Thermal characteristics of perforated self-rotating twisted tapes in a double-pipe heat exchanger

Applied Thermal Engineering 162 (2019) 114296

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Thermal characteristics of perforated self-rotating twisted tapes in a doublepipe heat exchanger

T

Shaojie Zhanga, Lin Lua, , Chuanshuai Dongb,a, Seung Hyun Chac ⁎

a

Department of Building Services Engineering, The Hong Kong Polytechnic University, Hung Hom, Kowloon, Hong Kong, China Key Laboratory of Enhanced Heat Transfer and Energy Conservation of Education Ministry, School of Chemistry and Chemical Engineering, South China University of Technology, Guangzhou, China c Department of Interior Architecture Design, Hanyang University, Seoul, Republic of Korea b

HIGHLIGHTS

self-rotating twisted tapes performed better than perforated stationary twisted tapes. • Perforated performance factor tended to increase sharply at initial stage of rotation behavior. • Thermal in perforation ratios could improve heat transfer performance for given cases. • Increase correlations varying with perforation ratio were established within 10% deviation. • Some • Perforated self-rotating twisted tapes are an alternative choice to raise thermal performance factor. ARTICLE INFO

ABSTRACT

Keywords: Thermal characteristic Self-rotating twisted tapes Perforation ratio Rotation behavior Nusselt number Friction factor

The present study experimentally investigated thermal characteristics of a double-pipe heat exchanger fitted with perforated self-rotating twisted tapes with six perforation ratios of 0%, 1.16%, 3.63%, 6.46%, 10.1% and 14.49%. The experimental results showed that perforation ratio significantly affects the initial stage of rotation behavior and rotational speed. Perforated self-rotating twisted tapes were experimentally shown to perform greater thermal performance than perforated stationary twisted tapes. In addition, the increase in perforation ratios raised the Nusselt number and pressure drop. Higher thermal performance factor of PR = 10.1% than PR = 14.49% under rotating condition could be found. When the self-rotating twisted tapes varied from stationary to rotating condition, it is observed that thermal performance factor increased from 0.862 to 0.924, 0.987 to 1.025, 1.04 to 1.078, 1.084 to 1.101, and 1.042 to 1.055, for perforation ratios of 0%, 1.16%, 3.63%, 6.46%, and 10.1%, respectively. Finally, some correlations associated with perforation ratios were established to predict Nusselt number and friction factor, and perforated self-rotating twisted tapes were compared with perforated twisted tapes in terms of thermal performance factor. The optimal design of perforated self-rotating twisted tapes with proper perforated ratio could be offered for industrial application based on thermal performance evaluation.

1. Introduction Energy demand has been continuously on the rise, especially in developing countries, owing to a rapid increase in the industrial and domestic needs. To realize energy-efficient systems, it would be beneficial to improve heat transfer characteristics of many industrial applications, such as heat exchangers, refrigerators, and energy recovery devices. Without involving external energy input, many passive methods of heat transfer enhancement have been studied extensively by previous researches [1–15]. Twisted tapes, as a common swirl flow ⁎

generator, are widely utilized for enhancing the thermal efficiency in heat exchanger system [16]. Insertion of twisted tapes produces swirl flows and increases turbulence intensity near the near wall region, which reduces the thermal boundary layer and increase tangential fluid velocity for excellent fluid mixing, and considerably enhances the convective heat transfer [17–20]. Hence, many efforts were made to study geometrical features of various twisted tapes that could increase the heat transfer performance with an acceptable pressure drop. Hence, several studies were carried out to investigate the geometrical parameters of conventional twisted tapes, such as the twist ratio,

Corresponding author. E-mail address: [email protected] (L. Lu).

https://doi.org/10.1016/j.applthermaleng.2019.114296 Received 27 May 2019; Received in revised form 12 August 2019; Accepted 21 August 2019 Available online 22 August 2019 1359-4311/ © 2019 Elsevier Ltd. All rights reserved.

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Nomenclature A Cp D f h I L m Nu Pr ΔP PR Q Re T T¯ V¯ V ν W

μ η ρ

tube wall area [m2] specific heat of water [J kg−1 K−1] heat exchanger tube diameter [m] friction factor [–] heat transfer coefficient [W/m2 K] electric current [A] inner tube length [m] mass flow rate [kg/s] Nusselt number [–] Prandtl number [–] pressure drop [Pa] perforation ratio [–] heat transfer rate [W] Reynolds number [–] temperature [K] mean water temperature [K] Volume [m3] electric voltage [V] mean water velocity of inner tube [m/s] twisted tapes width [m]

dynamic viscosity [Pa·s] thermal performance factor [–] density [kg/m3]

Subscript b conv i in o out p pp s t w

bulk Convective Inner Inlet Outer Outlet Plain tube Pumping power Wall Tube fitted with twisted tapes Water

Abbreviations STT SRTT

stationary twisted tape self-rotating twisted tape

Greek symbols λ

thermal conductivity [W/m2 K]

tapes thickness, and tapes width. Some research have experimentally demonstrated that twisted tapes with lower twist ratios exhibit significantly higher Nusselt number relative to larger-twist ratio tapes in the range of turbulence flow [21,22]. Guo et al. [23] numerically examined the effect of the varying width ratio of the twisted tape (in the 0.2–0.9 range) on the heat transfer and thermo-hydraulic performance in laminar flow. Their outcomes suggested that the heat transfer rate,

the friction factor, and the thermal performance factor all decrease with lowering twisted tapes width. In addition, Esmaeilzadeh et al. [24] investigated the thermal behavior of a heat exchanger tube fitted with twisted tapes at various thicknesses (0.5–2 mm) in the CuO/water nanofluid. Their findings showed that increase of the twisted tapes thickness can significantly raise the heat transfer and the pressure drop characteristic. In addition, shorter-length twisted tapes were

Table 1 Previous studies on the fabrication of twisted tape. Twisted tapes type Peripherally-cut twisted tape

V-cut twisted tape

Geometry

Fabrication parameters

Proposed correlations

Depth ratio: (d/W) Width ratio: (w/W)

Nu = 0.244Re0.625Pr 0.4 (d/W )0.168 (w /W )

f = 39.46Re

0.591 (d/ W )0.195 (w / W ) 0.201

= 4.509Re

0.152 (d/ W )0.102 (w/ W ) 0.054

Depth ratio: (d/W) Width ratio: (w/W) Twisted ratio: (y)

Nu = 0.0296Re0.853 y

Square-cut twisted tape

Twisted ratio: (y)

Nu = 0.041Re0.826Pr 0.33 y

Perforated twisted tape

Hole ratio: (d/W) Pitch ratio: (s/W) Twist ratio: (y/W)

Perforated helical twisted tape

0.222 Pr 0.33 (1

0.615 y 0.269 (1

f = 8.632Re = 1.392Re

0.01 y 0.124 (1

+ d/W )1.148 (1 + w /W )

+ d/W ) 2.477 (1 + w /W ) + d/ W )0.252 (1 + w/ W )

[37]

0.325 (s / W ) 0.133 (d/ W )0.114

[35]

0.272 (y/ W ) 0.631 (s / W ) 0.204 (d/ W )0.428

= 1.764Re

0.059 (y / W ) 0.114 (s / W )0.065 (d/ W ) 0.028

[38]

0.145 (d/ w ) 0.045 (s / w )0.054 3 0.0013R2 + 0.0073R + 0.5501 0.33 p p Pr

Nu = CRe0.00005Rp

2 3 f = C1Re0.00009RP 0.0022Rp + 0.012Rp 0.6006 3 2 = 36.995CC1 0.676Re 0.000011y + 0.000187y 0.000808y 0.07168 3 2 Where , C = 0.0002Rp 0.0046Rp + 0.0334Rp + 0.6569 C1 = 0.0027Rp3 + 0.0583Rp2 + 0.0455Rp + 24.536

2

[26]

0.058

Diameter ratio: (d/w) Nu = 0.035Re0.795Pr 0.4 (d/w ) 0.068 (s /w )0.086 Pitch ratio: (s/w) f = 1.915Re 0.299 (d/ w ) 0.068 (s /w ) 0.094

Porosity: (Rp) Twist ratio: (y)

0.75

1.914

0.228

Nu = 0.09Re0.768Pr 0.4 (y /W )

f = 9.03Re

[29]

0.112

0.579 y 0.259

f = 6.936Re

= 4.058Re Perforated twisted tape

Reference

[34]

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demonstrated to have a weaker effect on enhancing thermal performance, compared with longer twisted tapes [25]. In addition, much efforts have been made to investigate the influence of the specific fabrication of twisted tapes on enhancing thermal performance, and these studies are summarized in Table 1. Many studies proposed different cuts to twisted tapes for additional improvement of their heat transfer performance, such as a V-cut [26], a U-cut [27], a square-cut [28], a peripherally-cut [29], and a rectangular-cut [30]. These studies reported that increasing the widths and depths of various cuts promotes the Nusselt number and thermal performance factor in comparison to conventional twisted tapes. Moreover, He et al. [31] have employed cross hollow twisted tape with different hollow widths of 6, 8 and 10 mm in heat exchanger tube. They found that the twisted tape with 6 mm hollow width could yield higher friction factor and Nusselt number by 883%-1042% and 93%-120% than plain tube. Thermal and flow behaviors of quadruple V-finned twisted tapes in square tube have been also experimentally studied. The experimental results represented that fin pitch of 4 and highest fin height of 0.21 could achieve the maximum thermal performance factor of 1.75 [32]. By using CFD simulation, Wang et al. [33] have evaluated three configuration parameters of regularly spaced short-length twisted tape, including free space ratio, twist ratio and rotated angle. The alternative design with twist ratio of 4.25–4.75, rotated angle of 270° and free space ratio of 28–33 was suggested for industrial application. Besides, some attempts have been made to perforate typical twisted tapes for improving heat transfer rate within an allowable pressure drop. Some studies have comprehensively compared perforated twisted tapes with other types of twisted tapes in terms of thermal characteristic in heat exchanger tube [19,27]. Bhuiya et al. [34] reported that a tube fitted with perforated twisted tapes accomplished greater thermal performance than a plain tube based on the Nusselt number increased by 110–340%, the friction factor increased by 110–360%, and the

thermal performance factor increased by 28–59%. Perforated twisted tapes with porosities of 4.5% exhibited the maximal thermal performance factor of 59% at the Re number of 7525. Thianpong et al. [35] explored the effects of the perforation diameter and spaced-pitch length on the tapes’ thermal characteristics for the Reynolds number in the 4000–18,000 range. Their results indicated that increasing the pitch length of the perforated hole and decreasing the perforation diameter could significantly improve the heat transfer rate by as much as 27.4% in comparison to conventional twisted tapes. Additionally, Sasanian et al. [36] derived empirical correlations using genetic algorithms to predict the thermal performance of perforated twisted tapes in form of friction factor and Nusselt number. Therefore, using modified twisted tapes with specific configurations has been demonstrated to be an alternative approach for heat transfer enhancement. In recent decades, an innovative form of twisted tapes, namely self-rotating twisted tapes (SRTTs), has been widely adopted in practical applications. The particular characteristic of SRTTs is their rotation behavior when a working fluid flows through the tube at high water velocity. Theoretically, such rotating behavior should generate additional swirl flow and thus increase the heat transfer efficiency without any external energy involved. As mentioned above, perforated twisted tapes could be a feasible solution to further enhance thermal performance of heat exchangers. It is possible that combination of SRTTs and perforation modification could have dual effects on thermal performance augmentation. Using such combination might enhance heat transfer performance with acceptable increase in flow resistance. However, only a few researches were implemented to examine the effect of perforation modification to SRTTs on changing thermal characteristics in a double-pipe heat exchanger. To best of our knowledge, this paper is the first one to study the dual effects of perforated SRTTs on the heat transfer and friction factor characteristic. Some valuable findings can be revealed for proper application of perforated SRTTs in

Fig. 1. (a) Perforated SRTTs and STTs with the same configuration; (b) Perforated SRTTs with different PRs. 3

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double-pipe heat exchanger. The experiments are carried out for six perforation ratios (PR = 0%, 1.61%, 3.63%, 6.46%, 10.1% and 14.49%) at Reynolds number ranging from 12,000 to 45,000. The measured data with thermal equilibrium are adopted for the following calculation of thermal indicators. Then, a comparative experiment between perforated SRTTs and stationary twisted tapes (STTs) is carried out. The effects of perforation ratios on Nusselt number, friction factor and thermal performance factor at investigated Reynolds number are examined. Accordingly, some correlations associated with perforation ratios are proposed for estimating the Nusselt number and friction factor.

constant water temperature, hot water was pumped back to a water tank and was re-heated using an electrical heater with a constant heat flux, while cold water was discharged to the heat sink for releasing heat to the outdoors. As for the data collection system, two temperature sensors (RTDs) were installed at the inlet and the outlet of the inner tube for estimating the bulk temperature of water. Some thermocouples were tapped on 10 positions along the inner tube for recording the local wall temperature. Two pressure tapes were placed at the inlet and the outlet of the inner tube for measuring the pressure drop across the inner tube. All of the experimental data, including the water temperature, pressure drop and volume water flow rate were steadily monitored using a data logger. For example, the inlet temperature at inner tube was kept at 40 °C ( ± 0.5 °C), and the inlet temperature at outer tube was controlled at 21.8 °C ( ± 0.2 °C).

2. Experimental methods SRTTs were made from 2000-mm-long, 1-mm-thick, and 14-mmwide polymer straight tapes, and were equipped with rotation and bearing. Perforated SRTTs and STTs with the same configuration were prepared to conduct comparative test, as shown as Fig. 1 (a). Bearing fixes the twisted tape at the inlet of inner tube, and rotation can help the twisted tape rotate along the axial center of the inner tube. Considering similar density between the polymer material and water, SRTTs can suspend into water for smooth rotation behavior. Hence, water should be chosen as heat transfer medium for the application of SRTTs in this study. In this experiment, five perforated SRTTs with different perforation ratios (PR = 0%, 1.61%, 3.63%, 6.46%, 10.1% and 14.49%) were prepared, as shown as Fig. 1(b). The twisted tapes had different perforation hole diameters. The definition of PR was a ratio of the perforation area to the total area of a twisted tape. It should be noted that all SRTTs used in this experiment had a constant twist ratio of four. A double-pipe heat tube with an observational section was modified for measuring the rotation speed of the SRTTs (Fig. 2(a)). The rotation speed was recorded by a digital tachometer RPM meter in the contactless mode (Fig. 2(b)). The test bed mainly consisted of a test section, a data collection system and a heat sink, as shown in Fig. 3. The test section (a double-pipe heat exchanger) contained an inner tube and an outer tube. The inner diameter and outer diameter of inner tube are 20 mm and 25 mm, respectively. The inner diameter and outer diameter of outer tube are 65 mm and 70 mm. In addition, outer tube was made of stainless steel, and inner tube was manufactured from copper with full length of 2000 mm. In order to reach convective heat transfer in the countercurrent manner, hot water (40 °C at the inlet of the inner tube) was circulated through the inner tube, and cold water (21.8 °C at the inlet of the outer tube) flowed through the outer tube, respectively. The water volume flow rate was controlled by adjusting the power capacity of a water pump. It should be noted that water volume flow rate was maintained at 0.55 m3/h in outer tube, and varied from 0.45 m3/s to 1.62 m3/h in inner tube for the investigated cases. To maintain a

3. Data processing Below, we describe the procedure of calculating the Nusselt number, friction factor, and thermal performance factor for the tube with the SRTTs between the Reynolds numbers of 12000–45000. The details are summarized below. 3.1. Heat transfer characteristic The heat transfer loss by the hot water across the inner tube is

Qw = m w Cp, w (Tw, in

Tw, out )

(1)

The transferred heat from the inner tube to outer tube is supposed to be the same as the convective heat transfer, as shown below: (2)

Qw = Qconv

For all experimental runs, the above two quantities should be in an excellent agreement owing to the thermal equilibrium between the heat supply and transferred heat, as follows:

QVI Qw QVI

100%

5%

(3)

The convective heat transfer in this experiment was

Qconv = hAi (T¯s

Tb)

(4)

where

Tb = (Tout + Tin)/2

(5)

T¯s =

(6)

Ts /10

where bulk temperature of water is calculated according to the average hot water temperature at inlet and outlet of inner tube. The local wall temperature is the average temperature of 10 positions along inner

Fig. 2. (a) Fabricated tube with an observational section; (b) Digital tachometer RPM meter in the contactless mode. 4

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Fig. 3. Diagrammatic sketch of the test bed.

tube. The heat transfer coefficient of local tube wall was

hi = Q w / Ai (T¯s

Tb )

3.4. Uncertainty analysis Uncertainty in the experimental results was calculated according to ANSI/ASME standard [45]. Due to the measurement errors, some measured variables are subject to certain uncertainties that determine combined uncertainties of non-dimensional parameters. In this experiment, uncertainties of measured variables were given as below: water temperature of 1.6%, inner diameter of 2.2%, water flow rate of 3.1% and pressure drop of 5.6%. The maximal uncertainties in these nondimensional parameters were estimated to be within ± 3.4% for the Reynolds number, ± 8.8% for the Nusselt number, and ± 9.2% for the friction factor. The equations that were used to estimate these uncertainties were [45]:

(7)

The heat transfer rate of inner tube was indicated by Nusselt number as below:

Nu =

hi Di

(8)

3.2. Friction factor characteristics The friction factor was estimated from the differential pressure across the entire length of inner tube:

f=

P L v2 ( D )( 2 ) i

Di µ

(

f ( p) 2 3 D 2 2 Re 2 L 2 0.5 ) = [( ) +( ) +( ) +( )] f p D Re L

(13)

(

Re m 2 D 2 0.5 ) = [( ) +( )] Re m D

(14)

4.1. Verification test: Plain tube The experimental data for the Nusselt number and friction factor were verified by some correlations that are frequently observed for single-phase fluids and plain tubes. These correlations are listed below [37]: The correlation of Dittus–Boelter (Eq. (15)):

Although the employment of twisted tapes usually can raise heat transfer coefficient, it also causes the increase in pressure drop that leads to more pumping power. In order to evaluate the potential of various twisted tapes for energy saving, the thermal performance factor has been commonly used to quantify the thermal efficiency of heat exchanger system. This parameter is defined by the relationship between the Nusselt number ratio and the friction factor ratio at a constant pumping power, which can be expressed as Eq. (11) [39–44]:

(Nut / Nup) ht |pp = hp (ft / fp )1/3

(12)

4. Results and discussion

(10)

3.3. Thermal performance factor

=

Nu h 2 D 2 0.5 ) = [( ) +( )] Nu h D

(9)

The Reynolds number, which indicates the working fluid’s condition, is expressed as

Re =

(

Nu = 0.023Re0.8Pr 0.3

(15)

The correlation of Gnielinski (Eq. (16)):

Nu =

(f /8)(Re 1000)Pr 1 + 12.7(f /8)0.5 (Pr 2/3 1)

(16)

The correlation of Blasius (Eq. (17)): (11)

f = 0.316Re 5

0.25

(17)

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The correlation of Petukhov (Eq. (18)):

f = (0.79 ln Re 1.64)

2

4.4. Friction factor characteristic (18)

The effect of the PRs on the friction factor characteristic is summarized in Fig. 8. Fig. 8(a) shows that the friction factor of the SRTTs with higher PRs is higher than that of the SRTTs with lower PRs for given operating conditions. A possible explanation is that stronger turbulence intensity generated by higher PR increases the viscous loss along the inner tube, resulting in a considerable differential pressure. Moreover, SRTTs with lower PRs can rotate faster than those with higher PRs. Hence, high rotational speed is likely to promote rotational flow that significantly reduces flow resistance and smoothen heat transfer surface. In addition, frication factor of perforated SRTTs becomes less great than those of perforated STTs under rotating condition. It is likely that presence of rotation behavior functions in reducing flow resistance that mitigate increase in pressure drop. As presented in Fig. 8(b). the ƒt/ƒp ratio overall tends to decrease gradually with the increase of Reynolds number. This might be partially owing to the higher rotation speed caused by higher water velocity and larger Reynolds numbers, which can mitigate the flow blockage and resistance along the flow path.

The results of the validation test are shown in Figs. 4 and 5. The experimental data were observed to reach a great agreement with the Dittus–Boelter ( ± 9.9%) and Gnielinski ( ± 7.8%) equations. In addition, the results obtained in the present work for the friction factor were validated by the equations of Blasius and Petukhov with deviation of ± 9.6% and ± 11.6%. Eqns. (15) and (17) are proposed to predict the Nusselt number and the friction factor for the SRTTs in Section 4.4. 4.2. Effect of the PR on the rotation speed SRTTs are stationary at low water velocities, and exhibit rotation behavior that is enforced by the working fluid at higher water velocities. For all given cases, SRTTs with PR of 14.49% cannot perform rotation behavior because contact area is not enough to be forced to rotate. Fig. 6 demonstrates that the PR significantly affects the initial stage of rotation behavior, and lower PRs induce SRTTs rotation behavior at lower Reynolds numbers and/or lower water velocity. In addition, the speed of rotation behavior increases sharply with increasing the Reynolds number, and the SRTTs with lower PRs (PR = 0) rotate faster than those with higher PR (PR = 1.61%, 3.63%, 6.45%, and 10.1%). This can be attributed to reason that reducing the perforation area raises the contact surface area between the working fluid and the twisted tape, which allows SRTTs rotation behavior at higher rates.

4.5. Thermal performance assessment Fig. 9 illustrates the dependence of the thermal performance factor on the Reynolds number for different PRs. Apart from PR = 14.49%, the thermal performance factors of other SRTTs were found to increase significantly (0.862 to 0.924, 0.987 to 1.025, 1.04 to 1.078, 1.084 to 1.101, and 1.042 to 1.055, for PR = 0%, 1.61%, 3.63%, 6.46%, and 10.1%, respectively) when the SRTTs started to rotate. A possible explanation is that rotation behavior is the main factor to produce rotational flow that increases the heat transfer rate by enhancing the turbulence intensity along the tangential direction, while it reduces the friction factor by smoothening the fluid motion and flow blockage. Augmentation of the heat transfer and reduction of the pressure drop can both remarkably increase the thermal performance factor. In addition to PR = 14.49%, it is seen that the tube fitted with the SRTTs with higher PR exhibits a higher thermal performance factor than those with lower PRs. It is likely that an increase in the perforation area is responsible for considerably enhancing the fluid motion along the longer flow path, which generate stronger turbulence intensity along tangential direction. Perforated SRTTs with PR = 1.61% are found to have greater thermal performance factor comparing with perforated STTs with PR = 1.61%. This can be explained by the fact that rotational flow can produce additional swirl flow with less increase in pressure

4.3. Heat transfer characteristic Fig. 7 presents the variation of the Nusselt number, friction factor, and thermal performance factor with the Reynolds number in the 12000–45000 range, for the SRTTs with different PRs. These results show that the tube fitted with the different SRTTs yields much higher Nusselt number, compared with the plain tube. This can be explained by the stronger swirl flow induced by the insertion of the SRTTs, which improves the motion of working fluid between the core region and the near wall surface. Also, it is observed that perforated SRTTs perform greater heat transfer rate than perforated STTs under rotating condition. It is consistent with previous results regarding comparison between SRTTs and STTs [20]. It also can be attributed to rotational flow caused by rotation behavior for heat transfer enhancement [46]. Moreover, larger PRs can significantly enhance the Nusselt number, compared with lower PRs. These results are somewhat different from previously reported results regarding the effect of the perforation area on heat transfer [34,35]. It is possible that perforated modification (multiple perforated hole) used in previous research is somehow different from the perforated modification (single perforated holes) used in this study. As mentioned in Section 4.2, an increase in the perforation ratio reduces the rotational speed of rotation behavior. The rotation behavior is considered to produce rotational flow that contributes to disrupting thermal boundary layer [46]. In addition, perforation modification has been demonstrated to effectively generate extra swirl flow. Thus, our results imply that the perforation modification plays more dominant role than the rotational speed for heat transfer enhancement in terms of yielding stronger swirl flow and increasing the residence time along the tangential direction. As shown in Fig. 7(b), the Nut/Nup ratio decreased from 1.22 to 1.08, 1.47 to 1.27, 1.55 to 1.2, 1.63 to 1.24, and 1.82 to 1.41, for PR = 0%, 1.61%, 3.63%, 6.46%, and 10.1%, respectively, with increasing the Reynolds number. It turns out that the perforation modification plays a more dominant role in inducing extra turbulence for effective convective heat transfer at lower Reynolds numbers compared with higher-Reynolds-number flows.

Fig. 4. Experimental results versus empirical correlations results: Nu. 6

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Fig. 5. Experimental results versus empirical correlation results: ƒ.

Fig. 6. Relationship between the rotation speed (RPM) and the Reynolds number. (The red circles denote the initial phase of rotation behavior).

Fig. 7. Variation of (a) the Nu and (b) the Nut/Nup ratio with Re for the SRTTs with different PRs.

drop. In addition, thermal performance factor of PR = 14.49% keeps decreasing for all investigated cases due to non-existence of rotation behavior. Although SRTTs with PR = 10.1% perform slight lower thermal performance under stationary condition, it appears to have higher thermal performance factor than those with PR = 14.49% under rotating condition. This can be explained by effects of existence of rotation behavior on additional enhancement of heat transfer and mitigation of increase in pressure drop. Despite higher PR decreases rotational speed and produces larger flow resistance that consumes some pumping power, it also attributed to enhancing heat transfer that reduces more energy consumption for excellent thermal efficiency.

displayed in Figs. 10 and 11 for Nusselt number and friction factor, respectively. The results showed that there are 10% discrepancy between experimental and correlations values for Nusselt number and friction factor. 4.7. Comparison of perforated SRTTs and perforated twisted tapes Perforated SRTTs were compared with perforated twisted tapes (PTTs) used in a previous study, in terms of the thermal performance factor [35]. From Fig. 12, the tube with the perforated SRTTs evidently has a larger thermal performance factor than those with the PTTs for the same PR. This is because of the vital influences of rotation behavior on producing extra residence time of the heat transfer process and decreasing the flow blockage. In addition, large perforation diameter of SRTTs was examined for improving the thermal performance factor, which was not consistent with the results for PTTs [35]. It seems possible that such perforation modification to SRTTs is more dominant than the Reynolds number as for affecting the thermal performance factor in comparison of PTTs.

4.6. Proposed correlations The derived correlations for the Nu and the ƒ were developed for the heat exchanger tube fitted with SRTTs at the Reynolds number in the 12000–45000 range and PRs of 0%, 1.61%, 3.63%, 6.46%, 10.1% and 14.49%. They are expressed in the following Eqs. (19) and (20):

NuSRTTs = 0.1638Re0.6811Pr 0.1712 (0.0135 + PR)0.1075

(19)

0.362 (0.0048

(20)

fSRTTs = 2.7315Re

+ PR)0.0591

The comparison between the experimental and predicted values are 7

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Fig. 10. Comparison of the experimental and predicted Nusselt numbers for the SRTTs with different PRs.

Fig. 11. Comparison of the experimental and predicted friction factors for the SRTTs with different PRs.

Fig. 8. Variation of (a) the ƒ and (b) the ƒt/ƒp ratio with Re for the SRTTs with different PRs.

5. Conclusion The thermal characteristics of SRTTs with different PRs in the doublepipe heat exchanger were experimentally investigated in the present study. Some of the major conclusions drawn in this study are listed as below:

• For SRTTs with smaller PRs, rotation behavior starts at lower water •

•

Fig. 9. Variation of the η with the Re for SRTTs with different PRs. (The red arrow denotes the change of the SRTTs from the stationary to rotation condition). 8

velocities or Reynolds numbers. Moreover, SRTTs with larger PRs seem to rotate slower than those with smaller PR. In comparison of perforated STTs, perforated SRTTs seem to execute higher thermal performance for given cases. Increasing the PR of SRTTs can significantly increase the Nusselt number and the friction factor, by 14.5% to 62.3%, and by 124% to 174%, respectively. Apart from SRTTs with PR = 14.45%, the thermal performance factor increases sharply when the SRTTs start to rotate from the stationary condition. Under rotating condition, SRTTs with PR = 10.1% can yield higher thermal performance factor than those with PR = 14.49%. Some correlations for SRTTs associated with the PRs were formulated to accurately establish the Nusselt number and the friction factor. The predicted value from the proposed correlations was validated to be within 10% of experimental data.

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Fig. 12. Comparison of ƒ of perforated SRTTs and those of perforated PTTs.

In summary, the present study revealed that the perforated SRTTs can significantly improve their thermal performance in comparison of perforated STTs. The derived empirical correlations associated with the PR could be employed to accurately estimate the Nusselt number and the friction factor of SRTTs. The findings of this study can provide the optimal solutions of SRTTs’ geometry for proper employment of SRTTs in double-pipe heat exchangers. Acknowledgements This study was partially supported by a grant from the NSFC/RGC Joint Research Scheme sponsored by the Research Grants Council of Hong Kong and the National Natural Science Foundation of China (Project No. N_PolyU513/18). We also would like to thank Hebei Engineering University for providing the experimental apparatus. Appendix A. Supplementary material Supplementary data to this article can be found online at https:// doi.org/10.1016/j.applthermaleng.2019.114296. References [1] K. Milani, M. Mamourian, S. Mirzakhanlari, R. Ellahi, Numerical investigation of heat exchanger effectiveness in a double pipe heat exchanger filled with nanofluid: A sensitivity analysis by response surface methodology, Powder Technol. 313 (2017) 99–111. [2] J.A. Esfahani, M. Akbarzadeh, S. Rashidi, M.A. Rosen, R. Ellahi, Influences of wavy wall and nanoparticles on entropy generation over heat exchanger plat, Int. J. Heat Mass Transf. 109 (2017) 1162–1171. [3] K. Milani, M. Mamourian, S. Mirzakhanlari, R. Ellahi, Two phase simulation and sensitivity analysis of effective parameters on combined heat transfer and pressure drop in a solar heat exchanger filled with nanofluid by RSM, J. Mol. Liq. 220 (2016) 888–901. [4] R. Ellahi, A. Zeeshan, N. Shehzad, S.Z. Alamri, Structural impact of kerosene-Al2O3 nanoliquid on MHD Poiseuille flow with variable thermal conductivity: Application of cooling process, J. Mol. Liq. 264 (2018) 607–615. [5] R. Ellahi, A. Zeeshan, F. Hussain, T. Abbas, Thermally charged MHD Bi-phase flow coatings with non-newtonian nanofluid and hafnium particles along slippery walls, Coatings 9 (2019) 300. [6] R. Ellahi, A. Zeeshan, F. Hussain, T. Abbas, Two-phase couette flow of couple stress fluid with temperature dependent viscosity thermally affected by magnetized moving surface, Symmetry. 11 (2019) 647. [7] M. Sheikholeslami, M. Jafaryar, S. Saleem, Z. Li, A. Shafee, Y. Jiang, Nanofluid heat transfer augmentation and exergy loss inside a pipe equipped with innovative turbulators, Int. J. Heat Mass Transf. 126 (2018) 156–163. [8] M. Sheikholeslami, M. Jafaryar, A. Shafee, Z. Li, Investigation of second law and hydrothermal behavior of nanofluid through a tube using passive methods, J. Mol. Liq. 269 (2018) 407–416. [9] C. Methods, A. Mech, M. Sheikholeslami, Numerical approach for MHD Al2O3-water nanofluid transportation inside a permeable medium using innovative computer

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