Heat transfer distribution in helical coil flow boiling system

International Journal of Heat and Mass Transfer 117 (2018) 710–728

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Heat transfer distribution in helical coil flow boiling system 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

Article history: Received 5 July 2017 Received in revised form 19 September 2017 Accepted 6 October 2017

Keywords: Temperature distribution Heat transfer coefficient Helical coil Flow boiling Correlation

a b s t r a c t The objective of the present work is to study the heat transfer distribution in the helical coil flow boiling system. Infrared thermal imaging technique is used to measure the local wall temperature. The wall temperature is measured across the circumference and in axial direction along the length of a helical coil. The literature showing circumferential heat transfer distribution in a helical coil during flow boiling process is scarce. The present work compares the wall temperature and heat transfer coefficient distribution on the inner side and the outer side of helical coils at different diameter ratios and density ratios. In the present study, the experimental databank (containing total 400 heat transfer coefficient data points) includes the data not only from the present experimental study but also from the literature. The data bank includes the subcooled and the saturated flow boiling data. The data includes two fluids namely water and R123. Data covers the range of parameters namely a density ratio of 30–1600, a mass flux of 100– 1300 kg/m2 s, a heat flux of 2–640 kW/m2, an exit quality of
0.5 to 1 and a coil to tube diameter ratio of 14–58. Ten empirical correlations which include well referred correlations of straight tubes and available correlations of helical coils are evaluated with the databank. The study concluded that the circumferential wall temperature variation in helical coils decreases with increase in a diameter ratio and with decrease in a density ratio. The circumferential averaged heat transfer coefficient during a saturated flow boiling in a helical coil is same as a straight tube. A correlation is suggested to measure the circumferential average heat transfer coefficient in helical coils. Ó 2017 Elsevier Ltd. All rights reserved.

1. Introduction Helical coils are widely used in many industrial applications due to their compact structures and good thermal expansion performances. The nuclear industries use a helical coil as the steam generator for electricity production. Due to compact structure, the helical coil reactor is an attractive option for the marine propulsion. Most helical coil heat exchangers used for industries and commercial application require the local heat transfer and local heat transfer coefficient information for design purposes to improve the effectiveness of heat exchanger. Research to use helical coil tubes for receiver of concentrating type solar collector for power generation system is going on. For this system, highest heat flux is at the concave side of the tube. To investigate this system, knowledge of local heat transfer coefficient on inner side and outer side require. The information should help to design and increase the efficiency of the receiver. ⇑ Corresponding author at: 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). https://doi.org/10.1016/j.ijheatmasstransfer.2017.10.029 0017-9310/Ó 2017 Elsevier Ltd. All rights reserved.

Flow boiling heat transfer represents one of the most efficient type of heat transfer mode. Flow boiling plays an important role in the design and analysis of evaporators and condensers. Flow boiling mechanism inside a helical coil may be different than that in a straight tube due to secondary flows generated inside a helical coil. The boiling results into two-phase flow of liquid and vapour which have different densities. The curvature of a helical coil generates the centrifugal force which may cause phase separation with a low density vapour being on the inner side and a high density liquid on the outer side of a helical coil during flow boiling process. Hence, the density ratio of boiling fluid and its vapour may affect the circumferential HTC distribution. The intensity of secondary flows and centrifugal force depend on coil curvature. Hence, diameter ratio of helical coil may affect the circumferential HTC variation during flow boiling process. Naphone and Wongwises [21], Vashisth et al. [28], Fsadni and Whitty [7,8] and many others reviewed two-phase flow in helical coils. Reviews concluded that there is scarcity of the literature on helical coils compared to straight tubes and there is a need of research on helical coil to understand the different aspect of heat transfer mechanism. Owhadi et al. [23] carried out pioneering research on heat transfer coefficient in helical coil flow boiling.

B.K. Hardik, S.V. Prabhu / International Journal of Heat and Mass Transfer 117 (2018) 710–728

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Nomenclature Symbol Definition (Unit) Cp specific heat at constant pressure (J/kg K) d tube diameter (m) D helical coil diameter (m) Deviation ðC cal
C exp Þ=C exp  100 (%) f friction factor G mass flux (kg/m2 s) g gravitational constant (9.81 m/s2) h heat transfer coefficient (W/m2 K) I current (A) i enthalpy (J/kg) k thermal conductivity (W/m K) L length (m) M molecular weight (g/mol) _ m mass flow rate (kg/s) Mean ðjC cal
C exp jÞ=C exp  100 (%) P pressure (N/m2) p pitch (m) Pr reduced pressure (Psystem/Pcritical) Q heat supply (W) q00 heat flux (W/m2) T temperature (°C) V voltage (V) x quality of steam
0:9 qg 0:5  ll 0:1 X lockhart Martinelli parameter X ¼ 1
x x q l l

Greek

l q

g

Definition dynamic viscosity (Ns/m2) density (kg/m3)

The work presented the circumferential variation in heat transfer coefficient in a helical coil during the flow boiling process. Most of the previous studies show overall averaged or circumferential averaged heat transfer coefficient in helical coils. Recently, Santini et al. [24] presented circumferentially averaged and axially local heat transfer coefficient (HTC) in a helical coil. The HTC is shown at twenty different axial locations of a helical coil. To the author’s knowledge, literature showing the variation in the heat transfer coefficient across the circumference of a helical coil in the flow boiling process is not described well. There is no work reported to compare the heat transfer on inner side and outer side of a helical coil with the straight tube for high density ratio fluids. Many investigations are carried out on experimental local heat transfer coefficient in single phase flows in helical coils. Hardik et al. [10] conducted the review on available correlations for single phase heat transfer coefficient. The study derived the local correlations to calculate circumferential averaged heat transfer coefficient on inner side, outer side and total circumference of helical coil. The study on single phase local HTC can be taken as the basis for investigation on flow boiling HTC in helical coils. Hardik and Prabhu [11] conducted the study on local heat transfer coefficient in helical coils with water. They compared local heat transfer coefficient along the axial length of a helical coil with different correlations. They concluded that the heat transfer coefficient in a saturated flow boiling process is same as that in a straight tube. Kandlikar [15] correlations for saturated flow boiling heat transfer coefficient are working reasonably for helical coils. Heat transfer coefficient in a subcooled boiling process is higher than the straight tube. The effect of the coil curvature on HTC in helical coils discussed in the literature is presented in Table 1 for saturated flow boiling process. Literature suggested three different effects of coil curva-

Subscript Definition b bulk f fluid fg fluid to gas g gas h heated i inlet l liquid lo liquid only sat saturated SC subcooled sys system TP two phase tt turbulent liquid and turbulent vapour w wall Abbreviation Definition HP high pressure HTC heat transfer coefficient LP low pressure R123 2,2-Dichloro-1,1,1-trifluoroethane Dimensionless number Bo Boiling number Bo ¼ q00 =Gifg Nu Nusselt number Nu ¼ h  d=K Pr Prandtl Number Pr ¼ l  Cp=K _ pdl Re Reynolds number Re ¼ 4m=

ture on HTC. (1) HTC in helical coils is higher than straight tubes and curvature effect in boiling process is different than the single phase flows. Some literature concluded HTC in a helical coil is constant along the length of coil and hence with increase of quality (2) Boiling HTC in a helical coil is predicted using a straight tube flow boiling correlation with single phase HTC correlation of helical coils. Hence, the effect of the helical coil is completely included in the single phase HTC correlation. (3) HTC in the helical coil is measured well with the straight tube correlations. Hence, it is same as straight tube. The objective of the present work is to study the boiling heat transfer distribution in the helical coil with two different fluids namely water and R123. The wall temperature is measured across the circumference of a helical coil and in the axial direction along the length of helical coil. Infrared thermal imaging technique is used to measure the local wall temperature. The wall temperature and heat transfer coefficient distribution is compared on the inner and outer sides of the helical coil for different diameter ratios and density ratios. Experimental databank is collected containing total 400 heat transfer coefficient data points which include the data from the present study and from the literature. The data bank includes the data of subcooled and saturated flow boiling. Data covers the parameter range of a density ratio 30– 1600, a mass flux 100–1300 kg/m2 s, a heat flux 2–640 kW/m2, an exit quality
0.5 to 1 and a coil to tube diameter ratio 14–58. Ten empirical correlations which include well referred correlations of straight tube and available correlations of helical coil are evaluated with the databank. The details of the available heat transfer coefficient correlations for the helical coils and for the straight tubes are given in Appendix A and B, respectively. The effect of fluid density ratio and helical coil diameter ratio is analysed.

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Table 1 Effect of helical coil curvature on boiling heat transfer coefficient. Authors (year)

Working condition fluid; boundary condition; d (mm); D (mm); G (kg/m2 s); q’’ (kW/m2); P (bar)

Effect of coil curvature

Owhadi et al. [23]

Water; uniform heat flux; d = 12.5; D = 250.4, 520.7; G = 79–314; q’’ = 60–255.5, P = Atmospheric Water; uniform heat flux; d = 12.5; D = 250.4, 520.7; G = 79–314; q’’ = 60–255.5; P = Atmospheric Water heated with water; d = 15.5, 16.1; D = 628, 682; G = 161–486; q’’ = 151–350; P = 5–21 R113; uniform heat flux; d = 10; D = 165, 320; G = 305–1650; q’’ = 30–200; P = 3.9

Saturated flow boiling HTC in a helical coil is same as a straight tube

Bell and Owhadi [4] Kozeki et al. [17] Kaji et al. [14]

Zhao et al. [30] Wongwises and Polsongkram [29] Ami et al. [1] Chen et al. [5] Aria et al. [2] Chung et al. [6] Hwang et al. [13] Santini et al. [24] Hardik and Prabhu [11]

Water; uniform heat flux; d = 9; D = 292; q’’ = 0–900; G = 236–943; P = 5–35 R134a heated with water; d = 7.2; D = 305; G = 400–800; q’’ = 5–10 Liquid nitrogen; uniform heat flux; d = 4; D = 100; G = 200–710; q’’ = 0–60; P = 3 R134a; uniform heat flux; d = 7.6; D = 300; G = 50–260; P = 2–7.5 R134a heated with water; d = 8.32; D = 305; G = 112, 132, 152 Water; uniform heat flux; d = 12; D = 577, 937, 1297; G = 176.8–530.5; P = 10–60 Water; uniform heat flux; d = 12; D = 606, 977; G = 88.4–530.5; q’’ = 30–1145.3; P = 10–60 Water; uniform heat flux; d = 12.53; D = 1000; G = 200–800; q’’ = 40–230; P = 20–60 Water; uniform heat flux; G = 92–1278; q’’ = 140–2830; P = 1.1–4.8

Saturated flow boiling HTC in a helical coil is predicted using the straight tube correlation with a Seban correlation for single phase Saturated flow boiling HTC in a helical coil is constant along the axial length of coil. HTC in a helical coil is different than that of a straight tube Helical coil curvature effect is included in a single phase flow. Saturated flow boiling HTC non-dimensionalize with the single phase helical correlation matches well with a straight tube. Straight tube saturated flow boiling HTC correlation non-dimensionalize with the single phase helical correlation works well for boiling HTC in helical coils Saturated flow boiling HTC in a helical coil is higher than that in a straight tube

Schrock correlation for HTC in straight tubes works well for helical coils Helical coil curvature effect is included in the single phase flow correlation Saturated flow boiling HTC in a helical coil is higher than that of a straight tube Saturated flow boiling HTC in a helical coil is same as that in a straight tube Saturated flow boiling HTC in a helical coil is same as that in a straight tube Saturated flow boiling HTC in a helical coil is same as that in a straight tube Saturated flow boiling HTC in a helical coil is same as that in a straight tube

2. Description of the experimental facilities A schematic diagram of the experimental set-up is shown in Fig. 1(A). The experimental set-up is a closed loop flow system with refrigerant R123 used as a working fluid. The test set-up includes an insulated fluid reservoir, magnetically coupled sealless gear pump, nitrogen cylinder, pre-heater, condenser, ball valves, helical coil test section and straight tube test section. The experimental facility is insulated thermally to minimize the heat loss from the set-up. Heated length of the test sections are kept open to the atmosphere to measure wall temperature using Infrared thermal imaging technique. Infra-Red thermal camera (Make: Themoteknix, Model: VisIR640) is used to analyses the wall temperature of the test section without disturbing helical coil. Thermal camera forms a thermal image by measuring the intensity of radiation emitted by the surface. The intensity of radiation depends on the temperature and the emissivity of the surface. The helical coil is painted with a thin coat of high temperature black board paint to have a uniform emissivity of 0.85. The thermal camera is set at two different positions as shown in Fig. 1(B) to cover the complete circumference of helical coil across the heated length. The helical coil test sections used in the present study are made of stainless steel SS304. Refrigerant R-123 has high boiling point temperature (Tsat = 42.9 °C at P = 1.7 bar). Due to the high boiling point for R-123, water is used as a secondary fluid to condense the vapour in a counterflow condenser. Secondary water circuit is an open loop cycle. Water inlet temperature is almost constant. Hence, inlet temperature of R123 flowing in a closed loop remains constant. This makes the system less complex, more stable and allows the system to reach steady state in less time. The gear pump with a mass flow rate range from 0 to 360 g/s is used to pump R123. The D.C. motor with speed varied between 0 and 3500 rpm is used to control the speed of gear pump. This speed variation of the gear pump controls the mass flow rate. The experiments are performed at different pressures. Pressurised nitrogen gas is used to develop and maintain the system pressure in the experimental set-up. Pres-

surised nitrogen cylinder filled with the nitrogen gas at 150 bar is attached with experimental set-up. A pressure regulator is fixed between the nitrogen cylinder and the experimental set-up to maintain a constant pressure in the experimental set-up. The experiments at low pressure with system pressure varying from 1.4 to 3.2 bar are performed without nitrogen gas. The experiments at high pressure with system pressure varying from 3.8 to 6.2 bar are performed with pressure generated using nitrogen gas. The temperature, pressure and mass flow rate measuring devices are instrumented at several locations to measure the system pressure and HTC in helical coils accurately. K-type thermocouples and pressure transmitters (Keller PA-21Y/10 bar) are installed at the inlet and outlet of the helical coil to measure the bulk fluid temperature and pressure of the fluid. Two differential pressure transmitters (capacities 0.622–62.2 bar and 0–5 bar) with parallel connection are installed across the test section to measure the pressure drop across the test section. The locations of the pressure taps are shown in Fig. 1(B). Differential pressure transmitters are fixed on the same pressure taps of pressure transmitters. The taps are drilled at 100 mm before the inlet of the test section and 50 mm after the exit of the test section in disturbance free part of the experimental set-up. Thermocouples are fixed on the surface of copper tubes at opposite diagonal end of pressure taps. Sight glasses are installed at the inlet and exit of the test section for a direct observation of the bubbles across the test section. The coriolis mass flow meter (Emerson CMF025 with Transmitter 1700R) is used to measure the mass flow rate of fluid. Flowmeter has competency to measure density of fluid and bulk fluid temperature. Fig. 1(C) shows an exploded view of the helical coil. Heated length of the helical coil is measured between the upper and bottom electrode. There is a non-heated coil length of minimum 150 mm at each end of the tube to stabilize the fluid flow and avoid the flow entrance effect. The moveable bus bar is adjusted at different lengths to measure HTC with different heated length. All the helical coils are heated electrically by passing DC current through the tube wall between two bus bars maintaining the uniform heat

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9

8

11 10

6

5

1a 7

4

3 1b

(A) Isometric veiw of experimental set-up (1) Test section; a - Helical coil, b - Straight tube, (2) Thermal Camera; a - 1st Position, b - 2nd Position, (3) Sight Glass, (4) Condenser, (5) Reservoir, (6) Level Indicator, (7) Pump, (8) Flow Meter (9) Pre-Heater (10) Pressure Regulator Valve, (11) Nitrogen Cylinder, (12) Pressure Tap Coil diameter (D)

2a

Black board Paint

Flange

1a Pitch (p)

Movable Busbar

12 2b

Tube inner diameter (d)

(B) Location of Thermal Camera

(C) Helical coil test section

Fig. 1. Schematic of the experimental set-up.

flux condition. DC power supply with 50 kW capacity (Make: Aplab, Model: CVCC50kW; 0–40 V voltage and 0–1250 A current) is used to supply power through the helical coil. The heat supplied is determined from the current and voltage across the test section. The current is measured using the power supply digital reading, while the voltage is measured using multimeter.

Uniform inlet condition of the test section is maintained using pre-heater and condenser. Pre-heater is heated by passing AC current through a Nichrome wire mounted on the wall of the preheater. Heat supplied to the pre-heater and the helical coil is removed in the counterflow condenser. Electromagnetic mass flow meter (Make: Manas, Model: SR1000P-DN25-PTFE) and K-type

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thermocouples are used to measure the heat absorbed by the water. All the thermocouples are inserted into the fluid to measure the actual water temperature at inlet and outlet of the condenser. All the instruments are connected to a Data Acquisition system (DAS) (Make: Atomberg, Model: AB4001) which is in turn connected to a computer. All the readings are taken, after the complete system reaches steady state, once the thermocouple at the exit of the test section records almost constant bulk fluid temperature.

90º o1

i1

o2

i2

o3

Axis of the helical coil

i3

3. Data reduction Local bulk fluid temperature calculated in the subcooled and the saturated flow boiling process is discussed. Procedure to measure the inner surface wall temperature from the thermal images is given in this section. Equations required to calculate local heat transfer coefficient are presented. The uncertainties involved in the experimental measurements are presented.

o4

i4

o5

Secondary flows

i5 i6

o6

i7

o7 i8

o8 i9

Local points

o9 o10

i10

o11

i11

270º

3.1. Temperature measurement The bulk fluid temperature is measured using thermocouples at the inlet and the exit of the helical coil. During the boiling process, the fluid temperature at the exit of the helical coil measured using a thermocouple shows the temperature same as the saturation temperature at that pressure measured using a pressure transmitter. In the subcooled boiling, local bulk fluid temperature is calculated with the linear interpolation between inlet temperature and temperature at zero quality. The fluid temperature at zero quality (at x = 0) is taken as the saturation temperature based on the inlet system pressure. The local saturation temperature in the saturated boiling region is calculated from the local pressure. Interpolation pressure profile between the inlet and exit pressure is calculated from the pressure drop profile as given in Eqs. (1)–(4) [11]. To draw the pressure drop profile accurately, the value of constant ‘C’ is changed in equation Eq. (2) such that pressure drop from the correlation is equal to the experimental pressure drop. Thermo-physical properties of the liquid in the subcooled flow boiling calculation are calculated at the local bulk fluid temperature. In the saturated flow boiling calculation, the properties are calculated at the local saturation temperature. The vapour properties in all the calculations are calculated at the local saturation temperature. All the thermo-physical properties used in the calculations are calculated from National Institute of Standards and Technology (NIST) tabulated values. Present two-phase pressure drop correlation

Table 2 Experimental uncertainties. Parameter

Relative uncertainty (%)

Parameter

Relative uncertainty (%)

Pipe diameter

1

1.3

Pipe length Coil diameter Current Voltage Bulk temperature

0.5 1 0.5 1 1.5

Wall temperature Mass flow rate Pressure Quality Heat flux Heat transfer coefficient

1.8 1.5 3.8 3 13.5

points show the circumferential temperature points of thermal image. The wall temperature averaged over a circumference from 90°–180°–270° is named as the inner side wall temperature. The wall temperature averaged over a circumference from 270°–0°–9 0° is named as the outer side wall temperature. Complete circumferential averaged wall temperature is named as the total wall temperature. Average of circumferential averaged along the axial length of a helical coil is named as the overall averaged.

(1)

DPfric ¼ £2l;tt DP l £2l;tt

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

¼ 1 þ XCtt þ X12 ;C ¼ 18  eð0:14dÞ ;d in mm tt 2f l LG2 ð1
xÞ2 d ql

DPl ¼ h
2 i201 0:079 ; Re ¼ Gd f l ¼ Re Dd l Re0:25

(2) (3) (4)

l

The axial and circumferential local wall temperature distribution of the helical coil is obtained by averaging ten thermal images. Thermal images show the outer surface wall temperature of the test section. Inner surface wall temperature is calculated from the measured outer surface wall temperature using one dimensional, steady state heat conduction method with uniform volumetric heat generation across the wall due to electrical heating. More details about this method with sample calculations of inner surface wall temperature from measured outer surface wall temperature are given in Baburajan et al. [3]. Fig. 2 shows the cross section of helical coil test section with illustrative direction of secondary flow inside helical coil. Local

3.2. Heat transfer coefficient The heat flux supplied to the helical coil is calculated from Eq. (5). Heat loss from the helical coil outer wall surface to the atmosphere for a given heat load is subtracted from the total heat supply. Convective and radiation heat loss are calculated theoretically. However, helical coil heat loss calibration tests are performed in a single phase flow to validate the calculation method. In the present study, the percentage of heat loss is varying from 0.2% to 6% of total heat supply. The procedure to calculate heat loss is given in Hardik and Prabhu [11].

q00 ¼

Q conv Q
Q loss VI
ðQ conv ;atm þ Q rad;atm Þ ¼ ¼ pdLh pdLh pdLh

ð5Þ

The local thermodynamic equilibrium quality and the local HTC in the subcooled and the saturated regions are calculated from Eqs. (6)–(8). Eq. (6) gives the quality at a specific length of a helical coil. The length of the helical coil from where, the subcooled flow transits into the saturated flow (zero quality) is calculated from Eq. (9)

Table 3 Test sections geometrical and operating parameters for water data [11]. Coil no

Tube characteristics

Operating characteristics

Outer diameter do (mm)

Coil characteristics Mean diameter D (mm)

Pitch p (mm)

D/d

System pressure P bar

Density ratio ql / qg

Mass flux G kg/m2s

Heat flux q’’(kW/m2)

Quality x

No of HTC data points

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

1.04–3.65 1.03–2.28 1.06–2.94 1.10–3.96 1.12–2.65 1.02–3.04

460–1560 730–1575 570–1535 430–1485 630–1460 550–1590

394–874 339–550 192–592 205–507 128–413 189–325

8–1048 26–319 17–626 26–807 45–600 14–604


0.22 to 0.15
0.19 to 0.18
0.2 to 0.62
0.22 to 0.79
0.1 to 0.71
0.21 to 0.42

9 11 25 20 28 13

Table 4 Test sections geometrical and operating parameters for R123 data. Coil no

Curvature ratio

Operating characteristics

Inner diameter d (mm)

Tube characteristics Outer diameter do (mm)

Mean diameter D (mm)

Coil characteristics Pitch p (mm)

D/d

System pressure P bar

Density ratio ql / qg

Mass flux G kg/m2s

Heat flux q’’(kW/m2)

Quality x

No of HTC data points

1

9.5

10

200

50

21.05

2

7.5

8

150

50

20

3

5.5

6

150

50

27.27

4 5

9.5 7.5

10 8

300 300

50 50

31.58 40

6

5.5

6

300

50

54.55

1.5–3.4 5.0–5.7 1.4–3.1 3.6–5.0 1.4–2.9 4.6–5.8 1.6–2.8 1.5–2.9 4.5–5.5 1.4–3.1 4.5–6.2

66–151 37–44 72–162 43–63 78–162 37–48 81–143 78–152 39–48 72–162 34–49

280–1008 285–713 436–1211 438–1153 457–920 400–1163 414–1276 240–1148 434–1202 422–881 389–1287

2.6–159 18–150 6.4–172 5.3–132 5.2–83.7 19–194 6.4–132 4.8–173 28–176 6–129 18–191


0.2 to 0.85
0.41 to 0.89
0.21 to 0.84
0.4 to 0.91
0.18 to 0.57
0.4 to 0.86
0.16 to 0.77
0.17 to 0.79
0.39 to 0.97
0.2 to 0.71
0.45 to 0.96

45 18 46 18 12 15 27 53 21 18 21

B.K. Hardik, S.V. Prabhu / International Journal of Heat and Mass Transfer 117 (2018) 710–728

1 2 3 4 5 6

Curvature ratio

Inner diameter d (mm)

715

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by keeping xlocal = 0. Local quality gives negative values in the subcooled boiling region, while in the saturated region, local quality gives the positive values.


if

ð6Þ

ifg

if ¼ C p ðT sat
T in Þ q00 T w;local
T b;local

ð8Þ

_ p ðT sat
T in ÞLh mC Q conv

ð9Þ

Location Total

Correlation



0:16 0:8 kl hl
Total ¼ 0:0456 Dd Relocal Pr0:4 local d
D
0:315 0:8 0:4 kl Relocal Pr local d hl
Outer ¼ 0:104 d
D0:088 0:8 kl Relocal Pr0:4 hl
Inner ¼ 0:012 d local d

Outer side Inner side

20

R123-HP

Water Data

10 0

20

0

30

60

90

120 150 300 600 900 1200 1500

Number of Data Points

Number of Data Points

100

Diameter Ratio R123-LP

80

R123-HP

60

Water

40 20 0

10

20

30

40

50

60

70

Exit Quality

60 50

R123-LP

40

R123-HP Water

30 20 10 0

0

Diameter Ratio (D/d) 80

Heat Flux 60 R123-LP R123-HP

40

Water

20 0

0

40

80

120

160

200

Heat Flux

300

400 (kW/m2 )

500

600

60

Mass Flux R123-LP

40

R123-HP Water

20

0

100

400

700

1000

Mass Flux (kg/m2 s)

1300

0.2

0.4

0.6

0.8

Exit Quality (x)

100

1

Two-Phase Length

80

R123-LP R123-HP

60

Water

40 20 0 800

1100

1400

1700

2000

Two-Phase Length (mm)

75

2300

System Pressure R123-LP

60

R123-HP

45

Water

30 15 0

1

2

3

4

5

System Pressure (kPa)

Fig. 3. Parameter distribution of experimental HTC databank (400 data points).

(10) (11) (12) (13)

Number of Data - Water

60

Density Ratio R123-LP

40

Number of Data - R123

hl
local ¼

0:4 kl 0:023Re0:8 local Pr local d

Liquid to Vapour Density Ratio

Number of Data Points

Lðx¼0Þ ¼

Number of Data Points

hlocal ¼

ð7Þ

Number of Data Points

Q conv L _ m Lh

Number of Data Points

xlocal ¼

Single phase heat transfer coefficient on inner side, outer side and total in helical coil is calculated from the correlations suggested by Hardik et al. [10] given in Eqs. (10)–(12). Local heat transfer coefficient for a single phase turbulent flow in straight tube is calculated using Dittus-Boelter correlation as given in Eq. (13). The local Reynolds number and local Prandtl number are calculated with properties taken at local bulk fluid temperature.

6

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Non-dimensional Axial length (Lh/D) 0

25

50

75

100

125

150

Non-dimensional Axial length (Lh/D)

175

0

140

O

Temperature ( C)

O

100 80 Inner Wall Tempareture Outer Wall Tempareture Bulk Fluid Temperature

60 40 20

350

40

Coil - 2; d = 6 mm; D = 347 mm

0 -0.16 -0.12 -0.08 -0.04

0

0.04 0.08 0.12 0.16

B

q'' = 319 kW/m2; G = 550 kg/m2s

0 -0.15 -0.1 -0.05

40

80

120

160

0

0.05

0.1

0.15

Quality (x) 200

Non-dimensional Axial length (Lh /D)

240

0 70

60

60

Temperature ( C)

70

40

80

120

160

200

240

280

50

O

50

O

Temperature ( C)

300

Inner Wall Tempareture Outer Wall Tempareture Bulk Fluid Temperature

60

Non-dimensional Axial length (Lh /D)

40 30

Outer Side Wall Temperature Inner Side Wall Temperature Bulk Fluid Temperature

20

Coil - 3; d = 5.5 mm; D = 144 mm

10 0

0

0.1

0.2

0.3

0.4

30

Outer Side Wall Temperature Inner Side Wall Temperature Bulk Fluid Temperature

20

Coil - 6; d = 5.5 mm; D = 300 mm

10

q'' = 45.67 kW/m2; G = 450 kg/m2s -0.1

40

0.5

0.6

D

q'' = 57.0 kW/m2; G = 454 kg/m2s

0 -0.1

0

0.1

0.2

Quality (x) 40

80

120

160

0.3

0.4

0.5

0.6

0.7

Quality (x)

Non-dimensional Axial length (Lh /D) 0

200

240

Non-dimensional Axial length (Lh /D) 280

0 100

80

80

40

80

120

160

200

240

O

Temperature ( C)

100

O

Temperature ( C)

250

80

20

q'' = 406 kW/m2; G = 444 kg/m2s

0

60 Outer Side Wall Temperature Inner Side Wall Temperature Bulk Fluid Temperature

40

20

kW/m2;

G = 647

-0.2

0

0.2

Outer Side Wall Temperature Inner Side Wall Temperature Bulk Fluid Temperature

40

Coil - 6; d = 5.5 mm; D = 300 mm q'' = 113.7 kW/m2; G = 624 kg/m2s

kg/m2s

0 -0.4

60

20

Coil - 3; d = 5.5 mm; D = 144 mm q'' = 84.8

E

200

100

Quality (x)

C

150

120

Coil - 1; d = 6 mm; D = 162 mm

A

100

140

120

Temperature ( C)

50

0.4

0.6

F

0 -0.4

-0.2

0

0.2

0.4

0.6

0.8

1

Quality (x)

Quality (x) Fig. 4. Wall temperature distribution during flow boiling.

3.3. Uncertainties in the measured and computed parameters The uncertainty in the measurement is calculated based on the method suggested by Moffat [20] and Kline and McClintock [16]. Total uncertainty in individual parameters is calculated by considering the error in repeatability, reproducibility and uncertainty of

the calibration system. The uncertainties in the helical coil tube diameter and coil diameter are obtained by measuring the values at different locations. The uncertainty in the heated length is obtained by repeatedly measuring the parameters. The uncertainties in mass flow rate, temperature, and pressure are calculated by comparing the reading of DAS with the value obtained from stan-

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Non-dimensional Axial length (Lh/D) 0

25

50

75

100

125

150

Non-dimensional Axial length (Lh/D)

175

0

50

100

150

200

250

300

350

120

Coil - 1; d = 6 mm; D = 162 mm

110

q'' = 406 kW/m2; G = 444 kg/m2s

Heat Transfer Coefficient (kW/m2K)

Heat Transfer Coefficient (kW/m2K)

130

100 90

Inner HTC Outer HTC

80 70 60 50 40 30 20 10

0 -0.16 -0.12 -0.08 -0.04

A

0

0.04 0.08 0.12 0.16

100

Coil - 2; d = 6 mm; D = 347 mm q'' = 319 kW/m2; G = 550 kg/m2s

90 80

Inner HTC Outer HTC

70 60 50 40 30 20 10 0

B

-0.15 -0.1 -0.05

80

120

160

200

0

240

Coil - 3; d = 5.5 mm; D = 144 mm

10

Heat Transfer Coefficient (kW/m2K)

Heat Transfer Coefficient (kW/m2K)

40

q'' = 45.67 kW/m2; G = 450 kg/m2s Outer Side Inner Side

8

6

4

2

0

C

-0.1

0

0.1

0.2

0.3

0.4

0.5

0.6

40

80

80

120

160

160

200

240

280

8 6 4 2 0

D

-0.1

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

Quality (x) 200

240

Non-dimensional Axial length (Lh /D) 280

0

40

80

120

160

200

240

25

Coil - 3; d = 5.5 mm; D = 144 mm 16

Heat Transfer Coefficient (kW/m2K)

Heat Transfer Coefficient (kW/m2K)

120

Outer Side Inner Side

10

18

E

0.15

q'' = 57.0 kW/m2; G = 454 kg/m2s

Non-dimensional Axial length (Lh /D) 40

0.1

Coil - 6; d = 5.5 mm; D = 300 mm

12

Quality (x) 0

0.05

Non-dimensional Axial length (Lh /D)

Non-dimensional Axial length (Lh /D) 0

0

Quality (x)

Quality (x)

q'' = 84.8 kW/m2; G = 647 kg/m2s Outer Side Inner Side

14 12 10 8 6 4 2 0 -0.4

-0.2

0

0.2

0.4

0.6

Quality (x)

F

Coil - 6; d = 5.5 mm; D = 300 mm q'' = 113.7 kW/m2; G = 624 kg/m2s 20

Outer Side Inner Side

15

10

5

0 -0.4

-0.2

0

0.2

0.4

0.6

0.8

1

Quality (x)

Fig. 5. Heat transfer coefficient distribution in helical coils during flow boiling.

dard instruments. Mass flow meter is calibrated with catch and time method, thermocouple is calibrated with standard thermometer in hot temperature bath. Pressure transmitter is calibrated with dead weight tester. The uncertainties in heat flux resulted from the accuracy of the ammeter and voltmeter. The uncertainty of different parameters used in the experimental analysis is shown in Table 2.

4. Experimental heat transfer coefficient databank Infrared thermal imaging technique is used to measure axial and circumferential local wall temperature. Local HTC is calculated from the measured local wall temperature and local bulk fluid temperature. HTC averaged over the half circumference is called as inner side and outer side HTC. HTC averaged over the full circum-

719

20 30

50

100

100

1000 100

Chen Correaltion

50

10 5 2

3

Deviation Analysis Average = 39.1 % Absolute Mean = 43.4 % ±20% Range = 30.1 %

10

Experimental HTC (kW/m2K)

20 30

50 20 30

-20 %

Water R123 - LP R123 - HP

Water R123 - LP R123 - HP

Deviation Analysis Average = 87.8 % Absolute Mean = 88.4 % ±20% Range = 10.3 %

+20 %

-20 %

1

1

1

C

10 1

B

+20 %

Kaji Correaltion

Predicted HTC (kW/m2K)

0.1

10

5

Experimental HTC (kW/m2K)

10

3

Deviation Analysis Average = 1524 % Absolute Mean = 1631 % ±20% Range = 0 %

5

2

+20 % -20 %

3

1

A

Water R123 - LP R123 - HP

2

2

Deviation Analysis Average = -10.4 % Absolute Mean = 27.2 % ±20% Range = 40.2 %

Aria Correaltion

1

3

5

10

Water R123 - LP R123 - HP

Predicted HTC (kW/m2K)

20 30

-20 %

Predicted HTC (kW/m2K)

+20 %

Zhao Correaltion

1

Predicted HTC (kW/m2K)

50

B.K. Hardik, S.V. Prabhu / International Journal of Heat and Mass Transfer 117 (2018) 710–728

2

3

5

10

20 30

50

100

Experimental HTC (kW/m2K)

1

D

2

3

5

10

20 30

50

Experimental HTC (kW/m2K)

Fig. 6. Comparison of HTC data with helical coil correlations.

ference is called as the total HTC. Local HTC averaged for a complete axial heated length of the helical coil is called as the overall averaged HTC. One data point represents the overall averaged heat transfer coefficient over one tube diameter at a specific mass flux and a specific heat flux. Total 400 cases of local heat transfer coefficient are analysed and based on those, 400 data points of overall averaged HTC are collected. The details of the experimental HTC databank collected from the author’s earlier work and from the present work are summarized in Tables 3 and 4. The databank includes fluids namely water and R123. The geometric details of the tested helical coils and operating parameters covered in the databank are given in Tables 3 and 4. Table 3 shows the details about water data collected from Hardik and Prabhu [11]. The details for R123 data collected in the present study are given in Table 4. The variables used in the databank are mass flux, heat flux, quality, density ratio, diameter ratio, heated length, tube diameter and coil diameter. Detailed descriptions of collected databank are presented with histograms. The histogram for different parameters is shown in Fig. 3. The histogram shows the number of data of both fluids with separate colours to get more information about parameters range of each fluid. Data of fluid R123 is collected in two different parts; first set of data collected for pressure range of 1.4–3.4 bar and second set of data collected for system pressure range of 3.6–6.2 bar. Pressure range 1.4–3.4 bar is named as a low pressure (LP) and the range

3.6–6.2 bar is named as a high pressure (HP) in the present study to differentiate both the data analysis. Total 400 data collected includes 106 data for water, 201 data for R123-LP and 93 data for R123-HP. The databank includes the data of a subcooled flow boiling and a saturated flow boiling. An exit quality is varying from
0.5 to 1. The data shown in an exit quality histogram for a quality less than zero is subcooled flow boiling data. The data of water and R123 are distributed over a complete quality range. The coil to tube diameter ratio is varying from 14 to 58. The length of test section is varying from 900 to 2300 mm. The system pressure is varying from 1 bar to 6.2 bar. The density ratio (liquid density divided by vapour density) for water (ql/qg = 1043 at P = 1.6 bar) and R123 (ql/qg = 142.8 at P = 1.6 bar) is different. Water vapour has low density while R123 vapour has high density. Hence, the databank contain the density variation from 30 to 1600. Latent heat of water (ifg = 2221.6 kJ/kg at P = 1.6 bar) is much higher than that of R123 (ifg = 164.5 kJ/kg at P = 1.6 bar). Hence, the heat flux of water data is higher than the heat flux of R123 data. Heat flux is varying from 2 to 640 kW/m2. The mass flux range is varying from 100 to 1300 kg/m2 s. 5. Results and discussion The experimental set-up and wall temperature measurement techniques using thermal camera for fluid R123 is validated for

B.K. Hardik, S.V. Prabhu / International Journal of Heat and Mass Transfer 117 (2018) 710–728

straight horizontal tubes. The single phase heat transfer coefficient in straight tubes matches well with Dittus-Boelter correlation. The flow boiling heat transfer coefficient in straight tubes predicted well with Kandlikar [15] correlation. The details of the validation are given in Hardik et al. [12]. The experimental analysis is carried out on the wall temperature and the heat transfer distribution in

50 20 30

+20 %

-20 %

10

Water R123 - LP R123 - HP

5

10 5 3

Deviation Analysis Average = -24.4 % Absolute Mean = 25.7 % ±20% Range = 36.9 %

2

Gungor Correaltion

Deviation Analysis Average = 9.8 % Absolute Mean = 22.1 % ±20% Range = 53.6 %

3

-20 %

1

Predicted HTC (kW/m2K)

20 30

+20 %

Water R123 - LP R123 - HP

1

Predicted HTC (kW/m2K)

50

Schrock Correaltion

helical coils. Circumferentially and axially local wall temperature is measured on the inner side and outer side of a helical coil. Circumferential variation in the wall temperature is compared for different diameter ratio and density ratio. HTC on the inner side and the outer side of a helical coil is compared for water and R123 and circumferential variation is analysed for different density ratio and

2

720

50

1

-20 %

5 3

Deviation Analysis Average = -23.5 % Absolute Mean = 25.3 % ±20% Range = 32.8 %

2

3

5

10

20 30

50

Experimental HTC (kW/m2K) Kandlikar Correaltions

50

+20 %

Water R-123 Line/Scatter Plot 6

+20 %

-20 %

Water R123 - LP R123 - HP

Deviation Analysis Average = -8.3 % Absolute Mean = 13.8 % ±20% Range = 76.3%

1

1

2

B

20 30

20 30

50

20 30

10

10

5

5

3

3

Liu Correaltion

10

Predicted HTC (kW/m2K)

2

Experimental HTC (kW/m2K)

Predicted HTC (kW/m2K)

1

2

A

50

-20 %

5

10

Water R123 - LP R123 - HP

2

3

Deviation Analysis Average = -18.4 % Absolute Mean = 20.3 % ±20% Range = 49.5 %

1

2

3

5

10

20 30

50

Experimental HTC (kW/m2K)

3

5

F

10

Lazarek Correaltion

50

+20 %

2

20 30

50

Experimental HTC (kW/m2K)

20 30

20 30

Predicted HTC (kW/m2K)

50

Shah Correaltions

1

D

+20 %

-20 %

Water R123 - LP R123 - HP

10

20 30

1

E

10

5

5

Deviation Analysis Average = -3 % Absolute Mean = 25.7 % ±20% Range = 60.6 %

3

3

Predicted HTC (kW/m2K)

2

Experimental HTC (kW/m2K)

2

1

1

C

1

2

3

5

10

20 30

50

Experimental HTC (kW/m2K)

Fig. 7. Comparison of straight tube correlations with the HTC data.

B.K. Hardik, S.V. Prabhu / International Journal of Heat and Mass Transfer 117 (2018) 710–728

diameter ratio. The HTC databank collected in the present study is compared with the available correlations for the boiling HTC in helical coils. Well referred correlations of straight tubes HTC are compared with the databank. The comparison is shown with different symbols for R123 and water data. Data for different pressure ranges for R123 (LP and HP) are shown with different colours. Local HTC (inner side, outer side and total) along the axial length of a helical coil and with increase of a quality is compared with various available correlations.

721

in HTC of R123 is less. The slope of HTC in the saturated boiling region decreases with the decrease in the density ratio. This is due to the increase of nucleation boiling domination compared to the convective boiling. As the diameter ratio increases, the inner side HTC increases, while the outer side HTC decreases. Circumferential HTC becomes almost uniform in a high diameter ratio tube and at a low density ratio as shown in Fig. 5(F). 5.3. Comparison of overall averaged heat transfer coefficient with available helical coil correlations

5.1. Wall temperature distribution in helical coils during flow boiling The circumferential wall temperature distribution for two different diameter ratio helical coils is shown in Fig. 4 for water, R123-LP and R123-HP. The density ratio of water-steam and R123 liquid and its vapour is different. The effect of density ratio is analysed by comparing the wall temperature distributions in water, R123-LP and R123-HP data. Fig. 4 shows that inner side and outer side wall temperature difference in a subcooled boiling is higher. Circumferential variation decreases during the nucleate boiling region. Temperature difference starts increasing in the convective boiling region. The variation becomes minimal in the nucleate boiling region. This may be due to the fact that effect of secondary flows is less in the laminar sublayer where bubbles are nucleating. In Fig. 4(A – B), the density difference of water and steam is higher. Hence, the effect of phase separation is higher, which increases the temperature gradient between the inner side and the outer side. The circumferential wall temperature difference in water flow boiling is nearly 10 °C between the inner side and the outer side for the present case. The density difference between R123 liquid and its vapour is less compared to water and steam for Fig. 4(C – F). Hence, the circumferential temperature difference is less. Further, as the system pressure increases, the density difference decreases. The variation in wall temperature is less for R123-HP data compared to R123LP data. R123-LP data has a variation of nearly 5 °C, while R123HP data has a variation of nearly 3 °C. In nucleate boiling region, the circumferential wall temperature variation is minimal for all R123-HP data. Fig. 4(A) and (B) shows the wall temperature distribution during the water flow boiling in two different diameter ratio helical coils. The circumferential wall temperature variation decreases with the increase in the diameter ratio. Diameter ratio effect on circumferential wall temperature variation for R123 LP and HP data is shown in Fig. 4(C, D) and (E, F), respectively. The effect remains same as that of water data. Circumferential temperature variation in Fig. 4(F) is very less due to a low density ratio and a high diameter ratio. 5.2. Heat transfer coefficient distribution in helical coils during flow boiling Local heat transfer coefficient is calculated from the local wall temperature and the bulk fluid temperature for all the data. Sample cases of local HTC distribution during water and R123 flow boiling are shown in Fig. 5. Fig. 5 represents the HTC for the cases of wall temperature distribution shown in Fig. 4. Fig. 5(A) and (B) shows the HTC in water flow boiling system. The HTC on the outer side of a helical coil increases with the increase in the quality in the subcooled and the saturated boiling region. HTC on the inner side of a helical coil increases in the subcooled boiling region and remains almost uniform in the saturated boiling region. Hence, the outer side is dominated with the convective boiling, while the inner side is dominated with the nucleate boiling region. HTC in the R123 flow boiling system is shown in Fig. 5(C – F). Compared to water data, circumferential variation

The HTC correlations available for helical coils are developed for a saturated flow boiling process. No correlation is developed for subcooled HTC in a helical coil. Hence, the helical coil correlations are compared with only saturated overall averaged HTC data. Zhao et al. [30] studied boiling heat transfer characteristics of water in a helical coil with a 32.4 coil to tube diameter ratio. The wall temperature is measured with four thermocouples across the circumference of a helical coil at nine axial locations. Circumferential averaged HTC is matched with Chen’s correlation. The data are centred with the Chen’s correlation. Modified Schrock and Grossman correlation is suggested for helical coils saturated flow boiling HTC with a Seban’s correlation for the single phase HTC in a helical coil. The correlation suggested by Zhao et al. [30] is compared with the present data as shown in Fig. 6(A). This correlation is not working well for the present data. This correlation underpredicts the present data. This correlation predicts all the data with a mean deviation of 27.2%. Aria et al. [2] studied the boiling heat transfer of R134a in a tube in tube helical coil heat exchanger. A correlation is developed base on HTC at three mass flux data. This correlation is compared with the present data as shown in Fig. 6(B). This correlation is not working for the present water and R123 data. This correlation overpredicts the water data and underpredicts the R123 data. The deviation in the R123 data decreases with the decrease in the density ratio. R123-HP data has less deviation than the R123-LP data. Kaji et al. [14] developed a correlation for HTC in helical coils with fluid R113. A correlation works for both nucleate boiling and convective boiling. This correlation is developed with two helical coils (10 mm tube diameter and 16 and 32 diameter ratio) at 3.9 bar system pressure. This correlation is compared with the present data as shown in Fig. 6(C). This correlation is not working for the present dataset. This correlation overpredicts the data of water and R123. This correlation predicts all the data with a mean deviation of 43.4%. Chen et al. [5] developed a correlation for R134a in a helical coil with 7.6 mm tube diameter and diameter ratio of 39.5. This correlation is compared with the present data as shown in Fig. 6(D). This correlation is developed with single helical coil and with fluid (R134a) different than the present fluids (water and R123). This correlation is not working for the present data. The scatter in the prediction is higher. This correlation predicts the data with a mean deviation of 88.4%. Saturated HTC correlations available for helical coils are developed with limited studies. The correlations are developed with only one or two helical coils and with a single fluid. Hence, the available helical coils correlations are not working well for the present dataset. 5.4. Comparison of overall averaged heat transfer coefficient with straight tube correlations Straight tube correlations are compared with the saturated and subcooled flow boiling data. The study of Hardik and Prabhu [11] observed that the overall averaged subcooled HTC in a helical coil is higher than a straight tube. The outer side subcooled HTC is

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Table 5 Statistical analysis of overall averaged HTC with correlations. Fluid

Analysis

Kandlikar [15]

Shah [26,27]

Liu and Winterton [19]

Gungor and Winterton [9]

Schrock and Grossman [25]

Lazarek and Black [18]

Aria et al. [2]

Zhao et al. [30]

Kaji et al. [14]

Chen et al. [5]

Water

Avg. Mean 20% 30% Avg. Mean 20% 30% Avg. Mean 20% 30% Avg. Mean 20% 30%


10.3 14.3 71.7 100.0
2.3 11.1 86.1 97.0
18.8 19.1 60.2 84.9
8.3 13.8 76.3 95.0


8.7 13.9 76.0 98.1
17.3 18.2 56.2 85.1
31.8 31.8 5.4 46.2
18.4 20.3 49.5 79.4


9.5 14.5 74.3 97.0
25.6 26.6 26.9 50.7
34.5 34.5 0.0 30.8
23.5 25.3 32.8 58.0

19.4 20.6 66.0 76.7 7.9 19.7 57.7 81.6 2.4 28.8 31.2 54.8 9.6 22.0 53.7 74.1


34.3 35.2 12.1 30.3
25.4 25.8 32.3 63.9
9.8 13.3 0.0 52.8
24.4 25.7 36.9 60.3

10.9 20.6 64.1 78.2
16.7 18.8 55.2 79.8 9.7 40.0 67.7 87.1
2.9 25.7 60.6 81.0

6022.7 6022.7 0.0 0.0
77.4 77.4 0.0 0.0
59.0 59.0 0.0 0.0 1524.1 1630.6 0.0 0.0


26.1 34.2 25.8 47.0
12.8 24.1 47.7 67.4 15.5 26.2 0.0 18.9
10.4 27.2 40.2 61.8

27.9 37.8 45.5 62.1 33.9 36.6 30.8 40.6 65.8 67.4 0.0 3.8 39.0 43.4 30.2 39.7

88.0 88.2 2.3 6.8 39.2 40.7 34.8 53.0 147.5 148.5 0.0 0.0 87.7 88.4 10.3 17.9

R123
LP

R123-HP

All

higher than that in a straight tube. The inner side subcooled HTC is same as that in a straight tube. Hence, the straight tube correlations are compared with the subcooled water data only for inner side HTC. Overall averaged HTC are compared with straight tube correlations for the subcooled data of R123 fluid and all the saturated data. Ami et al. [1] conducted the experiments of boiling HTC in helical coil with liquid nitrogen. A helical coil with 4 mm tube diameter and diameter ratio 25 is used. Experimental HTC data is compared with different correlations. Ami et al. [1] data match well with the Schrock and Grossman correlation. Nariai et al. [22] conducted the boiling HTC experiments on a helical coil steam generator with a 14.3 mm tube diameter and 41.6 diameter ratio. The data of boiling HTC match well with the Schrock and Grossman correlation. Zhao et al. [30] experimental data match reasonably with the Schrock and Grossman correlation. Schrock and Grossman [25] developed a correlation for vertical upward straight tube based on the experimental data with water. This correlation is developed for a steam quality up to 0.57 with three tube diameters and three heated lengths. The Schrock and Grossman [25] correlation is compared with the present data as shown in Fig. 7(A). This correlation works reasonably well with a mean deviation of 25.6%. The correlation works well for R123-HP data with a mean deviation 13.5%. The deviation increases with the increase in the density ratio. Nariai et al. [22] HTC data are generated for high system pressure and hence, with a low density ratio fluid. Ami et al. [1] data for liquid nitrogen and its vapour has a low density ratio. Hence, the Schrock and Grossman correlation matches well this low density ratio data. Data of Zhao et al. [30] has comparatively high density ratio of water and steam at 5–35 bar pressure. Hence, the deviation between the Schrok and Grossman correlation with the data of Zhao et al. [30] is large. Present study shows that the Schrok and Grossman correlation works well for a low density ratio data. Recently, Santini and Cioncolini [24] presented the experimental analysis of boiling HTC in a helical coil steam generator. The investigation is performed on a helical coil with tube diameter 12.5 mm and diameter ratio 80. The experimental data is compared with helical coil and straight tube correlations. Gungor and Winterton [9] and Liu and Winterton [19] correlations matched well with the experimental data. Gungor and Winterton [9] developed a general correlation for subcooled and saturated flow boiling HTC in straight vertical and horizontal tubes. This correlation is developed by collecting the large databank from the literature

and included different fluids with large parameters range. Gungor and Winterton [9] correlation is compared with the present databank as shown in Fig. 7(B). This correlation works reasonably well for the present data of water and R123. This correlation predicts all the data with a mean deviation of 22.1%. This correlation predicted the straight tube data from the literature with a mean deviation of 25.0%. The deviation of the present data with this correlation is within the deviation from the straight tube data from which the correlation is derived. Moreover, the data used for development of Gungor and Winterton correlation does not include R123 fluid. Liu and Winterton developed a correlation with the same databank of Gungor and Winterton [9] correlation and added the cryogenics data. This correlation is developed using water data but R123 data is not included. The comparison of the present data with this correlation is shown in Fig. 7(C). This correlation works well for water data. This correlation predicts the water data with a mean deviation of 14.5%. This correlation underpredicts R123 data. The deviation for R123-HP data is higher compared to R123-LP data. This correlation predicts all the data with a mean deviation 25.3%. The study of Hardik and Prabhu [11] with water suggested that the Kandlikar’s correlation works well for water data. Kandlikar [15] developed a general correlation for subcooled and saturated flow boiling in a straight tube. This correlation is developed for different fluids. This correlation has fluid dependent parameter which depends on the thermo-physical properties of the flowing fluid. Kandlikar [15] gave the values for different fluids. This correlation does not include the fluid R123. Hence, the fluid dependent parameter for R123 is not given by Kandlikar [15]. The properties of the fluid R123 are nearly similar to fluids R11 and R113. Hence, in the present study, fluid dependent parameter for R123 is taken as 1.30. Comparison of this modified correlation with the present data is shown in Fig. 7(D). This correlation works well for water data. This correlation works well for R123-LP data. This correlation gives a mean deviation of 14.1% and 11.1% for water data and R123-LP data, respectively. This correlation gives slightly higher deviation for R123-HP data. This correlation deviates higher for R123-HP subcooled data. This correlation predicts all the R123HP data with a mean deviation of 19.1%. This correlation predicts all the databank with a mean deviation 13.8%. Shah [26] and Shah [27] developed general correlations for subcooled and saturated HTC in straight tubes, respectively. The subcooled and saturated correlations are compared with the present data as shown in Fig. 7(E). These correlations work well for water

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R123 Data

Water Data

Non-dimensional Axial length (Lh /D) 0

60

90

120

150

0

180

30

60

Heat Transfer Coefficient (kW/m2K)

Coil - 2; d = 7.5 mm; D = 150 mm q'' = 74.96 kW/m2; G = 676 kg/m2s

12

Outer Side Inner Side Gungor Correlation Total

10 8 6 4

Average Deviation Saturated Subcooled Outer Side = -4 % Outer Side = -25 % Inner Side = 29 % Inner Side = --16 % Total = 10 % Total = -21 %

2 0 -0.1

A

0

0.1

0.2

0.3

0.4

B

60

Average Deviation Subcooled Outer Side = -17 % Inner Side = 26 % Total = -1 % Saturated Outer Side = -13 % Inner Side = 149 % Total = 29 %

20

0 -0.1

0

60

90

120

0.1

0.2

0.3

Quality (x) 150

Non-dimensional Axial length (Lh /D) 0

180

Coil - 2; d = 7.5 mm; D = 150 mm

Heat Transfer Coefficient (kW/m2K)

Heat Transfer Coefficient (kW/m2K)

30

Outer Side Inner Side Total Gungor Correlation

40

30

60

q'' = 74.96 kW/m2; G = 676 kg/m2s

90

120

150

180

12

Outer Side Inner Side Total Liu Correlation

10 8 6 4

Average Deviation Saturated Subcooled Outer Side = -35 % Outer Side = -41 % Inner Side = -12 % Inner Side = -34 % Total = -25 % Total = -38 %

2 0 -0.1

0

0.1

0.2

0.3

0.4

D

Coil - 3; d = 8.0 mm; D = 137 mm q'' = 293 kW/m2; G = 190 kg/m2s 80

60

Average Deviation Subcooled Outer Side = -30 % Inner Side = 6 % Total = -15 % Saturated Outer Side = -42 % Inner Side = 65 % Total = -15 %

20

0 -0.1

0

30

60

90

120

0.1

0.2

0.3

Quality (x)

Non-dimensional Axial length (Lh /D) 0

Outer Side Inner Side Total Liu Correlation

40

Quality (x) 150

Non-dimensional Axial length (Lh /D) 0

180

30

60

90

120

150

180

100

Coil - 2; d = 7.5 mm; D = 150 mm

Heat Transfer Coefficient (kW/m2K)

Heat Transfer Coefficient (kW/m2K)

180

100

14

q'' = 74.96 kW/m2; G = 676 kg/m2s 12

Outer Side Inner Side Total Lazarek Correlation

10 8 6 4

Average Deviation Saturated Outer Side = -32 % Inner Side = -9 % Total = -22 %

2

Coil - 3; d = 8.0 mm; D = 137 mm q'' = 293 kW/m2; G = 190 kg/m2s 80

60

Average Deviation

Outer Side Inner Side Total Lazarek Correlation

Saturated Outer Side = -42 % Inner Side = 67 % Total = -13 %

40

20

0

0

E

150

q'' = 293 kW/m2; G = 190 kg/m2s 80

Non-dimensional Axial length (Lh /D) 0

14

120

Coil - 3; d = 8.0 mm; D = 137 mm

Quality (x)

C

90

100

14

Heat Transfer Coefficient (kW/m2K)

30

Non-dimensional Axial length (Lh /D)

-0.1

0

0.1

0.2

0.3

0.4

Quality (x)

F

-0.1

0

0.1

0.2

0.3

Quality (x)

Fig. 8. Comparison of local HTC with selected correlations.

data. These correlations predict all the water data with a mean deviation of 13.9%. These correlations underpredict the data of R123. The deviation increases with the decrease in the density

ratio. These correlations predict the R123-LP data with a mean deviation of 18.2% and R123-HP data with a mean deviation of 31.8%.

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Water Data

R123 Data

Non-dimensional Axial length (Lh /D)

Non-dimensional Axial length (Lh /D) 0

60

90

120

150

180

0

Coil - 2; d = 7.5 mm; D = 150 mm

Heat Transfer Coefficient (kW/m2K)

Heat Transfer Coefficient (kW/m2K)

A

30

30

60

q'' = 74.96 kW/m2; G = 676 kg/m2s 12

Outer Side Inner Side Total Schrock Correlation

10 8 6 4

Average Deviation Saturated Outer Side = -37 % Inner Side = -16 % Total = -28 %

2 0 -0.1

0

0.1

0.2

0.3

0.4

B

80

60

40

20

0 -0.1

0

60

90

120

0.1

0.2

0.3

Quality (x) 150

Non-dimensional Axial length (Lh /D)

180

0

Coil - 2; d = 7.5 mm; D = 150 mm

Heat Transfer Coefficient (kW/m2K)

Heat Transfer Coefficient (kW/m2K)

30

Outer Side Inner Side Total Schrock Correlation

Saturated Outer Side = -49 % Inner Side = 47 % Total = -25 %

30

60

q'' = 74.96 kW/m2; G = 676 kg/m2s

90

120

150

180

12

Outer Side Inner Side Total Shah Correlation

10 8 6 4

Average Deviation Saturated Subcooled Outer Side = -30 % Outer Side = -26 % Inner Side = -6 % Inner Side = -17 % Total = -20 % Total = -22 %

2 0 -0.1

0

0.1

0.2

0.3

0.4

D

Coil - 3; d = 8.0 mm; D = 137 mm q'' = 293 kW/m2; G = 190 kg/m2s 80

60

Average Deviation Subcooled Outer Side = -33 % Inner Side = 2 % Total = -19 % Saturated Outer Side = -37 % Inner Side = 82 % Total = -6 %

20

0 -0.1

0

30

60

90

120

0.1

0.2

0.3

Quality (x) Non-dimensional Axial length (Lh /D)

Non-dimensional Axial length (Lh /D) 0

Outer Side Inner Side Total Shah Correlation

40

Quality (x) 150

180

0

30

60

90

120

150

180

100

Coil - 2; d = 7.5 mm; D = 150 mm

Heat Transfer Coefficient (kW/m2K)

Heat Transfer Coefficient (kW/m2K)

180

100

14

q'' = 74.96 kW/m2; G = 676 kg/m2s 12

Outer Side Inner Side Total Kandlikar Correlation

10 8 6 4

Average Deviation Saturated Subcooled Outer Side = -14.2 % Outer Side = -17.3 % Inner Side = -4.2 % Inner Side = 11.2 % Total = -5.1 % Total = -9.5 %

2 0

E

150

q'' = 293 kW/m2; G = 190 kg/m2s Average Deviation

Non-dimensional Axial length (Lh /D) 0

14

120

Coil - 3; d = 8.0 mm; D = 137 mm

Quality (x)

C

90

100

14

Coil - 3; d = 8.0 mm; D = 137 mm q'' = 293 kW/m2; G = 190 kg/m2s 80

60

Average Deviation Subcooled Outer Side = -36 % Inner Side = -2 % Total = -23 % Saturated Outer Side = -35 % Inner Side = 87 % Total = -3 %

Outer Side Inner Side Total Kandlikar Correlation

40

20

0 -0.1

0

0.1

0.2

0.3

0.4

F

-0.1

0

0.1

0.2

0.3

Quality (x)

Quality (x) Fig. 9. Comparison of local HTC with selected correlations.

Lazarek and Black [18] developed a correlation for R113 in straight tubes. This correlation is compared with the present data as shown in Fig. 7(F). This correlation works well for small diame-

ter tube. This correlation does not work well for 9.5 mm diameter tubes R123 data and 10 mm diameter tubes water data. This correlation predicts all the data with a mean of deviation 25.7%.

B.K. Hardik, S.V. Prabhu / International Journal of Heat and Mass Transfer 117 (2018) 710–728

The statistical analysis of the present dataset with all the correlations of helical coils and straight tubes are given in Table 5. Analysis shows average deviation, mean absolute average deviation and percentage of data fall within ±20% and ±30% deviation for all the data. The analysis is carried out for water, R123-LP and R123-HP data separately. Among all the correlations, Kandlikar [15] correlation works well for all the data followed by Shah correlations for subcooled and saturated flow boiling HTC.

6. Comparison of local heat transfer coefficient with selected correlations Flow boiling process is divided into three different boiling regions namely subcooled boiling, nucleate boiling and convective boiling. Mode of the heat transfer in different regions is different. Subcooled boiling and nucleate boiling is dominated with the heat transfer by nucleate boiling, while convection boiling region is dominated with forced convective heat transfer. The slope of HTC in different regions is different. The slope of heat transfer curve changes from one boiling region to another. Moreover, the heat transfer on the inner side and the outer side of a helical coil is different. Inner side is mostly dominated with nucleate boiling while the outer side is dominated by convective boiling due to secondary flows. Hence, from design point of view, it is important to predict the local heat transfer coefficient in different boiling regions. Any suggested correlation should have to represent the boiling process in different regions. Most of the literature available for helical coils show the average HTC and suggest the correlation that works well only for averaged HTC. The correlation that works well to predict overall averaged HTC need not essentially represent the complete boiling process accurately. Hence, in the present section, the axial local heat transfer coefficient measured along the length of tube is compared with the correlations those work well for overall averaged HTC with the increase of quality and non-dimensional axial length. A typical comparison for one sample case of water and R123 is shown in Fig. 8. The experimental heat transfer coefficient is measured in both subcooled and saturated regions. The correlations available for subcooled and saturated regions are compared in the respective regions. Gungor and Winterton [9] developed the correlation for subcooled and saturated flow boiling. This correlation is developed in the form of a single equation by adding the contribution of forced convection and nucleate boiling. Comparison of this correlation with local HTC data of water and R123 along the axial length of coil is shown in Fig. 8(A – B). Due to the addition of the effect of nucleate boiling and convective boiling, this correlation shows continuous increase in the subcooled and saturated boiling region. In the actual case, the HTC decreases in the nucleate boiling region and increases in the convective boing region. Hence, this correlation does not show the actual boiling process in the nucleate boiling region. Moreover, the equations for subcooled and saturated boiling are matching at zero quality for water data but fail to match for R123 data. These equations have large deviation in the transition region (at zero quality) for all R123 data. Liu and Winterton [19] developed a correlation for subcooled and saturated flow boiling regions. This correlation is developed by combining the effect of nucleate boiling and forced convection using root mean square method. Comparison of this correlation with the HTC data for water and R123 along the axial length of coil is shown in Fig. 8(C – D). This correlation shows continuous increase in HTC in subcooled and saturated boiling region. Hence, this correlation does not show the actual boiling process in the nucleate boiling region. In the present experimental data, a saturated HTC for R123 is almost uniform with the increase of quality, while this correlation shows increment.

725

Lazarek and Black [18] developed a correlation for saturated flow boiling Nusselt number as a function of liquid Reynolds number and Boiling number. Comparison of the present data with this correlation is shown in Fig. 8(E – F). For specific heat flux and mass flux, Boiling number and Reynolds number remain almost constant. Numbers are varying slightly in saturated boiling region due to the property variation with the decrease in the system pressure along the axial length of coil. This correlation varies with the variation in the mass flux and the heat flux and not with the variation in quality. Hence, the HTC predicted by Lazarek and Black [18] remains almost constant along the axial length of coil. This correlation predicts the trend of R123 HTC but does not predict the HTC variation for water. Schrock and Grossman [25] developed a correlation for saturated boiling Nusselt number as a function of Boiling number and Lockhart-Martinelli (LM) parameter. The LM parameter decreases with the increase in the quality. Hence, the HTC increases in the saturated boiling region with the increase of quality. This correlation predicts the boiling process for water data but does not predict the boiling process for R123 data. Shah [27] developed a correlation for saturated flow boiling. This correlation has three equations. Different equations are used to predict the HTC in different regions namely nucleate boiling, bubbles suppression and convective boiling regions. Maximum value among three equations is used to predict HTC. Shah [26] developed a correlation for subcooled flow boiling, which is similar to the equation of nucleate flow boiling. The comparison of Shah [27] and Shah [26] correlations with the present data is shown in Fig. 9(C – D). Shah [27] correlation represents different slopes for HTC in nucleate and convective boiling regions. The correlation gives smaller length of nucleate boiling region than the actual data for both R123 and water. Kandlikar [15] developed a correlation for subcooled and saturated flow boiling. The correlation has different equations for nucleate and convective boiling. Both the equations are functions of Collier number and Boiling number. Domination of both the numbers in different region are different. Collier number is dominated in the convective boiling, while the boiling number is dominated in the nucleate boiling. Kandlikar [15] equation for the subcooled flow boiling is similar to the nucleate boiling equation with Collier number equals to zero. The comparison of the present data with the correlation is shown in Fig. 9(E – F). This correlation represents different slopes for HTC in subcooled, nucleate and convective boiling regions. Overall, Kandlikar [15] correlation represents the boiling process for the present data of water and R123. Separate equations for different boiling region should have to intersect at the transition region (at zero quality). The individual equations developed for subcooled and saturated heat transfer coefficient should have to intersect at zero quality for both water and R123 data. Gungor and Winterton [9] gave separate equations for subcooled and saturated boiling regions. These equations have large deviation at the transition region (At zero quality) for R123 data. Subcooled and saturated regions equations given by Liu and Winterton [19], Shah [27] and Shah [26] and Kandlikar [15] are intersecting at zero quality for all the data.

7. Conclusions Experimental local HTC data and overall averaged HTC data are collected for helical coil flow boiling system. Total 400 data are collected for broad range of parameters. The data includes two different fluids namely water and R123. Data covers the parameters range of a mass flux of 100–1300 kg/m2 s, a heat flux of 2–640 kW/m2, a density ratio of 30–1600, an exit quality of
0.5 to 1 and a coil to tube diameter ratio 14–58. The effect of diameter ratio

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B.K. Hardik, S.V. Prabhu / International Journal of Heat and Mass Transfer 117 (2018) 710–728

(5) Kandlikar [15] correlation for saturated flow boiling works well for the present data followed by Shah [27] correlation. (6) Kandlikar [15] correlation for subcooled HTC works well for R123 data. Inner side subcooled HTC for water data is predicted well with the Kandlikar [15] correlation. (7) Fluid dependent parameter (Ffl) used in Kandlikar [15] correlation has a value of 1.3 for R123.

and density ratio is analysed on the inner side and outer side wall temperature distribution and the HTC of a helical coil. The correlations of helical coils and straight tubes are compared with the HTC data. Following are the conclusions that may be drawn from the present study; (1) Saturated flow boiling HTC in a helical coil is same as that of a straight tube. Coil curvature affects the HTC on the inner side and the outer side of helical coil. Inner side HTC increases with the increase in diameter ratio, while the outer side HTC decreases with the increase in diameter ratio. Total circumferential averaged HTC in a saturated boiling region remains same as that in a straight tube. (2) Circumferential variation in the HTC decreases with the decrease in the density ratio. (3) Inner side HTC in the subcooled boiling region for water data is same as that in a straight tube. Outer side HTC in the subcooled region is higher than that in a straight tube. Hence, the overall average HTC in the subcooled region for water is higher than that in a straight tube. (4) Circumferential variation of subcooled HTC for R123 is less. Hence, the inner side and outer side HTC are almost remain same. Circumferential averaged HTC for R123 is same as that in a straight tube.

Acknowledgements Authors hereby acknowledge the financial support given by Ministry of Defence (R and D). Authors wish to acknowledge the support given by Captain Binduraj from Ministry of Defence (R and D), Shri K.N. Vyas, Shri Joe Mohan and Shri Inder Kumar 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 and Mr. Gajendra Kumar for his assistance in experiments. Conflict of interest None declared.

Appendix A. Correlations for heat transfer coefficient in helical coils

Authors

Conclusions

Kaji et al. [14]

hTP hlo

3 1=3

3

¼ ½ð4  104 BoRe
0:12 Þ þ f2:6ð1=X tt Þ0:95 g   
1=12 0:4 0:061 Nulo ¼ Pr41 Re5=6 Dd 1þ 1=6 2:5 ½Reðd=DÞ



Zhao et al. [30]

þ 183000Bo1:46 htp =hDB ¼ 1:6X
0:74 tt

Wongwises and Polsongkram [29]

NuTP ¼ 6895:98De0:432 Pr
5:055 ðBo  104 Þ Eq l

0:132

Gð1
xÞd

DeEq

Rel ¼ l ; Reg ¼ l l g  l q 0:5
0:5 d ¼ Rel þ Reg lg qg D

2:84X
0:27 tt

l

l

Chen et al. [5]

þ ð46162Bo
0:88Þ hTP =hlo ¼ 0:1 hlo ¼ 0:023Re0:85 Pr0:4 ðd=DÞ

Aria et al. [2]

Pr
5:055 ðBo  104 Þ NuTP ¼ 7850De0:432 Eq l

1:15

0:125

Appendix B. Correlations for heat transfer coefficient in straight tubes Authors

Correlation

Shah [26] (subcooled)

u ¼ hhTPl ¼ DTqsat hl

00

ðDT SC =DT sat Þ < 2

SC u ¼ u0 ; DDTTsat < 6:3  104 Bo1:25

SC u ¼ u0 þ DT SC =DT sat ; DDTTsat > 6:3  104 Bo1:25

u0 ¼ 230Bo0:5 ; Bo > 0:3  10
4 u0 ¼ 1 þ 46Bo0:5 ; Bo < 0:3  10
4

0:4 hl ¼ 0:023ðkl =dÞRe0:8 l Pr l hTP ¼ q00 =ðT W
T B Þ ¼ q00=ðDT SC þ DT sat Þ Rel ¼ Gd l l

ðDT SC =DT sat Þ > 2

u ¼ u0 þ DT SC =DT sat DT sat ¼ T w
T sat DT SC ¼ T w
T b

Xtt
0:0238

Gxd

Xtt
0:036

727

B.K. Hardik, S.V. Prabhu / International Journal of Heat and Mass Transfer 117 (2018) 710–728 Appendix B (continued)

Authors

Correlation

u ¼ hhTPl u ¼ maxðunb ; ucb ; ubs Þ

Shah [27] (saturated)

0:8 hl ¼ 0:023ðkl =dÞRe0:8 Pr 0:4 l ð1
xÞ l

unb ¼ 230Bo0:5 ; Bo > 0:3  10
4 unb ¼ 1 þ 46Bo0:5 ; Bo < 0:3  10
4 2

Co ¼ Lazarek and Black [18] (saturated) Gungor and Winterton [9] (subcooled) Gungor and Winterton [9] (saturated) Liu and Winterton [19] (subcooled)

Fr ¼ g Gq2 d l
1
x0:8 qg 0:5

F ¼ 14:7; Bo P 11  10
4

Rel ¼ Gd ll

q00 ¼ hl DT b þ ShPool DT sat q00 ¼ hl ðT w
T b Þ þ ShPool ðT w
T sat Þ q00 hTP ¼ Dq00 T b ¼ ðT w
T b Þ

hPool ¼ 55P0:12 q002=3 ð
log10 P r Þ r

l


0:55

hTP ¼ Ehl þ ShPool

E

hTP ¼ Dq00 Tb  qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi T sat
T b DT b ¼ 1 þ f1 þ ð1 þ A2bp Þð1 þ A2pq Þg 2 1þAbp

Abp ¼ ShFhl Apq ¼ Sh 2

2

L

L

ql

x

d ¼ 30Re0:857 Bo0:714 Nu ¼ hTP l k

hTP ¼ ðFhL Þ þ ðShPool Þ

q00

Pool ðT sat
T b Þ

Pool

Liu and Winterton [19] (saturated) Kandlikar [15] (fully developed subcooled boiling flow) Kandlikar [15] (saturated)

ucb ¼ 1:8N
0:8 ; N > 1:0
4 ubs ¼ FBo0:5 expð2:74N
0:1 Þ; 0:1 < N 6 1:0 F ¼ 15:43; Bo < 11  10 N ¼ Co; Fr L P 0:04 ubs ¼ FBo0:5 expð2:47N
0:15 Þ; N 6 0:1 N ¼ 0:38Fr
0:3 Co; Fr < 0:04

2

M
0:5


1 S ¼ ð1 þ 1:15  10
6 E2 Re1:17 Þ l 0:8 0:4 hl ¼ 0:023ðkl =dÞRel Pr l Rel ¼ Gdð1
xÞ ll ¼ 1 þ 24000Bo1:16 þ 1:37ð1=X tt Þ0:86

0:4 hl ¼ 0:023ðkl =dÞRe0:8 l Pr l
0:55
0:5 0:12 2=3 hPool ¼ 55Pr q00 ð
log10 P r Þ M h q i0:35 F ¼ 1 þ xPr L qg
1 ;x > 0 l F ¼ 1; x 6 0
1

Þ S ¼ ð1 þ 0:055F 0:1 Re0:16 l Rel ¼ Gd l l



00

h ¼ DqT sat ¼ 1058Bo0:7 hl F fl hTP ¼ DT SC q00 þDT sat

Rel Pr l ðf =2Þ 2=3 0:5 1:07þ12:7ðPr l
1Þðf =2Þ
2 ½1:58 lnðRel Þ
3:28 Rel ¼ Gd ll

Nul ¼ hkl d ¼ l

f ¼

1

q00 ¼ ½1058ðGifg Þ
0:7 F fl hl DT sat 0:3

F fl ¼ 1 for Water

hTP ¼ maxðhTP;NB ; hTP;CB Þ 0:8 Pr 0:4 hl ¼ 0:023ðkl =dÞRe0:8 l ð1
xÞ l
1
x0:8 qg 0:5 Co ¼ x q l





hTP  hl  CB hTP hl NB

References [1] T. Ami, N. Nakamura, T. Tsuruno, H. Umekawa, M. Ozawa, Boiling heat transfer and flow characteristics of liquid nitrogen in helically coiled tube, Jpn. J. Multiphase Flow 24 (2011) 567–576. [2] H. Aria, M.A. Akhavan-Behabadi, F.M. Shemirani, Experimental investigation on flow boiling heat transfer and pressure drop of HFC-134a inside a vertical helically coiled tube, Heat Transfer En. 33 (2) (2012) 79–87. [3] P.K. Baburajan, G.S. Bisht, S.K. Gupta, S.V. Prabhu, Measurement of subcooled boiling pressure drop and local heat transfer coefficient in horizontal tube under LPLF conditions, Nucl. Eng. Des. 255 (2013) 169–179. [4] K.J. Bell, A. Owhadi, Local heat-transfer measurements during forcedconvection boiling in a helically coiled tube, Proc. Inst. Mech. Eng., Conf. Proc. 184 (3) (1969) 52–58. [5] C.N. Chen, J.T. Han, T.C. Jen, L. Shao, Thermo-chemical characteristics of R134a flow boiling in helically coiled tubes at low mass flux and low pressure, Thermochim. Acta 512 (1) (2011) 163–169. [6] Y.J. Chung, K.H. Bae, K.K. Kim, W.J. Lee, Boiling heat transfer and dryout in helically coiled tubes under different pressure conditions, Ann. Nucl. Energy 71 (2014) 298–303. [7] A.M. Fsadni, J.P.M. Whitty, A review on the two-phase heat transfer characteristics in helically coiled tube heat exchangers, Int. J. Heat Mass Transf. 95 (2016) 551–565. [8] A.M. Fsadni, J.P.M. Whitty, A review on the two-phase pressure drop characteristics in helically coiled tubes, Appl. Therm. Eng. 103 (2016) 616–638. [9] K.E. Gungor, R.H.S. Winterton, A general correlation for flow boiling in tubes and annuli, Int. J. Heat Mass Transfer 29 (1986) 351–358. [10] B.K. Hardik, P.K. Baburajan, S.V. Prabhu, Local heat transfer coefficient in helical coils with single phase flow, Int. J. Heat Mass Transfer 89 (2015) 522– 538.

For Water ¼ 1:136Co
0:9 þ 667:2Bo0:7 F fl ¼ 0:6683Co
0:2 þ 1058Bo0:7 F fl

[11] B.K. Hardik, S.V. Prabhu, Boiling pressure drop and local heat transfer distribution of helical coils with water at low pressure, Int. J. Therm. Sci. 114 (2017) 44–63. [12] B.K. Hardik, G. Kumar, S.V. Prabhu, Boiling pressure drop, local heat transfer distribution and critical heat flux in horizontal straight tubes, Int. J. Heat Mass Transf. 113 (2017) 466–481. [13] K.W. Hwang, D.E. Kim, K.H. Yang, J.M. Kim, M.H. Kim, H.S. Park, Experimental study of flow boiling heat transfer and dryout characteristics at low mass flux in helically-coiled tubes, Nucl. Eng. Des. 273 (2014) 529–541. [14] M. Kaji, K. Mori, T. Matsumoto, M. Oishi, T. Sawai, S. Nakanishi, Forced convective boiling heat transfer characteristics and critical heat flux in helically coiled tubes, Nippon Kikai Gakkai Ronbunshu 64 (1998) 3343–3349. [15] S.G. Kandlikar, Development of a flow boiling map for subcooled and saturated flow boiling of different fluids inside circular tubes, J. Heat Transfer 113 (1991) 190–200. [16] S.J. Kline, F.A. McClintock, Describing uncertainties in single sample experiments, Mech. Eng. (1953) 3–8. [17] M. Kozeki, H. Nariai, T. Furukawa, K. Kurosu, A study of helically coiled tube once-through steam generator, Bull. Jpn. Soc. Mech. Eng. 13 (60) (1970) 1485– 1494. [18] G.M. Lazarek, S.H. Black, Evaporative heat transfer, pressure drop and critical heat flux in a small vertical tube with R-113, Int. J. Heat Mass Transfer 25 (1982) 945–960. [19] Z. Liu, R.H.S. Winterton, A general correlation for saturated and subcooled flow boiling in tubes and annuli, based on a nucleate pool boiling equation, Int. J. Heat Mass Transfer 34 (1991) 2759–2766. [20] J.R. Moffat, Describing the uncertainties in experimental results, Exp. Therm. Fluid Sci. 1 (1988) 3–17. [21] P. Naphon, S. Wongwises, A review of flow and heat transfer characteristics in curved tubes, Renewable Sustainable Energy Rev. 10 (5) (2006) 463–490.

728

B.K. Hardik, S.V. Prabhu / International Journal of Heat and Mass Transfer 117 (2018) 710–728

[22] H. Nariai, M. Kobayashi, T. Matsuoka, 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. 19 (11) (1982) 936–947. [23] A. Owhadi, K.J. Bell, B. Crain, Forced convection boiling inside helically-coiled tubes, Int. J. Heat Mass Transfer 11 (12) (1968) 1779–1793. [24] L. Santini, A. Cioncolini, M.T. Butel, M.E. Ricotti, Flow boiling heat transfer in a helically coiled steam generator for nuclear power applications, Int. J. Heat Mass Transfer 92 (2016) 91–99. [25] V.E. Schrock, L.M. Grossman, Forced convection boiling in tubes, Nucl. Sci. Eng. 12 (4) (1962) 474–481. [26] M.M. Shah, A general correlation for heat transfer during subcooled boiling in pipes and annuli, ASHRAE Trans. 83 (1977) 202–217.

[27] M.M. Shah, Chart correlation for saturated boiling heat transfer: equations and further study, ASHRAE Trans. 88 (1982) 185–196. [28] S. Vashisth, V. Kumar, K.D. Nigam, A review on the potential applications of curved geometries in process industry, Ind. Eng. Chem. Res. 47 (10) (2008) 3291–3337. [29] S. Wongwises, M. Polsongkram, Evaporation heat transfer and pressure drop of HFC-134a in a helically coiled concentric tube-in-tube heat exchanger, Int. J. Heat Mass Transfer 49 (3) (2006) 658–670. [30] L. Zhao, L. Guo, B. Bai, Y. Hou, X. Zhang, Convective boiling heat transfer and two-phase flow characteristics inside a small horizontal helically coiled tubing once-through steam generator, Int. J. Heat Mass Transfer 46 (25) (2003) 4779– 4788.