of double-diffusive convection. The heat losses via the upper part, bottom, and vertical walls, as well as the internal heating of saltwater, are considered. In order to validate and compare both numerical models, a laboratory-scale SGSP is designed, built, and tested indoors for 82 h. Results indicate that the two numerical models developed can predict the SGSP thermal behavior with good accuracy. Furthermore, the average relative error between experimental and numerical results is around 9.39% for Upper Convective Zone (UCZ) and 2.92% for Lower Convective Zone (LCZ) based on the first model. This error reduces to about 5.98% for UCZ and 3.74% for LCZ by using the second model. Consequently, the neglect of double-diffusive convection in the SGSP modeling tends to overestimate the thermal energy stored in the storage zone by about 4.3%. Based on the calculation time analysis, results show that the second model returns a calculation time hundreds of times larger than the first one and, accordingly, an increase in computational cost.

Modeling of partial reduction of hematite with carbon-monoxide in tunnel furnace

DRI production in tunnel furnaces sometimes encounters an incomplete degree of reduction. A model is required to tackle heterogeneous reaction rates, crucible heat transfer, and oxide morphology. Herein, a three-phase model is proposed based on heat and mass conservation and reaction kinetics, to describe the reduction of hematite to magnetite in the crucibles. The model was implemented via a Fortran program using finite volume discretization, and the results were validated against available experimental data. The model moderated the uncertainties in the reaction rate with a reformulation considering the solid morphology. The results also revealed that the speed and diameter of the crucible have dominant effects on the overall progress of the reduction by changing the heat transfer rate within the crucible. In contrast, the crucible thickness has a minor effect on the reaction and could be regarded as an economical parameter.

Chemical Engineering Numerical Analysis with R: Peng-Robinson Equation of State

Likely, many text on MATLAB, C++, FORTRAN and Python programming languages exist in chemical engineering libraries, discussing their applications for chemical engineering numerical analysis. R programming language, which has been in existence for more than 40 years is just evolving as a language of choice for data analytics in science and engineering. Here, it is shown that, numerical analysis with equations of state (EOS), especially the Peng-Robinson EOS, typically taught in undergraduate chemical engineering introductory courses can be solved with a developed or existing R source codes. Out of several other mathematical methods, including Fixed-point iteration, Regula-Falsi, Bisection and their modified/hybrid methods recently developed, only Secant and Newton’s method algorithm were followed to solve a sample problem by writing an R program. Although sufficient, in-depth study of the R language using some recommended manuals in this work can be a guide in implementing a solution with R for other numerical methods, for the same problem, as well as several other existing analytical and statistical chemical engineering problems out there.

Revisited relativistic Dirac-Hartree-Fock X-ray scattering factors. I. Neutral atoms with Z = 2-118.

In this first of a series of publications, the X-ray scattering factors for neutral atoms are revisited. Using the recently developed DBSR_HF program [Zatsarinny & Froese Fischer (2016). Comput. Phys. Comm. 202, 287-303] the fully relativistic Dirac-Hartree-Fock ground-state wavefunctions for all atoms with Z = 2-118 (He-Og) have been calculated using the extended average level scheme and including both the Breit interaction correction to the electronic motion due to magnetic and retardation effects, and the Fermi distribution function for the description of the nuclear charge density. The comparison of our wavefunctions with those obtained in several previous studies in terms of the total and orbital (spinor) electronic energies, and a number of local and integrated total and orbital properties, confirmed the quality of the generated wavefunctions. The employed dense radial grid combined with the DBSR_HF's B-spline representation of the relativistic one-electron orbitals allowed for a precise integration of the X-ray scattering factors using a newly developed Fortran program SF. Following the established procedure [Maslen et al. (2006). International Tables for Crystallography, Vol. C, Section 6.1.1, pp. 554-589], the resulting X-ray scattering factors have been interpolated in the 0 ≤ sin θ/λ ≤ 2 Å-1 and 2 ≤ sin θ/λ ≤ 6 Å-1 ranges using the recommended analytical functions with both the four- (which is a current convention) and five-term expansions. An exhaustive comparison of the newly generated X-ray scattering factors with the International Union of Crystallography recommended values and those from a number of previous studies showed an overall good agreement and allowed identification of a number of typos and inconsistencies in the recommended quantities. A detailed analysis of the results suggests that the newly derived values may represent an excellent compromise among all the previous studies. The determined conventional interpolating functions for the two sin θ/λ intervals show, on average, the same accuracy as the recommended parametrizations. However, an extension of each expansion by only a single term provides a significant improvement in the accuracy of the interpolated values for an overwhelming majority of the atoms. As such, an updated set of the fully relativistic X-ray scattering factors and the interpolating functions for neutral atoms with Z = 2-118 can be easily incorporated into the existing X-ray diffraction software with only minor modifications. The outcomes of the undertaken research should be of interest to members of the crystallographic community who push the boundaries of the accuracy and precision of X-ray diffraction studies.

Investigation of inlet air pressure and evaporative cooling of four different cogeneration cycles

Abstract The objective of this study was to search the effects of the inlet air compressor pressure and evaporative cooling of four different cogeneration plants that are absorption cooling (ab), basic (bsc), air heating (airh), and air fuel heating (airfh) cogeneration systems by using the first law and the second law of thermodynamics, and the exergy analysis methods. For analysis, a program is written by the author in the FORTRAN programming language. Decreasing the atmospheric pressure or increasing the installation altitude of the plants increases the Z factor (ratio of lost exergy to useful exergy) of the four cycles about 10–13%. Also, decreasing inlet air pressure decreases the specific work about 25–28%, and the fuel energy saving ratio of the four cycles decreases about 29–30%. The method of water spray cooling of the compressor inlet air especially in the summer months, the humidity increases and the evaporative cooling can be obtained. By using this method, the ratio of lost exergy to useful exergy can be decreased for the four cycles about 0.5–2%. Also, the specific work of the four cycles can be increased about 1.2–6%.

Mathematical Modelling of the Removal of Basic Blue Dye from Effluent by a Mineral Membrane

Water contamination is a major challenge due to the discharging of wastes into the natural resources. In this study, a novel branched pore adsorption model was developed by utilizing external mass transfer coefficients, Kf , effective diffusivity, and lumped microspore diffusion rate parameters. This describes sorption kinetics from long-term adsorption that occurs between an adsorbent and an adsorbate. An investigation of the effects of dye concentration on Basic Blue 9 removal was conducted. Then by considering of initial and boundary conditions the government equations were solved. Using this model, the Basic Blue 9 (or methylene blue is an industrial inhibitor) was removed from a bentonite sample polluted by Basic Blue 9. The maximum adsorption capacity was achieved by using of Freundlich analysis. Based on the experimental data, theoretical concentration - time adjusted models were developed using a FORTRAN computer program to fit the experimental data more precisely and confirm the precision and accuracy of this research.

A Scheme of Full Kinetic Particle-in-cell Algorithms for GPU Acceleration Using CUDA Fortran Programming

The emerging computable devices, graphical processing units (GPUs), are gradually applied in the simulations of space physics. In this paper, we introduce an approach that implements full kinetic particle-in-cell simulations on GPU architecture devices using the CUDA Fortran language programming for the first time. Using the latest high-performance computing NVIDIA GPUs, this program, which follows the second-order leap-frog iteration method, can speed up the computing process by a factor of 150–285 on a single device compared with the time cost of running with a single core of an Intel Xeon Gold processor. Our scheme improves fast accessibility to the simulation results and provides valuable assistance in studying the physical process.