Error introduced by the disturbance of the local
temperature
p
using
g thermocouples
p
Heat flux and thin film temperature sensor
B. Garnier Lab. Thermocinétique (LTN) UMR CNRS6607 ‐
Polytech’Nantes
Advanced Spring School
Thermal Measurements&Inverse Techniques
- 6th Edition –
Domaine de Françon Biarritz, France March 1-6, 2015
Lecture L2 part2/3
/
1
B. Garnier LTN/Polytech’Nantes
Outline
1. Error introduced byy the disturbance off the local temperature
p
usingg thermocouples
p
- Surface temperature measurement or within a volume
- Error
E
analysis
l i andd model
d l
-Practical consequence and examples
- Semi intrinsic thermocouple
2. Heat flux measurement (direct and inverse methods)
3. Thin or thick film temperature sensor
2
Error introduced by the disturbance of the
local temperature using thermocouple
• Whatever the selected temperature measurement method, one have parasitic
effects
• Two type of errors :
 thermometric phenomenon
phenomenon + used device for its meas. interaction between sensor,
sensor medium and environment
which involves a local disturbance of the temperature field.
?
3
Illustration‐ Tutorial T4‐
4mm
60°C
5mm
5
5
5
1
2
3
7
4
5
6
19,8°C
20°C
Fig.1 : instrumented PMMA sample with 0.2mm dia. type K thermocouple
*, mm
5
10
15
#
1
2
3
T , °C
49 9
49,9
40,5
31,5
#
4
5
6
T , °C
43 5
43,5
35,4
27,7
#
T , °C
7
34,8
Table 3 : steady state temperature measurements
T7 - T2 = 5.7°C !
and
ΔT = 5.7/(60-20)=14 %
Rq: If we use inox sheathed thermocouple‐> it will be larger !
4
Error analysis and model
- Surface temperature measurement
Radiation
Sensor
Bardon 1999, Cassagne 1980 & 1986
Radiation
Conduction
Radiation
Tp: wall temp.
Tc: sensor temp.
convection
Measurement
T(t)
For an opaque medium:
3 effects •Macroconstriction
•Thermal contact
resistance
•Fin
Measurement error :
(t) = T(t) - Tc (t)
Tp(t)
(t)
Tc(t)
TE
5
-Temperature measurement within a volume
Conduction
Convection + radiation
Radiation
dV
Measurement
Same 3 effects:
•Macroconstriction
•Thermal contact resistance
•Fin
Measurement error :
(t) = T(t) - Tc (t)
6
- Error model
• Steady state surface temperature measurement of an opaque medium
10 yE
adiab.
TE
hE
T
hE  hc  hr
TE 
x
,c
2yE
hc T f  hr To  F
hE
 : thermal conductivity
a) Macroconstriction effect :
T ‐ Tp = rM 
with
1
rM 
4 yE 
for a disc of radius yE
 96% of the T - Tp temperature drop is within an hemisphere of center 0 and radius 10 yE
7
)
Error model
b) The contact resistance effect
Tp - Tc = rc 
rc=Rc /S
Rc (m
( 2 K W
K W‐11 )
c) The fin effect: Tc - TE = rE 
Measurement error
thermocouple assumed as a rod of radius yE
rE  1 /( y E 2hE E y E )
 =T – Tc ?
T - Tp = rM 
Tp - Tc = rc 
Tc - TE = rE 
 =T
T – Tc=K
K (T - TE)
T - Tc = (r
( M +rc )

with
ih
T  TE
rM  rc  rE
1
K
rE
1
rc  rM
8
 =T – Tc=K (T - TE)
with K 
1
rE
1
rc  rM
Discussion:
 small if:
•T- TE small
•K small
rE >> rc + rM
rM 
1
4 yE 
 high thermal conductivity medium
rM << rc
 low thermal conductivity medium
rM >> rc
9
Transient surface temperature measurement
and
K
(t) = K(t) [T(t) – TE ]
K(0)
K()
K(0) ?
T
t<0
0
•If rc 0, K(0)=1, the error is about 100% at t=0
•If rc =0 (perfect contact),
contact) the initial error is smaller:
t
TE
b
bE
TC
T  TC bE

TC  TE
b
 (0)  T  TC 
t  0
b= c
 (0)  T  TC 
bE
(T  TE )
b  bE
bE   EbE  E
bE
[(TC  T )  (T  TE )]
b
K ( 0) 
effusivities
bE
1
b  bE
10
Temperature measurement within a volume

h
T
2y
Temperature measurement p
with a cylindrical sensor inside the medium
Tc
•
Same error model but with :
•
rc= Rc/S
2
Log
rM 
2
y
1
S  2 y 
  y
11
2.4.3. Practical consequence and examples, semi intrinsic thermocouples
• Practical consequences :
1. even for perfect contact rc = 0 there is an error which depends on the ratio rM /rE.
2. For high thermal conductivity material, rM << rc Thus, one must take care that rc is
small
ll andd remains
i stable.
t bl The
Th contact
t t pressure will
ill have
h
to
t be
b high
hi h andd constant,
t t
surface will have to be plane without waviness, the interstitial medium with the
highest possible thermal conductivity (welding, grease…). In addition, one should
avoid oxide films as well as mechanical shocks and vibrations which can modify
considerably rc and consequently the measurement error.
3. For low thermal conductivity material , rM >>> rc. One can reduce macroconstriction
effect by increasing the radius of the sensitive element without increasing the section
of the connections A contact disc of high thermal conductivity material will be used.
y
D
E
12
4. Whatever the type of measurement, the fin thermal resistance rE should be as high as
possible. The transversal area, the conductivity, the heat transfer coefficient have to
be chosen the smallest possible. One also should have low emissivity surface,
connection protected from high temperature fluids movements or radiation, TE being
modified in those situations.
5. Finally, the error is all the more small as TE should be as close as possible to the
temperature T to measure . At the price of a technological complication, one can add
an external heat source on the connection so that its temperature
p
TE is controlled in
order to stay a close as possible as T “compensated heat flux sensors”. However
for correct measurement, the thermal resistance rE should stay high in order to
prevent the compensation heating from disturbing the temperature field in the
medium.
13
with contact disc
• Application -for steady state temperature measurement using a thermocouple
with and without a contact disc

thermocouple unique rod with a radius yB = 0.5 mm, an infinite length,
B = 15 W.m-1.K-1 and hB = 5 W.m-2K-1.

rE ?

rE = rB

rE  rB +
rB 
without
ith t contact
t t disc,
di
1
4 y B D
with contact disc
hB
D
1
y B 2hB y B B
yB
B
contact disc
14
Tab 1. Effect of the thermal conductivities of the medium and of the disc on rM, rc, rE and K
rM (K.W-1)
Rc (K.W-1m2)
rc(K.W-11)
rE (K.W-1)
K
Low thermal conductivity
=10-1 W.m-1.K-1
without
ith t disc
di
with
ith disc
di
5000
250
10-3
10-3
1270
3,18
1700
1733
0.786
0.127
hB

D
yB
High thermal conductivity
=100 W.m-1.K-1
without
ith t disc
di
with
ith disc
di
5
0.25
10-4
10-4
125
0.31
1700
1733
0.072
0.0003
 =T – Tc=K (T - TE)
with
ih
B
K
contact disc
1
rE
1
rc  rM
15
• Temperature measurement with semi intrinsic thermocouple
Medium M itself (presumately electrically conducting) is used as one wire
of the thermocouple
it
it has only one connection wire instead of two, thus rE is twice larger
the measured temperature T is intermediate between Tp and Tc
T
Tp
T
Tp
A
T
M
eA
M
M
Tc
i

M
A
Tc
TE
16
 i  T - T  K i ( T  TE )
Semi intrinsic thermocouple
Tp
T p  T  A

T  Tc M
Semi intrinsic T
i

T
Ki 
Traditionnal thermoc. A
rM  rc
 A  M
Tc
TE
rM  rc  rE
rM  rc
K
rM  rc  rE
Ki < K
• Error is considerably lower than with a traditional thermocouple (2 to 5 times)
but the calibration of the semi intrinsic thermocouple is almost always required.
17
Conclusion for the errors due to thermal disturbance
 Error model and recommandations for correct implementation of thermocouples
= ( rM , rc rE , T-TE )
 Thermocouples should be
implemented along isothermal lines
( 100 )

100 
 Thermocouples disturbance  hemisphere of radius 10 (/2)
20 
Thermocouples should not be too close
18
Heat flux measurement: direct and inverse methods
-Heat flux sensor HFS with gradient
Principles : measurement of the temperature difference or by covering the medium
with a polymer film with thin film sensors
Tangential
Normal
V
T2
T1
V

wall
A
B
A B
wall

It works whatever the heat flux direction with steady state or for slowly variable temperature.
Normal gradient HFS Omega :   8 to 10 % ‐Khaled 2009‐ Rq: it can be more ….
Omega
Rdf
Captec
Vatell
Hukseflux
Wuntronic
19
-Inertia heat flux sensor and heat flux sensor with electric dissipation (zero method)
P=UI
wall
wall
T(t)
Inertia heat flux sensor
works for heat flux coming
from the environment
T
T=0
0
T
heat flux sensor with electric dissipation
works only for heat flux leaving the wall
and for steady state or slowly variable
temperature
temperature.
20
-Enthalpic heat flux sensor
Tp

TF

wall
T=0
TE-S
It works for heat flux coming from the surrounding
21
Heat flux sensor with indirect measurement  Inverse method !
thermocouple (50m
50m )
• With wire thermocouple (
P t t JP Bardon
Patent
B d 1994
3 thermocouples
t) ? T1 T2 T3



6 mm
IHCP
t) ?
5 mm
2 thermocouples
Heat flux sensor with thermocouples (type K 50m)
(F Bouloc,
(F.
B l B.
B Bourouga
B
2007)
Exhaust pipe
  5% ( th. type K 50m) B Azerou et al. 2013
t) ?
Hot junctions
• criteria for correct locations of thermocouples Tutorial T4
22
m
m
m
m
5
6
•With thin film heat flux sensor (HFS)
HFS with wire th.
30 µm
r1
r2
R(T)
20 mm
•
Much accurate locations of the sensors (2 to 3 m)
•
Easier HFS mass production HFS mass production
23
• Comparison wire thermocoples and thin film heat flux sensors
• Measured temperature
28
TR1
TR2
TR3
TR4
26
Température ((°C)
HFS with wire
thermocouples(TH)
HFS with thin film
sensors (TR)
((copper
pp RTD))
24
22
20
18
Heat
exchanger
0
25
50
75 100 125 150 175 200
Temps (s)
• Measured heat flux (function specification Beck 1985)
HFS with wire
thermocouples
Thermocouples
HFS with thin
film RTD
Heater copper
etched foil
Azerou B. et al. , J. Phys. CS 2012 elec
Results
• Comparaison with elec (heating device):
 HFS with wire thermocouples : 5,3% / elec
 HFS with thin films : 2,2% / elec
• Same time constant tr (  0,3 to 1% ; tr 175 s)
• HFS with thin film: easy mass production
24
Thin or thick film temperature sensor
The smallest wire thermocouple has a  of 12 m (Lab FEMTO 5m) How to make them smaller ? (less
(
invasive))
 Thin film ( thick.100 nm) or thick
(
)
films (thick.a few m)
(
 )
• Temperature measurement bias 
• Time constant ‐> s
but
 Need surface with high quality (low surface roughness)
 Sensitivity V/°C ou /°C  ‐> calibration is required
 TTake
k care about connections :
b
i
columnar structure
Table1 : F.e.m
F e m constantan (0,4
(0 4 Ni 0,6
0 6 Cu) evaporated on quartz in vacuum
Thickness (nm)
Elaboration
F.e.m. at 20°C (V/K)
40
evaporated
‐30
100
evaporated
‐34
250
evaporated
‐38
‐‐>
bulk
‐42
25
How to realize thin or thick film temperature sensors ?
30m
 Thin film deposition
film deposition (PVD,CVD…)
(PVD CVD )
(a)
borosilicate
150m
PDMS
x
(b)
Thick 85nm gold
2D heat flux sensor
Hamadi et al. 2010
et al. 2010
 Electrolytic or galvanic
or galvanic deposition
1D heat flux sensor
Azerou et al. 2012
Thick 9m copper + tin
 Serigraphy
26
Glass temperature measurement during grinding
 Spray!
Sintered diamond
composite with
g
tungsten
Thermocouple junctions
40
9 layers
Fi
Figure 46
46 : Vue de dessous de la plaque du verre (Nickel pulvérisé).
V d d
d l l
d
(Ni k l l é i é)
6 layerss
25
20
 Thickness of 4 to 12 m
 Take care about increased oxydation
15
9 layers
10
 An annealing process at 400°C might
be necessary to stabilize
to stabilize electrical prop.
prop
5
0
Nickel
Glass
l
30
Voltage ((mV)
Figure 45 : Vue de dessus de la plaque du verre (Cuivre pulvérisé).
Copper
Nickel
Calibration
35
Copper
0
50 100 150 200 250 300 350 400 450 500
Temperature (°C)
annealing=« recuit » 27
Thanks for your
for your attention!
Nantes
28