Scholarly article on topic 'A case study on thermal performance assessment of a heat exchanger tube equipped with regularly-spaced twisted tapes as swirl generators'

A case study on thermal performance assessment of a heat exchanger tube equipped with regularly-spaced twisted tapes as swirl generators Academic research paper on "Materials engineering"

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{"Heat transfer" / "Swirl flow" / "Twisted tape" / "Regularly-spaced twisted tape"}

Abstract of research paper on Materials engineering, author of scientific article — P. Eiamsa-ard, N. Piriyarungroj, C. Thianpong, S. Eiamsa-ard

Abstract Effects of the regularly-spaced twisted tape (RS-TT) on the heat transfer, friction factor and thermal performance factor behaviors in a heat exchanger are reported along with those of a full length twisted tape. The full length (or typical) twisted tapes with two different twist ratios (y=P/W=6.0 and 8.0), and the regularly-spaced twisted tape (RS-TT) with two different twist ratios (y=6.0 and 8.0) and three free space ratios (s=S/P=1.0, 2.0, and 3.0) were employed for comparative study. The article also presents the application of a mathematical model for numerical simulation of the swirling flow in a tube induced by regularly-spaced twisted tape (RS-TT) insertion. The numerical simulation was performed in order to gain an understanding of physical behavior of the fluid flow (decaying swirling flow field), fluid temperature and local Nusselt number characteristics of a tube fitted with RS-TT in the turbulent flow regime. The Navier–Stokes equation in common with the energy equation was solved using the SIMPLE technique with the RNG k–ε turbulence model. The experimental results show that heat transfer rate and friction increased with decreasing twist ratio and space ratio. At similar conditions, full length twisted tapes (s=0) offered higher heat transfer rate, friction factor and thermal performance factor than RS-TT ones (s=1.0, 2.0 and 3.0) as they induced more consistent swirling flows and thus turbulence. This reveals that it is possible to gain promising tradeoff between enhanced heat transfer and increased friction by selecting the twisted tape with proper geometries.

Academic research paper on topic "A case study on thermal performance assessment of a heat exchanger tube equipped with regularly-spaced twisted tapes as swirl generators"

CASE STUDIES IN THERMAL ENGINEERING

Author's Accepted Manuscript

A case study on thermal performance assessment of a heat exchanger tube equipped with regularly-spaced twisted tapes as swirl generators

P. Eiamsa-ard, N. Piriyarungroj, C. Thianpong, S Eiamsa-ard

www.elsevier.com/locate/csite

PII: S2214-157X(14)00013-6

DOI: http://dx.doi.org/10.1016/j.csite.2014.04.002

Reference: CSITE30

To appear in: Case Studies in Thermal Engineering

Received date: 27 November 2013 Revised date: 22 April 2014 Accepted date: 22 April 2014

Cite this article as: P. Eiamsa-ard, N. Piriyarungroj, C. Thianpong, S. Eiamsa-ard , A case study on thermal performance assessment of a heat exchanger tube equipped with regularly-spaced twisted tapes as swirl generators, Case Studies

in Thermal Engineering , http://dx.doi.org/10.1016/jxsite.2014.04.002

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A case study on thermal performance assessment of a heat exchanger tube equipped with regularly-spaced twisted tapes as swirl generators

P. Eiamsa-ard1, N. Piriyarungroj2, C. Thianpong 2 and S. Eiamsa-ard3* 1Faculty of Industrial Technology, Phetchaburi Rajabhat University

Phetchaburi 76000, Thailand ^Department of Mechanical Engineering, Faculty of Engineering King Mongkut's Institute of Technology Ladkrabang Bangkok 10520, Thailand 3Department of Mechanical Engineering, Faculty of Engineering Mahanakorn University of Technology, Bangkok 10530, Thailand Corresponding author: E-mail addresses: smith@mut.ac.th

Abstract

Effects of the regularly-spaced twisted tape (RS-TT) on the heat transfer, friction factor and thermal performance factor behaviors in a heat exchanger are reported along with those of a full length twisted tape. The full length (or typical) twisted tapes with two different twist ratios (y = P/W = 6.0 and 8.0), and the regularly-spaced twisted tape (RS-TT) with two different twist ratios (y = 6.0 and 8.0) and three free space ratios (s = S/P = 1.0, 2.0, and 3.0) were employed for comparative study. The article also presents the application of a mathematical model for numerical simulation of the swirling flow in a tube induced by regularly-spaced twisted tape (RS-TT) insertion. The numerical simulation was performed in order to gain an understanding of physical behavior of the fluid flow (decaying swirling flow field), fluid temperature and local Nusselt number characteristics of a tube fitted with RS-TT in the turbulent flow regime. The

Navier-Stokes equation in common with the energy equation was solved using the SIMPLE technique with the RNG k-s turbulence model. The experimental results show that heat transfer rate and friction increased with decreasing twist ratio and space ratio. At similar conditions, full length twisted tapes (s = 0) offered higher heat transfer rate, friction factor and thermal performance factor than RS-TT ones (s = 1.0, 2.0 and 3.0) as they induced more consistent swirling flows and thus turbulence. This reveals that it is possible to gain promising tradeoff between enhanced heat transfer and increased friction by selecting the twisted tape with proper geometries.

Keywords: Heat transfer, Swirl flow, Twisted tape, Regularly-spaced twisted tape 1. Introduction

Swirl flows are found in nature, such as tornadoes, and have been of considerable interest over the past decades because of their promising characteristics for several industrial applications, such as cyclone separators, vortex tubes, agricultural spraying machines, heat exchangers, gasoline engines, diesel engines, gas turbines, furnaces, vortex dust collectors and many other practical heating devices. Swirl flow devices are designed to impart a rotational motion about an axis parallel to the flow direction to the bulk flow. Twisted tapes belong to one important group of swirl generator which mostly applied for heat transfer improvement. Figure 1 shows the visualized swirl flow induced by a typical twisted tape, achieved from dye-technique and numerical-technique. The heat transfer enhancement by twisted tapes are attributed to (1) a reduction of a hydraulic diameter causing resulting in an increase of flow velocity and curvature which in turn increases the shear stress at the wall and drives secondary motions and (2) an extra heat transfer through thermal contact (3) an increased shear stress at the wall and mixing by secondary flow. In general, the twisted tape with small twist ratios (y) give higher swirl

intensity, leading to higher shear stress at the wall and mixing then thinner of thermal boundary layer and higher heat transfer rate than the ones with larger twist ratios (y).

Modified twisted tapes with different tape geometries have been proposed in comparison with typical twisted tapes. Murugesan et al. [1] investigated the thermal performance characteristics in the heat exchanger tubes fitted with trapezoidal-cut twisted tapes. Saha [2] studied the effect of the rectangular/square duct with internal axial corrugations equipped by twisted tapes with oblique teeth on the heat transfer and friction factor. Sivashanmugam et al. [3] conducted experiments of heat transfer, friction and thermal performance using circular tubes fitted with right-left helical screws of equal and unequal length of different twist ratios. Eiamsa-ard et al. [4] examined the heat transfer, friction factor and thermal performance behaviors in a tube with a loose-fit twisted tape insert at different clearance ratios (CR = 0.0 (tight-fit), 0.1, 0.2 and 0.3). The experimental results revealed that thermal performance factor tended to increase with decreasing clearance ratio. Among the examined tapes, the tight-fit tape (CR = 0.0) gave the highest thermal performance factor. Jafari Nasr and Khalaj [5] analyzed heat transfer and friction factor in a corrugated tube fitted with a twisted tape through the artificial neural network approach. Bhuiya et al. [6] reported the effect of triple twisted tapes on heat transfer rate, friction factor and thermal performance characteristics. They showed that the presence of triple twisted tapes led to the higher heat transfer rate and friction factor over the plain tube up to 3.85 and 4.2 times which resulted in thermal performance up to 1.44. The thermal performance was up to 1.44 by the use of triple twisted tape inserts. Bhuiya et al. [7] reported the heat transfer, friction factor and thermal performance factor in tubes with perforated twisted tape inserts with different porosities. They found that the Nusselt number, friction factor and thermal performance factor in the tubes with perforated twisted tape inserts were respectively up to 340%, 360% and 59% above those of the plain tube. Eiamsa-ard et al. [8] conducted the heat transfer enhancement in a tube using twisted tapes with alternate axes at different alternate lengths (l/y). As found, the twisted tapes with both uniform and non-uniform alternate lengths

(TAs and N-TAs) yielded higher Nusselt number and friction factor than the typical tape. The thermal performance factors associated by TAs with ratios of alternate length to twist length of l/y = 0.5, 1.0, 1.5 and 2.0, were respectively, 20%, 16%, 12% and 7% higher than that given by TT. In addition, N-TAs yielded higher thermal performance factor than TT and TAs by around 3% and 8%, respectively. Bhattacharyya et al. [9] presented the friction factor and heat transfer in a tube having integral transverse ribs and centre-cleared twisted-tape. They showed that the centre-cleared twisted tapes in combination with transverse ribs perform significantly better than the individual technique acting alone.

Saha et al. [10] studied the turbulent heat transfer and pressure drop behaviors in a tube fitted with regularly spaced twisted-tape elements connected by thin circular rods at different twist ratios, space ratios, and rod-to-tube diameter ratios. They reported that on the basis of both constant pumping power and constant heat duty, regularly spaced twisted-tape elements did not perform better than full-length twisted tapes. Date and Saha [11] numerically studied the friction and heat transfer characteristics in a tube fitted with regularly spaced twisted-tape elements. The prediction showed that the considerably enhanced thermo-hydraulic performance was achievable by increasing the number of turns on the tape elements, reducing the connecting rod diameter, at high fluid Prandtl numbers. Saha et al. [12] investigated the heat transfer and pressure loss characteristics in a tube fitted with regularly spaced twisted-tape elements in laminar swirl flow regimes. The difference of heated friction factor and isothermal friction factor for the periodic swirl flow was substantially less than that in case of straight flow through plain tube. Eiamsa-ard et al. [13] examined the effect of the regularly spaced twisted tapes on the heat transfer and friction loss characteristics in a double pipe heat exchanger. It was found that the heat transfer rate increased with decreasing twist ratio and free space ratio. Hong et al. [14] investigated the heat transfer and friction loss behaviors in a converging-diverging tube with evenly spaced twisted-tapes at different twist ratios and rotation angles for Reynolds number ranging between 3400 and 20,000. Their results showed that the twisted-tape with twist

ratio (y) of 4.72 (the smallest twist ratio) and rotation angle 0 = 180° gave the highest thermal performance factor. It was also found that the tube inserts with space ratio s=48.6, yielded thermal performances from 0.85 to 1.21 times and from1.07 to 1.15 times of those offered by the plain tube and the converging-diverging tube alone, respectively. Jaisankar et al. [15] performed the comparative study of the heat transfer and friction factor characteristics of thermosyphon solar water heater with twisted tapes fitted with rod and spacers. As compared to full length twist tape, the twisted tapes fitted with rod and spacers, gave lower heat transfer rates around 11% and 19%, respectively which accompanied by the decreases of friction factors around 18% and 29%, respectively. Ananth and Jaisankar [16] examined the heat transfer and pressure drop behaviors of thermosyphon solar water heater fitted with regularly spaced twisted-tape with rod and spacer. Their results demonstrated that as spacer length increased, both heat transfer rate and friction factor decreased. Zhang et al. [17] performed numerical simulation to study the thermal and fluid flow of multi-longitudinal vortices in a tube induced by triple and quadruple twisted tape inserts for the Reynolds number from 300 to 1800. As compared to the plain tube, the tubes with triple and quadruple twisted tapes possessed higher heat transfer rates up to 171% and 182%, respectively, these accompanied with the increases of friction factors of around 4.06 to 7.02 times, respectively. In addition, the thermal performance factors of the tube inserts varied between 1.64 and 2.46.

The above literature shows that the performances of twisted tapes mainly depend on their geometries. Mostly, the modified twisted tape can further improve heat transfer rate as compared to typical twisted tapes. However, the enhanced heat transfer is usually accompanied by the increase of friction penalty. The evaluation of overall performance of twisted tape is therefore based on the tradeoff between both increased heat transfer and friction factor. According to the above literature, both experimental and numerical studies on heat transfer enhancement using twisted tapes. However, for each research either experimental work or numerical work was carried out. The present work offers both experimental and numerical

investigations on heat transfer enhancement using twisted tapes, in order to assess the agreement between the experimental and numerical results and to gain a better understanding of heat transfer enhancement. Although, numerical simulation is capable to analyze the effect of twisted tapes with different structure, the experimental study is an essential tool for evaluating the practical use of tape inserts. The main objective of this work is to study the effect of modified twisted tapes in form of the regularly-spaced twisted tape (RS-TT) with two different twist ratios (y = 6.0 and 8.0) and three space ratios (s = 1.0, 2.0, and 3.0) in comparison with that of the full length (or typical) twisted tapes, in order to find an optimum tradeoff between the enhanced heat transfer and the increased friction factor for Reynolds numbers between 5000 and 12,000. Details of flow structure, temperature field and local Nusselt number in a tube fitted with RS-TT at different space ratios are analyzed using numerical technique for better understanding the heat transfer mechanism.

2. Experimental setup

2.1 Concentric tube heat exchanger

The arrangement of the experimental system of a concentric tube heat exchanger was set up as depicted in Fig. 2. The double tube heat exchanger consisted of two concentric tubes arranged in a counter flow; an inner tube for hot air flow and an outer tube for water flow. The inner tube was made of copper with an inner diameter of 19 mm while the outer tube was made of steel with an inner diameter of 40 mm. Both tubes were 2000 mm long and 1 mm thick. The storage tank which supplied water was maintained at a constant head pressure. The outer tube of the heat exchanger was insulated lengthwise using asbestos disks to prevent the heat transfer to surroundings.

2.2 Regularly-spaced twisted tape (RS-TT)

Regularly-spaced twisted tapes (RS-TTs) were made of stainless steel strips with thickness of 1.0 mm and width of 18 mm. Typical or full length twisted tapes were formed by twisting a

straight tape, about its longitudinal axis, while being held under tension at desired twist ratio (y = P/W = 6.0 and 8.0). Regularly-spaced twisted tapes (RS-TTs) were produced by cutting a part of full length twisted tapes and connecting them together using stainless steel wire. The length of connecting wire was equal to a space between each pair of connected RS-TTs. In the present work the space is defined in term of space ratio, s = S/P which was varied from 0.0 (full length twisted tape) to 3.0. All of twisted tape geometry is depicted in Fig. 2.

2.3 Experimental procedure

In the apparatus setting above, hot air from a high pressure blower was directed through the inner tube, while cold water was pumped through the annulus (Fig. 3). Two rotameters were used to measure both water and air flow rates. The volumetric flow rates of the hot air and cold water were adjusted by control valves, situated before the inlet ports. The inlet air was heated by an adjustable electrical heater. Both the inlet and outlet temperatures of the hot air and the cold water were measured by multi-channel with thermocouple type T. Local temperatures at 15 stations were measured for evaluating an average Nusselt number. All fifteen thermocouples were installed 0.5 mm beneath the outer surface and connected to the data logger set. Pressure taps were located at the entrance and the exit of the inner-outer tubes to measure the pressure drop by connecting them to the U-tube manometer. All temperature, volumetric flow rate and pressure drop data of the hot air and the cold water were recorded at steady state conditions. During experiments, the temperatures of the inlet air and cold water were maintained at 80oC and 27oC, respectively. The Reynolds number of the heated air was varied from 5000 to 12,000. The calculations of Reynolds number, Nusselts number and friction factor were based on the average tube wall temperature.

3. Data reduction

For fluid flows in the concentric tube heat exchanger, the average of the heat transfer rate from the hot fluid (air) and cold fluid (water) of the test tube can be expressed as:

Qw = (fmhCp, h (Th,inlet Th,outlet) + (mcCp,c (Tc, outlet Tc,inlet))/2

The convective heat transfer rate of the inner tube can be calculated from

Qconv = hA(Tw - Tb)

whereas,

Tb - (To + T )/2

Tw -I Tw/15

Tw is the mean inside tube-wall temperature of the test section which is computed by taking the average temperatures of 15 axial stations of inner wall temperatures lined between the inlet and the exit of the inner tube (0.5 mm beneath the outer surface) as seen below. Tw is the local wall temperature, evaluated at the inner wall surface of the test tube. fw = E(Tw1 + Tw2 +.....Tw15)/15

The average heat transfer coefficient and the mean Nusselt number are estimated as follows:

h - Qw / A(Tw - Tb) Nu = hD/k

The Reynolds number is given by

Re = VD/v

Friction factor can be written as f -=- ^

V2 ^ P~2

4. Mathematical model and numerical method

The prediction of swirl flow characteristics in a tube fitted with RS-TTs was examined using mathematical modeling. The available finite difference procedures for swirling flows and boundary layer were employed to solve the governing partial differential equations. Some simplifying assumptions were applied for conventional flow momentum and energy equations to model the heat transfer process in a constant temperature wall tube with RS-TTs. The major assumptions are; (1) the flow is steady and incompressible, (2) the flow through the RS-TTs is turbulent, (3) natural convection and thermal radiation are neglected and (4) the thermo-physical properties of the fluid are temperature independent. Based on above approximations, the governing differential equations used to describe the fluid flow and heat transfer in a round tube with RS-TT inserts are established. The continuity, momentum and energy equations for the three dimensional models are employed. For steady flow, the time-averaged incompressible Navier-Stokes equations in the Cartesian tensor notation can be written in the following form: Continuity equation:

dr(pui ) = 0 dx

Momentum equation:

d(puiuj)

_h = -ÊL + A

dxj dxi dxj

( du. du 2 du, ^ j + —j—8 —-dx. dx. 3 dx,

Energy equation:

f [ (PE + p )] = -f

dx dx.

dT_ dx,.

E = h - P + u P 2

In the present numerical solution, the time-independent incompressible Navier-Stokes equations and the turbulence model were discretized using the finite volume technique. QUICK (Quadratic upstream interpolation for convective kinetics differencing scheme) and central differencing numerical schemes were applied for convective and diffusive terms, respectively. To evaluate the pressure field, the pressure-velocity coupling algorithm SIMPLE (Semi Implicit

Method for Pressure-Linked Equations) was selected. Impermeable boundary condition has been implemented over the tube wall. The turbulence intensity was kept constant at 10% at the inlet. The computation was performed until the difference between normalized residual of the algebraic equation and the prescribed value fell below a convergence criterion (10-6).

The computational domain for the flow in tube fitted with RS-TT was resolved by regular Cartesian elements. The numerical analysis was made for RS-TTs at three free space ratios (s = S/P = 1.0, 2.0 and 3.0). Grid independent solution was obtained by comparing the solution for different grid levels. The total numbers of elements used are approximately 401583, 385801, 386394 and 379073 for s = 0.0, 1.0, 2.0 and 3.0, respectively. The higher numbers of elements employed for the tape with s = 3.0, are due to the larger free space in comparison with the other tapes. The Reynolds number used for the computation are referred to the inlet value and set at 5000. The inlet temperature was kept constant 353 K while the tube wall was maintained under constant wall temperature condition at 298 K.

5. Experimental results

In this section, the heat transfer (Nusselt number, Nu), flow structure, thermal structure, pressure drop (friction factor, f) and thermal performance factor results of the tube with regularly-spaced twisted tapes (RS-TTs) with different twist ratios and space ratios are reported and compared with those of the tube with typical or full length twisted tapes as well as the plain tube.

5.1 Verification of experimental facility

To proof the reliability of the experimental facility, the benchmark test between the results of the present plain tube and those obtained from standard correlations was performed. The standard correlations include Dittus-Boelter and Blasius for the fully developed turbulent flow in circular tube, as stated below.

Nusselt number correlation:

Dittus-Boelter Correlation:

Nu = 0.023 Re08 Pr(

Friction factor correlation:

Blasius Correlation:

f = 0.316 Re

The comparisons between the experimental results of present work and those obtained from the standard correlations are shown in Figs. 4 and 5. The deviations of the experimental Nusselt number and friction factor were within ±8.9% and ±2.6% as compared to those from Dittus-Boelter correlation and Blasius correlation, respectively. In addition, the correlations for Nusselt number and friction factor were developed based on the experimental data, the resultant correlations are shown as follows:

5.2 Flow structure, temperature field and local Nusselt number distribution The predicted flow structure of the swirling flow, temperature field and local Nusselt number distribution of the tube fitted with RS-TTs, at Reynolds number of 5000 are shown in Figs. 6-9. Contour plots of streamline through the RS-TTs in a tube of different free space ratios (s = 1.0, 2.0 and 3.0) are predicted by RNG k-smodel using the QUICK scheme are demonstrated in Figs. 6(a-d) and 7(a-d). The predictions showed that swirl flows were induced due to the presence of twisted tapes. For all RS-TTs, the generated swirls apparently decayed in the spaces between tapes, resulting in the decrease of vortex intensity. Consequently, the decaying swirls associated with the RS-TTs with larger free space ratio (s) possessed poorer fluid mixing and thus lower heat transfer rate. As evidences shown in Figs. 6(d) and 7(d), the decaying swirl

Nu = 0.0188Re0832 Pr04

f = 0.388 Re

flows induced by the tapes with s of 3.0 transformed to axial flows in the space, prior to reach the next tape. On the other hand, more consistent swirl flows were induced by the TTs and RS-TTs with the smallest free space ratio (s = 1.0), leading to superior fluid mixing, resulting in uniform fluid temperature in tubes, and thus more efficient heat transfer in comparison with the larger free space ratio (s = 2.0 and 3.0) as comparisons shown in Figs. 8 and 9. This confirmed by the experimental results (Fig. 10) in which, Nusselt numbers in the tube fitted with TTs and RS-TTs at s = 1.0 were higher than those with RS-TTs at s = 2.0 and 3.0 (details in the next subsection).

5.3 Effect of regularly-spaced twisted tape inserts

The results of heat transfer enhancement in term of Nusselt number, with the use of regularly-spaced twisted tapes (RS-TTs) in comparison with those of the full-length twisted tapes are shown in Fig. 10(a-b). For all cases, Nusselt number increased with increasing Reynolds number. This phenomenon is related to the increase of swirl-flow speed, resulting in a more efficient destruction of the thermal boundary layer. Depending on Reynolds number and tape geometries, Nusselt numbers of the flows in the tube with twisted tapes were improved up to 56.8% as compared to those in the plain tube. In addition, heat transfer enhancement by twisted tape inserts as compared to that of the plain tube seemed to be more significant at higher Reynolds number. This can be attributed to a higher promoted flow turbulence by twisted tapes relative to that in the plain tube, as Reynolds number increased. At similar conditions, full length twisted tapes (s = 0) consistently gave higher Nusselt numbers than regularly-spaced ones (s = 1.0, 2.0 and 3.0). This can be explained by the fact that full length twisted tapes induced continuous swirl flow for the whole length of twisted tape while RS-TT ones intermittently produce swirl flow which is allowed to decay along free space. Regarding to the reason mentioned above, twisted tapes with larger free spaces provided poorer heat transfer than the ones with smaller spaces. As found Nusselt number with the use of RS-TTs with s = 1.0, 2.0 and 3.0 were respectively 7.7%, 16.4% and 22.1% lower than that given by full length twisted

tape (s = 0). At the same space ratio, the tapes with twist ratio y = 6.0 offered higher Nusselt numbers than the ones with y = 8.0 around 6.9%. This result is primarily due to a stronger swirl intensity induced by the tape with a smaller twist ratio or shorter twist-length resulting in higher shear force on tube wall/more effective thermal boundary disturbance and thus better heat transfer.

Figure 11(a-b) shows friction factor generated by an axial flow (in the plain tube) and a swirl flow (in tubes with twisted tape inserts). A similar trend is found for all cases in which friction factors decreased with increasing Reynolds number. Friction factors in the tubes with RS-TTs inserts were consistently higher than that in the plain tube, because of the dissipation of dynamic pressure of the fluid due to the flow resistance caused by the swirling flow. Friction factors of the flows in the tube with twisted tapes were increased up to 4.38 times of that the plain tube. The influences of twist ratio and free-space ratio on friction factor were in similar manners found for Nusselt number. According to the experimental results, friction factors with the use of RS-TTs with s = 1.0, 2.0 and 3.0 were respectively, 11.7%, 25.9% and 38.8 %, lower than that given by full length twisted tape (s = 0). At the same space ratio, the tapes with twist ratio y = 6.0 caused up to 18.2% higher friction factors than the ones with y = 8.0.

As mentioned previously, there is tradeoff between enhanced heat transfer and increased friction by utilizing RS-TTs. In general, RS-TTs which gave better heat transfer and caused higher friction penalty. For the present work, it was found that the RS-TTs with y = 6.0 and s = 1.0 provided similar Nusselt number with those the full length twisted tape with y = 8.0. This can be explained that the effect of the stronger swirl intensity and thus turbulence intensity at smaller twist ratio (y = 6.0) compensate the swirl decaying of the RS-TTs, and make their overall turbulence to be comparable to that the full length twisted tape with y = 8.0.

The tradeoff between enhanced heat transfer and increased friction is usually evaluated by comparing heat transfer and friction results of enhanced and unenhanced case, at the same pumping power, since a pumping power is relevant to the operation cost. For constant pumping power

(VAP)p =(VAP)t (16)

This leads to the relationship between friction and Reynolds number in both the plain tube (unenhanced case) and those with regularly-spaced twisted tapes (RS-TTs) (enhanced case) as (fRe3)p = (fRe3), (17)

The thermal performance factor (rj) is defined as the ratio of the enhanced heat transfer to the increased friction, where the enhanced heat transfer is termed as the ratio of Nusselt number in enhanced case to that in unenhanced case and the increased friction is termed as the ratio of friction factor in enhanced case to that in unenhanced case. With the application of the constant pumping criterion, thermal performance factor (rj) can be written as

n = (Nu/Nup)/(f/fp)1/3 (18)

Figure 12 shows the relationship between thermal performance factor and Reynolds number for the tapes with s = 0.0, 1.0, 2.0, and 3.0, y = 6.0 and 8.0. Justified from the result trend, thermal performance factor increased with reductions of the twist ratio (y), free space ratio (s) and Reynolds number (Re). For the tapes with twist ratio (y) of 6.0, thermal performance factor varied between 0.86 and 0.97, 0.82 and 0.94, 0.79 and 0.89, and 0.78 and 0.88 for the tapes with s = 0.0, 1.0, 2.0, and 3.0, respectively.

The correlations for Nusselt number, friction factor and thermal performance factor with the use of RS-TTs in the studied range, were developed. The resultant correlations (Eqs. 19 to 21) reveal that Nusselt number is affected by Reynolds number (Re), Prandtl number (Pr) and free

space ratio (s) while the friction factor and thermal performance factor are dependent on Reynolds number (Re) and free space ratio (s).

Nu = 0.144 Re0 697 Pr04 y~0-228 (s +1)~°179 (19)

f = 3.044 Re~000 y~0556 (s + ifM (20)

n = 3.854Re~0151 y~0043 (s + iy0 065 (21)

The predictions from Eqs. (19) to (21) are compared with the experimental values as shown in Figs. 13 to 15. Evidently, the predicted Nusselt number, friction factor and thermal performance factor are respectively within ±5%, ±7% and ±3% of the experimental data.

6. Conclusions

Heat transfer enhancement, friction and thermal performance factor characteristics by means of regularly-spaced twisted tapes (RS-TTs) with different twist ratios (y) and free space ratios (s), as compared to that of full length (or typical twisted tapes) are reported. From the experimental results, it can be concluded as follows:

1. At similar conditions, full length twisted tapes (s = 0) gave higher heat transfer rate, friction factor and thermal performance factor than regularly-spaced ones (s = 1.0, 2.0 and 3.0).

2. The augmented heat transfer, friction factor and thermal performance factor decreased with increasing space ratio. At the same twist ratio, the tapes with s = 0 (full length), 1.0, 2.0 and 3.0 gave heat transfer enhancement respectively up 56.8%, 46.2%, 30.5% and 22.6% which were accompanied with the increased friction factors up to 4.22, 3.78, 3.17, and 2.63 times as compared to those in the plain tube.

3. The augmented heat transfer and friction factor decreased with increasing twist ratio. At the same space ratio, the tapes with y = 6.0 and 8.0 gave heat transfer enhancement respectively up to 46.2% and 34.6% which were accompanied with the increased friction factors up to 3.78 and 3.21 times as compared to those in the plain tube.

4. RS-TTs with y = 6.0 and s = 1.0 provided similar Nusselt number with those the full length twisted tape with y = 8.0 as the effect of the stronger swirl intensity and thus turbulence intensity at smaller twist ratio (y = 6.0) compensate the swirl decaying of the RS-TTs, and make their overall turbulence to be comparable to that the full length twisted tape with y = 8.0. In addition, at RS-TTs with large free space ratio (s = 3.0) at both twist ratios (y = 6.0 and 8.0) gave considerably lower heat transfer rate than other tapes because of the significant decaying of swirl flows.

Appendix

In order to assess the reliability of the experimental facility and operation, the uncertainties of the experimental data were determined. The calculations of the data uncertainties were based on method of Kline and McClintock [18]. The uncertainty analyses of the Nusselt number and friction factor are presented and obtained from the equations below.

Nusselt Number:

i(Nu )Ah Í+{dD(Nu )AD (Nu )Ak Í

0.5 r 2 2 ^ 0.5

Ah i f AD h J +i ~D

where h =_-_then

Ah=1 h ~ h

% AT,]2 at] 2

Aq" 12 f A^

T„ - T

T, - T

where q" = nL [Qw + mhCp (Tbo - T,)]

nDL Friction Factor:

f=1 f f

f A(AP)1 + {fAl} + {fAD} + lf

A(AP )1 + {Alj2 + { 3AD]2 + { 2ARe

= ^ and AP h

A Re = 'fAm Ï2 + / AD )2 '

Re = { m J +i

The maximum uncertainties of dimensionless parameters were within ±4% for Reynolds number, ±4% for Nusselt number and ±7% for friction factor. The uncertainties of the volumetric flow rate, pressure and temperature measurements were within ±4%, ±5% and ±0.5%, respectively. The accuracies of the measured quantities are 0.05oC for temperature different (AT), and 0.001 m for AL.

References

[1] P. Murugesan, K. Mayilsamy, S. Suresh, Heat transfer in tubes fitted with trapezoidal-cut and plain twisted tape inserts, Chemical Engineering Communications 198 (2011) 886904.

[2] S.K. Saha, Thermohydraulics of turbulent flow through rectangular and square ducts with axial corrugation roughness and twisted-tapes with and without oblique teeth, Experimental Thermal and Fluid Science 34 (2010) 744-752.

[3] P. Sivashanmugam, P.K. Nagarajan, S. Suresh, Experimental studies on heat transfer and friction factor characteristics of turbulent flow through a circular tube fitted with right and left helical screw-tape inserts, Chemical Engineering Communications 195 (2008) 977987.

[4] S. Eiamsa-ard, K. Wongcharee, S. Sripattanapipat, 3-D numerical simulation of swirling flow and convective heat transfer in a circular tube induced by means of loose-fit twisted tapes, International Communications in Heat and Mass Transfer, 36 (2009) 947-955.

[5] M.R. Jafari Nasr, A.H. Khalaj, Heat transfer coefficient and friction factor prediction of corrugated tubes combined with twisted tape inserts using artificial neural network, Heat Transfer Engineering, 31 (2010) 59-69.

[6] M.M.K. Bhuiya, M.S.U. Chowdhury, M. Shahabuddin, M. Saha, L.A. Memon, Thermal characteristics in a heat exchanger tube fitted with triple twisted tape inserts, International Communications in Heat and Mass Transfer 48 (2013) 124-132.

[7] M.M.K. Bhuiya, M.S.U. Chowdhury, M. Saha, M.T. Islam, Heat transfer and friction factor characteristics in turbulent flow through a tube fitted with perforated twisted-tape inserts, International Communications in Heat and Mass Transfer 46 (2013) 49-57.

[8] S. Eiamsa-ard, P. Somkleang, C. Nuntadusit, C. Thianpong, Heat transfer enhancement in tube by inserting uniform/non-uniform twisted-tapes with alternate axes: Effect of rotated-axis length, Applied Thermal Engineering 54 (2013) 289-309.

[9] S. Bhattacharyya, S. Saha, S.K. Saha, Laminar flow heat transfer enhancement in a circular tube having integral transverse rib roughness and fitted with centre-cleared twisted-tape, Experimental Thermal and Fluid Science 44 (2013) 727-735.

[10] S.K. Saha, U.N. Gaitonde, A.W. Date, Heat transfer and pressure drop characteristics of turbulent flow in a circular tube fitted with regularly spaced twisted-tape elements, Experimental Thermal and Fluid Science 3 (1990) 632-640.

[11] A.W. Date, S.K. Saha, Numerical prediction of laminar flow and heat transfer characteristics in a tube fitted with regularly spaced twisted-tape elements, International Journal of Heat and Fluid Flow 11 (1990) 346-354.

[12] S.K. Saha, A. Dutta, S.K. Dhal, Friction and heat transfer characteristics of laminar swirl flow through a circular tube fitted with regularly spaced twisted-tape elements, International Journal of Heat and Mass Transfer 44 (2001) 4211-4223.

[13] S. Eiamsa-ard, C. Thianpong, P. Promvonge, Experimental investigation of heat transfer and flow friction in a circular tube fitted with regularly spaced twisted-tape elements, International Communications in Heat and Mass Transfer 33 (2006) 1225-1233.

M. Hong, X. Deng, K. Huang, Z. Li, Compound heat Transfer Enhancement of a Converging-Diverging Tube with Evenly Spaced twisted tapes, Chinese Journal of Chemical Engineering 15 (2007) 814-820.

S. Jaisankar, T.K. Radhakrishnan, K.N. Sheeba, S. Suresh, Experimental investigation of heat transfer and friction factor characteristics of thermosyphon solar water heater system fitted with spacer at the trailing edge of left—right twisted tapes, Energy Conversion and Management 50 (2009) 2638-2649.

J. Ananth, S. Jaisankar, Experimental studies on heat transfer and friction factor characteristics of thermosyphon solar water heating system fitted with regularly spaced twisted-tape with rod and spacer, Energy Conversion and Management 73 (2013) 207213.

X. Zhang, Z. Liu, W. Liu, Numerical studies on heat transfer and flow characteristics for laminar flow in a tube with multiple regularly spaced twisted tapes, International Journal of Thermal Sciences 58 (2012) 157-167.

S.J. Kline, F.A. McClintock, Describing Uncertainties in Single Sample Experiments, Mechanical Engineering, 75, 3-8, 1953.

(a) visualized swirl by dye technique

0 0.1 0.2 0.3 J^Q 0.4 0.5 0.6 0.7

(c) flow field and local Nusselt number for y = 8.0 by numerical method

Fig. 1. The visualization of swirl flow pattern and local Nusselt number in tube equipped with

twisted tape.

Cold water

Hot air Outer tube

Inner^tube equipped with a twisted tape

Warm air

Outer tube

Cold water

RS-TT " — \

Flow in

RS-twisted tape ^ \

-T-r_ — \

A set of thermocouple type T

Fig. 2. Details of a concentric double pipe heat exchanger fitted with regularly-spaced twisted

tape (RS-TTs) inserts.

PC computer

Data logger

Outet flow

Thermocouples type T

Concentric tube heat exchanger

Outet flow

Rotameter

Inlet flow

U-Manometer

Cold water tank

Water reservoir

Centrifugal water pump

Inlet flow (Hot air)

Rotameter

Inverter

Variac transformer

\MAAMMAAAAAAAMAAM7V-

electrical heater

High pressure blower

Fig. 3. Schematic diagram of experimental apparatus.

80 70 60 50

I 40 30 20 10 0

5000 6000 7000 8000 9000 10000 11000 12000 Re

Fig. 4. Data verification of Nusselt number of the plain tube.

.09 .08 .07 .06 .05

.04 .03 .02 .01

5000 6000 7000 8000 9000 10000 11000 12000 Re

Fig. 5. Data verification of friction factor of the plain tube.

X Plain tube O Dittus and Boelter

8 8 6 °

X X X o °

X Plain tube

- o Blasius

** B 8 » m

- ® » 8 » g

-0.0095

-0.0095 0 o 0095 z/D

Fig. 6. Contour plots of streamlines in the tubes with RS-TT at different free space ratios (s): (a) s = 0.0, (b) s = 1.0, (c) s = 2.0 and (d) s = 3.0.

High swirl flow

High swirl flow

decaying swirl flow

High swirl flow

decaying swirl flow

High swirl flow

axial flow

^ <■ a.«« vT>

Fig. 7. Contour plots of secondary flows in the tubes with RS-TT at different free space ratios (s): (a) s = 0.0, (b) s = 1.0, (c) s = 2.0 and (d) s = 3.0.

(a) ■ ■

T^mpiiaiuie; 298 298,4 29«Jt 299,2 299,G 3CW

ci n CO» Z.D

Fig. 8. Contour plots of fluid temperatures in the tubes with RS-TT at different free space ratios (s): (a) s = 0.0, (b) s = 1.0, (c) s = 2.0 and (d) s = 3.0.

'Nuttclt-mjrater HHJK! k_ t

0 10 10 id jn 50 60 70

-0.0095 o 0 0095

Fig. 9. Contour plots of local Nusselt numbers in the tubes with RS-TT at different free space ratios (s): (a) s = 0.0, (b) s = 1.0, (c) s = 2.0 and (d) s = 3.0.

80 70 60 50

40 30 20 10

5000 6000 7000 8000 9000 10000 11000 12000 Re

(a) Nu

2.2 2.0 1.8

!* 1.6

1.4 1.2 1.0

5000 6000 7000 8000 9000 10000 11000 12000 Re

(b) Nu/Nup

Fig. 10. Relationship between Nusselts number and Reynolds number for the tube fitted with twisted tapes at various twist ratios (y) and free space ratios (s).

O Full-length twisted tape, y=6

O Full-length twisted tape, y=8

□ RS-TT,y=6,s= 1.0

□ tfS-rr, ^8,5=1.0 A RS-TT, y=6,s=2.0

A RS-TT, y=S,s=2.0 O

V RS-TT, y=6,s=3.0 o 2 Q

V RS-TT, j=8,5=3.0 Q O Q g

X Plain tube o e LJ n a A

° O W a $

o 8 s s i i! i i *

* X X X

O Full-length twisted tape, y=6

O Full-length twisted tape, y=8

□ RS-TT, y=6, 5=1.0

□ RS-TT, y=S, 5=1.0 A RS-TT, y=6, 5=2.0 A RS-TT, y=8, 5=2.0

V RS-TT, y=6, 5=3.0

V RS-TT, y=8,s=3.0

° ° o

eBeefl:u°ooo

2 g □ □ □ 0 8 9 e ^

o o o o

e e 0 e

□ A □ A □ A □ A

V V V V

V v ! t * * * 0 ♦ ♦

Full-length twisted tape, y=6 Full-length twisted tape, y=8 RS-TT, y=6,s= 1.0 RS-TT, y=8,s=1.0 RS-TT, y=6, 5=2.0 RS-TT, y=S, 5=2.0 RS-TT, y=6, 5=3.0 RS-TT, y=8,s=3.0 Plain tube

o o o o o o

9 0 9 9 9 9

Q a a a Q n

❖ $ 0 ❖ ❖ ❖

V V V V V V

X X X X X X

5000 6000 7000 8000 9000 10000 11000 12000 Re

7.0 6.5 6.0 5.5 5.0 4.5 4.0 3.5 3.0 2.5 2.0 1.5

O Full-length twisted tape, y=6 O Full-length twisted tape, y=8 RS-TT, y=6,s= 1.0 RS-TT, y=S, 5=1.0 RS-TT, y=6, 5=2.0 RS-TT, y= 8, 5=2.0 RS-TT, j=6, 5=3.0

RS-TT, yo o =8,; O r=3.0 o o o o o o o

0 B B 8 B B 8 B B B

0 0 0 E 0 0 0 0 0 0

V V V V V V V V V V

5000 6000 7000 8000 9000 10000 11000 12000

(b) ff

Fig. 11. Relationship between friction factor and Reynolds number for the tube fitted with twisted tapes at various twist ratios (y) and free space ratios (s).

.75 5000

Full-length twisted tape, y=6 Full-length twisted tape, y=8 RS-TT, y=6, 5=1.0 RS-TT, y=S,s= 1.0 RS-TT, y=6, 5=2.0 RS-TT, y= 8, 5=2.0 RS-TT, y=6,s=3.0 RS-TT, y=8, 5=3.0

6000 7000 8000 9000 10000 11000 12000

Fig. 12. Relationship between thermal performance factor and Reynolds number for the tube fitted with twisted tapes at various twist ratios (y) and free space ratios (V).

2 50 u

/ / / /

/ / ///

; +5% w

- -5%

20 30 40 50 60

Nu (Experimental)

Fig. 13. Predicted Nusselt number versus experimental Nusselt number of the tubes with twisted

tapes.

f (Experimental)

Fig. 14. Predicted friction factor versus experimental friction factor of the tubes with twisted

tapes.

r| (Experimental)

Fig. 15. Predicted thermal performance factor versus experimental thermal performance factor

of the tubes with twisted tapes.