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Numerical study of nanofluid flow in flat tubes fitted with multiple twisted tapes
Advanced Powder Technology xxx (2015) xxx–xxx
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Original Research Paper
Numerical study of nanofluid flow in flat tubes fitted with multiple twisted tapes Hamed Safikhani ⇑, Farzad Abbasi Department of Mechanical Engineering, Faculty of Engineering, Arak University, Arak 38156-88349, Iran
a r t i c l e
i n f o
Article history: Received 13 June 2015 Received in revised form 30 August 2015 Accepted 14 September 2015 Available online xxxx Keywords: Multiple twisted tapes HTE Nanofluid Flat tubes Two phase model Mixture model
a b s t r a c t In this paper, while numerically simulating the Al2O3–water nanofluid flow in flat tubes fitted with twisted tapes, the effects of three different Heat Transfer Enhancement (HTE) methods are also separately evaluated and compared. These three HTE mechanisms include the use of nanofluid instead of the base fluid, use of flat tubes instead of circular tubes and the use of twisted tapes inside the tubes. The obtained results indicate that although all the three mentioned mechanisms improve the heat transfer within the tubes, the HTE due to the use of twisted tapes is greater than that caused by the other two mechanisms. After discovering that the simultaneous use of the three mentioned mechanisms can considerably increase the amount of heat transfer, three different arrangements of the twisted tapes in the nanofluid-containing flat tubes are also evaluated and compared. These three arrangements include the use of one twisted tape, use of two twisted tapes in the same direction and the use of two twisted tapes in different directions. The obtained results indicate that the use of two twisted tapes in different directions leads to the highest amounts of heat transfer and pressure drop in flat tubes. Ó 2015 The Society of Powder Technology Japan. Published by Elsevier B.V. and The Society of Powder Technology Japan. All rights reserved.
1. Introduction Heat Transfer Enhancement (HTE) in the tubes used in various industrial applications and consequently reducing the volume of industrial equipment is a subject that has been investigated by engineers and researchers for many years. In general, the heat transfer enhancing methods can be divided into active and passive approaches; which the passive method, due to its ease of use and lower cost, has greatly attracted the attention of the researchers and engineers. An important and useful way of passively enhancing the amount of heat transfer in tubes is the use of a nanofluid instead of base fluid. A nanofluid refers to a compound in which solid, and mostly metallic, particles at nano sizes (usually less than 100 nm) are added to an ordinary fluid and help increase the value of the mixture conductivity and thus improve the amount of heat transfer in that fluid. Due to a considerable enhancement of heat transfer and a negligible pressure drop achieved by nanofluids, relative to base fluids, the use of nanofluids has become very commonplace in recent years [1–7]. Another technique for passively enhancing the heat transfer in tubes is using the swirl flow devices such as Twisted Tapes (TTs) ⇑ Corresponding author. Tel./fax: +98 863664758. E-mail addresses: (H. Safikhani).
[email protected],
[email protected]
which produce secondary recirculation on the axial flow leading to an increase of tangential and radial turbulent fluctuation. This allows a greater mixing of fluid inside tubes. In recent years, the HTE by twisted tape inserts has been considered by several researchers [8–17]. Eiamsa-ard et al. [11] investigated the heat transfer and pressure loss behaviors in a double pipe heat exchanger fitted with regularly-spaced twisted tape elements at several space ratios. Effect of the combined conical-ring turbulator and twisted tape on the heat transfer, friction factor and thermal performance factor characteristics were also studied by Promvonge and Eiamsa-ard [12]. The effects of twist ratio and rotation angle of TTs on the HTE are very important. In recent years several researchers have investigated the effects of rotation angle and twist ratio on the TTs performance [14–17]. Mengna et al. [14] used a converging–diverging tube with evenly spaced twisted tape to investigate the pressure drop and compound heat transfer characteristics experimentally. By varying twist ratio and rotation angle various swirl patterns were generated. It was shown that the heat transfer and pressure drop increase with an increase in twist angle. Wang et al. [15] analyzed the numerical modeling for the optimization of regularly spaced short-length twisted tape in a circular tube. The parameters are given by the spacing between two twisted tapes, twist ratio and twist angle. It was found that the mean heat transfer and flow resistance increase with an increase in twist angle.
http://dx.doi.org/10.1016/j.apt.2015.09.002 0921-8831/Ó 2015 The Society of Powder Technology Japan. Published by Elsevier B.V. and The Society of Powder Technology Japan. All rights reserved.
Please cite this article in press as: H. Safikhani, F. Abbasi, Numerical study of nanofluid flow in flat tubes fitted with multiple twisted tapes, Advanced Powder Technology (2015), http://dx.doi.org/10.1016/j.apt.2015.09.002
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H. Safikhani, F. Abbasi / Advanced Powder Technology xxx (2015) xxx–xxx
Nomenclature a Cp C Dh dp f g h H k kB L Nu P Pr q00 Re T V W Z
acceleration (m s2) specific heat (J kg1 K1) constant in Eq. (14) hydraulic diameter of tubes (m) diameter of nanoparticles (m) skin friction coefficient gravitational acceleration (m s2) local heat transfer coefficient (W m2 K1) height of flat tube (m) thermal conductivity (W m1 K1) Boltzmann constant (=1.3807 1023 J K1) length of tubes (m) Nusselt number (¼ hDh =k) pressure (Pa) Prandtl number (¼ am =mm ) heat flux (W m2) Reynolds number (¼ VDh =mm ) temperature (K) velocity (m s1) width of flat tube (m) axial coordinate in the tubes
Greek symbols a thermal diffusivity (¼ k=qC p ) b volumetric expansion coefficient (K1)
One of the other methods to enhance the heat transfer in tubes is the use of flat tubes instead of circular ones. Compared to circular tubes, the flat tubes have higher surface area to cross sectional area ratio, which can be used to increase the compactness and enhance the heat transfer of the heat exchangers. In recent years, a number of researchers have investigated the use of flat tubes instead of circular tubes [18–22]. So far, no analytical, numerical or experimental research on combining the three HTE mechanisms has been carried out; although different combinations of two of these three mechanisms have been investigated. Eiamsa-ard and Kiatkittipong [23] studied the effect of the simultaneous use of twisted tapes and nanofluid on Nusselt number and friction factor. In their experimental and numerical investigations, they evaluated different arrangements of twisted tapes in circular tubes. Ibrahim [24] experimentally studied the simultaneous use of twisted tapes and flat tubes in turbulent flow. Razi et al. [25] experimentally investigated the concurrent use of flat tubes and nanofluid. In their research, the flow regime was laminar and the nanofluid used was CuO–oil. Safikhani and Abbassi [26] numerically studied the effect of using flat tubes and nanofluid together on the flow field of nanofluid. In another research, Safikhani et al. [27] applied multi-objective optimization to optimize the simultaneous use of nanofluids and flat tubes. Based on our information, no research has been conducted so far on the simultaneous use of three HTE mechanisms: nanofluid, twisted tapes and flat tubes. In this paper, the effect of using the three mentioned HTE mechanisms together on the thermal and hydraulic behaviors of flow are numerically explored. Different arrangements of twisted tapes and flat tubes will be analyzed.
d / kf
l m q sw
distance between particles (m) nanoparticles volume fraction mean free path of water molecular (m) dynamic viscosity (N s m2) kinematic viscosity (m2 s1) density (kg m3) wall shear stress
Subscripts BF base fluid P plain tube dr drift f fluid i inlet conditions k indices m mixture p nanoparticle phase w wall Abbreviations STT Single Twisted Tape D-Co-TT Dual Co-Twisted Tapes D-C-TT Dual Counter Twisted Tapes HTE Heat Transfer Enhancement
the schematics of the geometries investigated in this paper. The specifications of the tubes illustrated in this figure have been listed in Table 1. It should be mentioned that the flat tubes have a circumference equal to that of circular tubes [18,19,21,22]. As is indicated in Fig. 1, three different arrangements of twisted tapes will be evaluated in this paper, which include one twisted tape, two twisted tapes in the same direction and two twisted tapes in different directions.
2. Mathematical modeling 2.1. Geometry The geometries explored in this paper are different combinations of circular tubes, flat tubes and twisted tapes. Fig. 1 shows
Fig. 1. The details of geometries which will be investigated in this paper.
Please cite this article in press as: H. Safikhani, F. Abbasi, Numerical study of nanofluid flow in flat tubes fitted with multiple twisted tapes, Advanced Powder Technology (2015), http://dx.doi.org/10.1016/j.apt.2015.09.002
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H. Safikhani, F. Abbasi / Advanced Powder Technology xxx (2015) xxx–xxx
The acceleration (a) in Eq. (9) is
Table 1 Different geometrical parameters of tubes. Tubes length Tubes perimeter Twisted tapes pitch Twisted tapes thickness Twist ratio Rotation angle
a ¼ g ðV m rÞV m
1m 31.4 mm 18 mm 0.5 mm 1.8–3 180 deg
2.3. Nanofluid mixture properties The mixture properties for Al2O3–water nanofluid are calculated based on following expressions: Density [30]:
2.2. Mixture model In this article, numerical simulation of nanofluid flow in flat tubes fitted with twisted tapes is performed using mixture model which is a single fluid two phase method. This approach investigates equilibrium over spatial length scales. In this method each phase has its own velocity field, and in a given control volume there is a certain fraction of base fluid and nanoparticles. Instead of utilizing the governing equations of each phase separately, it solves the continuity, momentum and energy equations for the mixture of phases, and the volume fraction equation for nanoparticles. The equations for the steady state conditions: Continuity:
r ðqm V m Þ ¼ 0
ð1Þ
qm ¼ /qp þ ð1 /Þqf ðqC p Þm ¼ /ðqC p Þp þ ð1 /ÞðqC p Þf Dynamic viscosity [32]:
lm ¼ lf þ
1 VB ¼ dp
ð2Þ
C¼ ¼ r ðkm rTÞ
ð3Þ
k¼1
ð15Þ
3
p
ð16Þ
dp 6/
ðC 1 dp þ C 2 Þ/ þ ðC 3 dp þ C 4 Þ
where C1, C2, C3 and C4 are given as:
C 3 ¼ 0:00000009;
r ð/P qP V m Þ ¼ r ð/P qP V dr;P Þ
ð4Þ
where Vm is the mass average velocity:
Pn
k¼1 /k
qk V k
ð5Þ
qm
ð17Þ
lf
C 1 ¼ 0:000001133;
Volume fraction:
Vm ¼
sffiffiffiffiffiffiffiffiffiffiffiffiffiffi 18kB T pqp dp
!
n X /k V k ðqk Hk þ PÞ
ð14Þ
72Cd
C in Eq. (14) is defined as:
k¼1
Energy:
qp V B d2p
where VB and d are the Brownian motion of nanoparticles and the distance between nanoparticles respectively and is calculated from:
d¼
!
qm;i bm gðT T i Þ
ð13Þ
rffiffiffiffiffiffi
r ðqm V m V m Þ ¼ rP þ r ðlm rV m Þ þ r n X /k qk V dr;k V dr;k
ð12Þ
Specific heat capacity [31]:
Momentum:
r
ð11Þ
C 2 ¼ 0:000002771
C 4 ¼ 0:000000393
ð18Þ
Thermal conductivity [33]:
0:3690 0:7476 df km kp ¼ 1 þ 64:7/0:7460 Pr 0:9955 Ref1:2321 f kf dp kf
ð19Þ
where Ref and Prf can be expressed as:
In Eq. (2), Vdr,k is the drift velocity for nanoparticles:
ð6Þ
Ref ¼
qkB T 3pv2 kf
ð20Þ
The slip velocity is calculated as the velocity of nanoparticles relative to the velocity of base fluid:
Prf ¼
v qf af
ð21Þ
V dr;k ¼ V k V m
V pf ¼ V p V f
ð7Þ
The relation between drift velocity and relative velocity is as follows:
V dr;p ¼ V pf
n X /k q k¼1
qm
k
ð8Þ
V fk
qP d2P ðqP qm Þ a 18lf f drag qP (
f drag ¼
B
v ¼ A 10TC ; A ¼ 2:414 105 ; B ¼ 247:8; C ¼ 140 ð22Þ
The relative velocity and drag function are calculated using Manninen et al. [28] and Schiller and Naumann [29] relations respectively, as follows:
V pf ¼
where kf is the MFP (mean free path) of water molecular (kf = 0.17 nm), kB is Boltzmann constant (kB = 1.3807 1023 J/ K) and v can be defined by the following equation:
1 þ 0:15Re0:687 P
for ReP 1000
0:0183ReP
for ReP > 1000
ð9Þ
Thermal expansion coefficient [34]:
2
bm ¼ 4
3
1 1þ
ð1/Þqf /qp
bp 1 þ / bf 1 þ 1/
qp qf
5bf
ð23Þ
2.4. Boundary conditions
ð10Þ The boundary conditions are as follows:
Please cite this article in press as: H. Safikhani, F. Abbasi, Numerical study of nanofluid flow in flat tubes fitted with multiple twisted tapes, Advanced Powder Technology (2015), http://dx.doi.org/10.1016/j.apt.2015.09.002
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H. Safikhani, F. Abbasi / Advanced Powder Technology xxx (2015) xxx–xxx
Tubes inlet:
V m;z ¼ V i ; V m;x ¼ V m;y ¼ 0
ð24aÞ
T ¼ Ti
ð24bÞ
/ ¼ /i
ð24cÞ
dT P q00 ¼ cte ¼ dz A qUC p
ð26bÞ
2.5. Numerical methods Fluid–wall interface:
V m;x ¼ V m;y ¼ V m;z ¼ 0
ð25aÞ
@T q00w ¼ km @n w
ð25bÞ
Tubes outlet: Zero gradient is applied to hydrodynamic variables and constant gradient is applied to temperature [4,35]:
dV z ¼0 dz
ð26aÞ
Table 2 The detailed information in simulations. Base fluid Nanoparticles
Water Al2O3
Water Density (kg/m3) Heat Capacity (J/kg K) Thermal conductivity (W/m K)
998.2 4185 0.6028
Al2O3 Density (kg/m3) Heat Capacity (J/kg K) Thermal conductivity (W/m K) Average diameter (nm) Volume fraction (%)
3720 880 35 40 0–3
Wall heat flux (kW/m2) Reynolds number Inlet temperature (°C)
4 100–2000 28
The numerical simulation is performed using the finite volume method. A second order upwind method is used for the convective and diffusive terms and the SIMPLE algorithm is employed to solve the coupling between the velocity and pressure fields. More over the detailed information of simulations are presented in Table 2. To make sure that the obtained results are independent of the size and the number of generated grids, several grids with different sizes along the axial, radial and angular directions has been tested for each tube; and it has been attempted to consider for each tube the best grid, with the highest accuracy and the lowest computation cost. As an example of grid independency test (GIT) results, Table 3 shows the axial velocity and temperature at the centerline region for D-Co-TT tube. As it is shown in Table 3, except case 35 55 180, increasing and decreasing the grid numbers does not change significantly the velocity and temperature values. Hence for D-Co-TT tube, the case 45 65 190 is used. Fig. 2 shows a sample of grid generation for flat tubes fitted with twisted tapes.
Table 3 Grid independency test results for D-Co-TT tube. Node number (/ r z)
Axial velocity (m/s)
Temperature (K)
45 65 190 55 65 190 35 65 190 45 75 190 45 55 190 45 65 200 45 65 180 35 55 180 55 75 200
0.04112 0.04117 0.04113 0.04111 0.04115 0.04111 0.04119 0.04107 0.04112
321.857 321.855 321.850 321.851 321.859 321.857 321.852 321.848 321.855
Fig. 2. A sample of grid generation for D-Co-TT: (a) isometric view and related zoomed view, (b) sectioned view and related zoomed view.
Please cite this article in press as: H. Safikhani, F. Abbasi, Numerical study of nanofluid flow in flat tubes fitted with multiple twisted tapes, Advanced Powder Technology (2015), http://dx.doi.org/10.1016/j.apt.2015.09.002
H. Safikhani, F. Abbasi / Advanced Powder Technology xxx (2015) xxx–xxx
pares the local heat transfer coefficient of nanofluid flow for a plain tube of present study with the experimental data of Kim et al. [36] and numerical data of Ebrahimnia et al. [4]. As is evident from this figure the present simulations agree well with the available experimental and numerical data.
2.6. Validations To attain confidence about the simulations, it is necessary to compare the simulation results with the available data. Fig. 3 com-
Fig. 3. Comparison of local heat transfer coefficient with the available related data for circular tube working with nanofluid.
Fig. 4. Comparison of (a) Nu and (b)
Fig. 5. Comparison of (a) f and (b)
5
Fig. 6. Comparison of g for three different HTE mechanisms.
Nu , NuP;BF
f , f P;BF
for three different HTE mechanisms.
for three different HTE mechanisms.
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3. Results Numerical simulations of Al2O3–water nanofluid flow in plain and flat tubes fitted with different arrangements of twisted tapes are performed using two phase mixture model. All of the simulations are performed at / ¼ 3% and dp ¼ 40 nm. 3.1. Effect of each of the three different heat transfer enhancement mechanisms In this section, the effect of each of the three different heat transfer enhancement mechanisms on the thermal and hydrody-
namic behaviors of the fluid flow will be investigated. Fig. 4(a) shows the Nusselt number versus different Reynolds numbers in laminar flow for five different cases: circular tube without twisted tape and containing base fluid (base case), circular tube without twisted tape and containing nanofluid (mechanism 1), circular tube with twisted tape and containing base fluid (mechanism 2), flat tube without twisted tape and containing base fluid (mechanism 3) and, finally, flat tube with twisted tape and containing nanofluid (mechanism 1, 2 and 3). In fact, this figure compares the effects of three heat transfer enhancement mechanisms separately and with all these mechanisms applied together. Also, Fig. 4(b) demonstrates the increase in the values obtained by each
Fig. 7. Comparison of temperature distribution, axial velocity contour and secondary flow vectors at tubes outlet for three different HTE mechanisms: (a) plain tube-base fluid, (b) plain tube-nanofluid, (c) plain tube + STT-base fluid, (d) flat tube-base fluid, and (e) flat tube + STT- nanofluid.
Please cite this article in press as: H. Safikhani, F. Abbasi, Numerical study of nanofluid flow in flat tubes fitted with multiple twisted tapes, Advanced Powder Technology (2015), http://dx.doi.org/10.1016/j.apt.2015.09.002
H. Safikhani, F. Abbasi / Advanced Powder Technology xxx (2015) xxx–xxx
mechanism relative to the case in which no heat transfer enhancement mechanism is used (circular tube without any twisted tape and with a base fluid), at different Reynolds numbers. According to these two figures, although each of the three mentioned mechanisms increases the amount of heat transfer, using the twisted tapes in tubes have more of an increasing effect compared to the other two mechanisms and, on the average, can increase the heat transfer coefficient by 30% (with averaging performed at different Reynolds numbers). The use of flat tubes can increase the Nusselt number by an average of 16%. And finally, the use of nanofluid instead of base fluid can increase the Nusselt number by 8%. The very important point that should be mentioned here is that all the mentioned values pertain to the existing conditions in this research. For example, if twisted tapes with different dimension (different pitch) or a flat tube with different degree of flattening or a nanofluid with different concentration and diameter of nanoparticles are used, different values will be obtained. According to Fig. 5(b), in case of using all the three mentioned mechanisms together, the Nusselt number improves (increases) by 50% on the average. Fig. 5(a) and (b) shows the effects of using the three mentioned mechanisms on the friction factor of tubes. According to these two figures, although all the three mechanisms improve the amount of heat transfer, they also lead to the destruction of friction factor and consequently the increasing the pressure drop in fluid. The trend of friction factor increase is exactly similar to the trend of heat transfer improvement; meaning that the use of twisted tapes in the tubes causes the highest increase in the friction factor (an average
Fig. 8. Comparison of (a) Nu and (b)
Fig. 9. Comparison of (a) f and (b)
Nu , NuP;BF
f , f P;BF
7
increase of 160%). Following that, the use of flat tubes leads to about 50% increase in the value of friction factor. Finally, using a nanofluid instead of a base fluid increases the friction factor by about 5%. As is indicated by Fig. 5(b), the simultaneous use of the three mentioned mechanisms increases the friction factor by 220%. As preliminary design guidance to the selection of a technique, the thermal performance factor can be evaluated based on the power consumption per unit mass of fluid. The thermal performance factor, g is defined as the ratio between the heat transfer coefficient for the tube with heat transfer enhancement (ht) and the value for the plain tube (hp) at identical pumping power. g can be defined by the following equation [23]:
!13 ht Nut Nut ft g¼ ¼ ¼ hp pp Nup pp Nup fp
ð27Þ
where Nut and Nup, are respectively, Nusselt number for tube with HTE mechanism and plain tube while ft and fp, are respectively, friction factor for tube with HTE mechanism and plain tube. The effect of three different HTE mechanisms on thermal performance factor at the same pumping power is shown in Fig. 6. Apparently, in high Re numbers (Re > 1000), using nanofluid has the highest g and in low Re numbers (Re < 1000), using the combination of all of the three HTE mechanisms has the highest g. For displaying the details of the flow field in each of the mentioned cases, Fig. 7 shows the contours of temperature, velocity and secondary vectors at the outlet sections of pipes. The informa-
for nanofluid flow in flat tube fitted with three different twisted tape arrangements.
for nanofluid flow in flat tube fitted with three different twisted tape arrangements.
Please cite this article in press as: H. Safikhani, F. Abbasi, Numerical study of nanofluid flow in flat tubes fitted with multiple twisted tapes, Advanced Powder Technology (2015), http://dx.doi.org/10.1016/j.apt.2015.09.002
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H. Safikhani, F. Abbasi / Advanced Powder Technology xxx (2015) xxx–xxx
tion displayed in this figure can be useful in thermal designing of the tubes utilized in different industrial devices.
3.2. Effect of using different arrangements of twisted tapes in nanofluid-containing flat tubes It was shown in the previous section that all the three mechanisms used in this paper lead to the enhancement of heat transfer. In this section, by simultaneously using all the three mechanisms, the effect of different arrangements of twisted tapes in flat tubes containing nanofluid will be evaluated. Fig. 8(a) and (b) shows
Fig. 10. Comparison of g for nanofluid flow in flat tube fitted with three different twisted tape arrangements.
the Nusselt number at different Reynolds numbers in a laminar flow for three different cases: flat tube fitted with one twisted tape and containing nanofluid, flat tube with two twisted tapes in the same direction and containing nanofluid and flat tube with two twisted tapes in different directions and containing nanofluid. As these two figures indicate, by using two twisted tapes in the same direction a larger Nusselt number is obtained relative to using just one tape; which is attributed to the greater mixing of the fluid in the former case. Similarly, by using two twisted tapes in different directions a larger Nusselt number is obtained relative to the case where two tapes in the same direction are utilized. In fact, the use of two twisted tapes in the same direction increases the Nusselt number by 72% and the use of two twisted tapes in different directions increases the Nusselt number by 76% compared to the use of circular tube with no tapes inside and containing a base fluid. Fig. 9(a) and (b) illustrates the effects of the above mentioned arrangements for twisted tapes on the friction factor of tubes. According to these two figures, the use of two twisted tapes in the same direction increases the friction factor by an average of 320% and the use of two twisted tapes in different directions increases the friction factor by an average of 340% relative to the use of circular tube with no twisted tapes and containing base fluid. The effect of different twisted tapes arrangement on thermal performance factor at the same pumping power is shown in Fig. 10. As shown, in all of the Re numbers, using D-C-TT arrangement has the highest g. For displaying the details of the flow field in each of the 3 mentioned cases, Fig. 11 shows the contours of temperature, velocity and secondary vectors at the outlet sections of tubes. The information displayed in this figure can be useful in thermal designing of the tubes utilized in different industrial devices. An important point revealed by the findings of this paper is that each mechanism that causes an improvement in the amount of heat transfer also increases the friction factor and consequently contributes to more pressure drop in the tubes. Therefore, by per-
Fig. 11. Comparison of temperature distribution, axial velocity contour and secondary flow vectors at tubes outlet for nanofluid flow in flat tube fitted with three different twisted tape arrangements; (a) STT, (b) D-Co-TT, and (c) D-C-TT.
Please cite this article in press as: H. Safikhani, F. Abbasi, Numerical study of nanofluid flow in flat tubes fitted with multiple twisted tapes, Advanced Powder Technology (2015), http://dx.doi.org/10.1016/j.apt.2015.09.002
H. Safikhani, F. Abbasi / Advanced Powder Technology xxx (2015) xxx–xxx
forming a multi-objective optimization, the optimal working points that satisfy both the heat transfer and friction factor values can be determined. 4. Conclusions In this paper, while numerically simulating the flow of Al2O3– water nanofluid in flat tubes fitted with twisted tapes, the effects of three different heat transfer enhancement mechanisms were also separately evaluated and compared. These three mechanisms included the use of nanofluid instead of base fluid, use of flat tubes instead of circular tubes and the use of twisted tapes in the tubes. The obtained results indicated that although each of these mechanisms improves the amount of heat transfer in the tubes, a greater heat transfer enhancement results by the use of twisted tapes than by the other two mechanisms; of course the pressure drop in the tubes is also greater due to the use of twisted tapes. The results also indicated that the simultaneous use of all these three mechanisms can substantially increase the amounts of heat transfer and friction factor in the tubes by 50% and 220%, respectively. Three different arrangements of twisted tapes in nanofluid-containing flat tubes were also investigated and compared. These arrangements consisted of one twisted tape, two twisted tapes in the same direction and two twisted tapes in different directions. The findings revealed that the use of two twisted tapes in different directions leads to maximum improvement in the amount of heat transfer (by an average of about 76%) and maximum friction factor (by an average of about 340%) in the tubes. From the overall findings of this paper it can be concluded that each mechanism that causes an improvement in the amount of heat transfer, also increases the friction factor and thus contributes to more pressure drop in the tubes. Therefore, by performing a multi-objective optimization procedure, the optimal working points that are able to satisfy both the heat transfer and friction factor values can be determined. References [1] S. Das, N. Putra, P. Thiesen, R. Roetzel, Temperature dependence of thermal conductivity enhancement for nanofluids, J. Heat Transfer 125 (2003) 567– 574. [2] S. Murshed, K. Leong, C. Yang, A combined model for the effective thermal conductivity of nanofluids, Appl. Therm. Eng. 29 (2009) 2477–2483. [3] T. Teng, Y. Hung, T. Teng, H. Mo, H. Hsu, The effect of alumina/water nanofluid particle size on thermal conductivity, Appl. Therm. Eng. 30 (2010) 2213–2218. [4] E. Ebrahimnia-Bajestan, H. Niazmand, W. Duangthongsuk, S. Wongwises, Numerical investigation of effective parameters in convective heat transfer of nanofluids flowing under a laminar flow regime, Int. J. Heat Mass Transfer 54 (2010) 4376–4388. [5] M. Kalteh, A. Abbassi, M. Saffar-Avval, J. Harting, Eulerian–Eulerian two-phase numerical simulation of nanofluid laminar forced convection in a microchannel, Int. J. Heat Fluid Flow 32 (2011) 107–116. [6] R. Lotfi, Y. Saboohi, A. Rashidi, Numerical study of forced convective heat transfer of nanofluids: comparison of different approaches, Int. Commun. Heat Mass Transfer 37 (2010) 74–78. [7] M. Shariat, A. Akbarinia, A. Hossein Nezhad, A. Behzadmehr, R. Laur, Numerical study of two phase laminar mixed convection nanofluid in elliptic ducts, Appl. Therm. Eng. 31 (2011) 2348–2359. [8] S.K. Saha, A. Dutta, S.K. Dhal, Friction and heat transfer characteristics of laminar swirl flow through a circular tube fitted with regularly spaced twistedtape elements, Int. J. Heat Mass Transfer 44 (2001) 4211–4223. [9] S. Ray, A.W. Date, Friction and heat transfer characteristics of flow through square duct with twisted tape insert, Int. J. Heat Mass Transfer 46 (2003) 889– 902.
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Nasr, M.A. Akhavan Behabadi, S.E. Marashi, Performance evaluation of flattened tube in boiling heat transfer enhancement and its effect on pressure drop, Int. Commun. Heat Mass Transfer 37 (2010) 430–436. [20] R. Vajjha, D. Das, P. Namburu, Numerical study of fluid dynamic and heat transfer performance of Al2O3 and CuO nanofluids in the flat tubes of a radiator, Int. J. Heat Fluid Flow 31 (2010) 613–621. [21] J. Quiben, L. Cheng, J. Da Silva, J. Thome, Flow boiling in horizontal flattened tubes: Part I – Two-phase frictional pressure drop results and model, Int. J. Heat Mass Transfer 52 (2009) 3645–3653. [22] J. Quiben, L. Cheng, J. da Silva, J. Thome, Flow boiling in horizontal flattened tubes: Part II – Flow boiling heat transfer results and model, Int. J. Heat Mass Transfer 52 (2009) 3634–3644. [23] S. Eiamsa-ard, K. Kiatkittipong, Heat transfer enhancement by multiple twisted tape inserts and TiO2/water nanofluid, Appl. Therm. Eng. 70 (2014) 896–924. [24] E.Z. Ibrahim, Augmentation of laminar flow and heat transfer in flat tubes by means of helical screw-tape inserts, Energy Convers. Manage. 52 (2011) 250– 257. [25] P. Razi, M. Akhavan-Behabadi, M. Saeedinia, Pressure drop and thermal characteristics of CuO–base oil nanofluid laminar flow in flattened tubes under constant heat flux, Int. Commun. Heat Mass Transfer 38 (2011) 964–971. [26] H. Safikhani, A. Abbassi, Effects of tube flattening on the fluid dynamic and heat transfer performance of nanofluid flow, Adv. Powder Technol. 25 (3) (2014) 1132–1141. [27] H. Safikhani, A. Abbassi, A. Khalkhali, M. Kalteh, Multi-objective optimization of nanofluid flow in flat tubes using CFD, artificial neural networks and genetic algorithms, Adv. Powder Technol. 25 (2014) 1608–1617. [28] M. Manninen, V. Taivassalo, S. Kallio, On the Mixture Model for Multiphase Flow, VTT Publications, 1996. [29] L. Schiller, A. Naumann, A drag coefficient correlation, Z. Ver. Deutsch. Ing. 77 (1935) 318–320. [30] B. Pak, Y. Cho, Hydrodynamic and heat transfer study of dispersed fluids with submicron metallic oxide particles, Exp. Heat Transfer 11 (1998) 151–170. [31] Y. Xuan, W. Roetzel, Conceptions for heat transfer correlation of nanofluids, Int. J. Heat Mass Transfer 43 (2000) 3701–3707. [32] N. Masoumi, N. Sohrabi, A. Behzadmehr, A new model for calculating the effective viscosity of nanofluids, J. Appl. Phys. 42 (2009) 055501. [33] C. Chon, K. Kihm, S. Lee, S. Choi, Empirical correlation finding the role of temperature and particle size for nanofluid (Al2O3) thermal conductivity enhancement, J. Appl. Phys. 87 (2005) 153107 (3). [34] K. Khanafer, K. Vafai, M. Lightstone, Buoyancy driven heat transfer enhancement in a two dimensional enclosure utilizing nanofluids, Int. J. Heat Mass Transfer 46 (2003) 3639–3653. [35] A. Bejan, Convective Heat Transfer, John Wiley & Sons Inc., 2004. [36] D. Kim, Y. Kwon, Y. Cho, C. Li, S. Cheong, Y. Hwang, J. Lee, D. Hong, S. 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Original Research Paper
Numerical study of nanofluid flow in flat tubes fitted with multiple twisted tapes Hamed Safikhani ⇑, Farzad Abbasi Department of Mechanical Engineering, Faculty of Engineering, Arak University, Arak 38156-88349, Iran
a r t i c l e
i n f o
Article history: Received 13 June 2015 Received in revised form 30 August 2015 Accepted 14 September 2015 Available online xxxx Keywords: Multiple twisted tapes HTE Nanofluid Flat tubes Two phase model Mixture model
a b s t r a c t In this paper, while numerically simulating the Al2O3–water nanofluid flow in flat tubes fitted with twisted tapes, the effects of three different Heat Transfer Enhancement (HTE) methods are also separately evaluated and compared. These three HTE mechanisms include the use of nanofluid instead of the base fluid, use of flat tubes instead of circular tubes and the use of twisted tapes inside the tubes. The obtained results indicate that although all the three mentioned mechanisms improve the heat transfer within the tubes, the HTE due to the use of twisted tapes is greater than that caused by the other two mechanisms. After discovering that the simultaneous use of the three mentioned mechanisms can considerably increase the amount of heat transfer, three different arrangements of the twisted tapes in the nanofluid-containing flat tubes are also evaluated and compared. These three arrangements include the use of one twisted tape, use of two twisted tapes in the same direction and the use of two twisted tapes in different directions. The obtained results indicate that the use of two twisted tapes in different directions leads to the highest amounts of heat transfer and pressure drop in flat tubes. Ó 2015 The Society of Powder Technology Japan. Published by Elsevier B.V. and The Society of Powder Technology Japan. All rights reserved.
1. Introduction Heat Transfer Enhancement (HTE) in the tubes used in various industrial applications and consequently reducing the volume of industrial equipment is a subject that has been investigated by engineers and researchers for many years. In general, the heat transfer enhancing methods can be divided into active and passive approaches; which the passive method, due to its ease of use and lower cost, has greatly attracted the attention of the researchers and engineers. An important and useful way of passively enhancing the amount of heat transfer in tubes is the use of a nanofluid instead of base fluid. A nanofluid refers to a compound in which solid, and mostly metallic, particles at nano sizes (usually less than 100 nm) are added to an ordinary fluid and help increase the value of the mixture conductivity and thus improve the amount of heat transfer in that fluid. Due to a considerable enhancement of heat transfer and a negligible pressure drop achieved by nanofluids, relative to base fluids, the use of nanofluids has become very commonplace in recent years [1–7]. Another technique for passively enhancing the heat transfer in tubes is using the swirl flow devices such as Twisted Tapes (TTs) ⇑ Corresponding author. Tel./fax: +98 863664758. E-mail addresses: (H. Safikhani).
[email protected],
[email protected]
which produce secondary recirculation on the axial flow leading to an increase of tangential and radial turbulent fluctuation. This allows a greater mixing of fluid inside tubes. In recent years, the HTE by twisted tape inserts has been considered by several researchers [8–17]. Eiamsa-ard et al. [11] investigated the heat transfer and pressure loss behaviors in a double pipe heat exchanger fitted with regularly-spaced twisted tape elements at several space ratios. Effect of the combined conical-ring turbulator and twisted tape on the heat transfer, friction factor and thermal performance factor characteristics were also studied by Promvonge and Eiamsa-ard [12]. The effects of twist ratio and rotation angle of TTs on the HTE are very important. In recent years several researchers have investigated the effects of rotation angle and twist ratio on the TTs performance [14–17]. Mengna et al. [14] used a converging–diverging tube with evenly spaced twisted tape to investigate the pressure drop and compound heat transfer characteristics experimentally. By varying twist ratio and rotation angle various swirl patterns were generated. It was shown that the heat transfer and pressure drop increase with an increase in twist angle. Wang et al. [15] analyzed the numerical modeling for the optimization of regularly spaced short-length twisted tape in a circular tube. The parameters are given by the spacing between two twisted tapes, twist ratio and twist angle. It was found that the mean heat transfer and flow resistance increase with an increase in twist angle.
http://dx.doi.org/10.1016/j.apt.2015.09.002 0921-8831/Ó 2015 The Society of Powder Technology Japan. Published by Elsevier B.V. and The Society of Powder Technology Japan. All rights reserved.
Please cite this article in press as: H. Safikhani, F. Abbasi, Numerical study of nanofluid flow in flat tubes fitted with multiple twisted tapes, Advanced Powder Technology (2015), http://dx.doi.org/10.1016/j.apt.2015.09.002
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H. Safikhani, F. Abbasi / Advanced Powder Technology xxx (2015) xxx–xxx
Nomenclature a Cp C Dh dp f g h H k kB L Nu P Pr q00 Re T V W Z
acceleration (m s2) specific heat (J kg1 K1) constant in Eq. (14) hydraulic diameter of tubes (m) diameter of nanoparticles (m) skin friction coefficient gravitational acceleration (m s2) local heat transfer coefficient (W m2 K1) height of flat tube (m) thermal conductivity (W m1 K1) Boltzmann constant (=1.3807 1023 J K1) length of tubes (m) Nusselt number (¼ hDh =k) pressure (Pa) Prandtl number (¼ am =mm ) heat flux (W m2) Reynolds number (¼ VDh =mm ) temperature (K) velocity (m s1) width of flat tube (m) axial coordinate in the tubes
Greek symbols a thermal diffusivity (¼ k=qC p ) b volumetric expansion coefficient (K1)
One of the other methods to enhance the heat transfer in tubes is the use of flat tubes instead of circular ones. Compared to circular tubes, the flat tubes have higher surface area to cross sectional area ratio, which can be used to increase the compactness and enhance the heat transfer of the heat exchangers. In recent years, a number of researchers have investigated the use of flat tubes instead of circular tubes [18–22]. So far, no analytical, numerical or experimental research on combining the three HTE mechanisms has been carried out; although different combinations of two of these three mechanisms have been investigated. Eiamsa-ard and Kiatkittipong [23] studied the effect of the simultaneous use of twisted tapes and nanofluid on Nusselt number and friction factor. In their experimental and numerical investigations, they evaluated different arrangements of twisted tapes in circular tubes. Ibrahim [24] experimentally studied the simultaneous use of twisted tapes and flat tubes in turbulent flow. Razi et al. [25] experimentally investigated the concurrent use of flat tubes and nanofluid. In their research, the flow regime was laminar and the nanofluid used was CuO–oil. Safikhani and Abbassi [26] numerically studied the effect of using flat tubes and nanofluid together on the flow field of nanofluid. In another research, Safikhani et al. [27] applied multi-objective optimization to optimize the simultaneous use of nanofluids and flat tubes. Based on our information, no research has been conducted so far on the simultaneous use of three HTE mechanisms: nanofluid, twisted tapes and flat tubes. In this paper, the effect of using the three mentioned HTE mechanisms together on the thermal and hydraulic behaviors of flow are numerically explored. Different arrangements of twisted tapes and flat tubes will be analyzed.
d / kf
l m q sw
distance between particles (m) nanoparticles volume fraction mean free path of water molecular (m) dynamic viscosity (N s m2) kinematic viscosity (m2 s1) density (kg m3) wall shear stress
Subscripts BF base fluid P plain tube dr drift f fluid i inlet conditions k indices m mixture p nanoparticle phase w wall Abbreviations STT Single Twisted Tape D-Co-TT Dual Co-Twisted Tapes D-C-TT Dual Counter Twisted Tapes HTE Heat Transfer Enhancement
the schematics of the geometries investigated in this paper. The specifications of the tubes illustrated in this figure have been listed in Table 1. It should be mentioned that the flat tubes have a circumference equal to that of circular tubes [18,19,21,22]. As is indicated in Fig. 1, three different arrangements of twisted tapes will be evaluated in this paper, which include one twisted tape, two twisted tapes in the same direction and two twisted tapes in different directions.
2. Mathematical modeling 2.1. Geometry The geometries explored in this paper are different combinations of circular tubes, flat tubes and twisted tapes. Fig. 1 shows
Fig. 1. The details of geometries which will be investigated in this paper.
Please cite this article in press as: H. Safikhani, F. Abbasi, Numerical study of nanofluid flow in flat tubes fitted with multiple twisted tapes, Advanced Powder Technology (2015), http://dx.doi.org/10.1016/j.apt.2015.09.002
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H. Safikhani, F. Abbasi / Advanced Powder Technology xxx (2015) xxx–xxx
The acceleration (a) in Eq. (9) is
Table 1 Different geometrical parameters of tubes. Tubes length Tubes perimeter Twisted tapes pitch Twisted tapes thickness Twist ratio Rotation angle
a ¼ g ðV m rÞV m
1m 31.4 mm 18 mm 0.5 mm 1.8–3 180 deg
2.3. Nanofluid mixture properties The mixture properties for Al2O3–water nanofluid are calculated based on following expressions: Density [30]:
2.2. Mixture model In this article, numerical simulation of nanofluid flow in flat tubes fitted with twisted tapes is performed using mixture model which is a single fluid two phase method. This approach investigates equilibrium over spatial length scales. In this method each phase has its own velocity field, and in a given control volume there is a certain fraction of base fluid and nanoparticles. Instead of utilizing the governing equations of each phase separately, it solves the continuity, momentum and energy equations for the mixture of phases, and the volume fraction equation for nanoparticles. The equations for the steady state conditions: Continuity:
r ðqm V m Þ ¼ 0
ð1Þ
qm ¼ /qp þ ð1 /Þqf ðqC p Þm ¼ /ðqC p Þp þ ð1 /ÞðqC p Þf Dynamic viscosity [32]:
lm ¼ lf þ
1 VB ¼ dp
ð2Þ
C¼ ¼ r ðkm rTÞ
ð3Þ
k¼1
ð15Þ
3
p
ð16Þ
dp 6/
ðC 1 dp þ C 2 Þ/ þ ðC 3 dp þ C 4 Þ
where C1, C2, C3 and C4 are given as:
C 3 ¼ 0:00000009;
r ð/P qP V m Þ ¼ r ð/P qP V dr;P Þ
ð4Þ
where Vm is the mass average velocity:
Pn
k¼1 /k
qk V k
ð5Þ
qm
ð17Þ
lf
C 1 ¼ 0:000001133;
Volume fraction:
Vm ¼
sffiffiffiffiffiffiffiffiffiffiffiffiffiffi 18kB T pqp dp
!
n X /k V k ðqk Hk þ PÞ
ð14Þ
72Cd
C in Eq. (14) is defined as:
k¼1
Energy:
qp V B d2p
where VB and d are the Brownian motion of nanoparticles and the distance between nanoparticles respectively and is calculated from:
d¼
!
qm;i bm gðT T i Þ
ð13Þ
rffiffiffiffiffiffi
r ðqm V m V m Þ ¼ rP þ r ðlm rV m Þ þ r n X /k qk V dr;k V dr;k
ð12Þ
Specific heat capacity [31]:
Momentum:
r
ð11Þ
C 2 ¼ 0:000002771
C 4 ¼ 0:000000393
ð18Þ
Thermal conductivity [33]:
0:3690 0:7476 df km kp ¼ 1 þ 64:7/0:7460 Pr 0:9955 Ref1:2321 f kf dp kf
ð19Þ
where Ref and Prf can be expressed as:
In Eq. (2), Vdr,k is the drift velocity for nanoparticles:
ð6Þ
Ref ¼
qkB T 3pv2 kf
ð20Þ
The slip velocity is calculated as the velocity of nanoparticles relative to the velocity of base fluid:
Prf ¼
v qf af
ð21Þ
V dr;k ¼ V k V m
V pf ¼ V p V f
ð7Þ
The relation between drift velocity and relative velocity is as follows:
V dr;p ¼ V pf
n X /k q k¼1
qm
k
ð8Þ
V fk
qP d2P ðqP qm Þ a 18lf f drag qP (
f drag ¼
B
v ¼ A 10TC ; A ¼ 2:414 105 ; B ¼ 247:8; C ¼ 140 ð22Þ
The relative velocity and drag function are calculated using Manninen et al. [28] and Schiller and Naumann [29] relations respectively, as follows:
V pf ¼
where kf is the MFP (mean free path) of water molecular (kf = 0.17 nm), kB is Boltzmann constant (kB = 1.3807 1023 J/ K) and v can be defined by the following equation:
1 þ 0:15Re0:687 P
for ReP 1000
0:0183ReP
for ReP > 1000
ð9Þ
Thermal expansion coefficient [34]:
2
bm ¼ 4
3
1 1þ
ð1/Þqf /qp
bp 1 þ / bf 1 þ 1/
qp qf
5bf
ð23Þ
2.4. Boundary conditions
ð10Þ The boundary conditions are as follows:
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Tubes inlet:
V m;z ¼ V i ; V m;x ¼ V m;y ¼ 0
ð24aÞ
T ¼ Ti
ð24bÞ
/ ¼ /i
ð24cÞ
dT P q00 ¼ cte ¼ dz A qUC p
ð26bÞ
2.5. Numerical methods Fluid–wall interface:
V m;x ¼ V m;y ¼ V m;z ¼ 0
ð25aÞ
@T q00w ¼ km @n w
ð25bÞ
Tubes outlet: Zero gradient is applied to hydrodynamic variables and constant gradient is applied to temperature [4,35]:
dV z ¼0 dz
ð26aÞ
Table 2 The detailed information in simulations. Base fluid Nanoparticles
Water Al2O3
Water Density (kg/m3) Heat Capacity (J/kg K) Thermal conductivity (W/m K)
998.2 4185 0.6028
Al2O3 Density (kg/m3) Heat Capacity (J/kg K) Thermal conductivity (W/m K) Average diameter (nm) Volume fraction (%)
3720 880 35 40 0–3
Wall heat flux (kW/m2) Reynolds number Inlet temperature (°C)
4 100–2000 28
The numerical simulation is performed using the finite volume method. A second order upwind method is used for the convective and diffusive terms and the SIMPLE algorithm is employed to solve the coupling between the velocity and pressure fields. More over the detailed information of simulations are presented in Table 2. To make sure that the obtained results are independent of the size and the number of generated grids, several grids with different sizes along the axial, radial and angular directions has been tested for each tube; and it has been attempted to consider for each tube the best grid, with the highest accuracy and the lowest computation cost. As an example of grid independency test (GIT) results, Table 3 shows the axial velocity and temperature at the centerline region for D-Co-TT tube. As it is shown in Table 3, except case 35 55 180, increasing and decreasing the grid numbers does not change significantly the velocity and temperature values. Hence for D-Co-TT tube, the case 45 65 190 is used. Fig. 2 shows a sample of grid generation for flat tubes fitted with twisted tapes.
Table 3 Grid independency test results for D-Co-TT tube. Node number (/ r z)
Axial velocity (m/s)
Temperature (K)
45 65 190 55 65 190 35 65 190 45 75 190 45 55 190 45 65 200 45 65 180 35 55 180 55 75 200
0.04112 0.04117 0.04113 0.04111 0.04115 0.04111 0.04119 0.04107 0.04112
321.857 321.855 321.850 321.851 321.859 321.857 321.852 321.848 321.855
Fig. 2. A sample of grid generation for D-Co-TT: (a) isometric view and related zoomed view, (b) sectioned view and related zoomed view.
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H. Safikhani, F. Abbasi / Advanced Powder Technology xxx (2015) xxx–xxx
pares the local heat transfer coefficient of nanofluid flow for a plain tube of present study with the experimental data of Kim et al. [36] and numerical data of Ebrahimnia et al. [4]. As is evident from this figure the present simulations agree well with the available experimental and numerical data.
2.6. Validations To attain confidence about the simulations, it is necessary to compare the simulation results with the available data. Fig. 3 com-
Fig. 3. Comparison of local heat transfer coefficient with the available related data for circular tube working with nanofluid.
Fig. 4. Comparison of (a) Nu and (b)
Fig. 5. Comparison of (a) f and (b)
5
Fig. 6. Comparison of g for three different HTE mechanisms.
Nu , NuP;BF
f , f P;BF
for three different HTE mechanisms.
for three different HTE mechanisms.
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3. Results Numerical simulations of Al2O3–water nanofluid flow in plain and flat tubes fitted with different arrangements of twisted tapes are performed using two phase mixture model. All of the simulations are performed at / ¼ 3% and dp ¼ 40 nm. 3.1. Effect of each of the three different heat transfer enhancement mechanisms In this section, the effect of each of the three different heat transfer enhancement mechanisms on the thermal and hydrody-
namic behaviors of the fluid flow will be investigated. Fig. 4(a) shows the Nusselt number versus different Reynolds numbers in laminar flow for five different cases: circular tube without twisted tape and containing base fluid (base case), circular tube without twisted tape and containing nanofluid (mechanism 1), circular tube with twisted tape and containing base fluid (mechanism 2), flat tube without twisted tape and containing base fluid (mechanism 3) and, finally, flat tube with twisted tape and containing nanofluid (mechanism 1, 2 and 3). In fact, this figure compares the effects of three heat transfer enhancement mechanisms separately and with all these mechanisms applied together. Also, Fig. 4(b) demonstrates the increase in the values obtained by each
Fig. 7. Comparison of temperature distribution, axial velocity contour and secondary flow vectors at tubes outlet for three different HTE mechanisms: (a) plain tube-base fluid, (b) plain tube-nanofluid, (c) plain tube + STT-base fluid, (d) flat tube-base fluid, and (e) flat tube + STT- nanofluid.
Please cite this article in press as: H. Safikhani, F. Abbasi, Numerical study of nanofluid flow in flat tubes fitted with multiple twisted tapes, Advanced Powder Technology (2015), http://dx.doi.org/10.1016/j.apt.2015.09.002
H. Safikhani, F. Abbasi / Advanced Powder Technology xxx (2015) xxx–xxx
mechanism relative to the case in which no heat transfer enhancement mechanism is used (circular tube without any twisted tape and with a base fluid), at different Reynolds numbers. According to these two figures, although each of the three mentioned mechanisms increases the amount of heat transfer, using the twisted tapes in tubes have more of an increasing effect compared to the other two mechanisms and, on the average, can increase the heat transfer coefficient by 30% (with averaging performed at different Reynolds numbers). The use of flat tubes can increase the Nusselt number by an average of 16%. And finally, the use of nanofluid instead of base fluid can increase the Nusselt number by 8%. The very important point that should be mentioned here is that all the mentioned values pertain to the existing conditions in this research. For example, if twisted tapes with different dimension (different pitch) or a flat tube with different degree of flattening or a nanofluid with different concentration and diameter of nanoparticles are used, different values will be obtained. According to Fig. 5(b), in case of using all the three mentioned mechanisms together, the Nusselt number improves (increases) by 50% on the average. Fig. 5(a) and (b) shows the effects of using the three mentioned mechanisms on the friction factor of tubes. According to these two figures, although all the three mechanisms improve the amount of heat transfer, they also lead to the destruction of friction factor and consequently the increasing the pressure drop in fluid. The trend of friction factor increase is exactly similar to the trend of heat transfer improvement; meaning that the use of twisted tapes in the tubes causes the highest increase in the friction factor (an average
Fig. 8. Comparison of (a) Nu and (b)
Fig. 9. Comparison of (a) f and (b)
Nu , NuP;BF
f , f P;BF
7
increase of 160%). Following that, the use of flat tubes leads to about 50% increase in the value of friction factor. Finally, using a nanofluid instead of a base fluid increases the friction factor by about 5%. As is indicated by Fig. 5(b), the simultaneous use of the three mentioned mechanisms increases the friction factor by 220%. As preliminary design guidance to the selection of a technique, the thermal performance factor can be evaluated based on the power consumption per unit mass of fluid. The thermal performance factor, g is defined as the ratio between the heat transfer coefficient for the tube with heat transfer enhancement (ht) and the value for the plain tube (hp) at identical pumping power. g can be defined by the following equation [23]:
!13 ht Nut Nut ft g¼ ¼ ¼ hp pp Nup pp Nup fp
ð27Þ
where Nut and Nup, are respectively, Nusselt number for tube with HTE mechanism and plain tube while ft and fp, are respectively, friction factor for tube with HTE mechanism and plain tube. The effect of three different HTE mechanisms on thermal performance factor at the same pumping power is shown in Fig. 6. Apparently, in high Re numbers (Re > 1000), using nanofluid has the highest g and in low Re numbers (Re < 1000), using the combination of all of the three HTE mechanisms has the highest g. For displaying the details of the flow field in each of the mentioned cases, Fig. 7 shows the contours of temperature, velocity and secondary vectors at the outlet sections of pipes. The informa-
for nanofluid flow in flat tube fitted with three different twisted tape arrangements.
for nanofluid flow in flat tube fitted with three different twisted tape arrangements.
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H. Safikhani, F. Abbasi / Advanced Powder Technology xxx (2015) xxx–xxx
tion displayed in this figure can be useful in thermal designing of the tubes utilized in different industrial devices.
3.2. Effect of using different arrangements of twisted tapes in nanofluid-containing flat tubes It was shown in the previous section that all the three mechanisms used in this paper lead to the enhancement of heat transfer. In this section, by simultaneously using all the three mechanisms, the effect of different arrangements of twisted tapes in flat tubes containing nanofluid will be evaluated. Fig. 8(a) and (b) shows
Fig. 10. Comparison of g for nanofluid flow in flat tube fitted with three different twisted tape arrangements.
the Nusselt number at different Reynolds numbers in a laminar flow for three different cases: flat tube fitted with one twisted tape and containing nanofluid, flat tube with two twisted tapes in the same direction and containing nanofluid and flat tube with two twisted tapes in different directions and containing nanofluid. As these two figures indicate, by using two twisted tapes in the same direction a larger Nusselt number is obtained relative to using just one tape; which is attributed to the greater mixing of the fluid in the former case. Similarly, by using two twisted tapes in different directions a larger Nusselt number is obtained relative to the case where two tapes in the same direction are utilized. In fact, the use of two twisted tapes in the same direction increases the Nusselt number by 72% and the use of two twisted tapes in different directions increases the Nusselt number by 76% compared to the use of circular tube with no tapes inside and containing a base fluid. Fig. 9(a) and (b) illustrates the effects of the above mentioned arrangements for twisted tapes on the friction factor of tubes. According to these two figures, the use of two twisted tapes in the same direction increases the friction factor by an average of 320% and the use of two twisted tapes in different directions increases the friction factor by an average of 340% relative to the use of circular tube with no twisted tapes and containing base fluid. The effect of different twisted tapes arrangement on thermal performance factor at the same pumping power is shown in Fig. 10. As shown, in all of the Re numbers, using D-C-TT arrangement has the highest g. For displaying the details of the flow field in each of the 3 mentioned cases, Fig. 11 shows the contours of temperature, velocity and secondary vectors at the outlet sections of tubes. The information displayed in this figure can be useful in thermal designing of the tubes utilized in different industrial devices. An important point revealed by the findings of this paper is that each mechanism that causes an improvement in the amount of heat transfer also increases the friction factor and consequently contributes to more pressure drop in the tubes. Therefore, by per-
Fig. 11. Comparison of temperature distribution, axial velocity contour and secondary flow vectors at tubes outlet for nanofluid flow in flat tube fitted with three different twisted tape arrangements; (a) STT, (b) D-Co-TT, and (c) D-C-TT.
Please cite this article in press as: H. Safikhani, F. Abbasi, Numerical study of nanofluid flow in flat tubes fitted with multiple twisted tapes, Advanced Powder Technology (2015), http://dx.doi.org/10.1016/j.apt.2015.09.002
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forming a multi-objective optimization, the optimal working points that satisfy both the heat transfer and friction factor values can be determined. 4. Conclusions In this paper, while numerically simulating the flow of Al2O3– water nanofluid in flat tubes fitted with twisted tapes, the effects of three different heat transfer enhancement mechanisms were also separately evaluated and compared. These three mechanisms included the use of nanofluid instead of base fluid, use of flat tubes instead of circular tubes and the use of twisted tapes in the tubes. The obtained results indicated that although each of these mechanisms improves the amount of heat transfer in the tubes, a greater heat transfer enhancement results by the use of twisted tapes than by the other two mechanisms; of course the pressure drop in the tubes is also greater due to the use of twisted tapes. The results also indicated that the simultaneous use of all these three mechanisms can substantially increase the amounts of heat transfer and friction factor in the tubes by 50% and 220%, respectively. Three different arrangements of twisted tapes in nanofluid-containing flat tubes were also investigated and compared. These arrangements consisted of one twisted tape, two twisted tapes in the same direction and two twisted tapes in different directions. The findings revealed that the use of two twisted tapes in different directions leads to maximum improvement in the amount of heat transfer (by an average of about 76%) and maximum friction factor (by an average of about 340%) in the tubes. From the overall findings of this paper it can be concluded that each mechanism that causes an improvement in the amount of heat transfer, also increases the friction factor and thus contributes to more pressure drop in the tubes. Therefore, by performing a multi-objective optimization procedure, the optimal working points that are able to satisfy both the heat transfer and friction factor values can be determined. References [1] S. Das, N. Putra, P. Thiesen, R. Roetzel, Temperature dependence of thermal conductivity enhancement for nanofluids, J. Heat Transfer 125 (2003) 567– 574. [2] S. Murshed, K. Leong, C. Yang, A combined model for the effective thermal conductivity of nanofluids, Appl. Therm. Eng. 29 (2009) 2477–2483. [3] T. Teng, Y. Hung, T. Teng, H. Mo, H. Hsu, The effect of alumina/water nanofluid particle size on thermal conductivity, Appl. Therm. Eng. 30 (2010) 2213–2218. [4] E. Ebrahimnia-Bajestan, H. Niazmand, W. Duangthongsuk, S. Wongwises, Numerical investigation of effective parameters in convective heat transfer of nanofluids flowing under a laminar flow regime, Int. J. Heat Mass Transfer 54 (2010) 4376–4388. [5] M. Kalteh, A. Abbassi, M. Saffar-Avval, J. Harting, Eulerian–Eulerian two-phase numerical simulation of nanofluid laminar forced convection in a microchannel, Int. J. Heat Fluid Flow 32 (2011) 107–116. [6] R. Lotfi, Y. Saboohi, A. Rashidi, Numerical study of forced convective heat transfer of nanofluids: comparison of different approaches, Int. Commun. Heat Mass Transfer 37 (2010) 74–78. [7] M. Shariat, A. Akbarinia, A. Hossein Nezhad, A. Behzadmehr, R. Laur, Numerical study of two phase laminar mixed convection nanofluid in elliptic ducts, Appl. Therm. Eng. 31 (2011) 2348–2359. [8] S.K. Saha, A. Dutta, S.K. Dhal, Friction and heat transfer characteristics of laminar swirl flow through a circular tube fitted with regularly spaced twistedtape elements, Int. J. Heat Mass Transfer 44 (2001) 4211–4223. [9] S. Ray, A.W. Date, Friction and heat transfer characteristics of flow through square duct with twisted tape insert, Int. J. Heat Mass Transfer 46 (2003) 889– 902.
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Please cite this article in press as: H. Safikhani, F. Abbasi, Numerical study of nanofluid flow in flat tubes fitted with multiple twisted tapes, Advanced Powder Technology (2015), http://dx.doi.org/10.1016/j.apt.2015.09.002