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PL
W artykule przedstawione zostały wyniki symulacji numerycznych przedmuchiwania ciekłej stali argonem podczas obróbki ciekłej stali na stanowisku pieca kadziowego (PK). Symulacje przeprowadzono przy użyciu kodu komercyjnego ANSYS Fluent. Analizę złożonego zagadnienia, jakim jest przepływ dwufazowy dla płynów o znacznej różnicy gęstości (gaz−ciecz), przeprowadzono z wykorzystaniem trzech dostępnych w kodzie ANSYS Fluent modeli: Discrete Phase Model (DPM), Volume of Fluid (VOF) oraz Euler-Euler. W przypadku modelu DPM argon traktowany jest jako faza dyskretna, a równania ruchu opisane są w ujęciu Lagrange’a. Wyniki symulacji numerycznych uzyskanych z wykorzystaniem modeli DPM oraz VOF wykazują podobieństwo w analizowanych wielkościach dla przedstawionych chwil czasu. Zupełnie odmienne wyniki uzyskane zostały z wykorzystaniem metody Euler-Euler. Ponadto model Euler-Euler charakteryzowało niestabilne rozwiązanie.
EN
Article presents results of numerical simulation of argon injection to the liquid steel in the ladle furnance. Simulations were performed using ANSYS Fluent commercial code. Analysis of the complex problem of two-phase flow for high density difference liquids (gas-liquid steel) were carried out using three available ANSYS Fluent models: Discrete Phase Model (DPM), Volume of Fluid (VOF) and Euler-Euler. For DPM model, argon is treated as a discrete phase, and the motion equations are described in terms of Lagrange frame. Numerical results obtained using DPM and VOF models show similarity in the analyzed quantities for the presented time periods. Quite different results were obtained using the Euler-Euler method. In addition, results obtained with Euler-Euler model showed unstable solution.
EN
Thermal processes in domain of thin metal film subjected to a strong laser pulse are discussed. The heating of domain considered causes the melting and next (after the end of beam impact) the resolidification of metal superficial layer. The laser action (a time dependent bell-type function) is taken into account by the introduction of internal heat source in the energy equation describing the heat transfer in domain of metal film. Taking into account the extremely short duration, extreme temperature gradients and very small geometrical dimensions of the domain considered, the mathematical model of the process is based on the dual phase lag equation supplemented by the suitable boundary-initial conditions. To model the phase transitions the artificial mushy zone is introduced. At the stage of numerical modeling the Control Volume Method is used. The examples of computations are also presented.
EN
Heating process in the domain of thin metal film subjected to a strong laser pulse are discussed. The mathematical model of the process considered is based on the dual-phase-lag equation (DPLE) which results from the generalized form of the Fourier law. This approach is, first of all, used in the case of micro-scale heat transfer problems (the extremely short duration, extreme temperature gradients and very small geometrical dimensions of the domain considered). The external heating (a laser action) is substituted by the introduction of internal heat source to the DPLE. To model the melting process in domain of pure metal (chromium) the approach basing on the artificial mushy zone introduction is used and the main goal of investigation is the verification of influence of the artificial mushy zone ‘width’ on the results of melting modeling. At the stage of numerical modeling the author’s version of the Control Volume Method is used. In the final part of the paper the examples of computations and conclusions are presented.
EN
Solid-state polycondensation (SSP) is a competitive method of semicrystalline polymers synthesis to conventional melt polycondensation process. The molecular weight of polymers obtained according to this method is exceptionally high and the process can be carried out under milder conditions than those of the melt state. In this method the side reactions are suppressed, especially those leading to the polymer degradation. In this paper, which is a continuation of our previous publication, application of the SSP method to obtain high molecular weight poly(lactic acid) (PLA) and poly(glycolic acid) (PGA) — polymers of high importance for medicine and environmental protection — is presented and discussed. The two-phase model according to which polycondensation proceeds in the amorphous regions, and the apparatus usually used in this process are also described.
PL
Polikondensacja w stanie stałym (ang. solid-state polycondensation, SSP) jest konkurencyjną metodą syntezy polimerów semikrystalicznych w stosunku do tradycyjnej polikondensacji prowadzonej w stopie. Za jej pomocą można otrzymywać polimery o dużym ciężarze cząsteczkowym w łagodniejszych warunkach w stosunku do metody w stopie, co skutkuje ograniczeniem reakcji ubocznych prowadzących do degradacji polimeru. W niniejszej pracy omówiono otrzymywanie metodą SSP wielkocząsteczkowego poli(kwasu mlekowego) (PLA) oraz poli(kwasu glikolowego) (PGA) — polimerów o rosnącym znaczeniu w kontekście ochrony środowiska naturalnego i zastosowań w medycynie. Polikondensacja w stanie stałym zachodzi według modelu dwufazowego. Reakcja między grupami końcowymi łańcuchów zachodzi w fazie amorficznej częściowo krystalicznego polimeru, a powstające produkty uboczne są usuwane z fazy amorficznej dzięki zastosowaniu przepływu gazu obojętnego lub obniżonego ciśnienia. Opisano również aparaturę jaka jest najczęściej wykorzystywana w tym procesie.
EN
Current work investigates influence of operating parameters on chemical reactions occuring within two-phase reacting flow. This particular flow analysed, corresponds to processes in coal gasifier unit supplied in heat by a high temperature gas cooled nuclear reactor (HTGR). Due to the fact that gasification is a complex process, in which multiphase mixture undergoes chemical reactions, it crucial to answer questions about sensitivity to parameters changes. Performed analysis was dedicated to answer question about the optimal flow parameters. Controll of flow patern, namely the swirl of coal-oxygen mixture traversing the gasifier domain, allowed creating efficiency curve, relating gas composition with non-axial component of the velocity vector. Using numerical model of the process, numbers of simulations were run in order to determine operation point yielding the highest efficiency, defined as a ratio of higher heating values of a syngas product of gasification process and coal feed into the unit. Obtained results concerning the most favorable operating parameters can be valuable information of evaluation of such gasification system from the economical point of view. Created tool can be used to study the system performance for various types of coal-fed.
EN
Generalization of Fourier law, in particular the introduction of two ‘delay times’ (relaxation time τq and thermalization time τT) leads to the new form of energy equation called the dual-phase-lag model (DPLM). This equation should be applied in a case of microscale heat transfer modeling. In particular, DPLM constitutes a good approximation of thermal processes which are characterized by extremely short duration (e.g. ultrafast laser pulse), extreme temperature gradients and geometrical features of domain considered (e.g. thin metal film). The aim of considerations presented in this paper is the identification of two above mentioned positive constants τq, τT. They correspond to the relaxation time, which is the mean time for electrons to change their energy states and the thermalization time, which is the mean time required for electrons and lattice to reach equilibrium. In this paper the DPLM equation is applied for analysis of thermal processes proceeding in a thin metal film subjected to a laser beam. At the stage of computations connected with the identification problem solution the evolutionary algorithms are used. To solve the problem the additional information concerning the transient temperature distribution on a metal film surface is assumed to be known.
7
Content available remote Herschel - Bulkley model for two-phase blood flow in narrow vessel
EN
A mathematical model for a two-phase blood flow through a circular narrow vessel has been developed by considering blood to be a non-Newtonian liquid of Herschel-Bulkley type and taking into consideration the slip velocity at the wall of the vessel. Analytical expressions for velocities of blood in the peripheral layer and central core layer, flow rate and apparent fluidity of blood have been obtained and their natures are portrayed graphically for different parameters.
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