Appendix E. Construction of a reduced thermal model of a Traveling Wave Tube with a modal method. Martin Raynaud (Thales Alenia Space, France)

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1 57 Appendix E Construction of a reduced thermal model of a Traveling Wave Tube with a modal method Martin Raynaud (Thales Alenia Space, France) Quentin Malartic Frederic Joly Alain Neveu (Universite Evry Val Essone, France)

2 58 Construction of a reduced thermal model of a Traveling Wave Tube with a modal method Abstract This work presents the principle of the construction of a reduced thermal model using a modal method based on branches combination. The method is applied to a Traveling Wave Tube and shows that it is possible to obtain accurate enough results by using only 10 degrees of freedom instead of several hundred thousands degrees of freedom as required by Finite Elements or Finite Volume methods. The robustness, i.e., sensitivity to boundary conditions and heat sources, of the method is also studied.

3 Construction of a reduced thermal model of a Traveling Wave Tube with a modal method 59 ESA / ESTEC October 24 & 25, 2017 Construction of a reduced thermal model of a Traveling Wave Tube with a modal method Martin RAYNAUD TAS-F Quentin MALARTIC, Frederic JOLY & Alain NEVEU, LMME, UEVE, France 1 31st European Space Thermal Analysis Workshop Summary Problem statement TWT Description TWT Nodal network Theory (ligth) of the modal reduction Application to TWT Results Conclusion 2

4 60 Construction of a reduced thermal model of a Traveling Wave Tube with a modal method PH1 Problem statement Thermal Reduced model of equipments are mandatory as input for the SC thermal model Reduced model are given by the suppliers Difficulty to know the accuracy of the model Most often they are not robust to boundary conditions TAS want to improve the accuracy & robustness of reduced thermal model The objective of this work is to evaluate a method that is able to generate a model that could be coupled with e- Therm. 3 Conductive traveling Wave Tube (TWT) Ka Band 170 W External view (276 mm x 40 mm : baseplate area 130 cm²) 4

5 Construction of a reduced thermal model of a Traveling Wave Tube with a modal method 61 Thermal power Dissipation Total thermal power varies with mode : 100 W to 140 W 5 Nodal Network provided by the supplier 32 nodes with 28 nodes on the baseplate. Thermal Reference point is node 441 6

6 62 Construction of a reduced thermal model of a Traveling Wave Tube with a modal method Baseplate nodal overview Smaller area in the region of high heat flux density 7 From Finite Elements Model to Reduced model Finite Elements Calculation Unknown : T(t) Modale base Unknown : X(t) Direct calculation for various set of boundary conditions Degres of Freedom (DOF) DOF Reduction by modes combination 8 10 or 20 DOF

Construction of a reduced thermal model of a Traveling Wave Tube with a modal method 63 PH8 Various

energy, mode sizes, ) : The information contained in the mode that are neglected is lost should be able

(quasi-automatic) that is very efficient the combinations allows to reduce the total number of modes

geometry from a step file Define thermal properties and boundary conditions Chose the number of training

7 Construction of a reduced thermal model of a Traveling Wave Tube with a modal method 63 PH8 Various methods to obtain a reduced model Most usual Neglect some modes based on various considerations (time, energy, mode sizes, ) : The information contained in the mode that are neglected is lost should be able to find a better process LMME has developed an original method based on mode combinations (quasi-automatic) that is very efficient the combinations allows to reduce the total number of modes while minimizing the loss of information 9 PH9 Construction of the reduced thermal model (1/2) Import geometry from a step file Define thermal properties and boundary conditions Chose the number of training cases very important as shown later Define the outputs that are desired define the observation matrix Exemple : Temperature Reference Point 10

64 Construction of a reduced thermal model of a

Construction of the reduced thermal model (2/2)

Conductance between baseplate and heat sink (W/(m²

5000 saturation no (Vacuum) 3 5000 3 db OBO no

saturation no (Vacuum) 6 3000 3 db OBO no (Vacuum) 7

preferred Compromise also to be find between

as shown later Decide the number of modes that will

11 Temperature field (FEM calculation) for a vacuum

8 64 Construction of a reduced thermal model of a Traveling Wave Tube with a modal method PH11 Construction of the reduced thermal model (2/2) Modes calculations for the following case : Case Conductance between baseplate and heat sink (W/(m² C) TWT mode Convection no drive no (Vacuum) saturation no (Vacuum) db OBO no (Vacuum) no drive no (Vacuum) saturation no (Vacuum) db OBO no (Vacuum) db OBO yes : h = 20 W/(m² C) Vacuum cases are preferred Compromise also to be find between transient and steady state govern the time of study as shown later Decide the number of modes that will be kept for the reduced model degree of freedom. 11 Temperature field (FEM calculation) for a vacuum case heat sink temperature is 87 C large temperature gradient from top to bottom in the collector area 12

9 Construction of a reduced thermal model of a Traveling Wave Tube with a modal method 65 Temperature field (FEM calculation) for the case in air heat sink temperatures is 20 C air temperature is 20 C Large temperature gradient along the TWT with a somewhat uniform temperature in the collector area The TWT temperature fields reallly differ for this two cases. 13 Comparison #1 BC3 : 10 modes «constructed» with 3 set of BC (1-2 & 3) Temperature Time variations of the Top temperature of the collector Difference between FEM & RM The difference between the two models increase but the result is still quite good with only 10 DOF. 14

10 66 Construction of a reduced thermal model of a Traveling Wave Tube with a modal method Comparison #1 BC3 : 10 modes «constructed» with 3 set of BC (1-2 & 3) Temperature Time variations of the Thermal Reference Point Difference between FEM & RM 15 Comparison #2 BC Air : 10 modes «constructed» with BC (1-2 & 3 : vacuum) Temperature Time variations of the Thermal Reference Point Difference between FEM & RM The difference is large but not out of base considering that the modes calculated for a case in air are not taken into account. 16

11 Construction of a reduced thermal model of a Traveling Wave Tube with a modal method 67 Comparison #3 BC Air : 10 modes «constructed» with BC (1-2-3 & 7) Temperature Time variations of the Thermal Reference Point Difference between FEM & RM The difference decreases since the modes calculated for a case in air are not taken into account but with a weight that is limited compared to the modes of vacuum cases. 17 Localisation of «errors» during transient (30 s) Difference between FEM & RM 18

68 Construction of a reduced thermal model

method Localisation of «errors» at steady

19 Conclusions This preliminary evaluation

required to built the appropriate thermal

observation matrix of the reduced model in

12 68 Construction of a reduced thermal model of a Traveling Wave Tube with a modal method Localisation of «errors» at steady state (300 s) Difference between FEM & RM 19 Conclusions This preliminary evaluation is very promizing. The method is quite robust to boundary conditions. It is possible to obtain an accurate enough model with a very limited number of degree of freedom (10 to 20 modes) the calculation is almost instanteneous. Complex theory but the development is mature enough to be used rapidly (by using mode combinations). Yet a minimum of thermal expertise is required to built the appropriate thermal modes Next step is to couple the observation matrix of the reduced model in e-therm. Then it will be necessary to improve the radiative heat transfer for the calculation of the modes Generalization to other unit 20 Thank you! Any questions?

Appendix B. GENETIK+ Near-real time thermal model correlation using genetic algorithm. Guillaume Mas (CNES, France)

Appendix B. GENETIK+ Near-real time thermal model correlation using genetic algorithm. Guillaume Mas (CNES, France) 19 Appendix B GENETIK+ Near-real time thermal model correlation using genetic algorithm Guillaume Mas (CNES, France) 20 GENETIK+ Near-real time thermal model correlation using genetic algorithm Abstract