The paper presents a comparative analysis of tortuosity calculations in two types of 2D random geometries: with non-overlapping circles and with overlapping squares. Both geometries were converted to binary geometries with different resolution. Next, simulations involving the Lattice Boltzmann Method were performed to obtain velocity fields in a pore space. Based on the obtained velocity fields, Hydraulic tortuosity and streamline tortuosity were calculated, based on the obtained velocity fields, for all considered cases. Hydraulic tortuosity was calculated with the methodology proposed by Koponen et al., whereas streamline tortuosity was determined with the use of a new iterative algorithm. Two variants of the algorithm were proposed. Additionally, the obtained results were compared with selected formulas from the literature. The study demonstrated that calculations of streamlines exiting local inlet velocity maxima are a good alternative to calculations where all possible streamlines are taken into account. Computation time was significantly shorter and estimation quality was comparable.
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The paper presents details of discretisation of a thermal diffusion equation in one-dimensional space in terms of the Finite Volume Method. In the following sections, the method of space discretisation is discussed along with the approximation of a spatial derivative, matrix notation of a system of equations, special cases, approximation of three types of boundary conditions and derivative approximation over time. Much attention is also given to the issue of averaging material properties which can generally be different in adjacent cells.The study aims to analyse various multilayer structures for their suitability as heat storage. The launch of studies described in the paper has been driven by the lack of methods for effective heat storage, which is currently one of the key problems faced by the renewable energy industry.
In the paper, functions describing different porosity-tortuosity relations were collected, and then the tortuosity values were calculated for a one granular bed consisting of spherical particles with normal distribution of diameters. Information about the bed porosity and particle sizes was obtained from measurements conducted for an artificial granular bed, consisting of glass marbles. The results of calculations were compared with the results of two other methods of tortuosity determination, performed for the same case (details are not described in this paper): the first of them uses the Path Tracking Method, the second one - information about the velocity components in a creeping flow (the Lattice-Boltzmann Method was applied to obtain the velocity field in the flow). The main aim of our article was to test whether the functions linking tortuosity with porosity, which are available in the literature, give similar results as the methods described above. To achieve this aim, the relative errors between results of calculations for the collected formulas and values from the both previous mentioned methods were calculated.
The paper presents the results of a fractal analysis of the cross-sections of a porous mineral deposit consisting of spherical elements which formed a spatial system with varying porosity (0.4 to 0.95). The virtual deposit was generated using the Discrete Element Method in the YADE code by means of the so-called Radius Expansion Method. The fractal analysis was carried out using the structure function method, determining the fractal dimension (D), the topothesy (L) and the corner frequency (l) (MAINSAH et al. 2001). The conducted simulations have confirmed to a considerable extent the test results available in the literature involving the fractal analysis of mineral deposits with varying porosity. They clearly indicate that the fractal dimension does not change along with the porosity of the deposit, if the autocorrelation function or their transformations (e.g. structure function) methods are used. Moreover, based on the information available in the literature, it can be concluded that the value of the fractal dimension corresponds to mineral deposits with the specified geometric shapes of the elements which form them.
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The article describes a study to verify the existing requirements used in the production process on insulating distances inside the ESP. The results confirmed the correctness of the distance used, in some cases, made it possible to reduce them. Additionally, checked during the test or the introduction of new or changed structurally elements will not adversely affect operating voltage ESP.
PL
W artykule opisano badania mające na celu zweryfikowanie dotychczasowych wymogów stosowanych w procesie produkcyjnym dotyczących odległości izolacyjnych wewnątrz komory elektrofiltru. Wyniki badań potwierdziły poprawność stosowanych odległości, a w kilku przypadkach pozwoliły na ich zmniejszenie. Dodatkowo sprawdzono podczas badań czy wprowadzenie nowych lub zmienionych konstrukcyjnie elementów nie wpłynie negatywnie na napięcie pracy elektrofiltru.
This article presents results of the experimental measurements of the cavitation phenomena in a Venturi tube with water as the working medium. Three variants of such tube were tested. Angles of converging and diverging sections are equal to 45o and 45o, 30o and 60o, 45o and 60o, respectively. In every case the throat diameter is equal to 3 mm and the throat length to 6 mm. The average flow velocity ranges from 0.1 to 0.5 m/s. During measurements, the average flow velocity, upstream and downstream pressure and water temperature were recorded. Additionally, by the use of a high-speed camera and a simple digital camera, information about the size and the shape of the bubble clouds for different flow conditions was collected. The aim of the article is data acquisition for the further numerical analyses. The experimental runs executed for this paper are to help provide more information about this type of flow, since numerical modeling of the cavitation phenomena in Venturi tubes is still very difficult and in many cases even quantitative agreement is impossible to obtain.
The content of this article is a direct continuation of the prior experimental works on the topic of cloud cavitation in Venturis. The results of the experimental tests were used to create a set of characteristics for three types of Venturis. The article has two aims: 1) verification of the similarity between the characteristics obtained and reported in the literature, 2) verification of the range of the obtained characteristics with respect to parallel diagrams. Both aims were achieved, which confirms that the quality of the prior results of the experimental measurements is at least sufficient to realize the main objective of the whole project: creation of numerical models of cavitating flow in Venturis. The literature overview showed that the issue has been not solved until today, even at the qualitative level. This reason was the motivation for the undertaken research, including contents of the article.
In the article, a new way for obtaining a set of geometrical parameters of granular porous beds is presented, if the data on the locations and sizes of all particles is available. The input data were prepared with the use of Discrete Element Method. The other way for acquiring the input data may be the application of Computed Tomography (CT) and Image Analysis (IA) techniques. All geometrical parameters are calculated with the use of own numerical code called PathFinder (freely available in the Internet together with its source code). In addition to description of the method of calculations, two examples of its use are presented. One simulation was performed in PFC3D code, and the other in YADE software. The aim of the article was to show clearly that a porosity is not sufficient to describe the spatial structure of a porous body. In both presented examples, the porosity value is almost the same, but other parameters, e.g. tortuosity, are different. The motivation to write the PathFinder code were significant problems with obtaining geometrical parameters needed in investigations related to granular porous media. The issues described in the article are a part of an overall research methodology relating to the linking the micro- and macro-scale investigations of granular porous beds. The areas of applications of this methodology are not discussed in the article.
The focus of research works on cavitation has changed since the 1960s; the behaviour of a single bubble is no more the area of interest for most scientists. Its place was taken by the cavitating flow considered as a whole. Many numerical models of cavitating flows came into being within the space of the last fifty years. They can be divided into two groups: multifluid and homogeneous (i.e., single-fluid) models. The group of homogenous models contains two subgroups: models based on transport equation and pressure based models. Several works tried to order particular approaches and presented short reviews of selected studies. However, these classifications are too rough to be treated as sufficiently accurate. The aim of this paper is to present the development paths of numerical investigations of cavitating flows with the use of homogeneous approach in order of publication year and with relatively detailed description. Each of the presented model is accompanied by examples of the application area. This review focuses not only on the list of the most significant existing models to predict sheet and cloud cavitation, but also on presenting their advantages and disadvantages. Moreover, it shows the reasons which inspired present authors to look for new ways of more accurate numerical predictions and dimensions of cavitation. The article includes also the division of source terms of presented models based on the transport equation with the use of standardized symbols.
Artykuł zawiera rozważania dotyczące obecnych możliwości wykorzystywania taranów wodnych. W pracy przedstawiono kilka przykładów potencjalnego wykorzystania tego typu urządzeń. Przykłady te podzielono na kilka grup, aby wyeksponować charakterystyczne cechy różnych rodzajów odbiorców, jednak jest to podział umowny i przykłady przedstawione w jednej grupie równie dobrze mogą być wykorzystane w innej. Oprócz tego omówiono charakterystykę ujęć oraz specyfikę źródeł wody przydatnych do zasilania taranów wodnych. W artykule zebrano podstawowe informacje o urządzeniu, opisano zasady jego funkcjonowania i przedstawiono rys historyczny. Motywacja do zajęcia się tematyką taranów wodnych wynikła z obserwacji i analizy działania dwóch historycznych systemów zaopatrzenia w wodę, znajdujących się obecnie w województwie warmińsko-mazurskim, z których jeden działa nieprzerwanie od 1897 r.
EN
The paper contains considerations about current possibilities of the use of hydraulic rams. Several examples of potential use of this type of equipment are presented. The examples are divided into several groups to expose characteristic features of different types of customers but the division is conventional and examples presented in one group may be used also in another group. Moreover, characteristics of water sources to supply hydraulic rams are presented. The paper presents basic information about the device, principles of its work and the history of its use. The study was motivated by observations and analyses of two historical water supply systems in the region of Warmia and Mazury in Poland, one of them working continuously since 1897.
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W artykule opisano stanowisko laboratoryjne przeznaczone do badań taranów wodnych. Przedstawione rozwiązania konstrukcyjne powstały na bazie wcześniejszych prototypów oraz prób pomiaru różnych parametrów układu. Głównym celem badań jest przygotowanie się do wyznaczania różnych charakterystyk pracy, a także do rejestracji ruchu zaworów oraz ruchów wody, zachodzących wewnątrz tarana wodnego podczas cyklu jego pracy. Aby zrealizować te cele, w artykule przedstawiono dwa warianty budowy tarana wodnego. W literaturze naukowej dotyczącej tego typu urządzeń nie udało się odnaleźć opisów takich pomiarów. Chęć uzupełnienia wiedzy w tym obszarze stanowiła główną motywację do rozpoczęcia badań.
EN
In the article described stand of laboratory designed for testing water rams. Shown there the design solutions were made on the basis earlier prototypes and test measures various parameters in the system. The main aim of the researches is prepare for determination various characteristic of the work of the ram and to record movements of the valve and water occurring inside of the ram during of his cycle operation. To realize these purposes in the article two variants of his constructions were shown. In the scientific literature relates on this type of equipment failed to find descriptions of such measurements. The willingness supplement knowledge in this area was the main motivation to start testing.
In the article a sensitivity analysis of linear and nonlinear terms in the Kozeny-Carman and Ergun equations was shown. In the first case the impact of the porosity, tortuosity, specific surface of the porous body and the model constant was investigated. In the second case the porosity, the particle diameter and the sphericity function were taken into account. To express the model sensitivity by numbers, an earlier developed method was used. In this way the order and the importance of the impact of individual parameters was determined. The motivations to create this article were questions, which occurred during developing a novel investigation method, linking the Discrete Element Method and the CFD techniques. The first aim was to predict what will happen, if individual parameters will be set with an error: which data should be set as accurately as possible and which data are not very important for the result value. The second intention was to state which of parameters used in porous media investigations should be expressed by functions and which by constant values. The article may be treated as set of pointers helping in using of Kozeny-Carman and Ergun laws or as an example of research methodology based on the sensitivity analysis.
This paper discusses a new approach to analyzing fluid flow through a granular bed. The analysis involves the determination of a set of geometric parameters characterizing a granular bed based on information about the location and diameter of all bed particles. The above task has been achieved with the use of the PathFinder numeric code developed by the authors. The study proposes a new algorithm for calculating the parameters of granular beds composed of spherical particles with various diameters in the PathFinder program. The algorithm has been verified with the use of independent tools and implemented in the new version of the PathFinder code. The modified algorithm’s effect on flow path tortuosity has been analyzed. Path length is used to determine tortuosity, a key parameter of pore geometry that is difficult to calculate. Comparative calculations were performed in a granular bed generated by the Discrete Element Method in the PFC3D program.
Our study is based on a column experiment of water flow through a porous granular bed. In Part 1 we propose eight methods to derive parameters of flow models based on measurement data. These parameters are permeability and Forchheimer coefficient for Darcy’s and Forchheimer’s laws. The approach presented in this part uses two numerical models to perform simulations of flow. One model is based on the Finite Element Method implemented in the authors’ code. The second model, which is ANSYS/Fluent package, uses the Finite Volume Method. Results of numerical computations are compared with experimental data that allows determination of the best method of parameter evaluation (in which the error was less than 3% over the whole range of filtration velocities). The problem of identification of ranges of applicability of the Darcy’s and Forchheimer’s laws is also addressed. In the conclusions, a set of guidelines is given, which should facilitate planning a similar experiment and its computational processing.
The aim of this study is to derive flow parameters, which are permeability and Forchheimer coefficient, based on experimentally measured flow rates and pressure drops. When flow rates used in measurements exceed the limits of linear Darcy’s flow regime we discuss what needs to be taken into account while processing the measurements. The study consists of two parts. In this part we briefly recall Darcy’s and Forchheimer’s laws and address the issue of detecting transition between ranges of their applicability. Then we describe the experiment and discuss 8 different ways to process measurement data, four for Darcy’s, and four for Forchheimer’s models. The main topic of the second part is to provide recommendations for the best ways to process data, so that the results obtained with numerical models are in the best agreement with the experimental data. The results shown in the two papers belong to a larger work devoted to modeling fluid flows through porous media, with a special interest in granular beds.
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W artykule przedstawiono rozważania dotyczące opływu liniowej palisady profili kołowych powietrzem przy zmiennej prędkości przepływu. Pokazano prostą i praktyczną metodę określania liczby Strouhala, bez konieczności wykonywania kosztownych eksperymentów. Po wyznaczeniu liczby Strouhala dla jednej prędkości, można ją następnie wykorzystać w kolejnych symulacjach, z innymi prędkościami przepływu, o ile geometria układu nie ulegnie zmianie. Zaproponowane podejście ma charakter uniwersalny i może być stosowane w dowolnych opływach zarówno palisad, jak i profili pojedynczych. Model symulacyjny wykonano Metodą Objętości Skończonych w środowisku obliczeniowym ANSYS. Celem badań było sprawdzenie skuteczności i czasochłonności metody.
EN
This article presents considerations for linear flow around a stockade of circular profiles with variable flow rates. Shown a simple and practical method for determining of the Strouhal number, without the need for costly experiments. After determining of the Strouhal number for single-speed, it can then be used in subsequent simulations, with the other flow rates, as long as the geometry of the system is not changed. The proposed approach is universal and can be used both in any flow around stockades and individual profiles. The simulation model was performed by Finite Volume Method in the ANSYS computing environment. The aim of the study was to examine the effectiveness and time-consuming of this method.
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W artykule przedstawiono szczegółowo zasadę działania urządzenia zwanego taranem wodnym oraz omówiono etapy jego pracy w odniesieniu do zjawiska uderzenia hydraulicznego, stanowiącego podstawę działania tego typu urządzeń. W poszczególnych punktach opisano historię taranów wodnych, klasyczną teorię uderzenia hydraulicznego opracowaną w roku 1889 przez Nikolaja Żukowskiego oraz jej współczesne rozszerzenia, omówiono budowę typowego tarana wodnego, scharakteryzowano funkcje poszczególnych jego elementów oraz przedstawiono warunki, przy których taran wodny może poprawnie pracować. Najważniejszym elementem pracy jest opis cyklu pracy tarana wodnego z podziałem na etapy. Motywacją do napisania artykułu było spostrzeżenie, że w literaturze fachowej, zarówno polskiej jak i zagranicznej, brak jest podobnego typu opisów, a materiały popularno-naukowe, spotykane głównie na różnych stronach internetowych, są przeważnie zbyt ogólne (a czasami i błędne), przez co nie spełniają wymogów źródeł naukowych. Najważniejszą nowością zawartą w pracy, a zarazem głównym jej celem, jest połączenie opisu działania taranów wodnych z przebiegiem uderzenia hydraulicznego. Artykuł stanowi kontynuację cyklu związanego z poszukiwaniem obecnych możliwości praktycznego wykorzystania taranów wodnych w możliwie szerokim obszarze zastosowań.
EN
The article presents in detail the principle of operation of a device called a ram pump and discusses the operational steps of its work in relation to the water hammer phenomenon, which is the basis of operation of this type of equipment. In different points of article described history rams water, classical theory of hammer developed at the Nikolai Zhukovsky in 1889 and it a modern extension, described the typical ram of water, characterized the function of each of its components and presents the conditions under which water ram can properly work. The most important element of the work is the description of the water cycle ram broken down into stages. The motivation to write this article was the observation that in the literature, both Polish and foreign, there is a similar type descriptions, and popular-science materials, mostly found on various websites are often too general (and sometimes incorrect), which not meet the requirements of scientific sources. The most important new feature included in the work, and at the same time its main objective is to combine the description of action rams the course of the water hammer. The article is a continuation of the cycle associated with the exploration of current possibilities of practical use of rams water as possible a wide range of applications.
This short article presents all basic “closures” that are needed to supplementation the general set of balance equations in form characteristic for the Finite Volume Method. In subsequent chapters the equation of state, viscous molecular stress tensor, turbulent stress tensor, molecular heat flux, turbulent heat flux and momentum and energy sources were described. This article is a second part of a cycle dedicated for the mathematical basis of Finite Volume Method. The motivation for writing the article follows from the observation that the Finite Volume Method is usually described in greater detail in monographic books, or very briefly in the basic books dedicated to fluid mechanics. This article is an attempt to center justifications of these approaches, so that in the simplest way show the readers the basic knowledge of the so-called Computational Fluid Mechanics. For this reason this article can be treated as a literature review.
This paper analyzes three popular methods of developing simulation models based on experimental data. The presented variants are discussed with emphasis on their strengths and weaknesses, and they are illustrated with examples in the area of numerical fluid mechanics. The principles of developing computer models, details and objectives of mathematical models are not discussed. The relevant information can be found in the author’s previous studies which are available in scientific literature. The last section of the article proposes the most effective methods for combining and designing real and virtual experiments.
The article presents the derivation of the basic balance equations in form characteristic of the Finite Volume Method. In the following sections the origin of the balance equation of momentum, mass and energy is presented. Next, the conservation equations in vector form are described. The Finite Volume Method is used in Computational Fluid Mechanics for numerical modeling of fluid flows in wide range. The motivation for writing the article was the difficulty in finding short and concise articles on this subject in the literature. The current article is a first part of a cycle dedicated to the mathematical basis of the Finite Volume Method.
PL
W artykule przedstawiono wyprowadzenie podstawowych równań bilansowych w formie charakterystycznej dla metody objętości skończonych. Przedstawiono pochodzenie równania bilansu pędu, masy i energii, następnie równania zachowania w formie wektorowej. Metoda objętości skończonych jest stosowana w tzw. numerycznej mechanice płynów do numerycznego modelowania przepływów płynów w możliwie szerokim zakresie. Motywacją do napisania artykułu była trudność w znalezieniu podobnego rodzaju krótkich i zwięzłych opracowań na ten temat w literaturze. Artykuł jest pierwszą częścią cyklu poświęconego matematycznym podstawom metody objętości skończonych.
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