Experimental Results Coiled Inverter HX

E x p e r i m e n t a l R e s u l t s C o i l e d F l o w I n v e r t e r H e a t E x c h a n g e r P a g e | 1

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


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.


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.


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


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 ∙¿¿


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


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


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


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


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.


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


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


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


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


Fig. 20 LabView Interface to visualize experimental results in real time

Experimental Results Coiled Inverter HX

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