183
1 INTRODUCTION
Heat exchange apparatus within the thermal systems
of steam power plants, i.e. condensers, low-pressure
and high-pressure recuperative exchangers and the
heating surfaces of boilers are exposed to the
gathering of deposits on their heat exchange surfaces.
The source of these sediments usually is the
insufficient quality of the working medium and
cooling media as well as the physicochemical
processes are taken place, e.g. corrosion and erosive
processes as several studies [7, 9, 14, 18] have
suggested.
The fouling deposited on the heat exchange
surfaces, above all, create additional thermal
resistance in heat exchange processes [2, 12]. This state
of affairs is highly associated with the loss of thermal
power of the heat exchange apparatus, leading
directly to its thermal (heat) degradation. Thermal
degradation is the cause of, among others increase in
value of the terminal temperature differences and
deterioration of the vacuum degree in condensers [4].
The fouling thermal resistances values of the heat
exchange surfaces of steam power plants' heat
exchangers, presented in the literature, vary in a wide
range. For instance, according to TEMA standards, the
values of the deposits specific thermal resistances
range from 8.8·10
-5
to 100·10
-5
m
2
K/W [5, 12, 17, 21].
Furthermore, literature on the subject states that the
value of thermal resistance of fouling is strongly
influenced by the following things: the type of
dissolved salts in the water, the surface condition, the
construction material of the heat transfer surface, flow
geometry, temperature and speed of the working
media, i.e. the lower the wall temperature and the
higher the speed the flow of water, the less
susceptibility of the wall to the deposition of
sediments on it [1].
Moreover, Cunningham's research [6] supported
the thesis that in the case of the steam power plants
condensers, the presence of inert gases within the
steam space has a similar effect as the presence of
An Influence of Fouling Gathered on the Heat Transfer
Surfaces on the Heat Performance Characteristics of the
Ship Steam Systems' Heat Exchangers
T. Hajduk
Gdynia Maritime University, Gdynia, Poland
ABSTRACT: Gathering of fouling on the heat transfer surfaces, both on the water side and the steam side of heat
exchangers of the ship steam systems leads usually to the loss of their heat transfer capacities. This loss appears
owing to the high value of the fouling heat resistance and is called the thermal degradation process. It is linked
to falling the heat flux transported by a heat exchanger and decreasing total efficiency of the heat unit as well as
increasing costs of operation and freight costs after all. The loss of thermal power of a heat exchanger does not
only depend on the fouling thermal resistance but is also strictly correlated with the thermal quantities of a
given heat exchanger, among others its overall heat transfer coefficient values at various operating modes. The
paper presents the aforementioned phenomena and results of the author’s own experimental studies, as well.
http://www.transnav.eu
the International Journal
on Marine Navigation
and Safety of Sea Transportation
Volume 15
Number 1
March 2021
DOI: 10.12716/1001.15.01.18
184
fouling on the heat transfer surfaces of these
exchangers. On the other hand, numerical research by
Butrymowicz [4] shows a very important conclusion,
i.e. the higher the value of the heat transfer coefficient
of a given exchanger, the more sensitive the one is to
the fouling presence on its heat exchange surface. The
above constatation is a very crucial in the field of heat
exchangers operation within the steam power plants,
and particuliary in the ship power plants, e.g. steam
condensers, because of their relatively high values of
the heat transfer coefficients.
At the same time, deposits collected inside the heat
exchanger tubes (the water side) initiate the process of
obliteration. In particular, this phenomenon features
the power condensers cooled with sea water [10, 21].
The reduce in cross-section area of the tubes due to
formation of various types of particle-dispersion
deposits (sulphate, carbonate and silica scale) and the
biofouling as well (macro-deposits, e.g. mussels,
crustaceans and microorganisms, e.g. bacteria, algae)
increases the flow resistance with a simultaneous
reduction in efficiency condenser cooling. And finally,
this state of things leads to a reduction in the flow
velocity of the condenser cooling medium with the
consequence that there is an additional increase in the
resistance to heat transmission. Hence, the presence of
fouling leads not only to thermal degradation of a
given exchanger, but it should be expressed stronger,
to its heat-and-flow degradation [3, 13].
In view of above-presented results of the research,
the issue of thermal degradation of heat transfer
apparatus in the steam systems is a vital issue for their
operation, e.g. due to the high values of heat transfer
coefficients of these apparatus [3, 8, 11, 12, 15, 20].
2 A PHENOMENON OF HEAT EXCHANGERS
THERMAL DEGRADATION
The heat output of a heat exchanger
Q
[W] can be
expressed as follows,
log
k
T
Q
R
=
(1)
where
Tlog,C, Rk represent the logarithmic temperature
difference of the heat exchanger [K] and overall heat
transfer resistance [K/W] respectively.
During the heat exchanger using within the normal
operational time
ope i.e. beyond the fouling induction
period
ind, the fouling thermal resistance Rf achieves a
positive value. It is worth to mention that
ind is an
initial period of heat exchanger operation in which the
accumulated deposits constitute a form of microribs
that enhance the heat transfer area and act
simultaneously as turbulizers breaking the laminar
boundary layer, resulting finally in increase of heat
yielding through a given heat exchanger [8]
0
ope ind f
R
(2)
Thermal resistances are featured by additivity,
,,k F k C f
R R R=+
(3)
where Rk,C, Rk,F constitute the heat transfer resistance
of a heat exchanger without fouling (subscript “C” –
Clean), and a heat exchanger with fouling (subscript
“F” – Fouled).
The thermal resistance R is related to the overall
specific thermal resistance r by means of a following
relationship,
cal
r
R
A
=
(4)
where Acal describes a calculating heat transfer surface
given in square meters.
The overall thermal specific resistance rk and the
heat transfer coefficient k are related by the
homographic function [2, 16, 19, 23],
1
k
r
k
=
(5)
The decrease in the heat capacity of the fouled heat
exchanger is expressed as the difference between the
following heat fluxes,
.
loss C F
Q Q Q = −
(6)
where
C
Q
,
F
Q
mean the heat power of the
exchanger without fouling and the heat power of heat
exchanger with fouling respectively.
3 DESCRIPTION OF THE RESEARCH METHOD
The experimental research were carried out for a
single tube of the L-P heat recovery exchanger from
the steam system. The measurement of the thermal
resistance of fouling was performed simultaneously
for two types of tubes (Tab.1) i.e. for the tube with a
heat exchange area covered with sediment (DKR#02)
and for the tube without sediments constituting the
reference tube (REB#00). The length of measuring
section for two tubes was one meter. The inner
diameter of tubes and their thickness equal 12 mm
and 2 mm respectively. Fouled tube has got deposit
on the outside (vapor side). Both reference and fouled
tube are clean inside.
Table 1. Photos of the tested materials: fouled tube DKR#02
and reference tube REB#00
_______________________________________________
Tube with fouling DKR#02
_______________________________________________
Tube without fouling (reference) REB#00
_______________________________________________
[author’s own photos, taken with a tripod by Nikon D70S
camera with MicroNikkor 105mm-1:2.8D lens]
185
The heat flux took by the water in the tube with
deposits
,wF
Q
,
( ) ( )
, , , , , , ,
,
w F w F p w wi F wo F wo F wi F
Q m c t t t t= −
(7)
and the heat flux took by the water in the reference
(model) tube
,wC
Q
,
( ) ( )
, , , , ,C , ,
,
w C w C p w wi C wo wo C wi C
Q m c t t t t= −
(8)
where
, ,
w wi wo
m t t
and
,
wo
wi
t
p wt
c
represent mass flow
of the condenser water cooling [kg/s], temperature
of water inlet to the tube [°C], temperature of water
outlet from the tube [°C] and average value of specific
heat of water in the temperature range from
wi
t
to
wo
t
[J/(kg·K)] respectively.
The fouling thermal resistance
f
r
has been
determined on the basis of the differential method for
the direct determination of thermal resistance, i.e. as
the difference between a value of the overall thermal
resistance of the heat transfer surface with deposits
,
kF
r
and a value of the overall thermal resistance for
the heat transfer surface without deposits
,
,
kC
r
,,f k F k C
r r r=−
(9)
The value of the maximum absolute systematic
uncertainty of measurement
δ
f
r
for the fouling
thermal resistance
f
r
was determined by means of
the measurements uncertainties spreading law in
accordance with the square error propagation rule
[22],
0.5
22
δ δ δ
ff
f F C
FC
rr
r k k
kk
= +
(10)
Considering an operating mode of the heat transfer
apparatus at a constant values of temperature
difference and the heat exchange surface as well,
,,
log log C log F C F
T T T A A A = =
(11)
and taking into account the following formulas (1)
and from (3) to (5), heat power of the heat exchanger
with fouling of the thermal resistance
f
r
can be
evaluated as follows,
1
1
FC
fC
QQ
rk
=
+
(12)
So, the heat power loss for the fouled tube was
calculated from the following relationship,
1
fC
loss C
fC
rk
QQ
rk
=
+
(13)
The relative heat power loss of the tube with the
fouling heat transfer surface was expressed by means
the undermentioned RPLt index,
100% 100%
1
fC
loss
t
fC
C
rk
Q
RPL
rk
Q
= =
+
(14)
On the other hand, the relative heat power loss of
the tested heat exchanger with a partially fouled heat
transfer surface was described by the RPLhe ratio,
1 100%.
F
he
C
Q
RPL
Q
= −
(15)
Experimental studies were carried out on the
SPOCZEWC test-bench located in the Laboratory of
the Heat Transfer Department of The Szewalski
Institute of Fluid-Flow Machinery of Polish Academy
of Sciences. This test-bench was made according to the
idea of Butrymowicz and Gardzilewicz and then has
been thoroughly modified mutatis mutandis
according to own design of the author of this paper.
The basic component of the test-bench is a
condenser in which there is a possibility of
condensation at lower pressure, at the pressure equal
to or higher than atmospheric one. The steam source
for this test-bench is a modern, fully automated, once-
through steam generator (Clayton, p=1.9 MPa, D=950
kg/h). The steam incoming to the test-bench stems
from the low-pressure part of the system (pLP=0.6
MPa). The test-stand cooling system is equipped with
two circulation pumps (Grundfos, CRE17 type) with a
precise control of the cooling water flow thanks to an
integrated frequency converter, the PI controller and
control valves with smooth positioning control
(Oventrop, Hydrocontrol-R type). The data
acquisition system was configured on the basis of a
modular measuring transducer (NI, SCXI module)
and software (LabVIEW v.8.6). It consists of the
following sensors and transducers: K-type
thermocouples (Czaki), absolute pressure transmitters
(Pnefal, 1151 type), Coriolis flowmeters
(Endress+Hauser, Promass40E type).
4 RESEARCH RESULTS
The series of measurements consisted of seven
measurement points. The following parameters were
kept at a constant level within the measuring series:
both the inlet condenser cooling water temperature
for tube with fouling and the one for tube without
fouling (the reference one) at the level 19.00°C±0.05K,
the condensing pressure of 135.0 kPa(a)±0.5kPa.
Within a single measuring point, the water mass flow
rates were kept constant in the fouled tube and in the
reference tube, as well. In the experiment plan, the
following values of cooling water mass flow rates
were assumed, the same for both tubes (ceteris
paribus), i.e. 1870, 1530, 1170, 1000, 800, 700 and 600
kg/h±5 kg/h , which were obtained at rotation speed
of the cooling water pumps, respectively: 2650, 2150,
1700, 1450, 1200, 1050 and 970 rpm. After reaching the
steady state in the measurement, an electronic test
protocol was prepared. The average values of the
measured values are presented in Table 2.
186
Table 2. The mean values of measured quantities for tested tubes DKR#02 and REB#00
__________________________________________________________________________________________________
Tested No. n n/nmax twi,F two,F twi,C two,C pk mw,F mw,C
tube [obr/min] % [°C] [°C] [°C] [°C] [kPa] [kg/h] [kg/h]
__________________________________________________________________________________________________
DKR#02 (F) 1 2650 93 19.05 25.79 19.01 27.59 135.6 1874.6 1859.9
REB#00 (C) 2 2150 76 19.03 26.93 18.99 28.93 135.7 1534.7 1519.8
3 1700 60 19.03 28.69 18.99 30.99 135.5 1174.2 1160.7
4 1450 51 19.06 29.88 19.01 32.35 135.4 1004.3 991.3
5 1200 42 19.01 31.37 18.95 34.05 136.9 834.4 820.2
6 1050 37 19.03 32.74 18.97 35.60 135.5 705.2 691.8
7 970 34 19.01 34.09 18.96 37.03 135.7 602.9 594.0
__________________________________________________________________________________________________
[author’s own research]
Table 3. The mean values of calculated quantities for tested tubes DKR#02 and REB#00
__________________________________________________________________________________________________
Tested No. tk Tlog,F Tlog,C Qw,F Qw,C kF kC rk,F rk,C
tube [°C] [K] [K] [kW] [kW] [W/m
2
K] [W/m
2
K] [m
2
K/W] [m
2
K/W]
__________________________________________________________________________________________________
DKR#02 (F) 1 108.4 85.9 85.0 14.59 18.63 3464 5019 0.000289 0.000199
REB#00 (C) 2 108.4 85.3 84.3 13.99 17.64 3342 4790 0.000299 0.000209
3 108.3 84.4 83.2 13.09 16.26 3163 4475 0.000316 0.000223
4 108.3 83.7 82.5 12.54 15.44 3054 4287 0.000327 0.000233
5 108.6 83.3 81.9 11.90 14.47 2913 4044 0.000343 0.000247
6 108.3 82.2 80.8 11.17 13.43 2768 3808 0.000361 0.000263
7 108.4 81.6 80.0 10.49 12.54 2622 3586 0.000381 0.000279
__________________________________________________________________________________________________
[author’s own study]
Table 4. The values of the fouling specific heat resistances (rf) and the values of absolute (rf) and relative (rf/rf) measuring
uncertainty as well as RPLt and RPLhe indexes
__________________________________________________________________________________________________
Tested No. rf rf rf/rf ∂rf/∂kF kF ∂rf/∂kC kC RPLt RPLhe
tube [m
2
K/W] [m
2
K/W] [%] [(m
2
K/W)
2
] [W/(m
2
K)] [(m
2
K/W)
2
] [W/(m
2
K)] [%] [%]
__________________________________________________________________________________________________
DKR#02 (F) 1 0.000089 1.6E-05 17.8 -8.34E-08 168 4.0E-08 193 19.2 10.8
REB#00 (C) 2 0.000090 1.4E-05 15.8 -8.96E-08 139 4.4E-08 160 18.5 10.4
3 0.000093 1.3E-05 13.6 -1.00E-07 109 5.0E-08 126 17.5 9.8
4 0.000094 1.2E-05 12.5 -1.07E-07 95 5.4E-08 110 16.9 9.4
5 0.000096 1.1E-05 11.5 -1.18E-07 80 6.1E-08 93 16.1 8.9
6 0.000099 1.1E-05 10.8 -1.31E-07 69 6.9E-08 81 15.3 8.4
7 0.000103 1.0E-05 10.2 -1.45E-07 61 7.8E-08 71 14.5 8.2
__________________________________________________________________________________________________
[author’s own study]
The calculated values of analysed quantities are
presented in Table 3. The properties of water and
steam were received due to the NIST Refprop SRD 23
software, ver. 8.0.
The thermal resistance values of the fouling
gathered on the heat transfer surface of the DKR#02
tube and the relative values and absolute values of
the measurement uncertainty of the thermal
resistance determination are presented in Table 4.
This table also includes the value of the relative heat
power loss of the fouled tube DKR#02 (the RPLt
index was calculated for the average value thermal
resistance rf,m=9.5·10
-5
m
2
K/W, average of
measurements points from 1 to 7) and the value of the
relative heat power loss for the heat exchanger
equipped with one clean and one fouled tube (the
RPLhe ratio).
Figure 1 shows the dependence of changes in the
relative increase in the heat transfer coefficient kF
(DKR#02) and kC (REB#00) on the condenser cooling
intensity n/nmax. The highest value of n/nmax=0.93 has
been achieved at the measurement point #1 a
contrario the lowest value of n/nmax=0.34 has been
gained at the measurement point #7). The model
values for kF and kC were assumed at their minimum
values kF,min and kC,min, respectively. Figure 2 presents
the course of changes in the relative heat power loss
for the tube with fouling (the RPLt) and for the heat
exchanger (the RPLhe), as well.
Figure 1. The changes in the relative increase in heat
transfer coefficient kF (DKR#02) and kC (REB#00) with
regard to their minimum values respectively kF,min and
kC,min depending on the condenser cooling intensity n/nmax
187
Figure 2. A comparison of changes in the heat power loss
indexes the RPLt and the RPLhe as a function of the heat
transfer coefficient kC (without fouling)
5 CONCLUSIONS
The experimental research was aimed at assessing the
thermal power of heat exchangers in ship steam
systems in relation to the thermal degradation caused
by the presence of deposits on the heat transfer
surfaces. Research results lead to the conclusion that
the appearance of deposits has a significant negative
impact on the thermal output of a heat exchange
apparatus. It is indicated by the percentage of loss of
thermal power of the fouled tube from 14.5% (the
condition of the condenser operation at the minimum
speed of the cooling water pump i.e. 34% of its
maximum speed) to about 19% (the state of the
condenser operation with the highest cooling
intensification, i.e. 93% of the maximum rotational
speed of cooling water).
From the operation point of view of the heat
exchangers in steam systems, it is worth emphasizing
that the research carried out by the author of this
paper also supported an important thesis, i.e. the
higher the value of the heat transfer coefficient of the
heat transfer apparatus, the more sensitive it is to the
presence of fouling on its heat transfer surface.
Indeed, because taking into account the averaged
value of the measured specific thermal fouling
resistance of 9.5·10
-5
m
2
K/W, the largest decrease in
heat output for the fouled tube was recorded at the
first measuring point about 19% (at the highest value
of the heat transfer coefficient for the model tube of
approx. 5000 W/m
2
K) compared to the last measuring
point (at the lowest value of the heat transfer
coefficient for the model tube of approx. 3600 W/m
2
K)
which was about 5 percentage points less.
When analyzing the test results for the entire heat
exchanger, the relative decrease in its heat
performance was about two times smaller than the
one of the fouled tube, i.e. from 8.5% (at the lowest
rotational speed of the cooling water pump) to ca.
11% (at the highest cooling-water pump speed). The
scope of heat power loss of the tested exchanger in
the whole range of its cooling intensity was approx.
two and one-half percentage point. In addition, the
intensification of the research condenser cooling
greatly improved the heat transport conditions - a
monotonic increase in the heat transfer coefficients
for both the fouled and the clean tube. Therefore, the
highest value of the relative increase in the heat
transfer coefficient k/kmin was scrutinize for the clean
tube i.e. 40% and it was by 8 percentage points higher
than for the fouled tube. The measured value of the
fouling thermal resistance confirmed the compliance
with the results presented in the research literature.
The obtained level of the relative measurement
uncertainty maximum value of the fouling thermal
resistance indicates a high measuring accuracy of the
test stand in the range of the measured values from
8.9 to 10.3 the rf/rf value was lower than 20%.
It is worth emphasizing that the operation subsoil
of the modern ship steam systems has a deep
sozologic dimension. In the case of heat exchangers
operation of ship steam systems, the distinguishing
feature of their proper use is the respect towards the
energy transferred through them. Hence, inter alios,
the care of the technical condition of the heat
exchange surfaces in the steam systems is one of the
substantial issues of their proper using. To put in
briefly such an attitude and action prevents, in
essence, the increase in shipping costs by sea.
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