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21
RECYCLING OF ASHES FROM BIOMASS COMBUSTION POWER PLANT IN SEWAGE SLUDGE MANAGEMENT
Fig.7.The influence of sewage sludge conditioning with biomass ash on the moisture content after vacuum filtration
4. Summary
The biomass ash is problematic waste which hasto
be managed in line with environmental and law re-
quirements. Stringent requirements prevent biomass
ashes from being used as a component in concrete and
cement production. For this reason, the new biomass
ash utilization methods are developed.
The article shows the proposal of recycling of
biomass combustion products. According to the specif-
ic physic-chemical properties, biomass ashes could be
used as a sewage sludge conditioner. Sewage sludge
after conditioning with ash showed a much stronger
dewatering capacity than raw sewage sludge. With a 30
g·dm-3
dosage of biomass ash, the moisture cake con-
tent decreased of approximately 10.23÷24.68 %, de-
pending on the method of dewatering. The main sludge
conditioning mechanisms with application of biomass
ash canimprove the floc formation and provide the wa-
ter transmitting passages by skeleton builder [8, 9].
The mixture of sewage sludge and biomass ash
may be successfully used in the cultivation of energy
plants plantations. For the application of sewage sludge
into the ground, the device for injection dosage of or-
ganic and mineral fertilizers can be used [11]. The ap-
plication of sludge after conditioning with biomass ash
enables to retain the turnover of nutrients. Moreover,
chemical compounds contained in sewage sludge are
excluded from human food chain [10].
References
[1] Poluszyńska J. (2013), Ocena możliwości
zanieczyszczenia środowiska glebowo-gruntowego
wielopierścieniowymi węglowodorami aromatycznymi
(WWA) zawartymi w popiołach lotnych pochodzących
z kotłów energetycznych. ScientificWorks of Institute
of Ceramics and Building Materials, 12, 60.
[2] Uliasz-Bocheńczuk A., Pawluk A., Skierka J. (2015),
Wymywalność zanieczyszczeń z popiołów lotnych ze
spalania biomasy. MineralResources Management,
31, 145-156.
[3] Rajczyk K., Giergiczny E., Szota M. (2013), Ocena
możliwości wykorzystania w drogownictwie
popiołów nowej generacji powstających ze spalania
biomasy. Scientific Works of Institute of Ceramics
and Building Materials, 12, 73.
[4] Czech T., Sobczyk T.A., Jaworek A., Krupa A.
Porównanie własności fizycznych popiołów lotnych
ze spalania węgla kamiennego, brunatnego i
biomasy. The Conference POL-EMIS, Sienna 2012,
73-82.
[5] Jarema-Suchorowska S. (2015), Popioły z
biomasy.http.://www.kierunekenergetyka.pl/magazyn
,popiołyzbiomasy.html, lastaccessed: January 10,
2017.
[6] GUS Report on Environmental Protection, 2015.
[7] Eye J. D., Basu T.K. (1970), The use of flyash in
wastewater treatment and sludge conditioning. Jour-
nal of The Water Pollution Control Federation, 42(5),
R125-R135.
[8] Zhang P., Haifeng L. (2010), Sewage sludge
conditioning with coal fly ash modified by sulfuric
acid, The Chemical Engineering Journal, 158(3),
616-622.
[9] Wang S., Viraraghavan T. (1997), Wastewater sludge
conditioning by fly ash. Waste Management, 17 (7),
443- 450.
[10] Stachowicz F., Trzepieciński T., Wójcik M., Masłoń
A.,Niemiec W., Piech A. (2016), Agricultural
utilisation of municipal sludge in willow plantation.
E3S Web of Conferences, 10, 1-6.
[11] Niemiec W., Stachowicz F., Trzepieciński T., Kępa
L., Dziurka M.: Development of harvestingmachines
for willow small-sizes plantation in East-Central
Europe, Croatian Journal of Forest Engineering, 37
(2016) 185-198.
[12] Szabo J., Kajtar L., Nyers J., Bokor B.: A new
approach and results of Wall and Air Temperature
Dynamic Analysis in Underground Spaces.
International J. Energy. Vol. 106, pp.520 -527, 1.
July 2016. doi:10.1016/j.energy.2016.03.008.
70
75
80
85
90
0 5 10 15 20 25 30
the
mois
ture
co
nte
nt
[%]
Dosage of ash [g·dm-3]
0.01 MPa
0.02 MPa
EXPRES 2017 ISBN 978-86-919769-1-0
Application of analogy of momentum and heat transfer at shell and tube condenser
O. MOLNARa, Z. ZSIGMOND
b
Department of Building Services and Process Engineering, Faculty of Mechanical Engineering,
Budapest University of Technology and Economics,
H-1111 Budapest, Műegyetem rkp. 3, Hungary aE-mail: [email protected] bE-mail: [email protected]
In environmental and chemical industry majority of processes are based on the simultaneous transfer of extensive properties.
These can be the heat, mass and momentum transfer. Because of the close relation of these transport phenomena, correlations
can be created between transport coefficients. These are the so-called transport analogies. In this paper relation of heat and
momentum transfer is studied. In order to perform the analysis, experimental investigations were made on a shell and tube
heat exchanger device. Goals of our work are to calculate tube side heat transfer coefficient and Nu number with formulas of
transport analogies; to validate them by measured data; to find reason of decreasing Nu number with increasing Re number in
the condenser at higher Re levels. Finally operation of the condenser is modelled by the analogy of heat and momentum
transfer.
Keywords: shell and tube heat exchanger, transport analogy, friction factor, heat transfer coefficient
1. Introduction
In environmental and chemical engineering
majority of processes are based on the
simultaneous transfer of extensive properties.
These can be the heat- mass- and momentum
transfer. Because of the close relation of these
transport phenomena, correlations can be created
among transport properties.
At the end of 19th
century Osborne
Reynolds was the first who recognized the
analogy between heat and momentum transfer
during his experimental investigation on rough
tubes. His observations resulted in the so-called
Reynolds analogy which describes the
connection between heat transfer coefficient and
friction factor [1, 2]:
= ∙ = ℎ = 2 (1)
Eq (1) is applicable for turbulent flow in a pipe
or over a flat plate when Pr is equal or close to
unity. This is a reasonable approximation for
many gases, but for liquids the Pr numbers are
much larger than 1. Therefore this analogy is not
appropriate for liquids.
Since applicability of the Reynolds analogy
is very limited, derivation of a more general
expression was necessary. In independent works
Ludwig Prandtl and Geoffry Ingram Taylor
modified the Reynolds analogy in the first half of
the 20th
century. A new formula was created
between heat transfer coefficient and friction
factor by combining the resistances of a viscous
sublayer where molecular effects dominate with
a turbulent outer layer where turbulent effects
control [1, 2]:
= ℎ =1 + 5 ( − 1) (2)
Prandtl-Taylor analogy can be applied in a wider
range, it allows Pr to differ from 1. Hence it is
applicable mainly in case of Pr smaller than 2
[1].
Theodore von Kármán (1881-1963)
extended Reynolds analogy even further by
including an intermittent boundary layer between
the viscous sublayer and the turbulent bulk.
Turbulent viscosity and turbulent heat
conductivity were determined from the universal
velocity profile. Thus the Kármán analogy is [1,
3]:
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22
APPLICATION OF ANALOGY OF MOMENTUM AND HEAT TRANSFER AT SHELL AND TUBE CONDENSER
2
= 1 + 5 ( − 1 + ) (3)
Thomas H. Chilton and Allan P. Colburn
expanded the Prandtl-Taylor analogy for fluids
with varying Prandtl number. Intensive
properties (velocity and temperature) were
assumed to be varying linearly in the intermittent
boundary layer similarly to the viscous sublayer
[1]. Chilton-Colburn analogy (1933) – also called
j factor analogy – is also a modification of the
Reynolds analogy based on purely experimental
results [4]. Regarding to heat and momentum
transfer [1]:
∙ = = 2 (4)
Where z is an experimentally determined
constant, e.g. at fluid flows inside tubes z = 2/3.
Above mentioned j factor in Eq(4) can be
determined with friction factor only, if drag
coefficient comes from friction and shape
resistance can be neglected (e.g. flows inside or
outside tube parallel to its longitudinal axis,
flows above a flat plate) [1]. Chilton-Colburn
analogy is still popular and widely used because
of its accuracy and simplicity. For instance it can
be applied reasonably for industrial sugarcane
juices in shell and tube heat exchangers [5], and
at shape optimization of chevron-type plate heat
exchangers [6].
At fluids characterized by small Pr numbers
(e.g. liquid phase metals) the Martinelly analogy
can be applied. At this analogy Nu-Re-Pr
correlation is represented by monograms.
In the middle of 20th
century Robert
Deissler proved that at increasing Pr numbers (Pr
>> 10) result of the Kármán analogy differ more
and more from the experimentally obtained data.
It was recognized that near to the wall where
high temperature gradients exist description of
the eddy diffusivity had to be modified. Result of
Diessler analogy is [3]:
= 0,111 ∙ 2 ∙ (5)
W.L.Friend and A.D Metzner made
measurements in a wide range of Sc and Pr
numbers to obtain a correlation between heat-,
mass- and momentum transfer [4]:
= ∙ ,1,2 + 11,8 ∙ ( − 1) ∙ (6)
Although Eq (6) is recommended for wide range
of Pr numbers, at small ones (Pr < 0.5) it can not
be applied.
2. Material and methods
Test device
Experimental measurements were
conducted on a shell and tube heat exchanger
system (Table 1, Fig. 1). The first unit of the
system is a condenser with moderate pressure
steam in the shell side and water as the product in
tube side. The second unit is a cooler where the
heated product coming from the first body is
cooled down before letting it to the drainage
system. This work is focused on the process
taking place in the condenser. The targeted
device is two pass on tube side and one pass on
shell side where the saturated steam coming from
an electric steam generator is admitted. The
temperature of steam is measured and kept
constant (≈103°C) during the measurement
process. Mass flow rate of steam is measured by
measuring weighing the mass of condensate after
the steam trap by using a stop watch and a
bucket. Flow rate of product is measured by a
rotameter. Inlet and outlet temperatures are
measured by temperature transmitters (Fe-CuNi
thermocouples), temperature data are collected
by an ALMEMO data collector and recorded by
Win Control. During the experimental work
product flow rate isvaried between 600 and
1300l/h. At different product flow rates - after
reaching the steady state operating mode -
temperature and flow rate data are recorded.At
each individual operating state heat balance and
heat transfer coefficients are evaluated.
Table1.Data of the shell and tube heat exchanger device
Heat transfer area Number of tubes Size of tubes Size of shell Heat conductivity of
the wall
A = 1.5 m2 N = 48 L = 1 m; dout/din = 10/8 mm
L = 1 m; dout/din = 200/196 mm kw = 14 W/mK
APPLICATION OF ANALOGY OF MOMENTUM AND HEAT TRANSFER AT SHELL AND TUBE CONDENSER
3
Evaluation of heat transfer coefficient
There is sensible heat transfer in tube side,
while condensation on shell side in the first unit
of the device. The tube side heat transfer
coefficient can be determined from the next
equation:
ℎ = 1 − − (7)
The condensation heat transfer coefficient along
vertical tubs can be calculated by the next
correlation [7]:
ℎ = 1.47 ∙ ∙ ∙ ∙ (8)
In Eq (8) the Reynolds number of the
condensation film:
= 4 ∙ ∙ ∙ ∙ (9)
The overall heat transfer coefficient can be
calculated from the transferred heat flow rate and
the logarithmic temperature difference:
= ∆ ∙ (10)
The transferred heat is the average of deflated
and admitted heat:
= ∙ 2 (11)
Deflated heat flow rate by the steam on shell
side: = ∙ ∆ℎ (12)
Admitted heat flow rate by the product on tube
side [9, 10]: = ∙ ∙ ( − ) (13)
During the conducted series of experimental
measurements it was found that - contrary to
expectations - the tube side heat transfer
coefficient (and Nu number)at a distinct level of
Re numberdoes not continue increasing but
slightly decreases instead (at Tst ≈ 103°C, this
level is Re ≈ 4000) (Fig. 2). Just before thislevel
of Re number temperature of the condensate
measured at the outlet pipe of the shell side starts
strongly falling (Fig. 3). It can be suspected that
condensate does not leave the device due to
inappropriate installation and shell side becomes
flooded (Fig. 4). This phenomenon is realized
directly through the cut down of the condensate
temperature. To verify this hypothesis we turned
to transport analogies to simulate the operation of
the condenser.
Fig. 1. Flow chart of the test equipment
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23
APPLICATION OF ANALOGY OF MOMENTUM AND HEAT TRANSFER AT SHELL AND TUBE CONDENSER
2
= 1 + 5 ( − 1 + ) (3)
Thomas H. Chilton and Allan P. Colburn
expanded the Prandtl-Taylor analogy for fluids
with varying Prandtl number. Intensive
properties (velocity and temperature) were
assumed to be varying linearly in the intermittent
boundary layer similarly to the viscous sublayer
[1]. Chilton-Colburn analogy (1933) – also called
j factor analogy – is also a modification of the
Reynolds analogy based on purely experimental
results [4]. Regarding to heat and momentum
transfer [1]:
∙ = = 2 (4)
Where z is an experimentally determined
constant, e.g. at fluid flows inside tubes z = 2/3.
Above mentioned j factor in Eq(4) can be
determined with friction factor only, if drag
coefficient comes from friction and shape
resistance can be neglected (e.g. flows inside or
outside tube parallel to its longitudinal axis,
flows above a flat plate) [1]. Chilton-Colburn
analogy is still popular and widely used because
of its accuracy and simplicity. For instance it can
be applied reasonably for industrial sugarcane
juices in shell and tube heat exchangers [5], and
at shape optimization of chevron-type plate heat
exchangers [6].
At fluids characterized by small Pr numbers
(e.g. liquid phase metals) the Martinelly analogy
can be applied. At this analogy Nu-Re-Pr
correlation is represented by monograms.
In the middle of 20th
century Robert
Deissler proved that at increasing Pr numbers (Pr
>> 10) result of the Kármán analogy differ more
and more from the experimentally obtained data.
It was recognized that near to the wall where
high temperature gradients exist description of
the eddy diffusivity had to be modified. Result of
Diessler analogy is [3]:
= 0,111 ∙ 2 ∙ (5)
W.L.Friend and A.D Metzner made
measurements in a wide range of Sc and Pr
numbers to obtain a correlation between heat-,
mass- and momentum transfer [4]:
= ∙ ,1,2 + 11,8 ∙ ( − 1) ∙ (6)
Although Eq (6) is recommended for wide range
of Pr numbers, at small ones (Pr < 0.5) it can not
be applied.
2. Material and methods
Test device
Experimental measurements were
conducted on a shell and tube heat exchanger
system (Table 1, Fig. 1). The first unit of the
system is a condenser with moderate pressure
steam in the shell side and water as the product in
tube side. The second unit is a cooler where the
heated product coming from the first body is
cooled down before letting it to the drainage
system. This work is focused on the process
taking place in the condenser. The targeted
device is two pass on tube side and one pass on
shell side where the saturated steam coming from
an electric steam generator is admitted. The
temperature of steam is measured and kept
constant (≈103°C) during the measurement
process. Mass flow rate of steam is measured by
measuring weighing the mass of condensate after
the steam trap by using a stop watch and a
bucket. Flow rate of product is measured by a
rotameter. Inlet and outlet temperatures are
measured by temperature transmitters (Fe-CuNi
thermocouples), temperature data are collected
by an ALMEMO data collector and recorded by
Win Control. During the experimental work
product flow rate isvaried between 600 and
1300l/h. At different product flow rates - after
reaching the steady state operating mode -
temperature and flow rate data are recorded.At
each individual operating state heat balance and
heat transfer coefficients are evaluated.
Table1.Data of the shell and tube heat exchanger device
Heat transfer area Number of tubes Size of tubes Size of shell Heat conductivity of
the wall
A = 1.5 m2 N = 48 L = 1 m; dout/din = 10/8 mm
L = 1 m; dout/din = 200/196 mm kw = 14 W/mK
APPLICATION OF ANALOGY OF MOMENTUM AND HEAT TRANSFER AT SHELL AND TUBE CONDENSER
3
Evaluation of heat transfer coefficient
There is sensible heat transfer in tube side,
while condensation on shell side in the first unit
of the device. The tube side heat transfer
coefficient can be determined from the next
equation:
ℎ = 1 − − (7)
The condensation heat transfer coefficient along
vertical tubs can be calculated by the next
correlation [7]:
ℎ = 1.47 ∙ ∙ ∙ ∙ (8)
In Eq (8) the Reynolds number of the
condensation film:
= 4 ∙ ∙ ∙ ∙ (9)
The overall heat transfer coefficient can be
calculated from the transferred heat flow rate and
the logarithmic temperature difference:
= ∆ ∙ (10)
The transferred heat is the average of deflated
and admitted heat:
= ∙ 2 (11)
Deflated heat flow rate by the steam on shell
side: = ∙ ∆ℎ (12)
Admitted heat flow rate by the product on tube
side [9, 10]: = ∙ ∙ ( − ) (13)
During the conducted series of experimental
measurements it was found that - contrary to
expectations - the tube side heat transfer
coefficient (and Nu number)at a distinct level of
Re numberdoes not continue increasing but
slightly decreases instead (at Tst ≈ 103°C, this
level is Re ≈ 4000) (Fig. 2). Just before thislevel
of Re number temperature of the condensate
measured at the outlet pipe of the shell side starts
strongly falling (Fig. 3). It can be suspected that
condensate does not leave the device due to
inappropriate installation and shell side becomes
flooded (Fig. 4). This phenomenon is realized
directly through the cut down of the condensate
temperature. To verify this hypothesis we turned
to transport analogies to simulate the operation of
the condenser.
Fig. 1. Flow chart of the test equipment
![Page 4: Application of analogy of momentum and heat transfer at ... · is very limited, derivation of a more general expression was necessary. In independent works Ludwig Prandtl and Geoffry](https://reader033.vdocuments.site/reader033/viewer/2022041423/5e204eb6235cfb0604450e66/html5/thumbnails/4.jpg)
24
EXPRES 2017 ISBN 978-86-919769-1-0
3. Results
Since all analogies are very sensible to
friction factor, exact determination of that has
high relevance. Several friction models were
investigated (Hagen-Poiseuille, Blasius, Kármán,
Colebrook-White, Panhandle-A) but two of them
can be considered due to roughness of the inside
pipe wall and Re restrictions: Blasius formula
can be applied in the turbulent range
(2300…3000 < Re < 105) for hydraulic smooth
tubes:
= 0.03164/ (14)
and Panhandle-A formula [8] is useful at the
lower part of turbulent range for smooth tubes:
= 447.22 ∙ ∙ . (15)
E is the efficiency coefficient which can vary
from 0.85 to 1. In Eq (14) and Eq (15) express
Darcy’s friction which is in direct connection
with Fanning friction applied in analogies’
equations Eq(1)…Eq(6):
= 4 (16)
Application of analogies was investigated
by looking for the minimum of sum of squared
residuals:
= − () (17)
All analogies were combined with different
friction correlations (Blasius, Panhandle-A with
E = 0.85, 0.9, 0.95, 1.0). SSR values can be
found in (Table 2). It can be seen that measured
Nu numbers do not fit on Reynolds analogy and
Diessler analogy at all. Prandtl-Taylor, Kármán,
Chilton-Colburn and Friend Metzner analogy can
be applied quite well with friction given by
Panhandle-A formula, but friction given by
Blasius formula can be applied only with Friend-
Metzner analogy. The minimum value of SSR is
obtained by Chilton-Colburn analogy with
friction by Panhandle-A with E = 0.9. Result of
this analogy with measured values can be seen in
Fig. 5.
Fig. 4.Flooded shell and tube condenser
Fig. 3Temperature of the condensate versus Re
Fig. 2.Measured Nu versus Re
APPLICATION OF ANALOGY OF MOMENTUM AND HEAT TRANSFER AT SHELL AND TUBE CONDENSER
5
Table 2. SSR values of the analogies with different
friction formulas
REYNOLDS ANALOGY with
Blasius Pan-A(E=0,85)
Pan-A (E=0,9)
Pan-A (E=0,95)
Pan-A (E=1)
741,7 437,6 277,0 170,3 100,4
PRANDTL-TAYLOR ANALOGY with
Blasius Pan-A (E=0,85)
Pan-A (E=0,9)
Pan-A (E=0,95)
Pan-A (E=1)
102,9 49,3 24,4 11,6 7,0
KARMAN ANALOGY with
Blasius Pan-A (E=0,85)
Pan-A (E=0,9)
Pan-A (E=0,95)
Pan-A (E=1)
31,7 12,7 7,1 7,7 12,7
CHILTON-COLBURN ANALOGY with
Blasius Pan-A (E=0,85)
Pan-A (E=0,9)
Pan-A (E=0,95)
Pan-A (E=1)
30,0 8,9 6,7 12,8 23,9
DEISSLER ANALOGY with
Blasius Pan-A(E=0,85)
Pan-A (E=0,9)
Pan-A (E=0,95)
Pan-A (E=1)
237,5 169,2 127,0 94,6 69,8
FRIEND-METZNER ANALOGY with
Blasius Pan-A (E=0,85)
Pan-A (E=0,9)
Pan-A (E=0,95)
Pan-A (E=1)
8,8 7,2 11,7 19,9 30,3
At Re > 4000 the measured heat transfer
coefficients and Nu numbers start falling because
of suspected reduction of condensation heat
transfer area of the device which is probably
caused by condensate retention. Due to
inadequate condensate drainage in the bottom of
the heat exchanger there is sensible heat transfer
instead of condensation (Fig. 4). At Re > 4000
modified heat transfer area can be calculated
from the predicted heat transfer coefficient from
the Chilton-Colburn analogy by Eq (18) and Eq
(19). The predicted condensate level is
represented in Fig. 6.
′ = 1 + + (18)
′ = ∆ ∙ ′ (19)
4. Conclusion
Several analogies of heat and momentum
transfer can be applied quite well at shell and
tube heat exchanger. Since all analogies are very
sensible on friction coefficient, determination of
its exact value needs further investigations.
Inappropriate operation of the condenser could
be modeled successfully. Installation of a
condensate pump in the system is recommended
to prevent flooding of the shell (Fig.6).
Fig. 6.Installation of a condensate pump in the system
Fig. 6.Condensate level in the shell at large Re range
Fig. 5.Measured and predicted (by Chilton-Colburn
analogy) Nu versus Re
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25
EXPRES 2017 ISBN 978-86-919769-1-0
3. Results
Since all analogies are very sensible to
friction factor, exact determination of that has
high relevance. Several friction models were
investigated (Hagen-Poiseuille, Blasius, Kármán,
Colebrook-White, Panhandle-A) but two of them
can be considered due to roughness of the inside
pipe wall and Re restrictions: Blasius formula
can be applied in the turbulent range
(2300…3000 < Re < 105) for hydraulic smooth
tubes:
= 0.03164/ (14)
and Panhandle-A formula [8] is useful at the
lower part of turbulent range for smooth tubes:
= 447.22 ∙ ∙ . (15)
E is the efficiency coefficient which can vary
from 0.85 to 1. In Eq (14) and Eq (15) express
Darcy’s friction which is in direct connection
with Fanning friction applied in analogies’
equations Eq(1)…Eq(6):
= 4 (16)
Application of analogies was investigated
by looking for the minimum of sum of squared
residuals:
= − () (17)
All analogies were combined with different
friction correlations (Blasius, Panhandle-A with
E = 0.85, 0.9, 0.95, 1.0). SSR values can be
found in (Table 2). It can be seen that measured
Nu numbers do not fit on Reynolds analogy and
Diessler analogy at all. Prandtl-Taylor, Kármán,
Chilton-Colburn and Friend Metzner analogy can
be applied quite well with friction given by
Panhandle-A formula, but friction given by
Blasius formula can be applied only with Friend-
Metzner analogy. The minimum value of SSR is
obtained by Chilton-Colburn analogy with
friction by Panhandle-A with E = 0.9. Result of
this analogy with measured values can be seen in
Fig. 5.
Fig. 4.Flooded shell and tube condenser
Fig. 3Temperature of the condensate versus Re
Fig. 2.Measured Nu versus Re
APPLICATION OF ANALOGY OF MOMENTUM AND HEAT TRANSFER AT SHELL AND TUBE CONDENSER
5
Table 2. SSR values of the analogies with different
friction formulas
REYNOLDS ANALOGY with
Blasius Pan-A(E=0,85)
Pan-A (E=0,9)
Pan-A (E=0,95)
Pan-A (E=1)
741,7 437,6 277,0 170,3 100,4
PRANDTL-TAYLOR ANALOGY with
Blasius Pan-A (E=0,85)
Pan-A (E=0,9)
Pan-A (E=0,95)
Pan-A (E=1)
102,9 49,3 24,4 11,6 7,0
KARMAN ANALOGY with
Blasius Pan-A (E=0,85)
Pan-A (E=0,9)
Pan-A (E=0,95)
Pan-A (E=1)
31,7 12,7 7,1 7,7 12,7
CHILTON-COLBURN ANALOGY with
Blasius Pan-A (E=0,85)
Pan-A (E=0,9)
Pan-A (E=0,95)
Pan-A (E=1)
30,0 8,9 6,7 12,8 23,9
DEISSLER ANALOGY with
Blasius Pan-A(E=0,85)
Pan-A (E=0,9)
Pan-A (E=0,95)
Pan-A (E=1)
237,5 169,2 127,0 94,6 69,8
FRIEND-METZNER ANALOGY with
Blasius Pan-A (E=0,85)
Pan-A (E=0,9)
Pan-A (E=0,95)
Pan-A (E=1)
8,8 7,2 11,7 19,9 30,3
At Re > 4000 the measured heat transfer
coefficients and Nu numbers start falling because
of suspected reduction of condensation heat
transfer area of the device which is probably
caused by condensate retention. Due to
inadequate condensate drainage in the bottom of
the heat exchanger there is sensible heat transfer
instead of condensation (Fig. 4). At Re > 4000
modified heat transfer area can be calculated
from the predicted heat transfer coefficient from
the Chilton-Colburn analogy by Eq (18) and Eq
(19). The predicted condensate level is
represented in Fig. 6.
′ = 1 + + (18)
′ = ∆ ∙ ′ (19)
4. Conclusion
Several analogies of heat and momentum
transfer can be applied quite well at shell and
tube heat exchanger. Since all analogies are very
sensible on friction coefficient, determination of
its exact value needs further investigations.
Inappropriate operation of the condenser could
be modeled successfully. Installation of a
condensate pump in the system is recommended
to prevent flooding of the shell (Fig.6).
Fig. 6.Installation of a condensate pump in the system
Fig. 6.Condensate level in the shell at large Re range
Fig. 5.Measured and predicted (by Chilton-Colburn
analogy) Nu versus Re
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26
APPLICATION OF ANALOGY OF MOMENTUM AND HEAT TRANSFER AT SHELL AND TUBE CONDENSER
6
Nomenclature
A [m2] surface
c [J/kgK] specific heat
d [m] diameter
E [1] hydraulic efficiency coefficient
f [1] friction factor
g [m/s2] gravitational acceleration
h [W/m2K] heat transfer coefficient
∆h [J/kg] heat of condensation
H [m] height
j [1] colburn factor
k [W/mK] heat conductivity
L [m] length [kg/s] mass flow rate
N [1] number of tubes
Nu [1] Nusselt number
Pr [1] Prandtl number [J/s] heat flow rate
Re [1] Reynolds number
s [m] wall thickness
SSR [1] sum of squared residuals
St [1] Stanton number
T [°C] temperature
∆T [°C] temperature difference
U [W/m2K] overall heat transfer coefficient
z [1] constant
µ [kg/ms] dynamic viscosity
ν [m2/s] kinematic viscosity
ρ [kg/m3] density
subscripts:
adm admitted
Ch-C Chilton-Colburn
cond condensation
D Darcy’s
defl deflated
F Fanning
f condensate film
H heat transfer
in inside/inlet
ln logarithmic
meas measured
out outside/outlet
p at constant pressure
pr product
pred predicted
s steam
sens sensible
tr transferred
w wall
References
[1] S. Szentgyörgyi, K. Molnár, M. Parti: Transzport
folyamatok, Tankönyvkiadó, Budapest (1986)
[2] E.U. Schündler: Analogy between heat and
momentum transfer, Chemical Engineering and
Processing, Vol.37 (1998), pp.103-107
[3] R.G. Deissler: Analysis of turbulent heat transfer,
mass transfer and friction in smooth tubes at high
Prandtl and Schmidt numbers – Lewis Flight
Propulsion Laboratory (1954)
[4] R.S. Brodkey, H.C. Hershey: Transport Phenomena:
A unified approach, McGraw-Hill Chemical
Engineering Series (1988)
[5] Z. Astolfi-Filho, E.B. de Oliveira: Friction factors,
convective heat transfer coefficients and the
Colburn analogy for industrial sugarcane juices,
Biochemical Engineering Journal, Vol.60 (2012),
pp.111-118
[6] L. Jonghyeok, L. Kwan-Soo: Friction and Colburn
factor correlations and shape optimization of
chevron-type plate heat exchangers, Applied
Thermal Engineering, Vol.89 (2015), pp.62-69
[7] T. Környei: Hőátvitel, Műegyetemi Kiadó, (1999)
[8] L. Tihanyi: A gázhálózati modellek kulcsparaméter,
Kőolaj és Földgáz Vol.35 No.7-8, (2002)
[9] J. Nyers, L. Garbai, A. Nyers: Analysis of Heat
Pump's Condenser Performance by means of
Mathematical Model, International J. Acta
Polytechnica Hungarica Vol. 11, No. 3, pp.139-
152, 2014. DOI: 10.12700/APH.11.03.2014.03.9.
[10] J. Nyers, L. Garbai, A. Nyers: A modified
mathematical model of heat pump's condenser for
analytical optimization, International J. Energy,
Vol. 80, pp. 706-714, 1 February 2015.
DOI:10.1016/j.energy.2014.12.028.
EXPRES 2017
ISBN 978-86-919769-1-0
Performance of heat pump's condenser in heating process
J. NYERS a, A. NYERS b
aObuda UniversityBudapest, Hungarye-mail:[email protected]
University BME, Budapest, Hugary e-mail:[email protected] The general aim of article is to analyze in wide range the behavior of performance of heat pump's plate condenser depending on
theexternal impacts. The external impacts are the inlet temperature of hot water, the hydraulic resistance of hot water circuit, the
powerof circulation pump, the surface dimension of condenser.The additional practical goal is to find the quasi-optimal power of
circulation pump to obtain the near maximum performance of condenser as a function of resistance to flow in the hot water
circuitand dimension of condenser.
The performance of condenser is the quantity of heat exchanged inside the condenser between the refrigerant and the hot water. The
analysis of performance and quasi-optimization is done using the non-linear lumped parameter mathematical model.
Themathematical model includes equations of heat transfer between the hot water and the refrigerant inside the condenser, the
power of circulation pump, the hydraulic resistance in hot water circuit.Mathematical model of condenser is divided into a section
ofsuperheated steam cooling and a section of saturation steam condensation of refrigerant.
In order to solve the mathematical model, who is consist of nonlinear algebraic equation system, the Newton-Taylor linearization
and Gauss elimination method has been applied.
By simulation obtained numerical results in two or three-dimensional graphics are presented.
Keywords:condenser, heat pump, quasi optimization,circulation pump, mathematicalmodel.
1. Introduction
In the scientific journals many articles deal with the
research of heat pumps in stationary regime using
various lumped parameter mathematical models.
Most of the mathematical models contain the main
four components including the condenser, as well.
Research of all reviewed articles focused on the
behavior of complete system rather than individual
components, such as the condenser.
In the enclosed article, research has focused on
investigating the performance of condenser as a
function of external impacts. The performance of
condenser represents the efficiency and the quantity
of heat transferred between the hot water and the
refrigerant inside the condenser. In the analyzed
system the external impacts are the power of
circulation pump, the inlet temperature of hot water,
the hydraulic resistance in hot water circuit, the
surface dimension of condenser. The hydraulic
resistance of hot water circuit is expressed in
measurable parameter of the system, in the pressure
drop.
The general aim of the investigation is to analyze in
wide range the behavior of performance of heat
pump's plate condenser.
The proposed procedure provides the analyze of
influence of above-mentioned four external impacts
on the performance of condenser.
The most influential external impact on the
performance of condenser is the inlet temperature of
hot water. If the inlet temperature is changed in the
range 21-50 °C then causes the increment of
performance of condenser for 17 kW.
The least impact on the performance of condenser
produces the hydraulic characteristics of hot water
circuit. Increases the power of circulation pump from
21-310 W hardly enhances the performance of
condenser only for 1 kW. From the above data it follows that the best
improvement of performance of condenser is achieved
with increasing the surface of heating bodies in the hot
water circuit. Advisable to apply panel heating bodies
instead radiators. Panels consist of pipe packages in the
floor, wall and ceiling and have a significantly higher
heating surfaces from the radiators, with that the inlet
temperature of hot water for heating decreases and
increases the performance of condenser. Increasing the
power of circulation pump very poorly enhances the
performance of condenser.
The additional practical goal is to find the quasi-optimal
power of circulation pump.The quasi-optimal
powerprovides the near maximum performance of
condenser at the defined hydraulic resistance of hot
water circuit and the defined dimension of condenser.
The theoretical optimum power of circulation pump is in
infinity.
Upper statement can to confirm the results of attached
simulations. With increasing the power of circulation
pump the performance of condenser at the beginning
exponentially but later slow monotonically increases and
in the infinity reaches maximum.
In practice, to the end of exponential increasing of
performance it makes sense to increase the power of
circulation pump. In this point are the quasi-optimal
power of circulation pump and the near maximum
performance of condenser.