Thermal performance of helical coils with reversed loops and wire coil inserts

International Journal of Heat and Mass Transfer 146 (2020) 118723

Contents lists available at ScienceDirect

International Journal of Heat and Mass Transfer journal homepage: www.elsevier.com/locate/ijhmt

Thermal performance of helical coils with reversed loops and wire coil inserts Yi Wang a, Jorge L. Alvarado b,⇑, Wilson Terrell Jr. c a

Department of Mechanical Engineering, Texas A&M University, College Station, TX 77843, USA Department of Engineering Technology and Industrial Distribution, Texas A&M University, College Station, TX 77843, USA c Department of Engineering Science, Trinity University, San Antonio, TX 78212, USA b

a r t i c l e

i n f o

Article history: Received 5 June 2019 Received in revised form 6 August 2019 Accepted 11 September 2019

Keywords: Convective heat transfer Helical coils Heat exchanger Passive heat transfer enhancement Wire coil spring inserts Turbulence promoter Pressure drop Friction factor Nusselt number Dean number

a b s t r a c t Flow and heat transfer characteristics of water in a newly designed helical coil heat transfer device were investigated in this experimental study. The conventional helical coil configuration was structurally modified aiming to improve its heat transfer performance. Specifically, 360° plastic tubing with or without wire coil inserts was added after each 180° of the main helical coil loop to enhance fluid mixing and redistribute the flow, which should have a direct effect on the thermal performance of the helical coil heat transfer device. Experimental results show that the structural modifications of the conventional helical coil configuration led to enhanced heat transfer in the test section while the pressure drop penalty increased slightly. Furthermore, the heat transfer performance of the overall test section improved by using wire coil inserts in the plastic tubing after every 180° of the main helical coil loop. The results reveal that the modified helical coil section offers a good trade-off between heat transfer enhancement and pressure drop penalty. Ó 2019 Elsevier Ltd. All rights reserved.

1. Introduction As the demand for thermal energy continues to increase, devices such as heat exchangers should be modified and optimized to meet the needs of energy-transport systems. Over the last century, heat exchangers have been designed and used to transfer thermal energy from one fluid to another in relatively compact configurations. In particular, coil heat exchangers (CHX) are efficient due to their compactness and good heat transfer performance. Secondary flows induced by centrifugal forces occur due to the curvature of the coil, which positively affects thermal performance in a CHX. Researchers have studied hydrodynamic and convective heat transfer performance of flows in conventional helically coiled tubes [7–16,20,23]. However, no study has investigated the effect of wire coil inserts on the thermal performance of helical coils with external reversed loops. Specifically, the use of wire coil inserts as passive enhancements only in the external reversed loops have not been considered before, which may enhance the heat transfer performance while avoiding higher

⇑ Corresponding author. E-mail address: [email protected] (J.L. Alvarado). https://doi.org/10.1016/j.ijheatmasstransfer.2019.118723 0017-9310/Ó 2019 Elsevier Ltd. All rights reserved.

pressure drop if used throughout the whole heat transfer loop. The effect of the wire coil pitch (3 mm and 20 mm) on pressure drop, heat transfer coefficient and overall performance enhancement index were investigated as part of this study. As shown in the results section, wire coil inserts in the reversed loops led to greater heat transfer rate and greater performance enhancement index values when compared to the standard helical coil systems. Accordingly, a new helical coil test configuration for CHX has been designed and tested successfully. Specifically, a 360° reversed plastic tubing with or without wire coil inserts have been integrated to the main helical loop at each 180° of the coil to further enhance heat transfer within the CHX. In summary, external reversed loops with inserts were used in the study to promote fluid mixing and enhance heat transfer in the CHX.

1.1. Flow characteristics in coiled tubes Dean [1] first discovered the presence of a secondary flow field in coiled tubes and formulated a non-dimensional (Dean) number to account for the effects of curvature ratio and Reynolds number on secondary flows. The Dean number is defined as follows:

2

Y. Wang et al. / International Journal of Heat and Mass Transfer 146 (2020) 118723

Nomenclature A cp CHX CH d D DAQ De DPT f FM h HX k L _ m Nu p P P1 PH Pr DP q00 r R

De ¼ Re 

helical coil surface area, m2 specific heat, J/kg-°C coil heat exchanger chiller inner tube diameter, m coil curvature diameter, m data acquisition Dean number differential pressure transducer friction factor flow meter heat transfer coefficient, kW/m2-°C heat exchanger thermal conductivity of the fluid, W/m-°C tube length, m mass flow rate, kg/s Nusselt number tube perimeter, m wire coil inserts pitch, m pump preheater Prandtl number pressure difference between inlet and outlet of the tube, kPa heat flux, kW/m2 tube inner radius, m coil curvature radius, m

rffiffiffi rffiffiffi r qud r ¼  R R l

ð1Þ

where q, l, u, d, r and R are the density, dynamic viscosity of the fluid, fluid mean velocity, inner diameter of the tube, inner radius of the tube, curvature radius of the coil, respectively. Dravid et al. [2] observed and validated the existence of a secondary flow field in coiled tubes. Numerical studies were conducted under laminar flow regime with Dean Numbers greater than 100. Their results revealed that cyclic oscillations in coil wall temperature could be observed along the tube axis, due to the presence of secondary flows. Pakdaman et al. [3] characterized the performance of nanofluids flowing inside helically coiled tubes. It was found that the corresponding heat transfer enhancement was significant in a helically coiled tube when compared to a straight tube. Huttl et al. [4] numerically studied turbulent flows in straight, curved and helically coiled pipes. It was found that a secondary flow was generated due to the curvature of the pipes, which made the corresponding flow structures different from those in straight pipes. Mishra and Gupta [5] experimentally measured pressure drop of water flowing through helical coils in both laminar and turbulent regimes. For turbulent flows, the following correlation was obtained based on the least-square analysis of the data.

 f c ¼ f s þ 0:0075 

d Dc

0:5

  p 2  Dc ¼ 2Rc 1 þ 2p R where 4000 < Re < 100,000,

ð2Þ

ð3Þ

Re R2 T u U x Xn

Reynolds number coefficient of determination temperature, °C fluid velocity, m/s given function of independent variables in uncertainty analysis axial position along the tube, m independent variable in uncertainty analysis

Greek symbols q fluid density, kg/m3 l dynamic viscosity, Pas g performance enhancement index between plain helical coil and modified coil r uncertainty associated with certain variable Subscripts b bulk c coil cri critical condition e effective r radius of test section with reversed loops rev reversed loop S straight pipe w tube wall/surface

0:00289 < r=R < 0:155 0 < p=Dc < 25:4 d is the inner diameter of the coil tube, Dc is the effective curvature diameter of the coil defined in Eq. (3), p is the pitch of the helical coil, and the Fanning friction factor ðf s Þ in a smooth straight tube under turbulent flow condition is as follows:

fs ¼

0:079 Re0:25

ð4Þ

where 4000 < Re < 100,000. Srinivasan et al. [6] conducted an experimental study comparing twelve coils with curvature ratios d/D from 0.0097 to 0.135. The experiments were carried out with water and oil under both laminar and turbulent conditions. A correlation for friction factor of laminar flows was defined based on Seban and McLaughlin’s approach [7], as follows:

fc ¼

qffiffiffi 6:7 Dd De0:5

ð5Þ

where D is the coil diameter, 30 < De < 300, 0.0097 < d/D < 0.135. Seban and McLaughlin [7], also provided a correlation for the friction factor in the transitional region, as follows:

1:8 f c ¼  qffiffiffi0:5 Re Dd

ð6Þ

where 300 < De < Decri, 0.0097 < d/D < 0.135, Decri is the critical Dean number. The critical Reynolds number was defined by Ito et al. [11], as follows:

Y. Wang et al. / International Journal of Heat and Mass Transfer 146 (2020) 118723

Recri

  r 0:5  ¼ 2100 1 þ 12 R

ð7Þ

The friction factor for turbulent flow conditions was predicted based on Huttl et al. [4], as follows:

fc ¼

0:2 0:084  Dd De0:2

ð8Þ

where Decri < De < 1400, 0.0097 < d/D < 0.135. 1.2. Heat transfer characteristics in coiled tubes Seban et al. [7] carried out heat transfer experiments for laminar flow of oil and turbulent flow of water in coiled tubes. For turbulent cases, the local heat transfer coefficient on the outer wall surface was found to be two to four times greater than those of the inner wall. Based on these results, it was found that the peak mean velocity in the coil shifted to the outer side of the tube, which led to higher fluid velocities near the outer side than near the inner side of the coil. An empirical correlation for the local Nusselt number of laminar flows in coiled tubes was proposed based on their experimental results, as follows:

Nuc ¼ A

   1=3 fc d  Pr1=3  Re2  x 8

ð9Þ

where fc, Re, d, x, Pr are the friction factor of the coil, Reynolds number of the fluid, inner diameter of the coil tube, longitudinal distance along the coil and Prandtl number of the fluid, respectively. Rogers and Mayhew [8] conducted heat transfer experiments for water flowing through steam heated coils under turbulent conditions, and modified the Nusselt number correlations from Seban et al. [7] and Kirpikov et al. [10] to better predict their heat transfer results in coiled tubes, as follows:

Nuc ¼ 0:0456  Re0:8  Pr 0:4 

 r 0:21

ð10Þ

R

where 0.056 < r/R < 0.1, 10,000 < Re < 45,000.

Nuc ¼ 0:021  Re0:85  Pr 0:4 

 r 0:1

ð11Þ

R

where 0.05 < r/R < 0.0093, 10,000 < Re < 45,000. Mori et al. [9] pointed out that the Nusselt number inside a curved pipe was found to be remarkably influenced by the presence of secondary flows induced by the pipe curvature. An empirical Nusselt number correlation based on the analytical study was postulated, as follows:

2

3

Pr 0:4 5=6  r 1=12 6 0:061 7 Nuc ¼ Re 41 þ n o1=6 5 2:5 R 41 Re Rr

ð12Þ

where (Re∙(r/R) 2.5) > 4.0, Pr > 1. The Nusselt number values calculated from the above theoretical Eq. (12) matched well with their experimental Nusselt number values for R/r equal to 18.7 and 40. Acharya et al. [12] numerically characterized the heat transfer enhancement of flows in coil heat exchangers due to chaotic mixing. Chaotic mixing was achieved by periodically rotating the coil axis in contrast with the common helical coil heat exchanger. Correspondingly, periodically hydrodynamic flow development occurred after each coil axis switch. The periodic breaking of the interior boundary layer led to increased convective mixing, which was suggested to be the main factor for heat transfer enhancement. Sreejith et al. [13] compared heat transfer performance of a helical coil heat exchanger to a straight tube heat exchanger under the same experimental conditions. It was claimed that the secondary flow induced by the curvature of the helical coil heat

3

exchanger was the main factor that enhanced heat transfer rate in relation to a straight tube heat exchanger. Results also showed increased heat exchanger effectiveness and greater overall heat transfer coefficient in helical coil heat exchangers than in straight tube heat exchangers for all mass flow rates and operating conditions. Kong et al. [14] experimentally evaluated the heat transfer characteristics of a Newtonian-like slurry flowing through a helical coil. It was indicated that the curvature ratio of the coil had a significant influence on heat transfer performance. A later study of Kong et al. [15] showed that the local heat transfer coefficients oscillated along the coil due to the potential prevalence of secondary flows. It was found that the secondary flow could enhance fluid mixing along the radial direction of a helically coiled tube, which in turn would result in better heat transfer of helically coiled tubes than in straight pipes. A new Nusselt number correlation as a function of Reynolds number and Prandtl number was postulated for water in helically coiled tubes, as follows:

Nuc ¼ 0:03  Re0:84  Pr 0:4

ð13Þ

where 6300 < Re < 27,000, 1000 < De < 4000. From the previous studies, it is evident that greater fluid mixing and better heat transfer can be achieved with helical coil heat exchangers.

1.3. The effect of wire coil inserts to coiled tubes Inserts have been used in coiled tubes to enhance fluid mixing and improve heat transfer performance. Webb [16] pointed out that wire coil inserts could enhance heat transfer inside tubes by inducing flow separation at the wire which in turn would disrupt the boundary layer growth. However, under those circumtances, it was found that the boundary layer mixing effect dissipated rapidly. Therefore, the spring wire pitch should be taken into consideration in order to optimize the heat transfer performance of flowing fluids in coiled tubes. Ravigururajan and Bergles [17] conducted a flow visualization study of water in a straight pipe that showed that inserted coil wires could induce flow rotation which in turn would improve heat transfer performance. The numerical experiments were conducted for different coil wire diameters and Reynolds number range between 150 and 2600. It was shown that the developing hydrodynamic length for tubes with coil wire inserts was much smaller than for plain tubes. Neal and Stephen [18] stated that most studies of internal flow with wire coil inserts showed heat transfer enhancement from 50% to 400%. It was claimed that one crucial feature of internal flow in tubes with wire coil inserts is the lack of a significant hydrodynamic entry length since the boundary layer breaks down and reforms continuously. In summary, the heat transfer coefficient is usually greater when wire coil inserts are used than in tubes without wire coil inserts. Chiou [19] investigated the effects of wire coil inserts inside tubes on heat transfer performance. It was proposed that the principal mechanism for heat transfer enhancement in tubes with compression spring wire inserts was the induced fluid mixing, which was capable of disrupting the laminar sub-layer and increasing the level of fluid turbulence. Yildiz et al. [20] carried out an experimental study of heat transfer and pressure drop of air in a helical pipe containing wire coil inserts with different pitch values. Their results showed that heat transfer in a helical pipe with wire coil inserts could be enhanced by as much as 5 times when compared to the heat transfer performance of a plain helical pipe. However, the pressure drop incre-

4

Y. Wang et al. / International Journal of Heat and Mass Transfer 146 (2020) 118723

ment could be 10 times higher while the Nusselt number increased with decreasing pitch-to-wire diameter ratio. Ali et al. [21] experimentally investigated convective heat transfer in a straight tube with different wire coil inserts in the turbulent regime. The effects of wire coil inserts on Nusselt number and friction factor were evaluated. It was found that the performance enhancement index was greater than one for all the experimental cases. The performance enhancement index, g was defined as follows:

gov erall ¼

 1=3 henhanced tube DPenhanced tube = hplain straigt tube DPplain straight tube

ð14Þ

which in this study, is a function of the heat transfer coefficient ratio and pressure drop ratio between the enhanced tube with wire coil inserts and the plain tube without wire coil inserts for the same pumping power [22–25]. As it can be seen, better convective heat transfer can be achieved in coiled tubes than in straight pipes. In addition, periodically switching coil axis or using wire coil inserts in tubes should disturb the boundary layer formation and increase the level of turbulence mixing. Therefore, a modified helical coil test configuration consisting of well-spaced reversed plastic coils for enhanced fluid mixing was designed and tested in the study. Wire coil inserts were also used in the reversed plastic coils to further promote turbulence mixing and enhance heat transfer performance. 2. Description of experimental apparatuses 2.1. Description of the pump-driven flow loop In order to experimentally characterize the heat transfer coefficient and pressure drop of water flowing through helical coils with and without (w/o) reversed loops and wire coil inserts, a pumpdriven flow loop was designed and constructed as shown in Fig. 1. The heat transfer and pressure drop characteristics were investigated independently with instrumented heat transfer and pressure drop test sections, respectively, with the same geometry and dimensions.

As Fig. 1 shows, a progressive cavity pump (P1) was used to circulate water through the entire flow loop. An electromagnetic flowmeter (FM1) was located downstream to measure the flow rate of the working fluid. In the pressure drop loop, a differential pressure transducer (DPT1) was used to measure pressure loss of the fluid flowing through the test section. An air-cooled water chiller (CH1) was used to cool the working fluid in HX1 by maintaining a constant fluid temperature at the inlet of the heat transfer test section. A preheater (PH1) was used after HX1 to ensure a constant inlet fluid temperature. All instruments were connected to a data logger (DAQ) to obtain real-time experimental data. 2.2. Description of heat transfer test section Fig. 2 shows the experimental heat transfer test section. The two-turn helical coiled tube was made of four copper coils, each with one 180° and 0.65-meter long subsection. The inner diameter of the copper coil tube and curvature diameter of the coil were 10.2 mm and 0.414 m, respectively. The radius of curvature ratio (or the tube diameter, d, to the coil curvature diameter, D) was set at 0.025 for this study. The pitch of the helical coil test section was 6.35 cm, which is the separation distance between the inlet and outlet of a complete (360°) helical loop. A 30 cm long straight tube was added before the helical coil test section to ensure hydrodynamically fully developed flow conditions at the inlet. To characterize the heat transfer performance of the working fluid (water) through the loop, multiple thermocouples were used in the heat transfer section. Insulated T-type thermocouple probes were used to measure the bulk fluid temperature at every 180°. Each coil subsection consisted of six T-type surface mount thermocouples, which were attached to the copper tubing at three different axial positions to measure wall surface temperatures. The thermocouples were attached on opposite sides of the periphery of the coil’s cross-section as seen in Fig. 2(b), so inside and outside coil surface temperatures could be recorded at each axial location. Subscripts ‘‘i” and ‘‘o” in cross-section AA‘ correspond to inside and outside locations of the coil, as shown in Fig. 2(b). Additional information about the experimental apparatus can be found in previous publications [14,15,25].

Fig. 1. Schematic diagram of the experimental pressure drop and heat transfer flow loop.

Y. Wang et al. / International Journal of Heat and Mass Transfer 146 (2020) 118723

5

Fig. 2. (a) Plain heat transfer test section without reversed loops and wire coil inserts (b) thermocouple installation in a heat transfer test subsection.

Coated nichrome wires were used as heating elements in the heat transfer section. They were wrapped tightly and evenly around the outer surface of each subsection coils. In each subsection, two independent nichrome wires were connected in parallel to a variable voltage transformer to provide each subsection with constant wall heat flux. External electrical resistances were added to each nichrome wire subsection to ensure uniform heat flux values. The electrical resistance of each nichrome wire subsection was measured using a Fluke multi-meter. The heat flux value for each subsection was verified based on a measured 200 AC voltage input. The measured heat flux values were quite uniform among all the subsections, deviating by less than 1%. Fiberglass was wrapped around the nichrome wires to thermally insulate each heat transfer subsection. The actual heat flux value used to calculate corresponding heat transfer coefficient was based on the measured thermal energy change of water flowing through the heated test configuration, which was calculated using the following equation: 00

q ¼

_  c p  DT m A

ð15Þ

_ is the mass flow rate of water, cp is the specific heat of where m water, A is the total internal surface area of the heated helical coils.

Fig. 3. Plain pressure drop test section.

Inlet and outlet water temperatures were measured using thermocouples to determine water temperature difference, DT. The constant heat flux value used in this study was 35.8 kW/m2 with a standard deviation of 0.5 kW/m2 or 1.5% of the average value. The

6

Y. Wang et al. / International Journal of Heat and Mass Transfer 146 (2020) 118723

ratio between the heat rate of water to the electric power was approximately 0.92 for all experimental cases. 2.3. Description of pressure drop test section The pressure drop test section, which has the same geometry and dimensions as the plain heat transfer test section (Fig. 2), is shown in Fig. 3. Two pressure taps were attached at the inlet and outlet of the pressure drop test section to measure pressure drop of the working fluid, which should be the same as the working fluid flowing through the plain heat transfer test section. The two pressure taps were connected to the data acquisition system to measure pressure drop for all the experiments.

Coil Curvature Radius

2.4. Modified heat transfer and pressure drop test sections After conducting baseline experiments, the two-turn helical pressure drop and coil heat transfer sections were modified to incorporate small plastic loops (i.e. reversed loops) to shift the radial location of the peak fluid velocity within the coil and enable greater fluid mixing. In the pressure drop test section, after each 180° subsection, a 360° plastic coil tube was connected to the preceding and proceeding subsections as shown in Fig. 4. Each reversed loop was connected in series to the main loop using plastic quick-connect couplings. The coil pitch of the reversed loops was set at 6.35 cm, which was the same as that of the main loop. Furthermore, the same modifications were incorporated in the heat transfer test section; however, the reversed loops were not wrapped with nichrome wire or heating elements. The plastic coils were thermally insulated with fiberglass layers to ensure adiabatic conditions within the reversed loops. Lastly, wire coils were inserted inside the reversed plastic loops only, as shown in Fig. 5, to promote fluid mixing and enhance heat transfer performance within the overall test section. Two types of stainless-steel wire coil inserts with a wire diameter of 0.7 mm were used with coil pitch values of 3 mm and 20 mm, respectively. 2.5. Data reduction and uncertainty analysis

Reversed Loop Curvature Radius

Fig. 4. Experimental test section with reversed loops for pressure drop testing.

Calibrated temperature and pressure measurements were used to obtain the corresponding heat transfer coefficient and pressure drop values. Uncertainty analysis of the experimental results was carried out using the Engineering Equation Solver (EES) software. The EES software follows the multivariate propagation of error approach, which is based on Eq. (16).

20 mm

(a)

3 mm

(b)

3 mm

20 mm

(c)

(d)

Fig. 5. (a) Plastic loop with loose wire coil inserts (pitch of 20 mm), (b) plastic loop with tight wire coil inserts (pitch of 3 mm), (c) 20 mm pitch wire coil and (d) 3 mm pitch wire coil.

7

Y. Wang et al. / International Journal of Heat and Mass Transfer 146 (2020) 118723

ð16Þ

where U: given function of independent variables, U = U (X1, X2, . . .. . ., Xn) Xn: independent variable rXn: uncertainty associated with corresponding independent variable, Xn rU: uncertainty associated with dependent variable U. The uncertainty values of the measurements are shown in Table 1. The calculated uncertainty values for pressure drop and Nusselt number are shown in Figs. 6, 7, 9, 10, and 12–14, respectively. 3. Results and discussions 3.1. Pressure drop results Pressure drop in the plain helical coils (without reversed loops and wire coil inserts) was measured for different flowrates. The experimental friction factor was calculated and compared with the correlations by Mishra et al. [5] and Srinivasan et al. [6]. Experimental conditions including curvature ratio, Reynolds and Dean Number were compared to the established correlations [5,6] as seen in Table 2. The friction factor is defined as follows:

f ¼

d  DP 2  q  L  u2

ð17Þ

where q, d, L and u are the fluid density, tube diameter, tube length, and fluid mean velocity, respectively. As seen in Fig. 6, the experimental friction factor values are in a good agreement with the established models with a relative error of about 6%, even though the experimental conditions (ranges of

Uncertainty

DP T Velocity L d

±0.2 kPa ±0.1 °C ±0.1 m/s ±1 cm ±0.1 mm

f ¼ 0:08  De0:20 

0:44

 Pe 0:11

Pe ¼

Lwire coil P Ltotal dcoil

ð19Þ

Experiment

Mishra et al. [5], Eq. (2)

0.010

0.005

Srinivasan et al. [6] Eq. (8)

0.015

0.010

0.005

Average uncertainty: ± 3.8% 0.000 0

7000

14000

ð18Þ

coil

0.020

0.015

R2 ¼ 0:98

wire coil pitch Pe is defined below, in which only a portion of the total test section length consists of the wire coil inserts.

Experiment

Friction Factor (-)

r rev Rcoil

where 1000 < De < 4500, 6000 < Re < 27,000, rrev is the reversed loop curvature radius, and Rcoil is the main loop curvature radius. The two Rrrev values used in this study were 1/2 and 1/3. The effective

0.020

(a)



where P is the actual wire coil pitch, Lwire coil is the total length of the wire coil in the test section, Ltotal is the total length of the test section and dcoil is the inner diameter of the coil tube. Four values of Pe (0.1, 0.15, 0.65 and 0.98) were used in the study. As it can be seen from Eq. (18), the reversed loop curvature ratio is a major contributor to friction factor given the magnitude of the corresponding exponent (i.e. 0.44). Furthermore, the correlation also indicates that tighter reversed loops should result in greater friction factor values. As shown in Fig. 8, the friction factor values

Table 1 Measured variables and uncertainties. Parameter

Reynolds number and Dean Number) do not completely match with the ones in [5,6], as shown in Table 2. After validation of the pressure drop loop, pressure drop tests using helical coils with reversed loops and wire coil inserts were conducted for different curvature ratios of the reversed loops, inlet velocities and pitch values of the wire coils. The results are shown in Fig. 7. As shown in Fig. 7, pressure drop increased after adding reversed loops. Furthermore, pressure drop increased with fluid velocity. The increased pressure drop was caused by the increased level of fluid mixing induced by the reversed loop itself. The results also show that pressure drop is inversely proportional to the curvature ratio of the reversed loop as shown in Fig. 7. Furthermore, pressure drop increased by 62–115% when using wire coil inserts in the reversed loops. As Fig. 7 shows, a wire coil insert with smaller coil pitch (i.e. 3 mm) has a greater effect on pressure drop than a loose wire coil (i.e. 20 mm). It is evident that smaller wire coil pitch would cause the hydrodynamic boundary layer to break up more frequently leading to greater pressure drop [20,21]. As Fig. 7 shows, the maximum pressure drop happened when using a reversed loop with curvature ratio of 1/3 and a 3 mm pitch wire coil insert at a fluid inlet velocity 2.7 m/s. A multiple regression analysis was conducted to postulate a friction factor correlation capable of predicting flow resistance of helical coils with reversed loops and wire coil inserts as a function of Dean number, reversed loop curvature ratio, and effective wire coil pitch. The correlation is as follows:

Friction Factor (-)

rU

sffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi  2  2  2 @U @U @U ¼ rX 1 2 þ rX2 2 þ    þ rXn 2 @X 1 @X 2 @X n

21000 28000

Reynolds Number (-)

Average uncertainty: ± 3.8% 0.000 0

(b)

1000 2000 3000 4000 5000

Dean Number (-)

Fig. 6. Comparison of friction factor values with established correlations in conventional helical coil.

8

Y. Wang et al. / International Journal of Heat and Mass Transfer 146 (2020) 118723

Table 2 Comparison between experimental and empirical correlations conditions (friction factor). Equation No.

Reference No.

r/R

Reynolds number

Dean No.

(17) (2) (8)

Current Experimental Study [5] [6]

0.025 0.00289–0.155 0.0097–0.135

6000–27,000 4000–100,000 N/A

1000–4500 N/A 962–14,000

40 35 Pressure Drop (kPa/m)

Table 3 Comparison between experimental and empirical correlations conditions (Nusselt number).

helical coils w/o reversed loop helical coils w/o reversed loops (repeat) 1/3 rev. loop (no inserts) 1/2 rev. loop (no inserts) 1/3 rev. loop (20 mm pitch inserts) 1/2 rev. loop (20 mm pitch inserts) 1/3 rev. loop (3 mm pitch inserts) 1/2 rev. loop (3 mm pitch inserts)

30 25

Equation No.

Reference No.

r/R

Reynolds number

(21)

Current Experimental Study [7] [8] [8] [9]

0.025

6000–27,000

0.01 or 0.06 0.056–0.1 0.05–0.093 0.025 or 0.05

12–65,000 10,000–45,000 10,000–100,000 > 40,000 or >6000

(9) (10) (11) (12)

20 15 10 5

Uncertainty: ± 0.2 kPa

200

0 1

1.5

2

2.5

Average uncertainty: ± 7.4%

3

160

Fig. 7. Pressure drop for helical coils with different reversed (rev.) loop curvature ratios and different wire coil inserts at different inlet velocities.

predicted by the Eq. (18) are in good agreement with the experimental results. 3.2. Heat transfer results

Nusselt Number (-)

Velocity (m/s)

120

Seban et al. [7] Eq. (9) Rogers et al. [8] Eq. (10)

40

Heat transfer experiments with water were conducted in helical coils with reversed loops and wire coil inserts. The heat transfer coefficient was calculated using Eq. (20):

q00 h¼ ðT w  T b Þ

Rogers et al. [8] Eq. (11) Mori et al. [9] Eq. (12)

0 10000

15000

ð20Þ

where q00 , Tw, and Tb are the wall heat flux, wall temperature, and bulk fluid temperature, respectively. The Nusselt number was calculated as follows,

Nu ¼

Experiment, (q''=35.8 kW/m^2)

80

hd k

20000

25000

Reynolds Number (-) Fig. 9. Average Nusselt number comparison in conventional helical coils without reversed loops.

ð21Þ

270

Average Nusselt Number (-)

Average uncertainty: ± 7.8%

Experimental friction factor (-)

0.030

+5%

0.025 -5%

0.020

0.015 0.015

220

170

helical coils w/o reversed loops helical coils w/o reversed loops (repeat) 1/3 rev. loop (no inserts) 1/2 rev. loop (no inserts) 1/3 rev. loop (20 mm pitch inserts) 1/2 rev. loop (20 mm pitch inserts) 1/3 rev. loop (3 mm pitch inserts) 1/2 rev. loop (3 mm pitch inserts)

120

70

20 0.020 0.025 Correlated friction factor (-)

0.030

Fig. 8. Comparison between experimental and friction factor correlation values, Eq. (18).

1

1.5

2

2.5

3

Velocity (m/s) Fig. 10. Average Nusselt number in helical coils with different reversed loop curvature ratios and wire coil inserts at different inlet velocities.

Y. Wang et al. / International Journal of Heat and Mass Transfer 146 (2020) 118723

Experimental Nusselt numer (-)

300

250 +10%

200 -10%

150

100 100

150

200

250

300

Correlated Nusselt number (-) Fig. 11. Comparison between the experimental and correlated Nusselt number values, Eq. (22).

where d is the inner tube diameter and k is the fluid thermal conductivity. Baseline heat transfer experiments with water in the plain helical coil (without reversed loops and wire coil inserts) under a constant heat flux of 35.8 kW/m2 were conducted twice.

280

240 220 200 180 160 140 120

280 260 240 220 200 180 160 140

Average uncertainty: ± 7.1%

120

Average uncertainty: ± 7.5%

100

100 0

(a)

Nu_i enhanced Nu_i plain Nu_o enhanced Nu_o plain

300

Nusselt Number (-)

260

Nusselt Number (-)

The Nusselt number values between two repeating experiments agreed within 5%. The Nusselt number values of water in plain helical coils were compared to the values obtained using known correlations for coiled tubes [7–9]. The current experimental conditions were compared with those of the established correlations as seen in Table 3. As it can be seen in Fig. 9, the experimental Nusselt number values agree with the Nusselt number correlations by Rogers et al. [8] and fairly with the other correlations even though the r/R and Reynolds number range values are different. In all cases, Nusselt number always increases with Reynolds number. Heat transfer experiments with water flowing in helical coils with reversed loops were conducted at different fluid inlet velocities (1.5 m/s, 1.9 m/s, 2.3 m/s, 2.7 m/s) and constant heat flux of 35.8 kW/m2 to evaluate the effects of reversed loop curvature ratio, fluid velocity and wire coil pitch values on heat transfer performance. As shown in Fig. 10, the Nusselt number value increased with fluid velocity, smaller reversed loop curvature ratios and smaller wire coil insert pitch values. The enhanced Nusselt number values can be attributed to increased level of turbulent mixing caused by the reverse loops and wire coils [17–21]. The maximum Nusselt number value occurred for a reversed loop curvature ratio of 1/3 with 3 mm wire coil pitch.

Nu_i enhanced Nu_i plain Nu_o enhanced Nu_o plain

300

9

0

90 180 270 360 450 540 630 720

Angle (degree)

(b)

90 180 270 360 450 540 630 720

Angle (degree)

Fig. 12. Local Nusselt number values for r/R = 1/2 in reversed loops with wire coil pitch of (a) 3 mm and (b) 20 mm at a fluid inlet velocity of 2.3 m/s (‘‘enhanced” and ‘‘plain” in the figure legend correspond to experimental cases with wire coil inserts and without, respectively).

Nusselt Number (-)

280 260 240 220 200 180 160

280 260 240 220 200 180 160 140

140 Average uncertainty: ± 7.6%

120 100

(a)

Nu_i enhanced Nu_i plain Nu_o enhanced Nu_o plain

300

Nusselt Number (-)

Nu_i enhanced Nu_i plain Nu_o enhanced Nu_o plain

300

Average uncertainty: ± 7.3%

120 100

0

0

90 180 270 360 450 540 630 720

Angle (degree)

(b)

90 180 270 360 450 540 630 720

Angle (degree)

Fig. 13. Local Nusselt number values for r/R = 1/3 in reversed loops with wire coil pitch of (a) 3 mm and (b) 20 mm at a fluid inlet velocity of 2.3 m/s.

10

Y. Wang et al. / International Journal of Heat and Mass Transfer 146 (2020) 118723

300

300 Nu_i enhanced Nu_i plain Nu_o enhanced Nu_o plain

240

270

Nusselt Number (-)

Nusselt Number (-)

270

Nu_i enhanced Nu_i plain Nu_o enhanced Nu_o plain

210 180 150 120

240 210 180 150 120 90

90

Average uncertainty: ± 7.4%

Average uncertainty: ± 7.6% 60

60 0

(a)

Nu_i enhanced Nu_i plain Nu_o enhanced Nu_o plain

270

Nu_i enhanced Nu_i plain Nu_o enhanced Nu_o plain

270

Nusselt Number (-)

210 180 150 120

240 210 180 150 120 90

Average uncertainty: ± 7.1%

Average uncertainty: ± 7.6%

60

60

(c)

Angle (degree)

300

240

90

90 180 270 360 450 540 630 720

(b)

Angle (degree)

300

Nusselt Number (-)

0

90 180 270 360 450 540 630 720

0

0

90 180 270 360 450 540 630 720

90 180 270 360 450 540 630 720

(d)

Angle (degree)

Angle (degree)

Fig. 14. Local Nusselt number values for r/R = 1/3 in reversed loops with 20 mm wire coil pitch at fluid inlet velocity of (a) 1.5 m/s, (b) 1.9 m/s, (c) 2.3 m/s, and (d) 2.7 m/s.

Table 4 Heat transfer enhancement for helical coils with reversed loops and wire coil inserts. Inlet Velocity (m/s)

1.5 1.9 2.3 2.7

Reynolds Number

14,037 17,780 21,523 25,266

henhanced helical coil loop hplain helical coil loop Reversed Loop Curvature Ratio, r/R, and Wire Coil Insert Pitch

Heat Transfer Enhancement Ratio, gheat

transfer

¼

1/2 (no inserts, reversed loops only)

1/2 (3 mm)

1/2 (20 mm)

1/3 (no inserts, reversed loops only)

1/3 (3 mm)

1/3 (20 mm)

1.04 1.06 1.09 1.12

1.09 1.28 1.29 1.23

1.04 1.10 1.12 1.11

1.04 1.09 1.16 1.17

1.10 1.26 1.27 1.22

1.07 1.20 1.23 1.18

Table 5 Pressure drop increment for helical coils with reversed loops and wire coil inserts. Inlet Velocity (m/s)

1.5 1.9 2.3 2.7

Reynolds Number

14,037 17,780 21,523 25,266

DP enhanced helical coil loop DP plain helical coil loop Reversed Loop Curvature Ratio, r/R, and Wire Coil Insert Pitch

Pressure Drop Increment Ratio, gpressure

penalty

¼

1/2 (no inserts, reversed loops only)

1/2 (3 mm)

1/2 (20 mm)

1/3 (no inserts, reversed loops only)

1/3 (3 mm)

1/3 (20 mm)

1.09 1.11 1.10 1.11

1.64 1.69 1.64 1.73

1.15 1.18 1.29 1.30

1.11 1.12 1.13 1.13

1.78 1.88 1.84 1.85

1.14 1.55 1.64 1.54

11

Y. Wang et al. / International Journal of Heat and Mass Transfer 146 (2020) 118723 Table 6 Performance enhancement index, Eq. (14), for helical coils with reversed loops and wire coil inserts. Inlet Velocity (m/s)

1.5 1.9 2.3 2.7

 1=3 henhanced helical coil loop DP enhanced helical coil loop = hplain helical coil loop DP plain helical coil loop Reversed Loop Curvature Ratio, r/R, and Wire Coil Insert Pitch

Reynolds Number

Performance Enhancement Index, gov erall ¼

14,037 17,780 21,523 25,266

1/2 (no inserts, reversed loops only)

1/2 (3 mm)

1/2 (20 mm)

1/3 (no inserts, reversed loops only)

1/3 (3 mm)

1/3 (20 mm)

1.01 1.02 1.06 1.08

0.92 1.07 1.09 1.02

1.08 1.13 1.17 1.17

1.10 1.09 1.08 1.07

0.91 1.02 1.04 0.99

1.02 1.04 1.04 1.02

As Fig. 10 shows, for a tighter reverse loop (r/R = 1/3), there is no significant difference in Nusselt number for a wire coil pitch of 3 mm or 20 mm. However, for a reverse loop with r/R of 1/2, a tighter wire coil pitch of 3 mm leads to better heat transfer performance. Furthermore, the reverse loop (r/R of 1/2, a wire coil pitch of 3 mm) performs as well as the tighter reverse loop (r/R = 1/3) with a wire coil pitch of 20 mm. As the results show, both r/R and wire coil pitch play a significant role in Nusselt number enhancement. A multiple regression analysis was conducted to postulate a Nusselt number correlation for water flowing through helical coils with reversed loops and wire coil inserts as a function of Dean number, reversed loop curvature ratio and wire coil insert pitch. The correlation is as follows:

Nu ¼ 0:28De0:80 

 r 0:16 R

 Pe 0:04

R2 ¼ 0:90

ð22Þ

where 6000 < Re < 27,000, 1000 < De < 4500, the two r/R values used in this study were 1/2 and 1/3, the effective wire coil pitch is defined as:

Pe ¼

Lwire coil P Ltotal dcoil

is most likely due to the radial shift of the peak axial velocity in the curved coil, as reported recently [15,25]. Furthermore, it is also evident that by adding reversed loops with or without wire coil inserts, the outer region of the coil showed greater local heat transfer. The effect of different inlet fluid velocities on local Nusselt number values are shown in Fig. 14. As it can be observed, the local Nusselt number values are greater when wire coil inserts are used. Furthermore, the enhancement increases with fluid inlet velocity, which is consistent with the results shown in Fig. 10. Moreover, the enhancement in Nusselt number for the inner side of the coil increases with fluid velocity, particularly when the fluid velocity exceeds 1.9 m/sec. The increase in Nusselt number can be attributed to the greater level of fluid mixing that occurs at greater fluid velocity when wire coils are used.

ð23Þ

where P is the actual wire coil pitch, Lwire coil is the total length of the wire coil in the test section, Ltotal is the total length of the test section and dcoil is the inner diameter of the coil tube. Four values of Pe (0.1, 0.15, 0.65 and 0.98) were used in this study. As it can be seen from Eq. (22), the heat transfer performance in a coil tube heat transfer section is largely dominated by Dean number when using reversed loops with wire coils inside. As shown in Fig. 11, the Nusselt number values predicted by the Eq. (22) are in good agreement with the experimental results. The local Nusselt number values for experimental cases at the same fluid inlet velocity but with different wire coil pitch values were compared as shown in Figs. 12 and 13. As Figs. 12 and 13 show, an r/R of 1/3 with a 3 mm wire coil pitch enhances the heat transfer process the most, while an r/R of 1/2 with a 20 mm wire coil pitch increases Nusselt number slightly. The enhanced heat transfer process can be attributed to the optimal combination of r/R and wire coil pitch, which leads to a continuous development of the hydrodynamic boundary layer and greater level of fluid mixing within the coil. In all cases, Nusselt number values varied along the heat transfer section as seen in a recent study [25]. The variation in Nusselt number values as a function of axial distance may be attributed to the onset and evolution of secondary flows within the curved coil as other studies also showed [2,4,7–9,15]. By comparing Fig. 12(a) and with (b), and Fig. 13(a) with (b), it is evident that a wire coil pitch of 20 mm diminishes the Nusselt number variation slightly, but without diminishing the overall heat transfer process. Therefore, the effect of wire coil pitch on the evolution of secondary flows should be studied in detail in the future. Nevertheless, the local Nusselt number on the outer region of the coil (Nu_o) is always greater than on the inner region (Nu_i), which

3.3. Summary of helical coil device thermal performance The performance enhancement index (PEC) of the modified helical coil device was evaluated using average Nusselt number and pressure drop data as shown in Tables 4 and 5. The performance enhancement index is based on Eq. (14), which takes into account the heat transfer coefficient ratio and pressure drop ratio between the enhanced loop (with reversed loops and wire coil inserts) and the plain loop for the same pumping power [22–25]. As shown in Tables 4–6, using reversed loops and wire coil inserts led to greater heat transfer rate, greater pressure drop, and in most instances, PEC values greater than one. By comparing the results, a reversed loop with a curvature ratio of 1/2, wire coil pitch value of 20 mm and Reynolds number in the range of 23,000 exhibited the best overall thermal performance among all the cases considered in the study. Table 6 reveals that there may exist a unique flow pattern under a unique set of experimental conditions, which leads to optimal heat transfer performance of the main helical coil loop even though wire coils are only present in the reversed loops. Furthermore, Table 4 shows that pressure drop increases with curvature ratio and lower pitch values of the wire coil [25].

4. Conclusions In this study, a commonly used helical coil heat transfer device has been modified by adding a 360° reversed plastic tubing with or without wire coil inserts after each 180° of the main helical coil loop. The experimental heat transfer and pressure drop results showed that the modified helical coils exhibited better thermal performance. Wire coils in the reversed loops enhanced heat transfer in the main helical coil loop. Overall, a unique combination of reversed loop curvature ratio, wire coil pitch and fluid flow rate led to optimal thermal performance in the modified heat exchanger configuration. In the future, the heat transfer and pressure drop characteristics inside the modified helical coil loop should be

12

Y. Wang et al. / International Journal of Heat and Mass Transfer 146 (2020) 118723

studied in greater detail by conducting CFD simulations and flow visualization studies. Declaration of Competing Interest The authors declared that there is no conflict of interest. Appendix A. Supplementary material Supplementary data to this article can be found online at https://doi.org/10.1016/j.ijheatmasstransfer.2019.118723. References [1] W.R. Dean, Philos. Mag. 4 (1927) 208. [2] A.N. Dravid, K.A. Smith, E.W. Merrill, P.L.T. Brian, Effect of secondary fluid motion on laminar flow heat transfer in helically coiled tubes, AIChE J. 17 (5) (1971) 1114–1122. [3] M.F. Pakdaman, M.A. Akhavan-Behabadi, P. Razi, An experimental investigation on thermo-physical properties and overall performance of MWCNT/heat transfer oil nanofluid flow inside vertical helically coiled tubes, Exp. Therm. Fluid Sci. 40 (2012) 103–111. [4] T.J. Huttl, R. Friedrich, Influence of curvature and torsion on turbulent flow in helically coiled pipes, Int. J. Heat Fluid Flow 21 (3) (2000) 345–353. [5] P. Mishra, S.N. Gupta, Momentum transfer in curved pipes. I. Newtonian fluids, Ind. Eng. Chem. Process Des. Dev. 18 (1978) 130–142. [6] P.S. Srinivasan, S.S. Nandapurkar, F.A. Holland, Friction factors for coils, Trans. Inst. Chem. Eng. 48 (1970) T156–T161. [7] R.A. Seban, E.F. McLaughlin, Heat transfer in tube coils with laminar and turbulent flow, Int. J. Heat Mass Transfer 6 (1963) 387–395. [8] G.F.C. Rogers, Y.R. Mayhew, Heat transfer and pressure loss in helically coiled tubes with turbulent flow, Int. J. Heat Mass Transfer 7 (1964) 1207–1216. [9] Y. Mori, W. Nakayama, Study on forced convective heat transfer in curved pipes, Int. J. Heat Mass Transfer 10 (1967) 681–695. [10] A.V. Kirpikov, Heat transfer in helically coiled pipes, Trudi Moskov. Inst. Khim. Mashinojtrojenija 12 (1957) 43–56.

[11] H. Ito, Friction factors for turbulent flow in curved pipes, J. Basic Eng. (1959) 123–134. [12] N. Acharya, M. Sen, H.C. Chang, Analysis of heat transfer enhancement in coiled-tube heat exchangers, Int. J. Heat Mass Transfer 44 (2001) 3189–3199. [13] K. Sreejith, T.R. Sreesastha Ram, Jaivin A. Varghese, Manoj Francis, V.J. Mossas, M.J. Nidhin, E.S. Nithil, S. Sushmitha, Experimental investigation of a helical coil heat exchanger, Int. J. Eng. Sci. 5 (8) (2015) 1–5. [14] M. Kong, K. Yu, J.L. Alvarado, W. Terrell, Thermal performance of microencapsulated phase change material slurry in a coil heat exchanger, J. Heat Transfer 137 (2015), 071801-1–8. [15] M. Kong, J.L. Alvarado, W. Terrell, C. Thies, Performance characteristics of microencapsulated phase change material slurry in a helically coiled tube, Int. J. Heat Mass Transfer 101 (2016) 901–914. [16] R. Webb, Principles of Enhanced Heat Transfer, John Wiley & Sons, 1994, pp. 166–199 (ch. Insert Devices for Single-Phase Flow). [17] T. Ravigururajan, A. Bergles, Visualization of flow phenomenon near enhanced surfaces, 28th National Heat Transfer Conference, Fouling and Enhancement Interactions ASME HTD-164 (1991). [18] Neal R. Herring, Stephen D. Heister, Review of the development of compact, high performance heat exchangers for gas turbine applications, Proceedings of IMECE2006, 2006 ASME International Mechanical Engineering Congress and Exposition, November 5–10, 2006, Chicago, Illinois, USA, 2006. [19] J.P. Chiou, Experimental investigation of the augmentation of forced convection heat transfer in a circular tube using spiral inserts, ASME J. Heat Transfer 109 (1987) 300–307. [20] C. Yildiz, Y. Bicer, D. Pehlivan, Heat transfer and pressure drop in a heat exchanger with a helical pipe containing inside springs, Energy Convers. Manage. 38 (6) (1997) 619–624. [21] R.K. Ali, M.A. Sharafeldeen, N.S. Berbish, M.A. Moawed, Convective heat transfer enhancement inside tubes using inserted helical coils, Therm. Eng. 63 (1) (2016) 42–50. [22] R.L. Webb, Performance evaluation criteria for use of enhanced heat transfer surfaces in heat exchanger design, Int. J. Heat Mass Transfer 24 (1981) 715– 726. [23] R.L. Webb, E.R.G. Eckert, Application of rough surface to heat exchange design, Int. J. Heat Mass Transfer 15 (1972) 1647–1658. [24] J.F. Fan, W.K. Ding, J.F. Zhang, Y.L. He, W.Q. Tao, A performance evaluation plot of enhanced heat transfer techniques oriented for energy-saving, Int. J. Heat Mass Transfer 52 (2) (2009) 33–34. [25] Y. Wang, J.L. Alvarado, W. Terrell, Thermal and flow characteristics of helical coils with reversed loops, Int. J. Heat Mass Transfer 126 (2018) 670–680.