VGVG11
i T ii T i
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
i T ii T i
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
i T ii T i
FEA Sandwich Core Summary
Based on reduced coolant density
VGVG44
i T ii T i
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
i T ii T i
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
i T ii T i
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
i T ii T i
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
i T ii T i
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
i T ii T i
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
i T ii T i
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
i T ii T i
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
i T ii T i
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
i T ii T i
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
i T ii T i
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
i T ii T i
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
i T ii T i
VGVG1717
i T ii T i
2m Stave Core Design
VGVG1818
i T ii T i
End Cap Model Only
Deflection of end cap for ½ stave mass
Pin diameter 0.173in
δ=.26μm
Pin diameter 0.25in
δ=.20μm
