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: omolnar@mail.bme.hu bE-mail: zsigmond06@gmail.com

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]:

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

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

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

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

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:nyers@uni-obuda.hu

University BME, Budapest, Hugary e-mail:nyarp@yahoo.com 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.