- Email: [email protected]
Thermal and friction characteristics of laminar flow through a circular duct having helical screw-tape with oblique teeth inserts and wire coil inserts
Accepted Manuscript Thermal and Friction Characteristics of Laminar Flow through a Circular Duct having Helical Screw-Tape with Oblique Teeth Inserts and Wire Coil Inserts Sarbendu Roy, Sujoy Kumar Saha PII: DOI: Reference:
S0894-1777(15)00184-3 http://dx.doi.org/10.1016/j.expthermflusci.2015.07.007 ETF 8517
To appear in:
Experimental Thermal and Fluid Science
Received Date: Revised Date: Accepted Date:
31 May 2015 5 July 2015 9 July 2015
Please cite this article as: S. Roy, S.K. Saha, Thermal and Friction Characteristics of Laminar Flow through a Circular Duct having Helical Screw-Tape with Oblique Teeth Inserts and Wire Coil Inserts, Experimental Thermal and Fluid Science (2015), doi: http://dx.doi.org/10.1016/j.expthermflusci.2015.07.007
This is a PDF file of an unedited manuscript that has been accepted for publication. As a service to our customers we are providing this early version of the manuscript. The manuscript will undergo copyediting, typesetting, and review of the resulting proof before it is published in its final form. Please note that during the production process errors may be discovered which could affect the content, and all legal disclaimers that apply to the journal pertain.
Thermal and Friction Characteristics of Laminar Flow through a Circular Duct having Helical Screw-Tape with Oblique Teeth Inserts and Wire Coil Inserts
Sarbendu Roy Email: [email protected]
Sujoy Kumar Saha Email: [email protected]
Mechanical Engineering Department Indian Institute of Engineering Science and Technology Shibpur Howrah 711 103, INDIA
Abstract
Helical screw-tape inserts and wire coil inserts both individually are enhancement techniques. Naturally, therefore, it is worthwhile to try their combinations as a potential enhancement technique. The experimental friction factor and Nusselt number data for laminar flow through a circular duct having helical screw-tape and wire coil inserts have been presented. Predictive friction factor and Nusselt number correlations have also been presented. The thermohydraulic performance has been evaluated. The major findings of this experimental investigation are that the helical screw-tape inserts in combination with wire coil inserts perform significantly better than the individual enhancement technique acting alone for laminar flow through a circular duct up to a certain value of the fin parameter.
Keywords
Laminar Flow, Forced Convection, Wire Coil Inserts, Helical Screw-Tape Inserts, Heat Transfer Enhancement, Swirl Flow
Nomenclature
A: heat transfer area, m2 Ac : axial flow cross-sectional area, = D 2 D , m2 4 Ao: plain duct flow cross-sectional area, = D 2 , m2 4 Cp : constant pressure specific heat, J/kgK D : internal diameter of the plain duct, m d : coil wire diameter, m e: height, m
D f : fully developed Fanning friction factor = 1 2 P 2 V0 z , dimensionless g : gravitational acceleration, m/s2 Gr: Grashof number = g 2 D3Tw / 2 , dimensionless Gz : Graetz number = m C p / kL , dimensionless H : pitch for 1800 rotation of twisted-tape and pitch for wire coil insert, m hz : axially local heat transfer coefficient, W/(m2K). k : fluid thermal conductivity, W/(mK). L : axial length, length of the duct, m
m : mass flow rate, kg/min L
Num : axially averaged Nusselt number =
1 hz Ddz , dimensionless L 0 k
Pz : pressure drop, mm
P : pressure drop, N/m2 P
: wetted perimeter in the particular cross-section of the duct, coil pitch, m
Pr : fluid Prandtl number =
C p k
, dimensionless
Ra : Rayleigh number = Gr Pr
Re : Reynolds number based on plain duct diameter =
V0 D
, dimensionless
T : temperature, K thl: Tooth horizontal length, dimensionless ∆Tw : wall to fluid bulk temperature difference, K Vo : mean velocity based on plain duct diameter = m
A0 , m/s
X: Prn, the value of n depends on the exponent of Pr in the correlation
Y: b w
0.14
1 5.172
z : axial length, the distance between the measuring pressure taps, m
Greek Symbols :
D α: coil helix angle, α= tan H o
-1
β : coefficient of isobaric thermal expansion, K-1 µ : fluid dynamic viscosity, kg/ms. ρ : density of the fluid, kg/m3. θ: tooth angle, Ө
Subscripts : b : at bulk fluid temperature m: axially averaged w : at duct wall temperature, with z : local value
1. Introduction Laminar flow is encountered in many industrial applications. In case of laminar flow, there is major thermal resistance in the bulk flow in addition to the dominant thermal resistance in the thin boundary layer adjacent to the flow. Helical screw-tape inserts can, therefore, be used to mix the gross flow effectively in laminar flow to reduce the thermal resistance in the core flow through the channel. Wire coil inserts are also heat transfer enhancement devices. A wire coil insert as shown in Figure 1 is made by tightly wrapping a coil of spring wire on a rod. When the coil spring is pulled through the tube, the wires form a helical roughness. The coil helix angle and coil wire diameter influence the heat transfer and friction characteristics. Two measurements of the local heat transfer coefficient downstream from a wall attached wire have been reported. Edwards and Sheriff [1] used a boundary layer over a flat plate. Emerson [2] worked with pipe flow. They [1, 2] have observed that coil wire diameter for maximum heat transfer enhancement is directly correlated with the viscosity-dominated boundary layer thickness. Larger wire diameters protrude into the turbulence-dominated boundary layer without additional thermal benefit. On the contrary, the larger wires give significantly higher pressure drop due to profile drag. Uttawar and Raja Rao [3] carried out experiments with seven different wire coil insert geometries in laminar flow (30 < Re < 675) for heating of an oil (300 < Pr < 675). The range of insert geometries was 0.08 < d/D < 0.13 and 32o < α < 61o. The flow was not fully developed since the heated tube length was only 60 diameters. They observed from 50% to 300% heat transfer enhancement. The friction increases were considerably less than the Nusselt number increase. The heat transfer data were correlated by
Nu 1.65 tan Re Pr m
0.35
b w
0.14
(1)
where
m 0.25tan
0.38
(2)
The Nu, f and Re were based on hydraulic diameter. They did not develop the friction factor correlation. Friction factor was only 5–8% higher than the smooth tube value for Re < 180. Chen and Zhang [4] experimented with seven wire coil insert geometries for laminar flow (273 < Re < 245) of oil (194 < Pr < 464) under heating condition. The range of insert geometries was 0.056 < d/D < 0.133 and 3.75 < P/e < 24. The heated tube length was 100 diameters. They proposed following correlations based on their own data:
D P e P D P e
Nu 1.258 Re0.566 Pr 0.169 P f 95.049 Re 0.129 Pr 0.230
0.186
0.848
0.408
1.428
(3) (4)
Helical screw-tape inserts [5] as shown in Figure 2(a) cause the flow to spiral along the tube length. Twisted tapes are similar to helical screw-tape inserts. Continuous twisted-tape as shown in Figure 2(b) has been extensively investigated. Variants of twisted-tape that have been evaluated include short sections of twisted tapes at the tube inlet, or periodically spaced along the tube length. Early works on twisted tapes have been reported in [6]. Later works have been reported in [7-50]. Saha and Dutta [36] have observed that, for regularly spaced twisted-tape elements, thermohydraulic performance of twisted tapes with multiple twists in the tape module is not much different from that with single twist in the tape module. Twisted tapes with gradually decreasing pitch perform worse than their uniform-pitch counterparts. Patil [21] have worked with varying width twisted-tape inserts for which both friction factor and Nusselt number are lower than those with full-width twisted tapes. Saha et al. [41, 42] have introduced regularly spaced twisted-tape elements which are better than full-length twisted tapes under certain
circumstances. Li et al. [18] have designed an optimal multi-layer spacer with optimal nonwoven nets in the outer layers and twisted tapes in the middle layer. Helical screw-tape inserts [25] behave the same way as the twisted tapes. Twin and triple twisted tapes [11] are also effective enhancement devices. Dewan et al. [14] have reviewed the studies on twisted tapes. Hong et al. [16] have employed evenly spaced twisted tapes in a convergent-divergent tube. Sarac et al. [49] have observed better performance with vortex generators having propeller-type geometry. Jaishankar et al. [17] have observed better performance of twisted tapes with spacer at the trailing edge. Chang et al. [11] experienced enhanced heat transfer in case of shaker-bored piston cooling channel with twisted-tape insert. Two co-rotating helical vortices superimposed over the main swirling flow exist in twisted-tape generated swirl flow, Cazan and Aidun [10]. The close proximity of the two co-rotating vortices creates a local reversing flow at the pipe centerline. Helical vortices are generated by vortices originating inside the twisted tape swirler. The main rotational flow accelerates the co-rotating vortices and decelerates the counter-rotating vortices. As a result, the counter-rotating vortices disappear while the co-rotating vortices reach the same maximum tangential velocity as the main flow. Thus the tangential velocity near the wall is approximately doubled by the presence of the secondary vortices. Ramakrishna et al. [24] have recently worked with twisted-tape having spaces in between. Hans et al. [15] have made a review of various roughness element geometries employed in solar air heaters for performance enhancement. Saha and co-workers [25-48] have studied experimentally laminar flow through ducts having twisted tapes, corrugations, ribs and wire coil inserts. It has been observed from the literature review that the combined effect of wire coil inserts and helical screw-tape inserts has not been studied in the past. The fluid flow due to wire coil inserts
coupled with helical screw-tape-generated swirl flow is likely to give better mixing in the flow resulting in increased heat and momentum diffusion. This may increase heat transfer even if it may also give increased pressure drop. In this paper, therefore, the laminar flow experimental heat transfer and pressure drop results of combined effect of wire coil inserts and full-length helical screw-tape inserts in circular ducts are presented. Friction factor and Nusselt number correlations are presented. Also the performance of this combined geometry is evaluated. It has been observed that the helical screw-tape inserts in combination with wire coil inserts perform significantly better than the individual enhancement technique acting alone for laminar flow through a circular duct up to a certain value of the fin parameter.
2. Experimental Set-Up, Operating Procedure and Data Reduction The heat transfer and pressure drop measurements were taken in nine test sections, three each with 13 mm, 16 mm and 19 mm ID brass tubes. All nine tubes had 1 mm thickness and 2m length. Figure 3 shows the self-explanatory experimental rig. Figure 4 and Figure 5 show the helical screw-tape inserts with oblique teeth and the wire coil inserts. The test section was electrically heated by nichrome heater wire giving uniform wall heat flux boundary condition. Nichrome heater wire had porcelain bead insulation on it. There was no direct contact of the Nichrome heater wire with the duct wall. First, there was fiber glass tape insulation (electrical but not thermal) on the duct wall. Then the porcelain-bead covered Nichrome heater wire was wrapped on the duct wall. Two consecutive turns of the heater wire seated side by side touching each other. The thermal conductivity of the duct wall material was high enough and the duct wall thickness was sufficient to ensure uniform wall heat flux. Asbestos rope and glasswool insulated the heat transfer test section after the heater wire. Finally the test section was covered with jute
bag for further thermal insulation. The usual fabrication method is described well in the literature [25-48]. Servotherm medium oil of Indian Oil Corporation was used as the working fluid. Wire coil inserts were placed at the centre of the duct cross-section. The calming section was 1.5 m long GI pipe of 25 mm ID. Oil mass flow rate was measured by rotameters. Pressure drops were measured by vertical mercury manometer. The local enhancement due to helical screw-tape inserts and wire coil inserts quickly dissipates due to boundary layer mixing dissipation downstream of the screw-tape inserts and wire coil inserts. Hence, rational selection of the geometrical parameters of the inserts requires knowledge of the local heat transfer coefficient. Therefore, heat transfer test section outer wall temperatures were measured at seven axial locations (each axial station had four thermocouples ninety degrees apart along the duct periphery) by copper-constantan thermocouples and digital multimeter. Typically, there was only 3% of maximum wall temperature variation in peripheral outside wall temperature measured at four locations in an axial station. Similar results have been observed for all cases irrespective of Reynolds number and Prandtl number. The peripheral wall temperature variation is due to buoyancy, effects of geometrical parameters of the inserts and induced swirl. However, the effects are not very strong. Thermocouples were installed on the duct outside wall by brazing. Axial locations of thermocouples were 5 cm, 50 cm, 1.00m, 1.25m, 1.5m, 1.75m and 1.95m along the downstream direction from the onset of heating at the upstream end of the duct. Duct inside wall temperatures were evaluated by calculating duct-wall temperature drop from the one-dimensional radial heat conduction equation. Oil bulk-mean temperatures at inlet and outlet of the test section were also measured by copperconstantan thermocouples. The oil temperature at outlet was measured after the mixing chamber
[item 6, Figure 3] and this was uniform. The mixing chamber was a cylindrical box of rectangular cross-section. The mixing chamber had rectangular plates arranged inside in such a fashion that the working fluid moved in a serpentine path. This gave a uniform temperature of the working fluid at its exit plane. At other locations, the fluid bulk-mean temperatures were interpolated since the fluid bulk-mean temperature increases linearly for the uniform wall heat flux boundary condition. The duct wall temperature also rises linearly in the downstream fully developed region. Heat input to the test section was evaluated by measuring resistance of and voltage across the heater wires and the enthalpy rise of oil in its passage through the test duct. Peripherally local temperatures in an axial station were arithmetically averaged to get axially local temperature and Nusselt number. Then axially local Nusselt numbers were averaged by trapezoidal rule. The electrical energy input and the enthalpy rise of the oil matched within 3%. The enthalpy rise of the oil was taken as the thermal energy input to the heat transfer test section. Fanning Friction factor was evaluated. Experimental uncertainty was determined by the method of Kline and McClintock [51]. The uncertainty (as shown in Appendix I) in Reynolds number, friction factor and Nusselt number were + 3.17%, ± 5.65% and ± 2.25%, respectively. The fluid temperature rise along the heated duct is not very high and fluid thermal properties being well documented, therefore, the uncertainties in fluid properties variation have been neglected without much loss in accuracy. Wire coil inserts were made of GI wire. Helical screw-tape inserts were made of brass. Wire coil inserts were made with three coil helix angles (α), 30o, 45o and 60o and fixed wire diameter ( ) of 1 mm giving non-dimensional coil wire diameters (
), 0.07692, 0.0625 and 0.0526 for
13 mm ID, 16 mm ID and 19 mm ID tubes, respectively. For helical screw-tape inserts, the dimensions of W, c and d (Figure 2 (a)) were as follows:
W= 8 mm (fixed), c= 2.5 mm (for 13 mm ID tube), c= 4 mm (for 16 mm ID tube) and c= 5.5 mm (for 19 mm ID tube), and d=0, 1.5 mm and 2 mm for each of the three tube IDs giving the value of P
Wc P = ∞, 13.33 mm and 10 mm and p = ∞, 1.025 and 0.769, respectively fr d D
13 mm ID tube. For those of 16 mm ID tube, the values are P= ∞, 21.33 mm and 16 mm; p = ∞, 1.33 and 1 and for those of 19 mm ID tube, the values are P= ∞, 29.33 mm and 22 mm; p = ∞, 1.54 and 1.1579. Oblique teeth angle ( and the tooth horizontal length horizontal lengths as mm ID tube were
on the helical screw-tape inserts was 30o, 45o and 60o
was 1 mm, 1.5 mm and 2 mm giving non-dimensional tooth of 0.0769, 0.1154 and 0.1538 for 13 mm ID tube. Those for 16
0.0625, 0.095 and 0.12 and those for 19 mm ID tube were
0.0526,
0.071 and 0.105. It has been established by earlier investigation [7] that reducing W gives worse performance than full W. In the present investigation, therefore, W was kept maximum and constant irrespective of the tube ID. Little variation of c does not make any difference in performance and, therefore, c was also kept constant for a given tube ID. Helical screw-tape inserts were placed at the centre of the duct cross-section by SS lugs.
3. Results and Discussion Figures 6 and 7 show the results of the confirmatory test and this validates the present experimental set up. Figures 8-12 and Figures 13-17 show the friction factor and Nusselt number data, respectively.
Both friction factor and Nusselt number increase with increase in the value of p, i.e. screwtape parameter. This is due to the increase in the tape-surface area and the hydrodynamic and thermal boundary layer shapes change and their thicknesses increase. The velocity and temperature profiles become flatter. Similar results are observed for both friction factor and Nusselt number with the increase in wire coil diameter, wire coil helix angle, tooth and and tooth horizontal length. It has been observed from the present work and [25] that friction factor increases 45-132 % with combined use of wire coil inserts and helical screw-tape with oblique teeth inserts as compared to the separate cases of wire coil inserts and helical screw-tape inserts with oblique teeth. In this connection, it must be appreciated that the conventional twisted tapes and helical screw-tape are fundamentally similar as far as the flow physics is concerned. From the heat transfer point of view, approximately 93-235 % increase in Nusselt number is observed. Both friction factor and Nusselt number behave similarly, i.e., they increase with the increase in the tooth angle, wire coil helix angle, helical screw-tape parameter, p, and wire coil diameter and tooth horizontal length. The friction factor and Nusselt number are strong functions of each of these parameters. The effect of twist ratio of the helical screw-tape has not been studied in this investigation since it is now well established that the helical tapes function effectively only for twist ratio 2.55. The above result is expected and it is explained by the fact that, in case of only helical screw-tapes, there is only swirl flow; whereas there is additional fluid mixing due to flow separation, reattachment and recirculation of fluid in presence of wire coil inserts. Also, there is faster momentum and thermal energy diffusion and transport in both molecular and bulk flow levels causing additional pressure loss and faster heat transmission. The inertia force due to swirl flow generated by helical screw-tapes enhances the periodic boundary
layer separation and reattachment with temperature and velocity profiles equally flatter, caused by wire coil inserts and hence the enhancement. It is also observed from the thermal and friction characteristics that the effect of wire coil inserts is equally prominent on friction factor and on Nusselt number, because the hydrodynamic boundary layer and the thermal boundary layer are equally affected. This reminds us of the Reynolds analogy. However, the thermohydraulic performance evaluation has shown that the combined use of wire coil inserts and helical screw-tapes with oblique teeth (with and without core-rod) are better than the individual enhancement technique and the combined use is recommended. 4. Correlations One major objective of the present work has been to develop correlations for friction factor and Nusselt number to predict pressure drop and heat transfer coefficient. These correlations have been developed by log-linear regression analysis. The laminar flow is influenced by the following conditions: (1) the thermal boundary condition, (2) entrance region effect, (3) natural convection at low Reynolds number, (4) fluid property variation across the boundary layer, and (5) the duct cross-sectional shape. Correlations developed here take care of all these effects. The heat transfer data are presented for uniform wall heat flux boundary condition. The friction factor data are for the isothermal condition. The heated/cooled condition data will need usual viscosity corrections. Correlation for predicting friction factor for combined helical screw-tape with oblique teeth inserts and wire coil inserts is given by Eq. (5):
f Re 17.355Re
0.29735
p 0.38253thl0.13879sin
sin 0.11836dc0.20371
0.28152
(5)
For individual helical screw-tape with oblique teeth inserts and wire coil inserts, friction factors are given by Eq. 6 and Eq. 7, respectively.
f Re 0.57391Re
0.25582
p 0.25902thl0.11826sin
0.26941
(6)
f Re 3.55827Re
sin 0.25811dc0.33739
0.32281
(7) The corresponding Nusselt number correlation is given by Eqs. (8-10)
Num 5.172Gz
Re
0.27481
0.25883
Pr
0.29649
Gr
sin
p
t
sin
0.26538
0.25381 0.24716 0.29982 hl
0.24715
d
b w
0.25931 c
(8)
Num 5.172Gz
Num 5.172Gz
Re
0.19743
Re
0.21172
0.33851
0.31778
Pr
Pr
0.38716
0.22855
Gr
Gr
sin
0.28512 0.33527 0.31385 hl
p
t
0.23379
0.26638 c
sin
0.27179
d
0.27492
b w
b w
0.14
(9)
0.14
(10) All correlations have been developed by log-linear regression analysis. The correlations predict experimental data within + 10.11 %.
5. Performance Evaluation Bergles et al. [52] have suggested several criteria for the performance evaluation of enhancement devices. The performance of the present geometry has been evaluated on the basis of the following two important criteria:
Criterion 1--- Basic geometry fixed, pumping power fixed --- increase heat transfer --- Performance ratio R1 given by Eq. (11).
0.14
R11
Nucom Nuohst
R12
Nucom Nuowci
(11)
Nucom at a given Re, Recom is obtained from the correlation for the combined case. Nuohst, owci for the case with ‘ohst’ and ‘owci’is taken at the Re, Reohst,owci where Reohst,owci is calculated from the constant pumping power consideration as given in Eq. (12) below:
f Re ohst,owci com Re3ohst,owci f ohst,owci
1/ 3
(12)
Criterion 2 --- Basic geometry fixed, heat duty fixed --- reduce pumping power --Performance ratio R2 given by Eq. (13).
R21
f Re f Re 3
com
3
ohst
R22
f Re f Re 3
com
3
(13)
owci
For a given Re, Recom, the Nucom is obtained from the correlation. Re ohst,owci corresponding to Nuohst,owci is obtained from the correlation for the case with ‘ohst’, ‘owci’. The performance ratios R1 and R2 are given in Table 2 and Table 3, respectively. It has been observed that the combined helical screw-tape with oblique teeth inserts and wire coil inserts performs better than the individual enhancement technique acting alone. From Table 2 and Table 3 it is observed that there is 36-133% increase in heat transfer for constant pumping power and 2-49% reduction in pumping power for constant heat duty. In case of combined enhancement techniques, the hydrodynamic boundary layer is less disturbed than the thermal boundary layer by wire coil insert in the duct. The velocity profile is not so flat as the temperature profile. Momentum loss due to mixing of fluid with asymmetric velocity profiles is less. Moreover, the hydrodynamic boundary layer decays faster than the thermal boundary layer. The thermal boundary layer separation and reattachment is more frequent than the hydrodynamic boundary layer. Therefore, the increase in heat transfer is more than the increase in pressure drop.
6. Conclusions The experimental friction factor and Nusselt number data for laminar flow through a circular duct having helical screw-tape with oblique teeth inserts and wire coil inserts
have been presented. Predictive friction factor and Nusselt number correlations have also been presented. The thermohydraulic performance has been evaluated. The major findings of this experimental investigation are that the helical screw-tape with oblique teeth inserts in combination with wire coil inserts performs significantly better than the individual enhancement technique acting alone for laminar flow through a circular duct up to a certain value of fin parameter. This research finding is useful in manufacturing better heat exchangers.
Reference 1. Edwards, F. J. and Sheriff, N., 1961, The heat transfer and friction characteristics for forced convection air flow over a particular type of rough surface, International Developments in Heat Transfer, ASME, New York, pp. 415–425. 2. Emerson, W. H., 1961, Heat transfer in a duct in regions of separated flow, in: Proceedings of the Second International Heat Transfer Conference, Colorado, USA, vol. 1, pp. 267–275. 3. Uttawar, S. B. and Raja Rao, M., 1985, Augmentation of laminar flow heat transfer in tubes by means of wire coil inserts, J Heat Transfer-Trans ASME, 106, 467–469. 4. Chen, L. and Zhang, H. J.,1993, Convection heat transfer enhancement of oil in a circular tube with spiral spring inserts, in: L.C. Chow, A.F. Emery (Eds.), Heat Transfer Measurements and Analysis, HTD-ASME Symposium, vol. 249, pp. 45– 50. 5. Eiamsa-ard, S. and Promvonge, P., 2007, Heat transfer characteristics in a tube fitted with helical screw-tape with/without core-rod inserts, International Communications in Heat and Mass Transfer, 34(2), 176-185. 6. Date, A. W., 1974, Prediction of fully-developed flow in a tube containing a twisted-tape, Int. J. Heat Mass Transfer, 17, 845-859.
7. Hong, S. W. and Bergles, A. E., 1976, Augmentation of laminar flow heat transfer in tubes by means of twisted-tape inserts, ASME J. Heat Transfer, 98, 251-256. 8. Bhattacharyya, S. and Saha, S. K., 2012, Thermohydraulics of laminar flow through a circular tube having integral helical rib roughness and fitted with centre-cleared twisted-tape, Exp. Thermal Fluid Science, 42,154-162 9. Bhattacharyya, S., Saha, S. and Saha, S. K., 2013, Laminar flow heat transfer enhancement in a circular tube having integral spiral rib roughness and fitted with centre-cleared twisted-tape, Exp. Thermal Fluid Science, 44, 727-735. 10. Cazan, R. and Aidun, C. K., 2009, Experimental investigation of the swirling flow and the helical vortices induced by a twisted-tape inside a circular pipe, Physics of Fluids, 21, 037102. 11. Chang, S., Yu, K. W. and Lu, M., 2005, Heat transfer in tubes fitted with single, twin, and triple twisted tapes, Experimental Thermal Fluid Science, 18(4), 279294. 12. Chang, S. W., Su, L. M., Yang, T. L. and Chiou, S. F., 2007, Enhanced heat transfer of shaker-bored piston cooling channel with twisted-tape insert, Heat Transfer Engineering, 28(4), 321-334. 13. Date, A. W. and Saha, S. K., 1990, Numerical prediction of laminar flow in a tube fitted with regularly spaced twisted-tape elements, Int. J. Heat Fluid Flow, 11 (4), 346-354. 14. Dewan, A., Mahanta, P., Raju, K. S. and Kumar, P. S., 2004, Review of passive heat transfer augmentation techniques, Proc. IMechE., Part A, J Power and Energy, 218(7), 509-527.
15. Hans, V. S., Saini, R. P. and Saini, J. S., 2009, Performance of artificially roughened solar air heaters---A Review, Renewable and Sustainable Energy Reviews, 13(8), 1854-1869. 16. Hong, M., Deng, X., Huang, K. and Li, Z., 2007, Compound heat transfer enhancement of a convergent-divergent tube with evenly spaced twisted tapes, Chinese J Chemical Engineering, 15(6), 814-820. 17. Jaishankar, S. Radhakrishnan, T. K. and Sheeba, K. N., 2009, Experimental studies on heat transfer and friction factor characteristics of thermosyphon solar water heater system fitted with spacer at the trailing edge of twisted tapes, Applied Thermal Engineering, 29(5-6), 1224-1231. 18. Li, F., Meindersma, W., de Haan, A. B. and Reith, T., 2005, Novel spacers for mass transfer enhancement in membrane separations, J. Membrane Science, 253 (1-2), 1-12. 19. Ashis K. Mazumder and Sujoy K. Saha, 2008, Enhancement of Thermohydraulic Performance of Turbulent Flow in Rectangular and Square Ribbed Ducts with Twisted-Tape Inserts, ASME J. Heat Transfer, 130 (8), 081702 (10 pages). 20. Pal, P. K. and Saha, S. K., 2010, Thermal and Friction Characteristics of Laminar Flow through Square and Rectangular Ducts with Spiral Ribs and Twisted Tapes with and without Oblique Teeth, J. Enhanced Heat Transfer, 17(1), 1-21. 21. Patil, A. G., 2000, Laminar flow heat transfer and pressure drop characteristics of power-law fluids inside tubes with varying width twisted tape inserts, ASME J Heat Transfer, 122, 143-149.
22. Pramanik, D. and Saha, S. K., 2006, Thermohydraulics of laminar flow through rectangular and square ducts with spiral ribs and twisted tapes, ASME J Heat Transfer, 128(10), 1070-1080. 23. Rahimi, M., Shabanian, S. R. and Alsairafi, A. A., 2009, Experimental and CFD studies on heat transfer and friction factor characteristics of a tube, equipped with modified twisted-tape inserts, Chemical Engineering and Processing: Process Intensification, 48(3), 762-770. 24. Ramakrishna, S., Pathipaka, G. and Sivashanmugam, P., 2009, Heat transfer and pressure drop studies in a circular tube fitted with straight full twist, Experimental Thermal Fluid Science, 33(3), 431-438. 25. Rout, P. K. and Saha, S. K., 2013, Laminar flow heat transfer and pressure drop in a circular tube having wire-coil and helical screw-tape inserts, ASME J Heat Transfer, 135(2), 021901, 8 pages. 26. Saha, S. K., 2010, Thermohydraulics of Laminar Flow through Rectangular and Square Ducts with Spiral Corrugation Roughness and Twisted Tapes with Oblique Teeth, ASME J Heat Transfer, 132(8), 081701 (1-12). 27. Saha, S. K., 2010, Thermal and friction characteristics of laminar flow through rectangular and square ducts with spiral ribs and wire coil inserts, Exp. Thermal Fluid Science, 34(1), 63-72. 28. S. K. Saha, Thermohydraulics of Turbulent Flow through Rectangular and Square Ducts with Spiral Corrugation Roughness and Twisted Tapes with and without Oblique Teeth, Exp. Thermal Fluid Sciene, 34(6),2010c, 744-752.
29. S. K. Saha, Thermal and Friction Characteristics of Turbulent Flow through Rectangular and Square Ducts with Spiral Ribs and Wire Coil Inserts, Exp. Thermal Fluid Scienc, 34(5), 2010d, 575-589. 30. S. K. Saha, Thermohydraulics of Turbulent Flow through Square and Rectangular Ducts with Spiral Ribs and twisted Tapes with and without Oblique Teeth, Journal of Enhanced Heat Transfer, 2011, 18(4), 281-293. 31. Sujoy Kumar Saha, (2012), ENHANCED HEAT TRANSFER, in Mechanical Engineering, [Eds. UNESCO-EOLSS Joint Committee], in Encyclopedia of Life Support Systems(EOLSS), Developed under the Auspices of the UNESCO, Eolss Publishers, Oxford, UK, [http://www.eolss.net] [Retrieved August 14, 2013] 32. Sujoy Kumar Saha, 2012, Thermohydraulics of laminar flow of viscous oil through a circular tube having spiral corrugations and fitted with centre-cleared twisted-tape, Exp Thermal Fluid Science, 38, 201-209. 33. Sujoy K. Saha, 2012, Heat Transfer, Thermodynamics and Thermal Power Laboratory Description, Int. J Microscale and Nanoscale Thermal and Fluid Transport Phenomena, 3(2). 34. Sujoy Kumar Saha, 2013, Thermohydraulics of laminar flow through a circular tube having integral helical corrugations and fitted with helical screw-tape inserts, Chemical Engg. Communications, 200(3), 418-436. 35. Saha, S. K. and Dayanidhi, G. L., 2012, Thermo-fluid characteristics of laminar flow of viscous oil through a circular tube having integral helical corrugations and fitted with centre-cleared twisted-tape, Heat and Mass Transfer, 012-1049-z.
DOI: 10.1007/s00231-
36. Saha, S. K. and Dutta, A., 2001, Thermohydraulic study of laminar swirl flow through a circular tube fitted with twisted tapes, ASME J Heat Transfer, 123, 417427. 37. S. K. Saha and P. Langille, 2002, Heat Transfer and Pressure Drop Characteristics of Laminar Flow through a Circular Tube with Longitudinal Strip Inserts under Uniform Wall Heat Flux, ASME J Heat Transfer, 124(3), 421-432. 38. Saha, S. K. and Mallick, D. N., 2005, Heat transfer and pressure drop characteristics of laminar flow in rectangular and square plain ducts and ducts with twisted tapes, ASME J Heat Transfer, 127(9), 966-977. 39. S. Saha and S. K. Saha, 2013, Enhancement of heat transfer of laminar flow through a circular tube having integral helical rib roughness and fitted with wavy strip inserts, Exp. Thermal Fluid Science, 50, 107-113. 40. Saha, S. and Saha, S. K., 2013, Enhancement of heat transfer of laminar flow of viscous oil through a circular tube having integral helical rib roughness and fitted with helical screw-tapes, Exp. Thermal Fluid Science, 47, 81-89. 41. Saha, U. N., Gaitonde, U. N. and Date, A. W., 1989, Heat transfer and pressure drop characteristics of laminar flow in a circular tube fitted with regularly spaced twisted-tape elements, Exp. Thermal Fluid Science, 2, 310-322. 42. S. K. Saha, U. N. Gaitonde and A. W. Date, 1990, Heat Transfer and Pressure Drop Characteristics of Turbulent Flow in a Circular Tube Fitted with Regularly Spaced Twisted-Tape Elements, Exp. Thermal Fluid Science, 3(6), 632-640.
43. S. K. Saha, A. Dutta and S. K. Dhal, 2001, Friction and Heat Transfer Characteristics of Laminar Swirl Flow through a Circular Tube Fitted with Twisted Tapes, Int. J. Heat Mass Transfer, 44(22), 4211-4223. 44. Sujoy Kumar Saha, Suvanjan Bhattacharyya and Pranab Kumar Pal, 2012, Thermohydraulics of laminar flow of viscous oil through a circular tube having integral spiral rib roughness and fitted with centre-cleared twisted-tape, Exp. Thermal Fluid Science,41, 121-129. 45. S. K. Saha, P. P. Polley and G. L. Dayanidhi, 2012, Laminar flow heat transfer enhancement using spiral ribs and helical screw-tape inserts, AIAA J Thermophysics and Heat Transfer, 26(3), July-Sept, 464-471. 46. S. K. Saha, B. N. Swain and G. L. Dayanidhi, 2012, Friction and thermal characteristics of laminar flow of viscous oil through a circular tube having spiral corrugations and fitted with helical screw-tape Inserts, ASME J Fluids Engineering, 134(5), 051210-1-9. 47. S. K. Saha, B. K. Barman and S. Banerjee, 2012, Heat Transfer Enhancement of laminar flow through a circular tube having wire-coil inserts and fitted with centre-cleared twisted-tape, ASME J Thermal Science and Engineering Applications, 4 (4), 031003-1-9. 48. S. K. Saha, S. Bhattacharyya and G. L. Dayanidhi, 2012, Enhancement of heat transfer of laminar flow of viscous oil through a circular tube having integral spiral rib roughness and fitted with helical screw-tape inserts, Heat Transfer Research, 43(2), pp. 1-2.
49. Sarac, B. A. and Bali, T., 2007, An experimental study on heat transfer and pressure drop characteristics of decaying swirl flow through a circular pipe with a vortex generator, Experimental Thermal Fluid Science, 32(1), 158-165. 50. Sivashanmugam, P. and Suresh, S., 2006, Experimental studies on heat transfer and friction factor characteristics of laminar flow through a circular tube fitted with helical screw-tape inserts, Applied Thermal Engineering, 26(16), 1990-1997. 51. Kline, S. J. and McClintock, F. A. , (1953), Describing Uncertainties in Single Sample Experiments, Mechanical Engineering, 75 (1), pp 3-8. 52. Manglik, R. M. and Bergles, A. E., (1993), Heat Transfer and Pressure Drop Correlations for Twisted-Tape Inserts in Isothermal Tubes: Part I—Laminar Flows, ASME J Heat Transfer, 115(4), pp 881-889. 53. Bergles, A. E., Blumenkrantz, A. R.
and Taborek, J., (1974), Performance
Evaluation Criteria for Enhanced Heat Transfer Surfaces, Paper FC 6.3, Proc. 5 th Int. Heat Transfer Conference, Tokyo, 2, pp 239-243.
Acknowledgments The author gratefully acknowledges the generous financial support of the UGC and DST, Government of India for the current research; DST Grant No. SR/S3/MERC-0045/2010 and UGC Grant No. 41-989/2012(SR).
APPENDIX
UNCERTAINTY ANALYSIS
All the quantities that are measured to estimate the Nusselt number and the friction factor are subject to certain uncertainties due to errors in the measurement. These individual uncertainties as well as the combined effect of these are presented here. The analysis is carried out on the basis of the suggestion made by Kline and McClintock [28].
ANALYSIS
First the analysis for the friction factor is presented. The analysis for the Nusselt number is presented after that. Friction Factor
3 1 P D f 2 2 ( A.1) 2 Lp Re
2 2 2 2 f 1 f f f f P Lp D Re f f P L D Re p
2 2 2 2 f P Lp 3D 2 Re f Lp P D Re
or,
0.5
( A.2)
0.5
( A.3)
P h (A.4)
P h (A.5) P h
Re
4m ( A.6) D
2 2 Re m D Re m D
0.5
( A.7)
The uncertainty in friction factor has been calculated from the above equations.
Nusselt Number
Nu
hD (A.8) k
2 2 2 Nu 1 ( Nu )h Nu D Nu k Nu Nu h D k
0.5
or
h
h 2 D 2 Nu Nu h D
( A.9)
q (A.10) Twi Tb
2 2 2 h h h 1 h q Twi Tb h h q Twi Tb
0.5
0.5
2 2 2 h q Twi Tb h q Twi Tb Twi Tb
q
0.5
( A.11)
0.5 V 2 / R m C p Tbo Tbi ( A.12) DLh
2 2 2 2 q R q V q m q Tbo V m Tbo q 1 R 2 2 2 q q T q Tbi D q D L q Lh h bi
2 2 1 4 R V 2 2 2 2 R V 1 m C R T / V 1 m C R T / V p b p b 2 2 Tbo q 1 1 m 2 2 2 2 q Tb m V V 1 1 Rm C T Rm C p Tb p b 2 2 2 Tbi D Lh 1 2 D L 2 T b h V 1 Rm C p Tb
0.5
0.5
( A.13)
where Tb Tbo Tbi
The uncertainty in Nusselt number has been calculated from the above equations.
The accuracies of the measured quantities are in given below in the tabular form:
Quantity
Accuracy
Quantity
Accuracy
ΔDh
0.00002 m
ΔL
0.001 m
Δ m
1.667E-5 kg/s
Δh
0.001 m
ΔT
0.025oC
ΔV
0.1 V
ΔR
0.000001Ω
Figure 1: Geometry of wire coil
Tooth Angle
0.5*H
0.5*H 0.5 thl*
0.5 thl*
Details of section A (a)
(b)
Figure 2
(a): Schematic diagram of Screw-Tape insert (b): Layout of a Circular Duct Containing a Full-Length TwistedTape
Figure 3: Schematic Diagram of the Experimental Rig
Figure 4: Helical screw-tape inserts (pictorial view)
(a)
(b) Figure 5: (a) Helical screw-tape insert (b) Helical screw-tape insert with wire coil insert (Inside the tube)
10
Exp Data Correlation
1
f
0.1
0.01 1
10
100
1000
Re
Friction factor Vs Reynolds number
Figure 6: Validation of the experimental setup: comparison of present experimental friction factor data with plain circular tube data
10
9
8
Correlation 7
Exp Data Linear (Correlation)
6
Nu 5
4
3
2
1 10
100
1000
Re
Nussely number vs. Reynolds number
Figure 7: Validation of the experimental setup: comparison of present experimental Nusselt number data with plain circular tube data
Figure 8: Friction factor results…d c 0.0697,
, thl 0.1248
Figure 9: Friction factor results…d c 0.064,
, p 1.0867
Figure 10: Friction factor results…d c=0.0625,
, thl
p 1.611
Figure 11: Friction factor results…d c
0.064,
, thl
p 1.301
Figure 12: Friction factor results…t hl 0.064,
, p=
Figure 13: Nusselt No. results…dc
0.064,
, thl
p 1.301
Figure 14: Nusselt No. results…dc=0.0625,
, thl
p 1.611
Figure 15: Nusselt No. results…thl 0.064,
, p=
Figure 16: Nusselt No. results…dc 0.0697,
, thl 0.1248
Figure 17: Nusselt No. results…dc 0.064,
, p 1.0867
Table 1: Value of geometrical parameter of test section for present study thl=thl */D
α (deg)
dc mm
dc/D
1
0.0769
30
1
0.07692
45
1.5
0.1154
30
1
0.07692
0.769
45
2
0.1538
45
1
0.07692
∞
∞
30
1
0.0625
45
1
0.0625
1.5
21.33
1.3333
45
1.5
0.09375
45
1
0.0625
4
2
16
1
60
2
0.125
45
1
0.0625
8
5.5
0
∞
∞
30
1
0.0526
60
1
0.0526
19
8
5.5
1.5
29.33
1.5438
45
1.5
0.0789
60
1
0.0526
19
8
5.5
2
22
1.15789
45
2
0.10526
45
1
0.0526
Test section no.
I.D. (D) mm
W mm
c mm
1
13
8
2.5
2
13
8
3
13
4
d mm
P= (W×c)/d mm
p = P/D
thl
0
∞
∞
30
2.5
1.5
13.33
1.0256
8
2.5
2
10
16
8
4
0
5
16
8
4
6
16
8
7
19
8 9
*
(deg)
mm
Table 2: Performance Ratio R1 Case: First digit for wire coil helix angle (α) and second digit for coil wire diameter (dc) α= 30o (1) and 60o (2) dc = 0.07692 (1) and 0.0526 (2) R1 22 p= ∞, thl = 0.0769, Ө = 30o, α=30o, dc=0.07692 p= 1.0256, thl = 0.1154, Ө = 45o, α=30o, dc=0.07692 p= 0.769, thl = 0.1538, Ө = 45o, α=45o, dc=0.07692 p= ∞, thl = 0.0625, Ө = 30o, α=45o, dc=0.0625 p= 1.3333, thl = 0.09575, Ө = 45o, α=45o, dc=0.0625 p= 1, thl = 0.125, Ө = 60o, α=45o, dc=0.0625 p= ∞, thl = 0.0526, Ө = 30o, α=60o, dc=0.0526 p= 1.5438, thl = 0.0789, Ө = 45o, α=60o, dc=0.0526 p= 1.15789, thl = 0.10526, Ө = 45o, α=45o, dc=0.0526
R11 1.74
R11
1.57
R11
1.60
R11 2.15
R11
1.82
R11 1.91
R11 1.70
R11
2.17
R11
1.42
12 R12 1.36
R12
2.27
R12
1.81
R12 2.33
R12
1.64
R12 1.56
R12 2.15
R12
2.25
R12
1.56
R11 1.86
R11
1.54
R11
2.01
R11 1.73
R11
1.78
R11 2.24
R11 2.08
R11
1.42
R11
1.37
21 R12 1.61
R12
1.73
R12
2.04
R12 1.83
R12
2.08
R12 1.37
R12 1.67
R12
1.44
R12
1.84
R11 2.18
R11
1.46
R11
2.34
R11 1.53
R11
1.64
R11 1.92
R11 1.95
R11
1.69
R11
1.71
11 R12 2.00
R12
1.86
R12
2.34
R12 1.82
R12
1.50
R12 2.24
R12 1.78
R12
1.71
R12
1.46
R11 1.66
R11
1.46
R11
1.92
R11 2.06
R11
2.23
R11 1.77
R11 2.05
R11
1.66
R11
1.58
R12 1.84
R12
1.62
R12
1.46
R12 1.41
R12
1.54
R12 1.85
R12 1.68
R12
2.09
R12
1.45
Table 3: Performance Ratio R2 Case: First digit for wire coil helix angle (α) and second digit for coil wire diameter (d c) α= 30o (1) and 60o (2) dc = 0.07692 (1) and 0.0526 (2) R2 22 p= ∞, thl = 0.0769, Ө = 30o, α=30o, dc=0.07692 p= 1.0256, thl = 0.1154, Ө = 45o, α=30o, dc=0.07692 p= 0.769, thl = 0.1538, Ө = 45o, α=45o, dc=0.07692 p= ∞, thl = 0.0625, Ө = 30o, α=45o, dc=0.0625 p= 1.3333, thl = 0.09575, Ө = 45o, α=45o, dc=0.0625 p= 1, thl = 0.125, Ө = 60o, α=45o, dc=0.0625 p= ∞, thl = 0.0526, Ө = 30o, α=60o, dc=0.0526 p= 1.5438, thl = 0.0789, Ө = 45o, α=60o, dc=0.0526 p= 1.15789, thl = 0.10526, Ө = 45o, α=45o, dc=0.0526
R21 0.86
R21
0.98
R21
0.93
R21 0.66
R21
0.74
R21 0.79
R21 0.96
R21
0.87
R21
0.90
12 R22 0.55
R22
0.70
R22
0.53
R22 0.76
R22
0.84
R22 0.94
R22 0.83
R22
0.76
R22
0.51
R21 0.70
R21
0.70
R21
0.77
R21 0.76
R21
0.73
R21 0.75
R21 0.54
R21
0.99
R21
0.95
21 R22 0.87
R22
0.82
R22
0.73
R22 0.79
R22
0.55
R22 0.98
R22 0.71
R22
0.52
R22
0.97
R21 0.93
R21
0.55
R21
0.58
R21 0.82
R21
0.69
R21 0.85
R21 0.70
R21
0.55
R21
0.93
11 R22 0.91
R22
0.75
R22
0.53
R22 0.62
R22
0.88
R22 0.63
R22 0.94
R22
057
R22
0.68
R21 0.60
R21
0.91
R21
0.90
R21 0.83
R21
0.56
R21 0.81
R21 0.55
R21
0.82
R21
0.80
R22 0.91
R22
0.57
R22
0.68
R22 0.51
R22
0.52
R22 0.58
R22 0.71
R22
0.62
R22
0.69
Highlights
Laminar flow in circular ducts with helical screw-tape with oblique teeth inserts and wire coil inserts is studied.
Friction factor and Nusselt number correlations are developed.
The thermohydraulic performance is evaluated.
This finned geometry performs significantly betters.
Results are useful for better heat exchangers.
S0894-1777(15)00184-3 http://dx.doi.org/10.1016/j.expthermflusci.2015.07.007 ETF 8517
To appear in:
Experimental Thermal and Fluid Science
Received Date: Revised Date: Accepted Date:
31 May 2015 5 July 2015 9 July 2015
Please cite this article as: S. Roy, S.K. Saha, Thermal and Friction Characteristics of Laminar Flow through a Circular Duct having Helical Screw-Tape with Oblique Teeth Inserts and Wire Coil Inserts, Experimental Thermal and Fluid Science (2015), doi: http://dx.doi.org/10.1016/j.expthermflusci.2015.07.007
This is a PDF file of an unedited manuscript that has been accepted for publication. As a service to our customers we are providing this early version of the manuscript. The manuscript will undergo copyediting, typesetting, and review of the resulting proof before it is published in its final form. Please note that during the production process errors may be discovered which could affect the content, and all legal disclaimers that apply to the journal pertain.
Thermal and Friction Characteristics of Laminar Flow through a Circular Duct having Helical Screw-Tape with Oblique Teeth Inserts and Wire Coil Inserts
Sarbendu Roy Email: [email protected]
Sujoy Kumar Saha Email: [email protected]
Mechanical Engineering Department Indian Institute of Engineering Science and Technology Shibpur Howrah 711 103, INDIA
Abstract
Helical screw-tape inserts and wire coil inserts both individually are enhancement techniques. Naturally, therefore, it is worthwhile to try their combinations as a potential enhancement technique. The experimental friction factor and Nusselt number data for laminar flow through a circular duct having helical screw-tape and wire coil inserts have been presented. Predictive friction factor and Nusselt number correlations have also been presented. The thermohydraulic performance has been evaluated. The major findings of this experimental investigation are that the helical screw-tape inserts in combination with wire coil inserts perform significantly better than the individual enhancement technique acting alone for laminar flow through a circular duct up to a certain value of the fin parameter.
Keywords
Laminar Flow, Forced Convection, Wire Coil Inserts, Helical Screw-Tape Inserts, Heat Transfer Enhancement, Swirl Flow
Nomenclature
A: heat transfer area, m2 Ac : axial flow cross-sectional area, = D 2 D , m2 4 Ao: plain duct flow cross-sectional area, = D 2 , m2 4 Cp : constant pressure specific heat, J/kgK D : internal diameter of the plain duct, m d : coil wire diameter, m e: height, m
D f : fully developed Fanning friction factor = 1 2 P 2 V0 z , dimensionless g : gravitational acceleration, m/s2 Gr: Grashof number = g 2 D3Tw / 2 , dimensionless Gz : Graetz number = m C p / kL , dimensionless H : pitch for 1800 rotation of twisted-tape and pitch for wire coil insert, m hz : axially local heat transfer coefficient, W/(m2K). k : fluid thermal conductivity, W/(mK). L : axial length, length of the duct, m
m : mass flow rate, kg/min L
Num : axially averaged Nusselt number =
1 hz Ddz , dimensionless L 0 k
Pz : pressure drop, mm
P : pressure drop, N/m2 P
: wetted perimeter in the particular cross-section of the duct, coil pitch, m
Pr : fluid Prandtl number =
C p k
, dimensionless
Ra : Rayleigh number = Gr Pr
Re : Reynolds number based on plain duct diameter =
V0 D
, dimensionless
T : temperature, K thl: Tooth horizontal length, dimensionless ∆Tw : wall to fluid bulk temperature difference, K Vo : mean velocity based on plain duct diameter = m
A0 , m/s
X: Prn, the value of n depends on the exponent of Pr in the correlation
Y: b w
0.14
1 5.172
z : axial length, the distance between the measuring pressure taps, m
Greek Symbols :
D α: coil helix angle, α= tan H o
-1
β : coefficient of isobaric thermal expansion, K-1 µ : fluid dynamic viscosity, kg/ms. ρ : density of the fluid, kg/m3. θ: tooth angle, Ө
Subscripts : b : at bulk fluid temperature m: axially averaged w : at duct wall temperature, with z : local value
1. Introduction Laminar flow is encountered in many industrial applications. In case of laminar flow, there is major thermal resistance in the bulk flow in addition to the dominant thermal resistance in the thin boundary layer adjacent to the flow. Helical screw-tape inserts can, therefore, be used to mix the gross flow effectively in laminar flow to reduce the thermal resistance in the core flow through the channel. Wire coil inserts are also heat transfer enhancement devices. A wire coil insert as shown in Figure 1 is made by tightly wrapping a coil of spring wire on a rod. When the coil spring is pulled through the tube, the wires form a helical roughness. The coil helix angle and coil wire diameter influence the heat transfer and friction characteristics. Two measurements of the local heat transfer coefficient downstream from a wall attached wire have been reported. Edwards and Sheriff [1] used a boundary layer over a flat plate. Emerson [2] worked with pipe flow. They [1, 2] have observed that coil wire diameter for maximum heat transfer enhancement is directly correlated with the viscosity-dominated boundary layer thickness. Larger wire diameters protrude into the turbulence-dominated boundary layer without additional thermal benefit. On the contrary, the larger wires give significantly higher pressure drop due to profile drag. Uttawar and Raja Rao [3] carried out experiments with seven different wire coil insert geometries in laminar flow (30 < Re < 675) for heating of an oil (300 < Pr < 675). The range of insert geometries was 0.08 < d/D < 0.13 and 32o < α < 61o. The flow was not fully developed since the heated tube length was only 60 diameters. They observed from 50% to 300% heat transfer enhancement. The friction increases were considerably less than the Nusselt number increase. The heat transfer data were correlated by
Nu 1.65 tan Re Pr m
0.35
b w
0.14
(1)
where
m 0.25tan
0.38
(2)
The Nu, f and Re were based on hydraulic diameter. They did not develop the friction factor correlation. Friction factor was only 5–8% higher than the smooth tube value for Re < 180. Chen and Zhang [4] experimented with seven wire coil insert geometries for laminar flow (273 < Re < 245) of oil (194 < Pr < 464) under heating condition. The range of insert geometries was 0.056 < d/D < 0.133 and 3.75 < P/e < 24. The heated tube length was 100 diameters. They proposed following correlations based on their own data:
D P e P D P e
Nu 1.258 Re0.566 Pr 0.169 P f 95.049 Re 0.129 Pr 0.230
0.186
0.848
0.408
1.428
(3) (4)
Helical screw-tape inserts [5] as shown in Figure 2(a) cause the flow to spiral along the tube length. Twisted tapes are similar to helical screw-tape inserts. Continuous twisted-tape as shown in Figure 2(b) has been extensively investigated. Variants of twisted-tape that have been evaluated include short sections of twisted tapes at the tube inlet, or periodically spaced along the tube length. Early works on twisted tapes have been reported in [6]. Later works have been reported in [7-50]. Saha and Dutta [36] have observed that, for regularly spaced twisted-tape elements, thermohydraulic performance of twisted tapes with multiple twists in the tape module is not much different from that with single twist in the tape module. Twisted tapes with gradually decreasing pitch perform worse than their uniform-pitch counterparts. Patil [21] have worked with varying width twisted-tape inserts for which both friction factor and Nusselt number are lower than those with full-width twisted tapes. Saha et al. [41, 42] have introduced regularly spaced twisted-tape elements which are better than full-length twisted tapes under certain
circumstances. Li et al. [18] have designed an optimal multi-layer spacer with optimal nonwoven nets in the outer layers and twisted tapes in the middle layer. Helical screw-tape inserts [25] behave the same way as the twisted tapes. Twin and triple twisted tapes [11] are also effective enhancement devices. Dewan et al. [14] have reviewed the studies on twisted tapes. Hong et al. [16] have employed evenly spaced twisted tapes in a convergent-divergent tube. Sarac et al. [49] have observed better performance with vortex generators having propeller-type geometry. Jaishankar et al. [17] have observed better performance of twisted tapes with spacer at the trailing edge. Chang et al. [11] experienced enhanced heat transfer in case of shaker-bored piston cooling channel with twisted-tape insert. Two co-rotating helical vortices superimposed over the main swirling flow exist in twisted-tape generated swirl flow, Cazan and Aidun [10]. The close proximity of the two co-rotating vortices creates a local reversing flow at the pipe centerline. Helical vortices are generated by vortices originating inside the twisted tape swirler. The main rotational flow accelerates the co-rotating vortices and decelerates the counter-rotating vortices. As a result, the counter-rotating vortices disappear while the co-rotating vortices reach the same maximum tangential velocity as the main flow. Thus the tangential velocity near the wall is approximately doubled by the presence of the secondary vortices. Ramakrishna et al. [24] have recently worked with twisted-tape having spaces in between. Hans et al. [15] have made a review of various roughness element geometries employed in solar air heaters for performance enhancement. Saha and co-workers [25-48] have studied experimentally laminar flow through ducts having twisted tapes, corrugations, ribs and wire coil inserts. It has been observed from the literature review that the combined effect of wire coil inserts and helical screw-tape inserts has not been studied in the past. The fluid flow due to wire coil inserts
coupled with helical screw-tape-generated swirl flow is likely to give better mixing in the flow resulting in increased heat and momentum diffusion. This may increase heat transfer even if it may also give increased pressure drop. In this paper, therefore, the laminar flow experimental heat transfer and pressure drop results of combined effect of wire coil inserts and full-length helical screw-tape inserts in circular ducts are presented. Friction factor and Nusselt number correlations are presented. Also the performance of this combined geometry is evaluated. It has been observed that the helical screw-tape inserts in combination with wire coil inserts perform significantly better than the individual enhancement technique acting alone for laminar flow through a circular duct up to a certain value of the fin parameter.
2. Experimental Set-Up, Operating Procedure and Data Reduction The heat transfer and pressure drop measurements were taken in nine test sections, three each with 13 mm, 16 mm and 19 mm ID brass tubes. All nine tubes had 1 mm thickness and 2m length. Figure 3 shows the self-explanatory experimental rig. Figure 4 and Figure 5 show the helical screw-tape inserts with oblique teeth and the wire coil inserts. The test section was electrically heated by nichrome heater wire giving uniform wall heat flux boundary condition. Nichrome heater wire had porcelain bead insulation on it. There was no direct contact of the Nichrome heater wire with the duct wall. First, there was fiber glass tape insulation (electrical but not thermal) on the duct wall. Then the porcelain-bead covered Nichrome heater wire was wrapped on the duct wall. Two consecutive turns of the heater wire seated side by side touching each other. The thermal conductivity of the duct wall material was high enough and the duct wall thickness was sufficient to ensure uniform wall heat flux. Asbestos rope and glasswool insulated the heat transfer test section after the heater wire. Finally the test section was covered with jute
bag for further thermal insulation. The usual fabrication method is described well in the literature [25-48]. Servotherm medium oil of Indian Oil Corporation was used as the working fluid. Wire coil inserts were placed at the centre of the duct cross-section. The calming section was 1.5 m long GI pipe of 25 mm ID. Oil mass flow rate was measured by rotameters. Pressure drops were measured by vertical mercury manometer. The local enhancement due to helical screw-tape inserts and wire coil inserts quickly dissipates due to boundary layer mixing dissipation downstream of the screw-tape inserts and wire coil inserts. Hence, rational selection of the geometrical parameters of the inserts requires knowledge of the local heat transfer coefficient. Therefore, heat transfer test section outer wall temperatures were measured at seven axial locations (each axial station had four thermocouples ninety degrees apart along the duct periphery) by copper-constantan thermocouples and digital multimeter. Typically, there was only 3% of maximum wall temperature variation in peripheral outside wall temperature measured at four locations in an axial station. Similar results have been observed for all cases irrespective of Reynolds number and Prandtl number. The peripheral wall temperature variation is due to buoyancy, effects of geometrical parameters of the inserts and induced swirl. However, the effects are not very strong. Thermocouples were installed on the duct outside wall by brazing. Axial locations of thermocouples were 5 cm, 50 cm, 1.00m, 1.25m, 1.5m, 1.75m and 1.95m along the downstream direction from the onset of heating at the upstream end of the duct. Duct inside wall temperatures were evaluated by calculating duct-wall temperature drop from the one-dimensional radial heat conduction equation. Oil bulk-mean temperatures at inlet and outlet of the test section were also measured by copperconstantan thermocouples. The oil temperature at outlet was measured after the mixing chamber
[item 6, Figure 3] and this was uniform. The mixing chamber was a cylindrical box of rectangular cross-section. The mixing chamber had rectangular plates arranged inside in such a fashion that the working fluid moved in a serpentine path. This gave a uniform temperature of the working fluid at its exit plane. At other locations, the fluid bulk-mean temperatures were interpolated since the fluid bulk-mean temperature increases linearly for the uniform wall heat flux boundary condition. The duct wall temperature also rises linearly in the downstream fully developed region. Heat input to the test section was evaluated by measuring resistance of and voltage across the heater wires and the enthalpy rise of oil in its passage through the test duct. Peripherally local temperatures in an axial station were arithmetically averaged to get axially local temperature and Nusselt number. Then axially local Nusselt numbers were averaged by trapezoidal rule. The electrical energy input and the enthalpy rise of the oil matched within 3%. The enthalpy rise of the oil was taken as the thermal energy input to the heat transfer test section. Fanning Friction factor was evaluated. Experimental uncertainty was determined by the method of Kline and McClintock [51]. The uncertainty (as shown in Appendix I) in Reynolds number, friction factor and Nusselt number were + 3.17%, ± 5.65% and ± 2.25%, respectively. The fluid temperature rise along the heated duct is not very high and fluid thermal properties being well documented, therefore, the uncertainties in fluid properties variation have been neglected without much loss in accuracy. Wire coil inserts were made of GI wire. Helical screw-tape inserts were made of brass. Wire coil inserts were made with three coil helix angles (α), 30o, 45o and 60o and fixed wire diameter ( ) of 1 mm giving non-dimensional coil wire diameters (
), 0.07692, 0.0625 and 0.0526 for
13 mm ID, 16 mm ID and 19 mm ID tubes, respectively. For helical screw-tape inserts, the dimensions of W, c and d (Figure 2 (a)) were as follows:
W= 8 mm (fixed), c= 2.5 mm (for 13 mm ID tube), c= 4 mm (for 16 mm ID tube) and c= 5.5 mm (for 19 mm ID tube), and d=0, 1.5 mm and 2 mm for each of the three tube IDs giving the value of P
Wc P = ∞, 13.33 mm and 10 mm and p = ∞, 1.025 and 0.769, respectively fr d D
13 mm ID tube. For those of 16 mm ID tube, the values are P= ∞, 21.33 mm and 16 mm; p = ∞, 1.33 and 1 and for those of 19 mm ID tube, the values are P= ∞, 29.33 mm and 22 mm; p = ∞, 1.54 and 1.1579. Oblique teeth angle ( and the tooth horizontal length horizontal lengths as mm ID tube were
on the helical screw-tape inserts was 30o, 45o and 60o
was 1 mm, 1.5 mm and 2 mm giving non-dimensional tooth of 0.0769, 0.1154 and 0.1538 for 13 mm ID tube. Those for 16
0.0625, 0.095 and 0.12 and those for 19 mm ID tube were
0.0526,
0.071 and 0.105. It has been established by earlier investigation [7] that reducing W gives worse performance than full W. In the present investigation, therefore, W was kept maximum and constant irrespective of the tube ID. Little variation of c does not make any difference in performance and, therefore, c was also kept constant for a given tube ID. Helical screw-tape inserts were placed at the centre of the duct cross-section by SS lugs.
3. Results and Discussion Figures 6 and 7 show the results of the confirmatory test and this validates the present experimental set up. Figures 8-12 and Figures 13-17 show the friction factor and Nusselt number data, respectively.
Both friction factor and Nusselt number increase with increase in the value of p, i.e. screwtape parameter. This is due to the increase in the tape-surface area and the hydrodynamic and thermal boundary layer shapes change and their thicknesses increase. The velocity and temperature profiles become flatter. Similar results are observed for both friction factor and Nusselt number with the increase in wire coil diameter, wire coil helix angle, tooth and and tooth horizontal length. It has been observed from the present work and [25] that friction factor increases 45-132 % with combined use of wire coil inserts and helical screw-tape with oblique teeth inserts as compared to the separate cases of wire coil inserts and helical screw-tape inserts with oblique teeth. In this connection, it must be appreciated that the conventional twisted tapes and helical screw-tape are fundamentally similar as far as the flow physics is concerned. From the heat transfer point of view, approximately 93-235 % increase in Nusselt number is observed. Both friction factor and Nusselt number behave similarly, i.e., they increase with the increase in the tooth angle, wire coil helix angle, helical screw-tape parameter, p, and wire coil diameter and tooth horizontal length. The friction factor and Nusselt number are strong functions of each of these parameters. The effect of twist ratio of the helical screw-tape has not been studied in this investigation since it is now well established that the helical tapes function effectively only for twist ratio 2.55. The above result is expected and it is explained by the fact that, in case of only helical screw-tapes, there is only swirl flow; whereas there is additional fluid mixing due to flow separation, reattachment and recirculation of fluid in presence of wire coil inserts. Also, there is faster momentum and thermal energy diffusion and transport in both molecular and bulk flow levels causing additional pressure loss and faster heat transmission. The inertia force due to swirl flow generated by helical screw-tapes enhances the periodic boundary
layer separation and reattachment with temperature and velocity profiles equally flatter, caused by wire coil inserts and hence the enhancement. It is also observed from the thermal and friction characteristics that the effect of wire coil inserts is equally prominent on friction factor and on Nusselt number, because the hydrodynamic boundary layer and the thermal boundary layer are equally affected. This reminds us of the Reynolds analogy. However, the thermohydraulic performance evaluation has shown that the combined use of wire coil inserts and helical screw-tapes with oblique teeth (with and without core-rod) are better than the individual enhancement technique and the combined use is recommended. 4. Correlations One major objective of the present work has been to develop correlations for friction factor and Nusselt number to predict pressure drop and heat transfer coefficient. These correlations have been developed by log-linear regression analysis. The laminar flow is influenced by the following conditions: (1) the thermal boundary condition, (2) entrance region effect, (3) natural convection at low Reynolds number, (4) fluid property variation across the boundary layer, and (5) the duct cross-sectional shape. Correlations developed here take care of all these effects. The heat transfer data are presented for uniform wall heat flux boundary condition. The friction factor data are for the isothermal condition. The heated/cooled condition data will need usual viscosity corrections. Correlation for predicting friction factor for combined helical screw-tape with oblique teeth inserts and wire coil inserts is given by Eq. (5):
f Re 17.355Re
0.29735
p 0.38253thl0.13879sin
sin 0.11836dc0.20371
0.28152
(5)
For individual helical screw-tape with oblique teeth inserts and wire coil inserts, friction factors are given by Eq. 6 and Eq. 7, respectively.
f Re 0.57391Re
0.25582
p 0.25902thl0.11826sin
0.26941
(6)
f Re 3.55827Re
sin 0.25811dc0.33739
0.32281
(7) The corresponding Nusselt number correlation is given by Eqs. (8-10)
Num 5.172Gz
Re
0.27481
0.25883
Pr
0.29649
Gr
sin
p
t
sin
0.26538
0.25381 0.24716 0.29982 hl
0.24715
d
b w
0.25931 c
(8)
Num 5.172Gz
Num 5.172Gz
Re
0.19743
Re
0.21172
0.33851
0.31778
Pr
Pr
0.38716
0.22855
Gr
Gr
sin
0.28512 0.33527 0.31385 hl
p
t
0.23379
0.26638 c
sin
0.27179
d
0.27492
b w
b w
0.14
(9)
0.14
(10) All correlations have been developed by log-linear regression analysis. The correlations predict experimental data within + 10.11 %.
5. Performance Evaluation Bergles et al. [52] have suggested several criteria for the performance evaluation of enhancement devices. The performance of the present geometry has been evaluated on the basis of the following two important criteria:
Criterion 1--- Basic geometry fixed, pumping power fixed --- increase heat transfer --- Performance ratio R1 given by Eq. (11).
0.14
R11
Nucom Nuohst
R12
Nucom Nuowci
(11)
Nucom at a given Re, Recom is obtained from the correlation for the combined case. Nuohst, owci for the case with ‘ohst’ and ‘owci’is taken at the Re, Reohst,owci where Reohst,owci is calculated from the constant pumping power consideration as given in Eq. (12) below:
f Re ohst,owci com Re3ohst,owci f ohst,owci
1/ 3
(12)
Criterion 2 --- Basic geometry fixed, heat duty fixed --- reduce pumping power --Performance ratio R2 given by Eq. (13).
R21
f Re f Re 3
com
3
ohst
R22
f Re f Re 3
com
3
(13)
owci
For a given Re, Recom, the Nucom is obtained from the correlation. Re ohst,owci corresponding to Nuohst,owci is obtained from the correlation for the case with ‘ohst’, ‘owci’. The performance ratios R1 and R2 are given in Table 2 and Table 3, respectively. It has been observed that the combined helical screw-tape with oblique teeth inserts and wire coil inserts performs better than the individual enhancement technique acting alone. From Table 2 and Table 3 it is observed that there is 36-133% increase in heat transfer for constant pumping power and 2-49% reduction in pumping power for constant heat duty. In case of combined enhancement techniques, the hydrodynamic boundary layer is less disturbed than the thermal boundary layer by wire coil insert in the duct. The velocity profile is not so flat as the temperature profile. Momentum loss due to mixing of fluid with asymmetric velocity profiles is less. Moreover, the hydrodynamic boundary layer decays faster than the thermal boundary layer. The thermal boundary layer separation and reattachment is more frequent than the hydrodynamic boundary layer. Therefore, the increase in heat transfer is more than the increase in pressure drop.
6. Conclusions The experimental friction factor and Nusselt number data for laminar flow through a circular duct having helical screw-tape with oblique teeth inserts and wire coil inserts
have been presented. Predictive friction factor and Nusselt number correlations have also been presented. The thermohydraulic performance has been evaluated. The major findings of this experimental investigation are that the helical screw-tape with oblique teeth inserts in combination with wire coil inserts performs significantly better than the individual enhancement technique acting alone for laminar flow through a circular duct up to a certain value of fin parameter. This research finding is useful in manufacturing better heat exchangers.
Reference 1. Edwards, F. J. and Sheriff, N., 1961, The heat transfer and friction characteristics for forced convection air flow over a particular type of rough surface, International Developments in Heat Transfer, ASME, New York, pp. 415–425. 2. Emerson, W. H., 1961, Heat transfer in a duct in regions of separated flow, in: Proceedings of the Second International Heat Transfer Conference, Colorado, USA, vol. 1, pp. 267–275. 3. Uttawar, S. B. and Raja Rao, M., 1985, Augmentation of laminar flow heat transfer in tubes by means of wire coil inserts, J Heat Transfer-Trans ASME, 106, 467–469. 4. Chen, L. and Zhang, H. J.,1993, Convection heat transfer enhancement of oil in a circular tube with spiral spring inserts, in: L.C. Chow, A.F. Emery (Eds.), Heat Transfer Measurements and Analysis, HTD-ASME Symposium, vol. 249, pp. 45– 50. 5. Eiamsa-ard, S. and Promvonge, P., 2007, Heat transfer characteristics in a tube fitted with helical screw-tape with/without core-rod inserts, International Communications in Heat and Mass Transfer, 34(2), 176-185. 6. Date, A. W., 1974, Prediction of fully-developed flow in a tube containing a twisted-tape, Int. J. Heat Mass Transfer, 17, 845-859.
7. Hong, S. W. and Bergles, A. E., 1976, Augmentation of laminar flow heat transfer in tubes by means of twisted-tape inserts, ASME J. Heat Transfer, 98, 251-256. 8. Bhattacharyya, S. and Saha, S. K., 2012, Thermohydraulics of laminar flow through a circular tube having integral helical rib roughness and fitted with centre-cleared twisted-tape, Exp. Thermal Fluid Science, 42,154-162 9. Bhattacharyya, S., Saha, S. and Saha, S. K., 2013, Laminar flow heat transfer enhancement in a circular tube having integral spiral rib roughness and fitted with centre-cleared twisted-tape, Exp. Thermal Fluid Science, 44, 727-735. 10. Cazan, R. and Aidun, C. K., 2009, Experimental investigation of the swirling flow and the helical vortices induced by a twisted-tape inside a circular pipe, Physics of Fluids, 21, 037102. 11. Chang, S., Yu, K. W. and Lu, M., 2005, Heat transfer in tubes fitted with single, twin, and triple twisted tapes, Experimental Thermal Fluid Science, 18(4), 279294. 12. Chang, S. W., Su, L. M., Yang, T. L. and Chiou, S. F., 2007, Enhanced heat transfer of shaker-bored piston cooling channel with twisted-tape insert, Heat Transfer Engineering, 28(4), 321-334. 13. Date, A. W. and Saha, S. K., 1990, Numerical prediction of laminar flow in a tube fitted with regularly spaced twisted-tape elements, Int. J. Heat Fluid Flow, 11 (4), 346-354. 14. Dewan, A., Mahanta, P., Raju, K. S. and Kumar, P. S., 2004, Review of passive heat transfer augmentation techniques, Proc. IMechE., Part A, J Power and Energy, 218(7), 509-527.
15. Hans, V. S., Saini, R. P. and Saini, J. S., 2009, Performance of artificially roughened solar air heaters---A Review, Renewable and Sustainable Energy Reviews, 13(8), 1854-1869. 16. Hong, M., Deng, X., Huang, K. and Li, Z., 2007, Compound heat transfer enhancement of a convergent-divergent tube with evenly spaced twisted tapes, Chinese J Chemical Engineering, 15(6), 814-820. 17. Jaishankar, S. Radhakrishnan, T. K. and Sheeba, K. N., 2009, Experimental studies on heat transfer and friction factor characteristics of thermosyphon solar water heater system fitted with spacer at the trailing edge of twisted tapes, Applied Thermal Engineering, 29(5-6), 1224-1231. 18. Li, F., Meindersma, W., de Haan, A. B. and Reith, T., 2005, Novel spacers for mass transfer enhancement in membrane separations, J. Membrane Science, 253 (1-2), 1-12. 19. Ashis K. Mazumder and Sujoy K. Saha, 2008, Enhancement of Thermohydraulic Performance of Turbulent Flow in Rectangular and Square Ribbed Ducts with Twisted-Tape Inserts, ASME J. Heat Transfer, 130 (8), 081702 (10 pages). 20. Pal, P. K. and Saha, S. K., 2010, Thermal and Friction Characteristics of Laminar Flow through Square and Rectangular Ducts with Spiral Ribs and Twisted Tapes with and without Oblique Teeth, J. Enhanced Heat Transfer, 17(1), 1-21. 21. Patil, A. G., 2000, Laminar flow heat transfer and pressure drop characteristics of power-law fluids inside tubes with varying width twisted tape inserts, ASME J Heat Transfer, 122, 143-149.
22. Pramanik, D. and Saha, S. K., 2006, Thermohydraulics of laminar flow through rectangular and square ducts with spiral ribs and twisted tapes, ASME J Heat Transfer, 128(10), 1070-1080. 23. Rahimi, M., Shabanian, S. R. and Alsairafi, A. A., 2009, Experimental and CFD studies on heat transfer and friction factor characteristics of a tube, equipped with modified twisted-tape inserts, Chemical Engineering and Processing: Process Intensification, 48(3), 762-770. 24. Ramakrishna, S., Pathipaka, G. and Sivashanmugam, P., 2009, Heat transfer and pressure drop studies in a circular tube fitted with straight full twist, Experimental Thermal Fluid Science, 33(3), 431-438. 25. Rout, P. K. and Saha, S. K., 2013, Laminar flow heat transfer and pressure drop in a circular tube having wire-coil and helical screw-tape inserts, ASME J Heat Transfer, 135(2), 021901, 8 pages. 26. Saha, S. K., 2010, Thermohydraulics of Laminar Flow through Rectangular and Square Ducts with Spiral Corrugation Roughness and Twisted Tapes with Oblique Teeth, ASME J Heat Transfer, 132(8), 081701 (1-12). 27. Saha, S. K., 2010, Thermal and friction characteristics of laminar flow through rectangular and square ducts with spiral ribs and wire coil inserts, Exp. Thermal Fluid Science, 34(1), 63-72. 28. S. K. Saha, Thermohydraulics of Turbulent Flow through Rectangular and Square Ducts with Spiral Corrugation Roughness and Twisted Tapes with and without Oblique Teeth, Exp. Thermal Fluid Sciene, 34(6),2010c, 744-752.
29. S. K. Saha, Thermal and Friction Characteristics of Turbulent Flow through Rectangular and Square Ducts with Spiral Ribs and Wire Coil Inserts, Exp. Thermal Fluid Scienc, 34(5), 2010d, 575-589. 30. S. K. Saha, Thermohydraulics of Turbulent Flow through Square and Rectangular Ducts with Spiral Ribs and twisted Tapes with and without Oblique Teeth, Journal of Enhanced Heat Transfer, 2011, 18(4), 281-293. 31. Sujoy Kumar Saha, (2012), ENHANCED HEAT TRANSFER, in Mechanical Engineering, [Eds. UNESCO-EOLSS Joint Committee], in Encyclopedia of Life Support Systems(EOLSS), Developed under the Auspices of the UNESCO, Eolss Publishers, Oxford, UK, [http://www.eolss.net] [Retrieved August 14, 2013] 32. Sujoy Kumar Saha, 2012, Thermohydraulics of laminar flow of viscous oil through a circular tube having spiral corrugations and fitted with centre-cleared twisted-tape, Exp Thermal Fluid Science, 38, 201-209. 33. Sujoy K. Saha, 2012, Heat Transfer, Thermodynamics and Thermal Power Laboratory Description, Int. J Microscale and Nanoscale Thermal and Fluid Transport Phenomena, 3(2). 34. Sujoy Kumar Saha, 2013, Thermohydraulics of laminar flow through a circular tube having integral helical corrugations and fitted with helical screw-tape inserts, Chemical Engg. Communications, 200(3), 418-436. 35. Saha, S. K. and Dayanidhi, G. L., 2012, Thermo-fluid characteristics of laminar flow of viscous oil through a circular tube having integral helical corrugations and fitted with centre-cleared twisted-tape, Heat and Mass Transfer, 012-1049-z.
DOI: 10.1007/s00231-
36. Saha, S. K. and Dutta, A., 2001, Thermohydraulic study of laminar swirl flow through a circular tube fitted with twisted tapes, ASME J Heat Transfer, 123, 417427. 37. S. K. Saha and P. Langille, 2002, Heat Transfer and Pressure Drop Characteristics of Laminar Flow through a Circular Tube with Longitudinal Strip Inserts under Uniform Wall Heat Flux, ASME J Heat Transfer, 124(3), 421-432. 38. Saha, S. K. and Mallick, D. N., 2005, Heat transfer and pressure drop characteristics of laminar flow in rectangular and square plain ducts and ducts with twisted tapes, ASME J Heat Transfer, 127(9), 966-977. 39. S. Saha and S. K. Saha, 2013, Enhancement of heat transfer of laminar flow through a circular tube having integral helical rib roughness and fitted with wavy strip inserts, Exp. Thermal Fluid Science, 50, 107-113. 40. Saha, S. and Saha, S. K., 2013, Enhancement of heat transfer of laminar flow of viscous oil through a circular tube having integral helical rib roughness and fitted with helical screw-tapes, Exp. Thermal Fluid Science, 47, 81-89. 41. Saha, U. N., Gaitonde, U. N. and Date, A. W., 1989, Heat transfer and pressure drop characteristics of laminar flow in a circular tube fitted with regularly spaced twisted-tape elements, Exp. Thermal Fluid Science, 2, 310-322. 42. S. K. Saha, U. N. Gaitonde and A. W. Date, 1990, Heat Transfer and Pressure Drop Characteristics of Turbulent Flow in a Circular Tube Fitted with Regularly Spaced Twisted-Tape Elements, Exp. Thermal Fluid Science, 3(6), 632-640.
43. S. K. Saha, A. Dutta and S. K. Dhal, 2001, Friction and Heat Transfer Characteristics of Laminar Swirl Flow through a Circular Tube Fitted with Twisted Tapes, Int. J. Heat Mass Transfer, 44(22), 4211-4223. 44. Sujoy Kumar Saha, Suvanjan Bhattacharyya and Pranab Kumar Pal, 2012, Thermohydraulics of laminar flow of viscous oil through a circular tube having integral spiral rib roughness and fitted with centre-cleared twisted-tape, Exp. Thermal Fluid Science,41, 121-129. 45. S. K. Saha, P. P. Polley and G. L. Dayanidhi, 2012, Laminar flow heat transfer enhancement using spiral ribs and helical screw-tape inserts, AIAA J Thermophysics and Heat Transfer, 26(3), July-Sept, 464-471. 46. S. K. Saha, B. N. Swain and G. L. Dayanidhi, 2012, Friction and thermal characteristics of laminar flow of viscous oil through a circular tube having spiral corrugations and fitted with helical screw-tape Inserts, ASME J Fluids Engineering, 134(5), 051210-1-9. 47. S. K. Saha, B. K. Barman and S. Banerjee, 2012, Heat Transfer Enhancement of laminar flow through a circular tube having wire-coil inserts and fitted with centre-cleared twisted-tape, ASME J Thermal Science and Engineering Applications, 4 (4), 031003-1-9. 48. S. K. Saha, S. Bhattacharyya and G. L. Dayanidhi, 2012, Enhancement of heat transfer of laminar flow of viscous oil through a circular tube having integral spiral rib roughness and fitted with helical screw-tape inserts, Heat Transfer Research, 43(2), pp. 1-2.
49. Sarac, B. A. and Bali, T., 2007, An experimental study on heat transfer and pressure drop characteristics of decaying swirl flow through a circular pipe with a vortex generator, Experimental Thermal Fluid Science, 32(1), 158-165. 50. Sivashanmugam, P. and Suresh, S., 2006, Experimental studies on heat transfer and friction factor characteristics of laminar flow through a circular tube fitted with helical screw-tape inserts, Applied Thermal Engineering, 26(16), 1990-1997. 51. Kline, S. J. and McClintock, F. A. , (1953), Describing Uncertainties in Single Sample Experiments, Mechanical Engineering, 75 (1), pp 3-8. 52. Manglik, R. M. and Bergles, A. E., (1993), Heat Transfer and Pressure Drop Correlations for Twisted-Tape Inserts in Isothermal Tubes: Part I—Laminar Flows, ASME J Heat Transfer, 115(4), pp 881-889. 53. Bergles, A. E., Blumenkrantz, A. R.
and Taborek, J., (1974), Performance
Evaluation Criteria for Enhanced Heat Transfer Surfaces, Paper FC 6.3, Proc. 5 th Int. Heat Transfer Conference, Tokyo, 2, pp 239-243.
Acknowledgments The author gratefully acknowledges the generous financial support of the UGC and DST, Government of India for the current research; DST Grant No. SR/S3/MERC-0045/2010 and UGC Grant No. 41-989/2012(SR).
APPENDIX
UNCERTAINTY ANALYSIS
All the quantities that are measured to estimate the Nusselt number and the friction factor are subject to certain uncertainties due to errors in the measurement. These individual uncertainties as well as the combined effect of these are presented here. The analysis is carried out on the basis of the suggestion made by Kline and McClintock [28].
ANALYSIS
First the analysis for the friction factor is presented. The analysis for the Nusselt number is presented after that. Friction Factor
3 1 P D f 2 2 ( A.1) 2 Lp Re
2 2 2 2 f 1 f f f f P Lp D Re f f P L D Re p
2 2 2 2 f P Lp 3D 2 Re f Lp P D Re
or,
0.5
( A.2)
0.5
( A.3)
P h (A.4)
P h (A.5) P h
Re
4m ( A.6) D
2 2 Re m D Re m D
0.5
( A.7)
The uncertainty in friction factor has been calculated from the above equations.
Nusselt Number
Nu
hD (A.8) k
2 2 2 Nu 1 ( Nu )h Nu D Nu k Nu Nu h D k
0.5
or
h
h 2 D 2 Nu Nu h D
( A.9)
q (A.10) Twi Tb
2 2 2 h h h 1 h q Twi Tb h h q Twi Tb
0.5
0.5
2 2 2 h q Twi Tb h q Twi Tb Twi Tb
q
0.5
( A.11)
0.5 V 2 / R m C p Tbo Tbi ( A.12) DLh
2 2 2 2 q R q V q m q Tbo V m Tbo q 1 R 2 2 2 q q T q Tbi D q D L q Lh h bi
2 2 1 4 R V 2 2 2 2 R V 1 m C R T / V 1 m C R T / V p b p b 2 2 Tbo q 1 1 m 2 2 2 2 q Tb m V V 1 1 Rm C T Rm C p Tb p b 2 2 2 Tbi D Lh 1 2 D L 2 T b h V 1 Rm C p Tb
0.5
0.5
( A.13)
where Tb Tbo Tbi
The uncertainty in Nusselt number has been calculated from the above equations.
The accuracies of the measured quantities are in given below in the tabular form:
Quantity
Accuracy
Quantity
Accuracy
ΔDh
0.00002 m
ΔL
0.001 m
Δ m
1.667E-5 kg/s
Δh
0.001 m
ΔT
0.025oC
ΔV
0.1 V
ΔR
0.000001Ω
Figure 1: Geometry of wire coil
Tooth Angle
0.5*H
0.5*H 0.5 thl*
0.5 thl*
Details of section A (a)
(b)
Figure 2
(a): Schematic diagram of Screw-Tape insert (b): Layout of a Circular Duct Containing a Full-Length TwistedTape
Figure 3: Schematic Diagram of the Experimental Rig
Figure 4: Helical screw-tape inserts (pictorial view)
(a)
(b) Figure 5: (a) Helical screw-tape insert (b) Helical screw-tape insert with wire coil insert (Inside the tube)
10
Exp Data Correlation
1
f
0.1
0.01 1
10
100
1000
Re
Friction factor Vs Reynolds number
Figure 6: Validation of the experimental setup: comparison of present experimental friction factor data with plain circular tube data
10
9
8
Correlation 7
Exp Data Linear (Correlation)
6
Nu 5
4
3
2
1 10
100
1000
Re
Nussely number vs. Reynolds number
Figure 7: Validation of the experimental setup: comparison of present experimental Nusselt number data with plain circular tube data
Figure 8: Friction factor results…d c 0.0697,
, thl 0.1248
Figure 9: Friction factor results…d c 0.064,
, p 1.0867
Figure 10: Friction factor results…d c=0.0625,
, thl
p 1.611
Figure 11: Friction factor results…d c
0.064,
, thl
p 1.301
Figure 12: Friction factor results…t hl 0.064,
, p=
Figure 13: Nusselt No. results…dc
0.064,
, thl
p 1.301
Figure 14: Nusselt No. results…dc=0.0625,
, thl
p 1.611
Figure 15: Nusselt No. results…thl 0.064,
, p=
Figure 16: Nusselt No. results…dc 0.0697,
, thl 0.1248
Figure 17: Nusselt No. results…dc 0.064,
, p 1.0867
Table 1: Value of geometrical parameter of test section for present study thl=thl */D
α (deg)
dc mm
dc/D
1
0.0769
30
1
0.07692
45
1.5
0.1154
30
1
0.07692
0.769
45
2
0.1538
45
1
0.07692
∞
∞
30
1
0.0625
45
1
0.0625
1.5
21.33
1.3333
45
1.5
0.09375
45
1
0.0625
4
2
16
1
60
2
0.125
45
1
0.0625
8
5.5
0
∞
∞
30
1
0.0526
60
1
0.0526
19
8
5.5
1.5
29.33
1.5438
45
1.5
0.0789
60
1
0.0526
19
8
5.5
2
22
1.15789
45
2
0.10526
45
1
0.0526
Test section no.
I.D. (D) mm
W mm
c mm
1
13
8
2.5
2
13
8
3
13
4
d mm
P= (W×c)/d mm
p = P/D
thl
0
∞
∞
30
2.5
1.5
13.33
1.0256
8
2.5
2
10
16
8
4
0
5
16
8
4
6
16
8
7
19
8 9
*
(deg)
mm
Table 2: Performance Ratio R1 Case: First digit for wire coil helix angle (α) and second digit for coil wire diameter (dc) α= 30o (1) and 60o (2) dc = 0.07692 (1) and 0.0526 (2) R1 22 p= ∞, thl = 0.0769, Ө = 30o, α=30o, dc=0.07692 p= 1.0256, thl = 0.1154, Ө = 45o, α=30o, dc=0.07692 p= 0.769, thl = 0.1538, Ө = 45o, α=45o, dc=0.07692 p= ∞, thl = 0.0625, Ө = 30o, α=45o, dc=0.0625 p= 1.3333, thl = 0.09575, Ө = 45o, α=45o, dc=0.0625 p= 1, thl = 0.125, Ө = 60o, α=45o, dc=0.0625 p= ∞, thl = 0.0526, Ө = 30o, α=60o, dc=0.0526 p= 1.5438, thl = 0.0789, Ө = 45o, α=60o, dc=0.0526 p= 1.15789, thl = 0.10526, Ө = 45o, α=45o, dc=0.0526
R11 1.74
R11
1.57
R11
1.60
R11 2.15
R11
1.82
R11 1.91
R11 1.70
R11
2.17
R11
1.42
12 R12 1.36
R12
2.27
R12
1.81
R12 2.33
R12
1.64
R12 1.56
R12 2.15
R12
2.25
R12
1.56
R11 1.86
R11
1.54
R11
2.01
R11 1.73
R11
1.78
R11 2.24
R11 2.08
R11
1.42
R11
1.37
21 R12 1.61
R12
1.73
R12
2.04
R12 1.83
R12
2.08
R12 1.37
R12 1.67
R12
1.44
R12
1.84
R11 2.18
R11
1.46
R11
2.34
R11 1.53
R11
1.64
R11 1.92
R11 1.95
R11
1.69
R11
1.71
11 R12 2.00
R12
1.86
R12
2.34
R12 1.82
R12
1.50
R12 2.24
R12 1.78
R12
1.71
R12
1.46
R11 1.66
R11
1.46
R11
1.92
R11 2.06
R11
2.23
R11 1.77
R11 2.05
R11
1.66
R11
1.58
R12 1.84
R12
1.62
R12
1.46
R12 1.41
R12
1.54
R12 1.85
R12 1.68
R12
2.09
R12
1.45
Table 3: Performance Ratio R2 Case: First digit for wire coil helix angle (α) and second digit for coil wire diameter (d c) α= 30o (1) and 60o (2) dc = 0.07692 (1) and 0.0526 (2) R2 22 p= ∞, thl = 0.0769, Ө = 30o, α=30o, dc=0.07692 p= 1.0256, thl = 0.1154, Ө = 45o, α=30o, dc=0.07692 p= 0.769, thl = 0.1538, Ө = 45o, α=45o, dc=0.07692 p= ∞, thl = 0.0625, Ө = 30o, α=45o, dc=0.0625 p= 1.3333, thl = 0.09575, Ө = 45o, α=45o, dc=0.0625 p= 1, thl = 0.125, Ө = 60o, α=45o, dc=0.0625 p= ∞, thl = 0.0526, Ө = 30o, α=60o, dc=0.0526 p= 1.5438, thl = 0.0789, Ө = 45o, α=60o, dc=0.0526 p= 1.15789, thl = 0.10526, Ө = 45o, α=45o, dc=0.0526
R21 0.86
R21
0.98
R21
0.93
R21 0.66
R21
0.74
R21 0.79
R21 0.96
R21
0.87
R21
0.90
12 R22 0.55
R22
0.70
R22
0.53
R22 0.76
R22
0.84
R22 0.94
R22 0.83
R22
0.76
R22
0.51
R21 0.70
R21
0.70
R21
0.77
R21 0.76
R21
0.73
R21 0.75
R21 0.54
R21
0.99
R21
0.95
21 R22 0.87
R22
0.82
R22
0.73
R22 0.79
R22
0.55
R22 0.98
R22 0.71
R22
0.52
R22
0.97
R21 0.93
R21
0.55
R21
0.58
R21 0.82
R21
0.69
R21 0.85
R21 0.70
R21
0.55
R21
0.93
11 R22 0.91
R22
0.75
R22
0.53
R22 0.62
R22
0.88
R22 0.63
R22 0.94
R22
057
R22
0.68
R21 0.60
R21
0.91
R21
0.90
R21 0.83
R21
0.56
R21 0.81
R21 0.55
R21
0.82
R21
0.80
R22 0.91
R22
0.57
R22
0.68
R22 0.51
R22
0.52
R22 0.58
R22 0.71
R22
0.62
R22
0.69
Highlights
Laminar flow in circular ducts with helical screw-tape with oblique teeth inserts and wire coil inserts is studied.
Friction factor and Nusselt number correlations are developed.
The thermohydraulic performance is evaluated.
This finned geometry performs significantly betters.
Results are useful for better heat exchangers.