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Experimental and numerical study and comparison of performance for wavy fin and a plain fin with radiantly arranged winglets around each tube in fin-and-tube heat exchangers
Accepted Manuscript Research Paper Experimental and numerical Study and Comparison of Performance for Wavy Fin and a Plain Fin with Radiantly Arranged Winglets around Each Tube in Finand-tube Heat Exchangers M.J. Li, H. Zhang, J. Zhang, Y.T. Mu, E. Tian, D. Dan, X.D. Zhang, W.Q. Tao PII: DOI: Reference:
S1359-4311(17)35702-2 https://doi.org/10.1016/j.applthermaleng.2018.01.012 ATE 11666
To appear in:
Applied Thermal Engineering
Received Date: Revised Date: Accepted Date:
2 September 2017 30 December 2017 4 January 2018
Please cite this article as: M.J. Li, H. Zhang, J. Zhang, Y.T. Mu, E. Tian, D. Dan, X.D. Zhang, W.Q. Tao, Experimental and numerical Study and Comparison of Performance for Wavy Fin and a Plain Fin with Radiantly Arranged Winglets around Each Tube in Fin-and-tube Heat Exchangers, Applied Thermal Engineering (2018), doi: https://doi.org/10.1016/j.applthermaleng.2018.01.012
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Experimental and numerical Study and Comparison of Performance for Wavy Fin and a Plain Fin with Radiantly Arranged Winglets around Each Tube in Fin-andtube Heat Exchangers M.J. Li, H.Zhang, J. Zhang, Y.T. Mu, E. Tian, D. Dan, X.D. Zhang, W.Q. Tao* Key Laboratory of Thermo-Fluid Science and Engineering, Ministry of Education, School of Energy and Power Engineering, Xi’an Jiaotong University, Xi’an, Shaanxi, 710049, P.R. China (*Corresponding Author: [email protected]) Abstract A new kind of plain plate fin with twelve vortex generators of delta winglet around each tube in fin-and-tube heat exchanger proposed by the present authors is experimentally studied in this paper. Experiments of four 4 heat exchanger surfaces of real size are conducted to compare the comprehensive characteristics of the proposed fin with a circular wavy fin: two wavy fin-and-tube heat exchangers with 6 rows of tubes at the fin pitch of 2.54mm and 2.117mm (10-wavy and 12-wavy for short) respectively; and two proposed fin-and-tube heat exchanger surfaces with five rows of tubes at the same fin pitches (10-LVG and 12-LVG) correspondingly. The inlet velocity of the air side varies from 1.5 m/s to 7.5m/s, and the water side flow rate is fixed at a certain value at each air inlet velocity. Experimental result indicates that the heat transfer rate and pressure penalty of heat exchanger surfaces using proposed fin with five-row tubes are almost the same with the six-row tubes wavy heat exchanger surfaces. Correlation of the Nusselt number Nu and the friction factor f on the air side are achieved. Entransy analysis is conducted to reveal the heat enhancement mechanism. Keywords: Winglets, Longitudinal vortex generator, Heat exchanger, Experiment, Entransy, Wavy fin 1 Introduction Fin-and-tube heat exchangers are one of the widely employed heat exchangers in industries, especially in air-conditioning and refrigeration industry. The heat transfer characteristics, pressure drop and exchanger size are three of the most concerned factors
in the design of high-efficiency heat exchangers. As the airside resistance generally comprises over 90% of the total thermal resistance in conventional air-water heat exchangers, it is essential to develop highly effective fin to enhance the airside heat transfer under comparatively low pressure penalty for reducing the plate-fin and tube heat exchanger size and the consumption of materials. Wavy fins and fins with punched longitudinal vortex generators are widely employed in the past few years. According to Jacobi and Shah [1] these two kinds of enhanced techniques bring force main-flow enhancement and secondary flow enhancement, respectively. The wavy structure periodically interrupts the growth of the thermal boundary layers on the heat transfer surface and induces transverse vortex in wavy trough at some combinations of wavy angle, fin pitch and Reynolds number, thus increasing fluid mixing. For the LVGs enhanced fin surface, when fluid flows over LVGs set at appropriate attack angle, longitudinal vortex are generated [2]. As the vortices develop longitudinally along the flow direction, LVGs can enhance heat transfer at a lower pressure penalty and, hence, has better comprehensive performance compared with the transverse vortex. For the situation of clear and dry air, no dust or condensed water drop may block the flow channel within the vortex generator, therefore LVGs are especially suitable and have been well accepted in both academic community and industry in the recently years. In the following a review of previous studies on longitudinal vortex generators (LVG) employed to enhance air-side heat transfer are briefly conducted. Early literatures such as [1-4] discussed the heat transfer enhancement mechanism of longitudinal vortices in detail and proposed 4 arrangements of LVGs, that is rectangular wing and delta winglet in common-flow-up and common-flow-down arrangement. Wang [5] presented an annular vortex generator, and conducted visualization experiments to clearly show the vortices development. Joardar and Jacobi [6] used the combination of louver fin and LVGs for a flat-tube (plate) heat exchanger and found that the average heat transfer enhancement is higher than 20% compared with louvered fin without LVGs, while the pressure drop penalty is less than 7% under both dry and wet surface conditions. Joardar and Jacobi [7] experimentally evaluated some full-scale compact plain-fin-and-tube heat exchangers at low Reynolds number (less than 960), and found that the single-row winglet arrangement has better pressure characteristic while the three-LVG array has better heat transfer performance. In [8,9] through
numerical simulation Wu and Tao indicated that the basic mechanism of heat transfer enhancement of LVGs is the improvement of synergy between fluid velocity and temperature gradient. Tian et al. [10] investigated punched delta winglets longitudinal vortex generators on a wavy fin and found that the winglets cause considerable augment of heat transfer amount with modest pressure drop. Fan et al. [11] utilized the combination of slotted protruding parallel strips with longitudinal vortex generators to replace a triangular wavy fin in fin-and-tube heat exchanger and by this new structure they were able to reduce the tube row from 3 to 2 for the same heat transfer load. Chu et al. [12] numerically studied fin-and-oval-tube heat exchangers with LVGs at a Reynolds range of 500 to 2500, and verified that the enhancement of heat transfer is resulted from a better synergy between velocity and temperature gradient. The results of literatures mentioned above indicate that no matter the tube used in fin-and-tube heat exchangers is flat, oval or round, the tube arrangement is inline or staggered, and Reynolds number is low or high, LVGs have the ability to enhance heat transfer, and the basic enhancement mechanism is the improvement of synergy. The affecting factors have been widely studied, including LVG shape [13, 14], position [15], and geometric dimensions [16-19]. The global arrangement of vortex generators is usually along the line of flow direction, either in-line or staggered.
In this paper,
however, we will try a new arrangement of delta winglets instead of in-line or staggered. Several typical arrangement formats of delta winglets in literature are summarized in Table 1, where arrows represent flow direction. In [20] the winglets lie in line in that the sole edges of winglets parallel to each other; in [21] the winglets lie in staggered array in that the sole edges of winglets are mutually perpendicular; in [22] the winglets have the most
typical
arrangement,
namely
common-flow-up
and
common-flow-down
arrangement; in [23,24] the winglets are deployed in a ‘V’ array; and in [11] the winglets arrangement can be regarded as a combination of common-flow-up and common-flowdown in [22]. It can be seen that LVGs used in the above literatures are put either before or behind or between the tubes and always come in pairs. In reference [25] the present authors proposed a totally different arrangement of LVGs, where the winglets are put around the tube annularly. Numerical simulations have shown the advantage of such an arrangement over conventional wavy fin-and-tube surface without experimental confirmation. One
major purpose of the present paper is to provide comparative test results for four surfaces of wavy fin-and-tube without LVGs and plain fin-and-tube with LVGs around tube. The other major purpose of the present paper is to analyze the enhanced surface performance by using the entransy theory which was recently proposed by Guo and his co-workers in [26]. For the readers’ convenience the concept of entransy is briefly reviewed as follows. Guo et al. introduced a new physical quantity termed entransy [26] to describe the heat transfer potential capacity. The entransy of a heat transfer medium is defined as the half product of its internal energy and its temperature. It can be regarded as the potential capacity of the medium to transfer heat to the environment with zero K. During a heat transfer process, the total entransy of the heat transfer media is reduced because of the process irreversibility while the energy is conserved. Hence, the entransy can be used to evaluate the irreversibility of a process. The entransy dissipation extreme principle (EDEP) was proposed in [27-29] and further enhanced in [30-36], and it states that for a fixed heat flux boundary condition, the heat transfer process is optimized when the entransy dissipation is maximized, while for a fixed temperature boundary condition, the thermal process is optimized when the entransy dissipation is minimized. And more recently, He and Tao [36] put forward a unique formulation of EDEP that for whatever boundary condition the best heat transfer process should have the minimum entransy dissipation per unit heat transferred. And they provided several numerical examples to demonstrate that there exists inherent consistency between the field synergy principle (FSP)[37,38] and EDEP. The performance of four heat exchangers studied in this paper will be evaluated according to the principle. The comprehensive characteristics are compared at 2 fin pitches to demonstrate that the proposed plain fin-and-tube heat exchanger of five tube rows with longitudinal vortex generators can transfer almost the same amount of heat transmitted by the heat exchanger with circular wavy fin-and-tube heat exchanger of 6 tube rows without LVGs. 2 Physical models The plain fin surface enhanced by radiantly arranged winglets [3] and the wavy fin are shown in Fig.1. Fig. 1(a) is a part of the collared wavy fin with six tubes in staggered arrangement. The wavelength of the fin is 10.334 mm, the amplitude of the fin is 2mm, and the
diameter of the step outside the tubes is 18.0mm. The fin thickness df is 0.115mm, tube diameter Dc is 13mm, transverse tube pitch Pt is 27.5mm and longitudinal tube pitch Pl is 15.875mm. The fin pitch fp has 2 different values, namely 2.54mm and 2.117mm. In Fig. 1(b) near each tube there are 12 surrounding winglets on the plain fin. The delta winglets are punched out from the plain fin. The chord of the winglets l is 5mm. The attack angle α of the six winglets, defined as the angle between the chord and the tube bank centerline, is 50, 50, 50, 50, 70 and 110 degree respectively. The height of winglets h is 2.002mm. The delta winglets stand just perpendicular to the base surface and act as an obstacle to the coming flow, hence, can increase the disturbance of air flow. The fin pitch, fin thickness, tube diameter, transverse tube pitch and longitudinal tube pitch are identical to the wavy fin structure shown in Fig. 1(a). The heat exchangers studied in this paper are two wavy fin-and-tube heat exchangers with 6 rows of tubes at the fin pitch of 2.54mm and 2.117mm. In the later presentation these two fins will be denoted by 10-wavy and 12-wavy for short, respectively, where 10 and 12 imply that 10 fins per inch and 12 fins per inch respectively; and two proposed plain fin-and-tube heat exchangers with 5 rows of tubes at the fin pitch of 2.54mm and 2.117mm (10-LVG and 12-LVG for short) correspondingly. The water circuit arrangements of the two forms of heat exchangers are shown in Fig.3. The tubes are made of copper and the fins of aluminum. 3 Experimental apparatus and procedure The experiments are conducted in an open suction wind-tunnel. The test system consists of two cycles: air cycle and water cycle. The air cycle is used to blow and heat the air across the finned tube bundles, and the water cycle is designed to supply cold water through the tubes of test core. The overall flow direction of air and water is counter-flow. The air-water system is schematically shown in Fig. 4. Air is induced to the wind-tunnel by a centrifugal blower. Section 2 in Fig.4 is an air heater composed of 6 rows of heating rods, for one of the heating rods its power is finetuned and the other five have fixed heating power; Air is heated to achieve an inlet temperature of about 75 degrees of centigrade before entering the heat exchanger. The transition section, contraction section and the straightening section are used to make the inlet air flow uniform. The test section is one of the above-mentioned four heat
exchangers, being an air–water heat exchanger in which air is going across the finned tubes and water is flowing inside tubes. The inlet air temperature and the temperature difference between inlet and outlet through the test core are measured by two sets of selfmade multi-junction T-type copper-constantan thermocouple grids. Each set has 16 grid points which are interconnected in series to give a single reading. The mixture of water and ice is used as cold terminal temperature compensation. After being cooled by cold water in the testing section, air leaves the test core and flows through the flow metering duct before being discharged outside the test room. The average static pressure before the test section and the pressure drop of the heat exchanger are measured by a U-tube water (or mercury) column manometer or an inclined manometer, depending on the range of the pressure drop. The air velocity is measured by a Pitot tube meter, which is located in the flow measuring duct far downstream of the test core. The heat exchangers and the windtunnel before the test section are covered by foam insulation of about 40 mm thick to reduce the heat loss to the surroundings. The cooling water is pumped into the system from a water tank, and passes through the tubes of the heat exchanger. Cooling water receives heat from air in the core section of fin-and-tube heat exchanger. After that, the heated water is cooled down by an outdoor cooling tower. Then it returns to the water tank for recycling. The temperature of the water is measured by four-wire Pt100 thermal resistance thermometers; the volume flow rate of water is adjusted by electrically operated valves located on the water pipeline; and the pressure drop of water side is obtained using pressure drop transducers. The air inlet temperature, temperature difference between inlet and outlet, volume flow rate of water, temperature of water at inlet and outlet, and pressure drop of water side are collected by the KEITHLEY 2700 multi-channel data acquisition unit and 7708 data acquisition card. This provides enormous convenience for displaying the test results on the screen graphically and monitoring the operational state. The accuracy of these apparatus will be shown in Section 4.2. The barometric pressure is also measured to determine the physical properties of air. 4 Data reduction and experimental uncertainty 4.1 Data reduction The main purpose of this part is to determine the Nusselt number (Nu) or Colburn
factor ( j ) and friction factor (f ) of the tested air-side surface from the experimental data, and then find out the corresponding correlations of Nu vs. Re and f vs. Re for each case. The air side heat transfer rate is given as:
a ma cp,a T
(1)
where ma is the air mass flow rate, T is the temperature difference between the inlet and the outlet, and cp,a is the specific heat at constant pressure of air. cp,a together with other physical properties of both water and air is evaluated at the average of the inlet and outlet temperature according [39]. The water side heat transfer rate is:
w mw cp,w (Tout Tin )
(2)
where mw is the water mass flow rate, Tout is the outlet temperature of water and Tin is the inlet temperature. The average heat transfer rate of the air side and the water side is defined as the heat transfer rate to determine the heat transfer coefficient:
m a w / 2
(3)
The heat balance deviation is defined as:
w a m 100%
(4)
During the experiment is controlled less than 5% to reach the thermal balance. The overall heat transfer coefficient k is obtained by:
k
m
Aa tm
(5)
where tm is the logarithmic-mean temperature difference defined by: tm
tmax tmin ln tmax tmin
tmax ta,in tw,out
(6) (7)
tmin ta,out tw,in
(8)
Aa in Eq.(5) is the total area of air side including outside area of the tubes A1 and the fin area A2 . The average heat transfer coefficient of tube side is calculated by Gnielinski equation [40, 41] with the effect of thermo-physical property variation being considered, shown by Equations (9-11), where the average value of the inlet and outlet temperature of working fluid is taken as the reference temperature. The characteristic dimension is the inner diameter of the tube.
Nuw
f ' 8 Re 1000 Pr 1 d w
1 12.7 f ' 8 Prw2/3 1
f ' 1.8lg Re 1.5 Pr c w Prt
l i
2/3
c
2
(9)
(10)
0.11
(11)
With the overall heat transfer coefficient and the tube-side heat transfer coefficient at hand, the average air-side heat transfer coefficient can be obtained by the so called thermal resistance separation method or the Wilson plot technique as described by[39,42]:
1 1 Aa Aa 1 k hw Aw Aw ha '
(12)
where ha , hw are the heat transfer coefficient of air side and water side, respectively,
is the wall thickness of the tube. Since ha ' in equation (12) always comes together when designing heat exchangers, and in order to avoid the uncertainty of fin efficiency , we define the product of ha ' as ha . The uncertainty of fin structure during process, the contact heat resistance are both included in ha . Thus the air side total heat transfer coefficient can be expressed as in equation (13) without considering the fin efficiency separately. From Equation (12) we can get the air side heat transfer coefficient:
ha
1
Aa A d o di 1 ( a ) k hw Aw 2 Aw
(13)
d o and d i are the outside and inside tube diameter, respectively, and is the heat
conductivity coefficient of heat exchanger tube. Air side Reynolds number and Nusselt number are obtained as follows：
Re
uin d o
Nu
a
ha d o
a
(14)
(15)
Air side friction factor is defined as：
f
P L
d o / (0.5 a uin2 )
(16)
where P is the pressure drop of air flowing through the test section, and L is the length of fin. 4.2 Experimental uncertainty The measurement uncertainties are estimated along the line described in [44]. Firstly the uncertainty of the overall heat transfer coefficient k in equation (5) is determined. As the heat balance deviation is controlled less than 5% during the experiment process, the heat transfer rate can be then treated approximately as m a w when calculate the uncertainty of heat transfer rate. All the geometric parameters including surface area Aa are offered by the heat exchanger producer, thus we ignore the uncertainty of these parameters. As for the uncertainty of logarithmic-mean temperature difference in equation (5), the accuracy of platinum resistance thermometers together with copperconstantan thermocouple (see Table 2) has to be considered. Then by taking the uncertainty of thermophysical properties like thermal conductivity and specific heat cp as 2%, and ignoring the uncertainty of fin efficiency, we can finally obtain the
uncertainty of Nu number through equations (12), (14) and (16). The same process can be done for calculating uncertainty of friction factor f. It is obvious that the larger the
measured value the smaller the related uncertainty. The uncertainty values for the entire measurement range are given in Table 3. It can be seen from the table that the maximum uncertainty of Nusselt number is about 7% and that of friction factor is about 9%. 5 Results and discussion 5.1 Experimental Results Experiments are carried out with the inlet air velocity from 1.5 to 7.5m/s. The heat transfer rate and pressure drop on the air side of the four heat exchangers are presented in Fig. 5. It is to be noted that 10- and 12-LVG are of five tubes,while 10- and 12-wavy are of six tubes. As shown in the figures, the heat transfer rate and pressure drop of five-row LVGs enhanced fin are almost the same with that of six-row wavy fin at the two fin pitches investigated, and more noticeably, the pressure drops of five-row LVGs enhanced fin are almost identical to that of six-row wavy fin. Thus we can conclude that the proposed fin-and-tube heat exchanger can replace the wavy fin-and-tube heat exchanger. The row number of tubes is reduced from 6 to 5. The average Nu and f values are shown in Fig. 6 and Fig. 7 respectively. As can be expected the Nusselt number increases with increasing air frontal velocity for all the four heat transfer surfaces tested in this paper. For both LVGs enhanced fin and the wavy fin, the Nusselt number with fin pitch of 2.117 mm is larger than that of fin pitch of 2.54mm. That is to say, for the cases studied small fin pitch can enhance heat transfer. For the same fin pitch, the LVGs enhanced fin has higher Nusselt number than that of the wavy fin. Fig. 7 shows that the friction factor f decreases with the increase of air frontal velocity. Among the four fin surfaces f of 12-LVG is the highest at the same frontal velocity, that of 10-wavy is the lowest, with 12-wavy and 10-LVG in between. Obviously, the friction factor increases with the decrease in fin pitch and at the same fin pitch, LVGs enhanced fin has higher f than that of the wavy fin. Data fitting is tried to get the correlations for heat transfer and friction factors and following results are obtained with their maximum deviation being provided within the brackets: 10-LVG：Nu=0.420Re0.592 (5.77%); f=3.00Re-0.153(3.39%) Re=2078-9390
10-wavy：Nu=0.101Re0.643 (6.22%); f=3.39Re-0.181(2.34%) Re=1980-9447 12-LVG：Nu=0.369Re0.624 (7.13%); f=4.44Re-0.150(2.87%) Re=1826-9432 12-wavy：Nu=0.467Re0.561 (4.86%); f=7.48Re-0.243(3.11%) Re=1890-9506 The heat exchangers used in most air conditioning operations are within this range, hence the correlations can be used for some design purpose.
5.2 Numerical analysis The authors also conduct numerical simulations of the four heat exchange surfaces with air as the heat transfer medium to find the reason of heat transfer enhancement. The fin pitch and the velocity range are different from that in [25]. In this paper the fin pitches of both 2.117 mm and 2.54mm are simulated, the height of winglet is remained as 2.002 mm for the convenience of machining. Laminar model is used for velocity from 1.5 to 3.5 m/s, and k- turbulence model is used for higher velocities. The computational region is extended upstream by two times of the streamwise fin length, and ten times of the fin region downstream [25]. Inlet velocity and air temperature is given at the inlet. The outflow boundary condition is employed for outlet. The neighboring two fins’ center planes are chosen as the lower and upper boundaries of the computational domain due to the periodicity of the airside channels in z direction. As for the spanwise direction, the computational region is bounded by two adjacent center lines of tubes and is set as symmetry boundary conditions. The tube temperature is constant during numerical simulation. After grid independence examination, around 1.95 million meshes are adopted for LVGs enhanced fins, and 1.85 million meshes for wavy fins. The Nu number and friction factor f for 10-wavy fin are descripted in Fig.8. It can be seen in the figure that the simulation coincides with the experimental variation tendency. The maximum deviation of Nu is 12.5%, and the average deviation is 8.33%; the maximum deviation of f is 14.4%, the average deviation is 8.66%. For such heat exchanger of real size, these numerical deviations from experiment data are acceptable and the numerical simulation results can be used to decipher the enhancement mechanism.
The velocity contours on the central plane of air channels of the four structures are shown in Fig.9. These results are obtained at the inlet velocity of 4m/s. The inlet air temperature is 305 K, and the tube temperature 280 K. It can be seen from Fig.9(a) that for 10-wavy fin, there exist obvious wake region after each tube, especially for the sixth one. According to field synergy principle[37,38], stagnation or wake region is always unfavorable in heat exchanger because in these zones fluid velocity is low, and heat transfer is also weak. As for the 12-wavy fin in Fig.9(c), the wake region is slightly reduced and velocity near the tubes is increased, but fluid gathers at the trough of the wavy fin and velocity is low there consequently. While for the 10-LVG and 12-LVG cases in Fig.9(b) and Fig.9(d) such low velocity regions after each tube have almost been disappeared. This is because the local flow channels (passages) formed between the latter two winglets for each tube are beneficial to the reduction of wake region. In addition the local flow passages formed by the first four pairs of winglets can guide the moving fluid from the main flow towards the tube wall, leading to some impinging effect on the tube wall for increasing the local velocity. And in the vicinity of each LVG, the fluid is fully disturbed and mixed, which also contributes to the enhancement of the proposed fin. The temperature distributions at the same plane are shown in Fig. 10. Because of the above-mentioned flow pattern of the LVG structure, the fluid temperature in the most part of the fin in Fig.10(b) and Fig.10(d) is more uniform than the fluid temperature distribution in wavy fin cases. It’s also shown in the figure that the fluid temperature variation around the last tube for the wavy cases are very small, which implies that the last tube is working in a very inefficient regime. This also provides the necessityof reducing the tube rows from 6 to 5. Both the temperature and velocity distributions in Fig.9 and Fig.10 are in full compliance with the heat transfer rate in Fig. 5, which gives a good explanation for the enhancement of heat transfer for the proposed fin. 5.3. Entransy analysis The definition of the entransy change when air flows over the finned tubes is as follows [36]:
1 1 E cv maTin 2 cv maTout 2 cv ma Tin Tout Tt 2 2
(17)
where ΔE is the entransy dissipation of the heat transfer process, cv is specific heat at constant volume for air, and ma is the mass flow rate. The variation of entransy dissipation versus Re for four different fins according to numerical simulation is shown in Fig.11. The entransy dissipation increases with the increase of Reynolds number. Under the constant tube wall temperature condition, 10-wavy and 10-LVG have almost the same amount of entransy dissipation. And the same is true for 12-wavy and 12-LVG. Noting that either 10-wavy or 12-wavy have 6-row tubes, while either 10-LVG or 12-LVG have only 5-row tubes (see Fig.10), this phenomenon once again demonstrates the feasibility of replacing the 6-row tubes heat exchanger with 5-row tube one. The entransy dissipation per unit heat transfer rate ΔE/Ф at different Re number is shown in Fig. 12. As indicated in [36], the smaller the value of entransy dissipation per unit heat transfer rate, the better the synergy between velocity and temperature difference. Therefore it’s concluded from the figure that 10-LVG fin has better synergy than 10wavy fin, and the same is true for 12-wavy and 12-LVG. 6 Conclusions In this study, four fin-and-tube heat exchangers are experimentally investigated and the following conclusions can be drawn: (1) The 5-row tubes of plain fin surface enhanced by LVGs can substitute the 6 rows wavy fin for the 2 fin pitches tested; (2) Both the LVGs enhanced fin and the wavy fin of smaller fin pitch have higher Nusselt number and friction factor. (3) Entransy analysis proves that the proposed LVG enhanced fin have better heat transfer performance than the wavy fin, theoretically supporting the replacement of sixrow wavy fin by five-row of plain fin with LVGs. Acknowledgments This study was supported by the National Basic Key Research Program of China (973 Program) (2013CB22830) and Key Project of International Joint Research of National Natural Science Foundation of China (51320105004) and 111 Project (B16038).
NOMENCLATURE Latin Symbols A
heat transfer area
cp
specific heat at constant pressure
cv
specific heat at constant volume
ΔE
entransy dissipation
f
friction factor
j
Colburn factor
L
effective length of fin
Nu
Nusselt number
ΔP
pressure drop
Re
Reynolds number
T
temperature Greek Symbols
attack angle
Ф
heat transfer rate
conductivity factor fluid
density of fluid
dynamic viscosity Subscripts
a
air side
f
fin
i
inside of the tube
in
inlet
m
mean value
o
outside of the tube
out
outlet
t
tube wall
w
water side
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Figure captions Fig. 1 Configurations of the proposed enhanced fin and wavy fin Fig. 2 Sketch of the LVGs enhanced fin Fig. 3 Sketch of water circuit arrangements Fig.4. Experimental facility Fig. 5 Heat transfer rate and pressure drop for the four kinds of heat exchanger Fig.6 Air side Nusselt number vs. Reynolds number for the four structures Fig.7 Air side friction factor vs. Reynolds number for the four structures Fig.8 Comparison of experimental and numerical Nu and f for 10-wavy fin Fig. 9. Temperature distribution of four structures Fig. 10. Velocity distribution of four structures Fig.11 Entransy dissipation of the four structures Fig.12 Entransy dissipation per unit heat transfer rate versus Re
air
(a)Wavy fin
(b) Proposed fin
Fig. 1 Configurations of the proposed enhanced fin and wavy fin
Fig. 2 Sketch of the LVGs enhanced fin
air
(a) Proposed fin(5 rows)
(b) Wavy fin(6 rows)
Fig. 3 Sketch of water circuit arrangements
1) Entrance; 2) Air heater; 3) Transition Section; 4) Contraction Section; 5) Straightening Section; 6) Test Heat Exchanger; 7) Flow Metering Duct; 8) Blower; 9) Water tank; 10)Water pump; 11) Volumetric Meter; 12) Data Acquisition System; 13) U Tube Manometer; 14) Cooling tower
Fig.4. Experimental facility
(a) Fin pitch of 2.002mm
(b)Fin pitch of 2.425mm Fig. 5 Heat transfer rate and pressure drop for the 4 kinds of heat exchanger
Fig.6 Air side Nusselt number vs. Reynolds number for the four structures
Fig.7 Air side friction factor vs. Reynolds number for the four structures
(a) Comparison of experimental and numerical results for Nu of 10-wavy fin
(b) Comparison of experimental and numerical results for f of 10-wavy fin
Fig.8 Comparison of experimental and numerical Nu and f for 10-wavy fin
Unit: m/s (a) 10-wavy
(b) 10-LVG
(c) 12-wavy
(c) 12-LVG Fig. 9. Velocity distribution of four structures
Unit: K (a) 10-wavy
(b) 10-LVG
(c) 12-wavy
(d)12-LVG Fig. 10. Temperature distribution of four structures
(a) Entransy dissipation versus Re for 10-LVG and 10-wavy
(b) Entransy dissipation versus Re for 12-LVG and 12-wavy Fig. 11 Entransy dissipation of the four structures
(a) Entransy dissipation per unit for 10-LVG and 10-wavy
(b) Entransy dissipation per unit for 12-LVG and 12-wavy Fig. 12 Entransy dissipation per unit heat transfer rate versus Re
Table Captions Tab. 1 Typical arrangement of LVGs in literatures Tab. 2 Test range and accuracy of the measuring instruments Tab. 3 The maximum measurement uncertainties of test range
Table 1 Typical arrangement of LVGs near tube in literatures Authors and year
LVGs arrangement
Chen, 1998 [20]
inline
Chen, 2000 [21]
staggered array
Torii, 2002 [22]
common-flow-up
Torii, 2002 [22]
common-flow-down
He,2010 [23]
“V”字形布置
Fan,2011 [11]
混合布置方式
Authors and year Chen, 1998 [2119]
Chen, 2000 [22 20]
Torii, 2002 [23 21] He,2010 [24 22] He,2012 [25 23] Fan,2011 [11 10]
LVG arrangement
Table 2 Test range and accuracy of the measuring instruments Measuring instruments Platinum resistance thermometers Turbo volume flow meters Copper-constantan thermocouple U-tube manometer Inclined tube micro pressure gauge
Range -100-200℃ 8.5-60m3/h -200-100℃
Accuracy 0.15℃ 1% 0.2℃ 0.1mm 0.5%
Table 3 The maximum measurement uncertainties of test range Item
10LVG
10wavy
12LVG
12wavy
Air side Nusselt number (%)
6.53
6.15
6.60
6.92
Air side friction factor (%)
8.15
8.22
8.92
8.95
Highlights The 5-row tubes of LVGs enhanced fin can substitute the 6 rows wavy fin; The 12-LVG fin has the highes Nu number and friction factor compared with other fins. Entransy analysis proves that the proposed fin have better heat transfer performance.
S1359-4311(17)35702-2 https://doi.org/10.1016/j.applthermaleng.2018.01.012 ATE 11666
To appear in:
Applied Thermal Engineering
Received Date: Revised Date: Accepted Date:
2 September 2017 30 December 2017 4 January 2018
Please cite this article as: M.J. Li, H. Zhang, J. Zhang, Y.T. Mu, E. Tian, D. Dan, X.D. Zhang, W.Q. Tao, Experimental and numerical Study and Comparison of Performance for Wavy Fin and a Plain Fin with Radiantly Arranged Winglets around Each Tube in Fin-and-tube Heat Exchangers, Applied Thermal Engineering (2018), doi: https://doi.org/10.1016/j.applthermaleng.2018.01.012
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Experimental and numerical Study and Comparison of Performance for Wavy Fin and a Plain Fin with Radiantly Arranged Winglets around Each Tube in Fin-andtube Heat Exchangers M.J. Li, H.Zhang, J. Zhang, Y.T. Mu, E. Tian, D. Dan, X.D. Zhang, W.Q. Tao* Key Laboratory of Thermo-Fluid Science and Engineering, Ministry of Education, School of Energy and Power Engineering, Xi’an Jiaotong University, Xi’an, Shaanxi, 710049, P.R. China (*Corresponding Author: [email protected]) Abstract A new kind of plain plate fin with twelve vortex generators of delta winglet around each tube in fin-and-tube heat exchanger proposed by the present authors is experimentally studied in this paper. Experiments of four 4 heat exchanger surfaces of real size are conducted to compare the comprehensive characteristics of the proposed fin with a circular wavy fin: two wavy fin-and-tube heat exchangers with 6 rows of tubes at the fin pitch of 2.54mm and 2.117mm (10-wavy and 12-wavy for short) respectively; and two proposed fin-and-tube heat exchanger surfaces with five rows of tubes at the same fin pitches (10-LVG and 12-LVG) correspondingly. The inlet velocity of the air side varies from 1.5 m/s to 7.5m/s, and the water side flow rate is fixed at a certain value at each air inlet velocity. Experimental result indicates that the heat transfer rate and pressure penalty of heat exchanger surfaces using proposed fin with five-row tubes are almost the same with the six-row tubes wavy heat exchanger surfaces. Correlation of the Nusselt number Nu and the friction factor f on the air side are achieved. Entransy analysis is conducted to reveal the heat enhancement mechanism. Keywords: Winglets, Longitudinal vortex generator, Heat exchanger, Experiment, Entransy, Wavy fin 1 Introduction Fin-and-tube heat exchangers are one of the widely employed heat exchangers in industries, especially in air-conditioning and refrigeration industry. The heat transfer characteristics, pressure drop and exchanger size are three of the most concerned factors
in the design of high-efficiency heat exchangers. As the airside resistance generally comprises over 90% of the total thermal resistance in conventional air-water heat exchangers, it is essential to develop highly effective fin to enhance the airside heat transfer under comparatively low pressure penalty for reducing the plate-fin and tube heat exchanger size and the consumption of materials. Wavy fins and fins with punched longitudinal vortex generators are widely employed in the past few years. According to Jacobi and Shah [1] these two kinds of enhanced techniques bring force main-flow enhancement and secondary flow enhancement, respectively. The wavy structure periodically interrupts the growth of the thermal boundary layers on the heat transfer surface and induces transverse vortex in wavy trough at some combinations of wavy angle, fin pitch and Reynolds number, thus increasing fluid mixing. For the LVGs enhanced fin surface, when fluid flows over LVGs set at appropriate attack angle, longitudinal vortex are generated [2]. As the vortices develop longitudinally along the flow direction, LVGs can enhance heat transfer at a lower pressure penalty and, hence, has better comprehensive performance compared with the transverse vortex. For the situation of clear and dry air, no dust or condensed water drop may block the flow channel within the vortex generator, therefore LVGs are especially suitable and have been well accepted in both academic community and industry in the recently years. In the following a review of previous studies on longitudinal vortex generators (LVG) employed to enhance air-side heat transfer are briefly conducted. Early literatures such as [1-4] discussed the heat transfer enhancement mechanism of longitudinal vortices in detail and proposed 4 arrangements of LVGs, that is rectangular wing and delta winglet in common-flow-up and common-flow-down arrangement. Wang [5] presented an annular vortex generator, and conducted visualization experiments to clearly show the vortices development. Joardar and Jacobi [6] used the combination of louver fin and LVGs for a flat-tube (plate) heat exchanger and found that the average heat transfer enhancement is higher than 20% compared with louvered fin without LVGs, while the pressure drop penalty is less than 7% under both dry and wet surface conditions. Joardar and Jacobi [7] experimentally evaluated some full-scale compact plain-fin-and-tube heat exchangers at low Reynolds number (less than 960), and found that the single-row winglet arrangement has better pressure characteristic while the three-LVG array has better heat transfer performance. In [8,9] through
numerical simulation Wu and Tao indicated that the basic mechanism of heat transfer enhancement of LVGs is the improvement of synergy between fluid velocity and temperature gradient. Tian et al. [10] investigated punched delta winglets longitudinal vortex generators on a wavy fin and found that the winglets cause considerable augment of heat transfer amount with modest pressure drop. Fan et al. [11] utilized the combination of slotted protruding parallel strips with longitudinal vortex generators to replace a triangular wavy fin in fin-and-tube heat exchanger and by this new structure they were able to reduce the tube row from 3 to 2 for the same heat transfer load. Chu et al. [12] numerically studied fin-and-oval-tube heat exchangers with LVGs at a Reynolds range of 500 to 2500, and verified that the enhancement of heat transfer is resulted from a better synergy between velocity and temperature gradient. The results of literatures mentioned above indicate that no matter the tube used in fin-and-tube heat exchangers is flat, oval or round, the tube arrangement is inline or staggered, and Reynolds number is low or high, LVGs have the ability to enhance heat transfer, and the basic enhancement mechanism is the improvement of synergy. The affecting factors have been widely studied, including LVG shape [13, 14], position [15], and geometric dimensions [16-19]. The global arrangement of vortex generators is usually along the line of flow direction, either in-line or staggered.
In this paper,
however, we will try a new arrangement of delta winglets instead of in-line or staggered. Several typical arrangement formats of delta winglets in literature are summarized in Table 1, where arrows represent flow direction. In [20] the winglets lie in line in that the sole edges of winglets parallel to each other; in [21] the winglets lie in staggered array in that the sole edges of winglets are mutually perpendicular; in [22] the winglets have the most
typical
arrangement,
namely
common-flow-up
and
common-flow-down
arrangement; in [23,24] the winglets are deployed in a ‘V’ array; and in [11] the winglets arrangement can be regarded as a combination of common-flow-up and common-flowdown in [22]. It can be seen that LVGs used in the above literatures are put either before or behind or between the tubes and always come in pairs. In reference [25] the present authors proposed a totally different arrangement of LVGs, where the winglets are put around the tube annularly. Numerical simulations have shown the advantage of such an arrangement over conventional wavy fin-and-tube surface without experimental confirmation. One
major purpose of the present paper is to provide comparative test results for four surfaces of wavy fin-and-tube without LVGs and plain fin-and-tube with LVGs around tube. The other major purpose of the present paper is to analyze the enhanced surface performance by using the entransy theory which was recently proposed by Guo and his co-workers in [26]. For the readers’ convenience the concept of entransy is briefly reviewed as follows. Guo et al. introduced a new physical quantity termed entransy [26] to describe the heat transfer potential capacity. The entransy of a heat transfer medium is defined as the half product of its internal energy and its temperature. It can be regarded as the potential capacity of the medium to transfer heat to the environment with zero K. During a heat transfer process, the total entransy of the heat transfer media is reduced because of the process irreversibility while the energy is conserved. Hence, the entransy can be used to evaluate the irreversibility of a process. The entransy dissipation extreme principle (EDEP) was proposed in [27-29] and further enhanced in [30-36], and it states that for a fixed heat flux boundary condition, the heat transfer process is optimized when the entransy dissipation is maximized, while for a fixed temperature boundary condition, the thermal process is optimized when the entransy dissipation is minimized. And more recently, He and Tao [36] put forward a unique formulation of EDEP that for whatever boundary condition the best heat transfer process should have the minimum entransy dissipation per unit heat transferred. And they provided several numerical examples to demonstrate that there exists inherent consistency between the field synergy principle (FSP)[37,38] and EDEP. The performance of four heat exchangers studied in this paper will be evaluated according to the principle. The comprehensive characteristics are compared at 2 fin pitches to demonstrate that the proposed plain fin-and-tube heat exchanger of five tube rows with longitudinal vortex generators can transfer almost the same amount of heat transmitted by the heat exchanger with circular wavy fin-and-tube heat exchanger of 6 tube rows without LVGs. 2 Physical models The plain fin surface enhanced by radiantly arranged winglets [3] and the wavy fin are shown in Fig.1. Fig. 1(a) is a part of the collared wavy fin with six tubes in staggered arrangement. The wavelength of the fin is 10.334 mm, the amplitude of the fin is 2mm, and the
diameter of the step outside the tubes is 18.0mm. The fin thickness df is 0.115mm, tube diameter Dc is 13mm, transverse tube pitch Pt is 27.5mm and longitudinal tube pitch Pl is 15.875mm. The fin pitch fp has 2 different values, namely 2.54mm and 2.117mm. In Fig. 1(b) near each tube there are 12 surrounding winglets on the plain fin. The delta winglets are punched out from the plain fin. The chord of the winglets l is 5mm. The attack angle α of the six winglets, defined as the angle between the chord and the tube bank centerline, is 50, 50, 50, 50, 70 and 110 degree respectively. The height of winglets h is 2.002mm. The delta winglets stand just perpendicular to the base surface and act as an obstacle to the coming flow, hence, can increase the disturbance of air flow. The fin pitch, fin thickness, tube diameter, transverse tube pitch and longitudinal tube pitch are identical to the wavy fin structure shown in Fig. 1(a). The heat exchangers studied in this paper are two wavy fin-and-tube heat exchangers with 6 rows of tubes at the fin pitch of 2.54mm and 2.117mm. In the later presentation these two fins will be denoted by 10-wavy and 12-wavy for short, respectively, where 10 and 12 imply that 10 fins per inch and 12 fins per inch respectively; and two proposed plain fin-and-tube heat exchangers with 5 rows of tubes at the fin pitch of 2.54mm and 2.117mm (10-LVG and 12-LVG for short) correspondingly. The water circuit arrangements of the two forms of heat exchangers are shown in Fig.3. The tubes are made of copper and the fins of aluminum. 3 Experimental apparatus and procedure The experiments are conducted in an open suction wind-tunnel. The test system consists of two cycles: air cycle and water cycle. The air cycle is used to blow and heat the air across the finned tube bundles, and the water cycle is designed to supply cold water through the tubes of test core. The overall flow direction of air and water is counter-flow. The air-water system is schematically shown in Fig. 4. Air is induced to the wind-tunnel by a centrifugal blower. Section 2 in Fig.4 is an air heater composed of 6 rows of heating rods, for one of the heating rods its power is finetuned and the other five have fixed heating power; Air is heated to achieve an inlet temperature of about 75 degrees of centigrade before entering the heat exchanger. The transition section, contraction section and the straightening section are used to make the inlet air flow uniform. The test section is one of the above-mentioned four heat
exchangers, being an air–water heat exchanger in which air is going across the finned tubes and water is flowing inside tubes. The inlet air temperature and the temperature difference between inlet and outlet through the test core are measured by two sets of selfmade multi-junction T-type copper-constantan thermocouple grids. Each set has 16 grid points which are interconnected in series to give a single reading. The mixture of water and ice is used as cold terminal temperature compensation. After being cooled by cold water in the testing section, air leaves the test core and flows through the flow metering duct before being discharged outside the test room. The average static pressure before the test section and the pressure drop of the heat exchanger are measured by a U-tube water (or mercury) column manometer or an inclined manometer, depending on the range of the pressure drop. The air velocity is measured by a Pitot tube meter, which is located in the flow measuring duct far downstream of the test core. The heat exchangers and the windtunnel before the test section are covered by foam insulation of about 40 mm thick to reduce the heat loss to the surroundings. The cooling water is pumped into the system from a water tank, and passes through the tubes of the heat exchanger. Cooling water receives heat from air in the core section of fin-and-tube heat exchanger. After that, the heated water is cooled down by an outdoor cooling tower. Then it returns to the water tank for recycling. The temperature of the water is measured by four-wire Pt100 thermal resistance thermometers; the volume flow rate of water is adjusted by electrically operated valves located on the water pipeline; and the pressure drop of water side is obtained using pressure drop transducers. The air inlet temperature, temperature difference between inlet and outlet, volume flow rate of water, temperature of water at inlet and outlet, and pressure drop of water side are collected by the KEITHLEY 2700 multi-channel data acquisition unit and 7708 data acquisition card. This provides enormous convenience for displaying the test results on the screen graphically and monitoring the operational state. The accuracy of these apparatus will be shown in Section 4.2. The barometric pressure is also measured to determine the physical properties of air. 4 Data reduction and experimental uncertainty 4.1 Data reduction The main purpose of this part is to determine the Nusselt number (Nu) or Colburn
factor ( j ) and friction factor (f ) of the tested air-side surface from the experimental data, and then find out the corresponding correlations of Nu vs. Re and f vs. Re for each case. The air side heat transfer rate is given as:
a ma cp,a T
(1)
where ma is the air mass flow rate, T is the temperature difference between the inlet and the outlet, and cp,a is the specific heat at constant pressure of air. cp,a together with other physical properties of both water and air is evaluated at the average of the inlet and outlet temperature according [39]. The water side heat transfer rate is:
w mw cp,w (Tout Tin )
(2)
where mw is the water mass flow rate, Tout is the outlet temperature of water and Tin is the inlet temperature. The average heat transfer rate of the air side and the water side is defined as the heat transfer rate to determine the heat transfer coefficient:
m a w / 2
(3)
The heat balance deviation is defined as:
w a m 100%
(4)
During the experiment is controlled less than 5% to reach the thermal balance. The overall heat transfer coefficient k is obtained by:
k
m
Aa tm
(5)
where tm is the logarithmic-mean temperature difference defined by: tm
tmax tmin ln tmax tmin
tmax ta,in tw,out
(6) (7)
tmin ta,out tw,in
(8)
Aa in Eq.(5) is the total area of air side including outside area of the tubes A1 and the fin area A2 . The average heat transfer coefficient of tube side is calculated by Gnielinski equation [40, 41] with the effect of thermo-physical property variation being considered, shown by Equations (9-11), where the average value of the inlet and outlet temperature of working fluid is taken as the reference temperature. The characteristic dimension is the inner diameter of the tube.
Nuw
f ' 8 Re 1000 Pr 1 d w
1 12.7 f ' 8 Prw2/3 1
f ' 1.8lg Re 1.5 Pr c w Prt
l i
2/3
c
2
(9)
(10)
0.11
(11)
With the overall heat transfer coefficient and the tube-side heat transfer coefficient at hand, the average air-side heat transfer coefficient can be obtained by the so called thermal resistance separation method or the Wilson plot technique as described by[39,42]:
1 1 Aa Aa 1 k hw Aw Aw ha '
(12)
where ha , hw are the heat transfer coefficient of air side and water side, respectively,
is the wall thickness of the tube. Since ha ' in equation (12) always comes together when designing heat exchangers, and in order to avoid the uncertainty of fin efficiency , we define the product of ha ' as ha . The uncertainty of fin structure during process, the contact heat resistance are both included in ha . Thus the air side total heat transfer coefficient can be expressed as in equation (13) without considering the fin efficiency separately. From Equation (12) we can get the air side heat transfer coefficient:
ha
1
Aa A d o di 1 ( a ) k hw Aw 2 Aw
(13)
d o and d i are the outside and inside tube diameter, respectively, and is the heat
conductivity coefficient of heat exchanger tube. Air side Reynolds number and Nusselt number are obtained as follows：
Re
uin d o
Nu
a
ha d o
a
(14)
(15)
Air side friction factor is defined as：
f
P L
d o / (0.5 a uin2 )
(16)
where P is the pressure drop of air flowing through the test section, and L is the length of fin. 4.2 Experimental uncertainty The measurement uncertainties are estimated along the line described in [44]. Firstly the uncertainty of the overall heat transfer coefficient k in equation (5) is determined. As the heat balance deviation is controlled less than 5% during the experiment process, the heat transfer rate can be then treated approximately as m a w when calculate the uncertainty of heat transfer rate. All the geometric parameters including surface area Aa are offered by the heat exchanger producer, thus we ignore the uncertainty of these parameters. As for the uncertainty of logarithmic-mean temperature difference in equation (5), the accuracy of platinum resistance thermometers together with copperconstantan thermocouple (see Table 2) has to be considered. Then by taking the uncertainty of thermophysical properties like thermal conductivity and specific heat cp as 2%, and ignoring the uncertainty of fin efficiency, we can finally obtain the
uncertainty of Nu number through equations (12), (14) and (16). The same process can be done for calculating uncertainty of friction factor f. It is obvious that the larger the
measured value the smaller the related uncertainty. The uncertainty values for the entire measurement range are given in Table 3. It can be seen from the table that the maximum uncertainty of Nusselt number is about 7% and that of friction factor is about 9%. 5 Results and discussion 5.1 Experimental Results Experiments are carried out with the inlet air velocity from 1.5 to 7.5m/s. The heat transfer rate and pressure drop on the air side of the four heat exchangers are presented in Fig. 5. It is to be noted that 10- and 12-LVG are of five tubes,while 10- and 12-wavy are of six tubes. As shown in the figures, the heat transfer rate and pressure drop of five-row LVGs enhanced fin are almost the same with that of six-row wavy fin at the two fin pitches investigated, and more noticeably, the pressure drops of five-row LVGs enhanced fin are almost identical to that of six-row wavy fin. Thus we can conclude that the proposed fin-and-tube heat exchanger can replace the wavy fin-and-tube heat exchanger. The row number of tubes is reduced from 6 to 5. The average Nu and f values are shown in Fig. 6 and Fig. 7 respectively. As can be expected the Nusselt number increases with increasing air frontal velocity for all the four heat transfer surfaces tested in this paper. For both LVGs enhanced fin and the wavy fin, the Nusselt number with fin pitch of 2.117 mm is larger than that of fin pitch of 2.54mm. That is to say, for the cases studied small fin pitch can enhance heat transfer. For the same fin pitch, the LVGs enhanced fin has higher Nusselt number than that of the wavy fin. Fig. 7 shows that the friction factor f decreases with the increase of air frontal velocity. Among the four fin surfaces f of 12-LVG is the highest at the same frontal velocity, that of 10-wavy is the lowest, with 12-wavy and 10-LVG in between. Obviously, the friction factor increases with the decrease in fin pitch and at the same fin pitch, LVGs enhanced fin has higher f than that of the wavy fin. Data fitting is tried to get the correlations for heat transfer and friction factors and following results are obtained with their maximum deviation being provided within the brackets: 10-LVG：Nu=0.420Re0.592 (5.77%); f=3.00Re-0.153(3.39%) Re=2078-9390
10-wavy：Nu=0.101Re0.643 (6.22%); f=3.39Re-0.181(2.34%) Re=1980-9447 12-LVG：Nu=0.369Re0.624 (7.13%); f=4.44Re-0.150(2.87%) Re=1826-9432 12-wavy：Nu=0.467Re0.561 (4.86%); f=7.48Re-0.243(3.11%) Re=1890-9506 The heat exchangers used in most air conditioning operations are within this range, hence the correlations can be used for some design purpose.
5.2 Numerical analysis The authors also conduct numerical simulations of the four heat exchange surfaces with air as the heat transfer medium to find the reason of heat transfer enhancement. The fin pitch and the velocity range are different from that in [25]. In this paper the fin pitches of both 2.117 mm and 2.54mm are simulated, the height of winglet is remained as 2.002 mm for the convenience of machining. Laminar model is used for velocity from 1.5 to 3.5 m/s, and k- turbulence model is used for higher velocities. The computational region is extended upstream by two times of the streamwise fin length, and ten times of the fin region downstream [25]. Inlet velocity and air temperature is given at the inlet. The outflow boundary condition is employed for outlet. The neighboring two fins’ center planes are chosen as the lower and upper boundaries of the computational domain due to the periodicity of the airside channels in z direction. As for the spanwise direction, the computational region is bounded by two adjacent center lines of tubes and is set as symmetry boundary conditions. The tube temperature is constant during numerical simulation. After grid independence examination, around 1.95 million meshes are adopted for LVGs enhanced fins, and 1.85 million meshes for wavy fins. The Nu number and friction factor f for 10-wavy fin are descripted in Fig.8. It can be seen in the figure that the simulation coincides with the experimental variation tendency. The maximum deviation of Nu is 12.5%, and the average deviation is 8.33%; the maximum deviation of f is 14.4%, the average deviation is 8.66%. For such heat exchanger of real size, these numerical deviations from experiment data are acceptable and the numerical simulation results can be used to decipher the enhancement mechanism.
The velocity contours on the central plane of air channels of the four structures are shown in Fig.9. These results are obtained at the inlet velocity of 4m/s. The inlet air temperature is 305 K, and the tube temperature 280 K. It can be seen from Fig.9(a) that for 10-wavy fin, there exist obvious wake region after each tube, especially for the sixth one. According to field synergy principle[37,38], stagnation or wake region is always unfavorable in heat exchanger because in these zones fluid velocity is low, and heat transfer is also weak. As for the 12-wavy fin in Fig.9(c), the wake region is slightly reduced and velocity near the tubes is increased, but fluid gathers at the trough of the wavy fin and velocity is low there consequently. While for the 10-LVG and 12-LVG cases in Fig.9(b) and Fig.9(d) such low velocity regions after each tube have almost been disappeared. This is because the local flow channels (passages) formed between the latter two winglets for each tube are beneficial to the reduction of wake region. In addition the local flow passages formed by the first four pairs of winglets can guide the moving fluid from the main flow towards the tube wall, leading to some impinging effect on the tube wall for increasing the local velocity. And in the vicinity of each LVG, the fluid is fully disturbed and mixed, which also contributes to the enhancement of the proposed fin. The temperature distributions at the same plane are shown in Fig. 10. Because of the above-mentioned flow pattern of the LVG structure, the fluid temperature in the most part of the fin in Fig.10(b) and Fig.10(d) is more uniform than the fluid temperature distribution in wavy fin cases. It’s also shown in the figure that the fluid temperature variation around the last tube for the wavy cases are very small, which implies that the last tube is working in a very inefficient regime. This also provides the necessityof reducing the tube rows from 6 to 5. Both the temperature and velocity distributions in Fig.9 and Fig.10 are in full compliance with the heat transfer rate in Fig. 5, which gives a good explanation for the enhancement of heat transfer for the proposed fin. 5.3. Entransy analysis The definition of the entransy change when air flows over the finned tubes is as follows [36]:
1 1 E cv maTin 2 cv maTout 2 cv ma Tin Tout Tt 2 2
(17)
where ΔE is the entransy dissipation of the heat transfer process, cv is specific heat at constant volume for air, and ma is the mass flow rate. The variation of entransy dissipation versus Re for four different fins according to numerical simulation is shown in Fig.11. The entransy dissipation increases with the increase of Reynolds number. Under the constant tube wall temperature condition, 10-wavy and 10-LVG have almost the same amount of entransy dissipation. And the same is true for 12-wavy and 12-LVG. Noting that either 10-wavy or 12-wavy have 6-row tubes, while either 10-LVG or 12-LVG have only 5-row tubes (see Fig.10), this phenomenon once again demonstrates the feasibility of replacing the 6-row tubes heat exchanger with 5-row tube one. The entransy dissipation per unit heat transfer rate ΔE/Ф at different Re number is shown in Fig. 12. As indicated in [36], the smaller the value of entransy dissipation per unit heat transfer rate, the better the synergy between velocity and temperature difference. Therefore it’s concluded from the figure that 10-LVG fin has better synergy than 10wavy fin, and the same is true for 12-wavy and 12-LVG. 6 Conclusions In this study, four fin-and-tube heat exchangers are experimentally investigated and the following conclusions can be drawn: (1) The 5-row tubes of plain fin surface enhanced by LVGs can substitute the 6 rows wavy fin for the 2 fin pitches tested; (2) Both the LVGs enhanced fin and the wavy fin of smaller fin pitch have higher Nusselt number and friction factor. (3) Entransy analysis proves that the proposed LVG enhanced fin have better heat transfer performance than the wavy fin, theoretically supporting the replacement of sixrow wavy fin by five-row of plain fin with LVGs. Acknowledgments This study was supported by the National Basic Key Research Program of China (973 Program) (2013CB22830) and Key Project of International Joint Research of National Natural Science Foundation of China (51320105004) and 111 Project (B16038).
NOMENCLATURE Latin Symbols A
heat transfer area
cp
specific heat at constant pressure
cv
specific heat at constant volume
ΔE
entransy dissipation
f
friction factor
j
Colburn factor
L
effective length of fin
Nu
Nusselt number
ΔP
pressure drop
Re
Reynolds number
T
temperature Greek Symbols
attack angle
Ф
heat transfer rate
conductivity factor fluid
density of fluid
dynamic viscosity Subscripts
a
air side
f
fin
i
inside of the tube
in
inlet
m
mean value
o
outside of the tube
out
outlet
t
tube wall
w
water side
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Figure captions Fig. 1 Configurations of the proposed enhanced fin and wavy fin Fig. 2 Sketch of the LVGs enhanced fin Fig. 3 Sketch of water circuit arrangements Fig.4. Experimental facility Fig. 5 Heat transfer rate and pressure drop for the four kinds of heat exchanger Fig.6 Air side Nusselt number vs. Reynolds number for the four structures Fig.7 Air side friction factor vs. Reynolds number for the four structures Fig.8 Comparison of experimental and numerical Nu and f for 10-wavy fin Fig. 9. Temperature distribution of four structures Fig. 10. Velocity distribution of four structures Fig.11 Entransy dissipation of the four structures Fig.12 Entransy dissipation per unit heat transfer rate versus Re
air
(a)Wavy fin
(b) Proposed fin
Fig. 1 Configurations of the proposed enhanced fin and wavy fin
Fig. 2 Sketch of the LVGs enhanced fin
air
(a) Proposed fin(5 rows)
(b) Wavy fin(6 rows)
Fig. 3 Sketch of water circuit arrangements
1) Entrance; 2) Air heater; 3) Transition Section; 4) Contraction Section; 5) Straightening Section; 6) Test Heat Exchanger; 7) Flow Metering Duct; 8) Blower; 9) Water tank; 10)Water pump; 11) Volumetric Meter; 12) Data Acquisition System; 13) U Tube Manometer; 14) Cooling tower
Fig.4. Experimental facility
(a) Fin pitch of 2.002mm
(b)Fin pitch of 2.425mm Fig. 5 Heat transfer rate and pressure drop for the 4 kinds of heat exchanger
Fig.6 Air side Nusselt number vs. Reynolds number for the four structures
Fig.7 Air side friction factor vs. Reynolds number for the four structures
(a) Comparison of experimental and numerical results for Nu of 10-wavy fin
(b) Comparison of experimental and numerical results for f of 10-wavy fin
Fig.8 Comparison of experimental and numerical Nu and f for 10-wavy fin
Unit: m/s (a) 10-wavy
(b) 10-LVG
(c) 12-wavy
(c) 12-LVG Fig. 9. Velocity distribution of four structures
Unit: K (a) 10-wavy
(b) 10-LVG
(c) 12-wavy
(d)12-LVG Fig. 10. Temperature distribution of four structures
(a) Entransy dissipation versus Re for 10-LVG and 10-wavy
(b) Entransy dissipation versus Re for 12-LVG and 12-wavy Fig. 11 Entransy dissipation of the four structures
(a) Entransy dissipation per unit for 10-LVG and 10-wavy
(b) Entransy dissipation per unit for 12-LVG and 12-wavy Fig. 12 Entransy dissipation per unit heat transfer rate versus Re
Table Captions Tab. 1 Typical arrangement of LVGs in literatures Tab. 2 Test range and accuracy of the measuring instruments Tab. 3 The maximum measurement uncertainties of test range
Table 1 Typical arrangement of LVGs near tube in literatures Authors and year
LVGs arrangement
Chen, 1998 [20]
inline
Chen, 2000 [21]
staggered array
Torii, 2002 [22]
common-flow-up
Torii, 2002 [22]
common-flow-down
He,2010 [23]
“V”字形布置
Fan,2011 [11]
混合布置方式
Authors and year Chen, 1998 [2119]
Chen, 2000 [22 20]
Torii, 2002 [23 21] He,2010 [24 22] He,2012 [25 23] Fan,2011 [11 10]
LVG arrangement
Table 2 Test range and accuracy of the measuring instruments Measuring instruments Platinum resistance thermometers Turbo volume flow meters Copper-constantan thermocouple U-tube manometer Inclined tube micro pressure gauge
Range -100-200℃ 8.5-60m3/h -200-100℃
Accuracy 0.15℃ 1% 0.2℃ 0.1mm 0.5%
Table 3 The maximum measurement uncertainties of test range Item
10LVG
10wavy
12LVG
12wavy
Air side Nusselt number (%)
6.53
6.15
6.60
6.92
Air side friction factor (%)
8.15
8.22
8.92
8.95
Highlights The 5-row tubes of LVGs enhanced fin can substitute the 6 rows wavy fin; The 12-LVG fin has the highes Nu number and friction factor compared with other fins. Entransy analysis proves that the proposed fin have better heat transfer performance.