1 Philosophy behind QW-BHM
Standard electromagnetic (EM) simulators assume that a particular scenario remains invariant throughout the analysis. This assumption is not met when modelling practical microwave power processes since constitutive parameters of all typical foodstuffs, timber, rubber, and other treated materials vary substantially as a result of heat dissipation, temperature rise and/or phase changes. Moreover, the load may be rotating (as in a house-hold oven) or shifting (as in industrial tunnel applicators). It may also be advantageous to analyse EM effects coupled to the thermodynamic ones.
QWED develops specialised versions of its QuickWaveTM software, which obviate the above limitations of standard EM solvers, and facilitate faster and more accurate simulations of microwave power processes. Basic Heating Module for QuickWave (further referred to by an abbreviation QW-BHM) is the key module of the family. It provides a novel regime of operating the FDTD solver, with modification of media parameters as a function of dissipated energy. It also allows modelling of load rotation and, starting with version 7.5, load movement along arbitrary trajectories. It facilitates heat flow analysis through the additional QW-HFM module, bilaterally coupled to the EM analysis. It also provides a regime of automatic tuning of the source to the deepest in-band resonance.
QW-BHM brings major new features into QW-Simulator, but to make them operational, the user should appropriately set up the scenario in QW-Editor, and also create external data files:
1. QW-BHM allows describing any medium of the dielectric isotropic or dielectric anisotropic type in the scenario in a separate medium text file, containing tabulated values of constitutive parameters (e, m, s, sm - possibly anisotropic; also specific heat capacity, density, and heat transfer parameters) versus enthalpy and/or temperature. Each medium file should be of the same name as the name assigned to the corresponding medium in QW-Editor, with *.pmo extension. All media files must be placed in the current project directory.
2. Initial temperature distribution T0(x,y,z) can be defined in QW-Editor, by assigning a particular value of the temperature to each medium. If the medium has its *.pmo file, and both temperature and enthalpy are listed in that file, initial enthalpy H0 corresponding to the initial temperature T0 of the medium is read from the file. Otherwise initial enthalpy of the medium is assumed to be zero.
3. QW-Editor also allows the user to define specific heat capacity and density for each medium. These values will further be applied for converting enthalpy distribution to temperature distribution, if such a conversion cannot be accomplished based on the *.pmo file. However, values of specific heat capacity and density defined in QW-Editor are ignored by QW-HFM, which requires them to be listed in *.pmo files.
4. Make sure that Allow BHM option is checked in Export options dialogue of QW-Editor (File-Export Options command). This instructs QW-Simulator to allocate additional memory for storing temperature and enthalpy in QW-BHM operation. It also activates the Details... dialogue used for setting up QW-BHM options.
5. The File-Export Options-Allow BHM-Details... dialogue allows choosing BHM mode. Option Allow heat flow needs to be checked together with Allow rotation or Movement, if heat flow and/or load rotation are to be modelled at each BHM step, respectively. In the latter case, Rotation parameters need to be set (see Single object rotation). Tasker times are used to set physical time steps and FDTD iterations in tasker files automatically generated by QW-Editor (see Frequency tuning). To generate the old type of the tasker file (with only Run command possibly preceded by template generation), and to further control the BHM operation manually, the First EM steady state field should be set to 0 periods.
6. QW-Simulator always starts its operation by converting the shape and material data into the so-called lcsm matrices. We shall call this stage the lcsm compilation. QW-BHM makes two changes in this regard. Firstly, during the lcsm compilation QW‑Simulator looks for media *.pmo files. If a particular medium file is found, its contents (at a particular temperature or enthalpy) supersede the default settings of constitutive parameters made in QW-Editor. Secondly, the lcsm compilation is repeated during the simulation, taking new values of media parameters, which correspond to the current temperature or enthalpy. This modifies the matrices while maintaining the same divergence-free field distribution.
7. The modelling of convective boundary conditions in the thermodynamic analysis with QW-HFM requires that the convective heat transfer coefficient be defined. This is done through media *.pm2 files described in Defining of boundary conditions.
Electromagnetic simulation with the use of QW-BHM proceeds in the following steps:
1. Run the FDTD analysis with sinusoidal excitation until the electromagnetic steady-state is reached.
2. Produce the 3D pattern of average dissipated power P(x,y,z).
3. The enthalpy per cell is upgraded by:
Enthalpym+1(x,y,z)= Enthalpym(x,y,z)+ P(x,y,z) Dt
where Dt is the assumed (user-defined) time of heating in [s] at a particular steady-state, with constant average power P(x,y,z) per cell in [W]. Enthalpy increases in all lossy media. Moreover, within one medium, each FDTD cell will typically have different enthalpy. QW-BHM actually operates in terms of enthalpy density denoted by symbol H (icon H is used in GUI to avoid confusion with the magnetic field) and expressed in [J/cm3], updated with equation:
Hm+1(x,y,z)= Hm(x,y,z)+ P(x,y,z) Dt / DV(x,y,z)
where DV is volume of the cell centered at (x,y,z), in [cm3].
4. Upgrade the temperature distribution in each FDTD cell, in one of the two ways:
A. If a medium filling the cell has its *.pmo file, and both temperature and enthalpy are listed in the file, a value of temperature corresponding to the value of enthalpy is read from the file:
Tm+1(x,y,z) = T [Hm+1(x,y,z)]
Linear interpolation is applied between any two listed points, and flat extrapolation is applied outside the listed range. No reference is made to specific heat.
B. In other cases, a new value temperature is calculated using specific heat Cm and density rm:
Tm+1(x,y,z) = Tm(x,y,z)+ P(x,y,z) Dt / (r m (x,y,z) Cm(x,y,z) )=
=Tm(x,y,z) + [Hm+1(x,y,z) - Hm(x,y,z)] / (r m (x,y,z) Cm(x,y,z))
If *.pmo file exists and contains the listing of specific heat, a value of Cm at enthalpy Hm or temperatureTm is read from the file. Otherwise a default constant C as set in QW‑Editor is used. The same rule applies to density.
5. If Allow Rotation or Movement option has been checked, load movement is now performed. The temperature and enthalpy fields are rotated or translated together with the load.
6. If Allow Heat flow option has been checked, heat diffusion is now simulated with QW-HFM. Note that QW-HFM reads thermodynamic media parameters from *pmo files only, and ignores the settings of QW-Editor. When working in the nonlinear mode, it requires that Temperature, Enthalpy and Ka (or Kx, Ky, Kz) columns be included in media *pmo files; Density and Specific heat listed in these files are ignored.
7. Repeat the process of lcsm compilation. For each FDTD cell, QW-Simulator takes media constitutive parameters corresponding to the cell’s current temperature Tm+1 or enthalpy Hm+1. There are three ways of detecting current values of all media parameters. Since these ways are the same for each medium parameter, consider ez as an example:
A. If a medium filling the cell has its *.pmo file, ez is listed in the file, and enthalpy is listed in the file, a value of ez corresponding to the value of enthalpy is read from the file:
ezm+1(x,y,z) =ez [Hm+1(x,y,z)]
Linear interpolation is applied between any two listed points, and flat extrapolation is applied outside the listed range. No reference is made to temperature or default settings for ez made in QW-Editor.
B. If a medium filling the cell has its *.pmo file, ez is listed in the file, but enthalpy is not listed (which means that temperature must be listed), a value of ez corresponding to the value of temperature is read from the file:
ezm+1(x,y,z) = ez [Tm+1(x,y,z)]
Linear interpolation is applied between any two listed points, and flat extrapolation is applied outside the listed range. No reference is made to default settings for ez made in QW-Editor.
C. If a medium filling the cell does not have its *.pmo file, or ez is not listed in the file, a default constant value of ez (as defined QW-Editor) is maintained.
8. Resume the FDTD analysis starting with the previously obtained steady-state fields, but using the newlcsm parameters, until a new steady state is reached.
The process is iteratively repeated.
In batch operation of QW-BHM, with advanced tasker files generated by QW-Editor, (see Batch operation with exported tasker files) or via Configure-Breakpoints command of QW-Simulator (Batch operation with user tasker files) all the above tasks are performed automatically, and selected data is stored at each BHM step.
In manual operation of QW-BHM (activated by setting First EM steady state field to 0 periods in the Heating Details dialogue) a majority of the above tasks are also performed automatically by QW-BHM but the user interaction is necessary at the level of decision making and concerns:
- deciding when the steady state has been reached (end of step 1) – by either watching the fields and power, or based on previous experience with a similar scenario,
- activating the average power calculations (start of step 2),
- deciding that the average power pattern remains unchanged (end of step 2), and activating the “heating” part of the process with a particular “heating time” Dt.
Steps 3, 4, 5, 6, 7, 8 that constitute the thermal analysis are then performed automatically.
QW-BHM automatically modifies media parameters in thousands of FDTD cells filled with different media and heated up differently – all accomplished in a matter of seconds! This is a major advantage of this software module for microwave power applications.
Each “thermal” iteration requires many FDTD iterations to reach the new electromagnetic steady state starting from the previous steady state – but less than would be needed to reach the new steady state starting from the initial zero field distribution. This is another advantage of QW-BHM.
The choice of heating time Dt at each “thermal” iteration is very important. This choice determines the convergence, and the rate of converge, of the modelling:
· Too big Dt may cause immediate divergence – at hot spots of an intermediate electromagnetic steady state, it may produce temperature rise above the highest temperature that would ever be reached in the medium. This will obviously happen in a self-controlled thawing process, where the frozen parts of the food absorb more energy than the already thawed parts.
· Too small Dt means that the complete heating process is sub-divided into many “heating iterations”, each requiring many FDTD iterations. The process will converge, but the computing time will be long.
It is assumed that the user will be able to set an appropriate value of Dt based on his previous experience with (and understanding of) the particular substance heating. To this end, it is important to note that Dt simply equals to the physical heating time in seconds, with no additional scaling factors involved. This convenient arrangement follows from the fact that the physical power levels can be rigorously controlled in QW software. For example, consider heating in a 800W microwave oven. In standard manufacturers' data, this denotes 800 W of time-average power available from the magnetron, that is, 1600 W of time-maximum available power. By setting the sinusoidal source amplitude to Ö1600=40 in QW‑Editor, the user ensures that the QW-Simulator will work with the source of 800W time-average available power, producing correct levels of dissipated power in the load.
Moreover, QW-BHM is prepared to assist the users with establishing appropriate Dt by numerical experiments. Especially when modelling new media or unusual heating systems, the user is strongly recommended to prepare graphical plots of the media characteristics versus enthalpy or temperature, and to correlate these plots to the outcomes of the numerical process. The following options are available QW-BHM:
A. The user may watch the levels of average dissipated power over the scenario and choose Dt so that the resulting increase of enthalpy / temperature will nowhere cause a “jump” over local maxima / minima on the media characteristics.
B. After performing a “thermal” iteration (steps 3 through 7, 3, 4, 5 above) the user may verify that choice by checking the new values of media parameters over the TestMesh display.
C. If the changes of media parameters produced by one “thermal” iteration with Dt1 are negligible, the user may make another “thermal” iteration with Dt2, before re-starting the EM analysis (i.e., repeat steps 3 through 7, 3, 4, 5 before going to step 8 step 6). This is equivalent to one “thermal” iteration with (Dt1 + Dt2).
D. If the changes of media parameters produced by one “thermal” iteration with Dt1 are too big, so that important intermediate effects seem to have been skipped, the user may make another “thermal” iteration with -Dt2 (0<Dt2<Dt1) before re-starting the EM analysis (i.e., repeat steps 3 through 7, 3, 4, 5 before going to step 8 step 6). This is equivalent to one “thermal” iteration with (Dt1 - Dt2).
Note that “adding” some more heating time (+Dt2) is like heating up a still unready meal for a few more seconds in a real oven. “Subtracting” some of the heating time (-Dt2) is a feature unavailable in real ovens, which cannot cool down or “unburn” overcooked meals!
The rate of convergence issue needs to be considered also when analysing scenarios with load movement (rotation and movement). The shift between consecutive load positions becomes also a quantisation step of the process.
Let us consider this part of the process based on typical scenario of moving load placed in air surrounding. At the end of the BHM step, when the load is moved to a new position, the cells that were previously filled with the load (permittivity>1) become air filled. Since QuickWave assumes the Gauss law conservation, the value of E-field increases proportionally in those cells and we observe some "peeks". This field distribution becomes a starting point for reaching new steady state (before the following BHM step). The disturbance introduced by those "peeks diminishes with time and eventually the steady state is reached (the field distribution is smooth). When the changes of the load position are relatively small the time required for reaching the new steady state is shorter. When the load changes its position rapidly, the time required to reach new steady state extends and is problem dependent. Summarising, the potential disturbance on the field distribution origins from the transformation of non-linear problem to a parametric one and results directly from the chosen quantization step. To eliminate this effect it is recommended to increase the "Consecutive EM steady states" parameter (what will unfortunately increase the simulation time) or decrease the load shift (movement step) per BHM step.