http://fluxtrol.com A presentation on the factors influencing the cooling of an inductor. Flux 2D coupling magnetic and thermal calculations is used to make 2D simulations of a single shot inductor. The simulations are used to analyze the effect frequency, current, water pressure, and wall thickness have on the cooling of the inductor.

1. Factors Influencing
Inductor Cooling
By Kevin Kreter
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2. Overview
• Factors influencing the cooling of an inductor are
studied
• Flux 2D coupling magnetic and thermal
calculations is used to make 2D simulations of a
single shot inductor
• The simulations are used to analyze the effect
frequency, current, water pressure, and wall
thickness have on the cooling of the inductor
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3. Overview
• The results from simulation are used to
investigate the following:
– Effect of radiation from heated part
– Cycling and reaching steady state
– Effect of changing water pressure
– Temperature distribution in coil
– Influence of variables on coil losses
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4. Variables
• Combinations of the following variables are used in
the simulations
– Frequency: 10 KHz, 3 kHz, 1 kHz
– Current: 10,000 A, 7,500 A, 5,000 A
– Water Pressure: 40 psi, 20 psi across inlet and outlet of
inductor leg
– Wall Thickness: 0.125 in, 0.062 in, 0.048 in
• Heating lasts for 10 seconds
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5. Assumptions
• The heat transfer coefficients used are calculated
at a constant temperature when in reality they will
change with temperature
• When the temperature of the inductor wall is 250 C
or higher there is a risk of vapor layer formation on
the inner wall
– The heat transfer coefficient will drop dramatically
leading to a rapid rise in temperature
– The results from these cases will be dropped from the
study
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6. Single Shot Coil 2D Simulation
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7. Dimensions and Materials
1045 Steel
Fluxtrol A (Above 800 C Non-Magnetic) Copper
0.02”
0.355”
5/8” 1/8” 1 3/8”
1”
0.062”
5/8”
1/4”
JB Weld 1”
1045 Steel
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8. Coil Wall Thicknesses
0.125”
0.048” 0.062”
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9. Effect of Radiation
During the entire cycle 1000 C radiation
No Radiant Heat Transfer from part considered
• 3 kHz 10000A 40psi 0.125in
• With radiation accounted for the copper temperature increases 2 C and the
concentrator temperature increases 10 C
• Since the influence is not very strong, radiation can be neglected
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10. Percent of Power Lost in Coil
10 kHz
• The percent of power in the coil out 60
50
of the total power is plotted
40
• For the data shown here, the water Percent of
Total Power
30
0.048
0.062
pressure is 40 psi 20
0.125
10
0
5000 A 7500 A 10000 A
1 kHz 3 kHz
60 60
50 50
40 40
Percent of 0.048 Percent of 0.048
30 30
Total Power 0.062 Total Power 0.062
20 20
0.125 0.125
10 10
0 0
5000 A 7500 A 10000 A 5000 A 7500 A 10000 A
*Cases where the induction coil wall reached over 250 C are
dropped from the graphs
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11. Coil Losses
• There are more coil losses as current increases,
due to the copper having a higher resistivity at
higher temperatures
• There is a correlation between the frequency
and wall thickness with the coil losses. Losses
are higher when the reference depth is less than
the wall thickness
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12. Reference Depth and Wall Thickness
Frequency (kHz) 10 3 1
Reference Depth (in) 0.031 0.057 0.099
0.048 1.55/27.6 0.84/30.0 0.48/35.0
Wall Thickness 0.062 2.00/28.6 1.09/27.6 0.63/30.0
0.125 4.03/29.0 2.19/28.6 1.26/24.8
*The first value is t/δ, the second is the percent of power lost in the coil
*For the values shown, current is 5000A the water pressure is 40psi
• The ratio between the wall thickness and reference depth
can be used to minimize coil losses
• Historically, it has been found that losses will be at their
minimum when the ratio is 1.6, but as long as the ratio is
over 1, the losses are almost the same
• As the ratio gets less than approximately 1 the losses will
rise dramatically
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13. Reference Depth and Wall Thickness
60
55
50
45
Power Lost in Coil
(%)
40
35
30
25
20
0 0.5 1 1.5 2 2.5 3
t/δ
• Shown here is a curve for the 3kHz, 5000A case
• Coil losses are highest when the coil wall thickness to
reference depth ratio falls below 1
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14. Power Density in Coil
1kHz, 7,500A, 20psi 0.048 (t/δ = 0.48) 0.062 (t/δ = 0.63) 0.125 (t/δ = 1.26)
3kHz, 7,500A, 20psi 0.048 (t/δ = 0.84) 0.062 (t/δ = 1.09) 0.125 (t/δ = 2.19)
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15. Corner and Center Temperature Difference
• The percent difference between 0.048
the temperature of the corner and 20
center of the copper tubing is 15
plotted 10
• A positive difference correlates to
5 10 kHz
Percent
0 3 kHz
Difference
the corner being hotter -5 5000 A 7500 A 10000 A 1 kHz
• For the data shown here, the water -10
-15
pressure is 40 psi -20
0.062 0.125
20
20
15
15
10 10
5 10 kHz 5 10 kHz
Percent Percent
0 3 kHz 0 3 kHz
Difference Difference
5000 A 7500 A 10000 A -5 5000 A 7500 A 10000 A 1 kHz
-5 1 kHz
-10 -10
-15 -15
-20 -20
*Cases where the induction coil wall reached over 250 C are
dropped from the graphs
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16. Corner and Center Temperature Difference
t/δ = 0.48 t/δ = 4.03
• The reference depth is
shown to influence the
thermal profile in the coil
• As shown here, when the
wall thickness to reference
depth ratio is small the
temperature is higher in the
center, but when the ratio is
large it is higher in the
1 kHz corners. 10 kHz
7500 A 7500 A
40 psi 40 psi
0.048 in 0.125 in
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17. Effect of Water Pressure
• The percent decrease in temperature 10 kHz
50
when water pressure across the leg of 45
40
the inductor is dropped from 40 psi to 35
20 psi is plotted Decrease in
30
0.125
25
Temperature
• The temperature of the center of the 20
15
0.062
0.048
copper tubing is analyzed here 10
5
0
5000 A 7500 A 10000 A
1 kHz 3 kHz
50 50
45 45
40 40
35 35
30 30
Decrease in 0.125 Decrease in 0.125
25 25
Temperature 0.062 Temperature 0.062
20 20
15 0.048 15 0.048
10 10
5 5
0 0
5000 A 7500 A 10000 A 5000 A 7500 A 10000 A
*Cases where the induction coil wall reached over 250 C are
dropped from the graphs
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18. Effect of Increasing Water Pressure
• With increasing current the percent temperature
drop is greater. This is due to the higher
temperature gradient.
• The percent temperature drop is higher for
thinner wall thicknesses. The water cooled
surface is in closer proximity to the hottest
points on the copper for thin walled tubing.
3 kHz
50
40
30 0.125
Decrease in
Temperature 20 0.062
10 0.048
0
5000 A 7500 A 10000 A
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19. Effect of Increasing Water Pressure
• 3 kHz, 7,500A
40 to 20 psi
0.048” pressure increase 0.048”
40 to 20 psi
0.125” pressure increase 0.125”
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20. Cycling
• A cycling process is modeled with intervals of 10
seconds of heating following by 5 seconds with
no current
• Analyses of different points on the inductor are
done to determine if and when a steady state is
reached
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21. Cycling Results
10kHz 7500A 0.062 40psi
200
Center Temperature
Corner Temperature
Concentrator Corner
Concentrator Backside
150
Temperature
( C)
100
50
0
0 20 40 60 80 100 120 140 160
Time (s)
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22. Thermal Profile During Cycling
10kHz, 7,500A
40psi, 0.062
10 s 25 s 40 s 55 s
70 s 85 s 100 s 115 s
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23. Cycling Results
• The copper reaches steady state after the first cycle, since
it has a high thermal conductivity and is in contact with the
cooling source
• The corner of the concentrator closest to the copper
reaches steady state after 4-5 cycles. The Layer of epoxy
causes it to reach a much lower temperature than the
corner of the copper tube adjacent to it.
• The backside of the concentrator is slow to reach steady
state, but the fact that it did within a reasonable amount of
time shows that the whole inductor reaches a steady state
during continuous cycling
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24. Conclusions
• Heat loss from radiation has little effect compared to
the heat generated from coil losses in single shot
coils
• Coil losses are higher when the reference depth is
greater than the wall thickness
• Coil losses are higher when the temperature of the
copper is greater, since the resistivity of copper
increases with temperature
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25. Conclusions Continued
• When the reference depth is greater than the wall
thickness, the temperature tends to be higher in the
center of the tubing, and vice versa
• Thin walled tubing cools more efficiently and has a
higher response to an increase in water pressure
• During cycling the copper tubing reaches steady
state immediately, while the concentrator is slow to
reach it on the backside.
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