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Analysis of heat transfer in heat exchangers
by using the NTU method and empirical
relations
Oddgeir Gudmundsson
Olafur Petur Palsson
Halldor Palsson
Outline
Introduction
Data
Application
Model
Fouling detection
Conclusion
Further work
2
Introduction
Fouling is inevitable when using heat exchangers. Fouling has negative effect on heat transfer and will therefore increase cost and
pollution to the environment.
District heating in Iceland is based on geothermal energy. Geothermal water is rich in minerals which can cause fast and
severe fouling.
Simple, effective and online fouling detection can therefore save cost and decrease pollution.
The method proposed uses measurements that are readily available during normal operation of the heat exchanger, temperatures and
mass flows.
3
Data used in the study
Since data from cross flow heat exchangers are scarce simulated data was used in the study
The simulator is designed to calculate the outflow condition of the two
fluids in a unmixed cross-flow heat
exchanger
In the simulator it is possible to vary all physical parameters of the heat
exchanger and the inflow condition
of the two fluids
4
Data used in the study
Fouling is simulated by decreasing the overall heat transfer coefficient, U
It is possible
to target the fouling in specific places of the heat exchanger or,
decrease U uniformly over the whole heat exchange area
For fouling detection with the proposed method the location of the fouling is not an issue
5
Simulator Heat exchanger
The following assumptions are made The heat exchanger is perfectly insulated, that is the heat loss to
the surroundings is negligible
There is no heat conduction in the direction of the flow in the metal separating the fluids nor in the fluids themselves
There is a uniform temperature in each section of the heat exchanger and that complete mixing takes place just before the
fluids exit each passage
The specific heat capacities are constant through the heat exchanger
6
Simulator Simulated data
The simulated data used was of a heat exchanger with water on both sides
The temperatures and mass flows were allowed to vary
Hot inlet temperatures were on the interval: [50, 70]C
Cold inlet temperatures were on the interval: [10, 30] C
Hot mass flow were on the interval : [0.3, 1.4] kg/s
Cold mass flow were on the interval : [0.3, 1.4] kg/s
These operating conditions were chosen so that the velocities in the passages were in the turbulent region as is usually
observed in industrial heat exchangers
7
Simulator Simulated data
8
0 100 200 300 400 500 600 7000
20
40
60
80T
em
pera
ture
[C
]
0 100 200 300 400 500 600 7000.4
0.6
0.8
1
1.2
1.4
mass f
low
[kg/s
]
Seconds
Simulator - Fouling
Research has shown that the fouling typically starts slowly and the fouling rate increases with time.
In fact it has been pointed out that fouling may enhance the heat transfer during early stages by increasing the
turbulence in the heat exchanger
9
Simulator Simulated fouling
The evolution of the fouling started slowly but the accumulation increased with time
The first 25% of the data was simulated without fouling
10
Simulator Simulated fouling
Heat exchangers are typically designed to withstand mild fouling
The line at fouling factor Rf = 0.0001 indicates typical lower limit that heat exchangers
are designed to withstand
Typical design upper limit of fouling factor is Rf = 0.0007
11
Simulator Simulated data
Two cases of data sets was produced with the same fouling growth
Short time series, which corresponds with fast fouling
Long time series, which corresponds with slow fouling
The long time series where 2 times longer than the short time series
In both cases the same inputs intervals where used, the only difference between the data sets is that the fouling growth is
faster for short data sets than long data sets
12
Application Fouling detection
Fouling detecting effectiveness is dependent on the excitation of the system.
The more excited the system is the harder it is to detect effects of fouling.
This can easily be seen in the following figures where NTU method without empirical relations is used to estimate the overall
heat transfer coefficient.
13
Application Effect of inputs
From the 4 figures to the right it is apparent
that the excitation in
the system plays vital
role when trying to
detect fouling in heat
exchangers
The line is the average of the first 25% of the
data
14
0 1000 2000 3000 4000 50002
2.5
3
3.5
4
4.5
Uest
0 1000 2000 3000 4000 50002
2.5
3
3.5
4
4.5
Uest
0 1000 2000 3000 4000 50002
2.5
3
3.5
4
4.5
Uest
0 1000 2000 3000 4000 50002
2.5
3
3.5
4
4.5
Uest
Sample number
Application Fouling detection
As fouling accumulates the overall heat transfer coefficient decreases
It is therefore possible to detect fouling by monitoring a shift in the overall heat transfer coefficient
It is convenient to use CuSum chart to detect the shift
15
Application Fouling detection
During normal use of heat exchangers the overall heat transfer coefficient is unknown
For a cross flow heat exchanger with both fluid unmixed NTU can be found from a relation to the effectiveness
16
Application Estimation of NTU
It is known that effectiveness can be calculated with:
and
NTU can be found by solving
17
21
Application Empirical relations
As already shown it can be hard to detect the effect of fouling on the overall heat transfer coefficient with basic
calculations
By introducing empirical relations
it is possible to decrease the influence of the mass flow
on the calculation of the overall heat transfer coefficient
18
Application Empirical relations
It is practical to normalize the overall heat transfer coefficient with a reference mass flow
Now the overall heat transfer coefficient can be calculated as
19
Application Results
After the empirical relations have been
applied and the new
estimation of the
overall heat transfer
coefficient plotted on
the previous figure it
can be seen that the
empirical relations
perform well in
filtering the signal
20
0 1000 2000 3000 4000 50002
2.5
3
3.5
4
4.5
Uest
0 1000 2000 3000 4000 50002
2.5
3
3.5
4
4.5
Uest
0 1000 2000 3000 4000 50002
2.5
3
3.5
4
4.5
Uest
0 1000 2000 3000 4000 50002
2.5
3
3.5
4
4.5
Uest
Sample number
Application Fouling detection
In 95% of the cases the detection interval was
Fast fouling: [0.26, 0.40] in dimensionless time
Slow fouling: [0.23, 0.35] in dimensionless time
The corresponding fouling factor interval is [0.00001, 0.00003]
These can be considered good results comparing to design limits for the fouling factor which commonly are
chosen to be in the range [0.0001, 0.0007]
21
Further work
Further work will include validating the simulator by comparing the simulations to real
data from a test rig that is currently under
construction in Iceland
Temperature dependency of the overall heat transfer coefficient will be included in the
method
22
Acknowledgements
Environmental and Energy Research Fund of Orkuveita Reykjavkur,
National Energy Fund and Energy Research Fund of Landsvirkjun.
Energy Research Fund of Orkustofnun
Sylvain Lalot, professor at the University of Valenciennes in France
23
24
Thank you for your attention