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1

Numerical investigation of noise generated by an axial fan installed in a pipeline

Romik Dawid

Vibrations in Physical Systems

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2022

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Vol. 33, nr 1

art. no. 2022104

EN

The article presents the results of numerical calculations of noise generated by an axial fan installed in a ventilation duct with a circular cross-section. The research takes into account the installation of the axial fan due to the distance of the rotor from the curvature of the pipeline. The uRANS turbulent flow modeling methods were used in the calculations. The uRANS stands for the Navier-Stokes equation with Reynolds averaging in the version that takes into account the non-stationarity of the flow. The purpose of the work is to determine the sound power in the vicinity of the sound source. The decisive parameters affecting the noise emitted will be the length of the installation in front of and behind the rotor. The propagation of acoustic disturbances in the far field was modeled using the aeroacoustic analogy of Ffowcs-Williams and Hawkings. Based on the calculations, the directional characteristics of the sound source were determined.

2

Analiza porównawcza wybranych metod symulacji nieustalonego przepływu gazu w gazociągu

Osiadacz Andrzej J.

Gaz, Woda i Technika Sanitarna

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2022

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Nr 2

25--31

PL

Celem niniejszego artykułu jest porównanie wykorzystując prosty gazociąg dwóch różnych metod (metody charakterystyk oraz metody prostych) do symulacji nieustalonego przepływu gazu w sieciach gazowych. Założono, że nieustalony przepływ jest opisany przez układ równań quasi-liniowych hiperbolicznych. Rezultaty badań wykazały, że metoda prostych jest zdecydowanie bardziej przydatna do symulacji stanów nieustalonych.

EN

The purpose of this paper is to compare using simple gas pipeline two different numerical methods (the method of characteristics and the method of lines) which can be used for transient simulation of gas transmission networks. It was assumed that flow through the pipe is described by set of quasi-linear hyperbolic partial differentia equations. The results of investigations have shown that the method of lines is much more efficient for this purpose.

3

On the robustness of the topological derivative for Helmholtz problems and applications

Leugering Günter, Novotny Antonio André, Sokolowski Jan

Control and Cybernetics

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2022

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Vol. 51, No. 2

227--248

EN

We consider Helmholtz problems in two and three dimensions. The topological sensitivity of a given cost function J(uɛ) with respect to a small hole Bɛ around a given point x0ɛ ∈ Bɛ ⊂ Ω depends on various parameters, like the frequency k chosen or certain material parameters or even the shape parameters of the hole Bɛ. These parameters are either deliberately chosen in a certain range, as, e.g., the frequencies, or are known only up to some bounds. The problem arises as to whether one can obtain a uniform design using the topological gradient. We show that for 2-d and 3-d Helmholtz problems such a robust design is achievable.

4

Nonlinearity of incomplete Boolean functions: prioritizing spectra calculation

Porwik Piotr

Archives of Control Sciences

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2022

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Vol. 32, No. 4

663--676

EN

In this paper, a class of linear Boolean functions is analyzed. The Boolean function can be represented as disjoint cubes or in the form of a truth vector. The primary purpose of this analysis is to decide whether an incompletely defined function can be extended to a complete linear form. A simple algorithm for generating all states of this function has been proposed if the Boolean function can have a full representation. The algorithm is beneficial for large functions. The proposed approach can be applied to completely and incompletely defined Boolean functions.

5

Matlab implementation of direct and indirect shooting methods to solve an optimal control problem with state constraints

Karbowski Andrzej

Journal of Automation Mobile Robotics and Intelligent Systems

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2021

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Vol. 15, No. 1

43--50

EN

The paper presents a general procedure to solve nume‐ rically optimal control problems with state constraints. It is used in the case, when the simple time discretization of the state equations and expressing the optimal cont‐ rol problem as a nonlinear mathematical programming problem is too coarse. It is based on using in turn two multiple shooting BVP approaches: direct and indirect. The paper is supplementary to the earlier author’s paper on direct and indirect shooting methods, presenting the theory underlying both approaches. The same example is considered here and brought to an end, that is two full listings of two MATLAB codes are shown.

6

Mathematical model bounds for maximizing the minimum completion time problem

Jemmali Mahdi, Alourani Abdullah

Journal of Applied Mathematics and Computational Mechanics

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2021

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Vol. 20, nr 4

43--50

EN

This paper focuses on the parallel machine scheduling problem related to maximizing the minimum completion time. This problem affects several industrial applications. The application of this problem in real life is very impressive. This paper is based on the development of new lower bounds for the exact solution of the studied problem. It is shown in the literature that the problem is strongly NP-hard. The first developed lower bound is obtained by utilizing the probabilistic method to generate several solutions for the lower bound. The second is based on the knapsack problem with the iterative method. These numerical methods give new, better lower bounds.

7

A new numerical scheme for solving the two dimensional fractional diffusion equation

Altan Koç Dilara, Gülsu Mustafa

Journal of Applied Mathematics and Computational Mechanics

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2021

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Vol. 20, nr 2

5--16

EN

In this study, the locally one dimensional (LOD) method is used to solve the two dimensional time fractional diffusion equation. The fractional derivative is the Caputo fractional derivative of order α. The rate of convergence of the finite difference method is presented. It is seen that this method is in agreement with the obtained numerical solutions with acceptable central processing unit time (CPU time). Error estimates, numerical and exact results are tabulated. The graphics of errors are given.

8

Zastosowanie metod numerycznych w projektowaniu rozdzielnic średniego napięcia

Kondratowicz-Kucewicz Beata, Krasuski Krzysztof, Hejduk Artur, Wojtasiewicz Grzegorz

Inżynieria Elektryczna

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2021

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nr 8

40--42

PL

Rozwój przemysłu oraz powiększanie obszarów miejskich powodują wzrost obciążenia sieci zasilającej i konieczność wdrożenia inteligentnych urządzeń i systemów sterowania zasilaniem odbiorców. Zmieniają się także oczekiwania odbiorców finalnych i zarówno oni, jak i dostawcy energii na całym świecie mają większą świadomość wpływu na środowisko procesów wytwarzania energii. W związku z tym sposób, w jaki się produkuje, rozdziela i zużywa energię musi również ewoluować. Aby sprostać tym wyzwaniom, sieci dystrybucyjne wyposaża się w nowoczesne, inteligentne rozwiązania, które podwyższają poziom efektywności i bezpieczeństwo użytkowania. Nowatorskie technologie, innowacyjne rozwiązania konstrukcyjne oraz nowoczesna architektura systemów lokalnej dystrybucji energii elektrycznej to cechy współczesnych sieci zasilających. Przetwarzanie energii elektrycznej, które odbywa się w węzłowych punktach sieci zasilającej zwanych stacjami elektroenergetycznym oraz rozdział energii w rozdzielnicach, są newralgiczne w całym procesie zasilania odbiorców energią elektryczną. Prawidłowe projektowanie, dobór urządzeń i aparatów dla rozdzielnic, stacji transformatorowych i nastawni może zatem zagwarantować bezpieczną pracę całej infrastruktury zasilającej, ale również zapewnić właściwą jakość dostarczanej energii elektrycznej.

9

An Introduction to the Special Issue on Numerical Techniques Meet with OR - Part II

Gürbüz Burcu, Weber Gerhard-Wilhelm

Foundations of Computing and Decision Sciences

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2021

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Vol. 46, No. 3

201--204

EN

The special issue: “Numerical Techniques Meet with OR” of the Foundations of Computing and Decision Sciences consists of two parts which are of the main theme of numerical techniques and their applications in multi-disciplinary areas. The first part of this special issue was already collected in the FCDS Vol. 46, issue 1. In this second part of our special issue editorial, a description of the special issue presents numerical methods which can be used as alternative techniques for Scientific Computing and led Operational Research applications in many fields for further investigation.

10

Numerical Analysis of Large Deflections of a Flat Textile Structure with Variable Bending Rigidity and Verification of Results Using Fem Simulation

Szablewski Piotr

Autex Research Journal

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2021

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Vol. 21, no. 1

108--114

EN

The paper presents the numerical modeling of large deflections of a flat textile structure subjected to a constant force acting on the free end. It was assumed that the examined structure is inextensible. The effect of the structure's own weight was also taken into account. In order to solve the problem, the flat textile structure was modeled using the heavy elastica theory. An important element of the analysis involves taking into account the variable bending rigidity of the examined textile structure along its length, which is often found in this type of products. The function of variable bending rigidity was assumed in advance. Numerical calculations were carried out in the Mathematica environment using the shooting method for the boundary value problem. The obtained results were verified using the finite element method.

11

Investigations of thermal-flow characteristics of minichannel evaporator of air heat pump

Kowalczyk Michał Jan, Łęcki Marcin, Romaniak Artur, Warwas Bartosz, Gutkowski Artur

Archives of Thermodynamics

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2021

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Vol. 42, no 4

261--279

EN

The results of experimental investigations of heat transfer and a friction factor in an air channel of the minichannel heat exchanger are presented. The main aim of the analysis was to examine an influence of geometrical parameters of the fin shape with two geometries on heat transfer and flow characteristics of the air channel. The test rig was designed to monitor the parameters of the airflow during cooling by the minichannel heat exchanger. The analysis was conducted with the airflow in the range of 1–5 m/s. The temperature of the evaporation in a refrigeration system was set at 288.15 K. The energy balance of the refrigeration system was carried out. A numerical model describes the airflow through a part of the heat exchanger. Numerical simulations were validated with the experimental data. Numerical methods were used to evaluate the performance of the system and possibilities to improve the fin geometry. The characteristics of the friction factor (a measure of the pressure loss in the airflow) and the Colburn j-factor (heat transfer performance) were calculated. For the maximal velocity of the airflow, the Colburn factor was equal to 0.048 and the evaporator capacity equaled 1914 W.

12

Convergence of Monte Carlo algorithm for solving integral equations in light scattering simulations

Kraszewski Maciej, Pluciński Jerzy

Optica Applicata

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2020

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Vol. 50, nr 1

17--35

EN

The light scattering process can be modeled mathematically using the Fredholm integral equation. This equation is usually solved after its discretization and transformation into the system of algebraic equations. Volume integral equations can be also solved without discretization using the Monte Carlo algorithm, but its application to the light scattering simulations has not been sufficiently studied. Here we present the implementation of this algorithm for one and three-dimensional light scattering computations and discuss its applicability in this field. We show that the Monte Carlo algorithm can provide valid and accurate results but, due to its convergence properties, it might be difficult to apply for problems with large volumes or refractive indices of scattering objects.

13

Application of the Monte Carlo algorithm for solving volume integral equation in light scattering simulations

Kraszewski Maciej, Pluciński Jerzy

Optica Applicata

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2020

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Vol. 50, nr 1

1--15

EN

Various numerical methods were proposed for analysis of the light scattering phenomenon. An important group of these methods is based on solving the volume integral equation describing the light scattering process. The popular method from this group is the discrete dipole approximation. Discrete dipole approximation uses various numerical algorithms to solve the discretized integral equation. In the recent years, the application of the Monte Carlo algorithm as one of them was proposed. In this research, we analyze the application of the Monte Carlo algorithm for two cases: the light scattering by large particles and by random conglomerates of small particles. We show that if proper preconditioning of the numerical problem is applied, the Monte Carlo algorithm can solve the underlying systems of linear equations. We also show that the efficiency of the Monte Carlo algorithm can be increased by reusing performed computations for various incident electromagnetic waves and the applicability of the Monte Carlo algorithm depends on the particular use case. It is unlikely to be used in the case of light scattering by the large particles due to computational times inferior comparing with the other numerical methods but may become useful in the case of light scattering by the random conglomerates of small scattering particles.

14

Development of real gas model operating in gas turbine system in Python programming environment

Trawiński Paweł

Archives of Thermodynamics

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2020

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Vol. 41, no 4

23--61

EN

Identification of working fluids and development of their mathematical models should always precede construction of a proper model of the analysed thermodynamic system. This paper presents method of development of a mathematical model of working fluids in a gas turbine system and its implementation in Python programming environment. Among the thermodynamic parameters of the quantitative analysis of systems, the following were selected: specific volume, specific isobaric and isochoric heat capacity and their ratio, specific enthalpy and specific entropy. The development of the model began with implementation of dependencies describing the semi-ideal gas. The model was then extended to the real gas model using correction factors reflecting the impact of pressure. The real gas equations of state were chosen, namely due to Redlich–Kwong, Peng–Robinson, Soave– Redlich–Kwong, and Lee–Kesler. All the correction functions were derived analytically from the mentioned equations of real gas behaviour. The philosophy of construction of computational algorithms was presented and relevant calculation and numerical algorithms were discussed. Created software allowed to obtain results which were analysed and partially validated.

15

Comparison of solvers performance for load flow analysis

Suresh Vishnu

Transactions on Environment and Electrical Engineering

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2019

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Vol. 3, No. 1

26--32

EN

Load flow studies are carried out in order to find a steady state solution of a power system network. It is done to continuously monitor the system and decide upon future expansion of the system. The parameters of the system monitored are voltage magnitude, voltage angle, active and reactive power. This paper presents techniques used in order to obtain such parameters for a standard IEEE – 30 bus and IEEE-57 bus network and makes a comparison into the differences with regard to computational time and effectiveness of each solver.

16

Wykorzystanie metod numerycznych w konstruowaniu osadników wielostrumieniowych

Kołodziejczyk Krzysztof, Banaś Marian

Przemysł Chemiczny

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2019

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T. 98, nr 9

1417--1419

PL

Zastosowano metodę numeryczną do modelowania układów wielofazowych. Główny nacisk położono na weryfikację i sposób zdefiniowania takich parametrów analizy, jak skład ziarnowy oraz krok czasowy. Zaproponowano metodykę wykonania numerycznych symulacji pracy osadnika pod kątem wykorzystania w procesie optymalizacji konstrukcji osadnika wielostrumieniowego.

EN

Sedimentation process was modeled by a multiphase system simulation, in which the dispersed phase was defined on the basis of its phys. properties. The numerical simulations were carried out as variables in time (time step 0.5 s) by using the Ansys Fluent package. Good agreement between modeling results and lab. tests was obsd.

17

Ocena skuteczności działania ładunków kumulacyjnych na podstawie rozwiązań numerycznych

Bagrowski Jan, Bazela Rafał, Borkowski Jacek, Podgórzak Paweł, Jach Karol

Problemy Techniki Uzbrojenia

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2019

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R. 48, z. 149

7--22

PL

W artykule przedstawiono oceny maksymalnych głębokości wnikania strumieni kumulacyjnych w stal pancerną w funkcji odległości od podstawy wkładki. Dane – chwilowe współrzędne położeń, mas oraz prędkości elementów strumieni były wynikiem obliczeń numerycznych działania wybranych konstrukcji ładunków kumulacyjnych. Pokazano, iż głębokość krateru jest funkcją dopuszczalnego wydłużenia elementów strumienia oraz ich minimalnej prędkości. Wyniki porównano z danymi doświadczalnymi.

EN

The paper shows the estimations of maximal penetration depths of shaped charge jets in a steel armour as a function of stand-off distance to the liner base. The data – instantaneous coordinates of positions, masses, and velocities of jet elements was received as results of numerical calculations for selected examples of designs of shaped charges. It was shown that the crater’s depth is a function of acceptable maximal extension of jet elements and their minimal velocity. The results were compared with experimental data.

18

A study of thermal conductivity in multilayer building materials and products

Ryndiuk Svitlana, Shvets Vitaliy, Maksymenko Marina

Budownictwo o Zoptymalizowanym Potencjale Energetycznym

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2019

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Vol. 8 Nr 1

59--66

EN

At this time, the solution to the problem of energy use, namely: energy conservation and energy efficiency is extremely important. Saving energy in buildings by solving the practical problems of reducing the total consumption of energy resources, is implemented through the use of effective thermal insulation materials, energy-efficient structures of external walls and a significant increase in thermal protection of the operated Fund. The actual solution to these problems is the development of new approaches to the calculation, design and manufacturing of insulation materials in wall constructions and how they are implemented. Therefore, it is necessary to improve the theoretical and scientific basis in order to make a more thorough study of the distribution of temperature within the material from which the design is made. Different methods of researching the thermal conductivity of multilayer structures and methods for calculating the temperature field of single- and multi-layered building structures have been proposed in studies of temperature distribution and energy efficiency improvements of building materials and products.

PL

Obecnie rozwiązanie problemu zużycia energii, a mianowicie: oszczędzanie energii i efektywność energetyczna, jest niezwykle ważne. Oszczędzanie energii w budynkach poprzez rozwiązywanie praktycznych problemów zmniejszenia całkowitego zużycia zasobów energetycznych realizowane jest poprzez zastosowanie efektywnych materiałów termoizolacyjnych, energooszczędnych konstrukcji ścian zewnętrznych oraz znaczny wzrost ochrony cieplnej. Rzeczywistym rozwiązaniem tych problemów jest opracowanie nowych podejść do obliczania, projektowania i produkcji materiałów izolacyjnych wykorzystywanych w konstrukcjach ścian oraz sposobu ich zastosowania. Dlatego konieczne jest ulepszenie podstaw teoretycznych i naukowych w celu dokładniejszego zbadania rozkładu temperatury w materiale, z którego wykonany jest dany element konstrukcji. Do analizy rozkładu temperatury i poprawy efektywności energetycznej materiałów i produktów budowlanych zaproponowano różne metody badania przewodności cieplnej konstrukcji wielowarstwowych oraz obliczania pola temperatur jedno- i wielowarstwowych konstrukcji budowlanych.

19

Peridynamic Simulation of Crushing Processes in Copper Open-Cell Foam

Postek E., Pęcherski R. B., Nowak Z.

Archives of Metallurgy and Materials

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2019

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Vol. 64, iss. 4

1603--1610

EN

In the last 20 years, a new meshless computational method has been developed that is called peridynamics. The method is based on the parallelized code. The subject of the study is the deformation of open-cell copper foams under dynamic compression. The computational model of virtual cellular material is considered. The skeleton structure of such a virtual cellular material can be rescaled according to requirements. The material of the skeleton is assumed as the oxygen free high conductivity (OFHC) copper. The OFHC copper powder can be applied in additive manufacturing to produce the open-cell multifunctional structures, e. g., crush resistant heat exchangers, heat capacitors, etc. In considered peridynamic computations the foam skeleton is described with the use of an elastic-plastic model with isotropic hardening. The dynamic process of compression and crushing with different impact velocities is simulated.

20

Assessment of some numerical methods for estimating the parameters of the one‑dimensional advection–dispersion model

Silavwe Davy D., Brink Isobel C., Wallis Steve G.

Acta Geophysica

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2019

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Vol. 67, no. 3

999--1016

EN

This study appraised optimisations of numerical solutions of the one-dimensional advection–dispersion model (AD-Model) to synthetic data generated using an analytical solution. The motivation for the work was to identify reliable methods for estimating stream solute transport parameters from observed events in small rivers. Numerical solutions of the AD-Model must contend with several effects that might disturb the solution, with the introduction of numerical diffusion and numerical dispersion being particularly important issues. This poses a problem if physical dispersion is being identified by optimising model coefficients using observations of solute transport from field experiments. The discretisation schemes used were the Backward-Time/Centred-Space, Crank–Nicolson, Implicit QUICK, MacCormack and QUICKEST methods. Optimisations were obtained for several grid resolutions by keeping the time step constant whilst varying the space step: the range of Peclet number, Pe, was 1.5–12.0. Generally, increasing the space step led to poorer estimated coefficients and poorer fits to the synthetic concentration profiles. For Pe < 5 only Crank–Nicolson, MacCormack and QUICKEST gave reliable optimised dispersion coefficients: those from Backward-Time/Centred-Space and Implicit QUICK being significantly underestimated. For Pe > 5 Crank–Nicolson and MacCormack gave slightly overestimated dispersion coefficients whilst the other methods gave significantly underestimated dispersion coefficients. These findings were generally consistent with the known presence of numerical diffusion and numerical dispersion in the methods.