Boiling pressure drop and local heat transfer distribution of helical coils with water at low pressure

International Journal of Thermal Sciences 114 (2017) 44e63

Contents lists available at ScienceDirect

International Journal of Thermal Sciences journal homepage: www.elsevier.com/locate/ijts

Boiling pressure drop and local heat transfer distribution of helical coils with water at low pressure B.K. Hardik, S.V. Prabhu* Department of Mechanical Engineering, Indian Institute of Technology, Bombay, India

a r t i c l e i n f o

a b s t r a c t

Article history: Received 9 August 2016 Received in revised form 28 November 2016 Accepted 7 December 2016

The objective of the present work is to study the influence of curvature on local boiling heat transfer coefficient and two-phase pressure drop in helically coiled tubes with water as the working medium. In helically coiled tubes, the geometric parameters like pipe diameter and coil diameter vary the curvature and hence secondary flow which affects the heat transfer distribution and pressure drop. The present work investigates the characteristics of flow boiling in helically coiled tubes. Very less information is available on the influence of curvature on flow boiling system. The local wall temperature is measured not only in the axial direction (along the length of coil) but also in the circumferential direction using thermal imaging technique. Experiments are performed with six helically coiled test sections made of SS 304 tubes having inner diameters varying from 6 to 10 mm. The coil diameter to the tube diameter ratio ranges from 14 to 58 and coil pitch is 50 mm. The effect of geometric and operating parameters like tube diameter, coil diameter, heat flux and mass flux on local boiling heat transfer coefficient and two-phase pressure drop is analysed. In the subcooled region and in a low quality region, boiling heat transfer coefficient in helical coils is much higher (12%e100%) than in straight tubes. However, in a high quality region, the boiling heat transfer coefficient in helical coils is same as in straight tubes. A correlation is suggested for two-phase pressure drop in helical coils. © 2016 Elsevier Masson SAS. All rights reserved.

Keywords: Local heat transfer coefficient Two-phase pressure drop Low pressure Flow boiling Infrared thermal camera

1. Introduction The heat transfer through helical coil is better choice where the space for heat exchanger is limited and difficult to lay straight pipe. Literature on single phase flow through helical coil shows the enhancement in heat transfer coefficient due to secondary flow. Compact design, easy manufacturing and high heat transfer efficiency compared to straight tube make the helical coil favourable for heat exchanger application. Helical coiled steam generators are of major interest in the nuclear industry for electricity production. Boiling phenomena is studied well for flow inside a straight tube. However, boiling mechanism inside helical coils may differ from straight tubes due to phase separation with low density vapour being inner side and high density liquid on outer side of curved tube or the appearance of thin liquid film on circumference caused by the gravity and centrifugal forces. Thus, a large temperature distribution may occur on the circumference of tube wall. This may

* Corresponding author. Department of Mechanical Engineering, Indian Institute of Technology, Bombay, Powai, Mumbai, Pin: 400 076, India. E-mail addresses: [email protected] (B.K. Hardik), [email protected] (S.V. Prabhu). http://dx.doi.org/10.1016/j.ijthermalsci.2016.12.004 1290-0729/© 2016 Elsevier Masson SAS. All rights reserved.

affect the heat transfer performance and can cause dryout of liquid film on inner side of curved tube. Therefore, a detailed study of the wall temperature distribution and heat transfer characteristics in the helical coils is required. The ranges for subcooled and saturated flow strongly depend on the saturation temperature and hence saturation pressure. In the saturated boiling region, distribution of local bulk fluid temperature is dependent on the pressure drop distribution. To predict the local heat transfer coefficient accurately, it is necessary to know the saturation pressure at different points in the test sections. The present section reviews the characteristics of two-phase pressure drop and heat transfer coefficient in different region i.e. subcooled and saturated, of flow boiling. Published correlations of flow boiling heat transfer in helical coils are collated. This review presents the status of the research in the area of twophase pressure drop in helical coils.

1.1. Review of flow boiling heat transfer inside helical coils Naphon and Wongwises [1] and Vashisth et al. [2] conducted a review on single and two phase flow in curved tubes. They state that, in spite of wide range of applications of curved geometry in industrial devices, there is a lack of fundamental knowledge and

B.K. Hardik, S.V. Prabhu / International Journal of Thermal Sciences 114 (2017) 44e63

Nomenclature

Symbol Cp Specific heat at constant pressure J=kgK d Diameter of tube m D Diameter of helical coil m Deviation ðCcal  Cexp Þ=Cexp  100 % Enhancement ðCHelical  CStraight Þ=CStraight  100 % f Friction factor G Mass flux kg=m2 s g Gravitational constant m=s2 h Heat transfer coefficient W=m2 K i Enthalpy J=kg k Thermal conductivity W=mK L Length m M Molecular Weight g/mol m_ Mass flow rate kg=s P Pressure N=m2 Q Heat supply W 00 q Heat flux W=m2 T Temperature x Quality of steam !0:1
 X, XLM Lockhart Martinelli 0:9
0:5parameter rg ml X ¼ 1x m r x l

Greek Ø

m r s

g

DP

Two phase flow multiplier ∅2 ¼ DTP;fric P1P Dynamic viscosity N$s=m2 Density kg=m3 Surface tension N=m

literature studied on curved tubes compare to that of straight tubes. Few works on the two-phase heat transfer characteristics in helically coiled tubes are reported. There are contradictory conclusions reported in the literature on the influence of the secondary flow on the heat transfer coefficient. Several authors report almost no influence of secondary flow and suggest straight tube heat transfer correlation for helical coils. However, few authors report enhancement of heat transfer due to the secondary movement of bulk fluid and report a correlation for heat transfer for helical coils. The overview of literature studied on boiling heat transfer in helical coils is given in Table 1. It may be observed that most of the works show that the straight tube heat transfer correlations slightly underpredict in comparison with the experimental data of helical coils. Table 1 shows that the boiling mechanism inside helical coils is not conclusive. Kozeki et al. [3], Hwang et al. [4], Chung et al. [5] heat transfer experiments on water and Ami et al. [6] experiments with liquid nitrogen at saturated boiling condition shows nearly constant value of heat transfer coefficient with increase of thermodynamic equilibrium quality. Thus, nucleate boiling may be a dominant phenomenon. However, others suggest an increase in heat transfer coefficient with quality. Hence, boiling mechanism includes both nucleate boiling and convective boiling. Available correlations of helical coil heat transfer coefficient are collated in Table 1. 1.2. Review of two phase pressure drop inside helical coils Compared to heat transfer, reasonably large body of literature is available on two-phase pressure drop in helical coils. The overview

Subscript acc b f fg fric g h l lo P sat SC sys T TP tt lt w

45

Acceleration Bulk Film Fluid to gas Friction Gas Heated Liquid Liquid only Phase Saturated Subcooled System Total Two phase Turbulent liquid and Turbulent vapour Laminar liquid and Turbulent vapour Wall

Abbreviation HTC Heat Transfer Coefficient Dimensionless number 00 Bo Boiling number Bo ¼ q =Gifg Ja Jakob number Ja ¼ Cp$DTsc =ifg Nu Nessult number Nu ¼ h$d=K Pr Prandtl Number Pr ¼ m$Cp=K _ pdm Re Reynolds number Re ¼ 4m=

of literature studied on two-phase pressure drop in helical coils is given in Table 2. Most of the literature on two-phase pressure drop reported an increase in the pressure drop compared to that of straight tube. Literature on two-phase pressure drop divides into gas liquid two-phase flow (Adiabatic) and boiling two-phase flow (Diabatic). Most of the studies on two-phase pressure drop are referred gas liquid co-current flow. Less work is done on boiling pressure drop in helical coils. Most of the authors in the literature reported their own correlation for two-phase pressure drop. This may be because of the complexities involved in studying the twophase flow in helical coils. Literature review on two-phase pressure drop concluded that pressure drop in helical coils can correlated with LockhartMartinelli parameter. Wongwises and Polsongkram [12], Nariai et al. [9] and many others derived their correlations in the form of Lockhart-Martinelli parameter for diabatic and adiabatic flow. Enhancement of pressure drop in two-phase flow is almost same as in single phase flow. Available correlation of diabatic two-phase pressure drop and the detail of operational and geometry experiments condition are collated in Table 2. Few important correlations for adiabatic two-phase pressure drop are also presented in Table 2. Following are the conclusions that may be drawn from literature review.
No work is reported on subcooled heat transfer in helical coil
No literature is available on the circumferential variation in the wall temperature distribution and heat transfer distribution.

46

B.K. Hardik, S.V. Prabhu / International Journal of Thermal Sciences 114 (2017) 44e63

Table 1 Details of literature work on boiling heat transfer coefficient. Authors

Fluid/Condition

Operating range P Temperature measurement Geometric range (MPa), G (kg/m2S), q0 0 technique d (mm), D (mm), L (mm), p (mm), t (mm) (kW/m2), T ( C)

Owhadi et al. [7] (1968)

Water; Uniform heat flux; Circumferential average; Vertical Water at 1 atm

P ¼ Atmospheric L ¼ 2850; d ¼ 12.5; Fluid - using pressure profile; HTC is higher on outer side of helical coils; G ¼ 79e314 t ¼ 1.7; Wall - Four thermocouple at HTC in helical coils is same as straight tubes; q0 0 ¼ 60e255.5 D ¼ 250.4, 520.7 Chen (1963) [7] correlation for HTC is working well; nine locations D/d ¼ 20, 41.8 x ¼ 0.014e1 Parameter range is same as Owhadi et al. [7]; HTC correlated by the Lockhart-Martinelli parameters, using the Seban correlation; HTC at 270 position are significantly higher and at the 90 position are significantly lower than those at the 0 and 180 positions for low and medium quality; For high quality thing become opposite 90 and 270 are same and higher than 0 and 180

Water; Uniform heat flux; Circumferential average; Horizontal

d ¼ 9; D ¼ 292; p ¼ 30; t ¼ 1.5; L ¼ 1380; D/d ¼ 32.4

Conclusions

Bell and Owhadi [8] (1969) P ¼ 0.5e2.1 Kozeki et al. Water heated water; d ¼ 15.5, 16.1; Fluid - bulk temperature very Heat transfer coefficient is constant along the length of t ¼ 3.1; D ¼ 628, 682; G ¼ 161e486 Circumferential coil; [3] linearly x ¼ 0e1 L ¼ 45000; average; Vertical (1970) Wall - Four thermocouple at Pressure drop is greater than that of straight tube; q0 0 ¼ 151e350 D/d ¼ 40.5e44 HTC in coiled tubes is different than that of straight tube; three different locations P ¼ 2, 3, 5 Fluid - One thermocouple at Coil curvature has no significant effect on average HTC; D ¼ 595; d ¼ 14.3; Nariai et al. Water Heated Schrock-Grassman correlation for straight tube works centre at fifteen different t ¼ 2.85; L ¼ 56000; D/ G ¼ 150e850 Water; Total [9] well; locations d ¼ 41.6 Average; Vertical (1982) 1=3 ­4 ­2=3 0:8 Schrock and Grossman (1962) [9] Correlation Nutp ¼ 170Relo Prl ðBoþ1:5  10 X tt Þ Kaji et al. Fluid - In Japanese R113 D ¼ 165, 320 P ¼ 0.39 No circumferential HTC difference in Nucleate boiling; [10] Wall - Four thermocouple at HTC non-dimensionalized with single phase helical Uniform heat flux; d ¼ 10 G ¼ 305e1650 (1998) Circumferential D/d ¼ 16.5, 32 q0 0 ¼ 30e200 sixteen locations correlation match with straight tube; xin ¼ 0.1 to 0.65 average; Vertical Derived correlation for HTC )
1=12 ( hTP ¼ ½ð4  104 BoRe­0:12 Þ3 þf2:6ð1=X tt Þ0:95 g3 1=3 0:4 0:061 hlo Nulo ¼ Pr41 Re5=6 Dd 1þ 2:5 1=6 ½Reðd=DÞ

Zhao et al. [11] (2003)

htp =hDB ¼ 1:6X ­0:74 þ183000Bo1:46 tt Wongwises R134a heated with L ¼ 5786; d ¼ 7.2; do ¼ 9.52; Water; [12] D ¼ 305; Total Average; (2006) D/d ¼ 42.36 Vertical;



x ¼ 0e0.95; P ¼ 0.5e3.5 q0 0 ¼ 0e900 G ¼ 236e943

Fluid - linear interpolation of inlet and outlet Wall - Four thermocouple at nine different location

New modified SchrockeGrossman correlation flow boiling heat transfer; SchrockeGrossman's correlation works well, slightly under predict the data; Chen correlation also works well, data is well centred;

G ¼ 400e800 Q0 0 ¼ 5e10

Fluid - average of inlet and outlet; Wall - Four thermocouple at seven different locations

Studied the effect of different parameters on HTC; HTC is enhanced by 30e37%; Developed correlations for the convection heat transfer coefficient; 

0:5 
0:5 m rg d DeEq ¼ Rel þReg mg r D

Nutp ¼ 6895:98De0:432 Prl­5:055 ðBo104 Þ0:132 Xtt ­0:0238 Eq

Rel ¼

Gð1­xÞd

ml

; Reg ¼ Gxd mg

l

Suzuki et al. [13] (2009) Ami et al. [6] (2011) Chen et al. [14] (2011)

Aria et al. [15] (2012)

Water heated with Oil Local Liquid Nitrogen Uniform heat flux; Circumferential average; Vertical R134a; Uniform heat flux; Circumferential average; Vertical

l

L ¼ 1571; d ¼ 10; t ¼ 1; D ¼ 200 D/d ¼ 20 L ¼ 3150; D ¼ 100 d ¼ 4; D/d ¼ 25

UL ¼ 0.02e0.21 Toil ¼ 200e210 Tin ¼ 20 G ¼ 200e710 q0 0 ¼ 0e60; P ¼ 0.3; DTsub ¼ 10

Circumferential distribution and Temporal variation of Fluid - not explain Wall - Four thermocouple at wall temperature to understand the mechanism of boiling heat transfer in low quality conditions five locations Schrock-Grossman (1962) [6] Correlation works well; Fluid - not explain Wall - Four thermocouple at HTC remain constant with the increase in quality; eleven locations

L ¼ 7070; d ¼ 7.6 t ¼ 1.2; D ¼ 300 p ¼ 40 D/d ¼ 39.5

P ¼ 0.2e0.75 G ¼ 50e260 x ¼ 0.18e0.4

Fluid - linear interpolation of The outside temperature was lower than the inside one; Bai (1997) [14] and Kozeki [3] correlation is not working; inlet and outlet; Wall - Four thermocouple at Derived New heat transfer coefficient correlations; eight different location

htp =hlo ¼ 2:84X ­0:27 þð46162Bo1:15  0:88Þ tt R134a heated with L ¼ 5786; D ¼ 305; p ¼ 45; Water; t ¼ 0.62; d ¼ 8.32 Total Average; Outer di ¼ 29 Vertical D/d ¼ 36.7

x ¼ 0.1e0.8 G ¼ 112, 132, 152

hlo ¼ 0:023Re0:85 Pr0:4 ðd=DÞ0:1 Heat transfer coefficient and pressure drop is enhanced; Fluid - at average system pressure between inlet and Wongwises and Polsongkram correlation of HTC work well, slightly underpredict results (þ2 to 28%); outlet Wall - Two thermocouple at Developed modified Wongwises correlation for heat transfer coefficient; six location

Nutp ¼ 7850De0:432 Pr­5:055 ðBo104 Þ0:125 Xtt ­0:036 Eq l Elsayed et al. R134a; Uniform heat flux; Total [16] Average; Vertical (2012)

D ¼ 30, 60 d ¼ 1.1e2.8 D/d ¼ 10.7e54.5

Chung et al. Water; Uniform heat flux; [5] Circumferential (2014) average; Vertical Hwang et al. Water; Uniform heat flux; [4] Circumferential (2014) average; Vertical Santini et al. Water; Uniform heat flux; [17] Circumferential (2016) average; Vertical

D ¼ 577, 937, 1297 L ¼ 2050 d ¼ 12; t ¼ 2.5 D/d ¼ 48, 78, 108 d ¼ 12; t ¼ 2.5 D ¼ 606, 977 Lh ¼ 2000 D/d ¼ 50.5, 81.4 d ¼ 12.53; D ¼ 1000; p ¼ 790 t ¼ 2.35; L ¼ 24000; D/ d ¼ 79.8

G ¼ 123e450; q0 0 ¼ 2.5e12; P ¼ 3.5e6; x ¼ 0.2e0.9 P ¼ 1e6 G ¼ 176.8e530.5

G ¼ 88.4e530.5 P ¼ 1e6 q0 0 ¼ 30e1145.3

Coil diameter enhanced HTC by 150%; Tube diameter enhanced HTC by 63%; Derived correlation for the boiling heat transfer coefficient; SteinereTaborek correlation works reasonably well Fluid - not explain slightly under predict the data; Wall - Four/two thermocouple at twenty four Shows circumferential temp distribution; HTC remain constant with increase in quality; locations Fluid - outlet of test section; Steiner and Taborek HTC correlation for straight vertical Wall - Four thermocouple at tubes works well, slightly under predict results; nineteen different locations HTC remain constant with increase in quality;

P¼2-6 G ¼ 200e800 q0 0 ¼ 40e230

Fluid - using pressure profile; Curvature effects on flow boiling are small; Wall - Four thermocouple at Chen, Shah, Gungor and wintorton, liu and wintorton, kandlikar, are working well, slightly underpredict data; twenty one locations

Fluid - average of inlet and outlet; Wall - At each half turn one thermocouple

B.K. Hardik, S.V. Prabhu / International Journal of Thermal Sciences 114 (2017) 44e63 Table 2 Available pressure drop correlations for two-phase flow [7,18,9,19,11,12,16,20,21,22,23,24,25,26].

47

48

B.K. Hardik, S.V. Prabhu / International Journal of Thermal Sciences 114 (2017) 44e63


Literature on helical coil heat transfer coefficient shows either enhancement in comparison with the straight tube or similar to straight tube.
Literature available on boiling heat transfer coefficient is not conclusive.
Numerous works are reported on two-phase pressure drop in helical coils. Most of the reported work is studied adiabatic two phase e.g. Air þ Water or Air þ Mixture of different liquid. Very few works are available on boiling two-phase pressure drop. Literature shows the conventional method to measure local heat transfer coefficient by placing thermocouples at different circumferential and axial locations. Table 1 shows that maximum twenty thermocouples placed at axial location of 2 m long test section gives resolution of around 100 mm. Maximum four thermocouple placed around circumference gives only four circumferential data points. Because of this, only average heat transfer coefficient results are reported. However, there is a need to measure the local heat transfer distribution in different regions of flow boiling in helical coils for identifying the hot spots. Hence, in the present study, local wall temperature distribution on inner side and outer side of the helical coil is measured using non-intrusive infrared thermal imaging technique with a resolution of around 0.5 mm. Local heat transfer distribution analysed in present work on inner side and outer side of helical coils helps in designing helical coil heat exchanger. Subcooled flow boiling in helical coils shows large enhancement compared to straight tubes in present study. This will encourage further research on this area with different parameters range. The parametric study helps in understanding the effect of heat flux, mass flux, tube diameter and coil curvature on the boiling heat transfer coefficient and two-phase pressure drop. Correlation for frictional pressure drop is presented in order to accurately calculate the two-phase pressure drop in a low pressure helical coil system. Axial distribution of wall temperature and heat transfer coefficient presented in this study would be serve as benchmark data for the validation of computational results of flow boiling. The objective of the present work is to study the influence of curvature on local boiling heat transfer coefficient and two-phase pressure drop in helically coiled tubes. The present work studies the characteristics of flow boiling in helical coils. The local wall temperature is measured in the axial direction and in the circumferential direction using thermal imaging technique. Experiments are performed with six helically coiled test sections made of SS 304 tubes having inner diameters varying from 6 to 10 mm. The coil diameter to the tube diameter ratio ranges from 14 to 58. The effect of geometric and operating parameters like tube diameter, coil diameter, heat flux and mass flux on local boiling heat transfer coefficient and two-phase pressure drop is investigated. 2. Description of the experimental rig Experimental facility as shown in Fig. 1, is an open loop flow system with water serving as working fluid. The test facility consists of an insulated water tank, magnetically coupled sealless gear pump, globe valve, ball valves, water mixing thermos flask. The system is facilitated to perform experiments on straight horizontal tube test section and helical coil test section. The gear pump with a mass flow rate capacity 0e360 g/s is driven by a D. C. motor. The D. C. motor speed is varied between 0 and 3500 rpm by a controller. The pressure transmitter, mass flow meter and thermocouples are instrumented with system to measure the pressure drop and heat transfer coefficient in the test sections. Bulk fluid temperature at the inlet and outlet of the test sections are measured with K-type thermocouples. Three thermocouples are submerged in an

insulated water tank to measure the inlet bulk fluid temperature and the outlet bulk fluid temperature is measured with five thermocouples immerse in an insulated thermo flask. All thermocouples are directly in contact with the fluid to measure the actual fluid temperature. Themoteknix - VisIR 640 Infra-Red thermal camera is used to measure the wall temperature of the test section. Thermal camera measures the intensity of radiation emitted from the test section surface. The intensity depends on the emissivity and the temperature of the wall. The test section is painted with a thin coat of high temperature black board paint (make: Pyromark) to have an emissivity of 0.85. The differential pressure transmitters range 0.622e62.2 kPa and 0e5 bar are used to measure the pressure drop across test sections. The pressure transmitter range 0e10 bar is used to measure the system pressure at the inlet of the test section. Electromagnetic mass flow meter with two different ranges adjustment 0e50 g/s and 50e500 g/s is used to measure low flow rate and high flow rate of water accurately. All the test sections are heated with Joule heating by passing DC current through the tube wall maintaining the uniform heat flux condition. Low voltage high current DC power supply (make: Aplab, Model: CVCC50kW) is used to supply power through the test section. The current is measured using the power supply digital reading, while the voltage is measured using digital multimeter. These are recorded manually. All the instruments are connected to Data Acquisition System (DAS) which is in turn connected to a computer. Eight thermocouple ports of DAS are connected to thermocouple connections fitted at the open end of the thermocouples. The mass flow meter and pressure transmitters are connected to DAS through 100 U registers to convert current signal (4e20 mA) into voltage signal (0.4e2 V). All the readings are taken after the reaching of steady state condition. Helical coil test sections used for experiments are made of stainless steel SS304 as shown in Fig. 1. Pressure taps are drilled at disturbance-free part of the straight lengths before and after the test section. Smoothness of inner surface of pipe is checked after the drilling of vents and brazing of copper tube on pipe vent for pressure taps. Pressure drop occurred in the inlet single phase length is subtracted from the total pressure drop data of the combination so as to give the pressure drop data for the two phase portion only. The geometric details of the six helical coils tested and operating parameters covered in the present study are listed in Table 3. The curvature of the coils is characterized by the ratio of coil to the tube diameter (inverse of curvature ratio). 3. Data reduction 3.1. Heat transfer coefficient The heat supplied to the helical coil test sections is calculated from the supplied electric current multiplied by the voltage across the test section as shown in Eq. (1).

Q ¼ VI

(1)

Heat loss from test section at given heat load is subtracted from the heat supply. Theoretical calculation is carried out to calculate convective and radiation heat loss from the test section outer wall surface to the atmosphere. Heat loss calculation procedure is given in Appendix A. Percentage of heat loss depends on the wall temperature and total heat supply. In the present study, the percentage of heat loss is varying from 0.2% to 3% of total heat supply. The heat flux is calculated from Eqs. (2) and (3).

Qconv ¼ Q  Qloss

(2)

B.K. Hardik, S.V. Prabhu / International Journal of Thermal Sciences 114 (2017) 44e63

49

Fig. 1. Schematic of the experimental set-up. Table 3 Geometric and parametric details of test sections used in analysis. Coil No

1 2 3 4 5 6

00

q ¼

Tube characteristics

Coil characteristics

Curvature ratio

System pressure

Mass flux

Heat flux

Quality

Inner diameter

Outer diameter

Mean diameter

Pitch

d (mm)

do (mm)

D (mm)

P (mm)

D/d

P (bar)

G (kg/m2s)

q0 0 (kW/m2)

x

6 6 8 8 9.7 10

8 8 9.4 9.4 11 11

162 347 137 383 140 301

50 50 50 50 50 50

27 57.83 17.13 47.88 14.43 30.1

1.2e4.8 1.2e4.0 1.2e3.6 1.2e3.6 1.1e3.1 1.1e2.8

228e1081 248e1278 192e844 166e525 108e567 92e491

140e2830 145e2361 229e2066 260e1778 211e1426 200e1452

0.23e0.95 0.23e0.78 0.20e0.94 0.20e0.92 0.23e0.96 0.23e0.94

Qconv Q  Qloss ¼ pdLh pdLh

(3)

In the subcooled flow boiling region, the liquid properties are calculated at local bulk fluid temperature. The local bulk fluid temperature is measured by the linear interpolation of inlet and saturation temperature at system pressure. In the saturated flow boiling region, the liquid properties are calculated at the local saturation temperature. Local saturation temperature decreases from the saturation point to the exit of test section. The variation of saturation temperature between the inlet and exit of test section depends on the local pressure. The pressure at exit of the test section is calculated from system pressure and pressure drop across the test section. The local pressure is calculated using the pressure drop profile given by modified Hardik and Prabhu [27] correlation as given in Section 4.6. Local saturation temperature in the saturated region is calculated using the local pressure. The vapour properties in all the calculations are calculated at local saturation temperature. The thermo-physical properties used in data reduction are calculated from the tabulated values of National Institute of Standards and Technology (NIST). The axial wall temperature distribution of the test section is obtained by averaging ten thermal images for each configuration. Fig. 2 shows the cross section of helical coil test section. Local points show the circumferential temperature points of thermal image. Circumference from 90 to

Fig. 2. Indication of local point for wall temperature measurement on circumference of helical coil.

180 -270 is considered as inner side and 270 -0 -90 is considered as outer side and complete circumference as total. Thermal images show the outer wall temperature of the test section. Inner wall temperature is calculated from measured outer

50

B.K. Hardik, S.V. Prabhu / International Journal of Thermal Sciences 114 (2017) 44e63

wall temperature using one dimensional, steady state heat conduction method with uniform volumetric heat generation across the wall due to electrical heating. The local quality and local heat transfer coefficient in subcooled and saturated region are calculated from Eqs. (4)e(6). An equation (4) gives the quality at a specific length of test section. The length of the test section from where, the subcooled flow transits into saturated flow (zero quality) is calculated from Eq. (7).

xlocal ¼

Qconv L m_ Lh

 il

(4)

ifg

il ¼ Cp ðTsat  Tin Þ

(5)

00

hlocal ¼

q Tw;local  Tb;local

Lðx¼0Þ ¼

(6)

_ p ðTsat  Tin ÞLh mC Qconv

Location Total

hlTotal

Outer Side

The measured experimental pressure drop is the sum of single phase liquid pressure drop, subcooled boiling pressure drop, saturated boiling pressure drop and adiabatic two-phase pressure drop. Fig. 3 shows the schematic of the total pressure drop involving pressure drops in different regions.

DPTotal ¼ DPl þ DPsc þ DPTP

kl d

(8)

Correlation
0:16 D 0:4 kl ¼ 0:0456 Re0:8 local Prlocal d d

hlOuter ¼ 0:104


0:315 D 0:4 kl Re0:8 local Prlocal d d

DP1P ¼ fC

 1 32 m_ 2 L 20 ; fC ¼ fs Reðd=DÞ2 ; fs ¼ 0:079Re0:25 5 2 r d p (16)


DPsc d ¼ 1 þ 32500Bo1:6 Ja1:2 9:53 DP1P

(10)

 (17)

The two-phase pressure drop in a flow boiling system is the sum of pressure drop due to fluid acceleration, frictional pressure drop and gravitational pressure drop as in Eq. (18). The acceleration pressure drop is calculated from separated flow model and void fraction is calculated from Steiner equation [32] as shown in Eq. (19) and (20);

DPTP ¼ DPfric þ DPacc þ DPgravity ("

(9)

(15)

Single phase pressure drop and subcooled boiling pressure drop are generally much lower than boiling and adiabatic two-phase pressure drop. Single phase liquid pressure drop in straight tube portion and helical coil curved portion is calculated from Blasius correlation and Ito's correlation respectively. The subcooled boiling pressure drop is calculated from Eq. (17) reported by Baburajan et al. [31]. In Eq. (17), the single phase pressure drop is calculated from helical coil correlation instead of straight tube correlation which is originally used by Baburajan et al. [31]. In Eq. (17), the tube diameter (d) is in mm and DP1P is adiabatic single phase friction factor with properties taken at saturated temperature.

(7)

Local heat transfer coefficient for a single phase turbulent flow in straight tube is calculated using Dittus-Boelter correlation as given in Eq. (8). Single phase heat transfer coefficient on inner side, outer side and total in helical coil is calculated from Hardik et al. [28] correlations as given in Eqs. 9e11. The local Reynolds number and local Prandtl number are calculated with properties taken at local bulk fluid temperature. Local heat transfer coefficient for subcooled flow boiling and saturated flow boiling in straight tube is calculated from Kandlikar [29] (Eq. (12)) and Kandlikar [30] (Eq. (13) and (14)) correlations respectively as suggested by Hardik and Prabhu [27]. 0:4 hllocal ¼ 0:023Re0:8 local Prlocal

3.2. Pressure drop

DPacc ¼ G2

ð1  xÞ2 x2 þ rl ð1  aÞ rg a

2 x4 a¼ ð1þ0:12ð1xÞÞ

rg

(18) "

#  out

# ) ð1  xÞ2 x2 þ rl ð1  aÞ rg a

(19)

in

i0:25 31 h  ! 1:18ð1xÞ gs rl rg 1x 5 þ þ rg rl G2 r0:5 l x

(20) Inner Side

hlInner ¼ 0:012


0:088 D 0:4 kl Re0:8 local Prlocal d d

00

hSC ¼

q ; Tw  Tb

Twall ¼



q

(11)

00 0:3

1058 Gifg

0:7

þ Tsat

(12)

h1

hTP ¼ maxðhNB ; hCB Þ   hCB ¼ 1:136Co0:9 þ 667:2Bo0:7 ð1  xÞ0:8 hl   ; hNB ¼ 0:6683Co0:2 þ 1058Bo0:7 ð1  xÞ0:8 hl 

1  x 0:8 rg 0:5 ¼ x rl

(13)

Co

(14)

3.3. Uncertainties in the measured and computed parameters The uncertainty of different parameters used in the experimental analysis is shown in Table 4. The uncertainties in the tube diameter, coil diameter and length of the test section are obtained by measuring the values at different locations. Ovilazation of tubes are checked after fabrication of helical coils. Difference in major and minor diameter of tube due to ovilazation is less than 2%. The uncertainties of mass flow rate, temperature, and pressure are calculated by comparing the reading of data acquisition system with the value obtained from standard instruments. The uncertainties of heat flux resulted from the accuracy of the ampere and volt meters. The uncertainty in thermo-physical properties of liquid and vapour are calculated by comparing the correlations with the values of National Institute of Standards and Technology (NIST).

B.K. Hardik, S.V. Prabhu / International Journal of Thermal Sciences 114 (2017) 44e63

51

Fig. 3. Different regions of pressure drop [27].

Table 4 Experimental uncertainties. Parameter

Relative uncertainty (%)

Parameter

Relative uncertainty (%)

Pipe diameter Pipe length Current Voltage Mass flow rate Wall temperature Pressure Bulk temperature Heat flux Mass flux Boiling number Heat transfer coefficient Two-phase pressure drop

1 0.5 0.5 1 1.8 1.3 1.5 1 3 2.7 4 13.5 9.9

Liquid density Liquid viscosity Thermal conductivity Specific heat Vapour density Vapour viscosity Surface tension Latent heat Prandtl number Reynolds number Liquid friction factor Nusselt number Quality

1 3 1 1 1 2 0.5 0.5 3.3 3.6 5.6 7.8 3.4

4. Results and discussion Experimental setup is validated with single phase pressure drop in a straight tube. Experimental friction factor for single phase flow inside a straight tube is measured and compared with Blasius correlation. The deviation between the experimental data and correlation is less than 10%. The wall temperature measurement technique using infrared thermal camera is validated for heat transfer coefficient of single phase in straight horizontal tubes. The maximum deviation is less than 10%. The details of the validation are given in Hardik et al. [28]. Experimental analysis is carried out on helical coil test sections for a single phase flow. Single phase friction factor in helical coils is predicted well with Ito [33] correlation as shown in Eq. (16). The transition from laminar to turbulent flow in helical coils is measured with Ito [33] correlation. A correlation is derived for average and local heat transfer coefficient on inner side and outer side of helical coil for single phase flow. The two-phase flow is analysed with experimental set-up in straight horizontal tubes [27]. Kandlikar [29] correlation for subcooled heat transfer coefficient matches reasonably well with experimental subcooled data. The average deviation with the correlation is less than 10%. Kandlikar [30] correlation for heat transfer coefficient in saturated flow matches reasonably with the experimental results in saturated boiling region. A correlation is derived for two-phase pressure drop in a straight tube for low pressure system. In the present work, experimental analysis is carried out on two-phase flow in helical coils. The wall temperature and heat transfer coefficient is analysed along the axial direction on inner side and outer side of helical coil. The effect of different parameters on heat transfer coefficient and pressure drop is studied. 4.1. Typical distribution of wall temperature and heat transfer coefficient Hardik et al. [28] studied circumferential and axial wall

temperature distribution in a single phase flow inside a helical coil. In single phase flow, inner side wall temperature is higher than outer side wall temperature. Hence, inner side heat transfer coefficient is much lower than the outer side. Hardik and Prabhu [27] shows that the wall temperature distribution during two-phase flow boiling is different than single phase flow in a straight tube. Temperature and heat transfer coefficient distribution on inner side and outer side of a helical coil is shown in Fig. 4 for two-phase flow boiling condition. In a helical coil similar to single phase flow, inner side wall temperature is higher than the outer side wall temperature in two-phase flow. Fig. 4 (A) shows the inner side wall temperature, outer side wall temperature and bulk fluid temperature distribution in subcooled and saturated boiling condition for coil-5. Bulk fluid temperature distribution is calculated from inlet bulk fluid temperature, saturated temperature at inlet and exit of test section and pressure profile. High wall temperature on inner side during single phase flow leads to early starting of boiling. At sufficiently high heat flux, subcooled boiling started on inner side of helical coil, while wall temperature on the outer side is less than the saturation temperature. In the subcooled region, outer side wall temperature increases with the increase in bulk temperature along the axial direction. However, on the inner side, the wall temperature remains constant due to nucleate boiling. Distribution of wall temperature on the inner side of helical coil is similar to that of straight tube. Outer side wall temperature increases with the bulk fluid temperature till the zero quality and then decrease with bulk fluid temperature in saturated boiling region. Fig. 4 (B) shows the heat transfer coefficient distribution on inner side and outer side of helical coil in subcooled and saturated boiling region. Heat transfer coefficient on the outer side of helical coil is much higher than on inner side of helical coil. In the subcooled region, heat transfer coefficient increases on the inner and outer side. In the saturated boiling region, distribution of heat transfer coefficient on outer side is similar to straight tube heat transfer distribution. Heat transfer coefficient remains uniform in low quality region and increases

52

B.K. Hardik, S.V. Prabhu / International Journal of Thermal Sciences 114 (2017) 44e63

Fig. 4. Temperature and heat transfer coefficient distribution in inner side and outer side of helical coil along the axial length of tube.

Fig. 5. Effect of heat flux on heat transfer coefficient and temperature distribution with constant mass flux.

with increase in quality in high quality region, shows the nucleate boiling dominant region and convective boiling dominant region. In the saturated boiling region, heat transfer on inner side remains almost constant. This shows that the inner side of helical coil is dominated by nucleate boiling in low quality as well as in high quality regions.

4.2. Effect of different parameters on the flow boiling heat transfer coefficient and temperature distribution The effect of tube diameter, heat flux and mass flux on inner side and outer side of helical coil is studied in the present section. Fig. 5 shows the effect of heat flux on heat transfer coefficient and

B.K. Hardik, S.V. Prabhu / International Journal of Thermal Sciences 114 (2017) 44e63

temperature distribution for (A) inner side and (B) outer side of helical coil. The profile of bulk fluid temperature, wall temperature and heat transfer coefficient along the axial length of coil is shown with the increase of heat flux at different qualities. Mass flux is kept uniform. Heat transfer coefficient increases with the increase in heat flux in subcooled and saturated region. High wall temperature on inner side of the helical coil starts the boiling from inlet. Heat transfer coefficient on inner side of helical coil remains almost constant in saturated boiling region with increase in quality for all the heat flux cases. Hence, the mode of boiling on inner side is mainly nucleation and convective boiling has secondary effect which shows by slight increase in heat transfer coefficient in high quality region. On the outer side of helical coil, nucleation starts later. The outer side wall temperature increases in the subcooled boiling region till zero quality and then starts decreasing in saturated region. In subcooled boiling region, wall temperature on the outer side increases even after the starting of nucleate boiling. The secondary flow and relative velocity between vapour and liquid increases the convective heat transfer on outer side of helical coil in subcooled region. The effect of mass flux on temperature and heat transfer distribution is analysed in helical coil 5 having tube diameter 9.7 mm and D/d ¼ 14.5. Fig. 6 shows the wall temperature, bulk fluid temperature and heat transfer coefficient distribution on inner side and outer side of helical coil for constant heat flux and heated

53

length for two different mass flux. The value of heat flux and heated length kept constant to 290 kW/m2 and 2084 mm respectively. Two mass fluxes of 129 kg/m2s and 258 kg/m2s are used to analyse the effect of mass flux. The heat transfer coefficient on subcooled boiling and in nucleate boiling remains almost same in inner side and in outer side. Heat transfer coefficient in convective boiling increases with increase in mass flux on inner side and outer side. Hardik and Prabhu [27] study on straight tube shows the mass flux affect the convective boiling heat transfer. Mass flux has no significant effect in subcooled boiling and in nucleate boiling. Hence, the effect of mass flux remains same in straight tube and in inner side and outer side of helical coils. Fig. 7 shows the effect of heat transfer and temperature distribution for uniform boiling number in helical coil 3. The value of heat flux and mass flux are changing by keeping the boiling number same. Two different cases with mass flux 190 kg/m2s and heat flux 293 kW/m2 and mass flux 400 kg/m2s and heat flux 620 kW/m2 having Boiling number 0.007 are compared. Distribution profiles for both inner side and outer side are shown in Fig. 7 (A) and Fig. 7 (B) respectively. Temperature distribution and heat transfer coefficient distribution on inner side and outer side remain parallel for uniform boiling number. The difference of wall temperature and bulk fluid temperature remain uniform for uniform boiling number on both inner side and outer side of helical coil. Heat transfer coefficient for higher value of heat flux is higher. Fig. 7 (C) and Fig. 7

Fig. 6. Effect of mass flux on heat transfer coefficient and temperature distribution.

54

B.K. Hardik, S.V. Prabhu / International Journal of Thermal Sciences 114 (2017) 44e63

(D) show the non-dimensional heat transfer coefficient as a ratio of two-phase flow and single phase flow heat transfer coefficient. The single phase heat transfer coefficient for outer side and inner side are calculated from Eqs. (10) and (11) respectively. Figures show that the normalised heat transfer coefficient of both the cases is almost overlapping on inner side and outer side. The normalised heat transfer coefficient for same boiling number remains same for both inner side and outer side. Hardik and Prabhu [27] shows the same effect of boiling number for straight tube. Hence the

characteristics of heat transfer on inner side and outer side of helical coil are same. The effect of different parameters on helical coil heat transfer is same as straight tube heat transfer. Eqs. (10) and (11) are similar to Dittus-Boelter correlation with coil to tube diameter ratio. For the same helical coil, Dittus-Boelter correlation can be used for both side instead of Eqs. (10) and (11) to calculate non-dimensional heat transfer coefficient on inner side and outer side. The effect of helical coil tube diameter on inner side and outer

Fig. 7. Effect of Boiling number on heat transfer coefficient and temperature distribution.

B.K. Hardik, S.V. Prabhu / International Journal of Thermal Sciences 114 (2017) 44e63

side heat transfer distribution is analysed. Heat transfer distribution in two helical coils coil 3 and coil 5 having tube diameter 8 mm and 9.7 mm is compared. The coil diameter of both the coils is almost same. The mass flux and heat flux in both the coils is constant. For uniform heat flux and mass flux, quality in small diameter tube is higher than in large diameter tube. Wall temperature, bulk fluid temperature and heat transfer coefficient distribution in both the coils is shown in Fig. 8. The pressure drop in helical coil 3 is higher than coil 5. Hence, the system pressure and saturation temperature in coil 3 are higher than coil 5. The wall temperature on inner side and outer side of helical coil 3 is higher than coil 5. Heat transfer coefficient on inner side and outer side of both the helical coils are same. As inner and outer side heat transfer coefficients are same for both the helical coils, circumferential heat transfer coefficient distribution in both the helical coils is same. Heat transfer distribution on helical coil remains uniform with change in the diameter for constant heat flux and mass flux. 4.3. Comparison of experimental local heat transfer coefficient with the straight tube correlation in a subcooled flow Local heat transfer coefficient in helical coils in subcooled boiling condition is studied. Bulk fluid temperature and well

55

temperature on inner side and outer side of the helical coil is shown in Fig. 9 to analyse the effect of curvature on temperature and heat transfer distribution in subcooled flow boiling. Hardik and Prabhu [27] study on straight tube suggests that the Kandlikar [29] correlation for subcooled flow boiling match to experimental results with reasonable accuracy. Experimental data of heat transfer coefficient in all six helical coils are compared with Kandlikar [29] fully developed subcooled flow boiling correlation. Fig. 9 shows the comparison of correlation with experimental heat transfer coefficient on inner side and outer side of the helical coil. One sample case from all the six coils is shown in Fig. 9 and the effect remains same for all cases. The inner side heat transfer coefficient of all the six coils are matching with correlation within less than 10% deviation. Hence, subcooled heat transfer coefficient on the inner side of helical coil is same as straight tube. The curvature of helical coil has no significant effect on heat transfer coefficient on inner side of helical coil. The outer side heat transfer coefficient is higher than inner side and hence straight tube heat transfer coefficient. The deviation between correlation and outer side heat transfer coefficient is different in high and low coil diameter helical coil with same tube diameter. This deviation decreases with increase in coil diameter. The curvature of helical coil affects the outer side heat transfer coefficient. The increment in average heat transfer

Fig. 8. Effect of tube diameter on heat transfer coefficient and temperature distribution.

56

B.K. Hardik, S.V. Prabhu / International Journal of Thermal Sciences 114 (2017) 44e63

Fig. 9. Temperature and Heat transfer distribution in subcooled boiling region.

B.K. Hardik, S.V. Prabhu / International Journal of Thermal Sciences 114 (2017) 44e63

Fig. 9. (continued).

57

58

B.K. Hardik, S.V. Prabhu / International Journal of Thermal Sciences 114 (2017) 44e63

coefficient on outer side of helical coil is varying from 23% to 200% for present experimental data. The enhancement in overall average heat transfer coefficient in subcooled region is varying from 12% to 100% for present experimental data. Single phase heat transfer coefficient in helical coils shows the increment on outer side of helical coils and decrement on inner side compared to the straight tube heat transfer coefficient. Subcooled boiling in helical coils gives higher enhancement in heat transfer coefficient compared to single phase flow. In a helical coil for diameter ratio 14.43, the enhancement in overall average heat transfer coefficient in single phase flow is 29%, while subcooled flow gives 100% enhancement compared to straight tube. 4.4. Comparison of local heat transfer coefficient with the straight tube correlation in a mixed (subcooled þ saturated) flow The heat transfer coefficient on inner side and outer side of helical coil is analysed in subcooled and saturated flow boiling condition. The fluid enters in a helical coil at subcooled condition and exits as saturated flow with some quality. Fig. 10 shows the heat transfer coefficient on inner side and outer side of helical coils in mixed flow boiling condition at different quality and axial length. The experimental heat transfer coefficient is compared with Kandlikar's correlation for all the helical coils. One case for each of the helical coils is shown in Fig. 10. The overall average deviation analysis between correlation and experimental heat transfer coefficient is presented in Fig. 10 for subcooled and saturated flow boiling condition. The deviation is calculated separately for inner side, outer side and total with correlation. The inner side subcooled heat transfer coefficient matches well with the correlation. Hence, heat transfer on inner side of helical coil in subcooled flow condition is almost same as straight tube. The outer side heat transfer coefficient in subcooled boiling condition is higher than inner side and hence straight tube. Outer side heat transfer coefficient varies with the variation in the curvature ratio. In the saturated boiling condition, the heat transfer coefficient on inner side remains almost uniform in entire saturated region for all the helical coils. With the increase in the quality, the inner side heat transfer coefficient in saturated region remains constant. The inner side heat transfer coefficient is deviating as high as 200% from the straight tube for high quality flow. The outer side heat transfer coefficient is higher than the straight tube. The outer side heat transfer coefficient is deviating as low as 50% from the straight tube for high quality flow. The temperature difference between outer side wall temperature and bulk fluid temperature is very low. Small change in outer wall temperature results in large fluctuation in the heat transfer coefficient. Hence, outer heat transfer coefficient has high fluctuations. In a saturated boiling region, decrease in the coil diameter increases the heat transfer coefficient on the outer side and decreases on the inner side. The total average of outer side and inner side heat transfer coefficient almost remains same as straight tube. The change in curvature ratio has no significant effect on total heat transfer coefficient in saturated boiling region. The comparison of overall averaged heat transfer coefficient in saturated boiling region with Kandlikar [30] correlation is shown in Fig. 11. The Overall averaged heat transfer coefficient in saturated boiling region is deviating from 14% to 26% with the Kandlikar's correlation. 4.5. Effect of different parameters on two-phase pressure drop The effect of different geometrical and operational parameters on two-phase pressure drop in helical coil is studied. The effect of mass flux, tube diameter and helical coil length for uniform heat flux and uniform quality is shown in present section. The effect of mass flux on two phase pressure drop is shown in

Fig. 12 for helical coil 2. Fig. 12 (A) shows the two-phase pressure drop for five different mass fluxes at uniform heat flux. For a given heat flux, as the mass flux increases, the single phase pressure drop increases. However, in a two-phase flow, for a given heat flux, as the mass flux increases, the two-phase pressure drop decreases. The pressure drop follows linear increment with increase in heat flux for constant mass flux. The difference in pressure drop for two different mass fluxes is almost constant with the increase in heat flux. Pressure drop for different mass fluxes remains parallel for different heat fluxes. The effect of two-phase pressure drop at different mass fluxes for uniform quality is shown in Fig. 12 (B). In a subcooled quality region, pressure drop increases with increase in mass flux for constant quality. The phenomenon remains same in high quality region also. In the high quality region, the pressure drop increases with increase in mass flux. Pressure drop increases almost linearly with increase in the quality. For same heat flux, quality decreases as the mass flux increases. Hence, the two-phase pressure drop is proportional to mass flux for uniform quality and inversely proportional to mass flux for uniform heat flux. The difference in pressure drop for two different mass fluxes increases with the increase in quality. The effect of two helical coils with different tube diameters (d ¼ 6 mm and 10 mm) with same mass flux and heated length on two-phase pressure drop is shown in Fig. 13. Fig. 13 (A) shows the two-phase pressure drop in two coils for a given mass flux. At specific heat flux, two-phase pressure drop increases with the decrease in the tube diameter. Fig. 13 (B) shows the two-phase pressure drop in both the coils for uniform quality. For the same quality and mass flux, pressure drop remains same in both the coils. For the same mass flux, mass flow rate is less in a small diameter coil. For same mass flux and heat flux, the quality in a small tube diameter coil is higher than large tube diameter coil. Hence, twophase pressure drop in both the coils is different for uniform heat flux while it remains almost same for uniform quality. 4.6. Comparison of experimental pressure drop with the available correlations Hardik and Prabhu [27] studied the two-phase pressure drop in straight tube for low pressure system. Work concluded that the available correlations are not able to predict two-phase pressure drop for low pressure system. Modified Chisholm correlation for the value of constant “C” is suggested for low pressure system as shown in Eq. 21e25. Present experimental two-phase pressure drop data for all helical coils are compared with Hardik and Prabhu [27] correlation. Fig. 14 (A) shows the comparison of predicted pressure drop and experimental pressure drop. In a predicted pressure drop calculation, single phase pressure drop is calculated using Blasius correlation for single phase straight tube pressure drop. The correlation underpredicts the experimental data. Hence, the two-phase pressure drop in helical coil is higher than straight tube.

DPfric ¼ ∅2Ltt DPl ∅2ltt ¼ 1 þ

C 1 þ Xtt Xtt2

C ¼ 18  eð0:14dÞ

DPl ¼

2fl LG2 ð1  xÞ2 drl

(21)

(22)

(23)

(24)

B.K. Hardik, S.V. Prabhu / International Journal of Thermal Sciences 114 (2017) 44e63

Fig. 10. Heat transfer distribution in mixed (Subcooled þ Saturated) boiling region.

59

60

B.K. Hardik, S.V. Prabhu / International Journal of Thermal Sciences 114 (2017) 44e63

Fig. 11. Comparison of overall averaged hear transfer coefficient with Kandlikar's correlation.

experimental data with overall average deviation of 5.7%. The deviation between present experimental data and data predicted using Hardik and Prabhu [27] correlation for straight tube is analysed to compare the two-phase pressure drop in straight tube and helical coil. Fig. 15 shows the value of deviation for different quality. In a low quality region the deviation is more scatter. The deviation is scattered around the centre line. Coil curvature has not much effect in the low quality region. In a high quality region, the deviation is negative and scatter is less. In a high quality region, the pressure drop in helical coil is higher than in straight tube. The deviation in the predicted data shows the effect of quality on the correlation. Regression analysis of all the experimental two-phase pressure drop data is done to derived the correlation that predict present data range with reasonably good accuracy. It is found that correlation in form of Chisholm parameter fit best for the present data. An equation is derived for the value of constant “C” in Chisholm correlation. The equation is improved form of the correlation derived by Hardik and Prabhu [27]. The quality term is added in the equation to compensate the effect of quality. The effect of tube diameter remains same as that in straight tube. The effect of coil diameter is included with single phase pressure drop correlation for helical coil. The effect of coil curvature in two-phase flow remains same as in single phase flow. A correlation suggested to measure the two-phase pressure drop in helical coil for low pressure system as given by Eqs. (27)e(31)

DPfric ¼ ∅2Ltt DPl fl ¼

fc ¼

0:079 ; Re0:25

Re ¼

Gd

ml

"
 #1=20 0:079 d 2 Re 0:25 D Re

(25)

(26)

Fig. 14 (B) shows the comparison of experimental pressure drop and pressure drop predicted using Hardik and Prabhu [27] correlation, where single phase pressure drop component in a correlation is calculated using Ito's correlation (Eq. (26)) for single phase helical coil pressure drop. The correlation predicted the experimental data reasonably well by incorporating the curvature effect in a straight tube correlation. The correlation predicted the

(27)

C 1 þ Xtt Xtt2

(28)

C ¼ 18  0:587  eð1:8xþ0:14dÞ

(29)

∅2ltt ¼ 1 þ

DPl ¼

2fl LG2 ð1  xÞ2 drl

(30)

"


2 #201 d 0:079 Gd ; Re ¼ fl ¼ Re D ml Re0:25

Fig. 12. Effect of mass flux on two-phase pressure drop.

(31)

B.K. Hardik, S.V. Prabhu / International Journal of Thermal Sciences 114 (2017) 44e63

61

Fig. 13. Effect of Tube diameter on two-phase pressure drop.

Fig. 15. Comparison of straight tube pressure drop and helical coil pressure drop.

Fig. 16 shows the comparison of experimental two-phase pressure drop and predicted using Eq. 27e31. Present correlation predicted the experimental data with reasonably good accuracy. The correlation predicts the data with overall average deviation of 0.3% and absolute average deviation of 9.4%. The correlation predicts the 91% of data within 20% deviation. The correlation is valid for saturated boiling flow, for the boundary condition of uniform wall heat flux. The operating parameters range for the correlation, mass flux from 92 to 1278 kg/m2s, heat flux from 140 to 2830 kW/m2, system pressure from 1.1 to 4.8 bar and quality from 0 to 0.96. The geometry parameter range for the correlation tube diameter from 6 to 10 mm, coil diameter from 137 to 383 mm and D/d ratio from 17.1 to 57.8. Fig. 14. Comparison with Straight tube correlation of Hardik and Prabhu [27].

62

B.K. Hardik, S.V. Prabhu / International Journal of Thermal Sciences 114 (2017) 44e63

significant effect, while at specific quality and mass flux, change in coil tube diameter and coil tube length has no significant effect. 8) The effect of curvature ratio remains same for single phase pressure drop and two-phase pressure drop in helical coil. 9) A correlation is derived to predict two-phase pressure drop in low pressure system helical coil. Acknowledgements Authors hereby acknowledge the financial support given by Ministry of Defence. Authors wish to acknowledge the support given by Captain Binduraj from Ministry of Defence (R and D), Shri K.N. Vyas and Shri Joe Mohan from Bhabha Atomic Research Centre and Dr. P.K. Baburajan from Atomic Energy Regulatory Board. Authors are grateful to Mr. Rahul Shirsat for his assistance in building the experimental setup and fabrication of test sections. Appendix A. Heat loss calculation

Fig. 16. Comparison with present correlation.

5. Conclusions Experiments are performed on six helical coil having tube diameter ranging from 6 mm to 10 mm and coil to tube diameter ratio varying from 14 to 58. The results are analysed for the effect of different parameters on inner side and outer side temperature and heat transfer coefficient distribution along the axial length of helical coil. The effect of different parameters on two-phase pressure drop is studied. The experimental results of heat transfer coefficient and two-phase pressure drop are compared with straight tube correlation. Following are the conclusions that may be drawn from the present study. 1) In a subcooled boiling region, the heat transfer coefficient on inner side of helical coil is same as that in straight tube. The outer side heat transfer coefficient is higher than that in straight tube. Hence, overall averaged heat transfer coefficient in helical coil is higher than in straight tube. 2) Enhancement in heat transfer coefficient in the subcooled boiling region is higher than in single phase flow region for the same helical coil. 3) Subcooled boiling heat transfer coefficient decreases with the increase in the coil to tube diameter ratio. 4) In a saturated boiling region, inner side of helical coil is dominated with nucleate boiling. 5) In a saturated boiling region, the heat transfer coefficient on inner side of helical coil is less than in straight tube. The outer side heat transfer coefficient is higher than that in straight tube. Total heat transfer coefficient in helical coil is almost same (14% to 26%) as in straight tube. 6) In a saturated boiling region, the curvature ratio changes the heat transfer coefficient on the inner side and outer side by keeping the total heat transfer coefficient same as in straight tube. Hence, curvature ratio has no significant effect on overall averaged heat transfer coefficient in saturated boiling region. 7) For two-phase pressure drop, at specific heat flux and mass flux, change in helical coil tube diameter and coil length has

Theoretical calculation is carried out to calculate convective and radiation heat loss from the test section outer wall surface to the atmosphere. Helical coil wall surface temperature is measured using Infra-red thermal camera. Heat loss due to convection is calculated from Eq. (33). Heat transfer coefficient of air is taken for Natural convection (Close surrounding). Heat loss due to radiation is calculated from Eq. (34). Heat loss from test section at given heat load is subtracted from the heat supply.

Qloss ¼ Qconv;atm þ Qrad;atm

(32)

. Qconv;atm ¼ hair Asur ðTwall  Tatm Þ; hair ¼ 10kW m2 K

(33)

  4 4  Tatm Qrad;atm ¼ sεAsur Twall

  4 4  Tatm ¼ 5:67  108  0:85Asur Twall

(34)

Above heat loss calculation method is first validated with single phase flow in straight horizontal tubes and in helical coils. The heat balance is done in single phase flow.

 _ p Tbulk;out  Tbulk;in Qconv ¼ Q  Qloss ¼ mC Q ¼ VI

(35)

ð1Þ

Moreover, single phase heat transfer coefficient is measured and validated with available correlation. The validation is given in Hardik et al. [26]. Heat supplied to the fluid calculated from Eq. (35) remains almost same for single phase flow heat transfer process. Hence in two phase flow, Convection and Radiation heat loss is calculated from measured wall temperature. References [1] Naphon P, Wongwises S. A review of flow and heat transfer characteristics in curved tubes. Renew Sustain energy Rev 2006;10(5):463e90. [2] Vashisth S, Kumar V, Nigam KD. A review on the potential applications of curved geometries in process industry. Industrial Eng Chem Res 2008;47(10): 3291e337. [3] Kozeki M, Nariai H, Furukawa T, Kurosu K. A study of helically coiled tube once-through steam generator. Bull Jpn Soc Mech Eng 1970;13(60):1485e94. [4] Hwang KW, Kim DE, Yang KH, Kim JM, Kim MH, Park HS. Experimental study of flow boiling heat transfer and dryout characteristics at low mass flux in helically-coiled tubes. Nucl Eng Des 2014;273:529e41. [5] Chung YJ, Bae KH, Kim KK, Lee WJ. Boiling heat transfer and dryout in helically coiled tubes under different pressure conditions. Ann Nucl energy 2014;71:

B.K. Hardik, S.V. Prabhu / International Journal of Thermal Sciences 114 (2017) 44e63 298e303. [6] Ami T, Nakamura N, Tsuruno T, Umekawa H, Ozawa M. Boiling heat transfer and flow characteristics of liquid nitrogen in helically coiled tube. Jpn J Multiph flow 2011;24:567e76. [7] Owhadi A, Bell KJ, Crain B. Forced convection boiling inside helically-coiled tubes. Int J heat mass Transf 1968;11(12):1779e93. [8] Bell K.J., Owhadi A., 1969, “Local heat-transfer measurements during forcedconvection boiling in a helically coiled tube”, In Proceedings of the institution of mechanical engineers, conference proceedings, vol. vol. 184(3), pp. 52e58. [9] Nariai H, Kobayashi M, Matsuoka T. Friction pressure drop and heat transfer coefficient of two-phase flow in helically coiled tube once-through steam generator for integrated type marine water reactor. J Nucl Sci Technol 1982;19(11):936e47. [10] Kaji M, Mori K, Matsumoto T, Oishi M, Sawai T, Nakanishi S. Forced convective boiling heat transfer characteristics and critical heat flux in helically coiled tubes. Nippon Kikai Gakkai Ronbunshu 1998;64:3343e9. [11] Zhao L, Guo L, Bai B, Hou Y, Zhang X. Convective boiling heat transfer and twophase flow characteristics inside a small horizontal helically coiled tubing once-through steam generator. Int J heat mass Transf 2003;46(25):4779e88. [12] Wongwises S, Polsongkram M. Evaporation heat transfer and pressure drop of HFC-134a in a helically coiled concentric tube-in-tube heat exchanger. Int J heat mass Transf 2006;49(3):658e70. [13] Suzuki M, Kaji M, Matsui G. Heat flux measurement of boiling heat transfer in a helically coiled tube heated by oil bath. J Jpn Soc Exp Mech 2009;9:s60e5. [14] Chen CN, Han JT, Jen TC, Shao L. Thermo-chemical characteristics of R134a flow boiling in helically coiled tubes at low mass flux and low pressure. Thermochim acta 2011;512(1):163e9. [15] Aria H, Akhavan-Behabadi MA, Shemirani FM. Experimental investigation on flow boiling heat transfer and pressure drop of HFC-134a inside a vertical helically coiled tube. Heat Transf Eng 2012;33(2):79e87. [16] Elsayed AM, Al-Dadah RK, Mahmoud S, Rezk A. Investigation of flow boiling heat transfer inside small diameter helically coiled tubes. Int J Refrig 2012;35(8):2179e87. [17] Santini L, Cioncolini A, Butel MT, Ricotti ME. Flow boiling heat transfer in a helically coiled steam generator for nuclear power applications. Int J heat mass Transf 2016;92:91e9. [18] Unal HC, Van MLGG, Verlaat PMV. Dryout and two-phase flow pressure drop in sodium heated helically coiled steam generator tubes at elevated pressures. Int J heat mass Transf 1981;24:285e98.

63

[19] Guo L, Feng Z, Chen X. An experimental investigation of the frictional pressure drop of steamewater two-phase flow in helical coils. Int J heat mass Transf 2001;44(14):2601e10. [20] Santini L, Cioncolini A, Lombardi C, Ricotti M. Two-phase pressure drops in a helically coiled steam generator. Int J heat mass Transf 2008;51(19):4926e39. [21] Cioncolini A, Santini L, Ricotti ME. Subcooled and saturated water flow boiling pressure drop in small diameter helical coils at low pressure. Exp Therm fluid Sci 2008;32(6):1301e12. [22] Cioncolini A, Santini L. Two-phase pressure drop prediction in helically coiled steam generators for nuclear power applications. Int J Heat Mass Transf 2016;100:825e34. [23] Colombo M, Colombo LP, Cammi A, Ricotti ME. A scheme of correlation for frictional pressure drop in steamewater two-phase flow in helicoidal tubes. Chem Eng Sci 2015;123:460e73. [24] Xin RC, Awwad A, Dong ZF, Ebadian MA, Soliman HM. An investigation and comparative study of the pressure drop in air-water two-phase flow in vertical helicoidal pipes. Int J heat mass Transf 1996;39(4):735e43. [25] Awwad A, Xin RC, Dong ZF, Ebadian MA, Soliman HM. Measurement and correlation of the pressure drop in air-water two-phase flow in horizontal helicoidal pipes. Int J Multiph flow 1995;21(4):607e19. [26] Akagawa K, Sakaguchi T, Ueda M. Study on a gas-liquid two-phase flow in helically coiled tubes. Bull JSME 1971;14(72):564e71. [27] Hardik BK, Prabhu SV. Boiling pressure drop and local heat transfer distribution of water in horizontal straight tubes at low pressure. Int J Therm Sci 2016;110:65e82. [28] Hardik BK, Baburajan PK, Prabhu SV. Local heat transfer coefficient in helical coils with single phase flow. Int J Heat Mass Transf 2015;89:522e38. [29] Kandlikar SG. Heat transfer characteristics in partial boiling, fully developed boiling, and significant void flow regions of subcooled flow boiling. ASME J Heat Transf 1998;120:395e401. [30] Kandlikar SG. A general correlation for saturated two-phase flow boiling heat transfer inside horizontal and vertical tubes. ASME J heat Transf 1990;112: 219e28. [31] Baburajan PK, Bisht GS, Gupta SK, Prabhu SV. Measurement of subcooled boiling pressure drop and local heat transfer coefficient in horizontal tube under LPLF conditions. Nucl Eng Des 2013;255:169e79. [32] Didi OMB, Kattan N, Thome JR. Prediction of two-phase pressure gradients of refrigerants in horizontal tubes. Int J Refrig 2002;25:935e47. [33] Ito H. Friction factors for turbulent flow in curved pipes. Transaction Am Soc Mech Eng 1959;D81:123e34.