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Effect of square wings in multiple square perforated twisted tapes on fluid flow and heat transfer of heat exchanger tube
Case Studies in Thermal Engineering 10 (2017) 28–43
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Effect of square wings in multiple square perforated twisted tapes on fluid flow and heat transfer of heat exchanger tube
MARK
⁎
Amar Raj Singh Suria, Anil Kumara, , Rajesh Maithanib a b
School of Mechanical and Civil Engineering, Shoolini University, Solan, Himachal Pradesh, India Department of Mechanical Engineering, DIT University, Dehradun, Uttarakhand, India
AR TI CLE I NF O
AB S T R A CT
Keywords: Energy Fluid flow Passive heat transfer Wing depth ratio
This work presents, an experimental study on Nusselt number (Nurs ) and friction factor ( frs ) of heat exchanger circular tube fitted with multiple square perforated with square wing twisted tape inserts. The experimental determination encompassed the geometrical parameters namely, wing depth ratio (Wd /WT) of 0.042–0.167, perforation width ratio (a/WT) of 0.250, twist ratio (TL /WT) of 2.5, and number of twisted tapes (NT ) of 4.0. The effect of multiple square perforated twisted tape with square wing has been investigated for the range of Reynolds number (Ren) varied from 5000 to 27,000. The maximum enhancement in Nurs and frs is observed to be 6.96 and 8.34 times of that of the plain circular tube, respectively. Correlations of Nurs , frs and ηp are established in term of Ren and geometrical parameters of wings twisted tape which can be used to predict the values of Nurs , frs and ηp with considerably good accuracy.
1. Introduction The heat exchanger (HE) is fundamental component of power and refrigeration cycles, which encourages the transfer of heat from one medium to another by virtue of temperature difference [1,2]. Industrial equipment utilizes heat exchanger to exchange or transfer heat energy from one medium of fluid to other at various temperatures [3,4]. Numerous technological process exchanges heat to cool one fluid and heat up the other, as in food and petrochemical industries, electronics and power production, airconditioning, refrigeration, and space uses [5–7]. An array of tubes encased in a casing for heating or cooling it down is the major aim of a heat exchanger. Heat exchanger parts like fans, condensers, coolants, extra tubes, alongside numerous elements assume a part in enhancing heating and cooling efficiency [8,9]. Twisted tapes are the metallic strips twisted with some suitable techniques at desired shape and dimension, inserted in the flow. The twisted tape inserts are popular and widely used in heat exchangers for heat transfer enhancement besides twisted tape inserts promote heat transfer rate with less friction factor penalty on pumping power. Insertion of twisted tapes in a tube provides a simple passive techniques for enhancing the convective heat transfer by introducing swirl into the bulk flow and disrupting the boundary layer at the tube surface due to repeated changes in the surface shape. This is to say such tapes induce turbulence and superimposed vortex motion which induces a thinner boundary layer and consequently results in a better heat transfer rate and higher local heat transfer due to the changes in the twisted tape shape. However, the pressure drop inside the tube will be increased by introducing the twisted tape to insert. Hence a lot of investigators have been carried out experimentally and numerically to investigate the optimal design and achieve the best thermal performance with less friction loss [10–13]. Noothong et al. [10] studied Nurs and frs description of a concentric double circular tube with single TT insertion with Twisted ⁎
Corresponding author. E-mail address: [email protected] (A. Kumar).
http://dx.doi.org/10.1016/j.csite.2017.03.002 Received 25 February 2017; Received in revised form 1 March 2017; Accepted 4 March 2017 Available online 08 March 2017 2214-157X/ © 2017 The Authors. Published by Elsevier Ltd. This is an open access article under the CC BY-NC-ND license (http://creativecommons.org/licenses/BY-NC-ND/4.0/).
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Nomenclature
a a / WT Ao Ap Cp Cd D frs fss H h k L ṁ Nurs Nuss (∆P )o (∆P )d ∆ P Pr Qu Ren
Tpm Tfm Ti To TL TL / WT V W , WT Wd Wd / WT y y /W PCR WPT HE TT PT
Perforated width (m) Perforation width ratio (dimensionless) Area of orifice plate (m2) Area of tube (m2) Specific heat (J/kg K) Coefficient of discharge (dimensionless) Hydraulic diameter of pipe (m) Friction factor twisted tape (dimensionless) Friction factor plain tube (dimensionless) Head difference (m) Heat transfer coefficient (W/m2 K) Thermal conductivity of air (W/m K) Tube length (m) Mass flow rate (kg/s) Nusselt number twisted tape tube (dimensionless) Nusselt number plain tube (dimensionless) Pressure drop across orifice plate (Pa) Pressure drop according to Darcy's equation (Pa) Pressure drop (Pa) Prandtl number (dimensionless) Useful heat transfer (W) Reynolds number (dimensionless)
Mean pipe temperature (K) Mean fluid temperature (K) Inlet temperature (K) Outlet temperature (K) Twist length (m) Twist ratio (dimensionless) Air flow velocity (m/s) Width of tape (m) Wing depth (m) Wing depth ratio (dimensionless) Pitch length of twisted tape (m) Pitch ratio (dimensionless) Perforated conical ring Winglet perforated tapes Heat exchanger Twisted tape Plain tube)
Greek symbols
ρ ηp θ
Density (kg/m3) Performance evaluation factor (dimensionless) Taper angle (degree)
ratios namely, y =5.0 and 7.0. TT induced the swirling stream inside the tube resultant in the augment in Nurs . The augmentation in Nurs by using Twist ratios, y =5.0 and 7.0 were 188.9% and 159.65%, respectively. Sarada et. al. [11] examined the Nurs and frs characteristics in a horizontal circular tube with/without TT inserts by varying their width and air as the working fluid for Ren varied from 7000 to 13,800. Eiamsa-ard et. al. [12] examined the impact of the TTs with centre wings in a tube. They inferred that improvement of Nurs and frs as comparison to smooth tube were maximum in the order of 2.89 and 3.12 times, respectively. Wongcharee and Eiamsa-ard [13] investigated TTs with alternate-axes and wings in a round tube. They reported that both Nurs and frs increments with the utilization of all TT in contrast with those TT. Krishna et. al. [14] explored straight HE half left-ring HE embedded in a laminar stream locale experimentally in a circular tube. It is noted that heat transfer increments by diminishing spacer slots and accomplishes the maximum heat transfer for spacer gap of 2.0 in. Wongcharee and Eiamsa-ard [15] used alternate clockwise and counter clockwise twisted-tapes in a circular tube to decide Nurs and frs and thermal hydraulic characteristics. It was reported that clockwise and anticlockwise Twisted-tapes yields a maximum augmentation of Nurs and frs in order of 2.980 and 3.160 times the smooth tube. Murugesan et al. [16] experimentally explored and revealed Nurs and frs and demonstrated a huge augmentation for a circular tube fixed with full length TT with trapezoidal-cut. Seemawute et al. [17] found that in a HE tube fitted with the PTA, PT and TT demonstrated a huge improvement in the Nurs namely 184%, 102% and 57% of that of the PT. Murugesan et. al. [18] examined the V-cut TT and reported that the mean Nurs and frs increment with reducing Twist and width ratios and increases with increasing depth ratios (DR ). Ibrahim [19] experimentally determined Nurs and frs performance of horizontal double pipes of flat tubes having full-length helical screw. The parameters considered were different Twist ratio and different spacer length. Thianpong et al. [20] experimentally explored and inferred that Nurs and frs are higher for dimpled tube fitted with the TT, than the dimple tube alone and PT. A decrease in PR and y / w yields to a higher Nurs and frs . Saha [21] researched Nurs and frs of a rectangular and HE tube with a mix of internal axial corrugations on surfaces of duct and insert in the form of Twisted-tape with and without oblique teeth. The axial corrugations combined with twisted-tapes of all types with oblique teeth performs superior to no oblique teeth combined with axial corrugations. Chiu and Jang [22] examined the longitudinal strip inserts (without hole) and detailed that Nurs and frs were 7.0–16% and 100– 170% higher than the PTs. Nurs and the pressure drop was 13–28% and 140–220%, respectively. Guo et al. [23] numerically analyzed the tubes with short width TTs and reported that Nurs and frs diminish by cutting off the tape edge. Whereas, tubes with centre-cleared TTs, the heat transfer is increased for a appropriate central clearance ratio. Garcia et al. [24] utilized the helical-wire-coils inside a round tube to decide the thermo-hydraulic behaviour in laminar, transition and turbulent stream. Water and water–propylene glycol blends was utilized at various temperatures and the outcomes demonstrates that in turbulent locale wire coils increase friction factor and heat transfer up 9.0 and 4.0 times in contrast to the smooth tube. Promvonge [25] experimentally found the effect of wire coils with TTs as an insert in a circular tube on Nurs and frs . It was reported that combination of wire coils with TTs increases Nurs to folds as compared to wire coil/TT alone. Gunes et al.[26] investigated the heat transfer and pressure drop for a coiled wire insert in a turbulent flow regime. It was observed that Nurs increases with the increase of Ren and wire thickness and decrease in pitch ratio. At a / D =0.0892 and P / D =1 at Re 29
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Table 1 Previous experimental determined on different TT inserts.
(continued on next page)
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Table 1 (continued)
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of 3858 maximum overall enhancement efficiency of 36.5% was achieved. Anvari et al. [27] reported an augmented Nurs for DR (diverging conical ring) arrangement as 521%, and for the converging conical ring arrangement as 355% for conical ring inserts. But the use of this inserts cause a considerable enhancement in frs . Eiamsa-ard et al. [28] concluded that the frs , Nurs and thermal performance factor of the CRT combined with TT are considerably more than those of CRT alone. The increases of Nurs , frs and thermal performance for CRT combined with TT are 25.8%, 82.8% and 6.3% as compared to tube with the CRT alone. For the CRT with l / D =1.0 and TT with y / W =3 the maximum thermal performance factor was found to be 1.42. Singh et al. [29] examined a roughened tube with incorporated SRT and TT for constant heat supply. For the integrated SRT and TT the Nurs , frs and thermal performance factor were found in the range of 107–293, 0.93–0.99 and 1.46–1.61, respectively. The maximum thermal performance factor was found to be 1.61 as compared to a smooth tube for the integrated roughness of the SRT with l / D =1.0 and y / W =2. Enbin Tu et al. [30] numerically investigated and concluded that a tube having pipe inserts, the Nusselt number decreases by increasing spacer length and the friction factor increases with decrease in the spacer length. The maximal PEC values resulted by four pipes inserts were approximately 1.4–3.0. Vashistha et al. [31] examined and reported the effect of multiple inserts oriented in co-swirl and counter-swirl position causes augment the heat transfer having twist ratio of 2.5. The enhancement of Nurs and frs were found to be 2.42 and 6.96 folds the smooth tube, and the thermo-hydraulic performance factor was found to be 1.26. Eiamsa-ard et al. [32] reported the benefits by the use of D − HTTs and T − HTTs that enhances the Nusselt number by 15.6– 17.6% and 19.5–23.4%, respectively and increase in friction factor by 83–206% and 143–335%, respectively. The thermal performance factor decrease by 3.9–20.3% and 8.3–26.2% as compared to those of S − HTT . Tamna et al. [33] investigated double twisted tapes with 30° V-shaped ribs to determine the heat transfer and friction factor. The V-ribbed twisted tape with BR=0.19 produces the maximum Nurs and frs . The thermal enhancement factor was found to maximum about 1.4 at BR=0.09 for the V-ribbed twisted tape and around 1.09 for the twisted tape with no rib. Hasanpour et al. [34] experimental studied Nurs and frs of perforated, V-cut and U-cut types twisted tapes in a double pipe heat exchanger. Results revealed that the use of twisted tape enhances the Nurs and frs for all cases as compared to a plane tube. Piriyarungrod et al. [35] investigated tapered twisted tapes insert at different taper angles (θ ) ranging from 0°–0.9° and different y / W values from 3.5 to 4.5. It was reported that the Nurs and frs increased by decreasing taper angle and y / W . The maximum thermal performance factor of 1.05 was found for the tape with taper angle (θ ) of 0.9° and twist ratio (y / W ) of 3.5 at Re of 6000. Table 1 shows previous experimental investigations on various twisted tape inserts. According to the above literature, it is evident that TTs possess great potentials as the heat transfer enhancing devices. Although the use of TT along with other enhancing technique gives attractive results, the use of only TT with a proper design offers comparable results. In the current work, the new design of multiple TT inserts is used as heat transfer augmentation devices. It is assumed that, the square wing part at the edge of the perforated TT can enhance degree of turbulence near wall tube and thus raise heat transfer rate. The experiments are performed using the tape with different wind depth ratio with a stream parameter range 5000–27,000, where air is used as the working fluid.
Fig. 1. Schematic of experimental setup.
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A.R. Singh Suri et al.
2. Experimental program A HE tube with multiple square perforated TT with square wing inserts is experimentally investigated to determine the Nurs and frs . The experimental setup has been fabricated as per the literature survey and validated with the data for PT of HE. The validation of experimental setup was followed by the wide experimentations on multiple square perforated TT with square wing inserts HE tube to yield the raw data of heated wall temperatures, fluid stream, and inflow and outflow temperature of air and pressure drop across the test section beneath stable conditions. 2.1. Details of experimental setup The multiple square perforated TT with square wing inserts of the HE tube has been investigated experimentally. The schematic diagram and photographic view of experimental setup is shown in Fig. 1. The tube is made of GI Pipe of 68 mm outer diameter and 65 mm outer diameter and is subdivided into different sections; entry section, test section and exit section with dimensions as 2.5 m, 1.4 m and 1.5 m, respectively. The hydro dynamically fully developed stream is ensured before entering the test section. The HE pipe is attached to the suction end of a 3 HP, 3 phase blower. A stable heat flux of 1000 W/m2 is provided to the test section with the help of Nicrome wire heater. Glasswool fiber tap and insulating pads were provided for reducing the heat loss. Total sixteen T-type (copper-nickel constant) thermocouples were used for measuring the temperature reading with the help of data logger 12.0 thermocouples were placed on tube wall, 1.0 at inlet and 3.0 at the outlet. 3. Range of parameters The multiple square perforated TTist inserts parameters are determined by perforated width (a ), width of tape (WT ), wing depth (Wd ) and twist length (TL ). These parameters have been expressed in the form of dimensionless roughness parameters, viz., perforation width ratio (a / WT ), twist ratio (TL / WT ) and wing depth ratio (Wd / WT ). The data of stream and roughness parameters for this determined are listed in Table 2. The schematic and photographic view of the square perforated TT with wing inserts used in the present determined is shown in Fig. 2(A) & (B). 4. Data reduction Under the steady state conditions and for given heat flux and mass stream rate of air the experimental data for HE was recorded. The heat transfer rate and friction factor in the tube was computed. The data reduction of the data was done as follows: The average tube temperature is the average of all temperatures recorded by thermocouples on the surface of tube test section.
Tpm =
TP 4 + TP5+…+TP16 13
(1)
The mean air film temperature, Tfm is an arithmetic mean of the inlet and the exit temperature of air streaming through the test section.
Tfm =
Ti + To 2
(2)
where
To =
TA1 + TA2 + TA3 3
The pressure drop measurement across the calibrated orifice meter is used to determine mass stream rate of air by using the following formula: ⎡ 2. ρ. (∆P) ⎤0.5 O ⎥ ṁ = Cd . A o. ⎢ ⎣ 1 − β4 ⎦
(3)
where (∆P )o = 9.81⋅(∆h )o ⋅ρm ⋅sinθ Using the value of mass stream rate the velocity of air is calculated from the given expression: Table 2 Range of parameters. Sr. No.
Parameters
Range
1. 2. 3. 4. 5.
Wing depth ratio (Wd /WT ) Perforation width ratio (a /WT ) Twist ratio (TL /WT ) Number of twisted tape (NT ) Reynolds number (Ren )
0.042–0167 0.250 2.5 4.0 5000–27,000
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A.R. Singh Suri et al.
Fig. 2. (A) Discuss square perforated TT with wing inserts HE tube parameters (B) Photographic view of different TT inserts.
V=
ṁ ρ⋅W⋅H
(4)
4.1. Reynolds number (Ren) The Reynolds number of air stream in the duct is calculated from:
Ren =
V⋅D. ρ μ
(5)
The friction factor is evaluated from the values of pressure drop (ΔP)d across the test section length using Darcy equation as:
f=
2⋅(∆P)d ⋅D 4⋅ρ⋅L⋅V2
(6)
where (ΔP)d=9.81×(Δh)d×ρm The heat transfer coefficient of the test section is calculated using the following equation:
h=
Qu A p⋅(Tpm − Tfm)
(7)
The Nusselt number is determined from the heat transfer coefficient using the following equation:
Nu =
h⋅D k
(8)
Considering the thermal and the hydraulic performance of a multiple square perforated TT inserts tube simultaneously and comparing it to a PT as:
ηp =
[Nurs / Nuss] [frs / fss ]1/3
(9)
5. Uncertainties analysis An uncertainty analysis has been carried to estimate the errors involved in experimental data measurement. The uncertainty is estimated based on errors associated with measuring instruments Klein and McClintock [36]. The uncertainties of the Nurs and frs are evaluated as follows: Mass flow rate:
⎡ 2ρ (∆P )o ⎤ ṁ = CdAo ⎢ o 4 ⎥ ⎣ 1−β ⎦
(10) 34
Case Studies in Thermal Engineering 10 (2017) 28–43
A.R. Singh Suri et al. 0.5 2 ⎡⎛ ⎛ 0.5δρ ⎞2 ⎛ δA ⎞2 ⎛ δ (∆P ) ⎞2 ⎤ δC ⎞ δṁ o o ⎥ ⎟⎟ + ⎜ o ⎟ + ⎜ = ⎢⎜ d ⎟ + ⎜⎜ ⎟ ⎢⎝ C ⎠ ṁ ⎝ Ao ⎠ ⎝ (∆P )o ⎠ ⎥⎦ ⎝ ρo ⎠ ⎣ d
(11)
0.5 δṁ = [(6.25 × 10−4) + (4.449 × 10−6) + (3.26 × 10−5) + (5.102 × 10−7)] ṁ
(12)
ṁ = 0.0257
(13)
Hence, uncertainty in mass flow rate measurement is 2.57%. Heat gain:
Qu = mC ̇ p(To − Ti ) = mC ̇ p∆T 2 ⎡ ⎛ δ (ΔT ) ⎞2 ⎤⎥ ⎛ δṁ ⎞2 ⎛ δCp ⎞ δQu ⎟⎟ + ⎜ = ⎢⎢⎜ ⎟ + ⎜⎜ ⎟ ⎝m⎠ Qu ⎝ (ΔT ) ⎠ ⎥⎦ ⎝ Cp ⎠ ⎣ ̇
(14) 0.5
(15)
0.5 2 ⎡ ⎛ δ (ΔT ) ⎞2 ⎤⎥ ⎛ δṁ ⎞2 ⎛ δCp ⎞ δQu ⎟⎟ + ⎜ = ⎢⎢⎜ ⎟ + ⎜⎜ ⎟⎥ ⎝m⎠ Qu ⎝ (ΔT ) ⎠ ⎦ ⎝ Cp ⎠ ⎣ ̇
(16)
δQu 0.5 = [(6.7081 × 10−4) + (9.9007 × 10−9) + (1.13 × 10−4)] Qu
(17)
δQu = 0.0277 Qu
(18)
Hence, uncertainty in heat gain is 2.77%. Heat transfer coefficient:
h=
Qu Qu = Ap (Tpm − Tfm ) Ap (∆Tfm )
(19)
0.5 ⎡⎛ 2 ⎛ δAp ⎞2 ⎛ δ (ΔTfm ) ⎞2 ⎤ δQ ⎞ δh ⎟⎟ ⎥ ⎟⎟ + ⎜⎜ = ⎢⎢⎜ u ⎟ + ⎜⎜ h Q ⎝ Ap ⎠ ⎝ (ΔTfm ) ⎠ ⎥⎦ ⎣⎝ u ⎠
(20)
0.5 δh = [(7.784 × 10−4) + (2.166 × 10−6) + (2.764 × 10−5)] h
(21)
δh = 0.284 h
(22)
Hence, uncertainty in heat transfer coefficient is 2.84%. Reynolds number:
Ren =
ρVD μ
⎡⎛ ⎞ 2 ⎛ ⎞ 2 ⎛ ⎞ 2 ⎛ ⎞ 2 ⎤ δRen δρ δμ δV δD = ⎢⎜ ⎟ + ⎜ ⎟ + ⎜ ⎟ + ⎜ ⎟ ⎥ ⎢⎣⎝ ρ ⎠ ⎝D⎠ ⎝V ⎠ Ren ⎝ μ ⎠ ⎥⎦
(23) 0.5
(24)
δRen 0.5 = [(6.66 × 10−7) + (1.5129 × 10−4) + (8.76 × 10−7) + (2.543 × 10−7)] Ren
(25)
δRen = 0.01237 Ren
(26)
Hence, uncertainty Reynolds Number is 1.23%. Nusselt number:
Nurs =
hD K
(27)
⎡⎛ ⎞2 ⎛ ⎞2 ⎛ ⎞2 ⎤0.5 δNurs δh δD δK = ⎢⎜ ⎟ + ⎜ ⎟ + ⎜ ⎟ ⎥ ⎝ K ⎠ ⎥⎦ ⎝D⎠ Nurs ⎣⎢⎝ h ⎠
(28) 35
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A.R. Singh Suri et al.
δNurs 2 0.5 = [(0.0284)2 + (0.000936)2 + (4.16×10−4) ] Nurs
(29)
δNurs = 0.02841 Nurs
(30)
Hence, uncertainty Nusselt Number is 2.84%. Friction factor:
frs =
δfrs frs δfrs frs
δfrs frs
2(∆p ) D d
4ρLV 2
(31)
2 ⎤0.5 ⎡ 2 2 ⎛ δρ ⎞2 ⎛ δD ⎞ ⎛ δL ⎞2 ⎛ δ (∆p )d ⎞ ⎥ ⎢⎛ δV ⎞ ⎜ ⎟ = ⎢⎜ ⎟ + ⎜ ⎟ + ⎜ ⎟ + ⎜ ⎟ + ⎜ ⎟⎥ ⎝L⎠ ⎝D⎠ ⎠ ⎝ ρ⎠ ⎝ (∆p )d ⎠ ⎥⎦ ⎢⎣⎝ V
(32)
0.5 2 ⎡⎛ ⎛ 0.1 ⎞2 ⎛ 0.01 ⎞2 ⎤ ⎛ 0.001 ⎞2 0.1 ⎞ = ⎢⎜ ⎟⎥ ⎟⎜ ⎟ + (0.000936)2 + ⎜ ⎟ +⎜ ⎢⎣⎝ 8.13 ⎠ ⎝ 1400 ⎠ ⎝ 1.94 ⎠ ⎥⎦ ⎝ 1.225 ⎠
(33)
= 0.01339 (34)
Hence, uncertainty friction factor is 1.33%. As the uncertainty calculation was done on a single test run, the uncertainty examination for whole test run for single TT was carried out and results are presented in Table 3 for the experimental data. 6. Validation of experimental results Experimental outcomes for PT were validated with empirical correlations of Gnielinski and Dittus-Boelter equation for Nuss and Petukhov correlation and Blasius equation for fss respectively. These correlations beside with their valid ranges are presented in Eqs. (35)–(38) below: The Nuss and fss for a PT is given by the Gnielinski (Eq. (35)) and modified Petukhov (Eq. (36)) are as:
Nuss =
(f /8)(Ren − 1000)Pr 1 + 12.7(fss /8)1/2(Pr 2/3 − 1)
for
3000 < Ren < 10,000
(35)
fss = (0.079lnRen − 1.64)−2
(36)
The Nuss and fss for a smooth channel is given by the Dittus-Boelter equation (Eq. (37)) and modified Blasius equation (Eq. (38)) are as:
Nuss = 0.023Ren 0.8Pr0.4forRen > 10,000
(37)
fss = 0.085Ren−0.25
(38)
The comparison of the experimental and estimated values of the Nuss and fss as a function of the Ren is shown in Fig. 3(A) & (B), respectively. A reasonably good agreement between the three sets of values ensures the accuracy of the data collected using this experimental setup. 7. Results and discussion The heat transfer and friction characteristics of HE tube with multiple (4 tapes) square perforated TT with square wing inserts HE tube have been determined by using the experimental data collected for different sets of geometrical parameters. A comparative Table 3 Range of uncertainty in the measurement of essential parameters. S. No.
Parameters
Error range (%)
1 2 3 4 5 6
Mass flow rate Heat gain Heat transfer coefficient Reynolds Number Nusselt number Friction Factor
2.57 2.77 2.84 1.23 2.84 1.33
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Fig. 3. Comparison of present experimental results with previous correlations for (A) Nuss and (B) fss .
determined of the multiple square perforated TT with square wing inserts is done with the multiple plain TT, multiple TT with square perforation and PT. The outcome of the extensive experimentation is discussed below: Fig. 4(A) & (B) shows the effect of Ren on Nurs and frs for multiple square perforated TT with square wing inserts, multiple (without square wings) twisted square perforated tape inserts, simple multiple TT inserts and that for PT. The values of Nurs are found to rise with rises Ren in all cases as expected. The multiple square perforated TT with square wing inserts tube can be seen to yield higher Nurs and frs as compared to that of the multiple (without square wings) twisted square perforated tape inserts, simple multiple TT inserts and that for PT (smooth surface). Creating square wings in the multiple TT produces higher heat transfer rate due to the higher potential turbulence streams induced by wings near the tube wall. This higher potential turbulence stream exerts a measurable effect in disturbing the axial stream profile which rise the Nurs and frs . In order to determine the improvement of the Nurs achieved as an results of providing a square wings in the multiple square perforated TT inserts tube arrangement, the values of the Nurs for fixed values of the a / WT of 0.250 and TL / WT of 2.5, and different values of Wd / WT is given in Fig. 5(A). The variation of Nurs with Ren for the multiple square perforated with square wing TT inserts, multiple square perforated TT inserts, without square perforated multiple TT inserts and smooth surface tube are shown in Fig. 5(A). Apparently, Nurs increases as Ren the use of multiple TT inserts tube leads to considerable increase of Nurs as compared to that smooth tube. This can be explained that the thermal boundary becomes thicker as Ren decreases thus the effect of boundary destruction by multiple inserts turns out to be more prominent. The Nurs increases with increase in Wd / WT from 0.042 to 0.167, attains maximum Nurs at, Wd / WT of 0.167. Fig. 5(B) shows the data of the Nurs as a function of Wd / WT for a fixed value of a / WT of 0.250 and TL / WT of 2.5 at different selected values of Ren . It can be observed that Nurs is the maximum for Wd / WT =0.167 for all data of Ren . Fig. 6(A) shows that the effect of Wd / WT on the Nurs / Nuss for a fixed values of a / WT of 0.250 and TL / WT of 2.5 respectively. It can be seen that Nurs / Nuss increase with an increase in Wd / WT from 0.042 to 0.167, attains a maxima at Wd / WT of 0.167. Fig. 6(B) shows the values of Nurs / Nuss as function of Wd / WT for the selected Ren values where a maxima in the values corresponding to a Wd / WT of 0.167 for all Ren . The secondary stream jets and swirl stream exerts a significant influence on the axial stream profile, which increases significant influence on the axial stream profile, which increases the frs in tubes. The effect of the Wd / WT on frs with Ren is shown in Fig. 7 (A). It is observed that the value of frs decreases with increasing Ren and moves towards a constant value as expected. The frs increases with
Fig. 4. (A) Variation of Nurs with Ren (B) Variation of frs with Ren .
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Fig. 5. (A) Variation of Nurs with Ren for different values of Wd /WT (B) Variation of Nurs with Wd /WT for different values of Ren .
increase the values of Wd / WT and observed maximum value of 0.167. The variation of frs with Wd / WT is shown in Fig. 7 (B) for selected Ren values. The maximum value of frs is obtained for Wd / WT of 0.167 and minimum for the Wd / WT of 0.042. Fig. 8(A) shows that the effect of Wd / WT on the frs / fss for a fixed values of a / WT of 0.250 and TL / WT of 2.5 respectively. It can be seen that frs / fss increase with an increase in Wd / WT from 0.042 to 0.167, attains a maxima at Wd / WT of 0.167. Fig. 8(B) shows the values of frs / fss as function of Wd / WT for the selected Ren values where a maxima in the values corresponding to a Wd / WT of 0.167 for all Ren . The variation of Nurs and frs as a function of Ren for different values of Wd / WT . It can be observed that in the Figs. 5–8 the Nurs increses with the increse of Ren , whereas the frs decreases with the increse of Ren . It can be observed from these Figures that the augmentation in heat transfer of the multiple square perforated with square wing TT inserts tube with respect PT also increases with an increase in Ren whereas augmentation in frs of the multiple square perforated with square wing TT inserts tube. Also, shows that the Nurs and frs increses with increasing values of wing depth ratio. TT inserts on the heat transfer surface in the form multiple square perforated with wing creates local wall turbulence as breaks the laminar sub layer due to swirl stream separation and reattachment between the TT, which reduces thermal resistance and greatly rise the Nurs and frs . A parameter known as thermal hydraulic performance ηp is used to evaluate the effectiveness of TT inserts tube accounting for the augmentation of Nurs and frs and is expressed as [Nuss / Nurs /(fss / frs ]0.33 [37–40]. The values of this parameter for the multiple square perforated with square wing inserts, multiple square perforated TT inserts as well as without square perforated multiple TT inserts are investigated in this work and have been plotted in Fig. 9. Fig. 9(A) shows the effect of Wd / WT on thermal hydraulic performance where it can be observed that the value of this parameter is seen to increase with increase Wd / WT upto about 0.167. The Wd / WT , varied from 0.042 to 0.167 and Ren varies from 5000 to 27,000. The results observed by experimental that the thermal hydraulic performance parameter was strongly dependent on the Wd / WT . Fig. 9(B) shows the values of thermal hydraulic performance as function of Wd / WT for the selected Ren where a maxima in the values corresponding to a Wd / WT of 0.167 for all values of Ren . A maximum value of thermal hydraulic performance parameter was found to be 4.1 for the range of parameters investigated. The values of thermal hydraulic performance parameter determined for the shape of multiple square perforated with wings twisted tape inserts have been compared with the values determined for other twisted tape inserts. It can be observed that from Table 4 multiple square perforated with wings twisted tape shape results in highest thermal hydraulic performance as compared other perforated and multiple twisted tape inserts heat exchanger tubes.
Fig. 6. (A) Variation of Nurs /Nuss with Ren for different values of Wd /WT (B) Variation of Nurs /Nuss with Wd /WT for different values of Ren .
38
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Fig. 7. (A) Variation of frs with Ren for different values of Wd /WT (B) Variation of frs with Wd /WT for different values of Ren .
Fig. 8. (A) Variation of frs /fss with Ren for different values of Wd /WT (B) Variation of frs /fss with Wd /WT for different values of Ren .
Fig. 9. (A) Variation of ηp with Ren for different values of Wd /WT (B) Variation of ηp with Wd /WT for different values of Ren .
8. Correlation development As discussed earlier that the Nurs and frs are strong functions of stream and TT parameters namely Ren and Wd / WT . The functional relationships for Nurs and frs can therefore be written as;
Nurs = fn (Ren , Wd / WT )
(39) 39
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Table 4 Overall thermal performance parameters compared with previous investigations. Investigator
Shape
Overall thermal performance
Noothong et al. [10] Sarada et al. [11] Eiamsa et al. [12] Wongcharee and Eiamsa ard [13] Krishna et al. [14] Wongcharee and Eiamsa-ard [15] Murugesan et al. [18] Sivashanmugam and Nagarajan [39] Present study
Twisted tape inserts Twisted tape inserts Twisted tape with centre wing Alternate clockwise and counter clock wise twisted tape inserts Straight half twisted left right inserts Rectangular and trapezoidal wings V-cut twisted tape Helical screw tape inserts Multiple square perforated with square wings twisted tape
2.14 1.43 2.04 5.13 1.56 1.92 1.64 2.98 4.1
Fig. 10. (A) Variation of ln(Nurs ) with ln(Ren ) (B) Variation of ln(Ao) with ln (Wd /WT ) for Nurs (C) Variation of ln(Ao) with ln (Wd /WT ) for frs (D) Variation of ln(Ao) with
ln (Wd /WT ) for ηp .
frs = fn (Ren , Wd / WT )
(40)
ηp = fn (Ren , Wd / WT )
(41)
Experimental results collected, processed and discussed in detail of terms of variation of Nurs , frs and ηp as a function of system and operating parameters in the previous section has been used to develop these relationships in the form of correlations. In order to determine the functional relationships between Nurs and Ren , the well known power law relationship between these parameters for turbulent heat transfer has been utilized, consequently.
Nurs = AO (Ren )n
(42)
Above functional relationships between Nurs and Ren can be expressed as;
ln(Nurs ) = nln(Ren ) + A1
(43)
where A1=lnAO 40
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Fig. 11. Comparison of experimental and predicted values for (A) Nurs (B) frs (C) ηp .
Fig. 10(A) shows a linear relationship between Nurs and Ren for the given range. The regression analysis gave a relation in terms of a straight line equation and is represented as,
Nurs = Ao (Ren )0.7498
(44)
The determined was carried out for different values of Wd / WT , thus the coefficient of Ao also depends on Wd / WT . The influence of geometrical parameter, Wd / WT on coefficient of Ao is plotted a graph between ln(Nurs /Ren 0.749) and ln (Wd / WT ) as shown in Fig. 10(B). Using the second order regression following correlation is obtained,
⎛ W ⎞0.4321 Exp(0.0633(ln (Wd /WT )2) Nurs = 0.345 × Ren 0.7498⎜ d ⎟ ⎝ WT ⎠
(45)
Similarly the correlation of frs and ηp were developed following the same procedure for a range of Wd / WT . The developed correlation for frs and ηp are shown in Fig. 10(C) & (D), respectively and the correlations are given as:
⎛ W ⎞0.5634 frs = 6.95 × Ren−0.2427⎜ d ⎟ Exp(0.08(ln (Wd /WT )2) ⎝ WT ⎠
(46)
⎛W ⎞ ηp = 16.3 × Ren−0.1007⎜ d ⎟ ⎝ WT ⎠
(47)
0.6506
Exp(0.1133(ln (Wd /WT )2 )
The comparison of experimental values with predicted values of Nurs , frs and ηp obtained from the respective correlations is done in order to find out the deviation in the values. It is seen that the values of correlations of Nurs , frs and ηp lie within ± 5.5%, ± 4.0% and ± 6.0%, respectively of experimentally determined values. The deviation in the predicted and the experimental values of Nurs , frs and ηp are shown in Fig. 11(A-C). 9. Conclusions Based on the present experimental determined on multiple square perforated with square wing TT inserts tube, the following conclusions can be drawn from present determined: 41
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1. Multiple square perforated with square wing TT inserts has been found to higher overall thermal performance as compared without wing multiple square perforated TT heat exchanger tube with similar operating conditions. 2. As compared to the PT, the multiple square perforated with square wings TT inserts tube yields an increase of about 6.96 and 8.34 times in the Nurs and frs , respectively, for the range of parameters investigated. 3. The maximum value of Nurs , frs and ηp occurs for multiple square perforated with square wing TT inert tube with Wd /WT of 0.167. 4. The results observed by experimental that the thermal hydraulic was strongly dependent on the Wd /WT . A maximum value of thermal hydraulic performance parameter was found to be 3.08 for the range of parameters investigated. 5. Correlations have been developed for Nurs , frs and ηp as function of TT parameter and stream parameters. The deviation between predicted and experimental value for Nurs , frs and ηp are of the order ± 5.5%, ± 4.0% and 6.0% respectively. References [1] S. Kumar, A.D. Kothiyal, M.S.H. Bisht, A. Kumar, Numerical analysis of thermal hydraulic performance Al2O3-H2O nanofluid flowing through a protrusion obstacles square mini channel, Case Stud. Therm. Eng. 9 (2017) 108–121. [2] R. Kumar, A. Kumar, R. Chauhan, M. Sethi, Heat transfer enhancement in solar air channel with broken multiple V-type baffle, Case Stud. Therm. Eng. 8 (2016) 187–197. [3] R. Kumar, V. Pedgopu, A. Kumar, R. Thakur, A. Pundir, CFD based analysis heat transfer and friction characteristics of broken multiple rib roughened solar air heater duct, Int. J. Mech. Prod. Eng. Res. Dev. 3 (2013) 165–172. [4] R. Thakur, A.R.S. Suri, S. Kumar, A. Kumar, A review of integrated renewable energy system in power generation, Int. J. Mech. Prod. Eng. Res. Dev. 3 (2013) 79–88. [5] A. Kumar, M.H. Kim, Numerical study on overall thermal performance in SAH duct with compound roughness of V-shaped ribs and dimples, J. Korean Sol. Energy Soc. 35 (2015) 43–55. [6] A. Kumar, M.H. Kim, Mathematical simulation on thermal performance of packed bed solar energy storage system, Trans. Korean Hydrog. New Energy Soc. 26 (2015) 331–338. [7] A. Kumar, R.P. Saini, J.S. Saini, Effect of roughness width ratio in discrete multi V-shaped rib roughness on thermo-hydraulic performance of solar air heater, Heat Mass Transf. 51 (2015) 209–220. [8] A. Kumar, M.H. Kim, Heat transfer and fluid flow characteristics in air duct with various V-pattern rib roughness on heated plate: a comparative study, Energy 3 (2016) 75–85. [9] A. Kumar, Analysis of heat transfer and fluid flow in different shaped roughness elements on the absorber plate solar air heater duct, Energy Procedia 57 (2014) 2102–2111. [10] W. Noothong, S. Eiamsa-ard, P. Promvonge, Effect of twisted-tape inserts on heat transfer in a tube. in: Proceedings of the 2nd Joint International Conference on Sustainable Energy and Environment (SEE 2006), Bangkok, Thailand, 21–23 November 2006, pp. 1–5. [11] S.N. Sarada, A.V.S.R. Raju, K.K. Radha, L.S. Sunder, Enhancement of heat transfer using varying width twisted tape inserts, Int. J. Eng. Sci. Technol. 2 (2010) 107–118. [12] S. Eiamsa-ard, K. Wongcharee, P. Eiamsa-ard, C. Thianpong, Thermohydraulic investigation of turbulent flow through a round tube equipped with twisted tapes consisting of centre wings and alternate-axes, Exp. Therm. Fluid Sci. 34 (2010) 1151–1161. [13] K. Wongcharee, S. Eiamsa-ard, Friction and heat transfer characteristics of laminar swirl flow through the round tubes inserted with alternate clockwise and counter-clockwise twisted-tapes, Int. Commun. Heat Mass Transf. 38 (2011) 348–352. [14] S.R. Krishna, G. Pathipaka, P. Sivashanmugam, Studies on heat transfer augmentation in a circular tube fitted with straight half twist left-right inserts in laminar flow, J. Environ. Res. Dev. 3 (2008) 437–441. [15] K. Wongcharee, S. Eiamsa-ard, Heat transfer enhancement by twisted tapes with alternate-axes and triangular, rectangular and trapezoidal wings, Chem. Eng. Process. Process Intensif. 50 (2011) 211–219. [16] P. Murugesan, K. Mayilsamy, S. Suresh, P. Srinivasan P, Heat transfer and pressure drop characteristics of turbulent flow in a tube fitted with trapezoidal-cut twisted tape insert, Int. J. Acad. Res. 1 (2009) 123–127. [17] P. Seemawute, S. Eiamsa-ard, Thermohydraulics of turbulent flow through a round tube by a peripherally-cut twisted tape with an alternate axis, Int. Commun. Heat Mass Transf. 37 (2010) 652–659. [18] P. Murugesan, K. Mayilsamy, S. Suresh, P.S.S. Srinivasan, Heat transfer and pressure drop characteristics in a circular tube fitted with and without V-cut twisted tape insert, Int. Commun. Heat Mass Transf. 38 (2011) 329–334. [19] E.Z. Ibrahim, Augmentation of laminar flow and heat transfer in flat tubes by means of helical screw-tape inserts, Energy Convers. Manag. 52 (2011) 250–257. [20] C. Thianpong, P. Eiamsa-ard, K. Wongcharee, S. Eiamsa-ard S, Compound heat transfer enhancement of a dimpled tube with a twisted tape swirl generator, Int. Commun. Heat Mass Transf. 36 (2009) 698–704. [21] S.K. Saha, Thermohydraulics of turbulent flow through rectangular and square ducts with axial corrugation roughness and twisted-tapes with and without oblique teeth, Exp. Therm. Fluid Sci. 34 (2010) 744–752. [22] Y.W. Chiu, J.Y. Jang, 3D numerical and experimental analysis for thermal-hydraulic characteristics of air flow inside a circular tube with different tube inserts, Appl. Therm. Eng. 29 (2009) 250–258. [23] J. Guo, A. Fan, X. Zhang, W. Liu, A numerical study on heat transfer and friction factor characteristics of laminar flow in a circular tube fitted with centre-cleared twisted tape, Int. J. Therm. Sci. 50 (2011) 1263–1270. [24] A. Garcia, P.G. Vicente, A. Viedma, Experimental study of heat transfer enhancement with wire coil inserts in laminar-transition-turbulent regimes at different Prandtl numbers, Int. J. Heat Mass Transf. 48 (2005) 4640–4651. [25] P. Promvonge, Thermal augmentation in circular tube with twisted tape and wire coil turbulators, Energy Convers. Manag. 49 (2008) 2949–2955. [26] S. Gunes, V. Ozceyhan, O. Buyukalaca, Heat transfer enhancement in a tube with equilateral triangle cross sectioned coiled wire inserts, Exp. Therm. Fluid Sci. 34 (2010) 684–691. [27] A.R. Anvari, R. Lotfi, A.M. Rashidi, S. Sattari, Experimental research on heat transfer of water in tubes with conical ring inserts in transient regime, Int. Commun. Heat Mass Transf. 38 (2011) 668–671. [28] S. Eiamsa-Ard, V. Kongkaitpaiboon, K. Nanan, Thermohydraulics of turbulent flow through heat exchanger tubes fitted with circular-rings and twisted tapes, Chin. J. Chem. Eng. 21 (2013) 585–593. [29] V. Singh, S. Chamoli, M. Kumar, A. Kumar, Heat transfer and fluid flow characteristics of heat exchanger tube with multiple twisted tapes and solid rings inserts, Chem. Eng. Process. Process Intensif. 102 (2016) 156–168. [30] T. Enbin, Y. Wang, Y. Tang, A numerical study on thermalhydraulic characteristics of turbulent flow through a circular tube fitted with pipe inserts, Appl. Therm. Eng. (2016). [31] C. Vashistha, A.K. Patil, M. Kumar, Experimental investigation of heat transfer and pressure drop in a circular tube with multiple inserts, Appl. Therm. Eng. 96 (2016) 117–129. [32] S. Eiamsa-Ard, K. Nanan, K. Wongcharee, K. Yongsiri, C. Thianpong, Thermohydraulic performance of heat exchanger tube equipped with single-, double-, and triple-helical twisted tapes, Chem. Eng. Commun. 202 (2015) 606–615. [33] S. Tamna, Y. Kaewkohkiat, S. Skullong, P. Promvonge, Heat transfer enhancement in tubular heat exchanger with double V-ribbed twisted-tapes, Case Stud.
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Effect of square wings in multiple square perforated twisted tapes on fluid flow and heat transfer of heat exchanger tube
MARK
⁎
Amar Raj Singh Suria, Anil Kumara, , Rajesh Maithanib a b
School of Mechanical and Civil Engineering, Shoolini University, Solan, Himachal Pradesh, India Department of Mechanical Engineering, DIT University, Dehradun, Uttarakhand, India
AR TI CLE I NF O
AB S T R A CT
Keywords: Energy Fluid flow Passive heat transfer Wing depth ratio
This work presents, an experimental study on Nusselt number (Nurs ) and friction factor ( frs ) of heat exchanger circular tube fitted with multiple square perforated with square wing twisted tape inserts. The experimental determination encompassed the geometrical parameters namely, wing depth ratio (Wd /WT) of 0.042–0.167, perforation width ratio (a/WT) of 0.250, twist ratio (TL /WT) of 2.5, and number of twisted tapes (NT ) of 4.0. The effect of multiple square perforated twisted tape with square wing has been investigated for the range of Reynolds number (Ren) varied from 5000 to 27,000. The maximum enhancement in Nurs and frs is observed to be 6.96 and 8.34 times of that of the plain circular tube, respectively. Correlations of Nurs , frs and ηp are established in term of Ren and geometrical parameters of wings twisted tape which can be used to predict the values of Nurs , frs and ηp with considerably good accuracy.
1. Introduction The heat exchanger (HE) is fundamental component of power and refrigeration cycles, which encourages the transfer of heat from one medium to another by virtue of temperature difference [1,2]. Industrial equipment utilizes heat exchanger to exchange or transfer heat energy from one medium of fluid to other at various temperatures [3,4]. Numerous technological process exchanges heat to cool one fluid and heat up the other, as in food and petrochemical industries, electronics and power production, airconditioning, refrigeration, and space uses [5–7]. An array of tubes encased in a casing for heating or cooling it down is the major aim of a heat exchanger. Heat exchanger parts like fans, condensers, coolants, extra tubes, alongside numerous elements assume a part in enhancing heating and cooling efficiency [8,9]. Twisted tapes are the metallic strips twisted with some suitable techniques at desired shape and dimension, inserted in the flow. The twisted tape inserts are popular and widely used in heat exchangers for heat transfer enhancement besides twisted tape inserts promote heat transfer rate with less friction factor penalty on pumping power. Insertion of twisted tapes in a tube provides a simple passive techniques for enhancing the convective heat transfer by introducing swirl into the bulk flow and disrupting the boundary layer at the tube surface due to repeated changes in the surface shape. This is to say such tapes induce turbulence and superimposed vortex motion which induces a thinner boundary layer and consequently results in a better heat transfer rate and higher local heat transfer due to the changes in the twisted tape shape. However, the pressure drop inside the tube will be increased by introducing the twisted tape to insert. Hence a lot of investigators have been carried out experimentally and numerically to investigate the optimal design and achieve the best thermal performance with less friction loss [10–13]. Noothong et al. [10] studied Nurs and frs description of a concentric double circular tube with single TT insertion with Twisted ⁎
Corresponding author. E-mail address: [email protected] (A. Kumar).
http://dx.doi.org/10.1016/j.csite.2017.03.002 Received 25 February 2017; Received in revised form 1 March 2017; Accepted 4 March 2017 Available online 08 March 2017 2214-157X/ © 2017 The Authors. Published by Elsevier Ltd. This is an open access article under the CC BY-NC-ND license (http://creativecommons.org/licenses/BY-NC-ND/4.0/).
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Nomenclature
a a / WT Ao Ap Cp Cd D frs fss H h k L ṁ Nurs Nuss (∆P )o (∆P )d ∆ P Pr Qu Ren
Tpm Tfm Ti To TL TL / WT V W , WT Wd Wd / WT y y /W PCR WPT HE TT PT
Perforated width (m) Perforation width ratio (dimensionless) Area of orifice plate (m2) Area of tube (m2) Specific heat (J/kg K) Coefficient of discharge (dimensionless) Hydraulic diameter of pipe (m) Friction factor twisted tape (dimensionless) Friction factor plain tube (dimensionless) Head difference (m) Heat transfer coefficient (W/m2 K) Thermal conductivity of air (W/m K) Tube length (m) Mass flow rate (kg/s) Nusselt number twisted tape tube (dimensionless) Nusselt number plain tube (dimensionless) Pressure drop across orifice plate (Pa) Pressure drop according to Darcy's equation (Pa) Pressure drop (Pa) Prandtl number (dimensionless) Useful heat transfer (W) Reynolds number (dimensionless)
Mean pipe temperature (K) Mean fluid temperature (K) Inlet temperature (K) Outlet temperature (K) Twist length (m) Twist ratio (dimensionless) Air flow velocity (m/s) Width of tape (m) Wing depth (m) Wing depth ratio (dimensionless) Pitch length of twisted tape (m) Pitch ratio (dimensionless) Perforated conical ring Winglet perforated tapes Heat exchanger Twisted tape Plain tube)
Greek symbols
ρ ηp θ
Density (kg/m3) Performance evaluation factor (dimensionless) Taper angle (degree)
ratios namely, y =5.0 and 7.0. TT induced the swirling stream inside the tube resultant in the augment in Nurs . The augmentation in Nurs by using Twist ratios, y =5.0 and 7.0 were 188.9% and 159.65%, respectively. Sarada et. al. [11] examined the Nurs and frs characteristics in a horizontal circular tube with/without TT inserts by varying their width and air as the working fluid for Ren varied from 7000 to 13,800. Eiamsa-ard et. al. [12] examined the impact of the TTs with centre wings in a tube. They inferred that improvement of Nurs and frs as comparison to smooth tube were maximum in the order of 2.89 and 3.12 times, respectively. Wongcharee and Eiamsa-ard [13] investigated TTs with alternate-axes and wings in a round tube. They reported that both Nurs and frs increments with the utilization of all TT in contrast with those TT. Krishna et. al. [14] explored straight HE half left-ring HE embedded in a laminar stream locale experimentally in a circular tube. It is noted that heat transfer increments by diminishing spacer slots and accomplishes the maximum heat transfer for spacer gap of 2.0 in. Wongcharee and Eiamsa-ard [15] used alternate clockwise and counter clockwise twisted-tapes in a circular tube to decide Nurs and frs and thermal hydraulic characteristics. It was reported that clockwise and anticlockwise Twisted-tapes yields a maximum augmentation of Nurs and frs in order of 2.980 and 3.160 times the smooth tube. Murugesan et al. [16] experimentally explored and revealed Nurs and frs and demonstrated a huge augmentation for a circular tube fixed with full length TT with trapezoidal-cut. Seemawute et al. [17] found that in a HE tube fitted with the PTA, PT and TT demonstrated a huge improvement in the Nurs namely 184%, 102% and 57% of that of the PT. Murugesan et. al. [18] examined the V-cut TT and reported that the mean Nurs and frs increment with reducing Twist and width ratios and increases with increasing depth ratios (DR ). Ibrahim [19] experimentally determined Nurs and frs performance of horizontal double pipes of flat tubes having full-length helical screw. The parameters considered were different Twist ratio and different spacer length. Thianpong et al. [20] experimentally explored and inferred that Nurs and frs are higher for dimpled tube fitted with the TT, than the dimple tube alone and PT. A decrease in PR and y / w yields to a higher Nurs and frs . Saha [21] researched Nurs and frs of a rectangular and HE tube with a mix of internal axial corrugations on surfaces of duct and insert in the form of Twisted-tape with and without oblique teeth. The axial corrugations combined with twisted-tapes of all types with oblique teeth performs superior to no oblique teeth combined with axial corrugations. Chiu and Jang [22] examined the longitudinal strip inserts (without hole) and detailed that Nurs and frs were 7.0–16% and 100– 170% higher than the PTs. Nurs and the pressure drop was 13–28% and 140–220%, respectively. Guo et al. [23] numerically analyzed the tubes with short width TTs and reported that Nurs and frs diminish by cutting off the tape edge. Whereas, tubes with centre-cleared TTs, the heat transfer is increased for a appropriate central clearance ratio. Garcia et al. [24] utilized the helical-wire-coils inside a round tube to decide the thermo-hydraulic behaviour in laminar, transition and turbulent stream. Water and water–propylene glycol blends was utilized at various temperatures and the outcomes demonstrates that in turbulent locale wire coils increase friction factor and heat transfer up 9.0 and 4.0 times in contrast to the smooth tube. Promvonge [25] experimentally found the effect of wire coils with TTs as an insert in a circular tube on Nurs and frs . It was reported that combination of wire coils with TTs increases Nurs to folds as compared to wire coil/TT alone. Gunes et al.[26] investigated the heat transfer and pressure drop for a coiled wire insert in a turbulent flow regime. It was observed that Nurs increases with the increase of Ren and wire thickness and decrease in pitch ratio. At a / D =0.0892 and P / D =1 at Re 29
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Table 1 Previous experimental determined on different TT inserts.
(continued on next page)
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Table 1 (continued)
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of 3858 maximum overall enhancement efficiency of 36.5% was achieved. Anvari et al. [27] reported an augmented Nurs for DR (diverging conical ring) arrangement as 521%, and for the converging conical ring arrangement as 355% for conical ring inserts. But the use of this inserts cause a considerable enhancement in frs . Eiamsa-ard et al. [28] concluded that the frs , Nurs and thermal performance factor of the CRT combined with TT are considerably more than those of CRT alone. The increases of Nurs , frs and thermal performance for CRT combined with TT are 25.8%, 82.8% and 6.3% as compared to tube with the CRT alone. For the CRT with l / D =1.0 and TT with y / W =3 the maximum thermal performance factor was found to be 1.42. Singh et al. [29] examined a roughened tube with incorporated SRT and TT for constant heat supply. For the integrated SRT and TT the Nurs , frs and thermal performance factor were found in the range of 107–293, 0.93–0.99 and 1.46–1.61, respectively. The maximum thermal performance factor was found to be 1.61 as compared to a smooth tube for the integrated roughness of the SRT with l / D =1.0 and y / W =2. Enbin Tu et al. [30] numerically investigated and concluded that a tube having pipe inserts, the Nusselt number decreases by increasing spacer length and the friction factor increases with decrease in the spacer length. The maximal PEC values resulted by four pipes inserts were approximately 1.4–3.0. Vashistha et al. [31] examined and reported the effect of multiple inserts oriented in co-swirl and counter-swirl position causes augment the heat transfer having twist ratio of 2.5. The enhancement of Nurs and frs were found to be 2.42 and 6.96 folds the smooth tube, and the thermo-hydraulic performance factor was found to be 1.26. Eiamsa-ard et al. [32] reported the benefits by the use of D − HTTs and T − HTTs that enhances the Nusselt number by 15.6– 17.6% and 19.5–23.4%, respectively and increase in friction factor by 83–206% and 143–335%, respectively. The thermal performance factor decrease by 3.9–20.3% and 8.3–26.2% as compared to those of S − HTT . Tamna et al. [33] investigated double twisted tapes with 30° V-shaped ribs to determine the heat transfer and friction factor. The V-ribbed twisted tape with BR=0.19 produces the maximum Nurs and frs . The thermal enhancement factor was found to maximum about 1.4 at BR=0.09 for the V-ribbed twisted tape and around 1.09 for the twisted tape with no rib. Hasanpour et al. [34] experimental studied Nurs and frs of perforated, V-cut and U-cut types twisted tapes in a double pipe heat exchanger. Results revealed that the use of twisted tape enhances the Nurs and frs for all cases as compared to a plane tube. Piriyarungrod et al. [35] investigated tapered twisted tapes insert at different taper angles (θ ) ranging from 0°–0.9° and different y / W values from 3.5 to 4.5. It was reported that the Nurs and frs increased by decreasing taper angle and y / W . The maximum thermal performance factor of 1.05 was found for the tape with taper angle (θ ) of 0.9° and twist ratio (y / W ) of 3.5 at Re of 6000. Table 1 shows previous experimental investigations on various twisted tape inserts. According to the above literature, it is evident that TTs possess great potentials as the heat transfer enhancing devices. Although the use of TT along with other enhancing technique gives attractive results, the use of only TT with a proper design offers comparable results. In the current work, the new design of multiple TT inserts is used as heat transfer augmentation devices. It is assumed that, the square wing part at the edge of the perforated TT can enhance degree of turbulence near wall tube and thus raise heat transfer rate. The experiments are performed using the tape with different wind depth ratio with a stream parameter range 5000–27,000, where air is used as the working fluid.
Fig. 1. Schematic of experimental setup.
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2. Experimental program A HE tube with multiple square perforated TT with square wing inserts is experimentally investigated to determine the Nurs and frs . The experimental setup has been fabricated as per the literature survey and validated with the data for PT of HE. The validation of experimental setup was followed by the wide experimentations on multiple square perforated TT with square wing inserts HE tube to yield the raw data of heated wall temperatures, fluid stream, and inflow and outflow temperature of air and pressure drop across the test section beneath stable conditions. 2.1. Details of experimental setup The multiple square perforated TT with square wing inserts of the HE tube has been investigated experimentally. The schematic diagram and photographic view of experimental setup is shown in Fig. 1. The tube is made of GI Pipe of 68 mm outer diameter and 65 mm outer diameter and is subdivided into different sections; entry section, test section and exit section with dimensions as 2.5 m, 1.4 m and 1.5 m, respectively. The hydro dynamically fully developed stream is ensured before entering the test section. The HE pipe is attached to the suction end of a 3 HP, 3 phase blower. A stable heat flux of 1000 W/m2 is provided to the test section with the help of Nicrome wire heater. Glasswool fiber tap and insulating pads were provided for reducing the heat loss. Total sixteen T-type (copper-nickel constant) thermocouples were used for measuring the temperature reading with the help of data logger 12.0 thermocouples were placed on tube wall, 1.0 at inlet and 3.0 at the outlet. 3. Range of parameters The multiple square perforated TTist inserts parameters are determined by perforated width (a ), width of tape (WT ), wing depth (Wd ) and twist length (TL ). These parameters have been expressed in the form of dimensionless roughness parameters, viz., perforation width ratio (a / WT ), twist ratio (TL / WT ) and wing depth ratio (Wd / WT ). The data of stream and roughness parameters for this determined are listed in Table 2. The schematic and photographic view of the square perforated TT with wing inserts used in the present determined is shown in Fig. 2(A) & (B). 4. Data reduction Under the steady state conditions and for given heat flux and mass stream rate of air the experimental data for HE was recorded. The heat transfer rate and friction factor in the tube was computed. The data reduction of the data was done as follows: The average tube temperature is the average of all temperatures recorded by thermocouples on the surface of tube test section.
Tpm =
TP 4 + TP5+…+TP16 13
(1)
The mean air film temperature, Tfm is an arithmetic mean of the inlet and the exit temperature of air streaming through the test section.
Tfm =
Ti + To 2
(2)
where
To =
TA1 + TA2 + TA3 3
The pressure drop measurement across the calibrated orifice meter is used to determine mass stream rate of air by using the following formula: ⎡ 2. ρ. (∆P) ⎤0.5 O ⎥ ṁ = Cd . A o. ⎢ ⎣ 1 − β4 ⎦
(3)
where (∆P )o = 9.81⋅(∆h )o ⋅ρm ⋅sinθ Using the value of mass stream rate the velocity of air is calculated from the given expression: Table 2 Range of parameters. Sr. No.
Parameters
Range
1. 2. 3. 4. 5.
Wing depth ratio (Wd /WT ) Perforation width ratio (a /WT ) Twist ratio (TL /WT ) Number of twisted tape (NT ) Reynolds number (Ren )
0.042–0167 0.250 2.5 4.0 5000–27,000
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Fig. 2. (A) Discuss square perforated TT with wing inserts HE tube parameters (B) Photographic view of different TT inserts.
V=
ṁ ρ⋅W⋅H
(4)
4.1. Reynolds number (Ren) The Reynolds number of air stream in the duct is calculated from:
Ren =
V⋅D. ρ μ
(5)
The friction factor is evaluated from the values of pressure drop (ΔP)d across the test section length using Darcy equation as:
f=
2⋅(∆P)d ⋅D 4⋅ρ⋅L⋅V2
(6)
where (ΔP)d=9.81×(Δh)d×ρm The heat transfer coefficient of the test section is calculated using the following equation:
h=
Qu A p⋅(Tpm − Tfm)
(7)
The Nusselt number is determined from the heat transfer coefficient using the following equation:
Nu =
h⋅D k
(8)
Considering the thermal and the hydraulic performance of a multiple square perforated TT inserts tube simultaneously and comparing it to a PT as:
ηp =
[Nurs / Nuss] [frs / fss ]1/3
(9)
5. Uncertainties analysis An uncertainty analysis has been carried to estimate the errors involved in experimental data measurement. The uncertainty is estimated based on errors associated with measuring instruments Klein and McClintock [36]. The uncertainties of the Nurs and frs are evaluated as follows: Mass flow rate:
⎡ 2ρ (∆P )o ⎤ ṁ = CdAo ⎢ o 4 ⎥ ⎣ 1−β ⎦
(10) 34
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A.R. Singh Suri et al. 0.5 2 ⎡⎛ ⎛ 0.5δρ ⎞2 ⎛ δA ⎞2 ⎛ δ (∆P ) ⎞2 ⎤ δC ⎞ δṁ o o ⎥ ⎟⎟ + ⎜ o ⎟ + ⎜ = ⎢⎜ d ⎟ + ⎜⎜ ⎟ ⎢⎝ C ⎠ ṁ ⎝ Ao ⎠ ⎝ (∆P )o ⎠ ⎥⎦ ⎝ ρo ⎠ ⎣ d
(11)
0.5 δṁ = [(6.25 × 10−4) + (4.449 × 10−6) + (3.26 × 10−5) + (5.102 × 10−7)] ṁ
(12)
ṁ = 0.0257
(13)
Hence, uncertainty in mass flow rate measurement is 2.57%. Heat gain:
Qu = mC ̇ p(To − Ti ) = mC ̇ p∆T 2 ⎡ ⎛ δ (ΔT ) ⎞2 ⎤⎥ ⎛ δṁ ⎞2 ⎛ δCp ⎞ δQu ⎟⎟ + ⎜ = ⎢⎢⎜ ⎟ + ⎜⎜ ⎟ ⎝m⎠ Qu ⎝ (ΔT ) ⎠ ⎥⎦ ⎝ Cp ⎠ ⎣ ̇
(14) 0.5
(15)
0.5 2 ⎡ ⎛ δ (ΔT ) ⎞2 ⎤⎥ ⎛ δṁ ⎞2 ⎛ δCp ⎞ δQu ⎟⎟ + ⎜ = ⎢⎢⎜ ⎟ + ⎜⎜ ⎟⎥ ⎝m⎠ Qu ⎝ (ΔT ) ⎠ ⎦ ⎝ Cp ⎠ ⎣ ̇
(16)
δQu 0.5 = [(6.7081 × 10−4) + (9.9007 × 10−9) + (1.13 × 10−4)] Qu
(17)
δQu = 0.0277 Qu
(18)
Hence, uncertainty in heat gain is 2.77%. Heat transfer coefficient:
h=
Qu Qu = Ap (Tpm − Tfm ) Ap (∆Tfm )
(19)
0.5 ⎡⎛ 2 ⎛ δAp ⎞2 ⎛ δ (ΔTfm ) ⎞2 ⎤ δQ ⎞ δh ⎟⎟ ⎥ ⎟⎟ + ⎜⎜ = ⎢⎢⎜ u ⎟ + ⎜⎜ h Q ⎝ Ap ⎠ ⎝ (ΔTfm ) ⎠ ⎥⎦ ⎣⎝ u ⎠
(20)
0.5 δh = [(7.784 × 10−4) + (2.166 × 10−6) + (2.764 × 10−5)] h
(21)
δh = 0.284 h
(22)
Hence, uncertainty in heat transfer coefficient is 2.84%. Reynolds number:
Ren =
ρVD μ
⎡⎛ ⎞ 2 ⎛ ⎞ 2 ⎛ ⎞ 2 ⎛ ⎞ 2 ⎤ δRen δρ δμ δV δD = ⎢⎜ ⎟ + ⎜ ⎟ + ⎜ ⎟ + ⎜ ⎟ ⎥ ⎢⎣⎝ ρ ⎠ ⎝D⎠ ⎝V ⎠ Ren ⎝ μ ⎠ ⎥⎦
(23) 0.5
(24)
δRen 0.5 = [(6.66 × 10−7) + (1.5129 × 10−4) + (8.76 × 10−7) + (2.543 × 10−7)] Ren
(25)
δRen = 0.01237 Ren
(26)
Hence, uncertainty Reynolds Number is 1.23%. Nusselt number:
Nurs =
hD K
(27)
⎡⎛ ⎞2 ⎛ ⎞2 ⎛ ⎞2 ⎤0.5 δNurs δh δD δK = ⎢⎜ ⎟ + ⎜ ⎟ + ⎜ ⎟ ⎥ ⎝ K ⎠ ⎥⎦ ⎝D⎠ Nurs ⎣⎢⎝ h ⎠
(28) 35
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δNurs 2 0.5 = [(0.0284)2 + (0.000936)2 + (4.16×10−4) ] Nurs
(29)
δNurs = 0.02841 Nurs
(30)
Hence, uncertainty Nusselt Number is 2.84%. Friction factor:
frs =
δfrs frs δfrs frs
δfrs frs
2(∆p ) D d
4ρLV 2
(31)
2 ⎤0.5 ⎡ 2 2 ⎛ δρ ⎞2 ⎛ δD ⎞ ⎛ δL ⎞2 ⎛ δ (∆p )d ⎞ ⎥ ⎢⎛ δV ⎞ ⎜ ⎟ = ⎢⎜ ⎟ + ⎜ ⎟ + ⎜ ⎟ + ⎜ ⎟ + ⎜ ⎟⎥ ⎝L⎠ ⎝D⎠ ⎠ ⎝ ρ⎠ ⎝ (∆p )d ⎠ ⎥⎦ ⎢⎣⎝ V
(32)
0.5 2 ⎡⎛ ⎛ 0.1 ⎞2 ⎛ 0.01 ⎞2 ⎤ ⎛ 0.001 ⎞2 0.1 ⎞ = ⎢⎜ ⎟⎥ ⎟⎜ ⎟ + (0.000936)2 + ⎜ ⎟ +⎜ ⎢⎣⎝ 8.13 ⎠ ⎝ 1400 ⎠ ⎝ 1.94 ⎠ ⎥⎦ ⎝ 1.225 ⎠
(33)
= 0.01339 (34)
Hence, uncertainty friction factor is 1.33%. As the uncertainty calculation was done on a single test run, the uncertainty examination for whole test run for single TT was carried out and results are presented in Table 3 for the experimental data. 6. Validation of experimental results Experimental outcomes for PT were validated with empirical correlations of Gnielinski and Dittus-Boelter equation for Nuss and Petukhov correlation and Blasius equation for fss respectively. These correlations beside with their valid ranges are presented in Eqs. (35)–(38) below: The Nuss and fss for a PT is given by the Gnielinski (Eq. (35)) and modified Petukhov (Eq. (36)) are as:
Nuss =
(f /8)(Ren − 1000)Pr 1 + 12.7(fss /8)1/2(Pr 2/3 − 1)
for
3000 < Ren < 10,000
(35)
fss = (0.079lnRen − 1.64)−2
(36)
The Nuss and fss for a smooth channel is given by the Dittus-Boelter equation (Eq. (37)) and modified Blasius equation (Eq. (38)) are as:
Nuss = 0.023Ren 0.8Pr0.4forRen > 10,000
(37)
fss = 0.085Ren−0.25
(38)
The comparison of the experimental and estimated values of the Nuss and fss as a function of the Ren is shown in Fig. 3(A) & (B), respectively. A reasonably good agreement between the three sets of values ensures the accuracy of the data collected using this experimental setup. 7. Results and discussion The heat transfer and friction characteristics of HE tube with multiple (4 tapes) square perforated TT with square wing inserts HE tube have been determined by using the experimental data collected for different sets of geometrical parameters. A comparative Table 3 Range of uncertainty in the measurement of essential parameters. S. No.
Parameters
Error range (%)
1 2 3 4 5 6
Mass flow rate Heat gain Heat transfer coefficient Reynolds Number Nusselt number Friction Factor
2.57 2.77 2.84 1.23 2.84 1.33
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Fig. 3. Comparison of present experimental results with previous correlations for (A) Nuss and (B) fss .
determined of the multiple square perforated TT with square wing inserts is done with the multiple plain TT, multiple TT with square perforation and PT. The outcome of the extensive experimentation is discussed below: Fig. 4(A) & (B) shows the effect of Ren on Nurs and frs for multiple square perforated TT with square wing inserts, multiple (without square wings) twisted square perforated tape inserts, simple multiple TT inserts and that for PT. The values of Nurs are found to rise with rises Ren in all cases as expected. The multiple square perforated TT with square wing inserts tube can be seen to yield higher Nurs and frs as compared to that of the multiple (without square wings) twisted square perforated tape inserts, simple multiple TT inserts and that for PT (smooth surface). Creating square wings in the multiple TT produces higher heat transfer rate due to the higher potential turbulence streams induced by wings near the tube wall. This higher potential turbulence stream exerts a measurable effect in disturbing the axial stream profile which rise the Nurs and frs . In order to determine the improvement of the Nurs achieved as an results of providing a square wings in the multiple square perforated TT inserts tube arrangement, the values of the Nurs for fixed values of the a / WT of 0.250 and TL / WT of 2.5, and different values of Wd / WT is given in Fig. 5(A). The variation of Nurs with Ren for the multiple square perforated with square wing TT inserts, multiple square perforated TT inserts, without square perforated multiple TT inserts and smooth surface tube are shown in Fig. 5(A). Apparently, Nurs increases as Ren the use of multiple TT inserts tube leads to considerable increase of Nurs as compared to that smooth tube. This can be explained that the thermal boundary becomes thicker as Ren decreases thus the effect of boundary destruction by multiple inserts turns out to be more prominent. The Nurs increases with increase in Wd / WT from 0.042 to 0.167, attains maximum Nurs at, Wd / WT of 0.167. Fig. 5(B) shows the data of the Nurs as a function of Wd / WT for a fixed value of a / WT of 0.250 and TL / WT of 2.5 at different selected values of Ren . It can be observed that Nurs is the maximum for Wd / WT =0.167 for all data of Ren . Fig. 6(A) shows that the effect of Wd / WT on the Nurs / Nuss for a fixed values of a / WT of 0.250 and TL / WT of 2.5 respectively. It can be seen that Nurs / Nuss increase with an increase in Wd / WT from 0.042 to 0.167, attains a maxima at Wd / WT of 0.167. Fig. 6(B) shows the values of Nurs / Nuss as function of Wd / WT for the selected Ren values where a maxima in the values corresponding to a Wd / WT of 0.167 for all Ren . The secondary stream jets and swirl stream exerts a significant influence on the axial stream profile, which increases significant influence on the axial stream profile, which increases the frs in tubes. The effect of the Wd / WT on frs with Ren is shown in Fig. 7 (A). It is observed that the value of frs decreases with increasing Ren and moves towards a constant value as expected. The frs increases with
Fig. 4. (A) Variation of Nurs with Ren (B) Variation of frs with Ren .
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Fig. 5. (A) Variation of Nurs with Ren for different values of Wd /WT (B) Variation of Nurs with Wd /WT for different values of Ren .
increase the values of Wd / WT and observed maximum value of 0.167. The variation of frs with Wd / WT is shown in Fig. 7 (B) for selected Ren values. The maximum value of frs is obtained for Wd / WT of 0.167 and minimum for the Wd / WT of 0.042. Fig. 8(A) shows that the effect of Wd / WT on the frs / fss for a fixed values of a / WT of 0.250 and TL / WT of 2.5 respectively. It can be seen that frs / fss increase with an increase in Wd / WT from 0.042 to 0.167, attains a maxima at Wd / WT of 0.167. Fig. 8(B) shows the values of frs / fss as function of Wd / WT for the selected Ren values where a maxima in the values corresponding to a Wd / WT of 0.167 for all Ren . The variation of Nurs and frs as a function of Ren for different values of Wd / WT . It can be observed that in the Figs. 5–8 the Nurs increses with the increse of Ren , whereas the frs decreases with the increse of Ren . It can be observed from these Figures that the augmentation in heat transfer of the multiple square perforated with square wing TT inserts tube with respect PT also increases with an increase in Ren whereas augmentation in frs of the multiple square perforated with square wing TT inserts tube. Also, shows that the Nurs and frs increses with increasing values of wing depth ratio. TT inserts on the heat transfer surface in the form multiple square perforated with wing creates local wall turbulence as breaks the laminar sub layer due to swirl stream separation and reattachment between the TT, which reduces thermal resistance and greatly rise the Nurs and frs . A parameter known as thermal hydraulic performance ηp is used to evaluate the effectiveness of TT inserts tube accounting for the augmentation of Nurs and frs and is expressed as [Nuss / Nurs /(fss / frs ]0.33 [37–40]. The values of this parameter for the multiple square perforated with square wing inserts, multiple square perforated TT inserts as well as without square perforated multiple TT inserts are investigated in this work and have been plotted in Fig. 9. Fig. 9(A) shows the effect of Wd / WT on thermal hydraulic performance where it can be observed that the value of this parameter is seen to increase with increase Wd / WT upto about 0.167. The Wd / WT , varied from 0.042 to 0.167 and Ren varies from 5000 to 27,000. The results observed by experimental that the thermal hydraulic performance parameter was strongly dependent on the Wd / WT . Fig. 9(B) shows the values of thermal hydraulic performance as function of Wd / WT for the selected Ren where a maxima in the values corresponding to a Wd / WT of 0.167 for all values of Ren . A maximum value of thermal hydraulic performance parameter was found to be 4.1 for the range of parameters investigated. The values of thermal hydraulic performance parameter determined for the shape of multiple square perforated with wings twisted tape inserts have been compared with the values determined for other twisted tape inserts. It can be observed that from Table 4 multiple square perforated with wings twisted tape shape results in highest thermal hydraulic performance as compared other perforated and multiple twisted tape inserts heat exchanger tubes.
Fig. 6. (A) Variation of Nurs /Nuss with Ren for different values of Wd /WT (B) Variation of Nurs /Nuss with Wd /WT for different values of Ren .
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Fig. 7. (A) Variation of frs with Ren for different values of Wd /WT (B) Variation of frs with Wd /WT for different values of Ren .
Fig. 8. (A) Variation of frs /fss with Ren for different values of Wd /WT (B) Variation of frs /fss with Wd /WT for different values of Ren .
Fig. 9. (A) Variation of ηp with Ren for different values of Wd /WT (B) Variation of ηp with Wd /WT for different values of Ren .
8. Correlation development As discussed earlier that the Nurs and frs are strong functions of stream and TT parameters namely Ren and Wd / WT . The functional relationships for Nurs and frs can therefore be written as;
Nurs = fn (Ren , Wd / WT )
(39) 39
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Table 4 Overall thermal performance parameters compared with previous investigations. Investigator
Shape
Overall thermal performance
Noothong et al. [10] Sarada et al. [11] Eiamsa et al. [12] Wongcharee and Eiamsa ard [13] Krishna et al. [14] Wongcharee and Eiamsa-ard [15] Murugesan et al. [18] Sivashanmugam and Nagarajan [39] Present study
Twisted tape inserts Twisted tape inserts Twisted tape with centre wing Alternate clockwise and counter clock wise twisted tape inserts Straight half twisted left right inserts Rectangular and trapezoidal wings V-cut twisted tape Helical screw tape inserts Multiple square perforated with square wings twisted tape
2.14 1.43 2.04 5.13 1.56 1.92 1.64 2.98 4.1
Fig. 10. (A) Variation of ln(Nurs ) with ln(Ren ) (B) Variation of ln(Ao) with ln (Wd /WT ) for Nurs (C) Variation of ln(Ao) with ln (Wd /WT ) for frs (D) Variation of ln(Ao) with
ln (Wd /WT ) for ηp .
frs = fn (Ren , Wd / WT )
(40)
ηp = fn (Ren , Wd / WT )
(41)
Experimental results collected, processed and discussed in detail of terms of variation of Nurs , frs and ηp as a function of system and operating parameters in the previous section has been used to develop these relationships in the form of correlations. In order to determine the functional relationships between Nurs and Ren , the well known power law relationship between these parameters for turbulent heat transfer has been utilized, consequently.
Nurs = AO (Ren )n
(42)
Above functional relationships between Nurs and Ren can be expressed as;
ln(Nurs ) = nln(Ren ) + A1
(43)
where A1=lnAO 40
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Fig. 11. Comparison of experimental and predicted values for (A) Nurs (B) frs (C) ηp .
Fig. 10(A) shows a linear relationship between Nurs and Ren for the given range. The regression analysis gave a relation in terms of a straight line equation and is represented as,
Nurs = Ao (Ren )0.7498
(44)
The determined was carried out for different values of Wd / WT , thus the coefficient of Ao also depends on Wd / WT . The influence of geometrical parameter, Wd / WT on coefficient of Ao is plotted a graph between ln(Nurs /Ren 0.749) and ln (Wd / WT ) as shown in Fig. 10(B). Using the second order regression following correlation is obtained,
⎛ W ⎞0.4321 Exp(0.0633(ln (Wd /WT )2) Nurs = 0.345 × Ren 0.7498⎜ d ⎟ ⎝ WT ⎠
(45)
Similarly the correlation of frs and ηp were developed following the same procedure for a range of Wd / WT . The developed correlation for frs and ηp are shown in Fig. 10(C) & (D), respectively and the correlations are given as:
⎛ W ⎞0.5634 frs = 6.95 × Ren−0.2427⎜ d ⎟ Exp(0.08(ln (Wd /WT )2) ⎝ WT ⎠
(46)
⎛W ⎞ ηp = 16.3 × Ren−0.1007⎜ d ⎟ ⎝ WT ⎠
(47)
0.6506
Exp(0.1133(ln (Wd /WT )2 )
The comparison of experimental values with predicted values of Nurs , frs and ηp obtained from the respective correlations is done in order to find out the deviation in the values. It is seen that the values of correlations of Nurs , frs and ηp lie within ± 5.5%, ± 4.0% and ± 6.0%, respectively of experimentally determined values. The deviation in the predicted and the experimental values of Nurs , frs and ηp are shown in Fig. 11(A-C). 9. Conclusions Based on the present experimental determined on multiple square perforated with square wing TT inserts tube, the following conclusions can be drawn from present determined: 41
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1. Multiple square perforated with square wing TT inserts has been found to higher overall thermal performance as compared without wing multiple square perforated TT heat exchanger tube with similar operating conditions. 2. As compared to the PT, the multiple square perforated with square wings TT inserts tube yields an increase of about 6.96 and 8.34 times in the Nurs and frs , respectively, for the range of parameters investigated. 3. The maximum value of Nurs , frs and ηp occurs for multiple square perforated with square wing TT inert tube with Wd /WT of 0.167. 4. The results observed by experimental that the thermal hydraulic was strongly dependent on the Wd /WT . A maximum value of thermal hydraulic performance parameter was found to be 3.08 for the range of parameters investigated. 5. Correlations have been developed for Nurs , frs and ηp as function of TT parameter and stream parameters. The deviation between predicted and experimental value for Nurs , frs and ηp are of the order ± 5.5%, ± 4.0% and 6.0% respectively. References [1] S. Kumar, A.D. Kothiyal, M.S.H. Bisht, A. Kumar, Numerical analysis of thermal hydraulic performance Al2O3-H2O nanofluid flowing through a protrusion obstacles square mini channel, Case Stud. Therm. Eng. 9 (2017) 108–121. [2] R. Kumar, A. Kumar, R. Chauhan, M. Sethi, Heat transfer enhancement in solar air channel with broken multiple V-type baffle, Case Stud. Therm. Eng. 8 (2016) 187–197. [3] R. Kumar, V. Pedgopu, A. Kumar, R. Thakur, A. Pundir, CFD based analysis heat transfer and friction characteristics of broken multiple rib roughened solar air heater duct, Int. J. Mech. Prod. Eng. Res. Dev. 3 (2013) 165–172. [4] R. Thakur, A.R.S. Suri, S. Kumar, A. Kumar, A review of integrated renewable energy system in power generation, Int. J. Mech. Prod. Eng. Res. Dev. 3 (2013) 79–88. [5] A. Kumar, M.H. 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