experimental results coiled inverter hx
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Experimental Results of Coiled Flow Inverter Heat Exchanger
This report shows the results obtained of the Coiled Flow Inverter Heat Exchanger to compare
the results of the internal film heat transfer coefficient with the results reported by Kumar et al.
2007 at different Reynolds number. The objective is to demonstrate that is possible to obtain the
same results in order to start to work with phase change of the fluid in this coiled flow inverter
heat exchanger.
The final results present a good agreement with the results presented by Kumar et al. 2007 when
the Reynolds number is between 8,000 and 12,000.
1. Design of the Coiled Flow Inverter Heat Exchanger - CFI
The CFI has been made of copper with an outlet diameter of 6.35 mm the wall thickness of 1.2
mm. the diameter of curvature measured from the center of the inner tube was 100 mm. The pitch
of the coil was taken as 10 mm. The total length of the CFI module was approximately 5.59 m –
see Fig, 1. Each section consists of 4 turns. This CFI is the half of the dimensions used by Kumar
et al. 2007.
Fig. 1 Layout and dimensions of the CFI prototype module made of copper tube
It is advantageous to consider devices, which do not increase the pressure drop and also not affect
the smoothness of the inner wall, but provide enhancement in the degree of fluid mixing. Flow in
a plane normal to the principal flow direction is very effective to enhance fluid mixing and heat-
transfer. In the coiled tubes, the modification of the flow is due to the centrifugal forces caused
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by the curvature of the tube, which produce a secondary flow field with a circulatory motion
pushing the fluid particles toward the core region of the tube –see Fig. 2. Because of the
stabilizing effects of this secondary flow, laminar flow persist too higher Reynolds number value
in helical coils as compared to straight tubes (Kumar et al. 2007).
Fig. 2 Generation of spatially chaotic particle paths in coiled tube by inserting a 90º bend. (Source:Kumar and Nigam, 2005; Castelain et al., 2000)
The strength of secondary flow is characterized by Dean Number:
Eq.1 N De=ℜ/√ λ
Where λ is the curvature ratio and is defined as the ratio of coil diameter to tube diameter i.e., λ
=D/d. Extensive reviews on flow fields in curved ducts were reported byBerger et al. (1983),
Shah and Joshi (1987), Nandakumar and Masliyah (1986) and Saxena and Nigam (1986).
2. Experimental Setup
A schematic diagram of the heat exchanger test facility is shown in Fig. 3. The test facility is
composed of a primary hotloop and a secondary cold loop. The primary hot loop consists of a
heater machine with a storage vessel of 45 lt. where the fluid is heat to maintain a required
temperature. A small gear pump (Model PQ-12 DC) capable of flow rates from 0.011 to 0.0297
lt./s to pump the hot distillate water inside the tubes of the CFI.
The secondary cold loop consists of a small container (45 x 45 x 80 cm) of tap water where the
CFI is placed; a chiller (Model PolyScience) is used to maintain a constant temperature of the tap
water inside the small container and a pump is used just to mix the tap water inside the small
container.
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The temperatures were measured using thermocouples type J of iron-constantan (-40 to +750 ºC;
55 µV/ºC) and type K of chromel-alumel (-200 to +1250 ºC; 41µV/ºC). The type K
thermocouples were used to measure the superficial temperature in the CFI. The internal
temperatures in the CFI and the others temperatures were measured using type J thermocouples.
Fig. 3and 4 show the evaluated temperatures in the experimental setup.
Fig. 3 Experimental setup of the coiled flow inverter heat exchanger.
An Omega adquisitor data PDAQ-55 and PDAQ-1 also were used to obtain and save the
measurement data of the temperatures, these data information were stored and visualized in a
laptop computer using LabView. Small transparent hoses that support temperatures of 90 ºC were
used for the hydraulics connections.
More detail of the equipment used can be seen in Annex A.
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Fig. 4 Thermocouples connected in the CFI heat exchanger
The volume flow was obtained for each pump independently using a chronometer and scale
recipient also the ambient temperature was measured.
Table 1. Volume flow of the pumps for different voltage used in the heat exchanger
lt/minTemp. 45 ºCVoltag
e Pump-hot3.0 0.5884.5 1.0536.0 1.2927.5 1.6099.0 1.903
3. Brief Theory and Equations for the CFI Heat Exchanger
Kumar et al. 2007 based on the experimental measurements developed new empirical correlations
for the fluid inside the tube for twodifferent range of Reynolds number as
Eq.2 N ui=0.08825 ∙ R eb0.7 ∙ Prb
0.4∙ λ−0.1 for Reb< 10,000Eq.3 N ui=0.0271 ∙ R eb
0.85 ∙Prb0.4 ∙ λ−0.1 for Reb> 10,000
T_hot, out
Tsup3
Tsup, out
Tsup2
Tsup1
Tsup4
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The maximum difference between the model resultsand the experimental data was
approximately±4%. The mechanism responsible for the enhancement in heat transfer in the tube
side is theperiodic switching of coil axis in the downstream direction.
Fig. 5 Inner heat-transfer coefficient vs. Reynolds number for various process conditions in the CFI heat exchanger.
The Reynolds number inside tubes can be defined as follow:
Eq.4 ℜi , b=4 ∙mi
π ∙ μi ∙d i
Where mi is the mass flow inside the tube (kg/s), µi is the viscosity of the fluid (Pa.s) and di is the
inner diameter of the tube (m).
Fig. 5illustrates the comparison of experimental values of fully developed Nusselt number in the
tube side of the heat exchanger with the empirical correlation predictions proposed by Kumar et
al. 2007.
In this case the following equations and procedures will be used to calculate our experimental
Nusselt number.
The values must be evaluated when steady state is reached. The hot side will be calculated with:
Eq.5 q ' hot=mhot ∙Cphot ∙¿¿
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Where q ' hot is the heat transfer rate per unit of length in W/m, L is the total length of the CFI in
m, mhot is the mass flow of the distillate water in the tube side in kg/s, Cphotis the specific heat of
the distillate water in the tube side in J/kg.K.The cold side will be kept at the same temperature in
the entire small container; this means that the heat must be approximately zero. The properties for
the distillate water will be evaluated using the IAPWS correlations (www.x-eng.com).
Then the inside wall temperature Tsup,iwill be calculated using the Fourier’s Law for heat
conduction in a tube:
Eq.6 q ' hot=2π ∙k t
ln (Do/Di)∙(T¿ ,i−T ¿ , o)
Where k t is the thermal conductivity of the copper in this case with a value of 401 W/m.K. The
superficial temperature will be calculated considering the average of the six values of the
thermocouples –see Fig. 3 and 4.
The internal convective heat transfer coefficient hi will be calculated using the Newton’s Law of
convective heat transfer mechanism:
Eq.7 q ' hot=h i ∙ π Di ∙ (T i−T ¿ , i )
Where the temperature of the fluid T i will be the average temperature between the inlet and outlet
internal temperature in the CFI heat exchanger.
Finally the experimental Nusselt number will be evaluated using the following equation:
Eq.8 N ui=h i ∙ d i /k f ,i
All these equations were introduced in a program in Excel and LabView for an easy visualization
and analysis of the results.
For comparative purposes also the correlation for straight smooth tube proposed by Gnielinski for
the average Nusselt number will be considered (Kakac, 2002):
Eq.9 N ui =(f2 )( Re-1000 ) Pr
1+12.7(f2 )0.5(Pr
23 -1)
For 2,300 < Re < 10,000 and Pr> 0.7
Where f is the friction factor defined as:
Eq.10 f=(1.58lnRe−3.28)−2
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4. Experimental Results
The data values of the temperatures and volume flow were manipulated in Excel® to obtain the
thermal and heat transfer results of the small shell and tube heat exchanger prototype. The scans
of the measurements were taken every 10 seconds. The volume flow of the hot side was changed
in order to obtain different range of Reynolds number.
1 17 33 49 65 81 97 1131291451611771932092252412572732893053213373533693854014170.000
0.005
0.010
0.015
0.020
0.025
0.030
0.035
m_hot, kg/s
Scans
m,
kg/s
Fig. 6 Mass flow profile in the CFI heat exchanger
1 17 33 49 65 81 97 11312914516117719320922524125727328930532133735336938540141720
25
30
35
40
45
Thot, out, °C Thot_in, °CTcold_in Tcold_out
T, °C
Fig. 7 Temperature Profile of the CFI heat exchanger
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1 17 33 49 65 81 97 1131291451611771932092252412572732893053213373533693854014170
200
400
600
800
1000Q_hot, WQ_cold, W
Scans
Q, W
Fig. 8 Power profile of the CFI heat exchanger
1 20 39 58 77 96 11513415317219121022924826728630532434336238140041930
32
34
36
38
40
42
44
Thot_in, °C Tsup1Tsup2 Tsup3Tsup4 Thot, out, °C
T, °C
Fig. 9 Superficial temperature profile in the CFI heat exchanger
1 17 33 49 65 81 97 113129145161177193209225241257273289305321337353369385401417-1
01
23
4
56
7
89
Delta_hot, °CDelta T_cold
T, °C
Fig. 10 Delta T temperature profile in the CFI heat exchanger
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From Fig. 6 to Fig. 10 it can see the thermal results obtained from the experimental setup of the
CFI heat exchanger. The values to calculate the Nusselt number were taken from the power and
temperature profile graphics where steady state was reached. The criterion for thermal
equilibrium is when the qhot and qcold are constant and qcold tends to zero.
Fig. 11 and Fig. 12 show the results and comparison of the experimental Nusselt number with the
correlation proposed by Kumar et al. 2007. The results show a good agreement when Reynolds is
between 9,000 and 12,000 with anaverage difference of 5% with the correlation of Kumar et al.
2007. When the Reynolds number is between 12,000 and 14,000 the average difference is of 11%
but above the value obtained by the correlation of Kumar et al. 2007.
6,000 7,000 8,000 9,000 10,000 11,000 12,000 13,000 14,000 15,000 0
20
40
60
80
100
120
140
160
180Nu_i theorNu_i experNu_i straight tube
Re
Nu_
i
Fig. 11 Nusselt number profile for different Reynolds number
20 40 60 80 100 120 140 16020
40
60
80
100
120
140
160Nu_i exper
Nu_i Theoretical
Nu_
i exp
erim
enta
l
Fig. 12 Comparison of the Nusselt proposed by Kumar et al. 2007 and the experimental Nusselt
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6,000 7,000 8,000 9,000 10,000 11,000 12,000 13,000 14,000 15,000 0.0
0.5
1.0
1.5
2.0
2.5
3.0
3.5
4.0
ΔT, in-sup1ΔT, sup2-sup3ΔT, sup3-sup4ΔT, sup4-out
Re
Del
ta T
, ºC
Fig. 13 Delta T superficial temperatures per section on the CFI heat exchanger for different Reynolds number
Fig. 13 shows the superficial temperature profile along the arms of the CFI for different Reynolds
number. As it can see in all the evaluated range the major temperature difference occurs in the
first arm. This means that the heat flux is not constant along the arms of the CFI heat exchanger.
Table 2. Statistical analysis of the results obtained from the CFI heat exchanger experimental setup
Voltage – Hot Pump 3V 4.5V 6V 7.5V 9VReynolds 5,184 7,227 8,842 11,512 14,296St. Dev. 3.53 7.65 6.07 10.49 9.37Nu_i, experimental 30.83 50.22 79.49 127.79 187.15St. Dev. 0.97 2 6 11 25Nu_i, theor - Kumar et al. 2007 47.92 59.95 69.15 104.03 124.38St. Dev. 1.92 2.4 2.77 4.16 4.98Nu_i, straight tube 35.71 49.15 59.47 75.75 91.37Qhot, W 553 628 596 652 701St. Dev. 2.91 4.34 5.07 6.76 8.29St. Dev. in percentage 0.53% 0.69% 0.85% 1.04% 1.18%
Table 2 and Fig. 14 show the standard deviation of the experimental results of the different
measurements performed in the CFI heat exchanger, the major deviation results when the
Reynolds number is up to 12,000.More exhaustive analysis must be done in order to explain this
phenomenon, one explanation is the possibility of the mass flow variation at high voltage.
Fig. 15 shows the influence of the curvature ratio ʎ in the Nusselt number for different Reynolds.
As it can observe, at Reynolds number greater than 10,000 the Nusselt starts to increase when the
curvature ratio is small, this is due to a reduction in the diameter curvature which increase the
centrifugal forces in the fluid inside the tube.
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4,000 6,000 8,000 10,000 12,000 14,000 16,000 0
20
40
60
80
100
120
140
160
180
200
47.92 59.95 69.15
104.03
124.38
30.83 50.22
79.49
127.79
187.15 Nu_i, exp
Nu_i, theor - Kumar et al. 2007
Nu_i, straight tube
Re
Nu_
i
Fig. 14 Results of the statistical analysis of the experimental Nusselt number
4000 6000 8000 10000 12000 14000 160000
20
40
60
80
100
120
140
160
ʎ_1 25.00 ʎ_2 16.67 ʎ_3 8.33
Re
Nu_
i
Fig. 15 Variation of the curvature ratio ʎ=D/d for different Reynolds number and different curve diameter: D_1=0.15 m, D_2=0.1 m, D_3=0.05m. Tube diameter d=0.006 m.
5. Conclusions
Thirteen experiments were performed in the CFI experimental setup from 26/09/2012 to
10/10/2012 but only the last six experiments were used since in the other experiments it was not
possible to obtain steady state. Also two different configurations in the cold side were used in
order to reach steady state; the major problem to reach steady state was the big volume of water
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compare with the small volume in the CFI heat exchanger. Also the capacity of the chiller was
less than the capacity of the heater, for that reason there were no isolation on to top to avoid an
excess heating of the cold water.
The results present a good agreement with the results presented by Kumar et al. 2007 when the
Reynolds number is between 8,000 and 12,000.In this range, the percentage of error of the
experimental results compare with the correlation proposed by Kumar et al. 2007 is of ±20%.
An uncertainty analysis must be performed in order to evaluate the error associated with the
calculated Nusselt and the uncertainties in the measurements of the temperatures and mass flow.
6. References
Kumar, V., Monisha, M., Gupta, A.K., Nigam, K.D.P., 2007.Colied flow inverter as a heat
exchanger. Chemical Engineering Science 62, 2386-2396.
Kakaç, S., Liu, H., 2002.Heat exchangers selection, rating and thermal design.CRC Press second
edition ISBN 0-8493-0902-6.
CengelYunus A., 2002. Heat Transfer: A practical approach.McGraw Hill second edition ISBN
0072458933.
Holman, J.P. 2002. Heat Transfer. 9 edition. McGraw-Hill.ISBN 0070634513.
7. Annexes
Annex A – Photos of the equipment used in the experimental setup
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Fig. 16 Experimental setup of the shell and tube heat exchanger prototype.
Fig. 17 Heater machine (left) and Chiller machine (right) used in the experimental setup
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Fig. 18 Gear pump model PQ-12 (left) and volume flow for different voltage (right)
Fig. 19 Adquisitor data Omega used in the experimental setup