- Email: [email protected]
Heat transfer in a circular tube fitted with free-spacing snail entry and conical-nozzle turbulators
International Communications in Heat and Mass Transfer 34 (2007) 838 – 848 www.elsevier.com/locate/ichmt
Heat transfer in a circular tube fitted with free-spacing snail entry and conical-nozzle turbulators ☆ P. Promvonge a,⁎, S. Eiamsa-ard b a
Department of Mechanical Engineering, Faculty of Engineering, King Mongkut's Institute of Technology Ladkrabang, Bangkok 10520, Thailand b Department of Mechanical Engineering, Faculty of Engineering, Mahanakorn University of Technology, Bangkok 10530, Thailand Available online 21 May 2007
Abstract The paper presents the effect of a free-spacing snail entry together with conical-nozzle turbulators on turbulent heat transfer and friction characteristics in a uniform heat-flux tube. The insertions of the conical or converging nozzle (C-nozzle) with different pitch ratios (PR) in common with the free-space snail entry are examined in a Reynolds number range from 8000 to 18000. A substantial augmentation of heat transfer for using the C-nozzles and snail entrance is expected by a strong influence from nozzleinduced reverse/re-circulation motion and snail-produced vortex/swirl motion for high Reynolds number. The experimental result shows a considerable increase in friction factor and heat transfer over the plain tube under the same operation conditions. Over the range investigated, the Nusselt numbers for employing both the enhancement devices with PR = 2.0, 4.0 and 7.0 are found to be higher than that for the plain tube around 315%, 300% and 285% respectively. The results obtained are correlated in the form of Nusselt number as a function of Reynolds number, Prandtl number and pitch ratio. For performance comparison at equal pumping power, both the enhancement devices with the smallest pitch ratio perform the best, especially at low Reynolds number. The present results are also compared with correlations obtained from similar enhancement devices but without free-spacing entry. © 2007 Elsevier Ltd. All rights reserved. Keywords: Heat transfer augmentation; Swirl flow; Re-circulation/reverse flow; Turbulator; Snail entry; Enhancement device
1. Introduction The development of high-performance thermal systems has still stimulated considerable interest in methods to improve heat transfer. The conventional heat exchangers are improved by means of various augmentation techniques with emphasis on many types of surface enhancements. Augmented surfaces can create one or more combinations of the following conditions that are favorable for the increase in heat transfer rate with an undesirable rise of friction: 1) disruption of the development of boundary layer and increase of the turbulence intensity, 2) increase in heat transfer area, and 3) generation of swirling/rotating and/or secondary flows. For the effective performance evaluation of passive augmentation methods for example twisted tape, wire coil, and extended surface which are used in force convection situations, both the heat transfer and flow friction characteristics of the enhancement technique must be known [1–3]. The convection heat transfer along
☆
Communicated by W.J. Minkowycz. ⁎ Corresponding author. E-mail address: [email protected] (P. Promvonge).
0735-1933/$ - see front matter © 2007 Elsevier Ltd. All rights reserved. doi:10.1016/j.icheatmasstransfer.2007.03.020
P. Promvonge, S. Eiamsa-ard / International Communications in Heat and Mass Transfer 34 (2007) 838–848
839
Nomenclature A Cp,a D Do f h I k L l m˙ Nu ΔP PR Pr Qa Qconv Re Ret Rep s S t Tb Ti To Tw T˜w U V V˙
Heat transfer surface area (m2) Specific heat of air (J/kg K) Inner diameter of tube (m) Outer diameter of tube (m) Friction factor Average heat transfer coefficient (W/m2 K) Current (amp) Thermal conductivity of air, (W/m K) Length of test tube (m) Pitch length (m) Mass flow rate (kg/s) Nusselt number Pressure drop (Pa) Pitch ratio, l/D = 1+S Prandtl number Heat transfer absorbed by air (W) Convective heat transfer (W) Reynolds number Reynolds number of turbulator Reynolds number of plain tube Space length (m) Space ratio, s/D Thickness of tube, m Bulk temperature (°C) Inlet temperature (°C) Outlet temperature (°C) Wall temperature (°C) Mean wall temperature (°C) Average axial velocity (m/s) Voltage (volt) Volume flow rate (m3/s)
Greek symbols ηe Enhancement efficiency ρ Density (kg/m3) μ Dynamic viscosity (kg/s m)
the tube wall can be improved significantly by introducing the reverse/re-circulation flow with a view to increasing the effective axial Reynolds number, decreasing the cross-sectional area of flow, and increasing the mean velocity and temperature gradient. This is because the reverse flow can induce the higher heat fluxes and momentum transfer due to the large effective driving potential force but also higher pressure drop. The strength of reverse flow and the reattached position are the main interest in many heat transfer applications such as heat exchangers, combustion chambers, gas turbine blades, and electronic devices. Yakut and Sahin [4] experimentally studied the heat transfer and friction characteristics in a uniform heat flux fitted with conical-ring turbulators used to provide reverse/turbulent flows in each module of the conical rings. Therefore, significant improvement of heat transfer along the tube wall was reported. The enhancements of heat transfer in a uniform heat-flux circular tube fitted with conical-nozzles and swirl generator were also experimentally investigated by Promvonge and Eiamsa-ard [5]. In their research, the conical-nozzles were placed in a test tube with three different pitch ratios of conical-nozzles, apart from the snail mounted at the tube inlet. The use of the conical-nozzle in conjunction with
840
P. Promvonge, S. Eiamsa-ard / International Communications in Heat and Mass Transfer 34 (2007) 838–848
the snail entrance led to maximum heat transfer rate up to 316% over the plain tube besides a substantial increase in pressure loss as well. Eiamsa-ard and Promvonge [6] again reported the influences of V-nozzle inserts on heat transfer, flow friction, and enhancement efficiency characteristics in a uniform heat-flux tube with three pitch ratios. They found that the use of V-nozzles led to a considerable increase in heat transfer rate and a maximum gain of 1.19 on enhancement efficiency was obtained for the smallest pitch ratio used at low Reynolds number. This indicates the crucial effect of the reverse/recirculation flow can promote the heat transfer rate in tubes. The snail/swirl flow generators have been known to be effective in increasing convection heat transfer coefficients and also used in augmentative heat transfer in many engineering applications such as heat exchanger, drying process and vortex combustor. The swirl flow devices can be classified into two types: the continuous swirl and the decaying swirl flows. The former represents the swirling motion that persists over the entire length of the tube for example twisted tape [7,8], coiled wires inserts [9,10] and helical grooves, while the latter means the swirl created at the entrance of the tube and then decays along the flow path [11–16] for example the radial guide vane swirl generator and the tangential flow injection device. In the decaying one, the heat transfer coefficient and the pressure drop decrease along with the axial distance, while in the continuous one, the heat transfer coefficient and the pressure drop keep constant throughout. Apart from experimental work as mentioned above, Zhang et al. [17,18] numerically studied swirling turbulent flows and heat transfer in an annular duct and in a novel vortex heat exchanger by considering the effect of swirl number, inlet axial velocity, and ratio of inner to outer radius on the mean flow and turbulence properties, as well as on enhancing heat transfer in the duct. Wei et al. [19] proposed a new algebraic turbulent mass flux model, which properly accounts for swirl-turbulence interactions while Lee et al. [20] conducted the numerical work using a large eddy simulation to investigate the effect of swirl on the heat and momentum transfer in an annular pipe flow with a rotating inner wall. Simulation of three-dimensional incompressible turbulent flow inside tubes with helical fins was also presented by Kim et al. [21]. The methods of generating swirl can be classified into three main categories [22]. The first is the tangential flow injection to induce a swirling fluid motion down the tube [5,11–15]. The second is the guide vanes swirl generators [16,22,23] which can be grouped into two types: radial guide vane and axial guide vane. The last type is the direct rotation of the tube. In the present work, the snail/swirl generator (tangential flow injection) is normally fitted at the entrance of the tube. Therefore, the swirl is intense at the entrance and decays downstream of the flow. This technique causes the rise in tangential flow velocity, prolonging residence time of the flow in the tube, thinning boundary layer and enhancing the tangential and radial turbulent fluctuation and therefore results in a significant increase in heat transfer rate inside the tube. The above literature review indicates that the tube fitted with conical-nozzle turbulators and snail swirl generators are among the most effective and practical methods for augmenting heat transfer in tubes. However, the common use of both enhancement devices leads to a substantial increase in pressure drop across the tube [5]. Thus, the efficient utilization of both enhancement devices can be compromised by arranging in a suitable configuration to obtain the optimum pressure loss and heat transfer. To reduce the rise of pressure loss from utilizing the enhancement devices but still favorable the heat transfer rate, a free-spacing snail entry is introduced. This concept comes from the fact that the local heat transfer is much high in the developing flow region or at around 10D downstream of the tube inlet in the turbulent decaying swirl flow as suggested by Ref. [16]. Therefore, this experimental investigation is to examine the heat transfer enhanced by the multiplicative effect of C-nozzle turbulators and a free-spacing snail entry. In the experimental test, the first C-nozzle is placed at 10D downstream of the tube inlet (with PR = 2.0, 4.0, and 7.0) while the snail is mounted at the test tube entrance. 2. Experimental investigation The experiments were carried out to examine the effect of free-space snail entry and C-nozzle inserts on heat transfer and fluid flow characteristics of air flow in a tube. A schematic diagram of the experimental setup is illustrated in Fig. 1. The flow system consisted of a 2.2 kW blower, orifice meter to measure the flow rate, and the heat transfer test section. The test-tube section made of copper having a 47.5 mm inner diameter (D) and 50.5 mm outer diameter (Do), was 1250 mm long (L) and 1.5 mm thick (t) as depicted in Fig. 2. The tube was heated by continually winding flexible electrical wire provided a uniform heat flux boundary condition. The electrical output power was controlled by a variac transformer to obtain a constant heat flux along the entire length of the test section and by keeping the current less than 3 amps. The outer surface of the test tube was well insulated to minimize convection and radiation heat losses to
P. Promvonge, S. Eiamsa-ard / International Communications in Heat and Mass Transfer 34 (2007) 838–848
841
Fig. 1. Schematic diagram of experimental heat transfer set-up.
surroundings, and necessary precautions were taken to prevent leakages from the system. The inner and outer temperatures of the bulk air were measured at certain points with a multi-channel temperature measurement unit in conjunction with the type-K thermocouples. Fifteen thermocouples were tapped on the local wall of the tube and the thermocouples were placed round the tube to measure the variation of circumferential temperature, which was found to be negligible. The mean local wall temperature was determined by means of calculations based on the reading of typeK thermocouples. Fig. 2 represents the C-nozzle arrangement together with free-spacing snail entry used in the present experiment. The C-nozzle was made of Aluminum with 95 mm (2.0D) in length and its end and throat diameters were 46 mm and 26 mm, respectively. The Converging nozzles or C-nozzles were placed with three different pitch lengths, l of arrangements, having l = 95 mm (s = 47.5 mm, PR = 2.0), l = 190 mm (s = 142.5 mm, PR = 4.0), and l = 332.5 mm (s = 285 mm, PR = 7.0), for each run of experiments. In addition, a snail type swirl generator was mounted at the entrance of the test tube as shown in Fig. 2. In the experiment, the combination of the two phenomena, (1) the recirculating flow between the two adjacent C-nozzles and (2) the swirling flow generated by the snail, are supposed to be effective in the vicinity of the tube wall, where thermal resistance is high. The combined techniques are expected to provide the better and fast mixing and rotating of fluid in this region as well as causing the increased viscous dissipation, thereby enhancing the heat transfer rate.
Fig. 2. Test tube fitted with C-nozzle turbulators and snail with free-spacing entry.
842
P. Promvonge, S. Eiamsa-ard / International Communications in Heat and Mass Transfer 34 (2007) 838–848
In the apparatus setting above, the inlet bulk air at 25 °C from a 2.2 kW blower was directed through the orifice meter and passed to the heat transfer test section. The air flow rate was measured by a calibrated orifice meter, built according to ASME standard [24]. Manometric fluid was used in U-tube manometers with specific gravity (SG) of 0.826 to ensure reasonably accurate measurement of the low pressure drop encountered at low Reynolds numbers. Also, the pressure drop of the heat transfer test tube and the snail were measured with inclined U-tube manometers. The volumetric air flow rates from the blower were adjusted by varying speed of the blower-motor through the inverter, situated before the inlet of test tube. During the experiments, the bulk air was heated by an adjustable electrical heater wrapping along the test section. Both the inlet and outlet temperatures of the bulk air from the tube were measured by multi-channel type-K thermocouples, calibrated within ± 0.2 °C deviation by thermostat before being used. It was necessary to measure the temperature at 15 stations altogether on the outer surface of the heat transfer test pipe for finding out the average Nusselt number. The data of temperature, volumetric flow rate and pressure drop of the bulk air were recorded for each run at steady state conditions in which the inlet air temperature was maintained at 25 °C. The Reynolds number of the bulk air was varied from 8000 to 18000. The various characteristics of the flow, the Nusselt number, and the Reynolds numbers were based on the average of tube wall temperature, inlet and outlet air temperatures. The local wall temperature, inlet and outlet air temperature, the pressure drop across the test section and air flow velocity were measured for heat transfer of the heated tube with combined C-nozzle inserts and the snail entrance. The average Nusselt numbers were calculated and discussed where all fluid properties were determined at the overall bulk mean temperature. To quantify the uncertainties of measurements, the reduced data obtained experimentally were estimated. The uncertainty in the data calculation was based on Ref. [25]. The maximum uncertainties of non-dimensional parameters are ± 5%, ± 10% and ± 15% for Reynolds number, Nusselt number and friction factor, respectively. The uncertainty in the axial velocity measurement was estimated to be less than ± 7%, and pressure has a corresponding estimated uncertainty of ± 5%, whereas the uncertainty in temperature measurement at the tube wall was about ± 0.5%. The experimental results were reproducible within these uncertainty ranges. 3. Data reduction and performance criteria In the present work, the air is used as the test fluid and flowed through a uniform heat flux and insulation tube. The steady state of the heat transfer rate is assumed to be equal to the heat loss from the test section which can be expressed as: Qa ¼ Qconv where
Qa ¼ mCp;a ðTo Ti Þ ¼ VI
ð1Þ ð2Þ
The heat supplied by electrical winding in the test tube is found to be 5–8% higher than the heat absorbed by the fluid for thermal equilibrium test due to convection and radiation heat losses from the test section to surroundings. Thus, only the heat transfer rate absorbed by the fluid is taken into account for internal convective heat transfer coefficient calculation. The convection heat transfer from the test section can be written by Qconv ¼ hAðT˜ w Tb Þ
ð3Þ
in which, Tb ¼ ðTo þ Ti Þ=2
ð4Þ
and T˜ w ¼ RTw =15
ð5Þ
where Tw is the local wall temperature and evaluated at the outer wall surface of the inner tube. The average wall temperatures are calculated from 15 points, lined between the inlet and the exit of the test pipe. The average heat transfer coefficient, h and the average Nusselt number, Nu are estimated as follows:
h ¼ mCp;a ðTo Ti Þ=AðT˜ w Tb Þ
ð6Þ
P. Promvonge, S. Eiamsa-ard / International Communications in Heat and Mass Transfer 34 (2007) 838–848
Nu ¼ hD=k
843
ð7Þ
The Reynolds number is given by Re ¼ UD=v
ð8Þ
Friction factor, f can be written as: f ¼
DP ðL=DÞðqU 2 =2Þ
ð9Þ
in which U is mean velocity of the tube. All of thermo-physical properties of the air are determined at the overall bulk air temperature from Eq. (4). A fruitful comparison between heat transfer coefficients of reverse/swirl and straight flows at equal pumping power can be made, since this is relevant to the operation expense. For a constant pumping power,
ð V DPÞp ¼ ð V DPÞt
ð10Þ
and the relationship between friction factor and Reynolds number can be expressed as: ð f Re3 Þp ¼ ð f Re3 Þt
ð11Þ
The enhancement efficiency (ηe) at constant pumping power is the ratio of the convective heat transfer coefficient of the tube with either enhancement devices to the plain tube which can be written as follows: ht ge ¼ ð12Þ hp pp
j
4. Results and discussion Verification of the heat transfer and friction of the plain tube was performed before by comparing with the previous correlations under a similar condition as can be seen in Ref. [5]. The present plain tube data was found to be in good agreement with previous correlations of Dittus-Boelter and Petukhov from the open literature [26] for both the Nusselt number and the friction factor within ±10% error limits. Thus, it will not be repeated here. 4.1. Influence of pitch ratio The present experimental results on heat and fluid flow characteristics in a uniform heat flux tube with C-nozzle inserts in common with free-space snail entry of various pitch ratios (PR) are presented in the form of Nusselt number, Nu and friction factor, f. In the experiment, the snail was placed at the entrance of test tube for generating swirl flow in the tube, apart from C-nozzle inserts. The results obtained under turbulent flow conditions for three pitch ratios are presented in Fig. 3. Fig. 3A shows the variation of the average Nusselt number with Reynolds number for three pitch ratios (PR = 2.0, 4.0, and 7.0) of using the C-nozzle turbulators and the snail. In the figure, the heat transfer rate increases considerably with the rise of Reynolds number. A close examination reveals that the heat transfer rate at the lower pitch ratio is greater than that at the higher ones over the Reynolds number range studied. This is because the turbulence intensity and the flow path obtained from the lower pitch ratio are greater and longer than that at the higher one. Due to the swirl/reverse flow and lower flow cross-sectional area, the better mixing of fluid between the core and the wall regions induced by the generated centrifugal force has a significant capability to enhance the heat transfer rate. For the lowest pitch ratio (PR = 2.0), the increase in heat transfer rate is in the range of 255 to 315% over the plain tube for the Reynolds number ranging from 8000 to 18,000. Though, similar trends are found for other pitch ratios and the improvement using PR = 2.0 is seen to be about 3-8% and 10–15% better than using PR = 4.0 and PR = 7.0, respectively. The variation of friction factor with Reynolds number for various pitch ratios is shown in Fig. 3B. In the figure, the friction factor tends to decrease with the rise of Reynolds number and pitch ratio values. It is interesting to note that there is a favorable reduction in the friction factor with PR = 4.0 and 7.0, in comparison with PR = 2.0. The increase in friction factor with the reverse/swirl turbulent flow, however, is much higher than that with the axial flow. This can be attributed to the dissipation of dynamic pressure of the fluid due to higher surface area and the act caused by the reverse flow. As expected, the friction factor obtained from the smallest pitch ratio is substantially higher than those from the higher pitch ratios. The average increases in pressure losses of using the C-nozzle with free-spacing snail entry for PR = 2.0, 4.0, and 7.0 are around 87, 75, 43 times the plain tube, respectively.
844
P. Promvonge, S. Eiamsa-ard / International Communications in Heat and Mass Transfer 34 (2007) 838–848
Fig. 3. Variation of (A) Nusselt number and (B) Friction factor with Reynolds number for various PR.
4.2. Influence of free-space snail entry The present results are compared with earlier published correlations for the C-nozzle turbulators and snail entry [5]. The previous correlations of the Nusselt number, friction factor, and enhancement efficiency for using the C-nozzle turbulators alone with three pitch ratios deduced from [5] were expressed as: Nu ¼ 0:174Re0:71 Pr0:4 ðPRÞ0:18 0:29
f ¼ 59Re
ðPRÞ
ð13Þ
0:4
ge ¼ 2:8Re0:13 ðPRÞ0:055 t
ð14Þ where Rep ¼ 6:1Re0:99 ðPRÞ0:147 t
ð15Þ
For using C-nozzles and snail entrance, they were correlated as follows: Nu ¼ 0:143Re0:736 Pr1=3 ðPRÞ0:12 f ¼ 29Re ge ¼
0:197
ðPRÞ
ð16Þ
0:22
2:84Re0:139 ðPRÞ0:052 t
ð17Þ where Rep ¼
4:7Re1:03 ðPRÞ0:08 t
ð18Þ
Comparisons of heat transfer in 1) tube with C-nozzle turbulator alone, 2) tube with C-nozzle turbulator and snail entrance, and 3) tube with C-nozzle turbulator and snail with free-space entry are depicted in Fig. 4 for PR = 2.0, 4.0 and 7.0 respectively. It is visible
P. Promvonge, S. Eiamsa-ard / International Communications in Heat and Mass Transfer 34 (2007) 838–848
845
Fig. 4. Nusselt number versus Reynolds number for various enhancement devices.
in the figure that the tube with a combination of C-nozzles and snail entrance proposed as a means of enhancing heat transfer by both of reverse and swirl flows provides higher heat transfer rate than the tube fitted with C-nozzles alone, Eq. (13). In addition, a close inspection reveals that the heat transfer augmentations from the C-nozzle with free-space snail entry and the C-nozzle with snail entry, Eq. (16), are nearly the same, as expected. The heat transfer obtained from the C-nozzle with free space snail entry is around 2– 5% more or less, depending on the Reynolds number interval.
Fig. 5. Friction factor against Reynolds number for various enhancement devices.
846
P. Promvonge, S. Eiamsa-ard / International Communications in Heat and Mass Transfer 34 (2007) 838–848
Fig. 6. (A) Nusselt numbers and (B) friction factors obtained by the present correlations and measurement.
Variations of friction factor with Reynolds number for using both enhancement devices with PR= 2.0, 4.0, and 7.0 are displayed in Fig. 5. In the figure, it is worth noting that a significant effect of the C-nozzle with free-spacing snail entry on the reduction of friction factor is apparent. The friction factor tends to decrease with increasing Reynolds number and PR values for all device arrangements. The friction factor value for the C-nozzle with free-spacing snail entry is around 10–20% less than that for the C-nozzle and snail, Eq. (17), but still higher than that for the C-nozzle alone, Eq. (14), at all pitch ratios used. The reduction of friction factor for the C-nozzle with free spacing snail entry can be attributed to the decrease in surface area from using less C-nozzle number, leading to lower friction loss in the tube. 4.3. Enhancement efficiency The present results of the Nusselt number, friction factor, enhancement efficiency for using the C-nozzle and snail with freespacing entry are correlated as follows: Nu ¼ 0:162Re0:73 Pr0:4 ðPRÞ0:18
ð19Þ
f ¼ 18:3Re0:166 ðPRÞ0:2
ð20Þ
ge ¼
ht j ¼ 3:71Re0:154 ðPRÞ0:118 ; t hp pp
in which Rep ¼ 3:98Re1:04 ðPRÞ0:073 t
ð21Þ
P. Promvonge, S. Eiamsa-ard / International Communications in Heat and Mass Transfer 34 (2007) 838–848
847
Fig. 7. Variation of enhancement efficiency with Reynolds number for various enhancement devices.
Comparisons between the Nusselt number and the friction factor obtained from the present measurement and the present correlations, Eqs. (19) and (20) are portrayed in Fig. 6A and B, respectively. In the figures, the majority of the data falls within ±15% and ±15% for the present correlations of the Nusselt number and friction factor. The enhancement efficiencies of enhancement devices, Eq. (21) including those obtained from Eqs. (15) and (18) along with Reynolds number values are depicted in Fig. 7. In the figure, it is interesting to note that the enhancement efficiency shows a rapid decrease with the rise of Reynolds number for all pitch ratios. At the same Reynolds number, the small pitch ratio value provides higher enhancement efficiency than the larger one. The enhancement efficiency is peak at the lowest Reynolds number and pitch ratio values. The C-nozzle with free-spacing snail entry at the lowest pitch ratio (PR = 2.0) yields the maximum enhancement efficiency of about 0.93, better than that without free-space entry around 9%. Again, the use of PR = 2.0 leads to better enhancement efficiency than that of PR = 4.0 at some 9% and of PR = 7.0 at about 15%. This suggests that the use of freespacing snail entry provides heat transfer rate better than that of no free-space entry in terms of pumping power apart from nozzle material savings.
5. Conclusions Experimental investigations have been conducted to examine the effect of a combination of C-nozzle turbulators and a snail with free-spacing entry on heat transfer rate and flow friction characteristics in a uniform heat flux tube using air as the test fluid. The application of the C-nozzles and free-spacing snail entry results in a considerable increase in heat transfer rate and friction loss, especially at smaller pitch ratio. This study indicates that instead of the snail with no entry length, the free-spacing snail entry should be introduced to lower friction loss associated but still favorable the heat transfer rate. Depending on the flow conditions and pitch ratio, the maximum improvements of heat transfer rate over the corresponding plain tube are found to be about 315%, 300% and 285%, for PR = 2.0, 4.0, and 7.0, respectively. The variations of the enhancement efficiency for Reynolds number ranging from 5000 to 18000 are between 0.76 and 0.93; 0.7 and 0.85; and 0.67 and 0.8 for PR = 2.0, 4.0 and 7.0, respectively. This means that the C-nozzle turbulators and snail with free-space entry are not feasible in terms of energy saving. Though, the devices of C-nozzle turbulators and a snail with free-spacing entry can be employed effectively at low Reynolds number or in places where pumping power is not important but compact sizes and ease of manufacture are needed.
848
P. Promvonge, S. Eiamsa-ard / International Communications in Heat and Mass Transfer 34 (2007) 838–848
Acknowledgement The author would like to gratefully acknowledge Prof. Kulthorn Silapabanleng for valuable discussion and the Thailand Research Fund (TRF) for the financial support of this research. References [1] A.E. Bergles, Techniques to augment heat transfer, in: W.M. Rosenhow (Ed.), Handbook of Heat Transfer Applications, McGraw-Hill, New York, 1985. [2] W.J. Marner, A.E. Bergles, J.M. Chenoweth, On the presentation of performance data for enhanced tubes used in shell-and tube heat exchangers, Transaction ASME Journal Heat Transfer 105 (1983) 358–365. [3] A.E. Bergles, R.L. Webb, Guide to the literature on convection heat transfer augmentation, Advanced in Enhanced Heat Transfer 43 (1985) 81–89. [4] K. Yakut, B. Sahin, Flow-induced vibration analysis of conical rings used of heat transfer enhancement in heat exchanger, Applied Energy 78 (2004) 273–288. [5] P. Promvonge, S. Eiamsa-ard, Heat transfer enhancement in a tube with combined conical-nozzle inserts and swirl generator, Energy Conversion and Management 47 (2006) 2867–2882. [6] S. Eiamsa-ard, P. Promvonge, Experimental investigation of heat transfer and friction characteristics in a circular tube fitted with V-nozzle turbulators, International Communication in Heat and Mass Transfer 33 (2006) 591–600. [7] R.M. Manglik, A.E. Bergles, Heat transfer and pressure drop correlations for twisted-tape inserts in isothermal tubes: Part II — Transition and turbulent flows, Transaction ASME Journal Heat Transfer 114 (1992) 99–106. [8] Z.Y. Yang, Enhanced condensation using twisted tape inserts, 6th ASME-JSME Thermal Engineering Joint Conference, March 16–20, 2003, Hawaii Island, USA, 2003. [9] S. Eiamsa-ard, P. Promvonge, Enhancement of heat transfer in a tube with regularly-spaced helical tape swirl generators, Solar Energy 78 (2005) 483–494. [10] R. Sethumadhavan, M.R. Rao, Turbulent flow heat transfer and fluid friction in helical-wire–coil-inserted tubes, International Journal of Heat and Mass Transfer 26 (1983) 1833–1845. [11] V.K. Dhir, F. Chang, J. Yu, Enhancement of single phase forced convection heat transfer in tubes using staged tangential flow injection, Final Report, June 1987–December 1989, GRI-90/0134, 1990. [12] V.K. Dhir, F. Chang, Heat transfer enhancement using tangential injection, ASHRAE Transactions 98 (1992) (BA-92-4-1). [13] G. Son, V.K. Dhir, Enhancement of heat transfer in an annulus using tangential flow injection, Transaction ASME Journal of Heat Transfer 115 (1993) 59–66. [14] V.X. Tung, V.K. Dhir, F. Chang, A.R. Karagozian, F. Zhou, Enhancement of forced convection heat transfer in tubes using staged tangential flow injection, Annual Report, June 1987–September, GRI report No.GRI-89/020, 1989. [15] Aydin Durmus, Ayla Durmus, M. Esen, Investigation of heat transfer and pressure drop in a concentric heat exchanger with snail entrance, Applied Thermal Engineering 22 (2002) 321–332. [16] M. Yilmaz, O. Comakli, S. Yapici, Enhancement of heat transfer by turbulent decaying swirl flow, Energy Conversion and Management 40 (1999) 1365–1376. [17] J. Zhang, L. Dong, L. Zhou, S. Nieh, Simulation of swirling turbulent flows and heat transfer in an annular duct, Numerical Heat Transfer. Part A, Applications 44 (2003) 591–609. [18] J. Zhang, J. He, L. Zhou, S. Nieh, Simulation of swirling turbulent heat transfer in a vortex heat exchanger, Numerical Heat Transfer. Part A, Applications 48 (2005) 607–625. [19] X. Wei, J. Zhang, L. Zhou, A new algebraic mass flux model for simulating turbulent mixing in swirling flow, Numerical Heat Transfer. Part B, Fundamentals 45 (2004) 283–300. [20] J.S. Lee, X. Xu, R.H. Pletcher, Large eddy simulation of the effects of inner wall rotation on heat transfer in annular turbulent flow, Numerical Heat Transfer. Part A, Applications 46 (2004) 323–341. [21] J.-H. Kim, K.E. Jansen, M.K. Jensen, Simulation of three-dimensional incompressible turbulent flow inside tubes with helical fins, Numerical Heat Transfer. Part B, Fundamentals 46 (2004) 195–221. [22] A.K. Gupta, D.G. Lilley, N. Syred, Swirl flows, Abacus Press, Kent, England, 1984. [23] T. Akiyama, M. Ikeda, Industrial engineering chemical process, Design and Development 25 (1986) 907. [24] ASME Standard, Measurement of fluid flow in pipes using orifice, nozzle and venture, ASME MFC-3M-1984, United Engineering Center 345 East 47th Street, New York, 1984, pp. 1–56. [25] ANSI/ASME, Measurement uncertainty, PTC 19, 1–1985, Part I, 1986. [26] F. Incropera, P.D. Dewitt, Introduction to heat transfer, 3rd edition. John Wiley & Sons Inc, 1996.
Heat transfer in a circular tube fitted with free-spacing snail entry and conical-nozzle turbulators ☆ P. Promvonge a,⁎, S. Eiamsa-ard b a
Department of Mechanical Engineering, Faculty of Engineering, King Mongkut's Institute of Technology Ladkrabang, Bangkok 10520, Thailand b Department of Mechanical Engineering, Faculty of Engineering, Mahanakorn University of Technology, Bangkok 10530, Thailand Available online 21 May 2007
Abstract The paper presents the effect of a free-spacing snail entry together with conical-nozzle turbulators on turbulent heat transfer and friction characteristics in a uniform heat-flux tube. The insertions of the conical or converging nozzle (C-nozzle) with different pitch ratios (PR) in common with the free-space snail entry are examined in a Reynolds number range from 8000 to 18000. A substantial augmentation of heat transfer for using the C-nozzles and snail entrance is expected by a strong influence from nozzleinduced reverse/re-circulation motion and snail-produced vortex/swirl motion for high Reynolds number. The experimental result shows a considerable increase in friction factor and heat transfer over the plain tube under the same operation conditions. Over the range investigated, the Nusselt numbers for employing both the enhancement devices with PR = 2.0, 4.0 and 7.0 are found to be higher than that for the plain tube around 315%, 300% and 285% respectively. The results obtained are correlated in the form of Nusselt number as a function of Reynolds number, Prandtl number and pitch ratio. For performance comparison at equal pumping power, both the enhancement devices with the smallest pitch ratio perform the best, especially at low Reynolds number. The present results are also compared with correlations obtained from similar enhancement devices but without free-spacing entry. © 2007 Elsevier Ltd. All rights reserved. Keywords: Heat transfer augmentation; Swirl flow; Re-circulation/reverse flow; Turbulator; Snail entry; Enhancement device
1. Introduction The development of high-performance thermal systems has still stimulated considerable interest in methods to improve heat transfer. The conventional heat exchangers are improved by means of various augmentation techniques with emphasis on many types of surface enhancements. Augmented surfaces can create one or more combinations of the following conditions that are favorable for the increase in heat transfer rate with an undesirable rise of friction: 1) disruption of the development of boundary layer and increase of the turbulence intensity, 2) increase in heat transfer area, and 3) generation of swirling/rotating and/or secondary flows. For the effective performance evaluation of passive augmentation methods for example twisted tape, wire coil, and extended surface which are used in force convection situations, both the heat transfer and flow friction characteristics of the enhancement technique must be known [1–3]. The convection heat transfer along
☆
Communicated by W.J. Minkowycz. ⁎ Corresponding author. E-mail address: [email protected] (P. Promvonge).
0735-1933/$ - see front matter © 2007 Elsevier Ltd. All rights reserved. doi:10.1016/j.icheatmasstransfer.2007.03.020
P. Promvonge, S. Eiamsa-ard / International Communications in Heat and Mass Transfer 34 (2007) 838–848
839
Nomenclature A Cp,a D Do f h I k L l m˙ Nu ΔP PR Pr Qa Qconv Re Ret Rep s S t Tb Ti To Tw T˜w U V V˙
Heat transfer surface area (m2) Specific heat of air (J/kg K) Inner diameter of tube (m) Outer diameter of tube (m) Friction factor Average heat transfer coefficient (W/m2 K) Current (amp) Thermal conductivity of air, (W/m K) Length of test tube (m) Pitch length (m) Mass flow rate (kg/s) Nusselt number Pressure drop (Pa) Pitch ratio, l/D = 1+S Prandtl number Heat transfer absorbed by air (W) Convective heat transfer (W) Reynolds number Reynolds number of turbulator Reynolds number of plain tube Space length (m) Space ratio, s/D Thickness of tube, m Bulk temperature (°C) Inlet temperature (°C) Outlet temperature (°C) Wall temperature (°C) Mean wall temperature (°C) Average axial velocity (m/s) Voltage (volt) Volume flow rate (m3/s)
Greek symbols ηe Enhancement efficiency ρ Density (kg/m3) μ Dynamic viscosity (kg/s m)
the tube wall can be improved significantly by introducing the reverse/re-circulation flow with a view to increasing the effective axial Reynolds number, decreasing the cross-sectional area of flow, and increasing the mean velocity and temperature gradient. This is because the reverse flow can induce the higher heat fluxes and momentum transfer due to the large effective driving potential force but also higher pressure drop. The strength of reverse flow and the reattached position are the main interest in many heat transfer applications such as heat exchangers, combustion chambers, gas turbine blades, and electronic devices. Yakut and Sahin [4] experimentally studied the heat transfer and friction characteristics in a uniform heat flux fitted with conical-ring turbulators used to provide reverse/turbulent flows in each module of the conical rings. Therefore, significant improvement of heat transfer along the tube wall was reported. The enhancements of heat transfer in a uniform heat-flux circular tube fitted with conical-nozzles and swirl generator were also experimentally investigated by Promvonge and Eiamsa-ard [5]. In their research, the conical-nozzles were placed in a test tube with three different pitch ratios of conical-nozzles, apart from the snail mounted at the tube inlet. The use of the conical-nozzle in conjunction with
840
P. Promvonge, S. Eiamsa-ard / International Communications in Heat and Mass Transfer 34 (2007) 838–848
the snail entrance led to maximum heat transfer rate up to 316% over the plain tube besides a substantial increase in pressure loss as well. Eiamsa-ard and Promvonge [6] again reported the influences of V-nozzle inserts on heat transfer, flow friction, and enhancement efficiency characteristics in a uniform heat-flux tube with three pitch ratios. They found that the use of V-nozzles led to a considerable increase in heat transfer rate and a maximum gain of 1.19 on enhancement efficiency was obtained for the smallest pitch ratio used at low Reynolds number. This indicates the crucial effect of the reverse/recirculation flow can promote the heat transfer rate in tubes. The snail/swirl flow generators have been known to be effective in increasing convection heat transfer coefficients and also used in augmentative heat transfer in many engineering applications such as heat exchanger, drying process and vortex combustor. The swirl flow devices can be classified into two types: the continuous swirl and the decaying swirl flows. The former represents the swirling motion that persists over the entire length of the tube for example twisted tape [7,8], coiled wires inserts [9,10] and helical grooves, while the latter means the swirl created at the entrance of the tube and then decays along the flow path [11–16] for example the radial guide vane swirl generator and the tangential flow injection device. In the decaying one, the heat transfer coefficient and the pressure drop decrease along with the axial distance, while in the continuous one, the heat transfer coefficient and the pressure drop keep constant throughout. Apart from experimental work as mentioned above, Zhang et al. [17,18] numerically studied swirling turbulent flows and heat transfer in an annular duct and in a novel vortex heat exchanger by considering the effect of swirl number, inlet axial velocity, and ratio of inner to outer radius on the mean flow and turbulence properties, as well as on enhancing heat transfer in the duct. Wei et al. [19] proposed a new algebraic turbulent mass flux model, which properly accounts for swirl-turbulence interactions while Lee et al. [20] conducted the numerical work using a large eddy simulation to investigate the effect of swirl on the heat and momentum transfer in an annular pipe flow with a rotating inner wall. Simulation of three-dimensional incompressible turbulent flow inside tubes with helical fins was also presented by Kim et al. [21]. The methods of generating swirl can be classified into three main categories [22]. The first is the tangential flow injection to induce a swirling fluid motion down the tube [5,11–15]. The second is the guide vanes swirl generators [16,22,23] which can be grouped into two types: radial guide vane and axial guide vane. The last type is the direct rotation of the tube. In the present work, the snail/swirl generator (tangential flow injection) is normally fitted at the entrance of the tube. Therefore, the swirl is intense at the entrance and decays downstream of the flow. This technique causes the rise in tangential flow velocity, prolonging residence time of the flow in the tube, thinning boundary layer and enhancing the tangential and radial turbulent fluctuation and therefore results in a significant increase in heat transfer rate inside the tube. The above literature review indicates that the tube fitted with conical-nozzle turbulators and snail swirl generators are among the most effective and practical methods for augmenting heat transfer in tubes. However, the common use of both enhancement devices leads to a substantial increase in pressure drop across the tube [5]. Thus, the efficient utilization of both enhancement devices can be compromised by arranging in a suitable configuration to obtain the optimum pressure loss and heat transfer. To reduce the rise of pressure loss from utilizing the enhancement devices but still favorable the heat transfer rate, a free-spacing snail entry is introduced. This concept comes from the fact that the local heat transfer is much high in the developing flow region or at around 10D downstream of the tube inlet in the turbulent decaying swirl flow as suggested by Ref. [16]. Therefore, this experimental investigation is to examine the heat transfer enhanced by the multiplicative effect of C-nozzle turbulators and a free-spacing snail entry. In the experimental test, the first C-nozzle is placed at 10D downstream of the tube inlet (with PR = 2.0, 4.0, and 7.0) while the snail is mounted at the test tube entrance. 2. Experimental investigation The experiments were carried out to examine the effect of free-space snail entry and C-nozzle inserts on heat transfer and fluid flow characteristics of air flow in a tube. A schematic diagram of the experimental setup is illustrated in Fig. 1. The flow system consisted of a 2.2 kW blower, orifice meter to measure the flow rate, and the heat transfer test section. The test-tube section made of copper having a 47.5 mm inner diameter (D) and 50.5 mm outer diameter (Do), was 1250 mm long (L) and 1.5 mm thick (t) as depicted in Fig. 2. The tube was heated by continually winding flexible electrical wire provided a uniform heat flux boundary condition. The electrical output power was controlled by a variac transformer to obtain a constant heat flux along the entire length of the test section and by keeping the current less than 3 amps. The outer surface of the test tube was well insulated to minimize convection and radiation heat losses to
P. Promvonge, S. Eiamsa-ard / International Communications in Heat and Mass Transfer 34 (2007) 838–848
841
Fig. 1. Schematic diagram of experimental heat transfer set-up.
surroundings, and necessary precautions were taken to prevent leakages from the system. The inner and outer temperatures of the bulk air were measured at certain points with a multi-channel temperature measurement unit in conjunction with the type-K thermocouples. Fifteen thermocouples were tapped on the local wall of the tube and the thermocouples were placed round the tube to measure the variation of circumferential temperature, which was found to be negligible. The mean local wall temperature was determined by means of calculations based on the reading of typeK thermocouples. Fig. 2 represents the C-nozzle arrangement together with free-spacing snail entry used in the present experiment. The C-nozzle was made of Aluminum with 95 mm (2.0D) in length and its end and throat diameters were 46 mm and 26 mm, respectively. The Converging nozzles or C-nozzles were placed with three different pitch lengths, l of arrangements, having l = 95 mm (s = 47.5 mm, PR = 2.0), l = 190 mm (s = 142.5 mm, PR = 4.0), and l = 332.5 mm (s = 285 mm, PR = 7.0), for each run of experiments. In addition, a snail type swirl generator was mounted at the entrance of the test tube as shown in Fig. 2. In the experiment, the combination of the two phenomena, (1) the recirculating flow between the two adjacent C-nozzles and (2) the swirling flow generated by the snail, are supposed to be effective in the vicinity of the tube wall, where thermal resistance is high. The combined techniques are expected to provide the better and fast mixing and rotating of fluid in this region as well as causing the increased viscous dissipation, thereby enhancing the heat transfer rate.
Fig. 2. Test tube fitted with C-nozzle turbulators and snail with free-spacing entry.
842
P. Promvonge, S. Eiamsa-ard / International Communications in Heat and Mass Transfer 34 (2007) 838–848
In the apparatus setting above, the inlet bulk air at 25 °C from a 2.2 kW blower was directed through the orifice meter and passed to the heat transfer test section. The air flow rate was measured by a calibrated orifice meter, built according to ASME standard [24]. Manometric fluid was used in U-tube manometers with specific gravity (SG) of 0.826 to ensure reasonably accurate measurement of the low pressure drop encountered at low Reynolds numbers. Also, the pressure drop of the heat transfer test tube and the snail were measured with inclined U-tube manometers. The volumetric air flow rates from the blower were adjusted by varying speed of the blower-motor through the inverter, situated before the inlet of test tube. During the experiments, the bulk air was heated by an adjustable electrical heater wrapping along the test section. Both the inlet and outlet temperatures of the bulk air from the tube were measured by multi-channel type-K thermocouples, calibrated within ± 0.2 °C deviation by thermostat before being used. It was necessary to measure the temperature at 15 stations altogether on the outer surface of the heat transfer test pipe for finding out the average Nusselt number. The data of temperature, volumetric flow rate and pressure drop of the bulk air were recorded for each run at steady state conditions in which the inlet air temperature was maintained at 25 °C. The Reynolds number of the bulk air was varied from 8000 to 18000. The various characteristics of the flow, the Nusselt number, and the Reynolds numbers were based on the average of tube wall temperature, inlet and outlet air temperatures. The local wall temperature, inlet and outlet air temperature, the pressure drop across the test section and air flow velocity were measured for heat transfer of the heated tube with combined C-nozzle inserts and the snail entrance. The average Nusselt numbers were calculated and discussed where all fluid properties were determined at the overall bulk mean temperature. To quantify the uncertainties of measurements, the reduced data obtained experimentally were estimated. The uncertainty in the data calculation was based on Ref. [25]. The maximum uncertainties of non-dimensional parameters are ± 5%, ± 10% and ± 15% for Reynolds number, Nusselt number and friction factor, respectively. The uncertainty in the axial velocity measurement was estimated to be less than ± 7%, and pressure has a corresponding estimated uncertainty of ± 5%, whereas the uncertainty in temperature measurement at the tube wall was about ± 0.5%. The experimental results were reproducible within these uncertainty ranges. 3. Data reduction and performance criteria In the present work, the air is used as the test fluid and flowed through a uniform heat flux and insulation tube. The steady state of the heat transfer rate is assumed to be equal to the heat loss from the test section which can be expressed as: Qa ¼ Qconv where
Qa ¼ mCp;a ðTo Ti Þ ¼ VI
ð1Þ ð2Þ
The heat supplied by electrical winding in the test tube is found to be 5–8% higher than the heat absorbed by the fluid for thermal equilibrium test due to convection and radiation heat losses from the test section to surroundings. Thus, only the heat transfer rate absorbed by the fluid is taken into account for internal convective heat transfer coefficient calculation. The convection heat transfer from the test section can be written by Qconv ¼ hAðT˜ w Tb Þ
ð3Þ
in which, Tb ¼ ðTo þ Ti Þ=2
ð4Þ
and T˜ w ¼ RTw =15
ð5Þ
where Tw is the local wall temperature and evaluated at the outer wall surface of the inner tube. The average wall temperatures are calculated from 15 points, lined between the inlet and the exit of the test pipe. The average heat transfer coefficient, h and the average Nusselt number, Nu are estimated as follows:
h ¼ mCp;a ðTo Ti Þ=AðT˜ w Tb Þ
ð6Þ
P. Promvonge, S. Eiamsa-ard / International Communications in Heat and Mass Transfer 34 (2007) 838–848
Nu ¼ hD=k
843
ð7Þ
The Reynolds number is given by Re ¼ UD=v
ð8Þ
Friction factor, f can be written as: f ¼
DP ðL=DÞðqU 2 =2Þ
ð9Þ
in which U is mean velocity of the tube. All of thermo-physical properties of the air are determined at the overall bulk air temperature from Eq. (4). A fruitful comparison between heat transfer coefficients of reverse/swirl and straight flows at equal pumping power can be made, since this is relevant to the operation expense. For a constant pumping power,
ð V DPÞp ¼ ð V DPÞt
ð10Þ
and the relationship between friction factor and Reynolds number can be expressed as: ð f Re3 Þp ¼ ð f Re3 Þt
ð11Þ
The enhancement efficiency (ηe) at constant pumping power is the ratio of the convective heat transfer coefficient of the tube with either enhancement devices to the plain tube which can be written as follows: ht ge ¼ ð12Þ hp pp
j
4. Results and discussion Verification of the heat transfer and friction of the plain tube was performed before by comparing with the previous correlations under a similar condition as can be seen in Ref. [5]. The present plain tube data was found to be in good agreement with previous correlations of Dittus-Boelter and Petukhov from the open literature [26] for both the Nusselt number and the friction factor within ±10% error limits. Thus, it will not be repeated here. 4.1. Influence of pitch ratio The present experimental results on heat and fluid flow characteristics in a uniform heat flux tube with C-nozzle inserts in common with free-space snail entry of various pitch ratios (PR) are presented in the form of Nusselt number, Nu and friction factor, f. In the experiment, the snail was placed at the entrance of test tube for generating swirl flow in the tube, apart from C-nozzle inserts. The results obtained under turbulent flow conditions for three pitch ratios are presented in Fig. 3. Fig. 3A shows the variation of the average Nusselt number with Reynolds number for three pitch ratios (PR = 2.0, 4.0, and 7.0) of using the C-nozzle turbulators and the snail. In the figure, the heat transfer rate increases considerably with the rise of Reynolds number. A close examination reveals that the heat transfer rate at the lower pitch ratio is greater than that at the higher ones over the Reynolds number range studied. This is because the turbulence intensity and the flow path obtained from the lower pitch ratio are greater and longer than that at the higher one. Due to the swirl/reverse flow and lower flow cross-sectional area, the better mixing of fluid between the core and the wall regions induced by the generated centrifugal force has a significant capability to enhance the heat transfer rate. For the lowest pitch ratio (PR = 2.0), the increase in heat transfer rate is in the range of 255 to 315% over the plain tube for the Reynolds number ranging from 8000 to 18,000. Though, similar trends are found for other pitch ratios and the improvement using PR = 2.0 is seen to be about 3-8% and 10–15% better than using PR = 4.0 and PR = 7.0, respectively. The variation of friction factor with Reynolds number for various pitch ratios is shown in Fig. 3B. In the figure, the friction factor tends to decrease with the rise of Reynolds number and pitch ratio values. It is interesting to note that there is a favorable reduction in the friction factor with PR = 4.0 and 7.0, in comparison with PR = 2.0. The increase in friction factor with the reverse/swirl turbulent flow, however, is much higher than that with the axial flow. This can be attributed to the dissipation of dynamic pressure of the fluid due to higher surface area and the act caused by the reverse flow. As expected, the friction factor obtained from the smallest pitch ratio is substantially higher than those from the higher pitch ratios. The average increases in pressure losses of using the C-nozzle with free-spacing snail entry for PR = 2.0, 4.0, and 7.0 are around 87, 75, 43 times the plain tube, respectively.
844
P. Promvonge, S. Eiamsa-ard / International Communications in Heat and Mass Transfer 34 (2007) 838–848
Fig. 3. Variation of (A) Nusselt number and (B) Friction factor with Reynolds number for various PR.
4.2. Influence of free-space snail entry The present results are compared with earlier published correlations for the C-nozzle turbulators and snail entry [5]. The previous correlations of the Nusselt number, friction factor, and enhancement efficiency for using the C-nozzle turbulators alone with three pitch ratios deduced from [5] were expressed as: Nu ¼ 0:174Re0:71 Pr0:4 ðPRÞ0:18 0:29
f ¼ 59Re
ðPRÞ
ð13Þ
0:4
ge ¼ 2:8Re0:13 ðPRÞ0:055 t
ð14Þ where Rep ¼ 6:1Re0:99 ðPRÞ0:147 t
ð15Þ
For using C-nozzles and snail entrance, they were correlated as follows: Nu ¼ 0:143Re0:736 Pr1=3 ðPRÞ0:12 f ¼ 29Re ge ¼
0:197
ðPRÞ
ð16Þ
0:22
2:84Re0:139 ðPRÞ0:052 t
ð17Þ where Rep ¼
4:7Re1:03 ðPRÞ0:08 t
ð18Þ
Comparisons of heat transfer in 1) tube with C-nozzle turbulator alone, 2) tube with C-nozzle turbulator and snail entrance, and 3) tube with C-nozzle turbulator and snail with free-space entry are depicted in Fig. 4 for PR = 2.0, 4.0 and 7.0 respectively. It is visible
P. Promvonge, S. Eiamsa-ard / International Communications in Heat and Mass Transfer 34 (2007) 838–848
845
Fig. 4. Nusselt number versus Reynolds number for various enhancement devices.
in the figure that the tube with a combination of C-nozzles and snail entrance proposed as a means of enhancing heat transfer by both of reverse and swirl flows provides higher heat transfer rate than the tube fitted with C-nozzles alone, Eq. (13). In addition, a close inspection reveals that the heat transfer augmentations from the C-nozzle with free-space snail entry and the C-nozzle with snail entry, Eq. (16), are nearly the same, as expected. The heat transfer obtained from the C-nozzle with free space snail entry is around 2– 5% more or less, depending on the Reynolds number interval.
Fig. 5. Friction factor against Reynolds number for various enhancement devices.
846
P. Promvonge, S. Eiamsa-ard / International Communications in Heat and Mass Transfer 34 (2007) 838–848
Fig. 6. (A) Nusselt numbers and (B) friction factors obtained by the present correlations and measurement.
Variations of friction factor with Reynolds number for using both enhancement devices with PR= 2.0, 4.0, and 7.0 are displayed in Fig. 5. In the figure, it is worth noting that a significant effect of the C-nozzle with free-spacing snail entry on the reduction of friction factor is apparent. The friction factor tends to decrease with increasing Reynolds number and PR values for all device arrangements. The friction factor value for the C-nozzle with free-spacing snail entry is around 10–20% less than that for the C-nozzle and snail, Eq. (17), but still higher than that for the C-nozzle alone, Eq. (14), at all pitch ratios used. The reduction of friction factor for the C-nozzle with free spacing snail entry can be attributed to the decrease in surface area from using less C-nozzle number, leading to lower friction loss in the tube. 4.3. Enhancement efficiency The present results of the Nusselt number, friction factor, enhancement efficiency for using the C-nozzle and snail with freespacing entry are correlated as follows: Nu ¼ 0:162Re0:73 Pr0:4 ðPRÞ0:18
ð19Þ
f ¼ 18:3Re0:166 ðPRÞ0:2
ð20Þ
ge ¼
ht j ¼ 3:71Re0:154 ðPRÞ0:118 ; t hp pp
in which Rep ¼ 3:98Re1:04 ðPRÞ0:073 t
ð21Þ
P. Promvonge, S. Eiamsa-ard / International Communications in Heat and Mass Transfer 34 (2007) 838–848
847
Fig. 7. Variation of enhancement efficiency with Reynolds number for various enhancement devices.
Comparisons between the Nusselt number and the friction factor obtained from the present measurement and the present correlations, Eqs. (19) and (20) are portrayed in Fig. 6A and B, respectively. In the figures, the majority of the data falls within ±15% and ±15% for the present correlations of the Nusselt number and friction factor. The enhancement efficiencies of enhancement devices, Eq. (21) including those obtained from Eqs. (15) and (18) along with Reynolds number values are depicted in Fig. 7. In the figure, it is interesting to note that the enhancement efficiency shows a rapid decrease with the rise of Reynolds number for all pitch ratios. At the same Reynolds number, the small pitch ratio value provides higher enhancement efficiency than the larger one. The enhancement efficiency is peak at the lowest Reynolds number and pitch ratio values. The C-nozzle with free-spacing snail entry at the lowest pitch ratio (PR = 2.0) yields the maximum enhancement efficiency of about 0.93, better than that without free-space entry around 9%. Again, the use of PR = 2.0 leads to better enhancement efficiency than that of PR = 4.0 at some 9% and of PR = 7.0 at about 15%. This suggests that the use of freespacing snail entry provides heat transfer rate better than that of no free-space entry in terms of pumping power apart from nozzle material savings.
5. Conclusions Experimental investigations have been conducted to examine the effect of a combination of C-nozzle turbulators and a snail with free-spacing entry on heat transfer rate and flow friction characteristics in a uniform heat flux tube using air as the test fluid. The application of the C-nozzles and free-spacing snail entry results in a considerable increase in heat transfer rate and friction loss, especially at smaller pitch ratio. This study indicates that instead of the snail with no entry length, the free-spacing snail entry should be introduced to lower friction loss associated but still favorable the heat transfer rate. Depending on the flow conditions and pitch ratio, the maximum improvements of heat transfer rate over the corresponding plain tube are found to be about 315%, 300% and 285%, for PR = 2.0, 4.0, and 7.0, respectively. The variations of the enhancement efficiency for Reynolds number ranging from 5000 to 18000 are between 0.76 and 0.93; 0.7 and 0.85; and 0.67 and 0.8 for PR = 2.0, 4.0 and 7.0, respectively. This means that the C-nozzle turbulators and snail with free-space entry are not feasible in terms of energy saving. Though, the devices of C-nozzle turbulators and a snail with free-spacing entry can be employed effectively at low Reynolds number or in places where pumping power is not important but compact sizes and ease of manufacture are needed.
848
P. Promvonge, S. Eiamsa-ard / International Communications in Heat and Mass Transfer 34 (2007) 838–848
Acknowledgement The author would like to gratefully acknowledge Prof. Kulthorn Silapabanleng for valuable discussion and the Thailand Research Fund (TRF) for the financial support of this research. References [1] A.E. Bergles, Techniques to augment heat transfer, in: W.M. Rosenhow (Ed.), Handbook of Heat Transfer Applications, McGraw-Hill, New York, 1985. [2] W.J. Marner, A.E. Bergles, J.M. Chenoweth, On the presentation of performance data for enhanced tubes used in shell-and tube heat exchangers, Transaction ASME Journal Heat Transfer 105 (1983) 358–365. [3] A.E. Bergles, R.L. Webb, Guide to the literature on convection heat transfer augmentation, Advanced in Enhanced Heat Transfer 43 (1985) 81–89. [4] K. Yakut, B. Sahin, Flow-induced vibration analysis of conical rings used of heat transfer enhancement in heat exchanger, Applied Energy 78 (2004) 273–288. [5] P. Promvonge, S. Eiamsa-ard, Heat transfer enhancement in a tube with combined conical-nozzle inserts and swirl generator, Energy Conversion and Management 47 (2006) 2867–2882. [6] S. Eiamsa-ard, P. Promvonge, Experimental investigation of heat transfer and friction characteristics in a circular tube fitted with V-nozzle turbulators, International Communication in Heat and Mass Transfer 33 (2006) 591–600. [7] R.M. Manglik, A.E. Bergles, Heat transfer and pressure drop correlations for twisted-tape inserts in isothermal tubes: Part II — Transition and turbulent flows, Transaction ASME Journal Heat Transfer 114 (1992) 99–106. [8] Z.Y. Yang, Enhanced condensation using twisted tape inserts, 6th ASME-JSME Thermal Engineering Joint Conference, March 16–20, 2003, Hawaii Island, USA, 2003. [9] S. Eiamsa-ard, P. Promvonge, Enhancement of heat transfer in a tube with regularly-spaced helical tape swirl generators, Solar Energy 78 (2005) 483–494. [10] R. Sethumadhavan, M.R. Rao, Turbulent flow heat transfer and fluid friction in helical-wire–coil-inserted tubes, International Journal of Heat and Mass Transfer 26 (1983) 1833–1845. [11] V.K. Dhir, F. Chang, J. Yu, Enhancement of single phase forced convection heat transfer in tubes using staged tangential flow injection, Final Report, June 1987–December 1989, GRI-90/0134, 1990. [12] V.K. Dhir, F. Chang, Heat transfer enhancement using tangential injection, ASHRAE Transactions 98 (1992) (BA-92-4-1). [13] G. Son, V.K. Dhir, Enhancement of heat transfer in an annulus using tangential flow injection, Transaction ASME Journal of Heat Transfer 115 (1993) 59–66. [14] V.X. Tung, V.K. Dhir, F. Chang, A.R. Karagozian, F. Zhou, Enhancement of forced convection heat transfer in tubes using staged tangential flow injection, Annual Report, June 1987–September, GRI report No.GRI-89/020, 1989. [15] Aydin Durmus, Ayla Durmus, M. Esen, Investigation of heat transfer and pressure drop in a concentric heat exchanger with snail entrance, Applied Thermal Engineering 22 (2002) 321–332. [16] M. Yilmaz, O. Comakli, S. Yapici, Enhancement of heat transfer by turbulent decaying swirl flow, Energy Conversion and Management 40 (1999) 1365–1376. [17] J. Zhang, L. Dong, L. Zhou, S. Nieh, Simulation of swirling turbulent flows and heat transfer in an annular duct, Numerical Heat Transfer. Part A, Applications 44 (2003) 591–609. [18] J. Zhang, J. He, L. Zhou, S. Nieh, Simulation of swirling turbulent heat transfer in a vortex heat exchanger, Numerical Heat Transfer. Part A, Applications 48 (2005) 607–625. [19] X. Wei, J. Zhang, L. Zhou, A new algebraic mass flux model for simulating turbulent mixing in swirling flow, Numerical Heat Transfer. Part B, Fundamentals 45 (2004) 283–300. [20] J.S. Lee, X. Xu, R.H. Pletcher, Large eddy simulation of the effects of inner wall rotation on heat transfer in annular turbulent flow, Numerical Heat Transfer. Part A, Applications 46 (2004) 323–341. [21] J.-H. Kim, K.E. Jansen, M.K. Jensen, Simulation of three-dimensional incompressible turbulent flow inside tubes with helical fins, Numerical Heat Transfer. Part B, Fundamentals 46 (2004) 195–221. [22] A.K. Gupta, D.G. Lilley, N. Syred, Swirl flows, Abacus Press, Kent, England, 1984. [23] T. Akiyama, M. Ikeda, Industrial engineering chemical process, Design and Development 25 (1986) 907. [24] ASME Standard, Measurement of fluid flow in pipes using orifice, nozzle and venture, ASME MFC-3M-1984, United Engineering Center 345 East 47th Street, New York, 1984, pp. 1–56. [25] ANSI/ASME, Measurement uncertainty, PTC 19, 1–1985, Part I, 1986. [26] F. Incropera, P.D. Dewitt, Introduction to heat transfer, 3rd edition. John Wiley & Sons Inc, 1996.