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

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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.

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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

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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

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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

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oddgeir@hi.is

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Thank you for your attention