Heat transfer enhancement of wavy finned flat tube by punched longitudinal vortex generators

International Journal of Heat and Mass Transfer 75 (2014) 368–380

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

Heat transfer enhancement of wavy finned flat tube by punched longitudinal vortex generators Xiaoze Du ⇑, Lili Feng, Li Li, Lijun Yang, Yongping Yang Key Laboratory of Condition Monitoring and Control for Power Plant Equipment, North China Electric Power University, Ministry of Education, Beijing 102206, China

a r t i c l e

i n f o

Article history: Received 16 May 2012 Received in revised form 4 December 2013 Accepted 31 March 2014

Keywords: Heat transfer enhancement Wavy finned flat tube Longitudinal vortex generators

a b s t r a c t Punched longitudinal vortex generators (LVGs) were employed to enhance air-side heat transfer on the wavy fin surface of flat tube used in direct air-cooled condenser. The heat transfer enhancement of four types of the longitudinal vortex generators with different attack angles were compared by numerical simulations. It was found that the delta winglet pair with attack angle 25° could reach the greatest performance evaluation criteria (PEC) under the conditions of the inlet air flow velocity varied from 1 m/s to 5 m/s. The influences of locations on the wavy fin surface and the row number of the longitudinal vortex generators were also discussed. One delta winglet pairs at the middle of the wavy fin surface and the minimum row number, n = 1, with the average PEC is 1.23, has the best heat transfer performance of all conditions, which can be recommended for practical applications. Experimental study in wind tunnel with flow field visualization by Particle Image Velocimetry (PIV), as well as the numerical simulations verified that the delta winglet pairs can generate obvious longitudinal vortex pairs at the down-sweep zone, which can enhance the heat transfer between the cooling air flow and heated wall surface with acceptable pressure loss. Ó 2014 Elsevier Ltd. All rights reserved.

1. Introduction Air-cooled condensers (ACCs) with obvious water conservation benefit can be an important alternative for power plant near coal mines where water source is of shortage. In direct air-cooled condensers of power generating units, the ambient air replaces water as cooling medium. In order to enhance the air-side heat transfer, different types of fin-tube bundles often serve as the fundamental components of ACCs. Among them, the flat tube with wavy fin is typically used for the single-row fin-tube bundle of ACCs recently because of its simple configuration and hence the low production cost, which is essential for the application in large scale direct air-cooled power generating unit. As shown in Fig. 1, the wavy fins form many long narrow channels along the long axis of flat tube, in which the latent heat of the exhaust steam condensation inside tube is taken away by air flow. Longitudinal vortex generators (LVGs) punched or mounted on heat transfer surface have been studied extensively due to their high heat transfer performance and the acceptable pressure drop penalty [1]. A lot of investigations were mainly focused on circular-tube-fin and oval-tube-fin with mounted and punched ⇑ Corresponding author. Tel.: +86 (10)51971326; fax: +86 (10)51971328. E-mail address: [email protected] (X. Du). http://dx.doi.org/10.1016/j.ijheatmasstransfer.2014.03.081 0017-9310/Ó 2014 Elsevier Ltd. All rights reserved.

longitudinal vortex generators to enhance the heat transfer [2–15]. Kundu and Barman [16] studied a cross-flow heat recovery-exchanger system operating with unmixed fluids. They obtained the variation of the effectiveness with the number of transfer unit of heat recovery unit. Chang et al. [17,18] studied the heat transfer enhancement in a channel formed by flat tube bank fin with vortex generators. Eibeck et al. [2] found the longitudinal vortices mounted in the turbulent boundary layer have a significant influence on heat transfer enhancement by experiments. Gentry and Jacobi [19,20] experimentally showed that the average heat and mass transfer could be enhanced by 50–60% at low Reynolds number in comparison with the original configuration, using a naphthalene sublimation technique, heat transfer enhancement characteristics of delta wing vortex generators in a flat-plate flow. Zhu et al. [21] obtained that both heat transfer and flow loss increase with Re in a smooth channel with vortex generators in a rectangular channel with rectangular winglets as longitudinal vortex generators on one wall by the k–e model. However, the increase in heat transfer is nearly linear, whereas the increase in flow loss is much faster. Fiebig [22] explored that longitudinal vortex generators generate higher heat transfer enhancement for the same pressure penalty than transverse vortex generators in detail a base configuration with embedded rectangular vortex generators in internal flow. Other researchers compared

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Nomenclature A a B b cp De f H h l _ m Nu n P p Q Re S sf T

major axial length of flat tube, m distance between longitudinal vortex generators, m minor axial length of flat tube, m distance between center of longitudinal vortex generator and flat tube, m specific heat, Jkg1K1 hydraulic diameter, m friction factor fin height, m winglet pair height, m; surface heat transfer coefficient, Wm2K1 chord length of winglet pairs, m mass flow rate, kgs1 Nusselt number row number of longitudinal vortex generator pressure, Pa spacing of winglet pairs, m heat flow, W Reynolds number area, m2 fin spacing, m temperature, K

the heat transfer enhancement of different configurations of vortex generators in a narrow rectangular channel experimentally [23,24]. Several researches experimentally studied the longitudinal vortices using particle image velocimetry (PIV) system [25,26]. Literature reviews found that there were few reports regarding heat transfer characteristics of the wavy finned flat tube in direct air-cooled condensers of power plant [27,28]. In the present study, the heat transfer enhancement of the wavy finned flat tube for single row condensers (SRC) with punched longitudinal vortex generators was explored by numerical simulation with experimental verification. The influences of different types of longitudinal vortex generators on air-side heat transfer enhancement were investigated in detail. 2. Physical and mathematic model 2.1. Physical model As shown in Fig. 2, four basic types of longitudinal vortex generators in modeling finned passages were employed, which were (1)

u,v,w W x,y,z

velocity components, ms1 fin length, m Cartesian coordinates

Greek symbols b the angle of attack, ° l dynamic viscosity, Pas m kinematic viscosity, m2s1 q density, kgm3 k thermal conductivity, Wm1K1 d thickness, m g fin efficiency Subscripts 0 value without longitudinal vortex generator exp experimental data f wavy fin in inlet m mean out outlet t flat tube

delta wing, (2) rectangular wing, (3) delta winglet pairs and (4) rectangular winglet pairs. A complete elementary model that involves the flat tube and wavy fins with longitudinal vortex generator is illustrated in Fig. 3. The dimension of the flat tube and wavy fins is shown in Fig. 3(a). To make the geometric model simplified, the rectangular wavy fins replace the real wavy fins, and are placed on both sides of the flat tube. The simplified fin is illustrated in the Fig. 3(b). The region occupied by dashed lines in Fig. 3(b) is selected as the computational domain. The longitudinal vortex generators are punched out of the wavy fin surface in the computational domain. The delta wing as example punched out of the fin surface is shown in Fig. 3(c). The simulated domain and boundary conditions are illustrated in Fig. 3(c) as well. A fixed area involving four various types of longitudinal vortex generators is studied: the delta wing of chord length h = l = 2sf, the rectangular wing of chord length h = sf and l = 2sf, the delta winglet pairs of height h = 0.5sf, winglet pairs pitch p = 0.5sf, and chord length l = 4sf, and the rectangular winglet pairs of height h = 0.5sf, winglet pairs pitch p = 0.5sf, and chord length l = 2sf, respectively. Due to the symmetric arrangement of the wavy finned flat tube, only half part of the fin tube is taken as physical model with periodic boundary conditions along the direction of the flat tube length. 2.2. Governing equations

Fig. 1. The wavy finned flat tube used in direct air-cooled condensers.

The fluid is considered incompressible with constant properties. Due to the low inlet velocity and the small fin pitch, the air flow in the fin channel is assumed to be steady. In order to maintain a uniform inlet velocity and ensure a recirculation-free at outlet, the import region and the export region of the physical model are extended. The temperature of the flat tube is given as the constant wall temperature boundary condition. Fin thickness and heat conduction in the fins and LVGs are taken into account. The temperature distribution for the fins can be determined by solving the conjugate heat transfer problem in the computational domain. In order to make the surface of fin top contact with the air, a distance of 1 mm is extended from the top of fin to the computational domain.

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h

β

l

h

β

β

l

p

h

β

h

l p

l

Fig. 2. Schematic diagram of four types of longitudinal vortex generators [3].

The airflow is governed by the continuity equation, the momentum equation and the energy equation.

@

@ ui ¼ 0; @xi

ði ¼ 1; 2; 3Þ

ð1Þ

where, ui is the xi components of velocity; the value of i is the x, y and z direction, respectively.

  @ðui uj Þ 1 @p @ @u ¼ þ g i  ui uj ; @xj q @xi @xj @uj

ði; j ¼ 1; 2; 3 and i–jÞ

ð2Þ

where, p is the xi components of pressure, q is the fluid density; g is the dynamic viscosity of the fluid.

qcp

  @ðui TÞ @ keff @T ði ¼ 1; 2; 3Þ ¼ @xi @xi @xi

ð3Þ

where, cp is the specific heat; keff is the effective heat transfer coefficient.In consideration of the fin thickness in the calculation, the equation of heat conduction within the fin is as follows:

  @ @t ¼ 0; @xi @xi

ð4Þ

where, t is the fin thickness. For the entrance of the boundary condition,

x ¼ 0;

u ¼ uin ¼ const; T ¼ T in ¼ 290K ¼ const;

v¼w

¼ 0 ðuin ¼ 1; 2; 3; 4; 5m=sÞ

ð5Þ

at the exit boundary condition,

x ¼ A þ 0:18;

@u @ v @w @T ¼ ¼ ¼ ¼0 @x @x @x @x

ð6Þ

of which, a length of 0.18 m was extended for the export region of the physical model to avoid the boundary effects on the results.and at the flat tube wall,

u ¼ v ¼ w ¼ 0;

T ¼ T t ¼ const

ð7Þ

for the symmetry condition of top and bottom boundaries at y coordinate direction,

y ¼ 0 and y ¼ B=2 þ H þ 0:001; ¼ 0;

v ¼ 0;

ð8Þ

and for the no-pressure-drop periodic boundary at the side boundaries of z coordinate direction, as well as impermeable, non-slip boundary condition for flat tube wall and the fin surface,

z ¼ 0 and z ¼ 2sf ;

u ¼ v ¼ w ¼ 0;

@T ¼ 0; @z

@P ¼0 @z

@ @ ðqkui Þ ¼ @xi @xj @ @ ðqeui Þ ¼ @xi @xj









gþ

lt @k þ Gk  qe; rk @xj

gþ

lt @ e e e2 þ C 1e Gk  C 2e q ; re @xj k k



ð10Þ



ð11Þ

2

where, the turbulent viscosity, lt ¼ C l q ke , Gk represents the generation of turbulence kine-tic energy because the mean velocity gra@u dients, Gk ¼ qu0i u0j @xj ; rk and re are the turbulent Prandtl numbers i for k and e, respectively. cu, c1e and c2e are constants. The parameters of low Re k–e model are listed in Table 2. 2.4. Parameter definitions

@u @w ¼ @y @y

@T ¼0 @y

Finite volume method using a SIMPLEC-based solution algorithm of the velocity–pressure coupling is applied with a segregated solver. The momentum and energy equations are solved by the second order upwind scheme. The standard k–e model, low Re k–e model, RNG k–e model, and laminar model are used as turbulent models for comparison. Table 1 shows the obtained air-side surface heat transfer coefficients, h, of the typical wavy finned flat tube without longitudinal vortex generators punched used in direct air-cooled condenser with different models. The low-Re k–e model is selected because of which the simulating result of h approximates most to the actual value 31.1 W/(m2K) under the design operating condition provided by the manufacturer. In turbulent convective heat transfer, the change of speed and temperature at near wall region are the largest. Therefore, it is important for the simulation of the near wall region in the turbulence simulation. For the present model that the air flows in small fin spacing of about 2.8 mm, the accurate simulation of the fin boundary layer is particularly important. In general, the method of wall functions in accordance with the law of the logarithm was used near wall in the stand k–e model, which is a rough calculation of the small spacing. Therefore the low Re k– e model was employed in near wall region, in which the viscous sublayer of the near wall region was calculated. For the low Re k–e model [29], the transport equations of turbulence kinetic energy, k, and dissipation rate, e, are followed by,

ð9Þ

The heat transfer coefficient, h, of the air-side fin-tube surface is calculated as follows,

h¼

Q S  DT m

ð12Þ

_ p ðT out  T in Þ, the where, Q is the air-side heat transfer rate, Q ¼ mc heat transferring surface is consist of Sf and St, but, S is the total area of the flat tube and effective wavy fins, S ¼ St þ gf Sf , of which, Sf is all fin surface that make contact with air; St is the flat tube surface without considering the fin surface which contact with the flat tube,

2.3. Numerical simulation

T a gf ¼ TTft T is the fin efficiency with T a ¼ 12 ðT in þ T out Þ, and DTm is loga

The mathematical model of the turbulent flow through the wavy finned flat tube is solved using FLUENT-6.2 CFD program.

arithmic mean temperature difference, DT m ¼

ðT t T inÞðT t T  out Þ ln

T t T in T t T out

.

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(a)

(b)

(c) Fig. 3. Physical model. (a) Geometry size of the wavy finned flat tube; (b) schematic diagram of computational domain; (c) simplified structure and computational region of model with punched one delta wing as example.

It is worthwhile to mention that a performance evaluation plot has been proposed [30] as the performance evaluation of heat transfer devices recently, which is suitable to evaluate energy saving effect of wavy fin surfaces of flat tube with LVGs investigated. However, in the present study, the performance evaluation criteria [31] of wavy-fin flat-tube with the longitudinal vortex generator is defined as,

 PEC ¼

Nu Nu0

 13 f f0

ð13Þ

where, Nu0 is Nusselt number of basic tube that the wavy finned flat tube without longitudinal vortex generators, Nu ¼ hDk e is Nusselt number of the wavy finned flat tube with longitudinal vortex generators, f0 is friction factor of basic tube that the wavy finned flat e tube without longitudinal vortex generators, f ¼ 2qDuPD 2 L is friction facin

tor of the wavy finned flat tube with longitudinal vortex generators, of which, the pressure drop DP, is calculated as, DP ¼ Pin  Pout . As the criteria of comparison, the uniform inlet air flow velocity, uin, and hydraulic diameter of inlet section, De, are defined for all types

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Table 1 Values of turbulence model verifications at uin = 1.8 m/s. Numerical calculation model

Surface heat transfer coefficient of airside, h (W/m2 K)

Stand k–e model Low Re k–e- model RNG k–e model Laminar model Design value at power plant (comparative standard)

49.72 38.9 22.36 22.46 31.1

Table 2 Parameters of low Re k–e model. cu

c1e

c2e

rk

re

rT

0.09

1.44

1.92

1.0

1.3

1.0

4ðB=2þHþ0:001Þs

f of fins discussed, De ¼ ð2s þB=2þHþ0:001Þ . The air-side Reynolds number f

is expressed as, Re ¼ uinmDe ; of which, m is the kinetic viscosity of air flow.

3. Experimental setup and test system The plates as the simplified fins with punched delta winglet pairs were adopted and inserted into a wind tunnel. In order to enhance spatial resolution of the experimental measurements, the test model was scaled up. The original steel flat tube, of long axis, A = 220 mm, short axis, B = 20 mm. Two neighboring fins form a channel of height, H = 19 mm, fin spacing, sf = 2.8 mm, and length, W = 190 mm. The fin material is aluminum and the fin thickness, df = 0.35 mm. The test model was located at the test section of wind tunnel. A wind tunnel experimental setup and related apparatus are shown in Fig. 4 schematically. The wind tunnel experimental system consists of entrance section, honeycomb, settling section, contraction section, test section, diffuser section and exhaust axial fan. Air flow is driven by a variable speed fan and passes through the

test section of the channel. The entrance section, honeycomb, settling section and contraction section of wind tunnel assure the smooth, streamline air flow into the test section. The flow field between the fins with delta winglet pairs and three-fin floors inserted in the test section was obtained by the CCD camera shooting the laser beam. The laser beam is generated by the Nd–Yag laser controlled by the computer and supply power. The visualization of the test section allows visible observation of the air flow field. In this work, fins with delta winglet pairs were arranged in the wind tunnel where the air was inhaled by an exhaust fan installed in the end. The test section of the wind tunnel was 47 mm wide, 30 mm high and 560 mm long. The field measurement technique, Particle Image Velocimetry (PIV) was employed to measure the flow fields between two plate fins with and without punched delta winglet pair. The tested plate fins were painted with black preventing reflections of laser. The tested plate fins were scaled as the full size, of which, p W exp H h ¼ Hexp ¼ exp ¼ exp ¼ 2:5, the delta winglet pairs attack angle W h p was b = 45°, and the uniform inlet velocity uin = 5 m/s. The air velocity was measured by a hotwire anemometer with the precision of ±2%. The PIV system manages to offer clearer and sharper images, which allows the particles are identified. In this experiment, incense mixed with air is inhaled into the wind tunnel. Then, two pictures are taken by the charge coupled device camera (CCD camera) in short time whose magnitude is lm. The photos are analyzed by the software named INSIGHT 3G™, which could get the correlation of the same particles in two pictures and produce an instantaneous velocity vector map. There are two Nd–Yag laser sources, from which the laser is inspired and the time delay between two pulses is 5 ls. Pairs of raw images are correlated using 64  64 pixels interrogation windows, and the overlap ratio between adjacent windows is 50%. The synchronizer is used to synchronize the camera and laser sources. More details of the experiments can refer to literature [32]. 4. Results with discussions In order to validate the independency of solution on the grid, three different grid systems are investigated, which include about 290,000, 550,000, and 1,030,000 cells, respectively for a wavy

10

9 1

2

3

4

5

6

7

8

13

11

12

14

1-Inlet; 2-Honeycomb; 3-Stable section; 4-Contraction section; 5-Test section; 6-Diffuser section; 7-Outlet; 8-Exhaust fan; 9-Hotwire anemometer; 10-CCD camera; 11-Computer; 12-Synchronizer; 13-Nd-Yag laser; 14-Power supply. Fig. 4. Schematic diagram of the experimental setup.

h,W/(m2K)

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373

vortex generators generates the down-sweep zone. The longitudinal vortex generators develop streamwise longitudinal vortices, which delay the boundary-layer separation from the fin, accelerate the local flow velocity, intensify the mixing between cold fluid and hot fluid, reduce the fin surface temperature and thus enhance heat transfer. The influences of different forms of longitudinal vortex generators on the heat transfer characteristics and flow fields for the wavy finned flat tube were investigated in further. The different forms of longitudinal vortex generators were punched at the geometric center of the fin surface. The attack angle b was set from 10° to 25°. The inlet velocity varied from 1 m/s to 5 m/s.

50 48 46 Re=596 Re=1200 44 Re=2418 42 40 38 36 34 32 30 28 200000 400000 600000 800000 1000000

Grid number

4.1. Influence of different forms of longitudinal vortex generators

Fig. 5. Variation of the air-side surface heat transfer coefficient with grid number.

Fig. 7 shows, respectively the relations between the air-side surface heat transfer coefficients, h, the pressure drop, DP, and the inlet velocity, uin, under different attack angles, b. It is showed that the air-side surface heat transfer coefficient and pressure drop for the wavy finned flat tube increase with the inlet velocity. Depending on design parameters, the average air-side surface heat transfer coefficient can be enhanced by 12.7%–45.4% in comparison with the wavy finned flat tube without longitudinal vortex generators, with increase by 5.4%–44.7% in average pressure drop. Generally meaning, h increases with increasing attack angle b. Fig. 7(c) displays the variation of the performance evaluation criteria, PEC, with the attack angle b under different Re number. The average PEC value reaches 1.17 and it is indicated that PEC is greater than 1 under various conditions, implying the potential of heat transfer enhancement by the delta wing. The variations of heat and flow characteristics of the wavy finned flat tube with one rectangular wing in the middle of the fin are similar to the wavy finned flat tube with one delta wing. Fig. 8(a) and (b) show the variations of air-side surface heat transfer coefficient, h, and pressure drop, DP, with the inlet velocity, uin, under different attack angles, b. It can be seen that both air-side surface heat transfer coefficient h and pressure drop DP for the wavy finned flat tube increase with the inlet velocity, but there is few increase with attack angle. As a result, the average air-side

finned flat tube without longitudinal vortex generators with computational fluid dynamics (CFD) simulations. The variation of the air-side heat transfer coefficient h with three different grid numbers of the wavy finned flat tube without longitudinal vortex generators is illustrated in Fig. 5. From the figure we can see that the change of the air-side heat transfer coefficient h is less than 5% among the three different grid systems. For the present study, the final grid number is selected as about 550,000. Similar validations are also conducted for other cases. The investigation was performed firstly regarding the wavy finned flat tube without longitudinal vortex generator on the heat transfer and flow characteristics. Fig. 6 shows the temperature distribution for the fin without longitudinal vortex generators and with one delta winglet pairs at uin = 2 m/s, respectively. Fig. 6(a) shows the temperature distribution for the fin without longitudinal vortex generators at uin = 2 m/s. It can be seen that the temperature at the leading of fin is lower than that of the other regions, which have a poor heat transfer. As a comparison, the low temperature region extends obviously on the fin surface with one delta winglet pairs as shown in Fig. 6(b), indicating the improvement of heat transfer performance. The fluid flow after the longitudinal

(a)

(b) Fig. 6. Numerical results of temperature distributions of the fin surface at uin = 2 m/s. (a) Fin without longitudinal vortex generators; (b) fin with one delta winglet pairs.

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100

80

uin=3m/s

100

uin=2m/s

uin=4m/s

90

uin=5m/s h , W/ m2K

h, W/(m 2K)

90

uin=1m/s

70 60 50

uin=2m/s

uin=4m/s

uin=5m/s

70 60 50 40

40 30

80

uin=1m/s uin=3m/s

30 non LVG

10

15

20

non LVG 10

25

β, deg

15 β , deg

20

25

(a)

(a) 140

120

P, Pa

100

uin=1m/s uin=2m/s uin=3m/s uin=4m/s uin=5m/s

80

120 100

P, Pa

140

40

20

20

0 10

15

β , deg

20

PEC

15 β , deg

20

25

1.7 1.6

Re=1200 Re=2418

1.4

Re=596 Re=1200 Re=1810 Re=2418 Re=3024

1.5

PEC

1.5

uin=5m/s

(b)

1.7

Re=596 Re=1810 Re=3024

non LVG 10

25

(b)

1.6

uin=4m/s

60 40

non LVG

uin=3m/s

uin=2m/s

80

60

0

uin=1m/s

1.4 1.3 1.2

1.3 1.1 1.2 1.0 1.1 1.0

10

15

20

β , deg

25

(c) Fig. 7. Influence of a delta wing on heat transfer performances with different attack angles. (a) Surface heat transfer coefficient; (b) pressure drop; (c) performance evaluation criteria.

surface heat transfer coefficient can be enhanced by 12.4%–54.5% in comparison with the wavy finned flat tube without longitudinal vortex generators, with increase by 5.4%–46.9% in average pressure drop. The comprehensive heat transfer enhancement with one rectangular wing is also illustrated in Fig. 8(c), of which, the performance evaluation criteria, PEC > 1 in most cases, especially for the low Reynolds number. The average PEC value reaches 1.18. The simulating results of the wavy finned flat tube with one delta winglet pair are illustrated in Fig. 9. We can obtain that the air-side surface heat transfer coefficient h and pressure drop DP for the wavy finned flat tube increase with the inlet velocity.

10

15 20 β , deg

25

(c) Fig. 8. Influence of a rectangular wing on heat transfer performances with different attack angles. (a) Surface heat transfer coefficient; (b) pressure drop; (c) performance evaluation criteria.

Depending on design parameters, the average air-side surface heat transfer coefficient h can be enhanced by 13.5%–61.2% in comparison with the wavy finned flat tube without longitudinal vortex generators. In the meantime, the average pressure drop increase by 5.6%–46.2% under different conditions. The additional pressure loss penalty results from the form drag of the delta winglet pairs. The air-side surface heat transfer coefficient, h, descends with range of attack angle from 10° to 20°, then, increases from 20° to 25°. The performance evaluation criteria PEC versus the attack angle b for the different Re number is illustrated in Fig. 9(c). The average PEC value reaches 1.2. The simulating results of the wavy finned flat tube with one rectangular winglet pair are illustrated in Fig. 10. Similar to that

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100

80

uin=3m/s

uin=2m/s

uin=4m/s

70 60 50

uin=3m/s

80

uin=4m/s

60 50

30 non LVG

140

10

15 β , deg

20

25

non LVG 10

15 β , deg

uin=1m/s uin=3m/s

140

uin=2m/s

uin=4m/s

uin=5m/s

120 100

80 60

20

20 0 10

15 β , deg

20

uin=1m/s uin=3m/s

25

non LVG 10

15 β , deg

Re=596 Re=1200 Re=1810 Re=2418 Re=3024

1.5

1.5

1.4

1.4

1.3

1.3

1.2

1.2

1.1

1.1 1.0 10

15

20

25

β , deg

(c)

Re=596

1.6

PEC

PEC

20

25

1.7

1.7

1.0

uin=5m/s

(b)

(b)

1.6

uin=2m/s

uin=4m/s

60 40

non LV G

25

80

40

0

20

(a)

P, Pa

P, Pa

100

uin=5m/s

70

(a)

120

uin=2m/s

40

40 30

uin=1m/s

90

uin=5m/s

h, W/ m2K

h , W/ m2K

90

100 uin=1m/s

Re=1810

10

Re=1200 Re=2418

15

β , deg

20

Re=3024

25

(c)

Fig. 9. Influence of a delta winglet pairs on heat transfer performances with different attack angles. (a) Surface heat transfer coefficient; (b) pressure drop; (c) performance evaluation criteria.

Fig. 10. Influence of a rectangular winglet pairs on heat transfer performances with different attack angles. (a) Surface heat transfer coefficient; (b) pressure drop; (c) performance evaluation criteria.

of the delta winglet pair, we can obtain that the average air-side surface heat transfer coefficient is enhanced by 13.5%–47.4% in comparison with that of the wavy finned flat tube without longitudinal vortex generators. The average pressure drop increments vary among 4.9%–47.1% under different conditions. The performance evaluation criteria PEC with the attack angle b for the different Re number is illustrated in Fig. 10(c), of which, the performance evaluation criteria, PEC > 1. The average PEC value reaches 1.19. The results indicate that the punched longitudinal vortex generators can obviously enhance the heat transfer with relatively less pressure loss penalty. The average PEC of the rectangular winglet pair and the delta winglet pair, 1.19 and 1.2, are superior to the

delta wing and the rectangular wing, 1.17 and 1.18. The results of Fiebig [1] also shows that winglets are superior to wing, but winglet form is of minor important. According to the above analysis, the average PEC of the delta winglet pairs with b = 25° is 1.2, which has the best heat transfer and flow characteristics under all heat transfer conditions discussed. This structure is selected for the further investigations. 4.2. Influence of locations of delta winglet pairs To consider the influence of locations of the delta winglet pairs on heat transfer and flow characteristics, different placement

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positions of the delta winglet pairs at attack angle of 25° were punched in the front part, middle part and rear part in fin surface relative to the air flow direction, respectively, of which, (a) front part, a = 1/6 W, (b) rear part, a = 5/6 W, and also, in the middle part of the wavy fin at (c) a = ½ W. Fig. 11 shows, respectively the variations of air-side surface heat transfer coefficient, h, and pressure drop, DP with inlet velocity, uin under different locations of the delta winglet pairs. The average air-side surface heat transfer coefficient in turn can be enhanced by 27.1% (front part), 28% (middle part) and 25.8% (rear part) in comparison with the wavy finned flat tube without longitudinal vortex generators under different placements, as well as the pressure drop in turn increases by 23% (front

part), 23.1% (middle part) and 21.8% (rear part) in average, respectively. Fig. 11(c) illustrates the variations of the performance evaluation criteria PEC with placements of the delta winglet pairs under different Re numbers. Respectively, for front part, middle

100 90

uin=3m/s

uin=2m/s

uin=4m/s

uin=5m/s

Fig. 12. Configurations for the wavy finned flat tube with multi delta winglet pairs (b = 25°).

70 100

60

non LVG

front middle position

rear

(a)

P, Pa

100

uin=1m/s uin=3m/s

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70 60 50 40 30 non LVG1

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50 h , W/ m2K

h , W/ m2K

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80

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P, Pa

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40

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(b)

0 non LVG 1

2

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1.7 1.6

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(b) Re=596 Re=1200 Re=1810 Re=2418 Re=3024

1.4 1.3 1.2 1.1 1.0

4

2.0 1.9 1.8 1.7 1.6 1.5 1.4 1.3 1.2 1.1 1.0

Re=596 Re=1200 Re=1810 Re=2418 Re=3024

PEC

PEC

1.5

n

front

middle position

rear

(c) Fig. 11. Influence of locations of a delta winglet pairs on heat transfer performances (b = 25°). (a) Surface heat transfer coefficient; (b) pressure drop; (c) performance evaluation criteria.

1

2

3

4

n

5

6

7

(c) Fig. 13. Influences of rows of delta winglet pairs on heat transfer performances (b = 25°). (a) Surface heat transfer coefficient; (b) pressure drop; (c) performance evaluation criteria.

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(a)

(b) Fig. 14. Flow and heat transfer characteristics with multi delta winglet pairs punched on the fin surface (z = 1/2sf, b = 25°, n = 6, at uin = 2 m/s). (a) Temperature distribution; (b) velocity vector distribution.

part and rear part, the average PEC are of 1.18, 1.19, and 1.17. It can be shown that PEC of the delta winglet pairs punched in the middle part of the fin surface is greater than that in the front part or rear part of the fin surface. At the leading edge of the flow passage, the cool coming air flow encounters with hot fin surface for first time, and the thickness of boundary layer is small, which results in the high Nu number. Due to the growth of the thermal boundary layer on the fins, the local Nu number decreases gradually along the flow passage. The longitudinal vortex generators punched on the fin surface generate longitudinal vortices, and the longitudinal vortices drag fluid from the near-wall region to the core of main flow, which generate down-sweep zone, intensify the fluid mixing and enhance the heat transfer. When the delta winglet pairs punched on the middle of fin, the longitudinal vortices introduce strong swirling flow into the wake region which can significantly augment the heat transfer. The high temperature zone of the fin is situated in the rear of fin surface. Consequently the delta winglet pairs punched middle of the fin surface is more effective than the delta winglet pairs punched ahead and rear of the fin surface for the heat transfer augmentation.

4.3. Influence of number of delta winglet pairs On the base of the above results, variations of heat transfer performances with number n of the delta winglet pairs at attack angle b = 25° are investigated, of which, n = 1(which located at a = 1/2W), n = 2, n = 3, n = 4, n = 5, n = 6 and n = 7, respectively. Fig. 12 shows the configuration of the wavy finned flat tube with six delta winglet pairs on the fin surface. With the number of the delta winglet pairs, n, varies from 1 to 7, Fig. 13 illustrates the variations of the air-side surface heat transfer coefficient, h, and pressure drop, DP, respectively. It can be seen that the air-side surface heat transfer coefficient h and pressure drop DP for the wavy finned flat tube increase with the inlet velocity. Fig. 13(a) provides the relation of the average air-side surface heat transfer coefficient, h, and the number of the delta winglet pairs, n. The air-side surface heat transfer coefficient h increases with the increasing delta winglet pairs number n. While n is 6 and 7, only slightly increase of the surface heat transfer coefficient, h was acquired. The change trend of the airside surface heat transfer coefficient, h, is almost the same for different inlet air flow velocities, uin. Fig. 13(b) shows the variation of

the pressure drop DP with the number of the delta winglet pairs n. It can be seen from the figure that the pressure drop DP increases with the increasing the number of the delta winglet pairs n. Similar variations of pressure drop DP can also be obtained under different inlet air flow velocities, uin. With the increasing of number n of the delta winglet pairs, the delta winglet pairs generate drastically longitudinal vortices. Each delta winglet pairs can generate down-sweep zone and restrain the development of the boundary layer by separating the boundary-layer from the fin and accelerating the swirling flow to enhance the heat transfer. However, the growth of pressure drop DP result from the form drag of multi-longitudinal vortex generators and the augmentation of momentum result from the swirling flow are also sharp. Comparing Fig. 13(a) with Fig. 13(b), we can see that the pressure drop DP increase rapidly than the average air-side surface heat transfer coefficient h, and the greater the more number of the delta winglet pairs. Fig. 13(c) shows relation of the performance evaluation criteria PEC and the number n of the winglet pairs. It can be seen that the performance evaluation criteria PEC decreases with the increasing the number of the delta winglet pairs, n. The change trend of the performance evaluation criteria PEC is almost the same for different Re numbers. The increase of the pressure drop DP is larger than the increase of the air-side surface heat transfer coefficient h with the number of the delta winglet pairs. From Fig. 14, we can see the low temperature zone in the fin

Fig. 15. Velocity distribution between two fins without longitudinal vortex generators by experiment at uin = 5 m/s.

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(a)

(b)

(c) Fig. 16. Comparison of velocity distributions on the fin with one delta winglet pairs by experiment and by numerical simulation (b = 25°, uin = 5 m/s). (a) Schematic field of view; (b) experimental result (x–y plane); (c) simulating results (x–y plane).

surface is extended and the mixture of fluid is obvious. Fig. 14(a) and (b) illustrate the temperature distribution for the fin surface and velocity vector of x–y plane (z = 1/2sf) in channel of the fins with the delta winglet pairs for b = 25° and n = 6, at uin = 2 m/s, respectively. According the above analysis, it is found that the minimal number n of the delta winglet pairs leads to the better heat transfer and air flow characteristics. Therefore, the number of the delta winglet

pairs n = 1 that the average PEC is 1.23 is recommended in practical applications. 4.4. Comparison experimental and numerical results Two types of plate fins were employed for experimental verification, which were plate fin and plate fin with one delta winglet pairs punched at the front edge of fin, at a = 40 mm. The velocity

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Fig. 17. Velocity vector of longitudinal vortices generated by a delta winglet pairs in channel of the fin.

vector of the flow field in the test section was obtained. Fig. 15 shows the velocity vector distribution of x–y plane (z = 1/2sf) in channel of the fins without delta winglet pairs at uin = 5 m/s. The uniform flow of air is displayed in channel of the fins. Fig. 16 shows the velocity vector distribution generated by one delta winglet pairs in channel of the fins acquired by experiments and simulations. Fig. 16(a) illustrates the drawing districts of experiment and simulation. The x–y plane and the z–y plane are taken velocity vectors of the flow field after the flow through the delta winglet pairs. The x–y plane is the PIV shooting velocity vectors and the z–y plane is the taken produce longitudinal vortex velocity vectors. We selected the x–y plane to analysis the velocity vector of the flow field in channel of the fins with one delta winglet pairs and without the delta winglet pairs (see Fig. 15), and to compare the velocity vector of the flow field in channel of the fins with the delta winglet pairs by experiment and by simulation. From Fig. 16(b) and (c), it can be showed that there are similar locations of vortexes and velocity patterns between the experiments and simulations. Behind the delta winglet pairs, the fluid comes into the down-sweep zone. The delta winglet pairs develop trailing vortices. The vortices disrupt the growth of the boundary layer and serve ultimately to bring about enhancement of heat transfer between the fluid and its neighboring fin surface. Apparently, the existence of the down-sweep region improves the rate of air flow between the delta winglet pairs. In this study, the main flow direction is x direction. Thus, the longitudinal vortices generate by the delta winglet pairs lie in the z–y plane. By the simulations of Fig. 17, it can be seen that there are vortex pairs disturbance after the air flow of the delta winglet pairs under the present condition. The axis of longitudinal vortices runs parallel to the axis of the main flow direction, so the flow spirals around the main flow direction. More details of the comparison of heat transfer between experimental investigations and numerical simulations at different Reynolds numbers can also refer to our studies in literature [32]. The results in a larger ranges of inlet air flow Reynolds numbers show the comparison of the Nusselt number between the wavy fins with six delta winglet pairs by experiments and numerical simulations, implying well consistency, as well as the increase of Nu with the Re number either in experiments or numerical simulations.

5. Conclusions The heat transfer enhancements of four types of longitudinal vortex generators punched on the wavy fin of flat tube were studied numerically with experimental verifications. The following results obtained can benefit the improvement of air-side heat transfer performance of direct air-cooled condensers.

(1) The delta winglet pairs is the best longitudinal vortex generators for air-side heat transfer enhancement among the four configurations. The average PEC of the delta winglet pairs with b = 25° can reach to 1.23 while the inlet air flow velocity varies from 1 m/s to 5 m/s. (2) The location of the longitudinal vortex generators on fin surface has influences on the heat transfer enhancement. It is found that the delta winglet pairs punched middle of the fin surface is more effective than the delta winglet pairs punched ahead and rear of the fin surface for the heat transfer augmentation. (3) The air-side heat transfer coefficient increases with the number of the delta winglet pairs punched on the fin surface. However, the pressure drop increases rapidly as well. The comparison of the performance evaluation criteria indicates that one can obtain the greatest PEC with the minimum number of the delta winglet pairs, n = 1. (4) The experimental and numerical studies verify in further that the delta winglet pairs can generator obvious longitudinal vortex pairs at the down-sweep zone, which can enhance the heat transfer between the cooling air flow and heated wall surface with acceptable pressure loss. Conflict of interest None declared. Acknowledgement The financial support from the National Natural Science Foundation of China (Grant Nos. U1261108 and U1361108) is gratefully acknowledged. References [1] M. Fiebig, Vortices, generators and heat transfer, Chem. Eng. Res. Des. 76 (1998) 108–123. [2] M. Sohal, J. O’Brien, Improving air-cooled condenser performance using winglets and oval tubes in a geothermal power plant, Geotherm. Res. Counc. Trans. 25 (2001) 1–7. [3] S. Tiwari, D. Maurya, G. Biswas, V. Eswaran, Heat transfer enhancement in cross-flow heat exchangers using oval tubes and multiple delta winglets, Int. J Heat Mass Transfer 46 (15) (2003) 2841–2856. [4] P. Chu, Y. He, Y. Lei, L. Tian, R. Li, Three-dimensional numerical study on finand –oval-tube heat exchanger with longitudinal vortex generators, Appl. Therm. Eng. 29 (2009) 859–876. [5] A. Joardar, A. Jacobi, A numerical study of flow and heat transfer enhancement using an array of delta-winglet vortex generators in a fin-and-tube heat exchanger, J. Heat Transfer 139 (2007) 1156–1168. [6] C. Lin, Y. Liu, J. Leu, Heat transfer and fluid flow analysis for plate-fin and oval tube heat exchangers with vortex generators, Heat Transfer Eng. 29 (2008) 588–596. [7] Y. Chen, M. Fiebig, N. Mitra, Conjugate heat transfer of a finned oval tube with a punched longitudinal vortex generator in form of a delta winglet–

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