Transcript Finite-difference Model of a Heat Flux Sensor

The Effects of Thermocouple
Materials and Insulating Mica in
an Erodable Surface
Thermocouple
Alan Grech, Tonio Sant, Mario Farrugia
University of Malta
2008 ASME Summer Heat Transfer Conference
Outline
•
•
•
•
•
Introduction
Project Motivation
Models, closed form and FDE
Results
Conclusion
2
Introduction
• Heat flux sensor
– At least 2 TCs (thermocouples) needed
– Presence of a temperature gradient
Surface
Thermocouple
Recessed
Thermocouple
A typical heat flux sensor
3
Eroding-type Surface TC (STC)
• Fast response due to small thermal junction
• Junction formed by abrasion
• ~30µs response times can be achieved
Junction:
Sliver formed
by abrasion
+ve
Thermocouple Material
Electrical
Insulation
-ve
Thermocouple Material
STC’s
Construction
4
Eroding-type Surface TC (STC)
• A product of Nanmac Corporation
Stainless Steel
Chromel
25µm thick
Heat Flux
Constantan
25µm thick
Mica sheets
5µm thick
Sliver formed
by abrasion
Configuration of Surface TC tested (Type E)
Dimensions from Oude Nijeweme
5
Project Motivation 1/3
• Transient tests performed at Oakland University
– Laser’s Frequency: 10kHz
– Laser’s power: 11W
Lens
Sensor

Laser beam
25mm diameter
focused to 6mm
6.35mm
Set-up of transient tests apparatus
6
Measurements:
125
MEASURED DATA
Surface Temperature
o
Measured Surface Temperature ( C)
120
115
110
105
100
95
0
200
400
600
800
1000
1200
Time (micro-seconds)
Measured Surface Temperature From Multiple Laser Pulses
7
Project Motivation 2/3
1D Analytical Model:
Temperature rise
Carslaw and Jaeger
  t
Energy per unit area
coming from laser
1
2
2 e  x 4 t
Q    c 
• Energy coming form laser was matched
better using properties of mica sheets
rather than body material
8
Project Motivation 3/3
• Conclusion of transient tests’ results:
– “At 10kHz properties of mica sheets
should be used to calculate heat flux
using a 1-D analytical model rather than
properties of body material, as is
usually done”
9
Finite-difference Model (FDM)
• A 1-D FDM was first built
• A 2-D FDM needed to analyze 2-D effects
present in STC due to mica-sheets
• Explicit schemes used
• Programming with Matlab and C
• Also made cross check with Ansys
10
1-D FDM
• Rod subjected to laser pulses at one end
• Other ends modeled as insulated
• Only heat flow by conduction considered
Laser
pulses
A
11
2-D FDM
50 elements
25 elements
Heat flux
from laser
pulses
5 elements
y
x
2mm
Square element size
= ∆s
=1µm
12
2-D FDM
• 1st Step:
Model discretization
Surface
Node
n
Square
Element
∆s
• Different FDEs for
different positions
derived using
“Energy-Balance
Method”
Internal
Node
∆s
2-D Model discretization
13
Results: 1-D Model
700
AISI 316
Temperature (deg C)
600
0.017t^(-1/2)
Mica
500
400
300
200
100
0
0
5000
10000
15000
Pulse Number
20000
25000
• Body Material (AISI 316) dominates
surface temperatures
14
Results: 1-D Model
25
Measured
Temperature (deg C)
20
Model: Finite-difference (Mica Properties)
Model: Finite-difference (Steel Properties)
15
Model: Source Solution (T=0.017t^-0.5)
10
5
0
0
20
40
60
Time (micro-seconds)
80
• Mica properties dictate the decay
between pulses
100
15
Results: 2-D Model
• Significant conduction from mica sheets to
surrounding materials due to higher
temperatures reached near the surface owing
to its lower diffusivity
Surface
Temperature
Profile
80
78
76
74
72
70
68
16
Results: 2-D Model
80
Mica
AISI 300
Constantan
Chromel
78
76
Just after Pulse
Temperature (deg C)
74
72
70
68
1/20 of TBP
after Pulse
66
64
62
15/20 of TBP after Pulse
60
0
5
10
15
20
25
30
35
40
45
TBP=Time between pulses = 10μs
100µs
Just after pulse
50
55
60
65
70
75
80
85
90
95
100 105 110 115 120 125 130 135 140 145 150 155 160 165
x (micrometers)- Along Surface
1/20 of TBP after pulse
15/20 of TBP after pulse
Surface Temperature Profile after 1 sec heating
17
Results: 2-D Model
6
Measured
Measured
y = 0.017x -0.5
Steel & TC
5
Mica Sheets
Temperature Rise (deg C)
1-D Source Solution
Mica 1-D
4
3
y = 0.0211x -0.4787
2
y = 0.0006x -0.7825
1
y = 0.0035x -0.4888
0
0.E+00
1.E-05
2.E-05
3.E-05
4.E-05
5.E-05
6.E-05
7.E-05
8.E-05
9.E-05
Time (seconds)
18
1.E-04
Conclusion 1/2
• 1D closed form and FDE models
• Bulk temp represented well with body
material
• Surface temp not represented well with a
single material
Hence the need for 2D model
19
Conclusion 2/2
• Nowhere on the surface of the model
followed precisely the measured data
Future
• Model junction, i.e. 3D ?
• Thermocouple voltages
Transient/SteadyState same?
20