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1
Content available Parameters affecting water hammer in plastic pipelines
Urbanowicz K., Firkowski M.
Zeszyty Naukowe Akademii Morskiej w Szczecinie
|
2018
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nr 54 (126)
35--43
EN
Pressure pipes made of selected plastics are widely used in current water supply systems. Unfortunately, the theoretical basis for modeling transient flows in these pipes has not been clarified yet. For simplified one-dimensional numerical modeling, a model is commonly used in which the total deformation of the pipe walls is expressed by the sum of instantaneous and retarded deformations. One of the main problems lies in the correct experimental determination of the creep function defining the properties of the polymer. The influence of other parameters on which the numerical solution of the method of characteristics is based is the subject of the research presented in this paper.
2
Content available Sufficient conditions for optimality for a mathematical model of drug treatment with pharmacodynamics
Leszczynski M., Ratajczyk E., Ledzewicz U., Schättler H.
Opuscula Mathematica
|
2017
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Vol. 37, no. 3
403--419
EN
We consider an optimal control problem for a general mathematical model of drug treatment with a single agent. The control represents the concentration of the agent and its effect (pharmacodynamics) is modelled by a Hill function (i.e., Michaelis-Menten type kinetics). The aim is to minimize a cost functional consisting of a weighted average related to the state of the system (both at the end and during a fixed therapy horizon) and to the total amount of drugs given. The latter is an indirect measure for the side effects of treatment. It is shown that optimal controls are continuous functions of time that change between full or no dose segments with connecting pieces that take values in the interior of the control set. Sufficient conditions for the strong local optimality of an extremal controlled trajectory in terms of the existence of a solution to a piecewise defined Riccati differential equation are given.
3
Content available remote Modeling of Pulsating Flows: Selected Issues
Pałczyński T.
Zeszyty Naukowe. Cieplne Maszyny Przepływowe - Turbomachinery / Politechnika Łódzka
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2015
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nr 148
91--100
EN
This paper presents the main assumptions of a 1D simulation model designed to estimate flow parameters in pipes with pulsating supply. The boundary conditions are defined with 3D maps of the variation of chosen parameters in the x-t domain.
PL
W artykule przedstawiono główne założenia jedno-wymiarowego modelu symulacyjnego do estymacji parametrów przepływowych w przewodach zasilanych pulsacyjnie. Zdefiniowano warunki brzegowe i zaprezentowano przykładowe wyniki obliczeń w postaci trójwymiarowych map przebiegu zmienności wybranych parametrów przepływowych w dziedzinie x-t.
4
Content available A numerical approach to the standard model of water hammer with fluid-structure interaction
Henclik S.
Journal of Theoretical and Applied Mechanics
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2015
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Vol. 53 nr 3
543--555
EN
In the classic water hammer (WH) theory, 1D liquid flow in a quasi-rigid pipe is assumed. When the pipe is flexible or is fixed to the foundation with elastic supports, the dynamic fluid structure interaction (FSI) should be taken into account for more accurate modelling of the system behaviour. The standard model of WH-FSI for a straight pipe reach is governed by fourteen hyperbolic partial differential equations of the first order, two for 1D liquid flow and twelve for 3D motion of the pipe. This model is presented in the paper and an algorithm for its numerical solution based of the method of characteristics is proposed. Basic boundary conditions (BC) are shortly discussed. The important condition at the junction of two subpipes fixed to the foundation with a viscoelastic support is presented in details and a general method of its solution is proposed.
5
Content available remote Effect of hydrogen injection into natural gas on the mechanical strength of natural gas pipelines during transportation
Elaoud S., Abdulhay B., Hadj-Taieb E.
Archives of Mechanics
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2014
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Vol. 66, nr 4
269--286
EN
The aim of this paper is to study the effect of hydrogen injection into natural gas transient flows on the mechanical strength of natural gas pipelines. The governing equations of hydrogen-natural gas mixtures are two nonlinear partial differential equations. The fluid pressure and velocity are considered as two principal dependent variables. The fluid is a homogeneous hydrogen-natural gas mixture for which the density is defined by an expression averaging the two gas densities where an adiabatic process is admitted for the two components. The problem has been solved by the nonlinear method of characteristics. By the use of Laplace’s law, the pipe’s circumferential stress has been analyzed for different hydrogen mass fraction in the mixture. It was then compared to the allowable stress of different grade pipeline steels used to transport natural gas. The obtained results have shown that the allowable stress for the natural gas pipelines is exceeded for some fractions of hydrogen in the hydrogen-natural gas mixtures.
6
Content available Symualcje jednowymiarowych przepływów pulsacyjnych w przewodach w oparciu o metodę charakterystyk
Pałczyński T.
Postępy Nauki i Techniki
|
2012
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Nr 14
197-207
PL
W pracy omówiono podstawowe informacje związane z koncepcją wykorzystania metody charakterystyk w modelowaniu przepływów w przewodach zasilanych pulsacyjnie. W dalszej części pracy zaprezentowano technologię opracowania modelu symulacyjnego. W końcowej części pracy przedstawiono przykładowe wyniki badań numerycznych, odniesione do badań eksperymentalnych, uzyskując potwierdzenie słuszności przyjętej koncepcji. Opisano główne zalety zaproponowanej koncepcji badań symulacyjnych a także kierunki dalszych badań
EN
At this paper there were presented basic information connected with concept of usage of Method of Characteristics at pipes with pulsating flow supplied modeling. At the next section of paper there were shown technology of simulation model building. Simulation results compared with experiment complained the wisdom of proposed conception. There were also presented the main advantages of described model and the next steps of research.
7
Content available A boundary condotions at modeling 1-D pulsating flows in pipes according to the method of characteristics
Pałczyński T.
Journal of KONES
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2012
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Vol. 19, No. 2
395-402
EN
At this paper, there were compared three conceptions of boundary conditions and their definition at partially opened pipes. This is typical at inlet and exhaust pipes of internal combustion engines and piston compressors. At an introduction there were listed the current state of affairs at a one dimensional modelling pulsations according to the Method of Characteristics (MOC). Subsequently, there was presented the main idea of MOC. At the third chapter there were presented general guidelines at initial and boundary conditions definition. Next there are three descriptions of the analyzed problem. Firstly, there was presented partially open end phenomena at space and stage plane. Secondly, there was shown the theory of acoustic wave propagation with description of stage waves at analyzed ends of pipe. Lastly, there is a new conception of constant pressure valve boundary conditions, which is the synthesis of the both mentioned earlier. At the fourth paragraph there was shortly presented existing test rig dedicated to research of pulsating flow in pipes. This test rig was built at Flow Metrology Division of Lodz University of Technology [9]. At the second part of this chapter there were shown main assumption of elaborated simulation algorithm at Matlab Simulink environment. Lastly there were discussed simulation results compared with presented conceptions of boundary conditions.
8
Content available Mathematical model and numerical computations of transient pipe flows with fluid-structure interaction
Henclik S.
Transactions of the Institute of Fluid-Flow Machinery
|
2010
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nr 122
77-94
EN
Transient flows in closed conduits are of interest from over a century, but the dynamic interaction between the fluid and the pipe is taken into consideration more thoroughly just from a few decades. A standard model of the phenomenon consists of fourteen first order partial differential equations (PDE), two for a one-dimensional (1D) liquid flow and twelve for 3D pipe motion. In many practical cases however, a simpler four equations (4E) model can be used, where 1D longitudinal pipe movement is assumed. A short description of waterhammer event with fluidstructure interaction taken into account is presented in the article. The 4E mathematical model is presented in detail with the assumptions and main algorithms of computer program that has been developed. Two phase flow is assumed not to take place, but the friction between the liquid and the pipe wall are taken into consideration. A method of characteristics (MOC) with time marching procedure is employed for finding the solutions, but instead of direct solving the resulting finite difference equations (FDE) the “wave method” is proposed. Some other important elements of the algorithm are presented and selected results of numerical computations as well.
9
Content available remote Method of Characteristics for Design of Centrifugal Pump Geometry
Puzyrewski R., Zochowski K., Flaszyński P.
TASK Quarterly : scientific bulletin of Academic Computer Centre in Gdansk
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2010
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Vol. 14, No 3
249-256
EN
The method of characteristics leads to the blade geometry of a centrifugal pump. The method is built taking the advantage of the governing equations of fluid mechanics written in a non-orthogonal coordinates system. The coordinate system is based on an analytically described boundary of a centrifugal pump. Some of the information concerning the designed geometry should be introduced in advance. The mass conservation equation needs the information of the blockage factor resulting from the blading thickness. In the momentum conservation equation the body force replaces the blading force together with the friction force. In the energy conservation equation the dissipation effects are represented by a loss coefficient. It is shown that while simplifying the body force vector, the set of equations reduces to a hyperbolic system which allows applying the method of characteristics. The shapes of surfaces representing the designed blading can be built from the trajectories of fluid particles.
10
Content available remote The influence of hydraulic pressure conduits' parameters on the course of unsteady flow with cavitation
Zarzycki Z., Urbanowicz K.
Scientific Problems of Machines Operation and Maintenance
|
2008
|
Vol. 43, nr 1
89-100
EN
The paper attempts to assess the influence of closed conduits' parameters on maximum pressure values recorded as a result of waterhammer and on the time of keeping unsteady flow with cavitation. A number of numerical tests, necessary for carrying out this research program, were performed using the authors' own programs written in Matlab and based on effective cavitation transient models, which take into account unsteady hydraulic friction. In particular, the results of two key models were investigated; i.e. bubbly cavitation model (BCM) and column separation model (CSM).
PL
W pracy podjęto próbę oszacowania wpływu parametrów przewodów zamkniętych na wartości maksymalnych ciśnień występujących w wyniku uderzenia hydraulicznego, jak i na czas utrzymywania się przepływu nieustalonego z kawitacją. Niezbędne do realizacji tej pracy liczne badania numeryczne, wykonane zostały z wykorzystaniem własnych programów napisanych w Matlabie bazujących na efektywnych modelach kawitacji przejściowej, w których uwzględniono niestacjonarne opory hydrauliczne. W szczególności rozpatrywano wyniki otrzymane z dwóch kluczowych modeli: kawitacji pęcherzykowej (bubbly cavitation model - BCM) oraz rozerwania słupa cieczy (column separation model - CSM).
11
Content available Hydraulic transients analysis in pipe networks by the method of characteristics (MOC)
Wichowski R.
Archives of Hydro-Engineering and Environmental Mechanics
|
2006
|
Vol. 53, nr 3
267-291
EN
The paper presents results of an experimental and theoretical study of the hydraulic transients in straight pipes and numerical simulations of unsteady flow in pipe networks. A mathematical model consists of a set of partial differential equations of hyperbolic type, which have been transformed by the method of characteristics into ordinary differential equations which are solved by the predictor-corrector method. Experimental tests have been performed, in order to examine the hydraulic transients phenomenon, in a single straight steel pipe. The experiments were carried out in the hydraulic laboratory of the Institute of Water Supply and Water Engineering, Environmental Engineering Faculty, Warsaw University of Technology. The numerical results show that the presented one dimensional model for a single pipe correctly describes the phenomenon since there is a good agreement with experimental maximum and minimum oscillations. In the paper, selected exemplary equations in a difference form for the pipe networks are also presented. One calculation example is given relating to the complex water-pipe network consisting of 17 loops, 48 pipelines and 33 nodes, supplied by two independent sources. Water-hammer throughout the whole pipeline network was caused by closing the gate valve at mid-point of one selected pipe. The results of the numerical calculations are presented in graphic form with respect to the final cross-sections of pipes.
12
Content available Simulation and discretization of random field in the slip-line method
Przewłócki J.
Archives of Hydro-Engineering and Environmental Mechanics
|
2003
|
Vol. 50, nr 4
343-358
EN
The paper deals with the problem of bearing capacity of a strip footing based on the random subsoil. The solution has been obtained in a framework of the slip-line method. In order to include randomness of the soil medium, a modification of the method of characteristics is proposed. In such an approach, the stochastic finite difference method based on the Monte Carlo technique has been adopted. It enables including a spatial variability of soil properties into the analysis and to determine its influence on the variance of the ultimate collapse load. It is assumed that the soil medium is purely cohesive and only its cohesion can be considered as a random field. The simulation algorithm of multi-dimensional random field, based on the diagonalisation of the covariance matrix by a transformation using a lower-triangle matrix is described. The problems of the medium discretization and stabilization of the solution are discussed.
13
Content available remote A variant of the method of characteristics
Šavar M., Virag Z., Korbar R.
Computer Assisted Mechanics and Engineering Sciences
|
2002
|
Vol. 9, No. 4
543-553
EN
A variant of the method of characteristics for hyperbolic conservation laws is proposed in this paper. It is based on the time interpolation instead of space interpolation as in the standard method of characteristics. A new method for calculating the propagation velocity is proposed as well. The numerical results of some presented typical tests indicate that algorithm is very accurate.
14
Content available remote Numeryczna analiza osiowo-symetrycznych procesów wyciskania przeciwbieżnego z wykorzystaniem metody charakterystyk
Siemieniuk M.
Zeszyty Naukowe Politechniki Białostockiej. Mechanika
|
1999
|
Z.21
109-125
PL
W pracy przedstawiono analizę osiowo-symetrycznych procesów wyciskania przeciwbieżnego przy użyciu stempli o czole płaskim, kulistym oraz stożkowym. Analizę przeprowadzono metodą charakterystyk, przy założeniu modelu materiału sztywno-idealnie plastycznego z warunkiem plastyczności Treski oraz postulatu pełnej plastyczności Haara-Karmana.
EN
In the present work axi-symmetric backward extrusion processes using flat, spherical and conical stamps have been analyzed. The analysis has been carried out using the method of characteristics under assumptions of rigid-perfectly plastic material model with Tresca yield condition and the Haar-Karman hypothesis of full plasticity.
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