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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)
180
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.
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)
181
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.
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)
182
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)
Outlet condition Pressure outlet
Initial gauge pressure Zero Pascal
Inlet temperature 353 K
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
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)
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.
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Website: www.ijetae.com (ISSN 2250-2459, ISO 9001:2008 Certified Journal, Volume 4, Issue 9, September 2014)
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
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)
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)
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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.
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)
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=
4.167, 5.556 and 6.944, are around 4.918 to 7.532, 4.831 to
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.
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Website: www.ijetae.com (ISSN 2250-2459, ISO 9001:2008 Certified Journal, Volume 4, Issue 9, September 2014)
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)
Outlet condition Pressure outlet
Initial gauge pressure Zero Pascal
Inlet temperature 353 K
Table VIII
Boundary Condition for Annulus Fluid
Inlet condition Velocity inlet (0.376 m/s)
Outlet condition Pressure outlet
Initial gauge pressure Zero Pascal
Inlet temperature 300 K
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
Inner pipe Annulus pipe
Figure 21. Velocity vector for Heat exchanger with twisted tape insert
Inner pipe Annulus pipe
Figure 22. Velocity vector for Heat exchanger with helical tape insert
Inner pipe Annulus pipe
Figure 23. Velocity vector for Heat exchanger with both twisted and
helical tape
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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
exchanger with helical tape insert
Figure 25. Numerical Friction factor vs Reynolds number for heat
exchanger with helical tape insert
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=
4.167, 5.556 and 6.944, are around 1.55 to 3.36, 1.408 to
3.101 and 1.336 to 3.009 times of that in the plain tube.
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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.
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)
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.
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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
International Journal of Emerging Technology and Advanced Engineering
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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