DSpace at VNU: Modelling and experimental validation for off-design performance of the helical heat exchanger with LMTD correction taken into account

Results showed that errors of thermal duty, outlet hot fluid temperature, outlet cold fluid temperature, shell-side pressure drop, and tube-side pressure drop were respectively ±5%, ±1%,

Journal of Mechanical Science and Technology 30 (7) (2016) 3357~3364 www.springerlink.com/content/1738-494x(Print)/1976-3824(Online)

DOI 10.1007/s12206-016-0645-0

Modelling and experimental validation for off-design performance of the helical heat

Faculty of Mechanical Engineering, University of Technology, Vietnam National University - Ho Chi Minh City, Vietnam

(Manuscript Received August 27, 2015; Revised March 15, 2016; Accepted March 27, 2016)

-

Abstract

Today the helical coil heat exchanger is being employed widely due to its dominant advantages In this study, a mathematical model was established to predict off-design works of the helical heat exchanger The model was based on the LMTD and e-NTU methods, where a LMTD correction factor was taken into account to increase accuracy An experimental apparatus was set-up to validate the model Results showed that errors of thermal duty, outlet hot fluid temperature, outlet cold fluid temperature, shell-side pressure drop, and tube-side pressure drop were respectively ±5%, ±1%, ±1%, ±5% and ±2% Diagrams of dimensionless operating parameters and a regression function were also presented as design-maps, a fast calculator for usage in design and operation of the exchanger The study is expected to be a good tool to estimate off-design conditions of the single-phase helical heat exchangers

Keywords: Effectiveness-NTU; Experimental validation; Helical heat exchanger; LMTD; Off-design; Pressure drop

-

1 Introduction

Heat exchangers are core components of thermal systems

Their improvements will allow efficient use of energy

There-fore researches on the heat exchangers have been often paid

attentions to and published with a high density for the past few

decades There are two problems which are often mentioned

in previous studies Those are to enhance heat transfer rate of

heat exchangers [1, 2] and predict off-design conditions of the

available heat exchangers [3, 4] Mostly the studies

concen-trated on the straight tube heat exchangers as confirmed by

Wongwises and Polsongkram [5, 6] However, the helical coil

heat exchangers show dominant advantages in comparison

with the straight tube heat exchangers Prabhanjan et al [7]

showed experimentally that heat transfer rate of helical heat

exchangers is higher than that of straight tube heat exchangers

due to centrifugal forces to act on the moving fluid, causing

the formulation of secondary flow Besides, the helical

capil-lary in a refrigeration system has a length which is 14%

shorter than the straight capillary as showed by Zareh et al [8]

Furthermore, the helical heat exchangers offer compactness,

compensation of thermal expansion, vibration reduction, easy

construction and low capital cost In recent years, there has

been a remarkable consideration on applications of helical

heat exchangers for thermal systems Seara et al [9] formed

an analytical model to investigate the helical coil rectifier in an ammonia-water absorption chiller Xiaowen and Lee [10] studied experimentally the helical heat exchanger for heat recovery air-conditioners Sogni and Chiesa [11] developed a model to calculate heat recovery boiler using a helical tube Also, helical heat exchangers are regularly used for the liquid-to-suction heat exchanger and liquid subcooler in refrigeration cycles [12] Enhanced heat transfer by adding fins to the gas side of the helical exchanger was also noted by researchers Crimped spiral fins are usually used because of their durability and reliability Srisawad and Wongwises [13] provided the experimental data of the crimped finned heat exchangers Boonsri and Wongwises [14] formed the rigorous mathemati-cal model for the helimathemati-cal exchanger with crimped spiral fins The theoretical results from their model coincided well with the experimental data Hardik et al [15] conducted experi-ments in order to investigate local temperature and Nusselt number distribution in helical coils Correlations of local Nus-selt numbers such as functions of diameter ratio, Reynolds number, and Prandtl number were given with maximum de-viation of 21% Bezyan et al [16] analyzed the results of nu-merical simulation by using CFD software package for helical heat exchangers The best configuration was indicated in their study Mukesh Kumar et al [17] performed CFD simulation for flow and thermal behavior of nanofluid in helical heat exchangers to estimate heat transfer coefficient and pressure drop

Generally, the previous studies were to find out the

charac-* Corresponding author Tel.: +84 906 929498, Fax.: +84 838 653823

E-mail address: nmphu@hcmut.edu.vn

† Recommended by Associate Editor Ji Hwan Jeong

© KSME & Springer 2016

teristics and design of helical heat exchangers But estimation

of off-design conditions (i.e temperature, pressure drop,

thermal duty) of an available helical heat exchanger has not

been noted In order to estimate those conditions, the

geomet-rical parameters inside the exchanger should be given and

inputted to heat transfer and pressure drop models

Unfortu-nately, the geometrical parameters are sometimes missed from

manufacturers Few parameters are known from

manufactur-ers’ catalogues This causes obstacles in prediction of

operat-ing conditions different from design conditions In practice,

heat exchangers usually run in part-load or overload modes

To overcome such a difficulty, Garcia et al [18] developed a

model for the straight tube condenser and evaporator of a

re-frigeration system Errors of the predicted temperatures and

capacities are from ±1 to ±7% in comparison to the measured

values However, the pressure drop model is somewhat

com-plicated and geometry of tube bundles has to be known

Fur-thermore, experimental validation of the pressure drop model

was not performed In this paper, a similar model to that of

Garcia et al [18] is formed for the helical heat exchanger

LMTD correction factor is taken into account so that the

pre-dicted results are closer to those of the experiment Moreover

the results of pressure drop are also presented regarding both

the modelling and experimental approaches

2 Model formulation

2.1 Heat transfer model

Fig 1 presents the schematic diagram of a helical heat

ex-changer A fluid is traveling inside a helical tube Another

fluid is passing across the helical tube The fluids carry

differ-ent thermal energies; therefore, heat is transferred from hot

fluid to cold fluid through the surface of the helical tube The

general ideal of the mathematical model can be seen in Ref

[18] Some equations are presented here for the sake of easy

understanding Overall conductance of a heat exchanger can

be written as the equation below if fouling and wall

resis-tances are neglected:

The above equation can be rewritten as follows:

1

+

Let the subscript “ref” be reference parameters

correspond-ing to known conditions The known conditions, for example, can be obtained from a manufacturer’s catalogue or experi-ment From Eq (2) a ratio can be created between the operat-ing conditions and the reference conditions of the same heat exchanger as follows:

i e

+

=

We can define ratios as:

,

i i

i ref

h h

,

e e

e ref

h h

In heat transfer design, thermal resistances should be equal

in order to gain an optimum design Thus an approximation can be done as the following equation:

Since the Eq (3) can be rewritten as:

,

UA

b b

b b

The heat transfer coefficient for the fluid flowing inside helical tube can be computed by means of the Rogers and Mayhew’s correlation [19] as:

0.1 0.85 0.4

i

h

for Re £ 50000 [15]

where Reynolds number and Prandtl number are, respectively:

Re

c

md

= &

k

m

D and d are respectively the outer and inner diameters of the

helical tube

Tube-side fluid

Shell-side fluid

Fig 1 Helical coil heat exchanger

Therefore h i can be rewritten as follows:

( ) ( 0.6 0.45 0.85 0.4)( 0.1 0.05)

Heat transfer and pressure drop of cross-flow straight tube

bundles can be used to model helical heat exchanger as shown

in previous studies [11, 20] Therefore the shell side heat

transfer coefficient is obtained from the Zukauskas’s

correla-tion (1000 < Re < 200000) for in-line tube bundles [21]:

0.25 0.63 0.36 Pr

Pr

w

k

D

where F N is a correction factor whose values are dependent on

the number of rows of tube bundle

Neglecting the influence of temperature-dependent

proper-ties, i.e (Pr/Prw)0.25 = 1, the coefficient h e can be rearranged

by:

(0.27) ( 0.64 0.27 0.63 0.36)( 0.37)

As can be seen in the above-mentioned equations, the heat

transfer coefficients are functions of three terms including

constant coefficient, properties of fluid, and geometry of the

helical heat exchanger The terms of constant coefficient, and

geometry will be eliminated in the ratio of heat transfer

coeffi-cients

Thus, the ratios of tube side and shell side heat transfer

co-efficients are respectively given by:

p i

i

c

m b

m

&

p e

e

c

m b

m

&

The effectiveness and number of transfer units (e-NTU)

re-lation of the helical heat exchanger are similar to those of a

cross-flow heat exchanger (with one fluid mixed and the other

unmixed) if the number of turns of the helical tube is equal or

more than six as pointed out by San et al [20] Therefore the

relation is:

1

C

C max mixed, C min unmixed

1

C

e= - ìí- éë - - ùûüý

C max unmixed, C min mixed

min max

C C C

where C min and C max are the smaller and the larger of m c&i p i,

and m c&e p e, , respectively

To enhance reliability of the heat transfer model, a LMTD correction factor is considered in the model The factor is that

of a cross-flow heat exchanger where the flow in the helical tube is considered to be unmixed and the flow outside the tube

is mixed [22] In this research tube-side flow is assigned as hot fluid and shell-side flow is cold fluid Therefore, the factor can

be found by means of:

0

r F r

1 ln

1

1

q r

q

=

ln 1

r

q p

-=

p

-=

q

-=

-2.2 Pressure drop inside helical tube

Pressure drop inside a tube of length L and inner diameter d

is given by:

2 2

c

L m

The Fanning friction factor inside a helical tube can be used correlation of Srinivasan et al [23] as follows:

0.2

0.084 Re

f

(21)

for

2 2

d

<

d

< <

where R is curvature radius of helical coil

Similarly to Eqs (14) and (15), the pressure drop ratio of operating conditions to reference conditions can be correlated as:

ref

r m

D

&

2.3 Shell-side pressure drop

From Ref [24] the Fanning friction factor of the fluid

across helical tube bundle can be expressed as:

0.117

0.26 yRe

where P y is shell-side porosity which depends on geometry of

the bundle

Finally, the shell-side pressure drop ratio can be computed

from the following relation:

ref

r m

D

&

The key equations are Eqs (14), (15), (22) and (24) As can

be seen they are independent on geometry of the exchanger

The models above should be programed by using a computer

program The system of equations has a lot of

temperature-dependent properties Therefore the EES software [25] is the

pertinent candidate for the current study The properties of

fluids are evaluated at bulk temperature The procedure for

solving the system of equations is summarized by Fig 2

From reference data the remaining temperatures and UA ref can

be calculated Effectiveness is then assumed Maximum

ther-mal duty at operating conditions Q&max is evaluated in the next step From these parameters Q& can be found After that the outlet fluid temperatures at operating conditions are computed Next bi, be , UA, and NTU are calculated Thereafter, new

ef-fectiveness is determined and compared to the assumed value

A new loop is carried out if the error is greater than a given tolerance.

3 Experimental validation

The experimental apparatus shown in Fig 3 was performed

to determine whether the present model could be validated In the apparatus, water is used as the working fluids for both sides of the tested helical heat exchanger Hot water is heated

by a three-phase electrical heater in a hot water tank The tank’s temperature can be adjusted to set various experiments The hot water is pumped to the tube-side of the exchanger Here the hot water is decreased in temperature by cold water The cold water almost at room temperature enters the shell-side of the exchanger The cold water rejects heat to the

envi-Input:

- Reference data: Q& , ref m&i ref, , m&e ref, , T i,in,ref , T e,in,ref, Dp h ref, , Dp c ref,

- Operating data: m& , i m & , T e i,in , T e,in

¯ Calculate the remain parameters of reference data:

T i,out,ref = T i,in,ref - Q& /( ref m&i ref, c p,i,ref )

T e,out,ref = T e,in,ref + Q& /( ref m&e ref, c p,e,ref )

F ref from Eq (19)

, , , , , , , , ,

, , , , , , , ,

ln

i in ref e out ref i out ref e in ref

lm ref

i in ref e out ref

i out ref e in ref

T

-,

ref ref ref lm ref

Q UA

= D

¯

¯

max min (i in, e in, )

Q& =C T -T

max

Q& = eQ&

T i,out = T i,in -Q& /( m & c i p,i)

T e,out = T e,in +Q& /( m & c e p,e)

i

p

D and D from Eqs (22) and (24) p e

b i and b e from Eqs (14) and (15)

UA from Eq (7) NTU=UA/C min

e new from Eqs (16) or (17)

­

|e -e new |< pre-specified value ®

¯ Yes

Output: Q& , T i,out , T e,out, D , p i D p e

Fig 2 Program flow chart

Table 1 Reference data

Heat transfer rate Q&ref =6.2 kW

Tube-side pressure drop Dp i ref, = 93 kPa Shell-side pressure drop Dp e ref, = 20 kPa Tube-side volumetric flow rate 0.278 l/s Shell-side volumetric flow rate 0.194 l/s Inlet tube-side fluid temperature T i,in,ref = 59.5°C Inlet shell-side fluid temperature T e,in,ref = 31.5°C

Hot water tank Pump

Pump

Air-cooled heat exchanger

t t

p

Flow meter

Flow meter

Heater

Cool water tank

Valve

p

Test section

Fig 3 Experimental apparatus

ronment by an air-cooled heat exchanger right after the test

section It then travels to a large tank and mixes water in the

tank Water volumetric flow rates are measured by floating

flow meters with 0.0028 l/s resolution Inlet and outlet

tem-peratures of both sides are measured by 4 thermocouples with

0.1°C precision Tube-side and shell-side pressure differences are processed by differential pressure transducers with an

ac-Table 2 Constant coefficients for Eq (30)

Constant coefficients

R 2

0.968806 0.382933 0.420696 -0.729444 2.050495 97.84%

0 10 20 30 40

Shell-side flow rate [lit/h]

Experimental Modelled

Fig 7 Shell-side pressure drop

20 40 60 80 100

Tube-side flow rate [lit/h]

Modelled Experimental

Fig 8 Tube-side pressure drop.

Fig 9 Comparison of theoretical results

4

5

6

7

8

QModelled (kW)

QM

+5%

-5%

Fig 4 Experimental vs theoretical heat transfer rate

36

37

38

39

40

41

42

43

44

Modelled outlet cold fluid temperature (oC)

o C

+1%

-1%

Fig 5 Experimental vs theoretical cold fluid temperature

46

48

50

52

54

56

58

Modelled outlet hot fluid temperature (oC)

o C

+1%

-1%

Fig 6 Experimental vs theoretical outlet hot fluid temperature

curacy of ±0.075% of the measured value Water flow rates

are adjusted by ball valves.

Table 1 presents reference data used in the current work

Figs 4-6 show the calculated results and experimental results

of thermal duty and outlet water temperatures Error of the

thermal duty is less than ±5%, and it can be noted that errors

of the outlet water temperatures are lower than ±1% This

confirmed that the heat transfer model is good

Figs 7 and 8 show the pressure drops between two

ap-proaches, modelling and experiment It can be concluded that

the results coincide well with each other The relative error of

shell-side pressure drop is no greater than ±5% The difference

of tube-side pressure drop is within ±2%, except the difference

up to ±8% at low flow rate

Fig 9 compares the analytical result of the present study

with that from previous study [14] Reference data used in the

comparison was marked in the Fig 9 The previous study

formed the analytic model for helical heat exchanger with

crimped spiral fin on outer tube The shell-side fluid was air

like a cold fluid It can be clearly seen that the trends are almost

the same and the deviation is moderate The difference is due

to the fact that the present model is formed for smooth pipes

However, geometrical parameters are eliminated Therefore,

the prediction in case of finned tube may be applicable

4 Parametric study

In this section, the effects of operating conditions on heat transfer rate are presented Results are displayed in the form of non-dimensional parameters so that they can be used as de-sign-maps in design or operation of arbitrary helical heat ex-changers Only the results of heat transfer rate are presented because pressure drop model is straightforward as shown by Eqs (22) and (24) If the fluids are not changed for an existing heat exchanger, the predicted pressure drops are much simpler because in that case the pressure drops are nearly proportional

to the square of flow rate

The dimensionless parameters can be defined as follows:

, , ,

e in e

e in ref

T ratioT

T

, , ,

i in i

i in ref

T ratioT

T

,

e e

e ref

m ratioM

m

= &

,

i i

i ref

m ratioM

m

= &

0.4 0.6 0.8 1

ratioM e

ratioTe=1

ratioTe=1.25

ratioTe=0.75

ratioMi=0.5 ratioTi=1

0.4 0.6 0.8 1 1.2 1.4

ratioM e

ratioMi=0.75 ratioTi=1

ratioTe=0.75

ratioTe=1

ratioTe=1.25

0.8 1 1.2 1.4 1.6 1.8 2

ratioM e

ratioM i =0.75 ratioT i =1.25

ratioT e =1.25

ratioT e =1 ratioT e =0.75

1 1.2 1.4 1.6 1.8 2 2.2 2.4

ratioM e

ratioT i =1.25 ratioM i =1.25

ratioT e =0.75

ratioT e =1

ratioT e =1.25

Fig 10 Effect of operating conditions on thermal duty.

ref

Q

ratioQ

Q

=

&

Four first ratios were selected as independent parameters to

explore their effects on the heat transfer rate, i.e ratioQ The

results can be seen in Fig 10 Generally ratioQ increases

when flow rate increases, the inlet hot water temperature

in-creases, or the inlet cold water temperature dein-creases, as

ex-pected These are obvious because increase in flow rates leads

to increase in heat transfer coefficients, and increase in hot

fluid temperature or decrease in cold fluid temperature results

in an increase in logarithm mean temperature difference

To facilitate use in design and rating of the helical heat

ex-changer, a correlation of heat transfer rate and operating

con-ditions is developed The heat transfer rate is a function of

flow rates and inlet temperatures in the following form:

3

(30) Table 2 shows the constant coefficients of the above

equa-tion The equation is valid for water as the working fluids,

e

i

5 Conclusions

The single phase heat transfer model and pressure drop

model were formulated to predict off-design conditions of the

helical heat exchanger The heat transfer model considered

LMTD correction factor to reach a better prediction The

models could evaluate outlet fluid temperatures, thermal duty,

and pressure drops for various operating conditions without

geometrical information of heat transfer surface An

experi-ment was set-up to determine the reliability of the models

Results showed that the differences between calculation and

experiment are from ±1 to ±5% The dimensionless figures of

the operating parameters were presented as the design-maps

Moreover a power regression model equation of

dimen-sionless heat transfer rate as a function of four parameters was

supplied The valid working fluid for the equation is water

The equation can be used in a range of heat transfer rates from

0.5 to 3 times reference data with the coefficient of

determina-tion R2 of 97.84%

Nomenclature -

A : Area (m2)

c p : Specific heat at constant pressure (J/kg.K)

d : Internal diameter of helical coil (m)

D : External diameter of helical coil (m)

F : LMTD correction factor

h : Heat transfer coefficient (W/m2.K)

k : Thermal conductivity (W/m.K)

L : Length of a pipe (m)

mp& : Mass flow rate (kg/s)

NTU : Number of transfer units

p : Pressure (Pa)

Pr : Prandtl number

R : Curvature radius (m)

Re : Reynolds number

T : Temperature (°C)

UA : Overall conductance (W/K)

Greek symbols

b : Heat transfer coefficient ratio

e : Effectiveness

m : Dynamic viscosity (N.s/m2)

r : Density (kg/m3)

Subscripts

c : Cross-sectional

in : Inlet

out : Outlet

References

[1] F Vitillo et al., An innovative plate heat exchanger of

en-hanced compactness, Applied Thermal Engineering, 87

(2015) 826-838

[2] Y Yujie et al., Performance evaluation of heat transfer en-hancement in plate-fin heat exchangers with offset strip fins,

Physics Procedia, 67 (2015) 543-550

[3] A Rovira et al., Thermoeconomic optimisation of heat re-covery steam generators of combined cycle gas turbine

power plants considering off-design operation, Energy Con-version and Management, 52 (4) (2011) 1840-1849

[4] N Kayansayan, Thermal behavior of heat exchangers in

off-design conditions, Heat Recovery Systems and CHP, 9 (3)

(1989) 265-273

[5] S Wongwises and M Polsongkram, Evaporation heat trans-fer and pressure drop of HFC-134a in a helically coiled

con-centric tube-in-tube heat exchanger, International Journal of Heat and Mass Transfer, 49 (3-4) (2006) 658-670

[6] S Wongwises and M Polsongkram, Condensation heat transfer and pressure drop of HFC-134a in a helically coiled

concentric tube-in-tube heat exchanger, International Jour-nal of Heat and Mass Transfer, 49 (23-24) (2006)

4386-4398

[7] D G Prabhanjan, G S V Raghavan and T J Rennie,

Comparison of heat transfer rates between a straight tube

heat exchanger and a helically coiled heat exchanger,

Inter-national Communications in Heat and Mass Transfer, 29 (2)

(2002) 185-191

[8] M Zareh et al., Numerical simulation and experimental

analysis of refrigerants flow through adiabatic helical

capil-lary tube, International Journal of Refrigeration, 38 (2014)

299-309

[9] J Fernández-Seara, J Sieres and M Vázquez, Heat and

mass transfer analysis of a helical coil rectifier in an

ammo-nia-water absorption system, International Journal of

Ther-mal Sciences, 42 (8) (2003) 783-794

[10] Y Xiaowen and W L Lee, The use of helical heat

ex-changer for heat recovery domestic water-cooled

air-conditioners, Energy Conversion and Management, 50 (2)

(2009) 240-246

[11] A Sogni and P Chiesa, Calculation Code for Helically

Coiled Heat Recovery Boilers, Energy Procedia, 45 (2014)

492-501

[12] W F Stoecker and J W Jones, Refrigeration & Air

condi-tioning, Second Ed., McGraw-Hill (1982)

[13] K Srisawad and S Wongwises, Heat transfer

characteris-tics of a new helically coiled crimped spiral finned tube heat

exchanger, Heat and Mass Transfer, 45 (4) (2008) 381-391

[14] R Boonsri and S Wongwises, Mathematical model for

predicting the heat transfer characteristics of a helical-coiled,

crimped, spiral, finned-tube heat exchanger, Heat Transfer

Engineering, 36 (18) (2015) 1495-1503

[15] B K Hardik, P K Baburajan and S V Prabhu, Local heat

transfer coefficient in helical coils with single phase flow,

International Journal of Heat and Mass Transfer, 89 (2015)

522-538

[16] B Bezyan, S Porkhial and A A Mehrizi, 3-D simulation

of heat transfer rate in geothermal pile-foundation heat

ex-changers with spiral pipe configuration, Applied Thermal

Engineering, 87 (2015) 655-668

[17] P C M Kumar et al., CFD analysis of heat transfer and

pressure drop in helically coiled heat exchangers using

Al2O3/water nanofluid, Journal of Mechanical Science and

Technology, 29 (2) (2015) 697-705

[18] F Vera-García et al., A simplified model for

shell-and-tubes heat exchangers: Practical application, Applied

Ther-mal Engineering, 30 (10) (2010) 1231-1241

[19] G F C Rogers and Y R Mayhew, Heat transfer and pres-

sure loss in helically coiled tubes with turbulent flow, Inter-national Journal of Heat and Mass Transfer, 7 (11) (1964)

1207-1216

[20] J Y San, C H Hsu and S H Chen, Heat transfer

charac-teristics of a helical heat exchanger, Applied Thermal Engi-neering, 39 (2012) 114-120

[21] Y A Cengel, Heat transfer - A practical approach,

McGraw-Hill (2003)

[22] R A Bowman, A C Mueller and W M Nagle, Mean

temperature difference in design, Trans Am Soc Mech Engrs., 62 (1940) 283-294

[23] S Kakaç and H Liu, Heat Exchangers - Selection, Rating, and Thermal Design, Second Ed., CRC Press (2002) [24] E M Smith, Advances in Thermal Design of Heat Ex-changers, John Wiley & Sons (2005)

[25] S A Klein, Engineering Equation Solver, F-Chart

Soft-ware (2013)

Nguyen Minh Phu received B.E in

2006, and M.E in 2009 from Ho Chi Minh city University of Technology (HCMUT), Vietnam, and Ph.D from University of Ulsan, Korea in 2012 He had been with the Arizona State Univer-sity at Tempe during the summer 2014

as exchange visitor.He has been a lec-turer of Mechanical Engineering Faculty in HCMUT since

2006 His research interests include the design of thermal sys-tems and the applied renewable energy

Nguyen Thi Minh Trinh received B.E

in 2002, and M.E in 2009 from Ho Chi Minh city University of Technology (HCMUT), Vietnam She is a lecturer of Mechanical Engineering Faculty in HCMUT At the same time, she is a lecturer of Energy management and Energy audit training project, organized

by Japan International Cooperation Agency (JICA) in Viet-nam through the Ministry of Industry and Trade of VietViet-nam Her research interests include energy efficiency and econom-ics, heat exchanger, refrigeration and air conditioning engi-neering