7-9 June 2003 Inverse Problem in engineering Symposium 1
Topic
FOULING PROBE DEVELOPMENT FOR TUBULAR HEAT EXCHANGERS:
A first step
Laetitia PEREZ
P. TOCHONB. LADEVIE
UMR CNRS 2392J.C. BATSALE
UMR CNRS 8508
7-9 June 2003 Inverse Problem in engineering Symposium 2
Overview
1. Industrial context
2. The Probe
3. Direct model
- theoretical sensitivity analysis
4. Experimental device
5. Experimental results
- experimental sensitivity analysis
6. Conclusions
7-9 June 2003 Inverse Problem in engineering Symposium 3
Industrial context
- heat exchangers in the power and process industries
- performance degradation
- thermal resistance increase
- pressure drop increase
- heat coefficient decrease
7-9 June 2003 Inverse Problem in engineering Symposium 4
Industrial context
Economic problems:
- oversizing equipment
- high maintenance costs
- energy expense
It is necessary to:
- detect the onset of fouling
- follow its development over time
Effectiveness of heat exchangers optimization
7-9 June 2003 Inverse Problem in engineering Symposium 5
The Probe
probeExchanger parts
TeflonReheater
Stainless steel
Transient heatflux
Recording of the temperature evolution Thermocouple
probeExchanger parts
TeflonReheater
Stainless steel
Transient heatflux
Recording of the temperature evolution Thermocouple
7-9 June 2003 Inverse Problem in engineering Symposium 6
Direct model
2 2 2
2 2 2 2
1 1 1T T T T T
r r r r x z a t
33
, , , if 0 otherwise 0
T r x z tr r z b
r
6
66 6
¨
, , , where air air air
r r
T r x z tr r h x S T S r L
r
0
, , ,0 0
z
T r x z tz
dz
, , , 0z L T r x L t
0 0 , , , 0r r T r x z t
even function in T x
0 00 , , ,0 where is the steady state temperaturet T r x z T T
Transient heat equation in cylindrical coordinates:
Boundary conditions:hair
hwater
r
zb
Cylinder axis
r0
r1
r2
r3r4
r5
r6
L
Exchanger part
Symetrie axis
hair
hwater
r
zb
Cylinder axis
r0
r1
r2
r3r4
r5
r6
L
Exchanger part
Symetrie axis
Stainless steel
Teflon
Reheater (sensor)
Stainless steel
Teflon
Reheater (sensor)
7-9 June 2003 Inverse Problem in engineering Symposium 7
Direct model
0 0 0
, , , , , , cos cos
12with where ,
L ptn n
n
r k p T r x z t z kx e dzdxdt
nn k
L
2 2
22 2
, , , , , ,1, , , 0n n
n n
d r k t d r k t k pr k t
dr r dr r a
0 0 0
*
*
, , , cos cos
, , , 0 for and
sin,0, , for n and 0
b ptn n
n
nn
n
r k p z kx e dzdxdt
r k p n k
br p k
p
,
, , , , , ,
, , , , , ,in outin out
n n
n nr rr r
r k p r k pA B
r k p r k pC D
7-9 June 2003 Inverse Problem in engineering Symposium 8
Direct model
1
1 1 23 3
1 1 2
,0, , ,0, ,air airn n
air air
C D h S Ar p r p
A B h S B
3 30
2, , , ,0, , cos
N
n nn
T r x z p r p zL
Finally, the temperature in the Laplace-Fourier space is:
The temperature in the real space is:
Too many approximations hard to check
Harsh industrial conditionsDirect model
7-9 June 2003 Inverse Problem in engineering Symposium 9
Sensitivity analysis
0 1 0 0 2 0 0 3 0 0 4 0 0 5 0 0 6 0 0 7 0 0 8 0 0 9 0 0 1 0 0 0-0 .2
0
0 .2
0 .4
0 .6
0 .8
1
1 .2
3
31
, 0 ,
1, 0 ,
N
nn
T r z t
T r z tN
3
31
, 0 ,
1, 0 ,
a ira ir
N
nn
T r z th
h
T r z tN
3
31
, 0 ,
1, 0,
pp
N
nn
T r z tC
C
T r z tN
t (s )
, , , ,i
ii
i
T r x z tX t
7-9 June 2003 Inverse Problem in engineering Symposium 10
Experimental device
Air at 323 K
with particles
Cooling water
AirFoulant particles generator
Heat exchanger parts and probe
Industrial water
sewer
Air at 323 K
with particles
Cooling water
AirFoulant particles generator
Heat exchanger parts and probe
Industrial water
sewer
7-9 June 2003 Inverse Problem in engineering Symposium 11
Experimental results
In clean conditions:
t (s)
Exp
erim
enta
l tem
pera
ture
s(°
C)
100 200 300 400 500 600 700 800 900 10008.5
9
9.5
10
Increase of air flow rate 50 Nm3/h
60 Nm3/h 70 Nm3/h 80 Nm3/h 90 Nm3/h 100 Nm3/h
t (s)
Exp
erim
enta
l tem
pera
ture
s(°
C)
100 200 300 400 500 600 700 800 900 10008.5
9
9.5
10
Increase of air flow rate 50 Nm3/h
60 Nm3/h 70 Nm3/h 80 Nm3/h 90 Nm3/h 100 Nm3/h
0 1 0 0 2 0 0 3 0 0 4 0 0 5 0 0 6 0 0 7 0 0 8 0 0 9 0 0 1 0 0 0- 0 . 2
0
0 . 2
0 . 4
0 . 6
0 . 8
1
1 . 2
t ( s )
e x p 3
e x p 31
, 0 , ,
1, 0 , ,
e r i m e n t a ln o r m N
e r i m e n t a ln
T r z t QT Q
T r z t QN
n o r m n o r mi jT Q T Q
0 1 0 0 2 0 0 3 0 0 4 0 0 5 0 0 6 0 0 7 0 0 8 0 0 9 0 0 1 0 0 0- 0 . 2
0
0 . 2
0 . 4
0 . 6
0 . 8
1
1 . 2
t ( s )
e x p 3
e x p 31
, 0 , ,
1, 0 , ,
e r i m e n t a ln o r m N
e r i m e n t a ln
T r z t QT Q
T r z t QN
n o r m n o r mi jT Q T Q
7-9 June 2003 Inverse Problem in engineering Symposium 12
Experimental sensitivity analysis
3, 0, .airT r z t f h g t
3 0, 0, .air airair
fT r z t f h h g t
h
1
3
32 1
1
, 0,
1. , 0,
T T
air
N
n nNn
nn
f h g t g t g t T r z t
g t T r z tg t
The temperature response can be written by:
For a little heat transfer coefficient variation:
the signal amplitude variation can be calculated by:
7-9 June 2003 Inverse Problem in engineering Symposium 13
12cov
T
air Tf h g t g t
40 50 60 70 80 90 100 1109.3
9.4
9.5
9.6
9.7
9.8
9.9
10
10.1
Standard deviationin considering only the steady state (t>100s)
Standard deviation in considering allthe signal
Q (Nm3/h)
f(h
air)
40 50 60 70 80 90 100 1109.3
9.4
9.5
9.6
9.7
9.8
9.9
10
10.1
Standard deviationin considering only the steady state (t>100s)
Standard deviation in considering allthe signal
Q (Nm3/h)
f(h
air)
Experimental sensitivity analysis
7-9 June 2003 Inverse Problem in engineering Symposium 14
Experimental results
In fouled conditions:
Cooling water
Air flow
with particles
Deposit pattern around the probe
- Fouling detection after 22h
- Fouling thickness after 78h : efouling = 2 mm
t = 22 ht = 35 ht = 40 ht = 70 ht = 78 h
0 100 200 300 400 500 600 700 800 900 1000
-0.01
-0.005
0
0.005
0.01
0.015
0.02
0.025
0.03
Growing fouling
0norm fouling norm foulingT e T e
t (s)
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