# Presentation: 357531

## Recent Study Topics

**Full length** model with wafers, hybrids and cable as dead weight
- 0.173in dia. support pins
- Clamped pin vertical supports, but with pins at one fixed in Z
- Core thickness 4.6mm
**Half length** model with wafers, hybrids and cable as dead weight
- _0.173in support pin_
- By necessity for symmetry the middle is fixed in Z, thus it looks like all pins clamped vertically at ends, but floating in Z
- Model will be modified to add structural coupling of wafers, and hybrids
- Core thickness 5.88m
- Model of pins and end cap alone with stave weight imposed
- 0.173in diameter
- 0.25in diameter

- Significant Changes
- Calculated apparent density of two phase fluid.  For entering and exit quality the mean density is 60kg/m3, whereas liquid density is 1660kg/m3
- Previous solutions used an average of 1000kg/m3, so the liquid dead weight is reduced noticeably
- Round circular tube in half length model
- Accommodated the change to 5.88mm core
- Varied core shear modulus, reflected in density change to material
- 66 to 210kg/m3, CVD carbon foam
- 56 and 110kg/m3, honeycomb

_*Models*_

## Sandwich Core Differences in Model

- FEA Models
- 4.6mm core height model has elongated cooling tubes and the foam does not contact the tubes
- Hydraulic diameter 5mm
- Less core material than in the half length model, possibly an effect in sag
- 5.88mm core height has round tubes and the core comes in contact, except at the very top.
- Internal diameter 5.27mm
- Intent is to use the core material to improve thermal contact

- 4.6mm

- 5.88mm

## FEA Sandwich Core Summary

- Based on reduced coolant density

## Core Thickness

- Estimated stave sag for two core thickness based on bending only, no core shear deflection (_analytical based on “fixed end supports”_)
- _Foam Shear Modulus (not included)_
- 4.6mm thick foam (facing separation), δ=35μm
- 5.88mm thick foam, δ=29μm
- FEA Solution for Shear Modulus=26.9MPa (lowest density foam) with facings 4 to 1 K13D2U fiber orientation (Coolant density 60kg/m3)
- 4.6mm, δ=59.4μm (_both ends free to move axially_)
- 5.88mm, δ=62.1μm (1/2 length model, since only one end modeled by necessity it simulates as if _both ends free to move axially_)
- Little difference in solutions

## Stave Gravity Sag

- Conditions
- Mass of cable, hybrids, wafers, and chips included in facing density
- Mass of two-phase fluid included in tube density
- Homogeneous two-phase fluid density average is 60kg/m3
- C3F8 liquid density is 1660kg/m3
- Fluid vapor fraction varies from ~0.3 to 0.8
- _Virgin RVC foam_
**Core foam density is 66kg/m****3**

- Peak deflection at stave center is 53.7μm

- Full Length Model- _***At One end, pins are Fixed in Z***_

- K13D2U 4/1

## Simple BC at Both Ends

- Full Length Model- _***Symmetrical Deflection***_
_**Sag increased from 53.7 to 59.4**__**μ**__**m**_ (_originally one end fixed in Z, now Z fixed in middle_)
- For same conditions the 1⁄2 length model with 5.88mm core thickness  was 62.1 μm

- Sandwich core thickness 4.6mm

- K13D2U 4/1

## Sandwich Core CVD Carbon

- Core foam density is 210kg/m3
- Other Conditions
- Mass of cable, hybrids, wafers, and chips included in facing density
- Mass of two-phase fluid included in tube density
- Homogeneous two-phase fluid density average is 60kg/m3
- C3F8 liquid density is 1660kg/m3
- Fluid vapor fraction varies from ~0.3 to 0.8

- Peak deflection at stave center is 54.8μm

- Full length model- _***One End, pins fixed Fixed in Z***_

- K13D2U 4/1

## Carbon Foam-No CVD

- Core foam density is 66kg/m3
- Other Conditions
- Mass of cable, hybrids, wafers, and chips included in facing density
- Mass of two-phase fluid included in tube density
- Homogeneous two-phase fluid density average is 60kg/m3
- C3F8 liquid density is 1660kg/m3
- Fluid vapor fraction varies from ~0.3 to 0.8
- _Sandwich height_
- 5.88mm versus 4.6mm

- Half Length Model_***-Pins fixed against vertical motion***_

- δ=62.1microns

- K13D2U 4/1

## Sandwich Core CVD Carbon

- Core foam density is 210kg/m3
- Other Conditions
- Mass of cable, hybrids, wafers, and chips included in facing density
- Mass of two-phase fluid included in tube density
- Homogeneous two-phase fluid density average is 60kg/m3
- C3F8 liquid density is 1660kg/m3
- Fluid vapor fraction varies from ~0.3 to 0.8
- _Sandwich height_
- 5.88mm versus 4.6mm

- Peak deflection at stave center is 65μm

- Half Length _***Model-Pins free to move axially***_

- K13D2U 4/1

## Carbon Foam-No CVD

- Core foam density is 66kg/m3
- Other Conditions
- Mass of cable included in facing density
- Mass of two-phase fluid included in tube density
- Homogeneous two-phase fluid density average is 60kg/m3
- C3F8 liquid density is 1660kg/m3
- Fluid vapor fraction varies from ~0.3 to 0.8
- _Sandwich height_
- 5.88mm

- Half Length Model_***-Includes Silicon Wafers and Hybrids in stiffness simulation***_

- δ=52microns

- K13D2U 4/1

## Detectors and Hybrids Stiffness Contribution

- 1/2 Length Model- K13D2U 4/1 fiber orientation, coolant density 60kg/m3
- Silicon modules and hybrids as dead weight-62microns
_*Silicon modules and hybrids part of stiffness-52microns*_
- Mass of 1st solution 0.1973kg without module stiffness
- Mass of second solution 0.1891kg _*with module and hybrid stiffness*_
- Difference in gravity loading 4.1%; had hoped for same mass
- Difference in central deflection 19.2%

## Fiber Orientation

- Comparing 4 to 1 K13d2U versus Quasi-isotropic K13D2U facings
- Modulus in direction of stave axis is different by _*factor of 1.96*_
- Thermal distortion solutions with the unbalanced lay up was OK
- Comparison made for pins free to move in axial direction
- Difference between pins fixed on one end and both free is 5.7μm
- Sag is reduced by a _*factor of 1.59*__* *_

- K13D2U
- Quasi-isotropic
- δmax=94μm

- K13D2U
- 4 to 1 lay up
- δmax=59.4μm

## Beryllium End Parts

- Conditions
- K13D2U quasi-isotropic fiber orientation
- 0.173in dia Be pins
- Be end cap
- Coolant 60kg/m3
- Pins at end free to move in Z, fixed in Y
- Z fixed at mid span, X constrained at two ends
- Sag decreased from 94.6μm to 80.6 μm through use of Be

## Solve for Effective Core Shear Modulus

- 96cm Model of Stave
- Use simple edge supports, K13D2U 4/1
- Apply forces at quarter points, 1⁄4 from each end
- Extract deflection at Δ4 and Δ2, quarter point and mid-span
- Use relationship
- Result for 4.6mm core with Al tubes
- ~128 MPa versus 26.9 MPa for virgin foam
- _Tubes contribute most of the shear stiffness, except at very high foam densities_

- P/2

- P/2

- Δbending est=36.7μm
- Δcore shear est=8.2 μm

- Division between bending and shear, based
- 0n estimate of core shear of 128MPa

- Combined Δ=45microns (FEA 53.7 μm
- for one end of the pins fixed)

_*Using sandwich relationships for fixed ends*_

## Estimate for 2m Stave

- Use analogy of a uniformly loaded beam
- G-core shear properties
- L- length of beam
- c- height of sandwich core
- b- width of sandwich
- t- facing thickness
- h-overall distance across facings
- B- expression
- w- uniform load
- Shear Deflection for 2m stave with 20mm core height quasi K13 facings
- G=26.9MPa, δ=56μm
- G=212MPa, δ=7μm
- Based on ~uniform load of 7.9N/m (does include an estimate for mass of 3 internal ribs
- Bending Deflection estimate for 2m stave
- 81μm for fixed end condition

- (fixed)

- (uniform loading)

## 2m Stave Core Design

## End Cap Model Only

**Deflection of end cap for 1⁄2 stave mass**

**Pin diameter 0.173in**

- δ=.26μm

**Pin diameter 0.25in**

- δ=.20μm