numerical and experimental investigation of heat transfer

International Journal of Emerging Technology and Advanced Engineering

Website: www.ijetae.com (ISSN 2250-2459, ISO 9001:2008 Certified Journal, Volume 4, Issue 9, September 2014)

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Numerical and Experimental Investigation of Heat Transfer

Augmentation in Double Pipe Heat Exchanger with Helical and

Twisted Tape Inserts Patnala Sankara Rao

1, K Kiran Kumar

2

1M.Tech Student,

2Faculty, Mechanical Department, National Institute of Technology, Warangal, India

Abstract— Nowadays, heat exchangers with twisted-tape

inserts have widely been applied for enhancing the convective

heat transfer in various industries such as thermal power

plants, chemical processing plants, air conditioning

equipment, refrigerators, petrochemical, biomedical and food

processing plants. In general, twisted tape insert introduces

swirl into the bulk flow which consequently disrupts a

thermal boundary layer on the tube surface.

A 3-D numerical model has been developed to study the

performance of (i) bare tube-in-tube heat exchanger, (ii) tube

in tube with twisted tape insert and (iii) helical insert at

annulus and twisted tape insert inside the inner tube of the

heat exchanger. Numerical results have been compared with

the available analytical solution. It has been observed that

there is a good agreement between these two results: within

±19.78 percentage error limit for Nusselt number

measurement and ±25 percentage error for friction factor.

The numerical simulation for twisted tape insert with twist

ratio (y) 5 has been performed using different turbulent

models by varying Reynolds number ranging from 2000 to

10000. SST k-ω turbulent model has been selected as better

turbulent model for further simulation. Experiments on

double pipe heat exchanger with twisted tape inserts with

twist ratios y= 4.167, 5.556, 6.944 and helical tape insert in

annulus has been performed with Reynolds number ranging

from 4000 to 20000. These experimental results have been

compared with the numerical results. From the results, it has

been found that, by using twisted and helical tape inserts the

heat transfer enhancement takes place in the expense of

pressure drop.

Keywords—Double pipe heat exchanger, Heat transfer

augmentation techniques, Twisted tape insert, Helical tape

insert, Twist ratio, Numerical and Experimental investigation,

Computational fluid dynamics, Turbulence modelling,

Friction factor, Nusselt number, Friction factor ratio, Nusselt

number ratio.

I. INTRODUCTION

Heat exchangers have several industrial and engineering

applications.

The design procedure of heat exchangers is quite

complicated, as it needs exact analysis of heat transfer rate

and pressure drop estimations apart from issues such as

long-term performance and the economic aspect of the

equipment. The major challenge in designing a heat

exchanger is to make the equipment compact and achieve a

high heat transfer rate using minimum pumping power.

A majority of heat exchangers used in thermal power

plants, chemical processing plants, air conditioning

equipment, and refrigerators, petrochemical, biomedical

and food processing plants serve to heat and cool different

types of fluids. Both the mass and overall dimensions of

heat exchangers employed are continuously increasing with

the unit power and the volume of production. This involves

huge investments annually for both operation and capital

costs. Hence it is an urgent problem to reduce the overall

dimension characteristics of heat exchangers.

The need to optimize and conserve these expenditures

has promoted the development of efficient heat exchangers.

Different techniques are employed to enhance the heat

transfer rates, which are generally referred to as heat

transfer enhancement, augmentation or intensification

technique.

A. Heat Transfer Augmentation Techniques

Heat transfer augmentation techniques are generally

classified into three categories namely: Active techniques,

Passive techniques and Compound techniques.

1 Active Techniques: Active techniques involve some

external power input for enhancement of heat transfer.

Example: Mechanical aids, Surface vibrations, Fluid

vibrations and Jet impingement.

2 Passive Techniques: Passive techniques do not require

any direct input of external power. They generally use

geometrical or surface modifications to the flow channel by

incorporating inserts or additional devices. Example:

Rough surfaces, Extended surfaces, Swirl flow devices and

Coiled tubes.



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3 Compound Techniques: Combination of active and

passive techniques may be employed simultaneously to

obtain enhancement in heat transfer that is greater than that

produced by any of those techniques separately. This

simultaneous utilization is termed compound enhancement

B. Twisted Tape Inserts

To enhance the heat transfer rate, some kind of insert is

placed in the flow passages and they also reduce the

hydraulic diameter of the flow passages. Heat transfer

enhancement in a tube flow is due to flow blockage,

partitioning of the flow and secondary flow. Flow

blockages increase the pressure drop and leads to viscous

effects, because of a reduced free flow area. The selection

of the twisted tape depends on performance and cost. The

performance comparison for different tube inserts is a

useful complement to the retrofit design of heat

exchangers.

1 Twisted Tape in Laminar Flow: Manglik and

Bergles[1]

developed the correlation for friction factor and

Nusselt number for laminar flows including the swirl

parameter, which defined the interaction between viscous,

convective inertia and centrifugal forces.

The heat transfer correlation,

0.14

0.767 0.30.106 Pr ......(1)w

w

Nu s

Where ws is the swirl parameter and is defined as

0.5

Rews

y .

Based on the same data, a correlation for friction factor,

2

1/66 2.5515.767 2

1 10 ......(2)Re 4

w

df s

d

Where, δ and d are the thickness and the tube inner

diameter of the twisted tape respectively.

Saha and Dutta[2]

, Ray and Date[3]

, Ujhidy et al[4]

and

Suresh Kumar et al.[5]

are also did heat transfer

investigations using twisted tape inserts for laminar flows.

2 Twisted tape in Turbulent Flow: Manglik and Bergles

developed the correlation for friction factor and Nusselt

number for turbulent flows.

Their correlations are as follows

1.75 1.25

0.25 1.29

0.079 2 2 2.7521

4 4Re

......(3)

df

d d y

0.180.8 0.2

0.8 0.4 2 20.023Re Pr .

4 4

.....(4)

w

dNu

d d

AI-Fahed et. al.[6]

, Rahimi et al[7]

, Agarwal and Raja

rao[8]

and Gupte and Date[9]

are also did heat transfer

investigations using twisted tape inserts for turbulent flows.

C. Computational Fluid Dynamics

Fluid (gas and liquid) flows are governed by partial

differential equations (PDE) which represent conservation

laws for the mass, momentum and energy. Computational

Fluid Dynamics (CFD) is used to replace such PDE

systems by a set of algebraic equations which can be solved

using digital computers. The basic principle behind CFD

modeling method is that the simulated flow region is

divided into small cells. Differential equations of mass,

momentum and energy balance are discretized and

represented in terms of the variables at any predetermined

position within or at the center of cell. These equations are

solved iteratively until the solution reaches the desired

accuracy (ANSYS FLUENT 14.0). CFD provides a

qualitative prediction of fluid flows by means of

Mathematical modeling (partial differential equations)

Numerical methods (discretization and solution

techniques)

Software tools (solvers, pre- and post-processing

utilities)

D. Turbulence Modeling

Turbulent flows are characterized by fluctuating velocity

fields. These fluctuations mix transported quantities such as

momentum, energy, and species concentration, and cause

the transported quantities to fluctuate as well. It is an

unfortunate fact that no single turbulence model is

universally accepted as being superior for all classes of

problems. The choice of turbulence model will depend on

considerations such as the physics encompassed in the

flow, the established practice for a specific class of

problem, the level of accuracy required, the available

computational resources, and the amount of time available

for the simulation.



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Turbulence models are classified as,

i) k–ε model

Standard k–ε model

RNG k–ε model

ii) k- ω model

Standard k- ω model

shear-stress transport (SST) k-ω model

II. NUMERICAL INVESTIGATION OF PLAIN AND TWISTED

TAPE HEAT EXCHANGER

A. Numerical Investigation of Plain Heat Exchanger

1 Geometrical Specifications to Model Double Pipe Heat

Exchanger:

TABLE I

SPECIFICATIONS OF DOUBLE PIPE HEAT EXCHANGER

Length of tube, L 2.2 m

Inner diameter of inner pipe, di 0.022 m

Outer diameter of inner pipe, do 0.026 m

Inner diameter of outer pipe, Di 0.054 m

Outer diameter of outer pipe, Do 0.058 m

Material Copper

Inner pipe fluid Cold water (300 K)

Annulus fluid Hot water (353 K)

Schematic diagram of double pipe heat exchanger is as

shown in Figure 1.

Figure 1. Plain double pipe heat exchanger

Numerical model and meshing of double pipe heat

exchanger are as shown in Figure 2.

Figure 2. Cfd model and meshing of double pipe heat exchanger

Table II

Properties of Water

Density, ρ 998.2 kg/m3

Specific heat capacity, Cp 4182 J/kg K

Thermal conductivity, k 0.6 W/m K

Viscosity, μ 1.003 x 10-3 kg/m s

Table III

Boundary Condition for Inner Fluid

Inlet condition Velocity inlet (varies from

0.037 to 0.47 m/s)

Outlet condition Pressure outlet

Initial gauge pressure Zero Pascal

Inlet temperature 300 K

Table IV

Boundary Condition for Annulus Fluid

Inlet condition Velocity inlet (0.377 m/s)




2 Data Reduction:

The area weighted average temperature and static

pressure were noted at the inlet and outlet surfaces of the

pipe. The friction factor and average heat transfer

coefficients were calculated as follows.

Friction factor, 22f P L D V

Nusselt number,

1

2

1 2

2

p ce ci

p hi he

avg

Q m C T T

Q m C T T

Q QQ



183

ln

hi ce he ci

hi ce

he ci

i

i

T T T TLMTD

T T

T T

A d L

Qh

A LMTD

hdNu

k

3 Heat transfer correlations:

i. Laminar flow, for Re < 2100

Nu= f(Gz)

For Gz <100, Hausen’s Equation [10]

is used.

0.14

23

0.0853.66

1 0.045 w

GzNu

Gz

For Gz>100, Seider – Tate [10]

equation is used.

1 0.143RePr

1.86w

NuL D

ii. Transition Zone:

For 2100 < Re < 10000, Hausen’s

Equation [10]

is used

0.142

32 13 30.116 Re 125 Pr 1

w

DNu

L

iii. Turbulent Zone

Re > 10000 (Dittus - Boelter equation [10]

) 0.8 0.40.023Re PrNu

4 Friction factor correlations:

Laminar region, ReD < 2100

16 Ref

Turbulent flow, ReD > 2100

(Colburn’s Equation [10]

) 0.20.046Ref

5 Results and discussion:

Three dimensional numerical simulations were

performed for inlet velocities of 0.037, 0.055, 0.073, 0.091,

0.18, 0.27, 0.37 and 0.46 m/sec of water corresponding to

Reynolds numbers of 800, 1200, 1600, 2000, 4000, 6000,

8000, and 10000 respectively.

Initially water temperature adjacent to the tube wall is

more compared to the center of tube as indicated in the

Figure 3. This will increase along the length of horizontal

tube. Inlet water temperature is held constant at 300 K for

all flow rates.

Because of the frictional resistance offered to fluid flow,

water pressure drops across flow field. Pressure drop varied

from 5.792 Pa to 333.926 Pa for the range of Reynolds

numbers considered for numerical analysis.

Figure 3. Temperature variation along the length of inner tube

Figure 4. Pressure distribution along the length of inner tube

6 Validation:

Numerical results were made compared with the

standard correlation values under similar condition, in

order to evaluate the validity of the plain tube results.

Comparison of analytical and cfd results for friction factor

and Nusselt number with Reynolds number are shown

below.



184

Figure 5. Friction factor vs Reynolds number for plain heat exchanger

Figure 6. Nusselt number vs Reynolds number for plain heat

exchanger

From the above results, it is observed that, the simulated

data are valid within +19.78 percentage error limit with

measurements for Nusselt number and + 25 percentage

error for friction factor.

B. Numerical Investigation of Double pipe Heat Exchanger

with twisted tape insert

The simulation studies were conducted with twisted tape

insert having twist ratio y= 5 for the Reynolds number

ranging from 800 to 10000, The mathematical models

including the turbulence models, numerical solution and

other computational details are described. Effects of the

twist ratio on heat transfer rate aNu and friction factor

af are examined.

1 Geometry of Twisted Tape Insert:

Figure 7. Twisted tape insert inside a tube

Terms used in twisted tape insert,

Pitch (H): Axial distance for 180 rotation of the tape

Twist Ratio (y): The twist ratio is defined as the ratio of

pitch to inside diameter of the tube, H

yd

Tape thickness = 0.001, twisted tape material: copper

Numerical model and meshing of double pipe heat

exchanger with twisted tape insert having twist ratio y=5 is

as shown in Figure 8.

Figure 8. Cfd model and meshing of twisted tape insert inside a tube

2 Boundary Condition:

Same boundary conditions of plain tube were applied to

the twisted tape heat exchanger.

3 Assumptions:

The major assumptions are:

The flow through the twisted tape inserted tube is

turbulent and incompressible

The flow is in steady state

Natural convection and thermal radiation are

neglected

The thermo-physical properties of the fluid are

temperature independent



185

4 Results and Discussions:

The characteristics of swirling turbulent flows in a

circular tube fitted with twisted tape insert by means of

mathematical equations in association with the standard k–

ε turbulence model, the Renormalized Group (RNG) k–ε

turbulence model, the standard k–ω turbulence model, and

Shear Stress Transport (SST) k–ω turbulence model were

determined Twisted tape with twist ratio, (y = 5) was used

for model verification. The present results are compared

with the correlations obtained suggested Manglik and

Bergles.

Figure 9. Friction factor vs Reynolds no for y=5

Figure 10. Nusselt number vs Reynolds number for y=5

5 Validation:

From the above results, it is clearly seen that the

predicted Nusselt numbers obtained from the SST k–ω

turbulence models is in better agreement compared to those

from other models. The SST k–ω turbulence model is valid

within ±20.38% error limit with measurements for Nusselt

number and ±25.4% for friction factor.

III. EXPERIMENTAL WORK

A. Experimental Setup

1 Geometrical Specifications:

The experimental study on passive heat transfer

augmentation using copper twisted tapes in inner pipe and

helical copper pipe in annulus were carried out in a double

pipe heat exchanger having the specification as listed

below

Table V

Specifications of Experimental Setup

Length of tube, L 0.8 m

Inner diameter of inner pipe, di 0.022 m

Outer diameter of inner pipe, do 0.026 m

Inner diameter of outer pipe, Di 0.054 m

Outer diameter of outer pipe, Do 0.058 m

Helical tape pitch, h 0.05 m

Twisted and helical tape

thickness

0.0005 m

Twist ratios of twisted tapes, y 4.167, 5.556 and 6.944

Schematic diagram of experimental setup is as shown in

Figure 11.

Figure 11. Schematic diagram of experimental setup

Table VI

Material Used For Making Heat Exchanger

Inner pipe Copper

Outer pipe Mild steel

Twisted and helical tape inserts Copper

Inner pipe fluid Hot water (353 K)

Annulus fluid Cold water (300 K)



186

2 Fabrication of Twisted Tape Inserts:

The copper tapes were first cut into 3 equal sizes. Holes

were drilled at both ends of each tape so that the two ends

could be clamped. Lathe was used to give the tapes the

desired twist. One end was kept fixed on the tool part of the

lathe while the other end was given a slow rotatory motion

by holding it on the tool part side to avoid its distortion,

thus creating the required twist in the tapes. Three tapes

with varying twist ratios were fabricated as shown in figure

12.

Figure 12. Twisted tape inserts

3 Fabrication of Twisted Tape Inserts:

Copper sheet of thickness 0.0005m was cut into hallow

circular shape, made them as helical tape by cutting at one

edge and joining one by one, now the helical tape is welded

to inner pipe as shown in figure 13. The experimental setup

is as shown in figure 14.

Figure 13. Helical tape insert

Figure 14. Experimental setup

4 Experimental Procedure:

Experimental setup was arranged as shown in Figure

14.

Thermocouples were checked at room temperature

using DAQ system.

Water heated up to 80 C using electrical heater.

Hot water was pumped through the inner pipe without

twisted tape inserts and ambient water was pumped

through the annulus pipe with helical tape insert.

Noted down the discharge, inlet and outlet

temperatures of cold and hot water.

For various discharges, inlet and outlet temperatures

of cold and hot water were noted down. 8 discharges

were taken for the experiment.

Then same procedure repeated by inserting twisted

tape inserts in inner pipe and helical tape insert in

annulus pipe.

5 Experimental results for double pipe heat exchanger

without twisted tape inserts and with helical tape insert:

Figure 15. shows the plot between Nusselt number and

Reynolds number, which gives the heat transfer rate in

double pipe heat exchanger with helical tape insert in

annulus and without twisted tape inserts in inner pipe. The

experiment was conducted for the Reynolds numbers

ranging from 4431.705 to 20134.596.



187

Figure 15. Experimental Nusselt number vs Reynolds number for

heat exchanger with helical tape insert

Figure 16. shows the plot between friction factor and

Reynolds number, which gives the heat transfer rate in

double pipe heat exchanger with helical tape insert in

annulus and without twisted tape inserts in inner pipe.

Figure 16. Experimental Friction factor vs Reynolds number for heat

exchanger with helical tape insert

6 Experimental results for double pipe heat exchanger

with twisted tape inserts and with helical tape insert:

The experiment was conducted with the twisted tape

inserts having twist ratios 4.167, 5.556 and 6.944 for

Reynolds number ranging from 4431.705 to 20134.596.

Figure 17. shows the plot between Nusselt number ratios

and Reynolds number and the Figure 18. shows the plot

between friction factor ratios and Reynolds number for

twist ratios 4.167, 5.556 and 6.944

Figure 17. Experimental Nua/Nu0 vs Reynolds number for heat

exchanger with both twisted and helical tape inserts

Figure 18. Experimental fa/fo vs Reynolds number for heat exchanger

with both twisted and helical tape inserts

The results for the tube fitted with all twisted tapes are

compared with those for a plain tube under similar

operating conditions. The Nusselt number in the tube with the twist ratios y=

4.167, 5.556 and 6.944, are around 1.601 to 3.540, 1.491 to

3.452, and 1.450 to 3.371 times of that in the plain tube.

The friction factor in the tube with the twist ratios y=


7.308, and 4.723 to 7.182 times of that in the plain tube.

From the results Nusselt number and friction factor

values were found to decrease with increasing in twist

ratio. Twisted tape inserts for twist ratio (y=4.167) can

enhance heat transfer rates up to 3.538 times at Reynolds

number 12073.782 and increase in friction factors nearly

7.406 times in comparison with those of the plain tube.



188

IV. NUMERICAL INVESTIGATION OF HEAT EXCHANGER

WITH TWISTED AND HELICAL TAPE INSERTS

A. Numerical Investigation without Twisted Tape Inserts in

Inner Pipe and with Helical Tape Insert in Annulus

The geometry was modeled in ansys work bench using

experimental specifications as mentioned earlier, geometry

and meshing of double pipe heat exchanger with helical

tape insert in annulus is as shown in figure 19. The Shear

Stress Transport (SST k-ω) model is used in the simulation

for finding the Nusselt number and friction factor.

Figure 19. CFD model and meshing of heat exchanger with helical

tape insert

1 Boundary Conditions:

Table VII

Boundary Condition for Inner Fluid

Inlet condition Velocity inlet (varies from

0.127 to 0.577 m/s)




Table VIII

Boundary Condition for Annulus Fluid

Inlet condition Velocity inlet (0.376 m/s)




The velocity vectors for plain heat exchanger, heat

exchanger with twisted tape insert in inner pipe, heat

exchanger with helical tape insert in annulus and heat

exchanger with both twisted and helical tape inserts are as

shown in Figure 20, Figure 21, Figure 22 and Figure 23.

Inner pipe Annulus pipe

Figure 20. Velocity vector for Plain double pipe heat exchanger


Figure 21. Velocity vector for Heat exchanger with twisted tape insert


Figure 22. Velocity vector for Heat exchanger with helical tape insert


Figure 23. Velocity vector for Heat exchanger with both twisted and

helical tape



189

From the velocity vectors, observed that the flow of

water in plain tube is straight lines, where as in case of

twisted and helical tape inserts the flow is swirl flow.

Because of swirl flow in heat exchanger, the effected heat

transfer area increases, thereby heat transfer rate increases,

but because of flow abstraction due twisted and helical tape

inserts, pressure drop also increases and this pressure drop

varies according to Reynolds number and twist ratio of

twisted and helical tape inserts.

1 Results and Discussions:

Three dimensional numerical simulations were

performed for inlet velocities of 0.577, 0.520, 0.433, 0.400,

0.346, 0.260, 0.208 and 0.127 m/sec of water

corresponding to Reynolds numbers of 4431.705,

7258.225, 9072.782, 12073.779, 13958.126, 15109.671,

18145.563 and 20134.596 respectively.

Because of the frictional resistance offered to fluid flow,

water pressure drops across flow field. Pressure drop varied

from 27.894 Pa to 972.191 Pa for the range of Reynolds

numbers considered for numerical analysis. Figure 24 and

Figure 25 shows the plots for Nusselt number and friction

factor with respect to Reynolds number.

Figure 24. Numerical Nusselt number vs Reynolds number for heat


Figure 25. Numerical Friction factor vs Reynolds number for heat


B. Numerical Investigation with Twisted Tape Inserts in

Inner Pipe and with Helical Tape Insert in Annulus

The geometry was modeled as per experimental

specifications, the twisted tape inserts with twist ratios

(4.167, 5.556 and 6.944) were inserted in inner pipe and the

geometry and meshing are as shown in figure 26. The

Shear Stress Transport (SST k-ω) model is used in the

simulation for finding the Nusselt number and friction

factor.

H=25cm H=20cm

H=15cm meshing file

Figure 26. CFD model and meshing for Heat exchanger with both

twisted and helical tape inserts

1 Boundary Conditions:

Same boundary conditions of Numerical investigation

without twisted tape inserts in inner pipe and with helical

tape insert in annulus has been applied for this case also

2 Heat Transfer Results:

Effect of the twist ratios on the heat transfer rate is

numerically studied. The results for the tube fitted with all

twisted tapes are also compared with those for a plain tube

under similar operating conditions. The heat transfer rate is

considered in terms of Nusselt numbers, the Nusselt

number ratio (Nua/NuO) with Reynolds number of the tube

equipped with three different twist ratios (y = 4.167, 5.556

and 6.944) are shown in figure 27.

The Nusselt number in the tube with the twist ratios y=


3.101 and 1.336 to 3.009 times of that in the plain tube.



190

Figure 27. Numerical Nua/Nu0 vs Reynolds number for heat

exchanger with both twisted and helical tape inserts

3 Friction Factor Results:

Effect of the twist ratios on the friction factor is

numerically studied. The friction factor ratio (fa/fo) with

Reynolds number of the tube equipped with four different

twist ratios (y = 4.167, 5.556 and 6.944) are shown in

figure 28.

Friction factor decreases with increasing twisted ratio.

The friction factors in the tube with the twist ratios y=

4.167, 5.556 and 6.944, are around 4.712 to 10.39 , 3.697

to 7.231 and 3.28 to 6.01 times of that in the plain tube.

Figure 28. Numerical fa/fo vs Reynolds number for heat exchanger

with both twisted and helical tape inserts

From the results, Nusselt number and friction factor

values were found to decrease with increasing in twist

ratio. Twisted tape inserts for twist ratio (y=4.167) can

enhance heat transfer rates up to 3.364 times at Reynolds

number 12073.779 and increase in friction factors nearly

9.630 times in comparison with those of the plain tube.

4 Validation:

The trend obtained from the graphs of Nusselt number

ratio and friction factor ratio for different twist ratios were

similar when compared the experimental results with

simulated results, therefore the experiment was validated

with the numerical simulation with ±25.4% of error.

V. CONCLUSIONS

From the experimental results, the twisted tape with

twist ratio y=4.167 can enhance maximum heat transfer

rate up to 3.540 times of plain heat exchanger at Reynolds

number 9072.782 with friction factor 7.532 times. Whereas

from Numerical results, twist ratio y=4.167 can enhance

maximum heat transfer rate up to 3.364 times at Reynolds

number 12073.779 with friction factor 10.39 times of plain

heat exchanger. Therefore, from the both experimental and

numerical results maximum heat transfer rate can occur at

Reynolds number 9072.782 and 12073.779 with increase in

friction factor.

Form the experimental results, the twisted tape with

twist ratio y=6.944 can give less friction factor up to 4.723

times of plain heat exchanger at Reynolds number

20134.596 with heat transfer rate up to 1.450 times.

Whereas from numerical results, twisted tape y=6.944 can

give less friction factor up to 3.151 times at Reynolds

number 20134.596 with heat transfer rate up to 1.336 times

of plain heat exchanger. Therefore, from both experimental

and numerical results, less friction factor can occur at

Reynolds number 20134.596 with decrease in heat transfer

rate.

From the experimental and numerical results, as the heat

transfer rate increases, friction factor also increases,

therefor at maximum heat transfer rate, pressure drop also

more. If pressure drop is more, then pumping power should

be more, it leads to increase the pumping cost. Therefore

instead of going for higher heat transfer rate and higher

pumping power, better to take moderate heat transfer rate

with less pumping power by selecting optimum Reynolds

numbers and twisted ratios.

Whenever higher heat transfer rate is required

irrespective of pressure drop then the twisted tape with

smaller twist ratio can be used for that operation. For lower

pressure drop and moderate heat transfer rate the twisted

tape with higher twist ratio can be used, therefore based on

the requirement, the twisted tape inserts will be selected.



191

REFERENCES

[1] Manglik, R. K. and Bergles, A. E. (1993), Heat transfer and pressure

drop correlations for twisted-tape inserts in isothermal tubes: Part I: laminar flows. Trans. ASME, J. Heat Transfer, Vol.115, pp.881–

889.

[2] Saha, S. K. and Dutta, A. (2001), Thermo-hydraulic study of laminar

swirl flow through a circular tube fitted with twisted tapes. Trans.

ASME, J. Heat Transfer, Vol.123, pp. 417–421.

[3] Ray, S. and Date, A. W.(2003), Friction and heat transfer

characteristics of flow through square duct with twisted tape insert,

Int. J. Heat and Mass Transfer, Vol. 46, pp.889–902.

[4] Ujhidy. A, Nemeth, J. Szepvolgyi, J. (2003), Fluid flow in tubes

with helical elements. Chem. Engg and Processing, Vol.42, pp.1–7.

[5] Suresh Kumar, P., Mahanta, P. and Dewan, A. (2003), Study of

laminar flow in a large diameter annulus with twisted tape inserts. In

Proceedings of 2nd International Conference on Heat Transfer, Fluid Mechanics, and Thermodynamics, Victoria Falls, Zambia, paper

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56.

[6] AI-Fahed, S. and Chakroun, W. (1996), Effect of tube tape clearance on heat transfer for fully developed turbulent flow in a horizontal

isothermal tube. Int. J. Heat and Fluid Flow, Vol.17, pp. 173–178.

[7] Rahimi, M. Shabanian, S.R. Alsairafi. A.A. (2009), Experimental

and CFD studies on heat transfer and friction factor characteristics of

a tube equipped with modified twisted tape inserts, Chemical Engineering and Processing, Vol.48, pp.762–770

[8] Agarwal, S. K. and Raja Rao, M. (1996), Heat transfer augmentation

for flow of viscous liquid in circular tubes using twisted tape inserts. Int. J. Heat Mass Transfer, Vol. 99, pp.3547– 3557.

[9] Gupte, N. S. and Date, A. W. (1989), Friction and heat transfer characteristics of helical turbulent air flow in annuli. Trans.ASME, J.

Heat Transfer, Vol. 111, pp. 337–344.

[10] Gaurav Johar and Virendra Hasda, (2010), Experimental studies on heat transfer augmentation using modified reduced width twisted

tapes as inserts for tube side flow of loquids. 33, 34.

Appendix

Nomenclature

Cp Specific heat capacity, J/Kg.K

Di Internal diameter of outer tube, m

Do Outer diameter of outer tube, m

di Internal diameter of inner tube, m

do Outer diameter of inner tube, m

E Energy per unit mass, J/kg

F External body force, N/m2

fO Friction factor for smooth tube, Dimensionless

fa Friction factor for the tube with inserts,

Dimensionless

Gz Graetz Number, (Re x Pr x D/L), Dimensionless

H Pitch of twisted tape for 180°rotation

h Heat transfer coefficient, W/m2°C

I Unit tensor, Dimensionless

J Diffusion flux, m2/sec

k Thermal conductivity, W/m-K

k Turbulence kinetic energy

effk Effective conductivity, W/m-K

L Length of the tube, m

Nu0 Nusselt number for plain tube, Dimensionless

Nua Nusselt number for the tube with inserts,

Dimensionless

m Mass flow rate, m/s

Pr Prandtl number, Dimensionless

Re Reynolds number, Dimensionless

SW Swirl parameter, Dimensionless

v Velocity, m/s

U Uncertainty

w Width of the twisted tape, m

y Twist ratio (H/w), Dimensionless

Δp Pressure difference, Pa

P Static pressure, Pa

Greek letters

μ Viscosity, kg/ m-s

δ Thickness of twisted tape, m

ε Turbulence dissipation rate

μt Turbulent viscosity

ρ Density, kg/m3

ω Specific dissipation rate

Stress tensor

Table IX

Numerical Nu and f for Plain Tube

Re CFD Analytical

Nu f Nu f

800 6.919 0.021 6.52 0.02

1200 8.465 0.014 7.49 0.0133

1600 9.690 0.011 8.965 0.01

2000 10.843 0.01 9.65 0.008

4000 27.1 0.0096 29.42 0.0088

6000 42.215 0.0085 47.645 0.0081

8000 54.116 0.0083 63.85 0.0076

10000 66.074 0.0073 78.75 0.0073

Table X

Numerical Nu VS Re for Twisted Tape Having Y=5

Re Analytical Standard

k–ε

RNG

k–ε

Standard

k–ω

SST

k–ω

800 17.276 13.04 13.19 13.15 13.19

1200 23.578 18.064 17.79 17.869 18.07

1600 29.379 22.408 22.09 22.17 22.41

2000 34.887 25.759 26.168 26.168 26.317

4000 44.52 44.286 39.59 42.56 44.025

6000 61.577 59.35 57.63 57.63 58.838

8000 77.512 75.959 72.92 72.67 72.924

10000 92.661 89.275 85.839 85.53 88.329



192

Table XI

Numerical f VS Re for Twisted Tape Having Y=5

Re Analytical Standard

k–ε

RNG

k–ε

Standard

k–ω

SST

k–ω

800 0.082 0.105 0.104 0.103 0.102

1200 0.063 0.081 0.082 0.075 0.076

1600 0.053 0.075 0.065 0.062 0.063

2000 0.046 0.061 0.055 0.053 0.055

4000 0.029 0.038 0.039 0.034 0.036

6000 0.026 0.03 0.031 0.027 0.027

8000 0.024 0.029 0.03 0.026 0.025

10000 0.023 0.024 0.025 0.023 0.023

Table XII

Experimental Nu and f for Plain Inner Tube with Helical Tape Insert

In Annulus

Re V (m/s) Nu f

4431.705 0.127 11.51 0.128

7258.225 0.208 15.65 0.116

9072.782 0.260 19.59 0.109

12073.779 0.346 24.21 0.103

13958.126 0.400 35.58 0.058

15109.671 0.433 56.58 0.044

18145.563 0.520 69.32 0.04

20134.596 0.577 81.61 0.037

Table XIII

Experimental Nua/Nuo VS Re for Heat Exchanger with Both Twisted

and Helical Tape Inserts

Re y=4.167 y=5.556 y=6.944

4431.705 2.876 2.653 2.431

7258.225 3.359 3.163 3.001

9072.782 3.540 3.452 3.371

12073.779 3.538 3.431 3.105

13958.126 2.424 2.352 2.262

15109.671 1.672 1.543 1.492

18145.563 1.622 1.521 1.473

20134.596 1.601 1.491 1.450

Table XIV

Experimental fa/fo VS Re for Heat Exchanger with Both Twisted and

Helical Tape Inserts

Re y=4.167 y=5.556 y=6.944

4431.705 7.039 6.853 5.513

7258.225 7.353 7.121 6.710

9072.782 7.532 7.308 7.182

12073.779 7.406 7.101 6.931

13958.126 6.536 6.453 6.305

15109.671 5.75 5.521 5.365

18145.563 5.025 4.981 4.801

20134.596 4.918 4.831 4.723

Table XV

Numerical Nu and f for Plain Inner Tube with Helical Tape Insert in

Annulus

Re V (m/s) Nu f

4431.705 0.127 13.19 0.102

7258.225 0.208 17.79 0.076

9072.782 0.260 22.09 0.063

12073.779 0.346 26.68 0.055

13958.126 0.400 39.59 0.036

15109.671 0.433 57.63 0.027

18145.563 0.520 72.92 0.025

20134.596 0.577 85.839 0.023

Table XVI

Numerical Nua/Nuo VS Re for Heat Exchanger with Both Twisted

and Helical Tape Inserts

Re y=4.167 y=5.556 y=6.944

4431.705 2.712 2.529 2.227

7258.225 3.113 2.718 2.428

9072.782 3.304 3.101 3.009

12073.779 3.364 3.063 2.643

13958.126 1.89 1.718 1.446

15109.671 1.65 1.517 1.47

18145.563 1.602 1.452 1.366

20134.596 1.559 1.408 1.336

Table XVII

Numericals fa/fo VS Re for Heat Exchanger With Both Twisted And

Helical Tape Inserts

Re y=4.167 y=5.556 y=6.944

4431.705 8.69 6.121 4.857

7258.225 9.78 6.813 5.472

9072.782 9.971 6.94 5.72

12073.779 10.39 7.231 5.5

13958.126 6.045 4.464 3.54

15109.671 5.247 4.175 3.2

18145.563 4.84 3.94 3.07

20134.596 4.712 3.697 3.151

numerical and experimental investigation of heat transfer

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