JP4804848B2 - Temperature distribution simulation apparatus and method - Google Patents

Description

  The present invention relates to a technology for simulating a temperature distribution in the presence of an electromagnetic wave absorber, and in particular, allows a temperature distribution to be accurately analyzed in consideration of thermal radiation phenomena in addition to heat conduction, convection and heat transfer. is there.

  In recent years, the situation where radio wave absorbers are used under high power is increasing. Under such an environment, the temperature of the absorber itself greatly increases due to the absorbed electric power, which may cause a fire accident due to heat generation and a change in characteristics of the absorber itself. Therefore, grasping the temperature distribution of the absorber and its surroundings has become extremely important in taking measures against usage limits and characteristic changes. In order to experimentally confirm the temperature distribution, a large-scale facility such as a high-power RF device or an anechoic chamber is required, which is often difficult in terms of safety and cost.

  The present inventors combined the SIMPLE method with the FDTD method (time domain finite difference method) to obtain the convection and heat conduction of the ambient air by the SIMPLE method, and strictly to the local heat transfer. It proposes to analyze (nonpatent literature 1).

Furthermore, the present inventors have conducted extensive research and have come to the knowledge that a more rigorous analysis can be performed by considering the thermal radiation phenomenon.
“Temperature analysis of a single-layer type wave absorber considering convection in a three-dimensional region”, Electronic Information and Communication Journal (C), Vol. J88-C, no. 1, pp. 76-78

  The present invention has been made in view of the above circumstances, and an object thereof is to provide a temperature distribution simulation technique for analyzing a temperature distribution in the presence of a radio wave absorber in consideration of a thermal radiation phenomenon.

  According to this invention, in order to achieve the above-mentioned object, the configuration as described in the claims is adopted. Here, prior to describing the invention in detail, supplementary explanations of the claims will be given.

運動方程式（ｘ方向）：

運動方程式（ｙ方向）：

運動方程式（ｚ方向）：

エネルギー方程式：

（ただし、ｕはｘ方向の速度、ｖはｙ方向の速度、ｗはｚ方向の速度、ｐは圧力、Ｔは温度、Ｔ∞は境界外の温度、Ｓは吸収電力、ρは密度、μは粘度、λは熱伝導率、ｃは比熱である）
上記第３のシミュレーション手段から出力される速度、圧力、および温度が収束した後に、上記第３のシミュレーション手段から出力される温度を上記電子レンジ内の温度分布として出力し、さらに、上記周囲環境設定手段は電子レンジから電子レンジ内の熱放射環境に関する情報を指定されるようにしている。 That is, according to one aspect of the present invention, a microwave oven temperature distribution simulation apparatus for simulating a radio wave absorber disposed in a microwave oven and a temperature distribution around the absorber is set: a heat radiation environment in the microwave oven is set. Ambient environment setting means; first simulation means for simulating the electromagnetic field distribution in the microwave oven by the FDTD method; and the microwave oven by the Monte Carlo Reed method based on the thermal radiation conditions set by the ambient environment setting means A second simulation means for simulating the self-absorption ratio of each wall element and the absorption ratio from other wall elements in the heat radiation in the inside; and the following continuity equation, equation of motion, and energy equation of thermal convection in the microwave oven: The absorbed power S of the energy equation From the absorbed power calculated from the electromagnetic field distribution obtained by the simulation means, subtract the amount of thermal radiation calculated from the absorption ratio from the self-absorption ratio of each wall element and the other wall elements obtained by the second simulation means. And a third simulation means for repeatedly calculating the speed, pressure, and temperature of the heat convection in the microwave oven by the SIMPLE method.
Continuous equation:

Equation of motion (x direction):

Equation of motion (y direction):

Equation of motion (z direction):

Energy equation:

(Where u is the velocity in the x direction, v is the velocity in the y direction, w is the velocity in the z direction, p is the pressure, T is the temperature, T∞ is the temperature outside the boundary, S is the absorbed power, ρ is the density, μ Is the viscosity, λ is the thermal conductivity, and c is the specific heat)
After the speed, pressure and temperature output from the third simulation means have converged, the temperature output from the third simulation means is output as a temperature distribution in the microwave oven , and the ambient environment setting The means is adapted to designate information relating to the heat radiation environment in the microwave oven from the microwave oven .

  The present invention can be realized not only as an apparatus or a system but also as a method. Of course, a part of the invention can be configured as software. Of course, software products used to cause a computer to execute such software are also included in the technical scope of the present invention.

  These and other aspects of the invention are set forth in the appended claims and will be described in detail below with reference to examples.

According to this invention, the heating condition in the microwave oven can be grasped based on a strict temperature distribution in consideration of thermal radiation.

  Examples of the present invention will be described below.

  FIG. 1 shows a temperature distribution simulation apparatus 100 according to a first embodiment of the present invention as a whole. The temperature distribution simulation apparatus 100 of the first embodiment is typically installed by installing a temperature distribution simulation program 102 (including a case where a plurality of simulation programs are used in cooperation) in a computer 101. Each unit described below using function blocks is realized by cooperating hardware resources and software resources of the computer 101.

  In FIG. 1, the temperature distribution simulation apparatus 100 includes an input unit 11, a simulation processing unit 12, and an output unit 16. The input unit 11 inputs various parameters necessary for the simulation. The output unit 16 visualizes the simulation result and outputs it to a display device or a printing device (not shown). The simulation processing unit 12 includes an FDTD method processing unit 13, an MR method processing unit 14, and a SIMPLE method processing unit 15. The FDTD method processing unit 13 performs numerical analysis by the FDTD method (time domain finite difference method). The MR method processing unit 14 analyzes thermal radiation by the Monte Carlo Read method (Monte Carlo READ method). The SIMPLE method processing unit 15 performs numerical analysis of both pressure and velocity by the SIMPLE method (Semi-Implicit Method for Pressure-Linked Equations method).

  First, the FDTD method processing unit 13 calculates the absorbed power distribution per unit volume in the steady state of the electromagnetic field using the FDTD method. Next, the MR method processing unit 14 calculates the self-absorption ratio αs of thermal radiation and the ratio (READ value) Rd absorbed from other wall surface elements using the Monte Carlo Reed method. The self-absorption ratio αs is the ratio of energy radiated from the target wall surface element that is returned and absorbed by the wall surface element due to reflection or scattering. Also, READ (Radial Energy Absorption Distribution) Rd is the ratio of energy radiated from each wall element other than the target wall element to reach and be absorbed by the wall element.

  In the Monte Carlo Reed method, uniform random numbers (pseudo-uniform random numbers. 0 to 1) Rθ and Rη are generated and the radiation directions (θ and η) are set to θ = 2πRθ and η = cos−1 (1-Rη) 1 / The above self-absorption rates αs and Rd are calculated by tracking the behavior of scattering, absorption, etc. of the radiating particles assuming that the radiant energy is particles determined by 2. The total number of particles from the radiation wall element is No, the number of particles returning to the wall element is Nsa, the number of particles from other wall elements is Nsl, and the self-absorption rate αs = Nsa / No, between the other wall surfaces READ value (Rd) = Nsl / (No−Nsa) is calculated.

  Furthermore, the SIMPLE method processing unit 15 uses the SIMPLE method to solve the continuous equation and the equation of motion, thereby obtaining the analysis values of the velocity field and the pressure field. Note that the iterative matrix solution is used as a method for solving these equations. (Here, as an example, the tridiagonal matrix algorithm TDMA (Tri-Diagonal Matrix Algorithm method) is used.) In addition, the buoyancy term in the y-direction equation of motion is expressed by approximating the density difference by the temperature difference by the Boussinesq approximation. is doing.

運動方程式（ｘ方向）：

運動方程式（ｙ方向）：

運動方程式（ｚ方向）：

エネルギー方程式：

（ただし、ｕはｘ方向の速度、ｖはｙ方向の速度、ｗはｚ方向の速度、ｐは圧力、Ｔは温度、Ｔ∞は境界外の温度、Ｓは吸収電力、ρは密度、μは粘度、λは熱伝導率、ｃは比熱である） Continuous equation:

Equation of motion (x direction):

Equation of motion (y direction):

Equation of motion (z direction):

Energy equation:

(Where u is the velocity in the x direction, v is the velocity in the y direction, w is the velocity in the z direction, p is the pressure, T is the temperature, T∞ is the temperature outside the boundary, S is the absorbed power, ρ is the density, μ Is the viscosity, λ is the thermal conductivity, and c is the specific heat)

  By using this discretization method, which is discretized by the implicit method using the control volume method for these equations, the preservability of mass flow rate, momentum flow rate and energy flow rate in the control volume method is kept good. It becomes possible.

  Further, the Hybrid method was applied to the convection term and the diffusion term in the equation of motion and the discretized equation. This Hybrid method changes the coefficient of the discretization equation of the equation of motion according to the magnitude of the Peclet number, which is a dimensionless quantity indicating the strength of the convection, so that the primary upwind difference or the central difference for this discretization equation Applies as appropriate. As a result, the calculation time can be shortened and the equation of motion can be analyzed with high accuracy.

  Since the continuity equation and the equation of motion both include the velocity, the analytical values of the velocity and the pressure were obtained by solving each of them by using the SIMPLE method. In the SIMPLE method, when the pressure required to solve the equation of motion is obtained, a pressure correction equation using the correction amount as a variable is derived from the continuous equation instead of the pressure itself, and the pressure correction amount is calculated using the pressure correction equation. In this method, the velocity field and pressure field are repeatedly calculated so as to be zero.

  In this tridiagonal matrix method, when solving an N unknown number of tridiagonal matrices, a solution can be obtained by 2N operations, which is more efficient than general solutions such as the sweep-out method and the Kramer method. Is.

Finally, radiant energy and absorbed energy at each wall element are calculated using αs and Rd obtained by the Monte Carlo Reed method. Then, these energy amounts are substituted into the energy equation together with the absorbed power obtained by the FDTD method, and the analysis value of the temperature field is obtained.

  Hereinafter, the operation will be described in detail.

[Step S1]: The electromagnetic field is calculated by the FDTD method.
[Step S2]: If the electromagnetic field reaches a steady state, the process proceeds to step S3. If the electromagnetic field has not reached the steady state, the process returns to step S1 and calculation is performed until the electromagnetic field reaches a steady state.
[Step S3]: Calculate the absorbed power.
[Step S4]: A self-absorption ratio is determined by the Monte Carlo Reed method.
[Step S5]: A READ value is obtained by the Monte Carlo Reed method.
[Steps S6 and S7]: In the SIMPLE method, an appropriate iterative matrix solution method (here, as an example, a tridiagonal matrix method (TDMA) is used), and a value that can be easily converged (may be 0). The speed u, the y-direction speed v, the z-direction speed w, the pressure p, and the temperature T are determined. That is, in the SIMPLE method, the pressure p is substituted into the motion equation discretized by the finite volume method, and the latest u, v, and w obtained from the discretized motion equation are obtained. In the SIMPLE method, the latest u, v, and w are substituted into the discretized continuous equation, and the latest pressure p is obtained from the discretized continuous equation.
[Step S8]: Thermal radiation (radiated energy and absorbed energy) in each wall surface element is obtained from the self-absorption ratio and the READ value obtained in Step S4 and Step S5.
[Step S9]: The absorbed power and thermal radiation obtained in Steps S3 and S8 are respectively substituted into the energy equation in the SIMPLE method to obtain the latest temperature T.
[Step S10]: Convergence of u, v, w, p, and T is confirmed. If confirmed, the process proceeds to step S11, and the time step of convection and heat conduction is advanced by Δt _SIM . If not confirmed, steps S6 to S9 are repeated.
[Step S11]: The thermal constant change (thermal conductivity, specific heat, density, etc.) of the substance is obtained from the temperature T obtained in Step S9, and is substituted into the continuous equation, the equation of motion, and the energy equation.
[Step S12]: From the temperature T obtained in Step S9, change in the electric constant of the substance (complex relative permittivity, complex relative permeability, conductivity, etc.) is calculated and substituted into the electromagnetic field equation.
[Step S13]: Since the electromagnetic field fluctuates due to the change in the electric constant of the substance substituted in step S12, the electromagnetic field is calculated for several cycles in order to mitigate it.
[Step S14]: It is determined whether or not the sum of the time steps Δt _SIM of convection and heat conduction has reached a desired time. If the desired time has been reached, the process proceeds to Step S15; Return, calculate the absorbed power, and repeat the process. If it is assumed that thermal radiation does not fluctuate due to temperature or electromagnetic field, the calculations in steps S4 and S5 may be omitted.
[Step S15]: Here, since the sum of the time steps Δt _SIM of convection and heat conduction has reached the desired time, the electromagnetic field and u, v, w, p, T are output.

  According to this embodiment, it is possible to acquire a precise temperature distribution in consideration of thermal radiation.

  Next, a second embodiment in which the present invention is applied to a temperature distribution simulation apparatus for a microwave oven that simulates the temperature distribution in the microwave oven will be described. In this embodiment, in addition to the same configuration as in the first embodiment, an ambient environment setting unit 17 and an ambient environment data storage unit 18 are provided. The ambient environment data storage unit 18 stores data related to surrounding objects that control heating to a heating target, such as radio wave absorbers and radio wave reflectors that can be placed in the microwave oven 300. Each time the ambient environment is changed in the microwave oven 300, the ambient environment setting unit 17 sets the ambient environment by an operation from the microwave oven 300 or automatic detection, or manually switches the ambient environment data. The ambient environment data is stored in the ambient environment data storage unit 18 for each ambient environment, and the corresponding ambient environment data is supplied to the simulation processing unit 12, particularly the MR method processing unit 14, via the input unit 11.

  Also in this embodiment, the electromagnetic field distribution is numerically analyzed by the FDTD method, the αs and Rd values are numerically analyzed by the MR method, the previous equation is simulated by the SIMPLE method, and the temperature distribution is calculated.

  In this embodiment, the ambient environment in the microwave oven 300 can be simulated in advance by the microwave temperature distribution simulation apparatus 200, and the heating state of the microwave oven can be verified in advance while selecting various ambient environments.

It is a figure which shows the example of a structure of Example 1 of this invention as a whole. It is a flowchart explaining the operation example of the said Example 1 in detail. It is a figure which shows the structural example of Example 2 of this invention as a whole.

Explanation of symbols

DESCRIPTION OF SYMBOLS 11 Input part 12 Simulation processing part 13 FDTD method processing part 14 MR method processing part 15 SIMPLE method processing part 16 Output part 17 Ambient environment setting part 18 Ambient environment data storage part 100 Temperature distribution simulation apparatus 101 Computer 102 Program 200 Microwave oven temperature distribution Simulation device 300 Microwave oven

Claims (1)

In a microwave oven temperature distribution simulation apparatus for simulating the electromagnetic wave absorber disposed in the microwave oven and the temperature distribution around it,
And the ambient environment setting means for setting the heat radiation environment of the microwave oven,
First simulation means for simulating the electromagnetic field distribution in the microwave oven by an FDTD method;
A second simulation for simulating the self-absorption ratio of each wall surface element and the absorption ratio from other wall surface elements in the heat radiation in the microwave oven by the Monte Carlo Reed method based on the heat radiation condition set by the ambient environment setting means Simulation means;
For the following continuous equation, equation of motion, and energy equation of heat convection in the microwave oven, the absorbed power S of the energy equation is calculated from the absorbed power calculated from the electromagnetic field distribution obtained by the first simulation means. After subtracting and substituting the amount of thermal radiation calculated from the absorption ratio from the other wall elements and the self-absorption ratio of each wall surface element obtained by the simulation means of 2, heat in the microwave oven by the SIMPLE method A third simulation means for repeatedly calculating the convection speed, pressure, and temperature ,
Continuous equation:

Equation of motion (x direction):

Equation of motion (y direction):

Equation of motion (z direction):

Energy equation:

(Where u is the velocity in the x direction, v is the velocity in the y direction, w is the velocity in the z direction, p is the pressure, T is the temperature, T∞ is the temperature outside the boundary, S is the absorbed power, ρ is the density, μ Is the viscosity, λ is the thermal conductivity, and c is the specific heat)
After the speed, pressure, and temperature output from the third simulation means converge, the temperature output from the third simulation means is output as a temperature distribution in the microwave oven ,
Furthermore, the surrounding environment setting means thermal radiation environment specified Ru electron range for temperature distribution simulation device information regarding the microwave oven from the microwave oven.

Images