(60-68) thermal-electromagnetic coupled system simulator using transmission-line matrix (tlm)

8/3/2019 (60-68) Thermal-Electromagnetic Coupled System Simulator Using Transmission-Line Matrix (TLM)

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Thermal-Electromagnetic Coupled System Simulator Using

Transmission-Line Matrix (TLM)

Hugo Fernando Maia Milan* Carlos Alberto Tenório de Carvalho Júnior Ciro José Egoavil

Electrical Engineering Department Electrical Engineering Department Electrical Engineering Department

Federal University of Rondonia Federal University of Rondonia Federal University of Rondonia

Porto Velho, Brazil Porto Velho, Brazil Porto Velho, Brazil

[email protected] [email protected] [email protected]

Carolina Yuakari Veludo Watanabe Cícero Hildenberg de Lima Oliveira Rogério Marcos da Silva

Computer Science Department Electrical Engineering Department Electrical Engineering Department

Federal University of Rondonia Federal University of Rondonia Federal University of Rondonia

Porto Velho, Brazil Porto Velho, Brazil Porto Velho, [email protected] [email protected] [email protected]

Abstract: The advancement of hardware and software to computers makes possible a faster processing. With this

technology, many researchers may develop numerical models about their study to test in computer, saving time and

resources. About numerical simulation in time domain, has the Transmission-Line Matrix (TLM) method that uses an

analogy of transmission lines to solve the differential equation of system in analysis through a relation between the

differential equation problems and arrangement of nodes. There are many nodes scheme to model different physical

parameters, such as electromagnetic, thermal, Pennes’ equation, particle diffusion, acoustic, elastic solids, Schrödinger-

Maxwell Equation, deformation, hydraulic systems, fluid mechanics, and so on. This work presents a basic theory about

TLM to electromagnetic, thermal and coupled electromagnetic-thermal system. Furthermore we present the SimEMTher

free software that solves these problems and shows a few applications of simulations in the industry and health.

Key word: TLM Transmission-Line Matrix Coupled Electromagnetic Thermal

I. INTRODUCTION

The use of the electromagnetic (EM) technology such as Wi-Fi, WiMAX, cellular phones, hyperthermia applications, ablation,nanotechnology, brings a great advantage for the man. With Wi-Fi or WiMAX it is possible to transfer faster data to work withcomputers with access in internet without the necessity of many wires, etc. Other EM applications are hyperthermia and ablation(that use the EM to thermal sources that are scattered with diffusion equation), which has been making possible treat tumor [1] andarrhythmias [2].

In the thermal study, the thermal comfort at humans and animals has been researched. For humans it is important to know thethermal comfort in vehicles [3] to get well-being in travels, such as in flying. Several researchers have used the numericalinvestigation [4] and proposing models for human thermoregulation and thermal sensations [5]. In animals, the major interest is

improving the production, avoiding the animal stress caused by the temperature.It is known that the Maxwell equations and the diffusion equation are differential. The analytical resolution of differential

equations in complex system is sometimes impossible. However, with the great evolution of computer hardware technology (suchas memory and time processing), the use of numerical methods to approximation results of differential equations in complex systemis becoming more widespread.

The Finite Difference Time Domain (FDTD) [6-8], Finite Element Method (FEM) [8-10], Moment Method (MoM) [8], MonteCarlo Method (MCM) [8, 11] and Transmission-Line Matrix Method (TLM) [8, 12-15] are some methods that are used to simulateEM and diffusion problems.

To development some prototypes, many circuits are tested and rebuilt. That is because during the test phase it is verified if thesystem is EM incompatible or if there are regions with large thermal gradient. However, when the circuit is pre-tested in a simulatorof EM, thermal or both, the chance of the prototype to be EM compatible and having a good thermal gradient in many regions isincreased. With this technique, the manufacturer does not expend recourses in creation of many mismatched prototypes and may

save time and money. In simulators of industry applications, it is possible to use a coupled thermal and electromagnetic model to

World Applied Programming, Vol (2), Issue (1), January 2012. 60-68Special section for proceeding of International e-Conference on Computer Engineering (IeCCE) 2012

ISSN: 2222-2510

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estimate the thermal effect due to the microwave curing of epoxy [16], to utilize a thermal-electromagnetic coupled system toestimate temperature increase in power transformers [17], to analyze the temperature behavior in magnetic shields fromelectromagnetic losses and thermal radiation with a coupled system [18] and so on.

The investigation of the biological effects caused by EM field, thermal or both, can be better understood using simulation. Forinstance, in a surgical using ablation or hyperthermia for treat tumor or cancer, it is possible to develop antennas to transmit the EMenergy in a specific case, because the characteristics of tissue and tumor or cancer dependent on many parameters such asgeometry, death temperature and some others response of body patient. Moreover, in a simulation it is possible to visualize thescatter of EM field, which is distributed in the body temperature and choose the ideal intensity, frequency and shape for the wave toimprove patient safety. Other characteristics of scientific interest are the direct effects of EM energy in biosystems. In thetemperature analysis it is possible to verify the scatter temperature to investigate damage in tissues and improve technics fortreatment of carcinomas.

For example, in [19] it is analyzed some shapes of hyperthermia applicator using simulation. The temperature distributionduring a ferromagnetic hyperthermia under the influence of blood flow is analyzed by [20] and compared with an experiment (withgood agreement). In the work [21] is analyzed the EM scattering in a head proving of cellular phones for estimate the specificabsorption rate (SAR). Bellia et al. [22] used a model of skin human to investigate the damage in thermal studies. Amri et al. [23]using a thermal model to investigate the temperature propagation in a human breast with an embedded tumor discovered that thetemperature gradient regulated by the body is changed with the presence of a tumor. In coupled system of electromagnetic-thermalanalysis to biosystem, [24, 25] simulated the induced temperature in a human eye and head in response to an implanted retinalstimulator. [26] estimated the temperature induced in a pig heart using an microwave ablation antenna with water-cooled and testedthe system in vitro pig heart with correspondent results and in [27] is simulated an estimation of heating in a duct bile to treatmentof a carcinoma using hyperthermia.

Finally, we can observe that the numerical analysis show interesting results of the real world. With this approaches, the systemscan improve the production process and analysis. In this way, with a faster simulator tool to EM problems, thermal diffusion andcoupled, with general use, easy manipulation and with a minimal knowledge about the theory of the numerical methods, the endedresults may be speed up. This is the beginnings of our simulator, SimEMTher v.1.06b (free software).

This paper is organized as follows: In section I, we show a basic introduction of the benefits of EM and thermal knowledge,about the methods for simulation and industrial and health simulation application; in section II it is treated about the TLM theory toEM, thermal and coupled systems. The results are showed in section III that have pictures about SimEMTher. Finally, in section IVit says the work conclusions.

II. BASIC THEORY ABOUT TRANSMISSION-LINE MATRIX METHOD

The optic theory of Isaac Newton (1643-1727) and Christian Huygens (1629-1695) are known as two different points of view

of light and its phenomenon. Newton associated the light to a conception corpuscular. However, Huygens said that the light is a

wave spread by a material medium. Huygens explained the effect of rectilinear propagation, refraction and reflection. Later,Fresnel improved the Huygens model, contributing to the base of the propagation model and problems dispersal involving

microwaves [28]. Huygens principles are the basic for the TLM theory.

In 1971 [29], Johns published a work that describe the TLM for problems solution in bi-dimensional scattering EM. Later,

papers wrote by Johns and Akhtarzad [28] and many researches improved the method, such three-dimensional, one-dimensional,

diakoptics, loss, graded mesh, uses in diffusion equations, algorithms for Laplace and Poisson equations, inverse problems,thermal diffusion, particle diffusion, mechanic problems, acoustic propagation, elastic solids, deformation models, hydraulic

systems, fluid mechanics, Schrödinger-Maxwell [14, 15, 30], and so on.

The TLM mesh is compound with an arrangement of transmission lines. It uses an analogy with a transmission line mesh to

discovery an isomorphic equation to the node (fig. 01) with differential equations of the problem. Thus, the propagation and

scattering of TLM is done through the transmission line theory.

To program the TLM is necessary a space discretization of medium. This is done through the node that has dimensions

oriented in the three axes ( ∆ x, ∆ y and ∆ z). In fig. 01, it can be seen a TLM node. This node is used for bi-dimensional EM

scattering in TM mode ( H x, H y and E z) [12]. The ports numbered make connection with other TLM node. The physicalrepresentation of the node are two transmission lines, one though x direction and other in y direction. Fig. 02 shows as the

connection with other nodes is made. The ports in fig. 02 are the same that is showed in figure 01. For example, in node (x,y): the

port 1 is connected with port 3 in node (x,y – 1), port 2 is connected with port 4 in node (x – 1,y), port 3 is connected with port 1in node (x,y + 1) and port 4 is connected with port 2 in node (x + 1,y).

The simulation time is discretized too. The correct choice of ∆t is based in the space discretization and the characteristic of

medium. In eq. 05 is showed how choice the appropriate ∆t to EM in TM mode. To thermal simulation is chosen ∆t ≤ λ/10 ( λ is

the wavelength of source).

At each port, there are an incident (V i) and reflected (V

r ) voltages. In all time-step it is necessary calculate the V i and V

r for the

processes of connection. The connection of time-step k to k + 1 is made by eq. 01:

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Hugo Fernando Maia Milan et al., World Applied Programming, Vol (2), No (1), January 2012.



Figure 1. Node utilized in TLM for TM propagation without loss. The elements

showed (inductors and capacitors) are inherited of the transmission line theory. The

ports numbered from 1-4 are connected with other node with similar configuration.

Figure 2. Nodes connection in TLM method with a mesh 3x3. The

figure show how is made the communication.

In that, the subscripts of impedances are 1 to impedance of the node (x,y) and 2 to the impedance of adjacent node.

The processes for calculate V r is done through the scatter matrix:

The voltages V r and V

i are in form of vectors of dimensional 4x1 and 5x1 to thermal and EM, respectively. The scatter matrix is

square matrix of dimensional 4 to thermal (eq. 08) and 5 to EM (eq. 07).

The boundaries are treated in a simple way in TLM. Imagine a pulse traveling through a transmission line. In a determined

instant, it sees a discontinuity and part of energy is reflected to the node and other is transmitted. It physical reaction is according

to eq. 03, which shows the reflected voltage equation. The Z B and Z TL mean the impedance of boundary and transmission line,

respectively [12].

Values of Z B are in function of the physical properties of boundary. If Z B = 0, ρ B = -1 in EM is equals electrical wall and heat-

sink for thermal. In other hand, if Z B = ∞, ρ B = 1 and we have magnetic wall and insulation boundary to EM and thermal,

respectively.

In fig. 03, it can be seen an example about the TLM mesh. This figure shows a mesh with dimensions (nodes) 10x10 and

detaches a node 8x4 as example. The thickest borders are the boundaries of simulation.

The diakoptics techniques consist in divide the mesh in minor meshes. The segmentation reduces the use of memory in

computer and makes possible the parallel simulation. In the software SimuEMThe, this mesh is segmented and simulate in

parallel. In the fig. 4 is showed the same mesh that appears in fig. 03, with diakoptics techniques.

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Figure 3. TLM mesh with 10x10 nodes. In detaches a node at position 8x4.

The darkest lines are the boundary of simulation. The number at left are theposition in axes y and the number at down are the position in axes x.

Figure 4. TLM mesh with 10x10 nodes with diakoptics technic with 3x3

subdomain. In detaches a subdomain 3x2 and the node 8x4. This mesh is thesame that appears in fig. 3.

To excite a mesh, is adopting the eq. 4. The constant F n is used to model the field of stimulation, with 1 ≤ n ≤ 4.

A. Transmission-Line Matrix to Electromagnetic

In bi-dimensional problems involving EM, there are the propagation in traverse magnetic (TM) mode, with H x, H y and E z, andtraverse electric (TE) mode, with E x, E y and H z. It will be explained about the basic theory of TM mode with loss and

heterogeneous medium. The complete theory about one-dimensional, bi-dimensional and three-dimensional can be found in [12].

For the TM node treatment it is used the model of shunt node [31] which is known as irregular mesh ( ∆ x≠

∆y≠

∆z ). Themodel of node is shows in fig. 05, where C T = C x + C y + C S. The additional port showed in the figure 5 (port 5) is used for treat

permittivity and conductivity.

The choice of ∆t follows the eq. 05. For choice de appropriate ∆t it is necessary analysis all points in the mesh and select the

minor value, which will be ∆t TLM .

√

To the connection process it is necessary an additional term in eq. 01. This addition term is necessary to model stub (port 5),

that considers conductivity and permittivity. This additional term is shown in eq. 06.

The scatter matrix to EM is shown in eq. 07. The value of variables that appears in eq. 07 and how to calculate the EM fields

( H x, H y and E z) are showed in table I.

[

( )]

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Figure 5. Model of node used in irregular mesh for heterogeneous medium. The ports are the same that appers in figure 4, with the additional port 5 that is used

to model permissivity and condutivity.

TABLE I. EQUATIONS WHICH ARE USED IN SCATTERING MATRIX SHOWED IN EQUATION 7 AND HOW TO CALCULATE THE ELECTROMAGNETIC FIELDS

*

+

( )

( )

( ) ( )

When is the electrical permittivity, is the electric conductivity and is the magnetic permeability. To stimulate the mesh, the user input a value and choice the field of excitation. In table II is shown the relation of the field of

excitation, the correction factor and the values of F n.

B. Transmission-Line Matrix to Thermal

The use of TLM in thermal is first explored by Johns and de Cogan [14]. For treatment of diffusion equations in two-

dimensional, has two models of nodes, the link-resistor and the link-line formulation. In the software, it is used the link-line

formulation with regular mesh. The theory of one-dimensional, bi-dimensional and three-dimensional models can be found in [14,

15]. Nodal model to thermal process is shown in fig. 06.

TABLE II. CONFIGURATION OF STIMULATION EM FIELDS, WITH THEIR CORRECTIONS FACTORS AND THE CONSTANT TO EACH PORT

Field Correction Factor Vector of Values of F n

Magnetic Field in x direction – Hx (A/m) [1 0 0 0]

Magnetic Field in y direction – Hy (A/m) [0 0 0 1]

Electric Field – Ez (V/m) [0.5 0.5 0.5 0.5]

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Figure 6. Node model used to thermal process in TLM. The ports are the same that appers in fig. 4.

The connection process in thermal is the same that the eq. 01. The choice of ∆t is depending of the excitation frequency and

need are minor that λ /10. The scatter matrix is shown in eq. 08. The terms that appear in eq. 08 are shown in eq. 09 and do the link

with the real world.

[

]

When is the thermal conductivity, is the density and is the specific Heat.

Temperature in thermal TLM is obtained with eq. 10.

In table III is shown how to excite the thermal TLM.

C. Transmission-Line Matrix to coupled

To model coupled system, it is necessary which the size and time-step of EM and thermal TLM mesh are the same. In coupledsystem, the EM is used with heat source. The heat source is adapted how is shown in eq. 11.

III. RESULTS

Knowing the theory of TLM in thermal and EM problems and that the effect of coupled system is adapted with a heat source

coming from EM, it was created one software that can connect the simulation to verify what is the temperature induced by the EM

field and the scattering of thermal or EM.

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TABLE III. CONFIGURATION OF STIMULATION FIELDS WITH THEIR CORRECTIONS FACTORS AND THE CONSTANT TO EACH PORT IN THERMAL TLM.

Field Correction Factor Values Vector of F n

Heat – Q (W) [0.5 0.5 0.5 0.5]

Temperature – T (K) [0.5 0.5 0.5 0.5]

The main problem to work in simulation is the memory processing. Under this problem, it is developed an algorithm that verify

how many RAM memory is necessary for simulation and how many memory have available for processing to segment the

simulation to work with fragments of simulation. With this fragment, the mesh is segmented in subdomains, with these

subdomains it is possible to realize parallel simulation depending on the condition of the computer.

The entrance variables are those characterize the medium. It is: mesh size, nodal size, source, time-steps, relative permittivity,

electrical conductivity (Ω/m), relative permeability, density (kg/m³ ), specific heat ( J/(kg.K )), thermal conductivity (W/(m.K )) and

initial iemperature (K ). The simplified flow chart of the software (SimEMThe v.1.06b) is shown in fig. 7.

Some pictures of the software SimEMThe v.1.06b are shown in fig. 8, 9, 10 and 11. In fig. 8, is showed the Initial Screen of the

software, which have link for all graphic interfaces and allow the user insert the quantity of time-step and chose the language

(English or Portuguese). The fig. 9 shows the Source Editor. In the source editor it is possible input all fields of interest ( H x, H y, E z

and heat) in the mesh with two standard antenna shapes (circular and rectangular) and four stimulation functions (sinusoidal,Gaussian, pulse and general wave).

Fig. 10 shows the graphic interface Simulate, which allows the user to select the field to simulate and save with the idea of

keep memory and increase speed. In fig. 11 is showed the interface Results that turns possible visualize the simulate fields in

interface Simulate. It is possible visualize nine forms of results (with dynamic and static results).

Figure 7. Simplified flow chart of the free software SimEMThe v.1.06b.

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Figure 8. Initial Screen. In this screen is possible chosen the language andthe time-step of simulation.

Figure 9. Source Editor of SimEMTher v.1.06b. This interface allow the userinput the fields of interest in the mesh.

Figure 10. Interface Simulte of SimEMThe v. 1.06b. In this interface, the

user chosen the fields to simulation and save.

Figure 11. Picture of the interface Results. This interface allow the user to chose

one in nine forms of results visualization.

IV. CONCLUSION AND DISCUSSION

It was seen in section I the importance of electromagnetic and thermal fields in the human’s life. It is showed that th e domainof EM technology has bringing improvement in industrial applications (curing epoxy [16] and analysis in power transformers

[17]) and health (hyperthermia [20] and ablation [27]).Some thermal effects are precisely connected with EM energy. With this knowledge, the main problem is to solve the

differential equation of problem, i.e., sometimes is impossible. Thus, other solution to continue the studies of complex systems is

using a numerical simulation. This decision make possible to visualize fields in many shapes and allows verify the transient state

of system. The principal difficult in work with numerical simulation is hardware and software limitation. However, these

problems can be avoided with some techniques. Diakoptic technique allows alleviating the RAM memory.

Based with these circumstances, we develop software free with the purpose of speed up the researches. The SimEMTher is the

software that allows the user simulates EM, thermal and coupled systems in a simple way making possible the use of numerical

techniques to increase the human knowledge.

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ACKNOWLEDGMENT

The authors would like to thanks for National Counsel of Technological and Scientific Development (CPNq) of Brazil for yourfinancial support.

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(60-68) thermal-electromagnetic coupled system simulator using transmission-line matrix (tlm)

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