manual validation v42

7/30/2019 Manual Validation v42

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Validation ManualVersion 4.2

P+Z Engineering GmbH, Munich

www.theseus-fe.com


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THESEUS-FE 4.2 Validations Manual

II

Legal Notices

Copyright 2012 P+Z Engineering GmbH. All Rights Reserved.

The information contained herein is the property of P+Z Engineering GmbH. Any use, copy, publication, distribution,

display, modification, or transmission of the information in whole or in part in any form or by any means without the priorexpress written permission of P+Z Engineering GmbH is strictly prohibited. Except when expressly provided by P+ZEngineering GmbH in writing, possession of this information shall not be construed to confer any license or rights underany of P+Z Engineering GmbHs intellectual property rights, whether by estoppel, implication, or otherwise.

ALL COPIES OF THE INFORMATION, IF ALLOWED BY P+Z ENGINEERING GMBH, MUST DISPLAY THIS NOTICEOF COPYRIGHT AND OWNERSHIP IN FULL.

THESEUS-FEis a copyright protected and registered trademark of P+Z Engineering GmbH.

All other brand and product names mentioned herein are the trademarks and registered trademarks of their respectiveowners.

Printed in Germany.June 2012


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III

About this manual

P+Z Engineering GmbH reserves the right to make changes or improvements to thesoftware product described in this document without notice. P+Z Engineering GmbHassumes no responsibility for any factual or typographical errors or omissions that may

have occurred. P+Z Engineering GmbH has however made every effort to ensure that theinformation contained in this Manual is accurate.

The idea of this manual is to demonstrate the high quality of our software THESEUS-FEby presenting a huge number of thermodynamic systems well validated with exact analyticresults, results from literature, or results achieved with our parent software tool INKA.

Additional background information can be found in the

GUI Manual

Keyword Manual

Tutorial Manual

Theory Manual

Transformer Manual

Oven Manual

also shipped with this release.

If you have any further questions, please contact:

P+Z Engineering GmbH

Anton-Ditt-Bogen 3

80939 MunichGermany

Phone: +49 89 31857 466

Fax: +49 89 31857 333

To see the latest THESUES-FE software and services, please visit our web site at:

http://www.theseus-fe.com

Questions about pricing, sales, availability and general issues should be directed to:

[email protected]

Technical and scientific support issues should be addressed to:

[email protected]


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IV

Contents

CONTENTS .................................................................................................. IV

LIST OF FIGURES ...................................................................................... VII1 ANALYTIC VALIDATIONS ...................................................................... 1

1.1 Steady State Problems .......................................................................................... 21.1.1 1D wall with internal heat generation .................................................................... 31.1.2 1D composite wall with internal heat generation and convection .......................... 51.1.3 Conduction through a fin (bound. cond.: temp./temp.) .......................................... 71.1.4 Conduction through a fin (bound. cond.: temp./adiabatic) .................................... 91.1.5 2D conduction in rectangular plate ..................................................................... 111.1.6 2D conduction in a disk (bound. cond.: temp./temp./convec.) ............................ 131.1.7 2D conduction in a disk (bound. cond.: temp./adiabatic./convec.) ...................... 151.2 Transient Solutions .............................................................................................. 171.2.1 1D wall cooling .................................................................................................... 181.2.2 Sphere heating ................................................................................................... 201.2.3 Cylinder heating .................................................................................................. 221.2.4 Infinite body with internal heat impulse ............................................................... 251.3 Thermal Radiation Boundary Conditions .......................................................... 281.3.1 Numeric view factor integration ........................................................................... 291.3.2 Solar short wave radiation (from sun) ................................................................. 301.3.3 Thermal long wave radiation (closed cavity) ....................................................... 371.3.4 Thermal long wave radiation (opened cavity) ..................................................... 41

2 ADVANCED CONDUCTION .................................................................. 442.1 Heat Bridges in Buildings ................................................................................... 452.1.1 Heat bridges: Example 1 .................................................................................... 462.1.2 Heat bridges: Example 2 .................................................................................... 482.1.3 Heat bridges: Example 3 .................................................................................... 502.1.4 Heat bridges: Example 4 .................................................................................... 522.2 Anisotropic Conductivity .................................................................................... 542.3 Temperature Dependent Conductivity ............................................................... 562.4 Phase Change ...................................................................................................... 582.5 Cylinder Radiation (open grey body cavity) ...................................................... 602.6 Disk Radiation ...................................................................................................... 63


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V

2.7 Cylinder Radiation Coupled with 1D Flow ......................................................... 663 THESEUS-FE COMPARED WITH INKA ................................................ 70

3.1 Model a .................................................................................................................. 713.1.1 Linear convective airzone heating - without considering humidity (a 1) .............. 723.1.2 Linear convective airzone heating - considering humidity (a 2) .......................... 733.1.3 Linear convective airzone cooling - considering humidity (a 3) ........................... 743.1.4 Non-linear convective airzone heating - without considering humidity (a 4) ....... 763.1.5 Sun heating airzone - without considering humidity (a 5) ................................... 773.1.6 Sun heating airzone - without considering humidity (a 6) ................................... 783.1.7 Airzone heated by ventilation FVT (a 7) .............................................................. 793.1.8 Airzone heated by ventilation RVT (a 8) ............................................................. 813.1.9 Airzone cooled by ventilation RVT (a 9) .............................................................. 823.1.10

Airzone heated by ventilation RET (a 10) ........................................................... 84

3.1.11Airzone cooled by ventilation HRET (a 11) ......................................................... 853.1.12Airzone heated by inverse mode ventilation FAT (a 12) ..................................... 873.1.13Airzone cooled by inverse mode ventilation RAT (a 13) ..................................... 893.2 Model b ................................................................................................................. 923.2.1 Glass transmission without refraction (b 1) ......................................................... 933.2.2 Glass transmission with refraction (b 2) .............................................................. 953.3 Model c .................................................................................................................. 963.3.1 Box with glas roof (c1) ........................................................................................ 97

4 MANIKIN FIALA-FE VALIDATIONS .................................................... 994.1 Passive System Validation ................................................................................ 1004.1.1 Spherical body element .................................................................................... 1014.1.2 Cylindr. body element with metabolism and blood perfusion (1) ....................... 1044.1.3 Cylindr. body element with metabolism and blood perfusion (2) ....................... 1064.1.4 Dead man in a cold environment (10C) ........................................................... 1084.2 Thermal Neutrality Validation ........................................................................... 1104.2.1 Naked Manikin .................................................................................................. 1114.2.2 Clothed Manikin ................................................................................................ 1134.3 Active System Validation .................................................................................. 1144.3.1 Cooling at 5C (1) ............................................................................................. 1154.3.2 Cooling at 5C (2) ............................................................................................. 1184.3.3 Cool environment at 13C ................................................................................. 1224.3.4 Cool environment at 15C ................................................................................. 1244.3.5 Changing environment 28-18-28C .................................................................. 1264.3.6 Changing environment 28-33-28C .................................................................. 1294.3.7 Changing environment 18-42-18C .................................................................. 132


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4.3.8 Changing environment 28-48-28C .................................................................. 1344.3.9 Changing activity in a cold environment at 10C............................................... 1374.3.10 Stepwise changing activity in a warm environment at 30C .............................. 1394.3.11 Cool environment at 10C ................................................................................. 1414.3.12 Changing environment 43-17-43C .................................................................. 1454.3.13 Naked manikin - 1 hr exposure - wide range of environmental conditions ........ 1484.3.14 Clothed manikin - 3 hr exposure - wide range of environmental conditions ...... 1504.4 Thermal Comfort Validation .............................................................................. 1524.4.1 Thermal comfort at changing bound. cond.: neutral-cold-neutral ...................... 1534.4.2 Thermal comfort at changing bound. cond.: neutral-hot-neutral ....................... 154

BIBLIOGRAPHY ....................................................................................... 155


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VII

List of figures

Fig. 1-1: Wall with heat generation system ....................................................................... 3Fig. 1-2: Wall with heat generation - results ......................................................................... 4Fig. 1-3: Composite wall with heat generation system ...................................................... 5Fig. 1-4: Composite wall with heat generation - results ....................................................... 6Fig. 1-5: Conduction through a fin with temp/temp BC system ......................................... 7Fig. 1-6: Conduction through a fin with temp/temp BC results .......................................... 8Fig. 1-7: Conduction through a fin with temp/adiabatic BC system ................................... 9Fig. 1-8: Conduction through a fin with temp/adiabatic BC - results .................................. 10Fig. 1-9: Rectangular plate conduction system ............................................................... 11Fig. 1-10: Rectangular plate conduction - results at x = 0.0833 and x = 0.5 ...................... 12Fig. 1-11: Rectangular plate conduction contour plot (temperature) ............................... 12Fig. 1-12: Conduction in a disk system ........................................................................... 13Fig. 1-13: Conduction in a disk temp. vs. Radius ............................................................ 14Fig. 1-14: Conduction in a disk contour plot (temperature) ............................................. 14Fig. 1-15: Conduction in a disk system ........................................................................... 15Fig. 1-16: Conduction in a disk temp. vs. Radius ............................................................ 16Fig. 1-17: Conduction in a disk contour plot (temperature) ............................................. 16Fig. 1-18: Cooling of wall system .................................................................................... 18

Fig. 1-19: Cooling of wall - FE model ................................................................................. 18Fig. 1-21: Results ............................................................................................................... 19Fig. 1-23: Sphere heating system ................................................................................... 20Fig. 1-24: Sphere heating time dep. results at center node ............................................ 21Fig. 1-25: Sphere heating contour plot (temperature) at t = 600s ................................... 21Fig. 1-26: Cylinder heating system ................................................................................. 22Fig. 1-27: Cylinder heating results for core & skin (t = 0..300s) ...................................... 23Fig. 1-28: Cylinder heating results for core & skin (t = 0..22500s) .................................. 23Fig. 1-29: Cylinder heating contour plot (temperatur) ..................................................... 24Fig. 1-30: Cylinder heating contour plot (convective heat flux density) ........................... 24Fig. 1-31: Internal heat impulse system .......................................................................... 25Fig. 1-32: Internal heat impulse results at t = 20 & 100s ................................................. 26Fig. 1-33: Internal heat impulse time dep. results at R = 0 .............................................. 26Fig. 1-34: Internal heat impulse contour plots (temperature) .......................................... 27Fig. 1-35: V21 system (closed cavity) ............................................................................. 28Fig. 1-36: V21viewfactors ............................................................................................... 29Fig. 1-37: V21 solar heating ............................................................................................ 30Fig. 1-38: THESEUS-FE shell group results stored in the hdf file ...................................... 31Fig. 1-39: V21 elementwise solar heatflux densities from THESEUS-FE (black body

cavity) ......................................................................................................................... 32


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VIII

Fig. 1-40: V21 interior diffuse transmittance and reflectance .......................................... 33Fig. 1-41: V21 results with and without interior diffuse transmittance and reflectance ... 33Fig. 1-42: V21 global energy balance for the BB-Cavity (Idf=0) ....................................... 34Fig. 1-43: V21 global energy balance for the PSDGB-Cavity (Idf=0) ............................... 34

Fig. 1-44: V21 global energy balance for the BB-Cavity (Idf=100W/m2) .......................... 35Fig. 1-45: V21 global energy balance for the PSDGB-Cavity (Idf=100W/m2) .................. 35Fig. 1-46: V21 global energy balance for the GB-Cavity (Idf=100W/m2) ......................... 36Fig. 1-47: V21 temperature boundary conditions for long wave radiation heat exchange

.................................................................................................................................... 37Fig. 1-48: THESEUS-FE shell group results stored in the hdf file ...................................... 38Fig. 1-49: V21 coarse mesh comparison between results (with and without reflection) .. 39Fig. 1-50: V21 fine mesh comparison between results (with and without reflection) ....... 40Fig. 1-51: V21 interior diffuse reflectance of long wave radiation .................................... 40Fig. 1-52: V21 temperature boundary conditions for long wave radiation heat exchange

.................................................................................................................................... 41Fig. 1-53: THESEUS-FE shell group results stored in the hdf file ...................................... 42Fig. 1-54: V21 fine mesh comparison between results (with and without reflection) ....... 43Fig. 1-55: V21 fine mesh view factor sum for elements of a closed cavity ...................... 43Fig. 2-1: T-shaped heat bridge with boundary conditions .................................................. 46Fig. 2-2: T-shaped heat bridge THESEUS-FE results ....................................................... 47Fig. 2-3: Right-angle heat bridge with boundary conditions ............................................... 48Fig. 2-4: Right-angle heat bridge THESEUS-FE results ................................................... 49Fig. 2-5: Right-angle heat bridge 2 with boundary conditions ............................................ 50Fig. 2-6: Right-angle heat bridge 2 THESEUS-FE results ................................................ 51Fig. 2-7: 3D heat bridge with boundary conditions. All units are specified in cm ................ 52Fig. 2-8: 3D heat bridge THESEUS-FE results ................................................................. 53Fig. 2-9: Anisotropic plate with boundary conditions .......................................................... 54Fig. 2-10: Anisotropic plate THESEUS-FE results compared with literature results.......... 55Fig. 2-11: Variable heat conductivity model with boundary conditions ............................... 56Fig. 2-12: THESEUS-FE results compared with isotropic lines from literature .................. 57Fig. 2-13: Phase Change model with boundary conditions ................................................ 58

Fig. 2-14: Table for assigning material property specific heat ............................................ 58Fig. 2-15: Phase change: THESEUS-FE results ............................................................... 59Fig. 2-16: Phase change: Comparison of FE results with analytical solution at x = 1 ........ 59Fig. 2-17: Cylinder Radiation example with boundary conditions ....................................... 60Fig. 2-18: Cylinder Radiation: THESEUS-FE results ........................................................ 61Fig. 2-19: Cylinder Radiation: THESEUS-FE results ........................................................... 62Fig. 2-20: Disk .................................................................................................................... 63Fig. 2-21: Fin Radiation: THESEUS-FE temperature results ............................................ 64Fig. 2-22: Fin Radiation: THESEUS-FEradiation per element results ................................. 65Fig. 2-23: Cylinder Radiation with 1D flow example: boundary conditions ......................... 66Fig. 2-24: Radiation Cylinder with 1D Flow: Theory discription .......................................... 67


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Fig. 2-25: Radiation Cylinder with 1D Flow: Comparison with results from literature ......... 68Fig. 2-26: Radiation Cylinder with 1D Flow: Field Results from Literature ......................... 69Fig. 3-1: Model a 1 system .............................................................................................. 72Fig. 3-2: Model a 1 - airzone temperature .......................................................................... 72

Fig. 3-3: Model a 2 system .............................................................................................. 73Fig. 3-4: Model a 2 - airzone temperature .......................................................................... 73Fig. 3-5: Model a 3 system .............................................................................................. 74Fig. 3-6: Model a 3 - airzone absolute humidity ................................................................. 74Fig. 3-7: Model a 3 - airzone temperature .......................................................................... 75Fig. 3-8: Model a 4 system .............................................................................................. 76Fig. 3-9: Model a 4 - airzone temperature .......................................................................... 76Fig. 3-10: Model a 5 system ............................................................................................ 77Fig. 3-11: Model a 5 - airzone temperature ........................................................................ 77Fig. 3-12: Model a 6 - system ............................................................................................ 78Fig. 3-13: Model a 6 - airzone temperature ........................................................................ 78Fig. 3-14: Model a 7 system ............................................................................................ 79Fig. 3-15: Model a 7 - airzone temperature ........................................................................ 79Fig. 3-16: Model a 7 - airzone absolute humidity ............................................................... 80Fig. 3-17: Model a 8 system ............................................................................................ 81Fig. 3-18: Model a 8 - airzone temperature ........................................................................ 81Fig. 3-19: Model a 9 system ............................................................................................ 82Fig. 3-20: Model a 9 - airzone absolute humidity ............................................................... 82Fig. 3-21: Model a 9 - airzone relative humidity ................................................................. 83Fig. 3-22: Model a 9 - airzone temperature ........................................................................ 83Fig. 3-23: Model a 10 - system .......................................................................................... 84Fig. 3-24: Model a 10 - airzone temperature ...................................................................... 84Fig. 3-25: Model a 11 - system .......................................................................................... 85Fig. 3-26: Model a 11 ventilation HRET .......................................................................... 85Fig. 3-27: Model a 11 airzone temperature ..................................................................... 86Fig. 3-28: Model a 11 - airzone relative humidity ............................................................... 86Fig. 3-29: Model a 12 system .......................................................................................... 87Fig. 3-30: Model a 12 - ventilation outlet temperature (Tout1) ............................................. 87Fig. 3-31: Airzone relative humidity .................................................................................... 88Fig. 3-32: Mode a 13 - system ........................................................................................... 89Fig. 3-33: Model a 13 - temperature at ventilation outlet .................................................... 89Fig. 3-34: Model a 14 abs. humidity at the ventilation outlet ........................................... 90Fig. 3-35: Model a 13 rel. humidity at the ventilation outlet ............................................. 90Fig. 3-36: Model a 13 airzone abs. humidity ................................................................... 90Fig. 3-37: Model a 13 airzone rel. Humidity .................................................................... 91Fig. 3-38: Model b 1 system ............................................................................................ 93Fig. 3-39: Model b 1 airzone temperature ....................................................................... 94


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Fig. 3-40: Model b 1 system ............................................................................................ 95Fig. 3-41: Model b 1 airzone temperature ....................................................................... 95Fig. 3-42: Model c 1 system ............................................................................................ 97Fig. 3-43: Model c 1 airzone temperature ....................................................................... 98

Fig. 3-44: Model c 1 FE temperatures (inside, t = 500s) ................................................. 98Fig. 4-1: Tissue temperature, radius 4.0 cm .................................................................... 102Fig. 4-2: Tissue temperature, radius 7.5 cm .................................................................... 102Fig. 4-3: Tissue temperature, radius 10.3 cm .................................................................. 103Fig. 4-4: Tissue temperature, radius 2.20 cm .................................................................. 105Fig. 4-5: Tissue temperature, radius 4.93 cm .................................................................. 105Fig. 4-6: Tissue temperature, radius 5.48 cm .................................................................. 105Fig. 4-7: Tissue temperature, radius 5.48 cm .................................................................. 107Fig. 4-8: Dead man rectal temp. vs time ....................................................................... 108Fig. 4-9: Dead man temperature distribution vs radius ................................................. 109Fig. 4-10: Thermo-neutral with KSU uniform .................................................................... 113Fig. 4-11: Mean skin temperature .................................................................................... 115Fig. 4-12: Metabolism ...................................................................................................... 116Fig. 4-13: Rectal temperature .......................................................................................... 116Fig. 4-14: Rectal temperature .......................................................................................... 117Fig. 4-15:Time dep. boundary cond.: ambient air temperature and relative humidity ...... 118Fig. 4-16: Mean skin temperature .................................................................................... 119Fig. 4-17: Metabolism ...................................................................................................... 119Fig. 4-18: Forehead temperature ..................................................................................... 119Fig. 4-19: Leg temperature .............................................................................................. 120Fig. 4-20: Chest temperature ........................................................................................... 120Fig. 4-21: Arm temperature .............................................................................................. 120Fig. 4-22: Rectal temperature .......................................................................................... 121Fig. 4-23: Mean skin temperature .................................................................................... 122Fig. 4-24: Metabolism ...................................................................................................... 123Fig. 4-25: Rectal temperature .......................................................................................... 123Fig. 4-26: Mean skin temperature .................................................................................... 125Fig. 4-27: Metabolism ...................................................................................................... 125Fig. 4-28: Rectal temperature .......................................................................................... 125Fig. 4-29: Time dependent boundary conditions: ambient air temperature ...................... 127Fig. 4-30: Mean skin temperature .................................................................................... 127Fig. 4-31: Metabolism ...................................................................................................... 128Fig. 4-32: Rectal temperature .......................................................................................... 128Fig. 4-33: Time dep. boundary cond.: ambient air temperature and relative humidity ..... 129Fig. 4-34: Mean skin temperature .................................................................................... 130Fig. 4-35: Evaporation heat loss ...................................................................................... 130Fig. 4-36: Rectal temperature .......................................................................................... 131


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Fig. 4-37: Time dependent boundary conditions: ambient air temperature ...................... 132Fig. 4-38: Mean skin temperature .................................................................................... 133Fig. 4-39: Evaporation heat loss ...................................................................................... 133Fig. 4-40: Rectal temperature .......................................................................................... 133

Fig. 4-41: Time dep. boundary cond.: ambient air temperature and relative humidity ..... 135Fig. 4-42: Mean skin temperature .................................................................................... 135Fig. 4-43: Evaporation heat loss ...................................................................................... 136Fig. 4-44: Rectal temperature .......................................................................................... 136Fig. 4-45: Time dependent boundary conditions: activity ................................................. 137Fig. 4-46: Mean skin temperature .................................................................................... 138Fig. 4-47: Weight loss ...................................................................................................... 138Fig. 4-48: Oesophageal temperature ............................................................................... 138Fig. 4-49: Time dependent boundary conditions: activity ................................................. 139Fig. 4-50: Mean skin temperature .................................................................................... 140Fig. 4-51: Skin evaporation .............................................................................................. 140Fig. 4-52: Rectal temperature .......................................................................................... 140Fig. 4-53: Time dependent boundary conditions: ambient air temperature ...................... 142Fig. 4-54: Mean skin temperature .................................................................................... 142Fig. 4-55: Metabolism ...................................................................................................... 143Fig. 4-56: Shoulder temperature ...................................................................................... 143Fig. 4-57: Arm temperature .............................................................................................. 143Fig. 4-58: Abdomen temperature ..................................................................................... 144Fig. 4-59: Deviation from inital value ................................................................................ 144Fig. 4-60: Time dependent boundary conditions: ambient air temperature ...................... 145Fig. 4-61: Mean skin temperature .................................................................................... 146Fig. 4-62: Metabolism ...................................................................................................... 146Fig. 4-63: Rectal temperature .......................................................................................... 146Fig. 4-64: Evaporation...................................................................................................... 147Fig. 4-65: Mean skin temperature, after 1hr exposure at different amb. Temperatures ... 148Fig. 4-66: Extra metabolism, after 1hr exposure at different ambient temperatures ........ 149Fig. 4-67: Rectal temperature, after 1hr exposure at different ambient temperatures ...... 149Fig. 4-68: Evaporation, after 1hr exposure at different ambient temperatures ................. 149Fig. 4-69: Skin blood flow, after 3hr expos. at diff. amb. temp. (rh = 85%) ...................... 150Fig. 4-70: Skin evaporation, after 3hr expos. at diff. amb. temp. (rh = 85%) .................... 151Fig. 4-71: Hypothal. temp., after 3hr expos. at diff. amb. temp. (rh = 85%) ..................... 151Fig. 4-72: Mean skin temperature, after 3hr expos. at diff. amb. temp. (rh = 85%) .......... 151Fig. 4-73: Comparison of comfort indices ........................................................................ 153Fig. 4-74: Comparison of comfort indices ........................................................................ 154


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1 Analytic Validations


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1.1 Steady State Problems


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3

1.1.1 1D wall with internal heat generation

System

Fig. 1-1: Wall with heat generation system

System and boundary conditions

Quantity Value Unit Description

Q 650 W / m Heat generation

k 0.79 W / m*K Conductivity

L 1 m Thickness

T1 = T2 20 C Temperature boundary condition

THESEUS-FE file Example_1_1_1.tfe

THESEUS-FE version 4.0

Problem description

Wall with internal heat generation Q has temperature boundary conditions T1 and T2. Thisis a steady state, 1D problem. The exact analytic solution is given in [14].

THESEUS-FE model

1 quad shell element (PSHELL3) with 1 layer and 3 discretization points.

T1

X

T2Q,k

L

System & boundary. cond.:

XL

THESEUS-FE model:

adiabatic

adiabatic


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4

Results

Fig. 1-2: Wall with heat generation - results


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1.1.2 1D composite wall with internal heat generation and convection

System

Fig. 1-3: Composite wall with heat generation system



Q 1.5E6 W / m Heat generation

k1 75 W / m*K Conductivity in left layer

L1 0.05 m Thickness in left layer

k2 150 W / m*K Conductivity in right layer

L2 0.02 m Thickness in right layer

h 1000 W / m2

*K Convective heat transfer coefficient

T 30 C Ambient temperature



Problem descriptionA two layer composite wall with heat generation in the first layer is modelled. Thecomposite wall is adiabatic on one side and has convection boundary condition on theother.

The exact analytic solution for the temperature distribution is given in [14].

THESEUS-FE model

1 quad shell element (PSHELL3) with 2 layers and 3 discretization points per layer.

X

T,hQ1,k1

L1

k2

L2

adiabatic

X

L1 L2

System & boundary. cond.: THESEUS-FE model:

adiabatic

adiabatic


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Results

Fig. 1-4: Composite wall with heat generation - results


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1.1.3 Conduction through a fin (bound. cond.: temp./temp.)

System

X

T2T1k

L

w

X

1 2 3 4 5 6 7 8 9 10 11 12


L

T, h

Fig. 1-5: Conduction through a fin with temp/temp BC system



k 81 W / m*K Conductivity

L 0.833 m Length

w 0.083 m Width

h 100 W / m2



T1 100 C Left side temperature boundary condition

T2 20 C Right side temperature boundary condition



Problem description

A 1D fin is modeled with temperature boundary conditions at both ends and convection onthe top and bottom surfaces. The depth of the beam is 0.05m.The temperature distributionis plotted along the length of the beam.

The exact analytic solution is given in[14].

THESEUS-FE model

12 PSHELL3 elements are used to model the beam, each with 1 layer and 2 discretization

points in the depth direction to represent the top and bottom surfaces. The length of the FEmodel is longer than the actual length, to set boundary conditions on the 1st and 12thelement. Convection boundary condition is assigned to the top and bottom of elements 2through 11.

Comment

Convection that would take place on the sides of the fin (in the depth direction) was notaccounted for in the FE model and is also ignored in the analytic solution.


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Results

10,0

20,0

30,0

40,0

50,0

60,0

70,0

80,0

90,0

100,0

0 0,1 0,2 0,3 0,4 0,5 0,6 0,7 0,8

Distance [m]

T[C]

THESEUS-FE

Analyt ical

Fig. 1-6: Conduction through a fin with temp/temp BC results


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1.1.5 2D conduction in rectangular plate

System

X

T2

T1k

L

Y

w

T1

T1

Group 4

Group 2

Gro

up3

Group1

Group 5


L

w

Fig. 1-9: Rectangular plate conduction system




L 0.833 m Length

w 0.83 m Width

T1 100 C Temperature boundary condition




Problem description

A 2D rectangle is modelled with temperature boundary conditions on all 4 sides.


THESEUS-FE model

12*12 PSHELL3 elements are used to model the rectangle; each with 1 layer and 2

discretization points in the depth direction to represent the top and bottom surfaces. The

length and width of the FE model are longer than the actual length, to set temperatureboundary condition on the faces of groups 1 through 4. Group 5 represents the domain inwhich temperature is calculated as a function of position.


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Results

20.0

30.0

40.0

50.0

60.0

70.0

80.0

90.0

100.0

0.00 0.10 0.20 0.30 0.40 0.50 0.60 0.70 0.80

Distance [m]

T[C]

THESEUS-FE: x=0.0833

Analytical: x=0.0833

THESEUS-FE: x= 0.5

Analytical: x= 0.5

Fig. 1-10: Rectangular plate conduction - results at x = 0.0833 and x = 0.5

Fig. 1-11: Rectangular plate conduction contour plot (temperature)


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1.1.6 2D conduction in a disk (bound. cond.: temp./temp./convec.)

System

k

T1

Rin Rout0

T1

Group 1

Group 2

Group 3


Rin Rout0

T

, h

Fig. 1-12: Conduction in a disk system




Rin 0.065 m Inner radius

Rout 0.185 m Outer radius

T1 50 C Temperature on inner/outer edge

h 100 W / m2


T 20 C Ambiant temperature



Problem description

A 2D disk with a hole of radius 0.065m is modelled with temperature boundary conditionsspecified at the inner and outer edges. Convective boundary conditions hold for the rest ofthe disc.


THESEUS-FE model

3 different groups are used to model the disk, each element is a PSHELL3 with 1 layer and2 discretization points in the depth direction to represent the top and bottom surfaces. Theinner and outer radius of the FE model are longer than the actual length, and are used to


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1.1.7 2D conduction in a disk (bound. cond.:temp./adiabatic./convec.)

System

k

T1

Rin Rout0

adiabatic

Group 1

Group 2

Group 3


Rin Rout0

T, h

Fig. 1-15: Conduction in a disk system




Rin 0.065 m Inner radius

Rout 0.185 m Outer radius

T1 50 C Temperature on inner edge

h 100 W / m2


T 20 C Ambiant temperature



Problem description

A 2D disk with a hole of radius 0.065m is modelled with temperature boundary conditionspecified on the inner edge, and adiabatic condition on the outer edge. Convectiveboundary conditions hold for the rest of the disc.


THESEUS-FE model

3 different groups are used to model the disk, each element is a PSHELL3 with 1 layer and2 discretization points in the depth direction to represent the top and bottom surfaces. Theinner and outer radius of the FE model are shorter and longer than the actual lengths, and


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16

are used for applying the boundary conditions (group 1 and 3). Group 2 represents thedomain on which temperature is calculated as a function of position.

Results

35.0

40.0

45.0

50.0

0.06 0.08 0.10 0.12 0.14 0.16 0.18

Radius [m]

T[C]

THESEUS-FE

Analytical

Fig. 1-16: Conduction in a disk temp. vs. Radius

Fig. 1-17: Conduction in a disk contour plot (temperature)


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1.2 Transient Solutions


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20

1.2.2 Sphere heating

System


R0

adiabaticT0

, k, c

adiabatic

R

T, h

T, h

Fig. 1-21: Sphere heating system




8000 kg / m Density

c 500 J / kg*K Heat capacitance

R 0.05 m Radius

h 100 W / m2 *K Heat transfer coefficient


T0 20 C Initial temperature



Problem description

A sphere with initial temperature T0 is modeled as it warms to the convective ambienttemperature over time.


THESEUS-FE model

Problem was modeled with 3 groups; group 1 is the center face (PSHELL3) where

adiabatic boundary condition is applied, group 2 is the outer shell (PSHELL3) where

convection is applied and group 3 is the inner solid comprised of HEXA elements.


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21

Results

20

25

30

35

40

45

50

0 100 200 300 400 500 600

time [sec]

T[C]

THESEUS-FE

Analytical

Fig. 1-22: Sphere heating time dep. results at center node

Fig. 1-23: Sphere heating contour plot (temperature) at t = 600s


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23

Results

20

25

30

35

40

45

50

55

60

65

70

0 50 100 150 200 250 300

time [sec]

T[C]

THESEUS-FE: Core Temp.

Analytical Solution: Core Temp

THESEUS-FE: Skin Temp

Analytical Solution: Skin Temp

Fig. 1-25: Cylinder heating results for core & skin (t = 0..300s)

0

100

200

300

400

500

600

700

0 5000 10000 15000 20000

time [sec]

T[C]

THESEUS-FE: Core Temp

Analytical Solution: Core Temp

THESEUS-FE: Skin Temp

Analytical Solution: Skin Temp

Fig. 1-26: Cylinder heating results for core & skin (t = 0..22500s)


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t = 200sec t = 300sec t = 600sect = 100sec t = 200sec t = 300sec t = 600sect = 100sec

Fig. 1-27: Cylinder heating contour plot (temperatur)

t = 200sec t = 300sec t = 600sect = 100sec t = 200sec t = 300sec t = 600sect = 100sec

Fig. 1-28: Cylinder heating contour plot (convective heat flux density)


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25

1.2.4 Infinite body with internal heat impulse

System


L

R

T0, , k, c

E


L

R

T0, , k, c

E

Fig. 1-29: Internal heat impulse system




10000 kg / m Density

c 500 J / kg*K Heat capacitance

L 0.6 m Length

R 0.3 m Radius

E 22643.38 J Initial energy input




Problem descriptionA cylinder under a Dirac internal heat impulse is modeled.


THESEUS-FE model

The problem was modeled with 2 groups. The heat impulse is applied on group 1, an

internal PSHELL3 mesh of area 2.26E-5 m2 over a time period of 1 second. Group 2 Is a

solid element mesh and serves as the body of the cylinder. The cylinder is large enoughas to represent an infinite solid for the point load.


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26

Results

0

5

10

15

20

25

30

35

40

0 0.02 0.04 0.06 0.08 0.1

Radius [m]

T[C]

Analytical (t=100sec)

Analytical (t=20sec)

THESEUS-FE (t=100sec)

THESEUS-FE (t=20sec)

Fig. 1-30: Internal heat impulse results at t = 20 & 100s

0

20

40

60

80

100

120

10 100 1000

time [sec]

T[C]

THESEUS-FE (R=0)

Analytical (R=0)

Fig. 1-31: Internal heat impulse time dep. results at R = 0


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t = 20sec t = 40sec

t = 60sec t = 80sec

t = 100sec t = 200sec

1C

0C

Tcore = 37.4C

Tcore = 7.0C

Tcore = 3.3C Tcore = 1.1C

Tcore = 4.5C

Tcore = 13.0C

t = 20sec t = 40sec

t = 60sec t = 80sec

t = 100sec t = 200sec

1C

0C

Tcore = 37.4C

Tcore = 7.0C

Tcore = 3.3C Tcore = 1.1C

Tcore = 4.5C

Tcore = 13.0C

Fig. 1-32: Internal heat impulse contour plots (temperature)


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1.3 Thermal Radiation Boundary Conditions

System

Fig. 1-33: V21 system (closed cavity)


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1.3.1 Numeric view factor integration

For the closed radiation cavity shown in Fig. 1-33 view factors from THESEUS-FE 3.0have been compared with some analytic results. Both results are shown in Fig. 1-34.

Fig. 1-34: V21viewfactors

THESEUS-FE file: Example_1_3_1.tfe

THESEUS-FE results: Example_1_3_1.rpt

In the tfe-file the Keyword VFCTRL that controls the view factor calculation is omitted.Thats why THESEUS-FE uses default settings:

#facets 10000 VF_MTH=S2S, INT_MTH=ADAPTIVE

The (adaptive) surface-to-surface method for view factor calculation does not deal withpartial shading. Partially shaded relations between facets in the matrix above get the viewfactor 0 as long as the element midpoint connection is interrupted by other elements. Toconsider the phenomenon of partial shading more realistic it is recommended to apply the

hemi-sphere (VF_MTH=HS) or hemi-cube method (VF_MTH=HC) together with a highrefinement level: e.g. RFL=5 and SUBELM=5.

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 VFSUM:0,0000 0,1401 0,0155 0,0161 0,0686 0,0161 0,0000 0,0000 0,0213 0,0155 0,1401 0,0000 0,0441 0,0441 0,1018 0,0892 0,0000 0,0000 0,2794 0,0213 0,0140 1,02713

0,0000 0,1401 0,0155 0,0213 0,0155 0,1401 0,0442 0,0442 0,1018 0,0892 0,2793 0,0213 0,0140 1,00000

0,1752 0,0000 0,0000 0,0000 0,0271 0,0338 0,0000 0,0000 0,0385 0,0336 0,1001 0,0551 0,0000 0,0709 0,0551 0,0936 0,0000 0,0000 0,2749 0,0385 0,0122 1,00866

0,1751 0,0000 0,0386 0,0336 0,1001 0,0552 0,0709 0,0552 0,0936 0,2748 0,0386 0,0122 1,00000

0,0387 0,0000 0,0000 0,0000 0,0673 0,0901 0,0000 0,0000 0,2116 0,0563 0,0673 0,0286 0,0000 0,0497 0,0000 0,0000 0,0000 0,0000 0,0768 0,2116 0,0768 0,97474

0,0387 0,0000 0,2116 0,0562 0,0673 0,0497 0,0772 0,2116 0,0772 1,00000

0,0134 0,0000 0,0000 0,0000 0,2566 0,1374 0,1353 0,0740 0,0211 0,0300 0,0225 0,0000 0,0000 0,0000 0,0000 0,0000 0,0000 0,0363 0,0130 0,0341 0,2198 0,99350

0,0000 0,2565 0,1374 0,1353 0,0741 0,0213 0,0363 0,0130 0,0341 0,2197 1,00000

0,0343 0,0109 0,0135 0,1540 0,0000 0,1540 0,1843 0,1315 0,0000 0,0135 0,0109 0,0000 0,0000 0,0000 0,0000 0,0000 0,0304 0,0304 0,0217 0,0269 0,1843 1,00022

0,1539 0,0000 0,1539 0,1842 0,1315 0,0852 0,0303 0,0303 0,0217 0,0269 0,1842 1,00000

0,0134 0,0225 0,0300 0,1374 0,2566 0,0000 0,1353 0,0740 0,0211 0,0000 0,0000 0,0000 0,0000 0,0000 0,0000 0,0000 0,0363 0,0000 0,0130 0,0341 0,2198 0,99350

0,1374 0,2565 0,0000 0,1353 0,0741 0,0211 0,0363 0,0130 0,0341 0,2197 1,00000

0,0000 0,0000 0,0000 0,1015 0,2304 0,1015 0,0000 0,1746 0,0000 0,0000 0,0000 0,0000 0,0000 0,0000 0,0000 0,0000 0,0828 0,0828 0,0000 0,0585 0,1709 1,00296

0,1015 0,2303 0,1015 0,0000 0,1746 0,0828 0,0828 0,1709 1,00000

0,0000 0,0000 0,0000 0,0888 0,2630 0,0888 0,2794 0,0000 0,0000 0,0000 0,0000 0,0000 0,0000 0,0000 0,0000 0,0000 0,0954 0,0954 0,0000 0,0000 0,0892 1,00005

0,0889 0,2630 0,0889 0,2793 0,0000 0,0954 0,0954 0,0892 1,00000

0,0266 0,0385 0,1058 0,0316 0,0000 0,0316 0,0000 0,0000 0,0000 0,1058 0,0384 0,0000 0,0000 0,0000 0,0000 0,0000 0,0000 0,0000 0,1686 0,2436 0,1686 0,95921

0,0266 0,0386 0,1058 0,0320 0,2130 0,0316 0,0000 0,1058 0,0386 0,1686 0,2436 0,1686 1,00000

0,0387 0,0673 0,0563 0,0901 0,0673 0,0000 0,0000 0,0000 0,2116 0,0000 0,0000 0,0286 0,0497 0,0000 0,0000 0,0000 0,0000 0,0000 0,0768 0,2116 0,0768 0,97470

0,0387 0,0673 0,0562 0,0000 0,0772 0,2116 0,0772 1,00000

0,1752 0,1001 0,0336 0,0338 0,0271 0,0000 0,0000 0,0000 0,0384 0,0000 0,0000 0,0551 0,0709 0,0000 0,0551 0,0936 0,0000 0,0000 0,2749 0,0385 0,0122 1,00854

0,1751 0,1001 0,0336 0,0386 0,0000 0,0552 0,0709 0,0552 0,0936 0,2748 0,0386 0,0122 1,00000

0,0000 0,0441 0,0114 0,0000 0,0000 0,0000 0,0000 0,0000 0,0000 0,0114 0,0441 0,0000 0,1401 0,1401 0,1612 0,2794 0,0000 0,0000 0,0892 0,0325 0,0294 0,98299

0,0442 0,0442 0,0000 0,1401 0,1401 0,1612 0,2793 0,0892 0,0325 1,00000

0,0551 0,0000 0,0000 0,0000 0,0000 0,0000 0,0000 0,0000 0,0000 0,0249 0,0709 0,1752 0,0000 0,1001 0,1752 0,2749 0,0000 0,0000 0,0936 0,0289 0,0000 0,99864

0,0552 0,0709 0,1751 0,0000 0,1001 0,1751 0,2748 0,0936 1,00000

0,0551 0,0709 0,0249 0,0000 0,0000 0,0000 0,0000 0,0000 0,0000 0,0000 0,0000 0,1752 0,1001 0,0000 0,1752 0,2749 0,0000 0,0000 0,0936 0,0289 0,0000 0,99864

0,0552 0,0709 0,0249 0,1751 0,1001 0,0000 0,1751 0,2748 0,0936 1,00000

0,1018 0,0441 0,0000 0,0000 0,0000 0,0000 0,0000 0,0000 0,0000 0,0000 0,0441 0,1612 0,1401 0,1401 0,0000 0,2794 0,0000 0,0000 0,0892 0,0000 0,0000 1,00003

0,1018 0,0442 0,0442 0,1612 0,1401 0,1401 0,0000 0,2793 0,0892 1,00000

0,0558 0,0468 0,0000 0,0000 0,0000 0,0000 0,0000 0,0000 0,0000 0,0000 0,0468 0,1746 0,1375 0,1375 0,1746 0,0000 0,0000 0,0000 0,1709 0,0585 0,0000 1,00293

0,0558 0,0468 0,0468 0,1746 0,1374 0,1374 0,1746 0,0000 0,1709 1,00000

0,0000 0,0000 0,0000 0,0000 0,1519 0,1088 0,3312 0,2385 0,0000 0,0000 0,0000 0,0000 0,0000 0,0000 0,0000 0,0000 0,0000 0,0540 0,0000 0,0326 0,0776 0,99450

0,1517 0,1088 0,3312 0,2384 0,0000 0,0540 0,0776 1,00000

0,0000 0,0000 0,0000 0,1088 0,1519 0,0000 0,3312 0,2385 0,0000 0,0000 0,0000 0,0000 0,0000 0,0000 0,0000 0,0000 0,0540 0,0000 0,0000 0,0326 0,0776 0,99450

0,1088 0,1517 0,3312 0,2384 0,0540 0,0000 0,0776 1,00000

0,1746 0,1375 0,0192 0,0098 0,0271 0,0098 0,0000 0,0000 0,0843 0,0192 0,1375 0,0558 0,0468 0,0468 0,0558 0,1709 0,0000 0,0000 0,0000 0,0000 0,0000 0,99497

0,1746 0,1374 0,0193 0,0098 0,0271 0,0098 0,0000 1,00000

0,0266 0,0385 0,1058 0,0512 0,0673 0,0512 0,1170 0,0000 0,2436 0,1058 0,0385 0,0407 0,0289 0,0289 0,0000 0,1170 0,0163 0,0163 0,0000 0,0000 0,0000 1,09348

0,0266 0,0386 0,1058 0,0512 0,0673 0,0512 0,2436 0,1058 0,0386 0,0407 0,0000 1,00000

0,0087 0,0061 0,0192 0,1648 0,2304 0,1648 0,1709 0,0558 0,0843 0,0192 0,0061 0,0184 0,0000 0,0000 0,0000 0,0000 0,0194 0,0194 0,0000 0,0000 0,0000 0,98758

0,0087 0,0061 0,0193 0,1648 0,2303 0,1648 0,1709 0,0558 0,0843 0,0193 0,0061 0,0194 0,0194 0,0000 1,00000

shell elm. id:

-

shell elm. id:

-

THESEUS FE resultsanalytic results


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31

The solar heat hitting the ground:

2grnd

z

m/W63010058cos1000q

583290

The solar heat hitting the exterior glass roof:

W321005305.0Q

W1271005305.0Q

W1561005305.0Q

W315100)58cos(10005.0Q

396.0,496.07.590

405.0,495.058,0F,1F,5.0A

sky,effrf,sun

sky,efftr,sun

sky,effab,sun

bc,sun

sky,effsky,effsky,eff

grndsky

Fig. 1-36: THESEUS-FE shell group results stored in the hdf file

The solar heat hitting the exterior surface of element 5:

2bc,sunrf,sun

2bc,sunab,sun

2

bc,sun

0grndsky

m/W1861qq

m/W744qq

m/W9305.01.05545.0100)32cos(1000q

8.0,32,5.0F,5.0F

In a first step reflection and diffuse transmittance remain unconsidered inside the cavity:

then the solar heat hitting the interior surface of element 9 can be derived from

2bc,sunrf,sun

2

bc,sunab,sun

2

bc,sun

0

m/W431qqm/W172qq

m/W21558cos1000405.0q

8.0,58


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35

Now we add diffuse solar boundary conditions (Idf=100W/m2) and start with the Black Body

Approach:

77%

10%

13%

transmitting roof

opaque: interior surface

31.8W

156W

107.3W

85.9W

21.5W

77% system absorbed

=100%*(156+85.9)/315

10% system reflected

=100%*31.8/315

13% neglected

265W + 50W = 315W

107.3W + 19.8W =127.1W

Fig. 1-42: V21 global energy balance for the BB-Cavity (Idf=100W/m2)

Here not only diffuse reflection but also the diffuse transmitted solar heat flux remainsunconsidered within the Cavity. All together 13% of the solar heat will be neglected.

To considere diffuse energy portions we choose a Pseudo Grey Body Cavity:

87%

11%2%

transmitting roof

opaque: interior surface

31.8W

156W

142.3W

113.8W

28.5W

6.5W

3.2W

0.7W

2.6W

87% system absorbed

=100%*(156+113.8+3.2)/315

11% system reflected

=100%*(31.8+2.6)/315

2% neglected

265W + 50W = 315W

107.3W + 19.8W =127.1W

Fig. 1-43: V21 global energy balance for the PSDGB-Cavity (Idf=100W/m2)

The transmitted diffuse solar heat load of20W now hits the opque interior surfaces andleads to a rise from 122.2W (see Fig. 1-41) to 142.3W. A good approximation of theenergy balance with 2% heat loss results from a Pseudo Grey Body Approach that onceupdates the diffuse reflected solar heat (1 iteration).

The heat load of 6.493 W hitting the interior surface of the roof is divided into 3 parts:

3.218 W absorbed, 2.561 W transmitted and 0.714 W reflected. From this balance we canderive the absorbance of 0.496 and the transmittance of 0.394. Those values result froman effective incidence angle of 60 degree that is assumed for diffuse reflected solar heat.


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fulfil the energy balance: outgoingingoingabsorbed QQQ

As shown here differences for the absorbed long wave radiation heat flux strongly dependon the surface reflectance 1 . From that reasons a Grey Body Cavity is

recommended for100C.

Reflection neglected: Black Body (BB) Cavity Reflection considered: Grey Body (GB) Cavity

Absorbed long wave radiation heat flux density [W/m2]

Reflected rad. heat flux density [W/m2]

Fig. 1-47: V21 coarse mesh comparison between results (with and without reflection)

Reflection neglected: Black Body (BB) Cavity Reflection considered: Grey Body (GB) Cavity

Absorbed long wave radiation heat flux density: 0..22000 W/m2

from reflection !

Absorbed long wave radiation heat flux density 0..1000 W/m2


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Fig. 1-48: V21 fine mesh comparison between results (with and without reflection)

elm.:19 20 21

1

12

16

15

9

8

7

5

Fig. 1-49: V21 interior diffuse reflectance of long wave radiation


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1.3.4 Thermal long wave radiation (opened cavity)

Here we use the same THESEUS-FE model as in the chapter above, with 2 modifications:We delet the elements on the roof (19, 20, 21) and add the sky temperature -100C to thecavity definition in the tfe-file. This operation changes the closed cavity from the chapterabove to an opened cavity. Long wave radiation heat exchang takes now place not onlyinside the cavity, but also between elements inside and a so called background with auser-defined temperature.

0Celm:1

12

16

15

9

8

7

5

1000C

Tsky = -100C

Fig. 1-50: V21 temperature boundary conditions for long wave radiation heat exchange



9T 1273.15 K

absolute temperature of the heated element

1810,81T 273.15 K

absolute temperature of all other elements

skyT 173.15 K absolute temperature of the background

5.67051E-8 W/(m2K

4) Stefan Bolzmann Constant

0.8 surface emissivity

= 1 - 0.2 surface reflectance

THESEUS-FE file V21_rad_BB_opencav.tfe

V21_fine2_rad_BB_opencav.tfe

V21_fine2_rad_GB_opencav.tfe



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2 Advanced Conduction

Several solved and experimental examples from literature have been taken and used for

further validation of THESEUS-FE.


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2.1 Heat Bridges in Buildings


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Results

THESEUS-FE: 19.92CLiterature: 17.92CTHESEUS-FE: 19.92CLiterature: 17.92C

Fig. 2-2: T-shaped heat bridge THESEUS-FEresults


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2.1.2 Heat bridges: Example 2

System


L

L

k1

k2

Tout, hout

Tin, hin

Tout, hout

Adiabatic

Adiabatic


L

L

k1

k2

Tout, hout

Tin, hin

Tout, hout

Adiabatic

Adiabatic

Fig. 2-3: Right-angle heat bridge with boundary conditions



k1 0.21 W / m*K Conductivity


L 0.30 m Length

Tout 5 C Outside air temperature

hout 25 W / m2

*K Heat transfer coefficient

Tin 22 C Inside air temperature

hin 5 W / m2

*K Heat transfer coefficient



Problem description

Heat bridge example, with heat conduction through a composite wall. Convectionboundary conditions are assigned on the outer and inner surface of the wall. THESEUS-FEresults are compared with experimanal results at the corner location[19].

THESEUS-FE model

The problem was modeled with two groups of solid elements and two groups ofPSHELL3elements. Shell elements are placed on the inner and outer surface and are used forassigning boundary conditions.


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Results

THESEUS-FE: 17.02C

Literature: 17.07C

THESEUS-FE: 17.02C

Literature: 17.07C

Fig. 2-4: Right-angle heat bridge THESEUS-FEresults


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51

Results

THESEUS-FE: 18.40C

Literature: 17.92C

THESEUS-FE: 18.40C

Literature: 17.92C

Fig. 2-6: Right-angle heat bridge 2THESEUS-FEresults


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Problem description

Three dimansional heat bridge example, with heat conduction through a composite wall.Convection boundary conditions are assigned on the outer and inner surfaces of thewall.THESEUS-FE results are compared with experimanal results at several corner

locations and along edges[19].

THESEUS-FE model

The problem was modeled with eight groups of solid elements representing the different

parts of the composite wall and two groups of PSHELL3 elements. Shell elements are

placed on inner and outer surfaces and are used for assigning convection boundaryconditions. A uniform mesh with quad elements of approximate length 1cm was used witha total of 390,276 elements.

Results

THESEUS-FE: 18.9CLiterature: 18.4C

THESEUS-FE: 19.5C

Literature: 19.8C

THESEUS-FE: 19.8C

Literature: 19.6C

THESEUS-FE: 17.5C

Literature: 17.2C

THESEUS-FE: 17.7C

Literature: 17.9C

THESEUS-FE: 18.9CLiterature: 18.4C

THESEUS-FE: 19.5C

Literature: 19.8C

THESEUS-FE: 19.8C

Literature: 19.6C

THESEUS-FE: 17.5C

Literature: 17.2C

THESEUS-FE: 17.7C

Literature: 17.9C

Fig. 2-8: 3D heat bridge THESEUS-FEresults


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2.2 Anisotropic Conductivity

System


L1

adiabatic

L1

T2T1

adiabatic

L2

L2

k1

k11

k22


L1

adiabatic

L1

T2T1

adiabatic

L2

L2

k1

k11

k22

Fig. 2-9: Anisotropic plate with boundary conditions








L1 1 m Length

L2 0.8 m Length

45 Degrees Angle of rotation

THESEUS-FE file Example_2_2.tfe


Problem description

A planar square with a tilted square insert is used to demonstrate the effect of anisotropicconductivity. Referring to Fig. 2-9, the outer square is an isotropic material withconductivity k1. Constant temperature boundary conditions are imposed on the verticaledges of the square while the horizontal edges are insulated. The inner material isorthotropic with k11 = k1 / 10 and k22 = k1 / 100. The orientation of the material axes withrespect to the global coordinate axes is 45 degrees. Fig. 2-10 shows the temperature field.The distortion of the results due to the anisotropy is clearly visualized. The dotted lines areisothermal lines from literature for validation[20].


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THESEUS-FE model

The problem was modeled with four groups ofPSHELL3 elements. Temperature boundary

conditions are assigned on the left and right vertical groups. Isotropic material propertiesare assigned to the outer square while anisotorpic material properties are assigned to thelocal coordinates in tensor form of the inner square.

Results

Isothermal lines from literature.

Fig. 2-10: Anisotropic plate THESEUS-FEresults compared with literature results


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2.3 Temperature Dependent Conductivity

System


L1

adiabatic

L3

adiabaticL2

R1

adiab

ati

c

adiab

ati

c

Tout, , hout

k1= Constant

k2= k1+ C1xTemp.

adiabatic

Tout, , hout

Q

Q


L1

adiabatic

L3

adiabaticL2

R1

adiab

ati

c

adiab

ati

c

Tout, , hout

k1= Constant

k2= k1+ C1xTemp.

adiabatic

Tout, , hout

Q

Q

Fig. 2-11: Variable heat conductivity model with boundary conditions



k1 1 W / m*K Conductivity

C1 0.01 Constant

Tout 0 C Temperature boundary condition

hout 0.875 W / m2

*K Heat transfer Coefficient

L1 3 m Length

L2 0.8 m Length

L3 1 m Length

R1 0.5 m Radius

Q 100 W / m2

Heat Flux

THESEUS-FE file Example_2_3.tfe


Problem description

This example illustrates the difference in results when conductivity variations are includedin the model. Fig. 2-11 contains a schematic and mesh for a simple planar geometry. Thetop and bottom halfes are occupied by different isotropic materials; the bottom materialhas constant conductivity, k1, while the top material has a conductivity that varies withtemperature as k= k1+C1*T. A constant heat flux is applied along the left edge of the thedomain. The right side boundaries are insulated. All other surfaces are convectively cooled

with a constant heat-transfer-coefficient and temperature[20].


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THESEUS-FE model

The problem was modeled with two groups of solid elements of arbitrary thickness and

four groups ofPSHELL3 elements. Heat flux and heat convection boundary conditions are

assigned on the shell elements. Transient 2nd order solver was used, due to the non-

liniearity of the problem, with an intial time step of 0.1 seconds and a run time of 25seconds. Variable conductivity is assigned to the second group of solid elements via theTemperature Table shown below:

Results

Isothermal lines from literature.Isothermal lines from literature.

Fig. 2-12: THESEUS-FEresults compared with isotropic lines from literature

Temperature[C]

Conductivity[W/mK]

0 1

100 2

200 3


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58

2.4 Phase Change

System


T0, k1TBC

Adiabatic

Adiabatic

L1

Ad

iab

atic

x

Fig. 2-13: Phase Change model with boundary conditions




1 kg / m3

Density

L 70.26 J / kg Latent heat

Tl -0.15 C Liqidus temperature


TBC -45 C Temperature boundary condition

L1 4 m Length

tfinal 2 s Simulation time

THESEUS-FE file phase_change.tfe


Problem Description

A standard test problem for phase change is the one-dimensional Stefan problem. Theproblem consists of a material region, with length 4 meters, held initially at a unifromtemperature, T0 = 0C, that is greater than the liquidus temperature Tl = -0.15C . At timezero, the left face of the region, x = 0, is lowered to a temperature below the solidustemperature, to TBC= -45C, causing a solidification front to propagate into the material. All

other surfaces are insulated. The schematic of the problem is shown in Fig. 2-13[20].

0

10

20

30

40

50

-50 -40 -30 -20 -10 0 10Temperature [C]

SpecificHeat[J/KgK]

11

10

33.63-0.15

33.63-2.15

1-2.3

1-45

Specific Heat

[J/kgK]

T [C]

Latent Heat

70.26 J/kg

Fig. 2-14: Table for assigning material property specific heat


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THESEUS-FE model

The example was solved using 64 PSHELL3 elements in the domain. Temperature

boundary conditions are applied on the left hand side and the material specific heatproperty, was applied via Fig. 2-14 shown above. Computation was carried out for a phase

change temperature interval of 2 degrees, with solidification staring at -0.15 degrees.

Results

Time=0.0s

Time=0.5s

Time=1.0s

Time=1.5s

Time=2.0s

Solid Liquid

x=1

Time=0.0s

Time=0.5s

Time=1.0s

Time=1.5s

Time=2.0s

Solid Liquid

x=1

Fig. 2-15: Phase change: THESEUS-FEresults

In Fig. 2-16 THESEUS-FE results are compared with the analytical solution. We see adiscrepancy of approxametaly 1 degree, which is attributed to the numerical calculation ofthe Latent Heat addition. In nature, phase change or Latent Heat addition occursinstantaneously. Numerically, the dirac impulse function can not be modeled, and therefore we apply the Latent Heat addtion through a 2 degree temperature band. Thisintroduces a modeling error that results in an approximately 1 degree solution error.

-15

-13

-11

-9

-7

-5

-3

-1

1

0 0.5 1 1.5 2

Time [s]

Temperature[C]

Analytic

THESEUS FE Results

Fig. 2-16: Phase change: Comparison of FE results with analytical solution at x = 1


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2.5 Cylinder Radiation (open grey body cavity)

System


D

Adiabatic

Adiabatic

L

k,

q

T0


D

Adiabatic

Adiabatic

L

k,

q

T0

Fig. 2-17: Cylinder Radiation example with boundary conditions



0.3 Surface emissivity


T0 0 K Surrounding temperature

L 4 m Length

D 1 m Diameter

q 200 W / m2 Applied heat flux

THESEUS-FE file cylinder_radiation.tfe


Problem Description

A simple heated enclosure is the circular tube, open at both ends and insulated on theoutside surface. For a uniform heat addition q = 200 W/m2 to the inside surface of the tubewall and a surrounding environment at 0K, we calculate the stead state temperaturedistribution along the inside surface[18].

THESEUS-FE model

The open ends of the tube are nonreflecting, and they are assumed to be black bodies atthe surrounding temperature 0 K. In THESEUS-FE, three major types of radiation heatexchange are realized; for the current problem the model used was open-cavity with graybody radiation. Gray body radiation considers reflection and absorption of each elementand performs a full view factor matrix calculation. On the inner surface of the cylinder wall,the boundary conditions applied are the background temperature and heat flux. This is apure thermal radiation and conduction problem; the material properties assigned are theemission coefficient and the conductivity k.


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Results

In Fig. 2-18 the THESEUS-FE results displayed are the view factor sum of each element,the radiation from each element, and the nodal temperature values.

The view factor is a quantity used to define the fraction of thermal power leaving oneelement and reaching another. The sum of the view factor on each element thenrepresents the fraction of thermal power leaving one elment and reaching all other elmentsin the domain. For enclosed bodies the view factor sum of each element is their fore one.For open cavitites, the value will be less then one, depending on how much thermal poweris lost to the environment. The radiation view factor depends strongly on distance and fromthe results we can see that thermal power is mainly lost near the cylinder ends, while verylittle power is lost from elements toward the center of the cylinder. The maximum andminimum view factor sums are 0.975 and 0.6.

The second diagram quantifies how much radiation heat is lost from each element. For

elements near the cylinder ends, it is of magnitude -55 W/m2

.In the last diagram, the temperature results are displayed and compared with the analyticsolution. There is a close agreement between THESEUS-FE results and the analyticresults. We can further see that there is a 75 degree temperature difference between thecenter of the cylinder, where little heat is lost compared with elements at the ends of thecylinder where most of the thermal power is lost via radiation.

View Factor Sum

Radiation [W/m2]

View Factor Sum

Radiation [W/m2]

Fig. 2-18: Cylinder Radiation: THESEUS-FEresults


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2.6 Disk Radiation

System


0 Ri Ro

AdiabaticAdiabatic

k,

T0TBC

a


0 Ri Ro

AdiabaticAdiabatic

k,

T0TBC

a

Fig. 2-20: Disk



0.7 Surface emissivity

k 15.0 W / (m K) Conductivity

T0 -273.15 C Initial temperature

TBC 100 C Boundary condition

a 0.01 m Thickness

Rl 0.04 m Inner radius

R0 0.24 m Outer radius

THESEUS-FE file disk_radiation.tfe


Problem Description

An annular fin in vacuum is insulated on one face and aournd its outside edge. The diskhas thickness of 0.01m, inner radius 0.04m, outer radius 0.24m, and thermal conductivity15.0 W/mK. Energy is supplied to the inner edge from a pipe that fits the central hole andmaintains the inner edge at 100 C. The exposed annular surface, which is diffuse-graywith emissivity 0.7, radiates to the environment at 0 K to investigate performance in a coldenvironment. Results are shown for the temperature distribution as a function of radialposition along the disk, the radiation flux from each element and the radiation efficiency ofthe disk calculated from THESEUS-FE is compared with results from literature[18]. In Fig.2-22, Qrad-total is the total heat radiation from the disk to the environment taken from theTHESEUS-FE simulation and Qrad-boundary= A(T

4BC - T

40) is the calculated theoretical

value, if the disk was held at a constant temperature of TBC. Where is the Stefan-Boltzmann constant and A is the disk surface area


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Radiation heat loss

[W/m2]

Convection heat loss

Radiation heat loss

[W/m2]

Convection heat loss

Fig. 2-26: Radiation Cylinder with 1D Flow: Field Results from Literature


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3.1 Model aThis model is composed of a shell element and an airzone, both are thermally connected

via convection. An airzone is a mixture of dry air and steam with a homogeneoustemperature distribution. Besides temperature the humidity is the second degree offreedom of the airzone.

1m

1m

1m

alu plate

airzone

Tairz, h


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3.1.3 Linear convective airzone cooling - considering humidity (a 3)

System

airzone: V=1m3

alu plate: 1m*1m*1mm

1 quad, PSHELL1, disc=2

conductivity: k = 238 W/mK

spec. heat: c = 945 J/kgK

density: = 2700 kg/m3

(pos. side)

z

x,y

airzone: V=1m3






(pos. side)

z

x,y

z

x,y

Fig. 3-5: Model a 3 system



T0 20 C Initial temperature for airzone and plate

RLF0 68.6 % Initial relative humidity

hpos = hneg 6.0 W / m2*C Convection coefficient at positive/negative side of

the plate

Tamb,pos = Tairz Ambient temp. at pos. side = airzone temp.

Tamb,neg -20 C Ambient temperature at negative side

tend 500 s End time of simulation

Solver file model_a3.tfe


Results

0

0.002

0.004

0.006

0.008

0.01

0.012

0 100 200 300 400 500

time [sec]

[kg/kg]

THESEUS-FE

INKA

Fig. 3-6: Model a 3 - airzone absolute humidity


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3.1.5 Sun heating airzone - without considering humidity (a 5)

System

airzone: V=1m3

(pos. side)

z

x,y

sun

alti = 60






airzone: V=1m3

(pos. side)

z

x,y

z

x,y

sun

alti = 60










RLF0 0 % Initial relative humidity

vpos = vneg 0 m / s Ambient air velocity

at positive/negative side of the plate (BC-FC)


Tamb,neg 20 C Ambient temp. at neg. side

qdr 1000 W / m2

Direct sun intensity




Results

0

10

20

30

40

50

60

70

0 100 200 300 400 500time [sec]

T[C]

THESEUS-FE

INKA

Fig. 3-11: Model a 5 - airzone temperature


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3.1.6 Sun heating airzone - without considering humidity (a 6)

System

airzone: V=1m3

(pos. side)

z

x,y

z

x,y

sun

alti = 20 alu plate: 1m*1m*1mm1 quad, PSHELL1, disc=2




Fig. 3-12: Model a 6 - system




RLF0 0 % Initial relative humidity




Tamb,neg 20 C Ambient temperature at negative sideqdr 1000 W / m

2Direct sun intensity




Results

0

5

10

15

20

25

30

35

40

0 100 200 300 400 500time [sec]

T[C]

THESEUS-FE

INKA

Fig. 3-13: Model a 6 - airzone temperature


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3.1.9 Airzone cooled by ventilation RVT (a 9)

System

airzone: V=1m3

(pos. side)

z

x,y

z

x,y

VENTILT - RVT

dV/dt = 0.001 m3/sec

T_out = 0C

RLF_out = 100%

X_out =0.00374 (saturated)










RLF0 68.6 % Initial relative humidity




Tamb,neg 20 C Ambient temperature at negative sidetend 500 s End time of simulation



Results

0.007

0.008

0.009

0.010

0 100 200 300 400 500

time [sec]

[kg/kg]

THESEUS-FE

INKA

Fig. 3-20: Model a 9 - airzone absolute humidity


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3.1.10 Airzone heated by ventilation RET (a 10)

System

airzone: V=1m3

(pos. side)

manual validation v42

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