ATLAS Calorimeter Argon Gap
Convection Test Bed
April 25, 2014
1
Test Model
This plane heated
Argon gap, 12 mm thick
Aluminum, 8 mm thick
Middle insulator, 12.7 mm
G10 CR, 10.7 mm thick
Aluminum, 3 mm thick
I added the 3 mm aluminum plate to reduce
small scale temperature variations on the
heated face of the middle insulator.
2
Earlier Results for Argon Layer
Conductance
• The equation used in the previous analyses gives a
conductance of 52.8 W/m2-°K for a 2 °K temperature
differential (see slide 4).
• At lower temperature differentials, heat was transported
from the lower regions of the inner cylinder to the upper
regions of the outer cylinder, ref. slide 5, suggesting that
size is more important at low temperature differentials (the
convective cells that form are larger).
• A test data point at a 2 °K differential temperature is
recommended. The predicted effective conductivity of the
Argon layer is 4.8 times the static conductance value. For
this case het was predicted to move radially from the inner
cylinder to the outer cylinder except at the top and bottom,
ref. slide 6.
3
Outer Annulus, Equation for H
120
12000
100
10000
80
8000
60
6000
y = 7.5091Ln(x) + 47.613
R2 = 0.9874
40
4000
20
2000
Re, dimensionless
H, W/m^2/K
Convection Coefficient Across 12 mm fluid filled
gap
H, Laminar
H, turbulent
0
0
0
2
4
6
8
10
Re, Laminar
Re, turbulent
Log. (H, Laminar)
Delta T
The equation fits the laminar results and was used in the runs reported on subsequent
slides.
4
Heat Flux at 0.5°K Differential (Turbulent Option Off)
Heat Flux, W/m^2, vs Angle (+90 at top)
60
50
Heat Flux, W/m^2
40
30
Inner Cylinder
20
Outer Cylinder
Inner Averaged
Inner Averaged
10
0
-90.00
-70.00
-50.00
-30.00
-10.00
10.00
30.00
50.00
70.00
90.00
Angle, deg
With inner and outer cylinders held at constant temperatures, heat tends to be
removed from the lower regions of the ID and deposited at the higher regions of the
OD.
The variation in heat removal on the inner cylinder is more pronounced for low
temperature differences.
5
Heat Flux at 2°K Differential
Heat Flux, W/m^2, vs Angle (+90 at top)
250
Heat Flux, W/m^2
200
150
100
Inner Cylinder
Outer Cylinder
Inner Averaged
50
0
-90.00
Inner Averaged
-70.00
-50.00
-30.00
-10.00
10.00
30.00
50.00
70.00
90.00
Angle, deg
At a 2°K differential the heat flow is more uniformly distributed making
the use of a convection coefficient dependent on the local inner wall
temperature justifiable.
6
Thermal Result for a 2°K Gradient Across the 12 mm Argon Layer, Net
Conductance of the Argon is 4.8 Times the Conductivity of Argon
Node
4570
Temp
deg K
97.083
Del T
deg K
Q center
W/m^ 2
5.045
125.36
Aluminum 0.009
105.2
M id I nsul
4620
4670
4720
4770
92.038
92.029
Argon
2.002
Copper
0.002
105.28
90.027
90.025
Total heat input =
22.4 W
Heat into 8 mm Al plate =
8.78 W
Heat into 12 mm Argon layer = 7.99 W (99.1 W/m2)
Heat lost through base =
13.6 W
61% of the input heat is lost through the base. Most of the rest passes through the
Argon layer (0.79 W is conducted laterally to the side walls by the 8 mm Aluminum
plate).
7
Transient Response to 22.4 W
1
97.6
insul_1
96.8
96
95.2
94.4
VALU
°K
93.6
92.8
insul_2
gap_1
92
91.2
Cu_2
90.4
gap_2
89.6
0
800
400
1600
1200
2400
2000
TIME
3200
2800
4000
3600
Seconds
Test bed to measure convection in Argon
This is the power required to develop a 2°K gradient in the Argon gap
8
Transient Response to 22.4 W
1
8
7.2
6.4
5.6
Insul_DT
4.8
VALU
°K
4
3.2
2.4
Argon_DT
1.6
.8
0
0
800
400
1600
1200
2400
2000
TIME
3200
2800
4000
3600
Seconds
Test bed to measure convection in Argon
The 2°K gradient is developed in 1200 to 1600 seconds.
The gradient through the middle insulator develops somewhat faster.
9
Thermal Result for an 0.5°K Gradient Across the 12 mm Argon Layer, Net
Conductance of the Argon is 3.86 Times the Conductivity of Argon
Node
4570
Temp
deg K
91.559
Del T
deg K
Q center
W/m^ 2
1.051
26.15
Aluminum 0.002
21.13
M id I nsul
4620
4670
4720
4770
90.508
90.506
Argon
0.5
Copper
0.001
21.14
90.006
90.005
Total heat input =
Heat into 8 mm Al plate =
Heat into 12 mm Argon layer =
Heat lost through base =
4.85 W
1.823 W
1.767 W (21.9 W/m2)
3.03 W
62% of the input heat is lost through the base. Most of the rest passes through the
Argon layer (0.06 W is conducted laterally to the side walls by the 8 mm Aluminum
plate).
10
Transient Response to 4.85 W
1
1.25
1.125
Insul_DT
1
.875
.75
VALU
.625
Argon_DT
.5
°K
.375
.25
.125
0
0
800
400
1600
1200
2400
2000
3200
2800
4000
3600
TIME
Test bed to measure convection in Argon
Seconds
The 0.5°K gradient is developed in 1200 to 2000 seconds.
The gradient through the middle insulator develops somewhat faster.
11
Suggested Test Design Modification
• Small spatial scale temperature variations on
the heater side of the middle insulator are
possible and might effect the accuracy of the
heat flux calculated from the differential
temperature across this member.
• This can be reduced by adding a 3 mm plate
on the heater side (assumed to be opposite
from the Argon gap). Heaters should be
bonded to the aluminum plate.
12
Initial Runs
• In these runs the thermal conductivity of G10
was input as an isotropic material with
K=0.0014
– This has been updated to K=0.000311 in-plane
and K = 0.000453 W/(mm-°K) in the thickness
direction
• The effective conductivity of the Argon gap
was set at ten times the static conductivity of
Argon.
W/(mm-°K) replaces W/(m-°K) above (Correction 26-Apr-14)
13
Middle Insulator Thermal Uniformity
There is no high conduction layer at the heater
Heater side, 90.0 to 92.4 °K
Heated nodes are 16.75 mm apart
horizontally
Horizontal bands occur where there is
an additional row of nodes between
heated rows
Argon gap side, 90.5 to 90.6 °K
14
Middle Insulator Backed by 3 mm
Aluminum Plate
Heater side, 90.6 to 91.6 °K
Argon gap side, 90.4 to 90.7 °K
Adding the 3 mm aluminum plate erases small scale temperature variations near
the center of the middle insulator that might result from spatial variations in heat
load due to heater wire spacing.
15