XXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXX''"> E.4 Problem 3 - Heated Reaction Chamber
This example represents a simple version of a reaction chamber. The main chamber is a short vertical cylinder with hemispherical caps on each end. The main chamber also has a smaller chamber teed off from its side. The smaller chamber is a short cylinder, with a smaller diameter than the large chamber, and capped with a hemispherical cap. The chamber walls are constructed of a high-strength steel which corresponds to material ID 365 in the material property database provided with the Patran Thermal module. The model was created using the MKS system of units for the physical and material properties.
The bottom cap of the main chamber is heated with a flux of 5000 watts per square meter applied to the exterior surface. The rest of the exterior surface is convectively coupled to the ambient environment at 300 K. The convection coefficients are constant with the value for the main chamber being 1 watt per square meter per degree K and the value for the smaller chamber being 20.
The interior of the chamber has only thermal radiation boundary conditions. A participating media node is included in the model in case we wish to use it in the future. However, it is not used in the analysis presented here.
The Patran model uses a very coarse mesh, since we do not want to use up a large amount of computer time on an example problem. The model files for this example were delivered with Patran Thermal and should be available on your computer system by typing ‘get_view’ and selecting the directory ‘chamber.’ For assistance in locating these files, please contact your system administrator.
A Patran Thermal TEMPLATEDAT file is needed. A TEMPLATEDAT file is shown below.
TEMPLATEDAT File |
MID 365 36501 36501 36501 36504 36505 36506 * VFAC 365 0 0.8 1.0 0 0 0 0 0 1 |
The material template ID 365 is for the high-strength steel used for the vessel walls and the VFAC template 365 is for the interior surfaces of the vessel. The template gives the emissivity as a constant value of 0.8. No other radiation property data is given in this case since this is a simple model.
Likewise, a Patran Thermal MATDAT file is needed. We have created a file by using our system editor and extracting the data from the material property data file for MKS units supplied with the Patran Thermal module in the THERMAL$DIR:[LIBRARY] directory as MPID.MKS. Our MATDAT file is shown below.
MATDAT File |
MPID 36501 CONSTANT KELVIN 1.0
STEEL, ULTRA HIGH STRENGTH TYPE 300-M --> Thermal Conductivity (W/(m*Sec*K))
References: 1
Data Quality: EXCELLENT
MDATA 5.77806E+01
/
MPID 36504 CONSTANT KELVIN 1.0
STEEL, ULTRA HIGH STRENGTH TYPE 300-M --> Density (Kg/m**3)
References: 1
Data Quality: EXCELLENT
MDATA 7.84000E+03
/
MPID 36505 CONSTANT KELVIN 1.0
STEEL, ULTRA HIGH STRENGTH TYPE 300-M --> Specific Heat (J/(Kg*K))
References: 1
Data Quality: EXCELLENT
MDATA 4.47324E+02
/
MPID 36506 PHASE KELVIN 1.0
STEEL, ULTRA HIGH STRENGTH TYPE 300-M --> Latent Heat (J/Kg)
References: 1
Data Quality: EXCELLENT
MDATA 1.77315E+03 1.51190E+05
/ |
The resulting Patran model is now translated into thermal input data files and Viewfactor input data files by clicking on Apply from the Patran Analysis menu.
This viewfactor analysis takes about 900 CPU seconds on a VAX 8600, so be forewarned that this job will require a significant amount of computer time and you may not wish to spend your computer resources running this example problem. Output for this analysis has been included with the Viewfactor delivery and is available on your system.
Remember to check the VFMSG file for error messages when the Viewfactor analysis is done. The last 40 lines of the VFDIAG file from this analysis is shown below. Since the interior of the chamber is a closed radiation enclosure, we expect the sums of viewfactors from any surface to all other surfaces to be one, or at least very close to one (after taking into account computer and numerical approximations and discretization errors during obstructed view checking). From the diagnostic data file, VFDIAG, we observe that the maximum deviation from one for these sums is about 0.03 and the average deviation is about 0.01. Both of these values are reasonable for a 108 surface enclosure.
VFDIAG File |
$TITLE: PDA VIEWFACTOR VER. 2.5 4-APR-91 17:58:55
$TITLE: HEATED REACTION CHAMBER WITH SIDE CHAMBER.
$TITLE: EXAMPLE PROBLEM, REACTION CHAMBER, 3D, ABOUT 110 ELEMENTS. $TITLE: 4-APR-91 17:44:28 2.5
$ENCL: 1 108 1
1 0.9969453812E+00 0.3054618835E-02 0.0000000000E+00
0.1003143072E+01 0.1001876235E+01 0.9858158231E+00
2 0.9985128045E+00 0.1487195492E-02 0.0000000000E+00
0.1004488468E+01 0.9986609221E+00 0.9923893809E+00
3 0.9980445504E+00 0.1955449581E-02 0.0000000000E+00
0.9956341982E+00 0.1000977635E+01 0.1001693606E+01 0.9938086867E+00
4 0.9978431463E+00 0.2156853676E-02 0.0000000000E+00
0.9944566488E+00 0.1001591563E+01 0.1000043273E+01 0.9952377677E+00
5 0.9988200068E+00 0.1179993153E-02 0.0000000000E+00
0.1005183816E+01 0.9964703321E+00 0.9948055148E+00
6 0.9989739060E+00 0.1026093960E-02 0.0000000000E+00
0.1002386332E+01 0.9964384437E+00 0.9980962276E+00
7 0.9983404279E+00 0.1659572124E-02 0.0000000000E+00
0.9980260730E+00 0.1000427961E+01 0.9992659688E+00
**some lines missing**
|
99 0.9866157770E+00 0.1338422298E-01 0.0000000000E+00
0.9843998551E+00 0.9941601753E+00 0.9812870622E+00
100 0.9874985814E+00 0.1250141859E-01 0.0000000000E+00
0.9909937382E+00 0.9941576719E+00 0.9773445725E+00
101 0.9940232038E+00 0.5976796150E-02 0.0000000000E+00
0.9886876345E+00 0.9990730286E+00 0.9977318645E+00 0.9905698895E+00
102 0.9940228462E+00 0.5977153778E-02 0.0000000000E+00
0.9993922710E+00 0.9883680344E+00 0.9906400442E+00 0.9976602793E+00
103 0.9908416271E+00 0.9158372879E-02 0.0000000000E+00
0.9801433682E+00 0.9940931797E+00 0.9982880354E+00
104 0.9921196103E+00 0.7880389690E-02 0.0000000000E+00
0.1005351782E+01 0.9940947294E+00 0.9769117832E+00
105 0.9946594238E+00 0.5340576172E-02 0.0000000000E+00
0.9900299907E+00 0.9957625866E+00 0.9983595610E+00 0.9941036105E+00
106 0.9946811795E+00 0.5318820477E-02 0.0000000000E+00
0.9960818887E+00 0.9897401333E+00 0.9942038655E+00 0.9983152747E+00
107 0.9866156578E+00 0.1338434219E-01 0.0000000000E+00
0.9844000340E+00 0.9941600561E+00 0.9812868237E+00[5;9H[21;H
108 0.9874987006E+00 0.1250129938E-01 0.0000000000E+00
0.9909937978E+00 0.9941574931E+00 0.9773442149E+00
0.3032351E-01 0.1014543E-01 0.9183009E-02 0.1014543E-01 0.9183009E-02
0.6392515E-01 0.1271649E-01 0.1550230E-01 0.1388588E-01 0.1445413E-01
0.6393278E-01 0.1234503E-01 0.1532391E-01 0.1322156E-01 0.1456719E-01
0.2590126E-01 0.8442800E-02 0.8157597E-02 0.9063553E-02 0.7455045E-02
0.2589691E-01 0.6228297E-02 0.7944188E-02 0.6822405E-02 0.7435330E-02
$ENDENCL:
$EOF:
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Under Solution, type select Viewfactor Analysis and make sure the option is for steady state, option 3.
A few minor modifications need to be made to the Patran Analysis form.
Under Viewfactor Solution Parameters, change the title to: Viewfactor EXAMPLE PROBLEM CHAMBER.
Under Solution Parameters, set EPSISS to1.0000000000d-03.
Under Output Requests, Diagnostic Output, set all of the toggles off, especially the radiation resistors to avoid receiving printout for tens of thousands of radiation resistors.
Under Solution Parameters, run control, set the initial temperature to 300 K.
The thermal analysis is spawned when Apply is selected on the Analysis menu. The analysis will take much longer than for a similar model without any radiative interchange. When the radiative interchange is modeled in this example, nearly every nodal subarea on the interior surface of the vessel is connected to nearly every other nodal subarea on the interior surface by means of radiation resistors. Thus the resistor network which QTRAN must solve has many times more resistors than a similar model without radiation coupling. Also, the heat transfer across the radiative resistors is highly nonlinear. This further increases the time required for QTRAN to solve the network equations. The QTRAN thermal network analysis will require approximately 6000 CPU seconds on a VAX 8600.
You may not wish to spend your computer resources running this example problem. Output for this analysis has been included with the Viewfactor delivery and should be available on your system.
When the analysis is done, the following results may be read into the Patran database under the Analysis menu with the Action set to Read Results. The results can be visualized with any of the visualization tools under Results.
Finally, you will want to look at the Patran Thermal output data in the QOUTDAT file. Use the system editor to find the first occurrence of the string '1TIME'. Note the system heat balance. This is approximately the imposed heat flux to the chamber’s bottom cap. Also note that although the temperatures are converged to high accuracy, the total system heat balance is not nearly so accurate. This illustrates the significance of the fourth power temperature dependence for radiant energy exchange. If accurate heat flows are required for a thermal analysis of a high temperature radiation environment, then very accurate temperatures must in general be calculated. The nodes numbered above 2000 are the radiosity nodes created by Viewfactor.