Experimental investigation of heat transfer in a channel with new winglet-type vortex generators

International Journal of Heat and Mass Transfer 78 (2014) 604–614

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Experimental investigation of heat transfer in a channel with new winglet-type vortex generators S. Caliskan ⇑ Department of Mechanical Engineering, Hitit University, 19030 Çorum, Turkey

a r t i c l e

i n f o

Article history: Received 19 May 2014 Received in revised form 14 July 2014 Accepted 16 July 2014

Keywords: Heat transfer enhancement Infrared thermal imaging technique Punched vortex generators Pressure drop

a b s t r a c t Both new punched triangular vortex generators (PTVGs) and punched rectangular vortex generators (PRVGs) have been developed. Both the triangular and rectangular vortex generators were directly punched from the longitudinal winglet at attack angles of 15°, 45° and 75°, respectively. Measurements were carried out for a rectangular channel of an aspect ratio of AR = 2, for a winglet transverse pitch (S) to a longitudinal winglet height (e) ratio of S/e = 0.59, and a winglet height (e) to a channel height (H) ratio of e/H = 0.6. The parameters included the location of the punched vortex generator on the longitudinal winglet, the geometric shapes of the punched vortex generators, and the attached angle of punched vortex generators. The Reynolds numbers considered for the channel flow case (based on the hydraulic diameter) ranged from 3288 to 37,817. The heat transfer results were obtained using the infrared thermal imaging technique. The heat transfer results of the vortex generators were compared with those of a smooth plate. The best heat transfer performance was obtained with the PTVGs. The presence of the vortex generators produced higher heat transfer coefficients than the smooth plate surfaces. Correlations were developed for the averaged Nusselt number for the PTVGs and PRVGs. Results showed a 23–55% increase in heat transfer due to the use of vortex generators. These vortex generators show a more significant increase in heat transfer coefficient for channel flows. Ó 2014 Elsevier Ltd. All rights reserved.

1. Introduction A longitudinal vortex generators (LVGs) on a heat transfer surface is one of the most widely employed heat transfer enhancement techniques. This technique is used for thermal equipment such as a heat exchanger and internal blade cooling of a gas turbine. The mechanism of heat transfer enhancement is based on flow separation and reattachment. In general, flow reattachment introduces a strong shear flow on the surface behind each rib or winglet, resulting in an effective disruption of the thermal boundary layer and thus the improvement of the heat transfer [1–10]. Tigglebeck et al. [11] found that in a rectangular channel flow, a pair of delta winglets performs slightly better heat transfer than a pair of rectangular winglets at higher attack angles and Reynolds numbers. Biswas et al. [12] reported that a winglet pair has less loss of flow than that of a single winglet, and winglet pairs can eliminate zones of poor heat transfer. Two kinds of vortex generators, a delta winglet pair (DWP) and a rectangular winglet pair (RWP), were numerically compared by ⇑ Tel.: +90 364 2274533; fax: +90 364 2274535. E-mail address: [email protected] http://dx.doi.org/10.1016/j.ijheatmasstransfer.2014.07.043 0017-9310/Ó 2014 Elsevier Ltd. All rights reserved.

Ferrouillat et al. [13]. Torii et al. [14] proposed a common-flowup delta winglet configuration, which was effective in delaying boundary layer separation from the tube, reducing form drag, and removing zones of poor heat transfer from the near-wake of the tube. Tian et al. [15] numerically investigated the effects of RWP and DWP with two different configurations, such as common-flow-down and common-flow-up heat transfers along with fluid flow characteristics. Fiebig et al. [16] studied the heat transfer enhancement of delta wings and winglets in flat plate channels for Reynolds numbers based on plate spacing between 1360 and 2270. Qualitative data was recorded using a laser-sheet flow visualization technique, and the heat transfer behavior was measured using unsteady, liquid crystal thermography. They concluded that the local heat transfer was enhanced up to 200% and the delta winglet caused the highest local enhancement. When the Reynolds number was 1360, the Colburn j factor was increased by 20–60%. Min et al. [17] developed a modified rectangular LVG obtained by cutting off the four corners of a rectangular wing. Their experimental results of this LVG mounted in a rectangular channel suggested that the modified rectangular wing pairs (MRWPs) have better flow and heat transfer characteristics than those of rectangular wing pairs (RWP). A numerical study by Biswas and

S. Caliskan / International Journal of Heat and Mass Transfer 78 (2014) 604–614

605

Nomenclature A AR b c Dh e f g H h I k L Nu Nuavg S DP Pr PTVGs PRVGs Re Q

convection heat transfer area of channel (m2) aspect ratio of channel (–) distance of punched winglet from the channel bottom (m) punched winglet length (m) hydraulic diameter (m) height of winglet (m) friction factor (–) spacing between punched winglet (m) channel height (m) averaged heat transfer coefficient (W/m2 K) current (A) thermal conductivity of air (W/m K) length of test channel (m) Nusselt number (–) averaged Nusselt number (–) spacing between longitudinal winglet (m) pressure drop (Pa) Prandtl number (–) punched triangular vortex generators punched rectangular vortex generators Reynolds number (–) heat transfer (W)

Chattopadhyay [18] on a delta wing with a punched hole in the base wall showed that the heat transfer enhancement and the friction factor at the exit were both relatively lower than those of the case without any punched hole. Akbari et al. [19] studied the heat transfer enhancement effects of two different configurations of delta winglet pair vortex generators in a narrow rectangular channel by experiment. Chen et al. [20,21] explored the punched longitudinal vortex generators in the form of winglets in both in-line and staggered arrangement, both of which could enhance heat transfers in a finned oval tube heat exchanger. Gentry and Jacobi [22,23], experimentally studied the heat transfer enhancement characteristics of delta wing vortex generators in a flat-plate channel flow. Results showed that the averaged heat could be enhanced by 50–60% at a low Reynolds number in comparison with the original configuration. Chung et al. [24] investigated the combined effect of the angle of attack and the louver angle of a winglet pair on heat transfer enhancement where the punched holes were considered but the thickness of the winglet pair was neglected. Results showed that the best performance was achieved when the angle of attack was at 30° and the louver angle was at 15°. Eiamsa-ard et al. [25], in an experiment, investigated the fluid flow and heat transfer characteristics in a tube fitted with delta winglet twisted tape, which resulted in a higher Nusselt number and friction factor in comparison with the typical twisted tape. Zhou and Ye [26], experimentally investigated the heat transfer performance of a new vortex generator called curved trapezoidal winglet and compared the results with the rectangular winglets. Promvonge et al. [27], experimentally studied the effects of combined ribs and winglet type of vortex generators (WVGs) on forced convection heat transfer and friction loss behaviors for turbulent air-flow through a constant heat flux channel. Zhu et al. [28] calculated three-dimensional turbulent flows and a heat transfer in a rectangular channel with a rectangular winglet on one wall and rib-roughened elements on the other wall by using the k–e model. They found that the combined effect of rib-roughened, vortex generators can enhance the averaged Nusselt number by nearly 450%. Zhou and Feng [29], experimentally studied the performance of

T t U V W V_ x/Dh y/Dh

temperature (K) thickness of longitudinal winglet (mm) mean velocity (m/s) voltage (V) width of channel (m) volumetric flow rate (m3/s) dimensionless distance along the streamwise (–) dimensionless distance along spanwise (–)

Greek symbols a attack angle of punched winglet (°) q density of the fluid (kg/m3) g thermal enhancement factor (–) m kinematic viscosity (m2/s) Subscripts a augmented avg average b bulk 0 channel without vortex generator pp pumping power

both plane and curved winglet (rectangular, trapezoidal and delta) vortex generators (VGs) both with and without the punched holes. They found that curved winglet type VGs (CRWP, CTWP and CDWP) have both a better heat transfer enhancement and lower flow resistance than corresponding plane winglet VGs in both laminar and turbulent flow regions. In the work currently being done, both new punched triangular vortex generators (PTVGs) and punched rectangular vortex generators (PRVGs) have been designed. In order to investigate the convective heat transfer performance of PTVGs and PRVGs, an experimental set-up was established. The effects of the attack angle and distance of both PTVGs and PRVGs from the channel bottom on the heat transfer and pressure drop characteristics were examined. In plate-fin heat exchangers the flow between the plates can be considered as a channel flow. For the reduction of the thermal resistance, the heat transfer coefficient needs to be augmented.

2. Experimental apparatus and procedure The heat transfer experiments were conducted in an open rectangular channel as shown in Fig. 1. The experimental system consisted of a honeycomb, an entrance section, a test section, a centrifugal blower, an infrared thermography system, vortex generators, and devices for measuring flow velocity, temperature and pressure difference. The triangular and rectangular vortex generators were directly punched from the longitudinal winglets. Air was drawn in by a variable speed fan and passed through the test section of the channel. The channel inner cross section dimensions were 100 mm (wide) and 50 mm (height). The entrance channel was 2500 mm long. The channel was constructed with 9 mm thick plexiglass plates. The dimensions of the heating plate were 100 mm (width) and 270 mm (length). In the experiments, the heating plate was made of stainless steel foil. It was firmly clamped and stretched between two copper bus bars. The foil was electrically heated by means of a high current DC power supply to provide a constant heat flux surface. In order to confirm the equal temperatures at the bottom and upper side of the 0.02 mm thick

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S. Caliskan / International Journal of Heat and Mass Transfer 78 (2014) 604–614

test section copper bus bars

IR camera Fig. 1. Experimental set-up.

stainless steel foil, each surface was equipped with K-type thermocouples, attached along the center line of the target plate. All thermocouples were separately calibrated. All values of the Reynolds numbers were considered for each surface at a fixed heat flux of 670 W/m2. Thermal images were obtained from an IR camera positioned on the bottom of the heater assembly vertical to the channel. The longitudinal winglets were mounted on the bottom of the channel (on top of the stainless steel foil) to enhance the convective heat transfer. The averaged heat transfer coefficient on the plate surface was measured for various rates of airflow through the channel. Views of both the PTVGs and PRVGs are shown in Fig. 2. The longitudinal winglets were made of high conductivity aluminum material. Each of the longitudinal winglets was fabricated from 0.8 mm thick aluminum plates, and 270 mm long (L). The longitudinal winglets were attached to the stainless steel foil plates by a thin layer of super-glue. The thermal contact resistance due to the super-glue introduced a minor conservative preference to the reported results [30]. In order to make the comparisons between both triangular and rectangular vortex generators, the open area for each generator was held constant at a value of 112.5 mm2. The positioning of the punched rectangular and triangular vortex generator was 33.5 mm (a) from the channel inlet. The minimum distance between the two longitudinal winglets was 18 mm (S). The punched length of the rectangular and triangular winglet (c) was 13 mm while the distance between the two punched winglets (g) was 20 mm. Air flow was described in a coordinate system (x, y, z), in which x, y, z were streamwise, spanwise, and, normal coordinates, respectively. Thermal images were obtained from an IR camera positioned on the bottom of the heater assembly vertical to the z-direction. The air velocity was measured by the Kimo LV107-type anemometer connected to the output of the blower. ALMEMO and a pressure transducer were used to determine the pressure drop between the air inlet and outlet at the test section. The inlet and outlet temperatures of the channel air were measured in different locations of the channel by using a K-type

thermocouple. All of these thermocouples were connected to a PC-based data acquisition system. The infrared thermography system, which included a ThermaCAM SC500 camera from FLIR systems and a PC with AGEMA Researcher software, could measure temperatures from 20 °C to 1200 °C with an accuracy of ±2%. The infrared camera used an uncooled focal plane array detector with 320  240 pixels, which operated over a wavelength range of 7.5–13 lm. The field of view was 25°  18.8°/0.4 m; the instantaneous field of view was 1.3 m-rad, and the thermal sensitivity was 0.07 °C at 30 °C. The images captured by the infrared camera were displayed and recorded using a computer for further analysis. The bottom side of the stainless steel foil was covered with a layer of black backing paint. The emissivity of each side of the plate was measured with an AE anemometer and was found to be 0.82 and 0.13 for the painted and unpainted surfaces, respectively. The local heat transfer coefficient and Nusselt number were defined as:

hx ¼

qconm ðT  T b;x Þ

ð1Þ

where T and Tbx were the local temperature of the heating surface and the bulk fluid, respectively.

Nux ¼

hx D h k

ð2Þ

The convective heat flux was evaluated as follows:

qconm ¼

Q el  Q loss A

ð3Þ

where Qel was the measured input power to the heater (Qel = VI). Radiation, free convection from the bottom side, and conduction were considered as heat losses. The radiation heat flux from both sides of the sheet was given by

  qfront ¼ et r T 4  T 4b r

ð4Þ

S. Caliskan / International Journal of Heat and Mass Transfer 78 (2014) 604–614

(a)

punched triangular vortex generators

607

longitudinal winglet

punched triangular vortex generators (PTVGs), stainless steel foil

punched rectangular vortex generators (PRVGs)

(b) Fig. 2. Schematic view of present vortex generators: (a) a channel with triangular vortex generators; (b) top view of the punched triangular and rectangular vortex generators.

  qback ¼ eb r T 4  T 41 r

ð5Þ

where et and eb are the emissivities of the unpainted and painted surfaces, respectively. r is the Stefan–Boltzmann constant. The free convection heat flux from the bottom side of the sheet was calculated using

qf ¼ hf ðT  T 1 Þ

ð6Þ

where the free convection coefficient hf was defined as 1.1 W/m2 K, for an air velocity of 0.1 m/s [31].The conduction was given by:

qc ¼ k

DT t

ð7Þ

where k was the thermal conductivity of the sheet, DT was the temperature difference across the sheet, and t was the thickness of the sheet. As a result of the thinness of the sheet, the lateral conduction was negligible as reported by Lytle and Webb [32]. The sum of Qloss was typically in the range of 7.4–10.6% of Qel at the highest Reynolds number. The averaged Nusselt number Nuavg was calculated by integrating the local Nusselt number over the heating surface, i.e.,

Nuav g ¼

1 L

Z

NuðxÞ@x

ð8Þ

The Reynolds number based on the channel hydraulic diameter was given by

Re ¼

quDh l

ð9Þ

where Dh = 2WH/(W + H) was the channel hydraulic diameter. Friction factor, f, can be written as

DP f ¼  L qU 2 =2 D

ð10Þ

h

where Dp was pressure drop across the length of the channel, L. The experimental uncertainties had been determined by a standard error analysis. Both the inlet and outlet temperatures of the air were measured by using calibrated K-type thermocouples with an accuracy of 0.3 °C. The inlet velocities at the centers were measured by an anemometer with an uncertainty of 0.03 m/s. The uncertainty in the experimental data was determined according to the procedure proposed by Kline and McClintock [33]. In our experiment, the fluid properties were assumed constant. The uncertainty in the calculation of the Nusselt number and Reynolds number was found to be less than 6.2% and 5.8%, respectively. The uncertainty in the friction factor f was estimated to be 4.2% at the highest Reynolds number and 6.7% at the lowest Reynolds numbers. The maximum uncertainty of the infrared thermography measurements was less than ±1.5%. 3. Results and discussion 3.1. Validation of smooth channel The experimental data for the forced convection heat transfer and friction factor in a rectangular duct with punched triangular

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S. Caliskan / International Journal of Heat and Mass Transfer 78 (2014) 604–614

vortex generators (PTVGs) and punched rectangular vortex generators (PRVGs) was examined under a turbulent flow regime. The present experimental results in a smooth wall channel were first validated in terms of the Nusselt number and the friction factor. The Nusselt number and the friction factor obtained from the present smooth channel were, respectively, compared with the correlations of Dittus-Boelter and Blasius found in the open literature [34] for turbulent flow in ducts. Correlation of Dittus-Boelter,

Nu ¼ 0:023Re0:8 Pr0:4

for heating

ðf Re3 Þ0 ¼ ðf Re3 Þa Re0 ¼ Rea ðfa =f0 Þ

g¼

for 3000  Re  20; 000

ð14Þ

1=3

ð15Þ

The thermal enhancement factor, g, was defined as the ratio of the heat transfer coefficient of an augmented surface, h, to that of a smooth surface, h0, at a constant pumping power:

ð11Þ

Correlation of Blasius,

f ¼ 0:316Re0:25

and the relationship between friction and Reynolds number can be expressed as:

    1=3 h  Nu  Nu f ¼ ¼ h0 pp Nu0 pp Nu0 f0

ð16Þ

ð12Þ

Fig. 3a and b show, respectively, a comparison of the Nusselt number and the friction factor obtained from the present work with those from correlations of Eqs. (11) and (12). In the figures, the present results reasonably agree well within the ±12% deviation for both the friction factor and Nusselt number correlations. For a constant pumping power,

ðV_ DPÞ0 ¼ ðV_ DPÞa

ð13Þ

3.2. Effects of attack angle and vortex geometry The present experimental results on heat and flow friction characteristics, in a channel equipped with PTVGs and PRVGs, are presented in the form of Nusselt number and friction factor. The Nusselt numbers obtained under turbulent flow conditions for both rectangular and triangular-type vortex generators, with different distances of punched winglet from the channel bottom

0.08

100

Smooth channel Blasius correlation

Smooth channel Dittus-Boelter correlation

80

0.06

fo

Nuo

60

0.04

40

0.02 20

0

0

5000

10000

15000

20000

25000

30000

35000

40000

0.00

45000

0

5000

10000

15000

20000

25000

Re

Re

(a)

(b)

30000

35000

40000

45000

Fig. 3. Verification of: (a) Nusselt number and (b) friction factor for smooth channel.

240

240

220

220

PTVGs, b/e=0.017, α=15o PTVGs, b/e=0.017, α=45o PTVGs, b/e=0.017, α=75o smooth channel

200 180

200 180 160

140

max.55%

Nuavg

Nuavg

160

120

120 100

80

80

60

60

40

40

20

20 0

5000

10000

15000

20000

25000

30000

35000

40000

45000

max. 51.3%

140

100

0

PRVGs, b/e=0.017, α=15o PRVGs, b/e=0.017, α=45o PRVGs, b/e=0.017, α=75o smooth channel

0

0

5000

10000

15000

20000

25000

Re

Re

(a)

(b)

30000

Fig. 4. Nusselt number for varying Reynolds number and b/e = 0.017 (a) triangular VGs (b) rectangular VGs.

35000

40000

45000

609

S. Caliskan / International Journal of Heat and Mass Transfer 78 (2014) 604–614 240

240

220

220

PTVGs, b/e=0.067, α=15o PTVGs, b/e=0.067, α=45o PTVGs, b/e=0.067, α=75o smooth channel

200 180

200 180 160

140

Nuavg

Nuavg

160

max. 51 %

120

140

100

80

80

60

60

40

40

20

20 0

5000

10000

15000

20000

25000

30000

35000

40000

0

45000

max. 49.7 %

120

100

0

PRVGs, b/e=0.067, α=15o PRVGs, b/e=0.067, α=45o PRVGs, b/e=0.067, α=75o smooth channel

0

5000

10000

15000

20000

25000

Re

Re

(a)

(b)

30000

35000

40000

45000

Fig. 5. Nusselt number for varying Reynolds number and b/e = 0.067 (a) triangular VGs (b) rectangular VGs.

240

240

220

220

PTVGs, b/e=0.2, α=15o PTVGs, b/e=0.2, α=45o PTVGs, b/e=0.2, α=75o smooth channel

200 180

200 180 160

140 120

Nuavg

Nuavg

160

max. 47.5 %

140 120

100

100

80

80

60

60

40

40

20

20

0

PRVGs, b/e=0.2, α=15o PRVGs, b/e=0.2, α=45o PRVGs, b/e=0.2, α=75o smooth channel

0

5000

10000

15000

20000

25000

30000

35000

40000

0

45000

max. 45.9 %

0

5000

10000

15000

20000

25000

Re

Re

(a)

(b)

30000

35000

40000

45000

Fig. 6. Nusselt number for varying Reynolds number and b/e = 0.2 (a) triangular VGs (b) rectangular VGs.

240

240

220 200 180

180

160

160

140

140

120

max. 39.2 %

100

120

80

60

60

40

40

20

20 0

5000

10000

15000

20000

25000

30000

35000

40000

45000

max. 37.2 %

100

80

0

PRVGs, b/e=0.33, α=15o PRVGs, b/e=0.33, α=45o PRVGs, b/e=0.33, α=75o smooth channel

200

Nuavg

Nuavg

220

PTVGs, b/e=0.33, α=15o PTVGs, b/e=0.33, α=45o PTVGs, b/e=0.33, α=75o smooth channel

0

0

5000

10000

15000

20000

25000

Re

Re

(a)

(b)

30000

Fig. 7. Nusselt number for varying Reynolds number and b/e = 0.33 (a) triangular VGs (b) rectangular VGs.

35000

40000

45000

610

S. Caliskan / International Journal of Heat and Mass Transfer 78 (2014) 604–614

Re=3288, PTVGs

Re=3288, PRVGs

Re=23676, PT VGs

Re=37817, PTVGs

Re=23676, PRVGs

a=x/Dh=0.5

x/Dh=4.13

Re=37817, PRVGs

x/Dh=0.0 Re=37817, smooth channel

Fig. 8. Temperature contours in the x–y plane for the triangular and rectangular VGs for b/e = 0.017 and a = 45.

(b/e = 0.017, b/e = 0.067, b/e = 0.2 and b/e = 0.33) and attack angle (a = 15, a = 45 and a = 75), are presented in Figs. 4–7. As shown in Figs. 4–7, the use of vortex generators lead to considerable heat

transfer enhancements in a similar trend in comparison with the smooth channel and the Nusselt number values, increase with the rise of the Reynolds number. It is found that the Nusselt num-

611

S. Caliskan / International Journal of Heat and Mass Transfer 78 (2014) 604–614 550

240 220

y/Dh=0.61, PTVGs, b/e=0.017, α=45o

200

y/Dh=0.61, Smooth plate

y/Dh=0.74, PTVGs, b/e=0.017, α=45o

500

y/Dh=0.74, Smooth plate

450

180

400

160

350 300

Nu

Nu

140 120

250

100 200

80

150

60 40

0 -0.5

0.0

0.5

1.0

1.5

100

Re=37817

VGs-position

20

2.0

2.5

3.0

3.5

4.0

0 -0.5

4.5

x/Dh

(a)

Re=37817

50

0.0

0.5

1.0

1.5

2.0

2.5

3.0

3.5

4.0

4.5

x/Dh

(b) 200

550

y/Dh=0.74, PTVGs, b/e=0.017, α=45o

500

smooth plate

y/Dh=0.61

y/Dh=0.74, PRVGs, b/e=0.017, α=45o

450

y/Dh=0.89

Re=37817

150

400

300

Nu

Nu

350

250

100

200 150

50

100

Re=37817

50 0 -0.5

(c)

0.0

0.5

1.0

1.5

2.0

2.5

3.0

3.5

4.0

0 -0.5

4.5

x/Dh

0.0

0.5

1.0

(d)

1.5

2.0

2.5

3.0

3.5

4.0

4.5

x/Dh

Fig. 9. Local Nusselt number distribution for b/e = 0.017 and a = 45.

ber decreases with the rise of the distance between the punched winglet and the channel bottom. This can be explained by strong turbulence intensity in the presence of vortex generators, leading to a rapid mixing between the core and wall flow, especially at a lower b/e ratio. As can be seen, from all the figures, the PTVGs provide a higher heat transfer of coefficients than the PRVGs for all Reynolds number values. This can be attributed to the higher flow blockage, which creates a stronger reverse/recirculation flow from the triangular vortex generators, leading to better mixing between the core and the wall flows. Furthermore, a close examination reveals that for PTVGs, the heat transfer augmentation from the rib with a = 45 is higher than that with a = 75, which provides higher heat transfer than one with a = 15. Similar trends are found for cases using PRVGs. This is because of a strong mixing of the

fluid induced from turbulent flow fluctuation. The maximum averaged Nusselt number were obtained at b/e = 0.067, a = 45 and Re = 37,817 for PTVGs. The maximum difference of the averaged Nusselt number between smooth and PTVGs plates is found to occur at b/e = 0.067, a = 45°, and Re = 37,817, with a value equal to 55%. As shown in Figs. 4–7, averaged Nusselt numbers between smooth and PTVGs plates, depending on b/e and a for Re = 3288 and Re = 37,817 varies between 26.7–38.4% and 39.2–55%, respectively. The averaged Nusselt number values do not change significantly with b/e and a values for a lower Reynolds number. Instead, at higher a Reynolds number (i.e., Re > 11,838), the averaged Nusselt number on the PTVGs and PRVGs arrangements decreases with the increase of b/e. This indicates that the use of different attack angles for lower Reynolds numbers is an inefficient way for heat

S. Caliskan / International Journal of Heat and Mass Transfer 78 (2014) 604–614 2.4

2.4

2.2

2.2

2.0

2.0

1.8

Nua/Nuo

Nua/Nuo

612

1.6 PTVGs, b/e=0.017, α=45o PTVGs, b/e=0.067, α=45o PTVGs, b/e=0.2 α=45o PTVGs, b/e=0.33, α=45o

1.4 1.2 1.0

0

5000

10000

15000

20000

25000

30000

35000

40000

1.8 1.6 PRVGs, b/e=0.017, α=45o PRVGs, b/e=0.067, α=45o PRVGs, b/e=0.2, α=45o PRVGs, b/e=0.33, α=45o

1.4 1.2 1.0

45000

0

5000

10000

15000

20000

Re

25000

30000

35000

40000

45000

35000

40000

45000

Re

(a)

(b)

Fig. 10. Nusselt number ratio Nua/Nuo for varying Reynolds number (a) triangular VGs (b) rectangular VGs.

3.0

3.0 o

PTVGs, b/e=0.017, α=45 PTVGs, b/e=0.067, α=45o PTVGs, b/e=0.2, α=45o PTVGs, b/e=0.33, α=45o

2.5

2.0

fa/fo

fa/fo

2.0

1.5

1.5

1.0

1.0

0.5

0.5

0.0

PRVGs, b/e=0.017, α=45o PRVGs, b/e=0.067, α=45o PRVGs, b/e=0.2, α=45o PRVGs, b/e=0.33, α=45o

2.5

0

5000

10000

15000

20000

25000

30000

35000

40000

45000

0.0

0

5000

10000

15000

20000

25000

Re

Re

(a)

(b)

30000

Fig. 11. Friction factor ratio fa/fo for varying Reynolds number (a) triangular VGs (b) rectangular VGs.

transfer enhancement, compared with the higher Reynolds numbers. From the results mentioned above, it is clear that the distances of punched winglets from the bottom of the channel, attack angle and vortex generator shapes have a significant effect on the averaged heat transfer. Fig. 8 presents the temperature contours for the PTVGs and PRVGs in both the streamwise and the spanwise directions. It is illustrated that the local temperature was high at the beginning of the channel (0 < x/Dh < 0.5) but the local temperature after the vortex generators changed in the streamwise and spanwise direction of the channel. The flow direction was influenced by the punched vortex generators, and at high temperature locations increased cooled air could pass through, which resulted in a decrease of the average temperature. The wall temperatures for the PRVGs were higher than those found in the PTVGs designs, which disrupted the boundary layer more, resulting in a better heat transfer. For the PTVGs, the temperature of the surface is higher and the variation in temperature is greater at a low Reynolds number because the fluid moves more slowly at a low Reynolds number. The temperature in the entrance region (a = x/Dh = 0.5) before PTVGs and PRVGs vortex generators is nearly the same (uniform).

The local Nusselt number distributions were presented in Fig. 9. As shown in Fig. 9, in all of the locations, the local Nusselt number of the PTVGs was higher than for the smooth channel and PRVGs. As shown in Fig. 9a, the Nusselt number of the PTVGs surface and smooth plate were gradually decreased, but after a distance of x/Dh = 0.5, the Nusselt number of the PTVGs surface are gradually increased due to the effect of the vortex generators. However, unlike for the smooth plate, the local Nusselt number increased rapidly along the plate after the first triangular or rectangular VGs. Triangular or rectangular VGs carried cooler fluid from the center of the channel towards the side walls which enhanced the heat transfer. At the channel outlet, the local Nusselt decreased because the vortex structures had weakened near the outlet. The Nusselt number was highest at the channel inlet where the thickness of the boundary layer is zero and decrease gradually, as shown in Fig. 9d. For PRVGs and PTVGs, maximum Nusselt number was obtained at nearly the location of x/Dh = 1.25. Also, at the closest point to the longitudinal winglet (y/Dh = 0.74), the maximum Nusselt number values along the winglet were obtained at x/ Dh = 1.25. In the Fig. 10a and b, the relation of Nua/Nuo is shown, and the Reynolds number for the four distances of punched winglet from

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240 PTVGs, b/e=0.017, α=45o PRVGs, b/e=0.017, α=45o PTVGs, b/e=0.33, α=45o PRVGs, b/e=0.33, α=45o

3.0

-1/3

Observed value (Nu)

2.5

(Nua/Nuo)/(fa/fo)

R 2 = 0.985

200

2.0

1.5

1.0

160

± 10%

120

80

40

0.5

0.0 0

5000

10000

15000

20000

25000

30000

35000

40000

0

45000

0

40

Re

the channel bottom (b/e) of 0.017, b/e = 0.067, b/e = 0.2 and b/e = 0.33, and also constant attack angle (a) of 45° in the PTVGs and PRVGs, respectively. It can be seen that Nua/Nuo of the channel with both PTVGs and PRVGs decreased as the b/e values increased. For the distance of punched winglet from the channel bottom (b/e) of 0.017, it showed the highest averaged Nusselt number for all of the b/e values. The shorter distance of the punched winglet from the channel bottom makes disturbance at the boundary layer more effectively and provides a better air flow mix. Hence, the heat transfer is enhanced. Under the same conditions, the heat transfer enhancement from the triangular vortex generator was more significant than that of the rectangular vortex generator. For the PRVGs, at the optimum dimensionless distance of b/e = 0.017, the Nusselt number ratio varied from 1.84 to 2.16 (with Re decreasing from 37,817 to 3288). For the PTVGs, the highest Nua/Nuo values (from 1.84 to 2.28, as Re is decreased from 37,817 to 3288) were achieved for b/e = 0.017. Variations of the ratio friction factor, f, vs. the Reynolds number for both triangular and rectangular vortex generators are shown in Fig. 11a and b, respectively. The friction factor found from using the vortex generators was observed to be higher than that from the smooth duct for all cases studied, as expected due to the suppression of the viscous sub-layer. This can be attributed to flow blockage and the act caused by the reverse flow due to the presence of the vortex generators. Therefore, the highest values of friction factor were observed for the smallest distance the punched winglet from the channel bottom ratio, or b/e = 0.017. The friction factor values of the vortex generators duct with b/e = 0.017 were higher than those with b/e = 0.067, b/e = 0.2 and b/e = 0.33, respectively. The friction factors for the channel with rectangular vortex generators were much larger than the triangular vortex generators. It can also be seen from Fig. 11a and b that the increase in the friction factor was due to both rectangular and triangular vortex generators at a higher Reynolds number was more significant than that of the low Reynolds number. The increase in the friction factor of the PTVGs and PRVGs was in a range of 0.18–1.95 over the smooth channel, depending on the b/e and Reynolds number values. Fig. 12 shows the variation in the thermal enhancement factor (g) with the Reynolds number for both triangular and rectangular vortex generators. Nusselt number and friction factor values were compared at an equal pumping power. It can be seen in this figure that the enhancement factors (g) are above unity for all the vortex generators. The enhancement factor tended to decrease with the rise in the Reynolds number values for all vortex generators. As shown in Fig. 12, enhancement factors (g) between PTVGs and

120

160

200

240

Predicted value (Nu) Fig. 13. Variation of the observed and predicted values of the averaged Nusselt numbers for triangular VGs.

PRVGs, for the lowest Reynolds number, varied between 2.92– 2.67 and 2.90–2.46, respectively. It is worth noting that the enhancement factors (g) of the PTVGs were higher than those with the PRVGs for all Reynolds number values. This indicated that the use of PTVGs leads to the advantage over that of PRVGs. The enhancement factor (g) of the PTVGs was found to be the best   1=3 Nu f for the PTVGs and PRVGs designs and was about 2.92. Nu f0 0 shown in Fig. 12 show that the b/e = 0.017 PTVGs are the best, while the b/e = 0.33 PRVGs have the worst performance. A correlation between the averaged Nusselt numbers was dependent on Reynolds number, the attack angle (a), and the distance of the punched winglet from the channel bottom to the longitudinal winglet height ratio (b/e) were obtained by a regression analysis. The statistical software program STATISTICA 5.0 was used for this analysis. A nonlinear estimation code was taken into consideration. The correlations derived from both the triangular and rectangular vortex generators are given in Eqs. (17) and (18), respectively. In the experiment, the values of the Nusselt numbers, shown in Figs. 13 and 14, respectively, were both observed and predicted. As can be seen, for PTVGs, PRVGs, and the Nusselt number, the regression coefficients of these correlations were 98.5% and 99.0%, respectively.

200

R 2 = 0.99 160 Observed value (Nu)

Fig. 12. Thermal enhancement factor g for varying Reynolds number.

80

± 10% 120

80

40

0 0

40

80

120

160

200

240

Predicted value (Nu) Fig. 14. Variation of the observed and predicted values of the averaged Nusselt numbers for rectangular VGs.

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S. Caliskan / International Journal of Heat and Mass Transfer 78 (2014) 604–614

NuPTVGs ¼ 0:074ðReÞ0:74 ðb=eÞ

1:148

ð1 þ cos aÞ0:013

ð17Þ

1:232

ð1 þ cos aÞ0:058

ð18Þ

NuPRVGs ¼ 0:068ðReÞ0:76 ðb=eÞ 4. Conclusions

An experimental investigation of both heat transfer and pressure loss characteristics in a rectangular duct with PTVGs and PRVGs under uniform heat flux conditions have been performed. The following conclusions have been drawn:  Both PTVGs and PRVGs arrangements had significantly enhanced the heat transfer rate, in comparison to a smooth duct. The averaged heat transferred from surfaces with PTVGs was higher than that of the PRVGs. The disturbance in the boundary layer was formed due to punched holes, which created higher turbulence due to the separated and reattached flows. Therefore, the geometric shapes of the punched hole could be one of the significant factors.  Both PTVGs and PRVGs with the distance of the punched winglet from the channel bottom (b/e) of 0.017, always provided the better, more effective heat transfer enhancement, the next is that with b/e of 0.067, and then, 0.2 and 0.3, in that order.  At low Reynolds number the effects of attack angles and the distance to the punched winglet from the bottom of the channel on both the heat transfer and the behaviors of the friction factor are insignificant.  The enhancement factor (g) between the PTVGs and the PRVGs, for the lowest Reynolds number, varies between 2.92–2.67, and also 2.90–2.46, respectively. The enhancement factor (g) of the PTVGs was found to be the best and was about 2.92.  A correlation was developed for the averaged Nusselt number. The averaged Nusselt number obtained from the correlation agreed within ±10.0% of the experimental data. Conflict of interest None declared. Acknowledgement The present work is financially supported by the Hitit University (Grant No. MUH01.13.010). References [1] D.D. Luo, C.W. Leung, T.L. Chan, W.O. Wong, Simulation of turbulent flow and forced convection in a triangular duct with internal ribbed surfaces, Numer. Heat Transfer A: Appl. 48 (2005) 447–459. [2] C.K. Lee, S.A. Abdel-Moneim, Computational analysis of heat transfer in turbulent flow past a horizontal surface with two-dimensional ribs, Int. Commun. Heat Mass Transfer 28 (2001) 161–170. [3] K.Y. Kim, Y.M. Lee, Design optimization of internal cooling passage with v-shaped ribs, Numer. Heat Transfer A: Appl. 51 (2007) 1103–1118. [4] G. Tanda, Heat transfer in rectangular channels with transverse and V-shaped broken ribs, Int. J. Heat Mass Transfer 47 (2004) 229–243. [5] S. Eiamsa-ard, P. Promvonge, Thermal characteristics of turbulent rib-grooved channel flows, Int. Commun. Heat Mass Transfer 36 (2009) 705–711. [6] S. Eiamsa-ard, P. Promvonge, Numerical study on heat transfer of turbulent channel flow over periodic grooves, Int. Commun. Heat Mass Transfer 35 (2008) 844–852. [7] H. Wee, Q. Zhang, P.M. Ligrani, S. Narasimhan, Numerical predictions of heat transfer and flow characteristics of heat sinks with ribbed and dimpled surfaces in laminar flow, Numer. Heat Transfer A: Appl. 5 (2008) 1156–1175.

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