ALMA Calibration Target Analysis Report (Preliminary)...Jun 11, 2009 · 2009‐06‐10, J. Eder 1. Scope This report summarizes the analyses performed on the calibration target for

ALMA Calibration Target Analysis Report (Preliminary) 2009‐06‐10, J. Eder

1. Scope This report summarizes the analyses performed on the calibration target for the ALMA (Atacama Large Millimeter Array) receivers, performed for sizing and optimization of the thermo‐mechanical design. The analysis includes the following:

• FEM modeling (ANSYS) • Analysis of the conceptual design and determination of needed thicknesses, thermal insulation,

optimization with respect to mass and performance • Definition of locations for heaters and temperature sensors as needed for control of the

temperature within requirements • Determination of temperatures, temperature gradients, thermo‐elastic deformations, stress

(compatibility of mating materials) for all operational conditions (considering range of elevation angle, air flow and air temperature)

• Determination of gravity induced deformations and stress • Determination of stress due to transport conditions

The status of the analysis summarized herein is preliminary. The results are focused on sizing of the parts. The analysis will be updated for the final design once decided. In fact, the design of the calibration target is meanwhile superseded but the main conclusions remain valid. Applicable documents AD01 Calibration Device Technical Specifications FEND‐40‐06‐04‐00‐009‐A‐SPE Reference documents RD01 ACT Prototype Calibration Load Test Report FEND‐40‐06‐04‐00‐005‐A‐REP RD02 ACT Design Report TBD

2. Reference design The ALMA receivers will be calibrated using two calibration targets in the receiver cabin. The ´hot target´ is heated to an elevated temperature up to 100°C (nominal operation at 70 ºC), while the ´ambient target´ remains at ambient temperature. The quality of these calibration targets is essential for the accuracy of the astronomical observations. A perfect black‐body radiator with a known and uniform temperature would be the ideal calibration target, but any practical target will have an emissivity smaller than unity. Here below the current concept is shown, which has been derived from various analyses and tests. The main elements and features of the calibration target design are outlined in the following sketch.

Main Absorber

Secondary Absorber

Main Reflector

Secondary Reflector

Housing Interface

290

200

100

12°

Eccosorb layer

Foil heaters

100

Thermal insulation

210

100

The calibration target consists of the following parts:

Main Absorber Main Absorber Structure Main Absorber Layer Thermo-foil heaters Temperature sensors Main Reflector Main reflector structure Thermo-foil heaters Temperature sensors

Thermal Washers Secondary Absorber Secondary Absorber Structure Secondary Absorber Layer Thermo-foil heaters Temperature sensors

Thermal Washers Secondary Reflector Secondary reflector structure Thermo-foil heaters Temperature sensors

Thermal Washers Main Absorber Support Structure Cone Absorber Frame Housing Frame

Housing Cylinder Cover Harness connector The main absorber structure is a cone with an absorber layer. The main absorber is supported by a conical support structure made from GFRP to provide thermal de‐coupling from the housing. The secondary absorber is made from a thin cylinder, also coated with an absorber layer. The secondary absorber is mounted to the housing via thermal washers. The absorber layer is composed of 2 mm Eccorsorb 110 and 2 mm Eccosorb 114. The main and secondary reflectors are thin Aluminium bodies. The surface is Alodine treated. The reflectors are mounted via thermal washers. Absorbers and reflectors are equipped with foil heaters and temperature sensors to ensure efficient thermal control in accordance with the stringent requirements outlined in the following section. The following parts and materials are used:

Structural parts Aluminium (general) GFRP (cone of main absorber structure) Absorber Eccosorb CR 110‐114 Thermal washers GFRP Fasteners Stainless Steel Thermo‐foil heaters TBD Temperature sensors total 8 PT 100 (3 for hot target, 2 for cold target and 3 for interfaces) Harness Loose cable with TBD length, with cable gland at housing or cover Connectors D‐Sub (25 pins for hot target and 15 pins for ambient target)

The temperature controller is not part of the targets. For detailed definitions refer to the design report.

3. Requirements ALMA has the goal to achieve an absolute radiometric accuracy better than 5% at frequencies between 30 ‐ 950 GHz. For the calibration of the receivers ambient and hot blackbody calibration target will be used, which can be inserted in the optical path. The calibration targets need to have a high emissivity, which is equivalent to a low value of integrated scattering into all possible directions. Even more critical is the coherent backscatter of the target, since it will lead to frequency dependent standing waves between the target and the receiver. In addition the targets have to be held at a uniform temperature to ensure that the surface brightness temperature corresponds to the reading of the thermometers in their body. The temperature requirements for nominal operation are:

Component Hot Target (1) Cold Target (2) Main absorber T=70 °C ± 0.5 K Ambient Secondary absorber T=70 °C ± 2 K Main reflector T=70 °C ± 5 K Secondary reflector TBD

(1) The hot target shall be capable of being heated to 100 °C (2) The temperature of the ambient target is not actively controlled, but shall be known to an accuracy of ± 0.3 K for the absorbers and ± 5 K for the reflectors.

The housing temperature shall not exceed 50 °C under hot operating conditions. The operational conditions are sketched here below for 0° altitude (Zenith pointing)

For other altitudes the gravity direction changes with respect to the calibration target axis. The air flow orientation and receiver position remain unchanged with respect to the calibration target axis. The following conditions are valid for design calculations:

Air temperature 16 °C to 22 °C (lower temperature is considered worst case) Air speed for calculations 0.2 m/s, 1 m/s, 3 m/s Receiver temperature Same as air temperature Mounting plate temperature Same as air temperature Telescope altitude 10°, 33°, 57°, 80°

The total mass shall be equal or less than 11 kg for two calibration targets (hot/cold). The difference between the two targets shall be less than 2 kg. The calibration targets shall comply with the following survival specification:

Shock

• 4 g shock load in the vertical direction • 3 g shock load in any horizontal direction

Vibration

4. Mathematical Model The analysis is performed by means of ANSYS. The model is described below.

X

YZ

Interface temperature 16°C Hard-mounts (UX=UY=UZ=0)

Model mass Total mass is 7.6 kg (Eccosorb modeled by means of additional distributed mass, stiffness and gradient through thickness are neglected) Material properties

Material Young

modulus [MPa]

Poisson ratio

Density [kg/m3]

CTE [°C-1]

Thermal conductivity

[W/mK] Emissivity Component

Aluminum 70000 0.33 2730 24*10-6 160 0.10 Structure (housing, reflectors, absorbers)

GFRP 18000 0.3 1800 10*10-6 0.3 0.80 Washers, insulation ring, main reflector support

Eccosorb 3000 3100 30*10-6 0.96 0.75 Absorber layer

Thickness

Component Material Thickness [mm]

Main reflector Aluminium 3.0

Main absorber Aluminium / Eccosorb 3.0 / 4.0

Secondary reflector Aluminium 3.0

Secondary absorber Aluminium / Eccosorb 3.0 / 4.0

5. Thermal analysis For thermal analysis assumptions have been made for the convection factors as follows:

Receiver

Mounting PlateConduction

Calibration Target

Air Flow

Convection coefficients

Forced convection for horizontal plateForced convection for cyclinderNatural convection (estimated)Natural convection (estimatedForced convection (estimated)

Air properties at 5000m altitude temperature T = 40 °C pressure p = 5.41E+04 Pa density ρ = 5.98E‐01 kg/m3 thermal conductivity k = 0.0273 W/mK specific heat Cp = 1101 J/kg K absolute viscosity μ = 1.71E‐05 N s/m2 at 19°C kinematic viscosity ν = 2.59E‐05 m2/s at 19°C Prandtl number Pr = 0.71thermal diffusivity α = 4.15E‐05 m2/s Convection coefficients (W/m2K)

Component No air flow (0m/s)

High air speed(3m/s)

Housing 3.0 11.3 Cover 6.2 12.2

Conductive links are calculated from geometry, convective and radiative links are determined by means of analytical method. Only relevant convective links are implemented (heat > 1 W). In order to avoid CFD analyses assumptions have been made as follows. The housing cylinder and cover can be determined analytically (see table above). For the interior the determination of the convection coefficients becomes difficult. In order to generate a worst case thermal gradient the following convection coefficients have been assumed. This ensures that at the tip of the main reflector a high cooling power is applied which has to be compensated by heating.

In order to see the influence of the convection coefficients various cases have been performed with a bandwidth of convection coefficients including a case completely without convection (conduction only). Convection coefficients inside the target are applied to secondary reflector (50% of housing coefficient) and main reflector tip (50% of housing coefficient). Enclosure 1 convection, being a thin air gap, was considering only conductivity of air. The heat exchange between housing (colder) and secondary absorber/reflector (warmer) is applied in the FEM by means of distributed heat at nodes. For the absorber a fraction of the convection coefficient of the cylinder is assumed. At the bottom section a higher value is assumed since there some air turbulence is expected. Then this is reduced in steps for two specific sections as follows. In the main absorber tip it is assumed as a baseline that the air is not moving and parts are at the same temperature anyway. Same for the secondary absorber tip, which is even better protected from any air flows. In order to find worst cases, iterations have been made for these areas.

Interface screws This are assumed by means of assumptions in conductance, according to tables below depending on screw size.

Screw size

Thermal Conductance

[W/K] M3 0.084 M4 0.15 M5 0.23 M6 0.34

Screws

Main Absorber

Secondary Absorber

Main Reflector

Secondary Reflector

Housing Interface

Screw set # Link Items Size

Thermal insulation

1 Interface/ Housing 6 M6 No

2a Housing / Main reflector / Main absorber support / Cover 6 M6 Insulation ring (Main reflector / Housing)

2b Housing / Cover 6 M6 No

3 Insulation support / Main absorber 8 M5 No

4 Housing / Secondary reflector 12 M3 Insulation ring

5 Housing / Secondary absorber bottom 6 M4 Thermal washers

6 Housing / Secondary absorber top 6 M4 Thermal washers

1

2

3

4 5 6

Heater power For compensation of heat loss, heater power has been applied around the absorbers and reflectors as defined below.

Component Conduction only

Convection max

N_HEAT_MAIN_ABSORBER_BOT ≈ 0 ≈ 0 N_HEAT_MAIN_ABSORBER_TOP ≈ 0 ≈ 0 N_HEAT_MAIN_REFLECTOR_BOT 0 7.0 N_HEAT_MAIN_REFLECTOR_TOP 12.9 15.0 N_HEAT_SECONDARY_ABSORBER_BOT 0.8 14.0 N_HEAT_SECONDARY_ABSORBER_TOP 0.8 14.0 N_HEAT_SECONDARY_REFLECTOR 13.1 26.9

total 27.6 77.0 The calculated temperatures are presented in the following temperature plots. For each case two plots are provided, one for the entire model and another one showing the absorbers and reflectors only (for better resolution of the color ranges).

Thermal analysis considering conduction only

ANSYS 11.0SP1 MAY 27 200915:47:32 NODAL SOLUTIONSTEP=1 SUB =1 TIME=1 TEMP (AVG) RSYS=0PowerGraphicsEFACET=1AVRES=MatSMN =16 SMX =73.382

1

MN

MX

X

Y

Z

16 22.376 28.751 35.127 41.503 47.879 54.254 60.63 67.006 73.382

ANSYS 11.0SP1 MAY 27 200915:47:47 NODAL SOLUTIONSTEP=1 SUB =1 TIME=1 TEMP (AVG) RSYS=0PowerGraphicsEFACET=1AVRES=MatSMN =68.302 SMX =73.382

1

MN

MX

X

Y

Z

68.302 68.866 69.431 69.995 70.56 71.124 71.688 72.253 72.817 73.382

Gradients ----------------------------------------------------------- Temperature [degC] Component Max Min Gradient Requirement ----------------------------------------------------------- Housing 38.0 29.5 8.47 < 50 Cover 37.6 37.6 0.00 - Main absorber 70.4 70.4 0.00 70+/-0.5 Main reflector 73.7 68.6 5.12 70+/-5 Secondary absorber 69.7 69.5 0.19 70+/-2 Secondary reflector 70.4 68.9 1.50 TBD Support Main reflector 70.4 68.6 1.86 - -----------------------------------------------------------

Thermal analysis considering high air speed and absorber convection coefficient set 50/25/0

ANSYS 11.0SP1 MAY 27 200915:50:09 NODAL SOLUTIONSTEP=1 SUB =1 TIME=1 TEMP (AVG) RSYS=0PowerGraphicsEFACET=1AVRES=MatSMN =16 SMX =72.895

1

MNMX

X

Y Z

16 22.322 28.643 34.965 41.287 47.608 53.93 60.252 66.573 72.895


1

MN

MX

X

Y Z

67.419 68.027 68.636 69.244 69.853 70.461 71.07 71.678 72.286 72.895

Gradients ----------------------------------------------------------- Temperature [degC] Component Max Min Gradient Requirement ----------------------------------------------------------- Housing 34.6 28.7 5.90 < 50 Cover 30.5 29.3 1.23 - Main absorber 69.7 69.7 0.00 70+/-0.5 Main reflector 72.9 67.4 5.48 70+/-5 Secondary absorber 70.5 69.3 1.26 70+/-2 Secondary reflector 70.8 68.8 1.96 TBD Support Main reflector 69.7 67.4 2.27 - -----------------------------------------------------------

Variation of absorber convection coefficients For assessment of the dependency of the gradients on the air flow conditions a variation of amplitude and distribution of the convection coefficients has been made as follows. The numbers refor to the percentage of the coeffecioncoefficient at *** Aparture/Mid Band/Tip *** of the main absorber. *** 50/0/0 *** ----------------------------------------------------------- Temperature [degC] Component Max Min Gradient Requirement ----------------------------------------------------------- Housing 34.6 28.7 5.90 < 50 Cover 30.5 29.3 1.23 - Main absorber 69.7 69.7 0.00 70+/-0.5 Main reflector 72.9 67.4 5.48 70+/-5 Secondary absorber 70.5 69.3 1.26 70+/-2 Secondary reflector 70.8 68.8 1.96 TBD Support Main reflector 69.7 67.4 2.27 - ----------------------------------------------------------- Total Heater Power 77.0 W *** 50/25/0 *** ----------------------------------------------------------- Temperature [degC] Component Max Min Gradient Requirement ----------------------------------------------------------- Housing 34.5 28.7 5.85 < 50 Cover 30.5 29.3 1.23 - Main absorber 70.0 70.0 0.00 70+/-0.5 Main reflector 72.5 67.1 5.42 70+/-5 Secondary absorber 70.7 69.5 1.27 70+/-2 Secondary reflector 71.0 69.0 1.97 TBD Support Main reflector 70.0 67.1 2.89 - ----------------------------------------------------------- Total Heater Power 78.3 W *** 50/25/12.5 *** ----------------------------------------------------------- Temperature [degC] Component Max Min Gradient Requirement ----------------------------------------------------------- Housing 34.5 28.7 5.81 < 50 Cover 30.5 29.3 1.22 - Main absorber 70.8 69.4 1.46 70+/-0.5 Main reflector 73.1 66.9 6.22 70+/-5 Secondary absorber 70.8 69.3 1.49 70+/-2 Secondary reflector 71.4 69.4 1.99 TBD Support Main reflector 69.5 18.2 51.30 - ----------------------------------------------------------- Total Heater Power 97.4 W *** 100/50/25 *** ----------------------------------------------------------- Temperature [degC] Component Max Min Gradient Requirement ----------------------------------------------------------- Housing 34.4 28.6 5.75 < 50 Cover 30.4 29.2 1.22 - Main absorber 71.2 68.4 2.85 70+/-0.5 Main reflector 73.0 66.2 6.85 70+/-5 Secondary absorber 71.1 69.4 1.71 70+/-2 Secondary reflector 71.0 68.8 2.21 TBD Support Main reflector 68.7 16.5 52.28 - ----------------------------------------------------------- Total Heater Power 132.5 W

*** 25/25/25 *** ----------------------------------------------------------- Temperature [degC] Component Max Min Gradient Requirement ----------------------------------------------------------- Housing 34.5 28.7 5.85 < 50 Cover 30.5 29.3 1.23 - Main absorber 71.2 68.4 2.85 70+/-0.5 Main reflector 74.1 67.1 6.99 70+/-5 Secondary absorber 71.1 69.4 1.71 70+/-2 Secondary reflector 70.8 69.0 1.84 TBD Support Main reflector 68.7 16.5 52.27 - ----------------------------------------------------------- Total Heater Power 108.0 W *** 10/10/10 *** ----------------------------------------------------------- Temperature [degC] Component Max Min Gradient Requirement ----------------------------------------------------------- Housing 34.5 28.7 5.85 < 50 Cover 30.5 29.3 1.23 - Main absorber 70.5 69.3 1.17 70+/-0.5 Main reflector 73.2 67.1 6.11 70+/-5 Secondary absorber 70.6 69.2 1.44 70+/-2 Secondary reflector 70.8 69.0 1.77 TBD Support Main reflector 69.4 19.2 50.15 - ----------------------------------------------------------- Total Heater Power 79.7 W The worst gradient occurs for 100/50/25. However, this can be improved by adjusting the heater power, see below: *** 100/50/25 *** with adjusted heater power ----------------------------------------------------------- Temperature [degC] Component Max Min Gradient Requirement ----------------------------------------------------------- Housing 34.4 28.6 5.75 < 50 Cover 30.4 29.2 1.22 - Main absorber 70.6 69.7 0.98 70+/-0.5 Main reflector 73.0 66.2 6.85 70+/-5 Secondary absorber 71.1 69.4 1.71 70+/-2 Secondary reflector 71.0 68.8 2.21 TBD Support Main reflector 69.3 16.5 52.86 - ----------------------------------------------------------- Total Heater Power 132.6 W It should be noted that the model does not consider radial temperature gradients through the thickness of the absorber. A preliminary assessment shows that this gradient can be up to 1.5°C for the main absorber. The gradient can vary along the absorber surface. A detailed analysis will be performed for the final design.

The results are summarised in the following table:

Component 50/0/0 50/25/0 50/25/12.5 100/50/25 25/25/25 10/10/10

Longitudinal gradients [°C]

Main absorber 0.00 0.00 0.52 0.89 0.89 0.45

Main reflector 5.48 5.42 6.22 6.85 6.99 6.11

Secondary absorber 1.26 1.27 1.49 1.71 1.71 1.44

Secondary reflector 1.96 1.97 1.99 2.21 1.84 1.77

Heater power [W]

Main absorber, bot 0.0 0.0 2.1 4.0 4.0 1.7

Main absorber, top 0.0 0.0 0.6 1.3 1.3 0.5

Main reflector, bot 7.0 7.4 10.5 23.0 10.0 2.5

Main reflector, top 15.0 15.8 21.0 25.0 26.0 20.3

Secondary absorber, bot 14.0 14.0 18.0 22.0 22.0 17.2

Secondary absorber, top 14.0 14.0 18.0 22.0 22.0 17.2

Secondary reflector 26.9 27.0 27.2 35.3 22.8 20.3

Total 77.0 78.3 97.4 132.6 108.1 79.7 For all cases reasonable temperature gradients can be achieved. The most probable worst case is assumed to be between 50/25/0 and 50/25/12.5. Therefore it is proposed to work with this as baseline but to design heaters capable for the worst case. Fine tuning of the heater power shall be performed by test. Here below the detailed temperature field is shown together with the heater locations. Main absorber


1

MN

MX

HEAT

X

Y Z

69.693 69.792 69.892 69.991 70.091 70.19 70.289 70.389 70.488 70.588

Main reflector


1

MN

MX

HEAT

X

Y Z

66.185 66.945 67.706 68.467 69.227 69.988 70.748 71.509 72.27 73.03

Secondary absorber


1

MN

MX

HEAT

X

Y Z

69.422 69.612 69.802 69.992 70.182 70.372 70.562 70.752 70.942 71.132

An additional case was calculated considering more pessimistic convective coupling as follows.

Component Convection coeff. [W/m2K]

Note

Housing 10.9 Cover 12.5 Other surfaces 50% 5.45 At secondary reflector and main reflector bottom tip Other surfaces 25% 2.73 At main reflector inner tip Other surfaces 12.5% 1.36 Innermost surfaces

Boundary conditions are applied according to LC1 (hot case 70°C maximum convection) with convective links according to annex 1, enclosure effective convection and radiation heat transfer according to annex 3, applied as distributed power on corresponding surfaces (nodal load, uniformly distributed).

Housing outer face

Enclosure 1, vertical gap

Enclosure 2

Enclosure 3

Cover top face

Convection coefficients

ANSYS 11.0SP1 JUN 3 200914:18:46 ELEMENTSPowerGraphicsEFACET=1

1

XY

Z

CONV-HCOE1.363 2.6 3.837 5.075 6.312 7.55 8.787 10.025 11.262 12.5

Enclosure and radiation heat exchange (see annex 3)

Component ThermXL model nodes (see annex 3)

Heat load exchange [W] Enclosure Radiation Sum 1 2 3

Housing 3,4 30.9 (neglected < 0.2 W)

1.8 32.7 Cover 5 3.9 1.2 5.1 Main absorber 18,19,20,21 -1.0 -1.8 -2.8 Main reflector 13,14,15,16,17 -1.5 -1.5 Secondary absorber 6,7,8,9,10 -26.2 -2.9 -29.1 Secondary reflector 11,12 -4.7 -1.5 -6.2 Support main absorber - -2.9 (2) -2.9

Total 0 0 0 -4.7 (1) -4.7

Notes: (1) radiation to environment (2) equally distributed to nodes 13 and 19

Heater power

Component LC1

(Hot case 70°C, max convection)

N_HEAT_MAIN_ABSORBER_BOT 3.2 N_HEAT_MAIN_ABSORBER_TOP 3.2 N_HEAT_MAIN_REFLECTOR_BOT 13.7 N_HEAT_MAIN_REFLECTOR_TOP 19.7 N_HEAT_SECONDARY_ABSORBER_BOT 19.2 N_HEAT_SECONDARY_ABSORBER_TOP 19.2 N_HEAT_SECONDARY_REFLECTOR 27.4

total 105.7

Temperature field

ANSYS 11.0SP1 JUN 4 200908:57:31 NODAL SOLUTIONSTEP=1 SUB =1 TIME=1 TEMP (AVG) RSYS=0PowerGraphicsEFACET=1AVRES=MatSMN =16 SMX =73.808

1

MN

MX

X

Y

Z

16 22.423 28.846 35.269 41.692 48.116 54.539 60.962 67.385 73.808

----------------------------------------------------------- Temperature [degC] Component Max Min Gradient Requirement ----------------------------------------------------------- Housing 35.9 29.1 6.80 < 50 Cover 34.2 33.7 0.49 - Main absorber 71.3 68.9 2.37 70+/-0.5 Main reflector 73.8 66.8 7.01 70+/-5 Secondary absorber 70.9 69.3 1.59 70+/-2 Secondary reflector 70.9 68.9 1.97 TBD Support Main reflector 68.7 18.3 50.44 - ----------------------------------------------------------- These conditions lead to more severe temperature gradients which, however, can be improved by optimising the position of the heaters. This will be performed in the next iteration.

Another iteration is done to simulate an unsymmetry transvers to the target axis. The convection coefficient around the housing cylinder is assumed to vary along tangential direction between 150% at +X and 50% of the nominal value at –X (approximately corresponding to air flow directed from +X to –X. Convection coefficients used in the analysis

ANSYS 11.0SP1 JUN 4 200909:22:29 ELEMENTSPowerGraphicsEFACET=1REAL NUM

1

X

YZ

CONV-HCOE1.363 3.028 4.693 6.358 8.024 9.689 11.354 13.019 14.685 16.35

Temperature field

ANSYS 11.0SP1 JUN 4 200909:19:42 NODAL SOLUTIONSTEP=1 SUB =1 TIME=1 TEMP (AVG) RSYS=0PowerGraphicsEFACET=1AVRES=MatSMN =16 SMX =73.893

1

MNMX

X

Y Z

16 22.433 28.865 35.298 41.73 48.163 54.595 61.028 67.46 73.893

----------------------------------------------------------- Temperature [degC] Component Max Min Gradient Requirement ----------------------------------------------------------- Housing 37.0 28.6 8.42 < 50 Cover 34.7 33.8 0.88 - Main absorber 71.3 68.9 2.37 70+/-0.5 Main reflector 73.9 66.8 7.12 70+/-5 Secondary absorber 70.9 69.3 1.60 70+/-2 Secondary reflector 71.0 68.8 2.19 TBD Support Main reflector 68.7 18.3 50.43 - ----------------------------------------------------------- It can be seen, that there is a temperature gradient on the housing which, however, does not continue into the absorbers. The main absorber has a gradient at the tip, which is due to the placement of the heater. This can be solved by adjustment of heater location and power distribution. It should be noted that the FEM analysis provides the temperature gradient over the absorber area. The trough thickness gradient is to be added.

Main absorber

ANSYS 11.0SP1 JUN 10 200917:01:27 NODAL SOLUTIONSTEP=1 SUB =1 TIME=1 TEMP (AVG) RSYS=0PowerGraphicsEFACET=1AVRES=MatSMN =68.941 SMX =71.309

1

MN MX

X

Y

Z

68.941 69.204 69.467 69.73 69.993 70.256 70.519 70.782 71.045 71.309

Secondary absorber temperature


1

MN

MX

X

Y Z

69.315 69.493 69.671 69.849 70.027 70.205 70.383 70.561 70.739 70.916

Secondary reflector temperature


1

MN

MX

X

YZ

68.849 69.093 69.336 69.579 69.823 70.066 70.309 70.553 70.796 71.04

Housing temperature


1

MN

MX

X

Y Z

28.559 29.495 30.43 31.366 32.302 33.238 34.173 35.109 36.045 36.981

6. Deformation analysis In order to assess necessary clearances between the parts, a deformation analysis has been performed for the main load cases. Deformation under operational temperature, high air speed (m) The peak deformation is less than 1mm, even when assuming the annealing case with a temperature of 100°C.

ANSYS 11.0SP1 MAY 27 200916:00:53 NODAL SOLUTIONSTEP=1 SUB =1 TIME=1 USUM (AVG) RSYS=0PowerGraphicsEFACET=1AVRES=MatDMX =.259E-03 SMX =.259E-03

1

MN

MX

X

Y Z

0 .287E-04 .575E-04 .862E-04 .115E-03 .144E-03 .172E-03 .201E-03 .230E-03 .259E-03

Secondary absorber out‐of‐roundness (m)

ANSYS 11.0SP1 MAY 27 200916:01:59 NODAL SOLUTIONSTEP=1 SUB =1 TIME=1 UX (AVG) RSYS=1 PowerGraphicsEFACET=1AVRES=MatDMX =.191E-03 SMN =-.571E-05 SMX =.190E-03

1

MN

MX

X

YZ

-.571E-05 .160E-04 .377E-04 .594E-04 .811E-04 .103E-03 .125E-03 .146E-03 .168E-03 .190E-03

Deformation under longitudinal gravity (m) The deformation is negligible, even when assuming higher load factors as may result from transportation and handling (actual load factors from random vibration to be checked).


1

MN

MX

X

Y Z

0 .118E-06 .235E-06 .353E-06 .470E-06 .588E-06 .705E-06 .823E-06 .940E-06 .106E-05

Deformation under lateral gravity (m) The deformation is negligible, even when assuming higher load factors as may result from transportation and handling (actual load factors from random vibration to be checked).


1

MN

MX

X

Y Z

0 .493E-06 .986E-06 .148E-05 .197E-05 .247E-05 .296E-05 .345E-05 .395E-05 .444E-05

7. Dynamic Analysis The eigenfrequencies and effective masses of the calibration target are summarised in the following table. The mode shapes are depicted there after. MODE

# FREQ. [Hz]

Effective Mass % (> 5 %) Description Tx Ty Tz Rx Ry Rz

1 345.0 0.0 12.2 0.0 5.7 0.0 0.0 Main absorber rotation around X axis 2 345.1 12.2 0.0 0.0 0.0 5.7 0.0 Main absorber rotation around Y axis 3 647.2 0 0 3 0 0 0 Cover bending 4 668.2 0.0 47.9 0.0 72.6 0.0 0.0 Main absorber bending around X axis 5 668.2 47.9 0.0 0.0 0.0 72.6 0.0 Main absorber bending around Y axis 6 834.3 0.0 0.4 0.0 15.5 0.0 0.0 Main reflector rotation around X axis 7 834.3 0.4 0.0 0.0 0.0 15.5 0.0 Main reflector rotation around Y axis 8 872.0 0.0 0.0 29.2 0.0 0.0 0.0 Main absorber translation along Z axis 9 955.1 0 0 0 0 0 0 10 1037.5 0 0 0 0 0 0 11 1037.5 0 0 0 0 0 0 12 1049.6 3 0 0 0 3 0 13 1049.8 0 3 0 3 0 0 14 1111.2 0 0 0 0 0 0 15 1111.3 0 0 0 0 0 0 16 1180.6 0 0 0 0 0 0 17 1180.6 0 0 0 0 0 0 18 1232.6 0 0 0 0 0 0 19 1260.5 0 0 0 0 0 0 20 1260.5 0 0 0 0 0 0 21 1302.4 0.0 0.0 0.0 0.0 0.0 5.1 22 1321.9 0 0 0 0 0 0 23 1321.9 0 0 0 0 0 0 24 1505.8 0.0 0.0 53.4 0.0 0.0 0.0 25 1540.6 0 0 0 0 0 0 26 1571.4 0 0 0 0 0 0 27 1591.4 0 0 3 0 0 0 28 1640.0 0 0 0 0 0 0 29 1644.5 0 0 0 0 0 0 30 1651.8 0 0 0 0 0 0 31 1696.3 0 0 0 0 0 0 32 1696.5 0 0 0 0 0 0 33 1704.2 0 0 0 0 0 0 34 1704.6 0 0 0 0 0 0 35 1722.6 0 0 0 0 0 0 36 1747.3 0 0 0 0 0 0 37 1754.4 0 0 0 0 0 0 38 1758.8 0 0 0 0 0 0 39 1911.8 0 0 0 0 0 0 40 1931.4 0 0 0 0 0 0

Total 63.9% 63.9% 89.2% 97.3% 97.3% 5.2%

ANSYS 11.0SP1 JUN 4 200914:34:18 NODAL SOLUTIONSTEP=1 SUB =1 FREQ=345.023 USUM (AVG) RSYS=0PowerGraphicsEFACET=1AVRES=MatDMX =1.999 SMX =1.999

1

MN

MX

X

Y

Z

0 .222065 .44413 .666195 .88826 1.11 1.332 1.554 1.777 1.999

Mode 1 at 345.0 Hz (Main absorber rotation around X axis)


1

MN

MX

X

YZ

0 .222062 .444124 .666186 .888248 1.11 1.332 1.554 1.776 1.999

Mode 2 at 345.1 Hz (Main absorber rotation around Y axis)


1

MN

MX

X

Y

Z

0 .481132 .962263 1.443 1.925 2.406 2.887 3.368 3.849 4.33

Mode 3 at 647.2 Hz (Cover bending)


1

MN

MX

XY

Z

0 .14667 .293341 .440011 .586681 .733351 .880022 1.027 1.173 1.32

Mode 4 at 668.2 Hz (Main absorber bending around X axis)


1

MN

MX

XY

Z

0 .146695 .293391 .440086 .586782 .733477 .880173 1.027 1.174 1.32

Mode 5 at 668.2 Hz (Main absorber bending around Y axis)


1

MN

MX

X

Y

Z

0 .144336 .288672 .433008 .577344 .72168 .866016 1.01 1.155 1.299

Mode 6 at 834.3 Hz (Main reflector rotation around X axis)


1

MN

MX

X

Y Z

0 .144348 .288696 .433045 .577393 .721741 .866089 1.01 1.155 1.299

Mode 7 at 834.3 Hz (Main reflector rotation around Y axis)


1

MN

MX

X

YZ

0 .130672 .261344 .392015 .522687 .653359 .784031 .914702 1.045 1.176

Mode 8 at 872.0 Hz (Main absorber translation along Z axis)

Quasi-static load from transportation Using the load spectrum applicable for transportation (see section 3) the following effective quasi-static load factor can be derived using Mile´s formula: Power spectral density PSD 0.0002 g2/Hz Magnification factor Q 10Eigenfrequency fo 345 Hz Random load factor R=3*√(π/2*PSD*Q*fo) 3 g

This load is covered by the static load factor of 4g according to section 3.

8. Stress analysis For assessment of the load capability of the calibration target a stress analysis has been performed for the main load cases. In the present version of the report only selected cases have been evaluated. A more detailed assessment of the worst cases (annealing case, dynamic response to vibration and shock) will be considered. On the basis of the actual results the thermal case provides the worst stresses as resulting from differential CTE of the different materials and temperature gradients. The design will be revised to ensure that stress concentrations will be minimized. For the mechanical loads the stresses are negligible and seem to allow reasonable dynamic loads (factor 4). Stress due to operational temperature (Pa)

ANSYS 11.0SP1 MAY 27 200916:03:22 ELEMENT SOLUTIONSTEP=1 SUB =1 TIME=1 SEQV (NOAVG)PowerGraphicsEFACET=1DMX =.259E-03 SMN =3113 SMX =.122E+09

1

MN

MX

X

YZ

3113 .136E+08 .272E+08 .407E+08 .543E+08 .679E+08 .814E+08 .950E+08 .109E+09 .122E+09

Stress due to longitudinal gravity (Pa)

ANSYS 11.0SP1 MAY 27 200916:07:58 ELEMENT SOLUTIONSTEP=1 SUB =1 TIME=1 SEQV (NOAVG)PowerGraphicsEFACET=1DMX =.106E-05 SMN =6.778 SMX =430554

1

MN

MX

X

YZ

6.778 47845 95684 143522 191361 239199 287038 334876 382715 430554

Stress due to lateral gravity (Pa)

ANSYS 11.0SP1 MAY 27 200916:06:13 ELEMENT SOLUTIONSTEP=1 SUB =1 TIME=1 SEQV (NOAVG)PowerGraphicsEFACET=1DMX =.444E-05 SMN =25.958 SMX =256957

1

MN

MX

X

YZ

25.958 28574 57122 85670 114218 142766 171314 199861 228409 256957

Annex 1: Assessment of Convection Coefficients Here below is an assessment of the convection coefficients for the various surfaces and enclosures.

Location Convection coefficient [W/m2K]

Maximum (forced, air speed 3 m/s)

Intermediate (forced, air speed 1 m/s)

Minimum (natural)

Housing outer face 10.9 5.51 2.81 Cover top face 12.5 7.21 4.58

Location Conduction factor ke/k

Maximum (forced, air speed 3 m/s)

Intermediate (forced, air speed 1 m/s)

Minimum (natural)

Enclosure 1 1.00 (pure conduction) Enclosure 2 4.19 (simplified geometry) Enclosure 3 12.2 (simplified geometry, worst case)

Convection coefficients are calculated according to the following tables (refer to Holman)..

Housing outer face


Enclosure 2

Enclosure 3

Cover top face

Housing, max convection (forced, air speed 3 m/s) Forced Convection - Across Cylinder

Diameter d = 0.2 m Air speed u = 3 m/s

Surface temperature Tw = 32 °C Fluid temperature Tfluid = 16 °C Film temperature Tfilm = 24 °C

Pressure p = 5.41E+04 Pa Density ρ = 6.30E-01 kg/m3

Thermal conductivity k = 2.61E-02 W/mK Specific heat cp = 1.10E+03 J/kg K

Absolute viscosity μ = 1.71E-05 N s/m2 Kinematic viscosity ν = 2.59E-05 m2/s

Prandtl number Pr = 7.10E-01Thermal diffusivity α = 3.76E-05 m2/s

Reynolds number Re = 2.21E+04 Re C n C = 1.93E-01 0.4-4 0.989 0.33 n = 6.18E-01 4-40 0.911 0.385

40-4000 0.683 0.466 Convection coefficient h = 10.9 W/m2K 4000-40000 0.193 0.618

40000-400000 0.0266 0.805 Housing, min convection (natural, no wind) Natural Convection - Vertical Isothermal Surface

Surface height H = 0.6 m Surface temperature Tw = 32 °C

Fluid temperature Tfluid = 16 °C Film temperature Tfilm = 24 °C



Absolute viscosity μ = 1.71E-05 N s/m2Kinematic viscosity ν = 2.59E-05 m2/s

Prandtl number Pr = 7.10E-01Thermal diffusivity α = 3.76E-05 m2/s

Volume expansion coeff. β = 0.00337 K-1

Grashof number Gr = 1.70E+08Rayleigh number Ra = 1.21E+08 0.1 < Ra < 10^12

Nusselt number Nu = 64.6

Convection coefficient h = 2.81 W/m2K

Cover, max convection (forced, air speed 3 m/s) Forced Convection - Plate

Lenght L = 0.18 m Air speed u = 3 m/s

Surface temperature Tw = 32 °C Fluid temperature Tfluid = 16 °C Film temperature Tfilm = 24 °C




Prandtl number Pr = 7.10E-01 Thermal diffusivity α = 3.76E-05 m2/s

Reynolds number Re = 2.05E+04

Nusselt number Nu = 84.84 Re < 5e5, laminar Convection coefficient h = 12.5

Cover, min convection (natural, no wind) Natural Convection for Horizontal Plate

Characteristic length L = 0.05 m D/4 for circular plate

Surface temperature Tw = 32 °C

Fluid temperature Tfluid = 16 °C Film temperature Tfilm = 24 °C

Temperature difference ΔT = 16 °C



Absolute viscosity μ = 1.71E-05 N s/m2

Kinematic viscosity ν = 2.59E-05 m2/s Prandtl number Pr = 7.10E-01

Thermal diffusivity α = 3.76E-05 m2/s

Grashof number Gr = 9.83E+04 Rayleigh number Ra = 6.98E+04

upper hot / lower cold 2e4 < Ra < 8e6

Nusselt number Nu = 8.8 convection coefficient h = 4.58

Enclosures are considered by means of equivalent conduction ke in air (multiplication of conduction by scaling factor ke/k) Enclosure 1 (vertical gap) Natural Convection - Enclosure Vertical Gap

Gap distance δ = 0.005 m valid range Gap length L = 0.255 m L/δ = 51.0 11 - 42

temperature wall 1 T1 = 70 °C temperature wall 2 T2 = 32 °C

fluid temperature Tf = 51 °C




Prandtl number Pr = 7.10E-01 0.5 - 2 Thermal diffusivity α = 4.42E-05 m2/s

Volume coeff of expansion β = 0.003085 K-1

Grashof number Gr = 2.14E+02 Gr*Pr C n m Gr*Pr = 1.52E+02 < 2e3 ke / k = 1

coefficients C = 1.00 6e3 - 2e5 0.197 0.250 -0.111 n = 0.00 2e5 - 1.1e7 0.073 0.333 -0.111 m = 0.00

ke/k = 1.00 ke = 2.81E-02 W/mK

Enclosure 2 (horizontal gap, simplified geometry) Natural Convection - Enclosure Horizontal Gap

Gap distance δ = 0.05 m valid range Gap length L = 0.17 m

Temperature wall 1 T1 = 70 °C Temperature wall 2 T2 = 32 °C

Fluid temperature Tf = 51 °C






Grashof number Gr = 2.14E+05Gr*Pr = 1.52E+05 Gr*Pr C n m

coefficients C = 0.212 < 1.7e3 ke / k = 1 n = 0.25 1.7e3 - 7e3 0.059 0.4 0 m = 0 7e3 - 3.2e5 0.212 0.25 0

> 3.2e5 0.061 0.33 0 ke/k = 4.19

ke = 0.118 W/mK

Enclosure 3 (horizontal gap, simplified geometry, worst case) Natural Convection - Enclosure Horizontal Gap

Gap distance δ = 0.235 m valid range Gap length L = 0.025 m

Temperature wall 1 T1 = 70 °C Temperature wall 2 T2 = 50 °C

Fluid temperature Tf = 60 °C






Grashof number Gr = 1.14E+07Gr*Pr = 8.08E+06 Gr*Pr C n m

coefficients C = 0.061 < 1.7e3 ke / k = 1 n = 0.33 1.7e3 - 7e3 0.059 0.4 0 m = 0 7e3 - 3.2e5 0.212 0.25 0

> 3.2e5 0.061 0.33 0 ke/k = 12.24

ke = 0.352 W/mK

Annex 2: Basic Concept TradeOff A simplified model based on lumped parameter thermal network was built to perform quick trade-offs and for better understanding of the thermal fluxes. The modeling and results are summarized below. Thermal network

Material properties

Material Conductivity

[W/mK] emissivity Component Aluminum 160 0.10 structure (housing, reflectors, absorbers)

GFRP 0.3 0.80 washers, insulation ring, main reflector support Eccosorb 0.96 0.75 absorber layer

Environment 0.50 Load cases Two load cases are considered (extreme cases) for hot case temperature:

‐ Only conductive thermal links (no radiation and no convection) ‐ Maximum convection (lateral wind 3 m/s)

Air and environment (interface) temperature is assumed to be 16°C. Heaters power is tuned in order to minimize gradients.

Conductive links

Label First Node Second Node Value [W/K] interface flange 2 3 2.04E+00 housing 3 11 3.37E-01 secondary reflector 11 12 1.06E+01 thermal washers 3 10 2.20E-02 secondary absorber 10 9 6.57E+00 secondary absorber 9 8 6.57E+00 secondary absorber 8 7 6.57E+00 secondary absorber 7 6 6.57E+00 thermal washers 6 4 2.21E-02 housing 3 4 2.25E+00 housing-cover 4 5 7.56E-01 insulation ring 4 13 4.07E-01 main reflector 13 14 3.70E+00 main reflector 14 15 3.13E+00 main reflector 15 16 2.56E+00 main reflector 16 17 1.58E+00 support main absorber 13 19 1.28E-03 main absorber 19 18 1.53E+00 main absorber 19 20 1.60E+00 main absorber 18 21 2.13E+00

Convective links

First Node Second Node Value [W/K]3 1 0.927 4 1 0.927 5 1 0.383 12 1 0.059 16 1 0.080 17 1 0.007 4 6 0.118 4 7 0.118 4 8 0.118 3 8 0.118 3 9 0.118 3 10 0.118 3 12 0.117 13 5 0.052 19 5 0.043 20 5 0.004 13 14 0.048

Radiative links

First Node Second Node Value View Factor ε1 ε2 A1 A2 3 2 0.00820 1.00 0.10 0.50 0.08 10.00 12 3 0.00169 1.00 0.10 0.10 0.02 0.08 10 3 0.00170 1.00 0.10 0.10 0.02 0.08 9 3 0.00170 1.00 0.10 0.10 0.02 0.08 8 3 0.00170 1.00 0.10 0.10 0.02 0.08 4 2 0.00820 1.00 0.10 0.50 0.08 10.00 8 4 0.00170 1.00 0.10 0.10 0.02 0.08 7 4 0.00170 1.00 0.10 0.10 0.02 0.08 6 4 0.00170 1.00 0.10 0.10 0.02 0.08 5 2 0.00314 1.00 0.10 0.50 0.03 10.00 13 5 0.00281 0.70 0.80 0.10 0.02 0.03 19 5 0.00028 0.30 0.10 0.10 0.00 0.03 19 5 0.00219 0.40 0.80 0.10 0.02 0.03 20 5 0.00016 0.30 0.10 0.10 0.00 0.03 12 2 0.00181 0.40 0.10 0.50 0.02 10.00 16 2 0.00123 0.40 0.10 0.50 0.01 10.00 17 2 0.00081 0.30 0.10 0.50 0.01 10.00 18 2 0.00139 0.20 0.75 0.50 0.01 10.00 19 2 0.00106 0.15 0.75 0.50 0.01 10.00 20 2 0.00020 0.10 0.75 0.50 0.00 10.00 13 14 0.00304 0.95 0.80 0.10 0.02 0.03

Heaters

Node

Description

Heater power [W] Conduction only Max Air speed

7 Sec absorber heater top 0.8 15.5 9 Sec absorber heater bot 0.8 15.5 12 Sec reflector top 13.3 22.2 14 Main reflector heater top 13.3 16.5 15 Main reflector heater bot 0 5.1 18 Main absorber heater bot ≈ 0 1.8 20 Main absorber heater top ≈ 0 1.8

Total heaters power 28.2 78.3 Interface temperatures

Node Description Temperature [°C]

Only conduction Max convection 1 Air 16.00 (Boundary) 16.00 (Boundary) 2 Interface 16.00 (Boundary) 16.00 (Boundary)

Conduction only Thermal budget

Temperatures

ComponentTemperature [degC]

max min grad Housing 36.09 29.84 6.25

Cover 36.09 - - Main absorber 70.26 70.25 0.00 Main reflector 72.36 68.77 3.59

Secondary absorber 70.17 70.01 0.16 Secondary reflector 70.61 69.36 1.25

Support Main reflector - - -

Maximum convection Thermal budget

Temperatures


max min grad Housing 34.35 30.40 3.95

Cover 32.40 - - Main absorber 70.36 69.43 0.92 Main reflector 71.93 67.66 4.28

Secondary absorber 70.42 69.36 1.06 Secondary reflector 70.45 69.22 1.23

Support Main reflector - - -

Annex 3: Load Case TradeOff Based on the following assumptions regarding the distribution of convective heat exchange, the various load cases were assessed.

Housing outer face


Enclosure 2

Enclosure 3

Cover top face

Load case definition

Node

Description

Heater power [W]

LC1 (70°C max convection)

LC2 (70°C intermed

convection)

LC3 (70°C min

convection)

LC4 (70°C

conduction only)

LC5 (100°C, max convection)

7 Sec absorber heater top 19.2 15.9 13.9 0.8 30.3 9 Sec absorber heater bot 19.2 15.9 13.9 0.8 30.3 12 Sec reflector top 25.9 21.3 18.7 13.3 40.6 14 Main reflector heater top 20.0 18.0 15.0 13.1 31.0 15 Main reflector heater bot 14.0 6.0 3.0 0 22.2 18 Main absorber heater bot 3.0 2.2 1.8 0 4.8 20 Main absorber heater top 3.0 2.2 1.8 0 4.8

Total heaters power 104.2 81.6 68.1 28.0 164.0 Interface temperatures

Node Description Temperature [°C]

Only conduction Max convection 1 Air 16.00 (Boundary) 16.00 (Boundary) 2 Interface 16.00 (Boundary) 16.00 (Boundary)

Radiative power in ACT system is about 10 W for hot operational case (70°C) and 17 W for hot survival case (100°C). About 50% of this heat is radiated to the cold environment, the rest is internal heat exchange.

LC1 - Operational hot case 70°C with maximum convection (lateral wind 3 m/s) Thermal budget

Temperatures


max min grad Housing 34.67 30.61 (4.06)

Cover 32.76 - - Main absorber 70.82 69.27 (1.55) Main reflector 72.52 67.45 (5.07)

Secondary absorber 70.51 69.22 (1.29) Secondary reflector 70.65 69.36 (1.29)

Support main absorber - - -

LC2 - Operational hot case 70°C with intermediate convection (lateral wind 1 m/s) Thermal budget

Temperatures






LC3 - Operational hot case 70°C with minimum convection (natural, no wind) Thermal budget

Temperatures






LC4 - Operational hot case 70°C with only conductive thermal links (no radiation and no convection) Thermal budget

Temperatures






LC5 - Survival hot case 100°C with maximum convection (lateral wind 3 m/s) Thermal budget

Temperatures






Sensitivity analysis on conductive links (from LC1)

Doubled thermal resistance at support of

Link Heater power [W]

Main reflector

Secondary absorber

Secondary reflector

Total power

Difference w.r.t. nominal case

Main reflector 4 - 13 28.5 39.8 26.2 100.2 -4.0

Secondary absorber 3 - 10 / 4 - 6 34.0 37.8 25.9 103.6 -0.6

Secondary reflector 11 - 3 34.0 39.4 19.8 99.1 -5.1

Nominal case (LC1) - 34.0 38.4 25.9 104.2 - LC1b and LC5b - Additional cases where secondary reflector is not heated are also considered for comparison.

Node

Description

Heater power [W]


LC1b (70°C, max

convection, no sec reflect heat)


LC5b (100°C, max

convection, no sec reflect heat)

7 Sec absorber heater top 19.2 20.7 30.3 32.5 9 Sec absorber heater bot 19.2 20.7 30.3 32.5 12 Sec reflector top 25.9 0 40.6 0 14 Main reflector heater top 20.0 21.0 31.0 33.0 15 Main reflector heater bot 14.0 14.0 22.2 21.5 18 Main absorber heater bot 3.0 3.0 4.8 4.9 20 Main absorber heater top 3.0 3.0 4.8 4.9

Total heaters power 104.2 82.4 164.0 129.2 Temperature from LC1b (70°C, max convection, no heat at secondary reflector)

Component Temperature [degC]

LC1 LC1b max min grad max min grad

Housing 34.67 30.61 (4.06) 32.48 26.33 (6.15) Cover 32.76 - - 31.51 - -

Main absorber 70.82 69.27 (1.55) 70.93 69.35 (1.58) Main reflector 72.52 67.45 (5.07) 72.68 67.60 (5.08)

Secondary absorber 70.51 69.22 (1.29) 70.98 69.50 (1.48) Secondary reflector 70.65 69.36 (1.29) 24.01 23.95 (0.06)

Support main absorber - - - - - -

Temperature from LC5b (100°C, max convection, no heat at secondary reflector)


LC5 LC5b max min grad max min grad

Housing 45.30 38.92 (6.38) 41.80 32.19 (9.61) Cover 42.55 - - 40.51 - -



Support main absorber - - - - - - LC1c - Support of main absorber made of Aluminum is considered for comparison, insulating washers are assumed at both ends. Temperature from LC1c (70°C, max convection, Alu support main absorber)


LC1 LC1c max min grad max min grad

Housing 34.67 30.61 (4.06) 34.67 30.61 (4.06) Cover 32.76 - - 32.76 - -



Support main absorber - - - - - - LC1d - Heater of main absorber at node 19 (instead of node 20 and 18) is also considered as possible option.

Node

Description

Heater power [W]


LC1d (70°C, max Convection,

heater at node 19) 7 Sec absorber heater top 19.2 19.2 9 Sec absorber heater bot 19.2 19.2 12 Sec reflector top 25.9 25.9 14 Main reflector heater top 20.0 20.0 15 Main reflector heater bot 14.0 14.0 18 Main absorber heater bot 3.0 N/A 19 Main absorber heater N/A 6.0 20 Main absorber heater top 3.0 N/A

Total heaters power 104.2 104.3

Temperature from LC1d (70°C, max convection, heater at node 19)


LC1 LC1d max min grad max min grad

Housing 34.67 30.61 (4.06) 34.68 30.61 (4.07) Cover 32.76 - - 32.84 - -



Support main absorber - - - - - -

Documents

ALMA Calibration Target Analysis Report (Preliminary)...Jun 11, 2009 · 2009‐06‐10, J. Eder 1. Scope This report summarizes the analyses performed on the calibration target for