VGVG11

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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

VGVG22

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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

VGVG33

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FEA Sandwich Core Summary

Based on reduced coolant density

VGVG44

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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

VGVG55

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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/m3

Peak deflection at stave center is 53.7μm

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

K13D2U 4/1

VGVG66

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Simple BC at Both Ends

• Full Length Model- Symmetrical Deflection– Sag increased from 53.7 to 59.4μm (originally one end fixed in Z, now Z fixed in middle)

– For same conditions the ½ length model with 5.88mm core thickness was 62.1 μm

Sandwich core thickness 4.6mm

K13D2U 4/1

VGVG77

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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

VGVG88

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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

VGVG99

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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

VGVG1010

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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

VGVG1111

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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%

VGVG1212

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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-isotropicδmax=94μm

K13D2U 4 to 1 lay upδmax=59.4μm

VGVG1313

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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

VGVG1414

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Solve for Effective Core Shear Modulus

• 96cm Model of Stave– Use simple edge supports, K13D2U

4/1– Apply forces at quarter points, ¼ 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

G.c11.5 P L1 c1

h1 c1( )2b 11 .4 8 .2

P/2 P/2

hc

Δbending est=36.7μmΔcore shear est=8.2 μm

Division between bending and shear, based0n estimate of core shear of 128MPa

Combined Δ=45microns (FEA 53.7 μmfor one end of the pins fixed)

Using sandwich relationships for fixed ends

VGVG1515

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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

c

chhGB

2

bB

wLshear

8)(

2

)1(12

)(2

2

chEt

D

Db

wLbending

384)(

4

(fixed)

(uniform loading)

VGVG1616

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VGVG1717

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2m Stave Core Design

VGVG1818

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End Cap Model Only

Deflection of end cap for ½ stave mass

Pin diameter 0.173in

δ=.26μm

Pin diameter 0.25in

δ=.20μm