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1
Content available Application of the Alternating Direction Implicit Method for numerical solution of the dual phase lag equation
Ciesielski M.
Journal of Theoretical and Applied Mechanics
|
2017
|
Vol. 55 nr 3
839—852
EN
The problem discussed in the paper concerns the numerical modeling of thermal processes proceeding in micro-scale described using the Dual Phase Lag Model (DPLM) in which the relaxation and thermalization time appear. The cylindrical domain of a thin metal film subjected to a strong laser pulse beam is considered. The laser action is taken into account by the introduction of an internal heat source in the energy equation. At the stage of numerical modeling, the Control Volume Method is used and adapted to resolve the hyperbolic partial differential equation. In particular, the Alternating Direction Implicit (ADI) method for DPLM is presented and discussed. The examples of computations are also presented.
2
Content available Sensitivity of transient temperature field in domain of forearm insulated by protective clothing with respect to perturbations of external boundary heat flux
Mochnacki B., Ciesielski M.
Bulletin of the Polish Academy of Sciences. Technical Sciences
|
2016
|
Vol. 64, nr 3
591--598
EN
The problem discussed in the paper is numerical modeling of thermal processes in the domain of biological tissue secured by a layer of protective clothing being in thermal contact with the environment. The cross-section of the forearm (2D problem) is treated as non-homogeneous domain in which the sub-domains of skin tissue, fat, muscle and bone are distinguished. The air gap between skin tissue and protective clothing is taken into account. The process of external heating is determined by Robin boundary condition and sensitivity analysis with respect to the perturbations of heat transfer coefficient and ambient temperature is also discussed. Both the basic boundary-initial problem and the sensitivity problems are solved by means of control volume method using Voronoi polygons.
3
Content available Dual Phase Lag Model of Melting Process in Domain of Metal Film Subjected to an External Heat Flux
Mochnacki B., Ciesielski M.
Archives of Foundry Engineering
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2016
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Vol. 16, iss. 4
85--90
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.
4
Content available Numerical simulation of the heating process in the domain of tissue insulated by protective clothing
Ciesielski M., Mochnacki B.
Journal of Applied Mathematics and Computational Mechanics
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2014
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Vol. 13, nr 2
13--20
EN
In this paper the 2D heterogeneous tissue domain (forearm cross-section) insulated by a layer of protective clothing is considered. The aim of considerations is to develop an algorithm simulating the tissue heating process resulting from the sudden change of external boundary conditions. Here, the authors exploit a certain version of the control volume method (CVM) using the Voronoi tessellation. The mathematical model of heat exchange in the domain analyzed is formulated in the form of a boundary-initial problem based on the system of partial differential equations (energy equations) supplemented by the adequate boundary and initial conditions. In the final part of the paper, the examples of numerical simulations are shown.
5
Content available Application of the control volume method in numerical modeling of cryosurgery treatment
Szopa R., Siedlecki J.
Journal of Applied Mathematics and Computational Mechanics
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2014
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Vol. 13, nr 4
131--136
EN
In the paper the problems of cryosurgery treatment are discussed. In particular the heat exchange between external cylindrical cryoprobe and human tissue is analyzed. The cryoprobe tip temperature changes from the initial temperature to the minimal one and back in a linear way (broken line). Thermophysical parameters determining the thermal properties of tissue can be treated as the temperature-dependent functions. The freezing model bases on the approach called ‘a one domain method’, and in the energy equation called a substitute thermal capacity appears. At the stage of computations the control volume method (CVM) is used. In the final part of paper the examples of computations are presented.
6
Content available Numerical model of solidification of cast composite with particles
Ciesielski M., Domański Z., Mochnacki B.
Civil and Environmental Engineering Reports
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2010
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No. 5
123-132
EN
In the paper the numerical model of heat transfer in non-homogeneous domain (cast composite) is considered. The composite is formed by the spherical particles (Pb) and the metal matrix (Al). Initial temperatures of components correspond to solid state (particle) and liquid one (matrix). The heat is transferred from the aluminum matrix and absorbed by the lead particle. The 3D problem, i.e. the cubic control volume with single spherical particle located at the center part of the cube, is considered. A numerical algorithm corresponding to the discussed mathematical model of the boundary-initial problem is constructed on the basis of control volume method and some examples of numerical results are shown.
PL
Praca dotyczy wymiany ciepła pomiędzy osnową i cząstkami tworzącymi materiał kompozytowy. W szczególności rozpatrywana jest objętość kontrolna (Al) w kształcie sześcianu, w którego środku umieszczona zostaje cząstka (Pb). Wymiary rozpatrywanej objętości kontrolnej zależą od gęstości cząstek wprowadzonych do osnowy. Założono, że objętość kontrolna umieszczona jest w centralnej części odlewanego kompozytu oraz, że warunki brzegowe zadane na powierzchni odlewu i formy nie wpływają na procesy cieplne w tej objętości. Oznacza to, że warunki przyjęte na powierzchniach granicznych sześcianu to warunki adiabatyczne. Równania różniczkowe i warunki brzegowe zapisano w konwencji entalpowej zakładając, że krzepnięcie osnowy i topnienie cząstek zachodzą w stałej temperaturze. Rozpatrywaną objętość kontrolną dzielono na 503 sześcianów. Do obliczeń numerycznych wykorzystano metodę bilansów elementarnych, przyjmując że pola temperatur w ciekłej osnowie i cząstce ołowianej są znane w chwili początkowej oraz, że kontakt między podobszarami układu jest idealny. W trakcie procesu obserwowano topnienie cząstki ołowianej i stygnięcie osnowy. W pracy przedstawiono wyniki symulacji numerycznych w postaci krzywych nagrzewania i stygnięcia w wybranych punktach obszarów, jak również przebieg izoterm w przekroju kompozytu dla kilku wybranych czasów. Ponadto zbadano wpływ zmian udziału objętościowego cząstki w osnowie na przebieg procesu wymiany ciepła.
7
Content available The analysis of gradient algorithm effectiveness - two dimensional heat transfer problem
Łopata S., Ocłoń P.
Archives of Thermodynamics
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2010
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Vol. 31, no. 4
37-50
EN
The analysis of effectiveness of the gradient algorithm for the two-dimension steady state heat transfer problems is being performed. The three gradient algorithms - the BCG (biconjugate gradient algorithm), the BICGSTAB (biconjugate gradient stabilized algorithm), and the CGS (conjugate gradient squared algorithm) are implemented in a computer code. Because the first type boundary conditions are imposed, it is possible to compare the results with the analytical solution. Computations are carried out for different numerical grid densities. Therefore it is possible to investigate how the grid density influences the efficiency of the gradient algorithms. The total computational time, residual drop and the iteration time for the gradient algorithms are additionally compared with the performance of the SOR (successive over-relaxation) method.
8
Content available remote Identification of thermal properties of solids by means of inverse hybrid method and measurement data
Kucypera S.
Archives of Thermodynamics
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2008
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Vol. 29, no. 4
73-86
EN
The aim of the paper is to combine the Levenberg-Marquardt method, optimal dynamic filtration method and measurement data for the simultaneous identification of the thermal properties or their temperature characteristics of anisotropic solids. The idea of the proposed method depends on measuring the time-dependent temperature distribution at selected points of the sample and identification of the thermal parameters (heat conductivity and specific heat) by solving a transient inverse heat conduction problem. To obtain the optimal experiment the series tests have been carried out by means of numerical simulations. The investigated system which was used for the identification of thermal parameters consists of two cylindrical samples, in which transient temperature field is forced by the electric heater located between them. The temperature response of the system is measured in the chosen point of the sample. Two dimensional discrete mathematical model of the transient heat conduction within the investigated sample has been formulated basing on the control volume method. The hybrid method as solution of inverse problem has been applied to identify unknown parameters. The chosen results have been presented in the paper.
9
Thermal model of stirling engine with using the control volumes method
Sikora M., Vlach R.
Modelling and Optimization of Physical Systems
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2007
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z. 6
137--142
EN
The enough precise numerical model of Stirling engine is necessary for design and optimalization of this engine. The most important and also most problematic is the thermal part of this model. The thermal processes have dominant effect to output power and efficiency. We are able to determine the temperatures in engine individual parts by using the thermal networks methods and control volumes method. It improves the accuracy of model.
10
Content available remote Application of Thiessen polygons in control volume model of solidification
Mochnacki B., Ciesielski M.
Journal of Achievements in Materials and Manufacturing Engineering
|
2007
|
Vol. 23, nr 2
75-78
EN
Purpose: In the paper the possibilities of Thiessen polygons (THP) application in numerical modelling of solidification process are presented. The control volumes of THP shapes (2D task is considered) are very convenient both for the construction of effective and exact control volume method algorithm and allow in simple way to approximate the real shape of domain considered. Additionally the positions of CV central points can be selected in a optional way. Design/methodology/approach: The control volume method algorithm bases of the energy balances for successive CV. They are constructed under the assumption that the boundary-initial problem considered is non-linear and the evolution of latent heat is taken into account using the one domain approach (the substitute thermal capacity of material is introduced). Findings: The method here presented allows to determine the transient temperature field in a non-homogeneous system casting-mould and to observe the course of casting solidification. The local cooling (heating) curves can be found at the optional set of points from the casting-mould system. The heat transfer model can be additionally supplemented by the model concerning the macrosegregation process. Practical implications: The control volume method in a version presented in this paper can be an effective numerical tool both on the stage of foundry technologies design and also in the case of existing technologies analysis. Originality/value: The coupling of the concept of Thiessen polygons application for 2D domain dicretization with the control volume method approach seems to be the original achievement of the authors of this paper.
11
Content available remote Identification of thermal properties of solids by means of solving the inverse problem using evolutionary algorithms and optimal dynamic filtration
Kucypera S.
Computer Assisted Mechanics and Engineering Sciences
|
2007
|
Vol. 14, No. 4
665-672
EN
The aim of the paper is to combine the evolutionary algorithms method, optimal dynamic filtration method and measurement data for the simultaneous identification of the thermal properties or their temperature characteristics of anisotropic solids. The idea of the proposed method depends on measuring the time-dependent temperature distribution at selected points of the sample and identification of the thermal parameters (heat conductivity and specific heat) by solving a transient inverse heat conduction problem. In the paper the discrete mathematical model has been formulated basing on the control volume method. The inverse problem was solved by using a hybrid method. Information about measurement data which are necessary to solve the inverse heat conduction problem was obtained by solving the direct heat conduction problem. The chosen results of analysis have been presented.
12
Content available remote The parametric sensitivity analysis of solidification process
Szopa R.
Archiwum Odlewnictwa
|
2005
|
R. 5, nr 15
397--404
EN
In the paper the new results concerning the application of sensitivity analysis in the numerical modelling of solidification process is presented. This approach allows to investigate the influence of external conditions (thermophysical parameters of the mould, pouring temperature, initial mould temperature etc.) on the course of casting solidification. The model of thermal processes proceeding in the casting domain can be constructed both in the macro scale (the I generation model) and in the macro/micro scale (the II generation model). As an example of the macro approach the continuous casting technology is considered and the sensitivity with respect to the substitute heat transfer coefficient in the continuous casting mould region is analyzed. In the second part of the paper the macro/micro model is introduced and the similar problem is solved again.
PL
W pracy przedstawiono wyniki badań dotyczących wykorzystania metod analizy wrażliwości w numerycznym modelowaniu procesu krzepnięcia. Takie podejście pozwala badać wpływ zaburzeń parametrów procesu (parametrów termofizycznych, temperatury zalewania, temperatury początkowej masy formierskiej itd.) na przebieg analizowanego procesu. Model procesów cieplnych zachodzących w krzepnącym odlewie może być formułowany zarówno w skali makro (modele I generacji), jak i makro/mikro (modele II generacji). Jako przykład zastosowań wykorzystano analizę wrażliwości procesu ciągłego odlewania stali na zmiany zastępczego współczynnika wymiany ciepła (model opisany w konwencji makro) oraz podobny problem dla wlewka aluminiowego (model II generacji). Na etapie obliczeń wykorzystano metodę bilansów elementarnych.
13
Construction of differential quotients using the control volume method
Lara S., Pawlak E.
Zeszyty Naukowe. Mechanika / Politechnika Opolska
|
2004
|
z. 78
221-224
EN
In the paper the control volume method is applied for the construction of differential quotients approximating the operator (delta2 T) being a typical component appearing in the well known diffusion equation (2D problem is discussed). It turned out that for non-typical differential meshes it is possible to find the form of (delta2 T) approximation using the equations resulting from the control volume method (CVM) [1]. The results obtained in this scope will be below presented.
14
Content available remote The influence of mould parameters on the casting solidification
Szopa R., Siedlecki J.
Archiwum Odlewnictwa
|
2004
|
R. 4, nr 14
520-525
EN
In the paper the methods of sensitivity analysis are applied for the estimation of the influence of mould parameters on the course of thermal processes proceeding in the system casting-mould. The mathematical considerations concern the non-homogeneous domain and on the contact surface the continuity of temperature and the continuity of heat flux are assumed. The sensitivity model with respect to [&LambdaM] and [CM] (thermal conductivity and volumetric specific heat of mould) has been constructed using the direct approach. On the stage of computations the control volume method has been applied [1]. In the final part of the paper the simple example of numerical simulation is shown.
PL
W pracy wykorzystano metody analizy wrażliwości do badania wpływu parametrów formy odlewniczej (współczynnika przewodzenia i ciepła właściwego) na przebieg procesów cieplnych w układzie odlew-forma-otoczenie. Na etapie obliczeń numerycznych wykorzystano metodę bilansów elementarnych.
15
Content available remote Numerical model of axially-symmetrical casting solidification. Part l
Ciesielski M., Mochnacki B., Suchy J. S.
Archiwum Odlewnictwa
|
2004
|
R. 4, nr 14
110-113
EN
In the paper the control volume method is applied for numerical modelling of thermal processes proceeding in the solidifying axiaIly symmetrical casting. The problem is treated as the non-linear one and the temperature-dependent thermophysical parameters of casting and mould materials are introduced. It is assumed that the solidification proceeds at the temperature T_L corresponding to the beginning of the process, but the temporary value of T_L results from the macrosegregation model (in the final stages of casting solidification it can be equal to T_e, this means the eutectic temperature). In the first part of the paper the balance equations for the control volumes in the shape of the Thiessen polygons will be presented.
PL
W pracy przedstawiono algorytm wykorzystujący metodę bilansów elementarnych do modelowania procesów cieplnych w krzepnącym odlewie. Uwzględniono nieliniowości w opisie matematycznym procesu, czyli zmieniające się z temperaturą wartości parametrów termofizycznych odlewu i formy. Uwzględniono również zmianę temperatury początku krzepnięcia wynikającą ze zmiany składu chemicznego stopu.
16
Content available remote Numerical model of axially-symmetrical casting solidification. Part 2
Ciesielski M., Mochnacki B., Suchy J. S.
Archiwum Odlewnictwa
|
2004
|
R. 4, nr 14
114-119
EN
In the paper [1] the theoretical considerations concerning the application of controI volume method for numerical modelling of thermal processes proceeding in the solidifying casting are presented. In particular, the formulas resulting from balance equations for the control volumes in the shape of the Thiessen polygons are collected. Here, the results of numerical simulations concerning the axially-symmetrical casting solidification will be shown. The computer program worked out by the authors cab be useful for computations of thermal processes proceeding in the 2D objects, for example the domains oriented in the cylindrical co-ordinate system {r, z}.
PL
W pracy przedstawiono wyniki obliczeń programu wykorzystującego metodę bilansów elementarnych do modelowania procesów cieplnych w krzepnącym odlewie. W szczególności rozpatrywano obszar o geometrii osiowo-symetrycznej. Przekroje poprzeczne objętości kontrolnych (pierścieni) mają kształt wieloboków Thiessena (w szczególnym przypadku - prostokątów). Uwzględniono nieliniowości w opisie matematycznym procesu, czyli zmieniające się z temperaturą wartości parametrów termofizycznych odlewu i formy. Uwzględniono również zmianę temperatury początku krzepnięcia wynikającą ze zmiany składu chemicznego (makrosegregacja).
17
Content available remote Micro/macro model of solidification using the control volume method
Mochnacki B., Ciesielski M.
Archiwum Odlewnictwa
|
2002
|
R. 2, nr 4
161--166
EN
In the paper the control volume method is applied for numerical modelling of thermal processes proceeding in the solidifying casting. The model belongs to the group of the 2nd generation ones (the micro/macro approach). The domain considered is covered by the mesh of control volumes. The control volumes correspond to the final shape of grains, while their central points to the position of crystal nuclei. The numerical model of crystallization process bases on the control volume method (CVM). In the final part of the paper the example of computations is shown.
PL
W pracy przedstawiono algorytm wykorzystujący metodę bilansów elementarnych do modelowania procesów cieplnych w krzepnącym odlewie. Model należy do tzw. modeli II generacji (podejście mikro/makro). Rozważany obszar pokryto siatką objętości kontrolnych, których kształt odpowiada końcowemu kształtowi ziaren, natomiast punkty centralne tych objętości odpowiadają położeniu zarodków krystalizacji. Algorytm numeryczny bazuje na pewnej odmianie metody bilansów. W końcowej części pracy zamieszczono przykład obliczeń numerycznych.
18
Content available remote Modelling of solidification using the control volume method
Szopa R., Siedlecki J.
Krzepnięcie Metali i Stopów
|
2000
|
R. 2, nr 44
349--354
EN
In the paper the control volume method is applied for numerical modelling of thermal processes proceeding in the system casting-mould. In particular, the oblique hot spot of L type (α=60º) is considered. The control volumes in the shape of equilateral triangles (2D problem is considered) are introduced. The balance equations concern the solidification of pure metal (e.g. aluminium). In the final part the example of computations is shown.
PL
W pracy przedstawiono algorytm metody bilansów (metody objętości kontrolnych) przystosowany do modelowania krzepnięcia odlewów, a w szczególności węzła cieplnego typu L o kącie rozwarcia 60º. Obszar podzielono na objętości kontrolne w kształcie trójkątów równobocznych (zadanie 2D), podano równania bilansów dla etapów stygnięcia i krzepnięcia. Pokazano przykład realizacji numerycznej (odlew aluminiowy).
19
Content available remote Determination of surface conditions from internal temperature measurement at selected points
Al-Khalidy N., Skorek J.
Bulletin of the Polish Academy of Sciences. Technical Sciences
|
1998
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Vol. 46, nr 1
73-84
EN
This paper examines the accuracy of a space marching formulation for solving two-dimensional inverse heat conduction problems. The parameters that have a major influence on the solution such as time step size, measurement errors and Biot number are investigated. The temperature and heat flux on the surface of a body are estimated on the base of the temperature measurement at a number of sensors located inside the body. The initial condition is assumed to be unknown. The solution is presented in terms of temperature data and their derivatives with respect to time.
20
Content available remote A control volume formulation of III posed inverse heat conduction problems
Al-Khalidy N.
Bulletin of the Polish Academy of Sciences. Technical Sciences
|
1998
|
Vol. 46, nr 1
61-72
EN
An inverse control volume code is developed for the study of transient boundary inverse heat conduction problems. A nonlinear numerical formulation of the Weber method is extended to relatively high noisy input data. The control volume method is combined with a digital filter method for solving the hyperbolic approximation of the inverse heat conduction problems. The results show that such combination allows to obtain more accurate results. This proposed solution method can be used to estimate the boundary conditions basing on the temperature history at an interior point inside the body. The accuracy of the method is verified by comparison with the analytical (exact) solution of a direct problem.
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