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Heat transfer augmentation in a circular tube using V-nozzle turbulator inserts and snail entry
Experimental Thermal and Fluid Science 32 (2007) 332–340 www.elsevier.com/locate/etfs
Heat transfer augmentation in a circular tube using V-nozzle turbulator inserts and snail entry Pongjet Promvonge a
a,*
, Smith Eiamsa-ard
b,1
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 Received 16 July 2006; received in revised form 24 February 2007; accepted 22 April 2007
Abstract Influences of V-nozzle turbulator inserts in conjunction with a snail entry on heat transfer and friction loss characteristics in a circular tube are experimentally investigated in this paper. In the present work, a set of converging-diverging nozzles like a venturi structure (referred to as V-nozzle) used as a turbulator/reverse-flow generator is placed inside the test tube through which air as the test fluid is passed. Also, the snail is mounted at the tube entrance to create a decaying swirl flow. The effects of the snail entry and insertion of V-nozzles with three different pitch ratios, PR = 2.0, 4.0, and 7.0 on heat transfer rate in the tube are examined for the Reynolds number ranging from 8000 to 18,000. The experimental results are displayed in terms of Nusselt number (Nu) and friction factor (f) as a function of Reynolds number (Re). The values of Nusselt number and friction factor for utilizing both the V-nozzle and the snail entry are found to be considerably higher than that for using the V-nozzle alone or the plain tube. The use of PR = 2.0 leads to higher Nusselt number and friction factor values than that of PR = 4.0 or 7.0. To assess the real benefits in using the turbulator and the swirl generator of the enhanced tube, empirical correlations in terms of Re and PR for Nusselt number, friction factor and performance evaluation criteria are also determined. Ó 2007 Elsevier Inc. All rights reserved. Keywords: Heat transfer enhancement; Swirl flow; Reverse flow; Turbulator; V-nozzle; Snail; Pitch ratio (PR=1 + S)
1. Introduction The need for high-performance thermal systems in many engineering applications has stimulated considerable interest in finding various methods to improve heat transfer in the system. The conventional heat exchangers are generally 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) interruption of boundary layer development *
Corresponding author. Tel.: +662 3264197; fax: +662 3264198. E-mail addresses: [email protected] (P. Promvonge), smith@ mut.ac.th (S. Eiamsa-ard). 1 Tel./fax: +662 9883666x241. 0894-1777/$ - see front matter Ó 2007 Elsevier Inc. All rights reserved. doi:10.1016/j.expthermflusci.2007.04.010
and increasing turbulence intensity; (2) increase in heat transfer area; and (3) generating of swirling and/or secondary flows. To date, many studies have been emphasized on passive heat-transfer enhancement methods and the fluid flow. Reverse/swirl flow devices form an important group of the passive augmentation techniques. The reverse flow, sometimes called ‘‘recirculation flow’’, device or the turbulator is widely employed in heat transfer engineering applications. This is because the convection heat transfer along the tube wall can be improved significantly by introducing the reverse/re-circulation flow to increase the effective axial Reynolds number and decrease the cross-sectional area of flow, leading to an increase in the mean velocity and temperature gradient. The reverse flow cannot only induce the higher heat fluxes and momentum transfer due to the large effective driving potential force but also the higher pressure drop. The strength of reverse flow and the
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333
Nomenclature A Cp D f h I k L m_ Nu DP PR Pr Q Re t T Te s S
heat transfer surface area of test tube [m2] specific heat [J/kg K] inner diameter of test tube [m] friction factor heat transfer coefficient [W/m2K] current [A] thermal conductivity of air [W/m K] length of the test section [m] mass flow rate [kg/s] Nusselt number pressure drop [Pa] pitch ratio [1 + S] Prandtl number heat transfer rate [W] Reynolds number thickness of test tube [m] temperature [°C] average temperature [°C] space length [m] space ratio [s/D]
reattached position are the main interest in many heat transfer applications such as heat exchangers, combustion chambers, gas turbine blades, and electronic devices. Yakut et al. [1] experimentally investigated the effect of conicalring turbulators on the turbulent heat transfer, pressure drop and flow-induced vibrations. Their experiments were analyzed and presented in terms of the thermal performances of the heat-transfer promoters with respect to their heat-transfer enhancement efficiencies for a constant pumping power. Yakut and Sahin [2] again reported the flow-induced vibration characteristics of conical-ring turbulators used for heat transfer enhancement in heat exchangers. They found that the Nusselt number increases with the rise of Reynolds number and the maximum heat transfer is obtained for the smallest pitch arrangement. Durmus [3] also studied the effect of cutting out conical turbulators, placed in a heat exchange tube, on the heat transfer rate with four different types of turbulators and different conical-angles and reported that the heat transfer improvement depends on the type and the angle of the turbulators. Ayhan et al. [4] numerically and experimentally examined the heat transfer augmentation in a tube by means of truncated hollow cone inserts. Eiamsa-ard and Promvonge [5] reported an effect of the V-nozzle turbulators on heat transfer rate in a circular tube and suggested that the nozzles has a significant effect on heat transfer enhancement. This indicates the crucial effect of the reverse/re-circulation flow can promote the heat transfer rate in tubes. Promvonge and Eiamsa-ard [6] again investigated the effect of conical-nozzle and snail entrance on heat transfer and friction characteristics in a uniform heat flux tube and found that the heat
U V V_
average axial velocity of test tube [m/s] voltage [volt] volume flow rate [m3/s]
Greek symbols g enhancement efficiency q density [kg/m3] l dynamic viscosity [Ns/m2] Subscripts a air b bulk conv convection in inlet o outer out outlet p plain tube pp pumping work t turbulator w wall
transfer rate increases considerably for using both enhancement devices. In general, the swirl flow generator is used in augmentative heat transfer in several engineering applications to enhance the rate of the heat and mass transfer equipment such as heat exchanger, vortex combustor, drying process, etc. The methods of generating swirl can be classified into three main categories. The first is the tangential flow injection to induce a swirling fluid motion along the tube [7– 10]. The second is the guide vanes swirl generators [11,12] classified into two types: the radial guide vane and the axial guide vane. The last one is the direct rotation of the tube. The above literature review indicates that both enhancement devices, the conical-nozzle turbulator and the snail swirl generator, are among the most effective and practical methods for augmenting heat transfer in tubes. The purpose of this study is to investigate the heat transfer and flow friction characteristics in a circular tube equipped with both the V-nozzle turbulator and the snail swirl generator. In the present study, the snail/swirl generator (tangential flow injection) [6,13] is fitted at the entrance of the tube and is expected to increase the tangential flow velocity, prolong the residence time of the flow in the tube and thin the boundary layer. The V-nozzles are placed inside the test tube at three pitch ratios (PR), defined as a ratio of pitch length to tube diameter; PR = 2.0, 4.0, and 7.0. The present experimental results are also compared with the results from using the V-nozzle turbulator or the snail swirl generator alone in another work [5,6]. All of the experiments are carried out at the same inlet conditions with the Reynolds
334
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number, based on the test tube diameter, in a range of 8000–18,000. 2. Experimental description 2.1. Experimental setup The experiments were conducted to examine the effect of using snail entry and V-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 7.5 kW blower, orifice meter to measure the flow rate, the 2200 mm calming section tube and the heat transfer test section. The copper test tube has a length of L = 1250 mm, with 47.5 mm inner diameter (D), 50.5 mm outer diameter (Do), and 1.5 mm tube thickness (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 A. The outer surface of the test tube was well insulated to minimize convective heat loss to 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 as can be seen in Fig. 2. In the experiment, two thermocouples were placed at 1860 mm (40D) upstream of the test section for measuring inlet air temperature while at 93 mm downstream of the test section for measuring outlet air temperature. Fifteen thermocouples were lined up along the test
tube wall surfaces (embedded in v-groove tube surfaces) and the thermocouples were placed round the tube to measure the circumferential temperature variation, which was found to be negligible. The mean wall temperature was determined by means of calculations based on the reading of the type-K thermocouples. Fig. 2 represented the V-nozzle arrangement used in the present work. The V-nozzle made of aluminum is 95 mm (2.0D) long and its end and throat diameters were 46 mm and 26 mm, respectively. The V-nozzles were placed with three different free-space lengths, s of arrangements, having s = 47.5 mm (PR = 2.0), s = 142.5 mm (PR = 4.0), and s = 205 mm (PR = 7.0), for each experiment. The test tube was fitted tightly with the V-nozzle turbulator by compression to prevent its movement and to reduce thermal contact resistance between the turbulator and the tube surface. For all cases of test runs, a snail type swirl generator was mounted at the entrance of the test tube to create swirling flow as seen in Fig. 2. In this experiment, the combination of the two phenomena: (1) the re-circulating flow induced by the Vnozzles and (2) the swirling flow created by the snail, are supposed to be effective in the vicinity of the tube wall, where thermal resistance is high. Furthermore, the combined techniques are expected to provide better chaotic mixing and rotating of the fluid in this region as well as causing increased viscous dissipation, thereby enhancing the heat transfer rate. 2.2. Experimental procedure In the apparatus setting above, the inlet bulk air at 25 °C from a 7.5 kW blower was directed through the orifice meter and passed to the heat transfer test section. The air
Fig. 1. Schematic diagram of experimental heat transfer setup.
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335
Fig. 2. Test tube fitted with V-nozzle turbulators and snail entry.
flow rate was measured by an orifice meter, built according to ASME standard [14]. Manometric fluid was used in Utube 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 drops across the heat transfer test tube and across the snail were measured with inclined U-tube manometers. The volumetric air flow rates from the blower were adjusted by varying motor speed through an inverter, situated before the inlet of test tube. 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 surface of the heat transfer test pipe for finding out the average Nusselt number. For each test run, it was necessary to record the data of temperature, volumetric flow rate and pressure drop of the bulk air at steady state conditions in which the inlet air temperature was maintained at 25 °C. 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 the heated tube with combined V-nozzles and snail entrance. The average Nusselt number and friction factor were calculated and discussed where all fluid properties were determined at the overall bulk mean temperature. In order to quantify the uncertainties of measurements, the reduced data obtained experimentally were determined. The uncertainty in the data calculation was based on Ref. [15]. 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 by a hot wire anemometer 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 In the present work, the air is used as a working 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
ð1Þ
where _ p;a ðT out T in Þ Qa ¼ mC
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 for internal convective heat transfer coefficient calculation. The convection heat transfer from the test section can be written by: Qconv ¼ hAð Te w T b Þ
ð3Þ
where T b ¼ ðT out þ T in Þ=2 and Te w ¼
X
T w =15
ð4Þ
ð5Þ
in which Tw is the local wall temperature and evaluated at the outer wall surface of the inner tube (thermocouples embedded in v-groove outer surfaces). In case of a copper tube, the thermal resistance of the tube wall can be neglected and therefore the measured Tw can be approximated to be the same as the inner wall surface temperature.
P. Promvonge, S. Eiamsa-ard / Experimental Thermal and Fluid Science 32 (2007) 332–340
The average wall temperatures are calculated from 15 points, lined between the inlet and the exit of the test pipe. The heating surface area, A based on the inner tube diameter (D) was used in all calculations for tube with/without turbulators. The average heat transfer coefficient, h and the average Nusselt number, Nu are estimated as follows: _ p;a ðT out T in Þ=Að Te w T b Þ h ¼ mC
ð6Þ
Nu ¼ hD=k
ð7Þ
The Reynolds number is given by Re ¼ UD=m
200
160
Plain tube
140 120 100
ð8Þ
DP ðL=DÞðqU 2 =2Þ
80 60
Friction factor, f can be written as: f ¼
V-nozzle and Snail, PR=2.0 V-nozzle and Snail, PR=4.0 V-nozzle and Snail, PR=7.0 Dittus-Boelter equation
180
Nusselt number
336
40 20
ð9Þ
0
in which U is mean velocity of the tube. All of thermal properties of the tested fluid are determined at the overall bulk air temperature, (Tout + Tin)/2.
8000
10000
12000
14000
16000
18000
Reynolds number Fig. 3. Effect of pitch ratio on Nusselt number for V-nozzle inserts and snail entry.
4. Experimental results and discussion 10
4.1. Verification of plain tube
Nu ¼ 0:023Re
4=5
Pr
0:4
for Re > 10; 000
ð10Þ
for Re 6 20; 000
f ¼ 0:423Re
0:275
6 5 4 3 2 1 0
8000
10000
12000
14000
16000
18000
Reynolds number
ð11Þ
In the figures, results of the present work reasonably agree well with the mentioned correlations with error limits of ±12% for friction factor and of ±7% for Nusselt number. The present Nusselt number and friction factor for the plain tube are correlated as follows: Nu ¼ 0:0135Re0:85 Pr0:4
Plain tube
7
Fig. 4. Effect of pitch ratio on friction factor for V-nozzle inserts and snail entry.
Friction factor correlation of Blasius [16]: f ¼ 0:316Re0:25
8
Friction factor
The present experimental results on Nusselt number and friction factor values in the plain tube without the V-nozzle inserts and snail entrance are first reported. The plain tube data are obtained to provide a reference against which the reverse/swirl data can be compared and to ensure that the plain tube data obtained from this system agree with predictions obtained from correlations in the open literature [16]. Verifications for this plain tube can be also found in another work [5]. The Nusselt number and the friction factor for the plain tube in the present work are compared with the previous correlations of Dittus-Boelter and of Blasius for the fully developed turbulent flow in circular tubes, as can be seen in Figs. 3 and 4, respectively. Nusselt number correlation of Dittus-Boelter [16]:
V-nozzle and Snail, PR=2.0 V-nozzle and Snail, PR=4.0 V-nozzle and Snail, PR=7.0 Blasius equation
9
ð12Þ ð13Þ
4.2. Effect of pitch ratio The present results on heat and fluid flow characteristics in a uniform heat flux tube with V-nozzle inserts together
with a snail entry of various pitch ratios (PR) are presented in the form of Nusselt number, Nu and friction factor, f. The results obtained under turbulent flow conditions for three pitch ratios are also presented in Figs. 3 and 4. Fig. 3 illustrates the variation of the average Nusselt number with Reynolds number for three pitch ratios (PR = 2.0, 4.0, and 7.0) using the V-nozzle turbulators along with the snail entry. In the figure, the heat transfer rate tends to increase considerably with the rise of Reynolds number for employing both enhancement devices. A close examination reveals that the heat transfer rate at the smaller pitch ratio is higher than that at the greater one over the Reynolds number range studied. This can be
P. Promvonge, S. Eiamsa-ard / Experimental Thermal and Fluid Science 32 (2007) 332–340
0:22
ð14Þ
The effect of using the V-nozzle turbulator in common with the snail entrance on the total pressure drop that includes the pressure drop across the test pipe and across the snail is presented in Fig. 4. The variation of the total pressure drop is shown in terms of friction factor with Reynolds number for various pitch ratios. 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 ones. The average increases in pressure losses of using the V-nozzles with the snail entry for PR = 2.0, 4.0, and 7.0 are around 61, 40, 22 times the plain tube, respectively. The losses mainly come from: (1) higher friction of increasing surface area and the blockage because of the presence of the nozzles and (2) the dissipation of the dynamical pressure of the air due to high viscous losses near the pipe wall, and to the extra forces exerted by rotation. Moreover, the increase in pressure drop is probably due to the secondary flows occurring as a result of the interaction of pressure forces with inertial forces in the boundary layer. The correlation for the friction factor can be written as follows: f ¼ 59Re0:29 ðPRÞ0:48
ð15Þ
The present results are compared with earlier published measurements for using the V-nozzle turbulators alone deduced from [5], conical-ring turbulator obtained from [1], and using the snail entry alone taken from [6]. Comparisons of the heat transfer and friction loss in: (1) tube with V-nozzle turbulator alone; (2) tube with conical-ring turbulator; (3) tube with snail entry and (4) tube with combined V-nozzle turbulator and snail entry are depicted in Figs. 5 and 6, respectively. It is visible in Fig. 5 that the tube with a combination of V-nozzles and snail entrance provides higher heat transfer rate than the tube fitted with either the V-nozzle or the snail alone. This can be attributed to 260 Conical-ring, PR=2.0 [1]
240
V-nozzle and Snail, PR=2.0 V-nozzle and Snail, PR=4.0 V-nozzle and Snail, PR=7.0 V-nozzle, PR=2.0 [5] V-nozzle, PR=4.0 [5] V-nozzle, PR=7.0 [5] Plain tube Snail [6]
220 200 180
Nusselt number
Nu ¼ 0:37Re0:635 Pr0:4 ðPRÞ
4.3. Influence of snail entry
160 140 120 100 80 60 40 20 0
8000
10000
12000
14000
16000
18000
Reynolds number Fig. 5. Variation of Nusselt number with Reynolds number for various enhancement devices.
12 Conical-ring, PR=2.0 [1]
11
V-nozzle and Snail, PR=2.0 V-nozzle and Snail, PR=4.0 V-nozzle and Snail, PR=7.0 V-nozzle, PR=2.0 [5] V-nozzle, PR=4.0 [5] V-nozzle, PR=7.0 [5] Plain tube Snail [6]
10 9
Friction factor
explained that the turbulence intensity and the flow path obtained from utilizing the smaller pitch ratio are greater and longer than that at the larger one and the appearance of reverse flow between two adjacent V-nozzle elements, leading to higher temperature gradients. In addition, due to the swirl/reverse flow and lower flow cross-sectional area, the better chaotic 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. It is worth noting that the tube fitted with the turbulators and the swirl generator can promote more heat transfer rate than the plain tube around 294%, 258% and 244% for PR = 2.0, 4.0 and 7.0, respectively. For the lowest pitch ratio (PR = 2.0), the increase in heat transfer rate is in the range of 229–294% over the plain tube for the Reynolds number ranging from 8000 to 18,000. Also, similar trends are found for other pitch ratios and the improvement for using PR = 2.0 is seen to be about 12–15% and 17–23% higher than for using PR = 4.0 and PR = 7.0, respectively. The result of the Nusselt number for utilizing V-nozzle turbulators and the snail entry is correlated as follows:
337
8 7 6 5 4 3 2 1 0
8000
10000
12000
14000
16000
18000
Reynolds number Fig. 6. Variation of friction factor with Reynolds number for various enhancement devices.
P. Promvonge, S. Eiamsa-ard / Experimental Thermal and Fluid Science 32 (2007) 332–340
better and fast mixing of the two flow phenomena: (1) the reverse flow from the V-nozzle and (2) swirling flow from the snail. The presence of V-nozzles in the test tube can be presumed to be a ribbed or grooved tube that can induce reverse flows inside [17]. Further, a close inspection reveals that the heat transfer augmentation from the V-nozzle alone with PR = 4.0 is slightly higher than that from the snail entrance. The heat transfer rate obtained from the V-nozzle together with the snail entry is around 2–10% and 5–12% over that from the V-nozzle alone and from the snail entry, respectively, depending on the Reynolds number interval. Variation of friction factor with Reynolds number for using various enhancement devices with PR = 2.0, 4.0, and 7.0 is displayed in Fig. 6. In the figure, the friction factor tends to reduce with the increase in Reynolds number and PR values for all device arrangements. The friction factor value for both the V-nozzle and the snail entry is around 80–110% higher than that for the V-nozzle alone, depending on PR used or about 250–300% over the snail. This indicates that the presence of the snail and the V-nozzle leads to a substantial increase in friction losses in the tube. It is worth noting that the friction factor value for the V-nozzle alone with PR = 4.0 and 7.0 is lower than that for the snail. The reduction of friction factor for the V-nozzle and snail entry with PR = 4.0 and 7.0 can be attributed to the decrease in surface area from using less V-nozzle number, leading to lower friction loss in the tube. In addition, it can be observed that the conical-ring with PR = 2.0 deduced from [1] provides higher heat transfer rate and friction factor than the V-nozzle alone or together with the snail entry. This is not surprising because the V-nozzle is basically come from the same root as the conical-ring. The V-nozzle is a compromise between the converging and diverging conical-rings in order to reduce high friction loss of the ring. It should be noted that the V-nozzle was built in a similar form of using two conicalnozzles mounted each other and thus, the V-nozzle is longer twice of the conical-ring. As can be seen in Figs. 5 and 6, the heat transfer rates obtained from using the conical-ring with PR = 2.0 (S = 1.0) are found to be higher than that from the present work around 22% for Nusselt number and 58% for friction factor. This indicates the merit of the V-nozzle in friction loss reduction, compared with the conical-ring. 4.4. Enhancement evaluation 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 constant pumping power, ðV_ DP Þp ¼ ðV_ DP Þt
ð16Þ
and the relationship between friction and Reynolds number can be expressed as:
ðfRe3 Þp ¼ ðfRe3 Þt
ð17Þ
The enhancement efficiency, g at constant pumping power is the ratio of the convective heat transfer coefficient of the tube with turbulators and the snail to the plain tube which can be written as follows: ht g ¼ ð18Þ h p pp
Using Eqs. (13), (15) and (17), the Reynolds number for the plain tube (Rep) can be written as a function of the Reynolds number for the V-nozzle turbulator and snail (Ret): Rep ¼ 5:63Re1:014 ðPRÞ t
0:26
ð19Þ
Employing Eqs. (12), (14), (18) and (19), the enhancement efficiency for the V-nozzle turbulator and the snail can be written as: ht 0:0012 g ¼ ¼ 6:31Re0:227 ðPRÞ ð20Þ t h p pp
The enhancement efficiencies of enhancement devices for PR = 2.0, 4.0, and 7.0, including those taken from [1,5,6] along with Reynolds number values are depicted in Fig. 7. In the figure, it is interesting to note that the enhancement efficiency shows a trend to reduce with the rise of Reynolds number for all pitch ratios. The enhancement efficiencies of the V-nozzle alone are found to be the highest and the conical-ring provides higher enhancement efficiency than the combined V-nozzle and snail entry. The enhancement efficiencies of the V-nozzle and snail entry for all pitch ratios having nearly the same values, are peak at the lowest Reynolds number and lower than those of the V-nozzle alone and the conical-ring. The efficiency of the V-nozzle and snail entry is also less than that of the snail except for Reynolds number less than 6000.
1.4 1.2
Enhancement efficiency
338
1 0.8 0.6 0.4 0.2 0 4000
Conical-ring, PR=2.0 [1] V-nozzle and Snail, PR=2.0 V-nozzie and Snail, PR=4.0 V-nozzle and Snail, PR=7.0 V-nozzle, PR=2.0 [5] V-nozzle, PR=4.0 [5] V-nozzle, PR=7.0 [5] Snail [6]
8000
12000
16000
20000
Reynolds number Fig. 7. Variation of enhancement efficiency with Reynolds number for various enhancement devices.
P. Promvonge, S. Eiamsa-ard / Experimental Thermal and Fluid Science 32 (2007) 332–340
339
lated by the present correlations are portrayed in Figs. 8 and 9. In the figures, the majority of the measured data falls within ±10% and ±15% for the present correlations of the Nusselt number and the friction factor, respectively.
150
120 +10%
Predicted Nu
5. Conclusions -10%
90
60
30 Nu=0.37Re0.635 Pr0.4(PR)-0.22 0
0
30
60
90
120
150
Experimental Nu Fig. 8. Nusselt numbers obtained from the present correlation and experimental data.
Enhancement efficiencies for Reynolds number ranging from 5000 to 18,000 vary between 0.71 and 0.91; 0.70 and 0.90; and 0.69 and 0.89 at PR = 2.0, 4.0, and 7.0, respectively. This means that the combined V-nozzle turbulators and snail entry are not feasible in terms of energy saving. Though, the devices of V-nozzle turbulators and the snail entry can be used effectively at very low Reynolds number or in places where pumping power is not important but compact sizes and ease of manufacture are needed. Comparison between the Nusselt number and the friction factor obtained from the present data with those calcu-
Experimental investigations have been conducted to examine the effect of V-nozzle turbulator inserts together with a snail 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 V-nozzles and snail entry results in a considerable increase in heat transfer rate and friction loss, especially at smaller pitch ratio. Depending on the flow conditions and pitch ratios, the maximum improvements of heat transfer rate over the corresponding plain tube are found to be about 294%, 258% and 244%, for PR = 2.0, 4.0, and 7.0, respectively. The enhancement efficiencies for all pitch ratios having nearly the same values, are found to be peak at the lowest Reynolds number and lower than those of the V-nozzle alone. Except for Reynolds number below 6000, the efficiency of both the V-nozzle and the snail entry is also lower than that of the snail. Enhancement efficiencies for Reynolds number ranging from 5000 to 18000 vary between 0.71 and 0.91; 0.70 and 0.90; and 0.69 and 0.89 for PR = 2.0, 4.0 and 7.0, respectively. In addition, the V-nozzle alone provides the best thermal performance over other turbulator devices. Acknowledgements The author gratefully acknowledges Prof. Kulthorn Silapabanleng for valuable discussion and the Thailand Research Fund (TRF) for the financial support of this research.
5
References 4
Predicted f
+15% 3 -15%
2
1 f=46.9Re-0.237 Pr-0.79 0
0
1
2 3 Experimental f
4
5
Fig. 9. Friction factors obtained from the present correlation and experimental data.
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P. Promvonge, S. Eiamsa-ard / Experimental Thermal and Fluid Science 32 (2007) 332–340 injection, Final Report, June 1987–December 1989, GRI-90/0134, 1990. V.K. Dhir, F. Chang, Heat transfer enhancement using tangential injection, ASHRAE Transactions 98 (1992) BA-92-4-1. G. Son, V.K. Dhir, Enhancement of heat transfer in an annulus using tangential flow injection, Trans ASME Journal Heat Transfer 246 (1993) 59–66. 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 1988, GRI Report No. GRI-89/020, 1989. ¨. C M. Yılmaz, O ¸ omaklı, S. Yapıcı, Enhancement of heat transfer by turbulent decaying swirl flow, Energy Conversion Management 40 (1999) 1365–1376. ¨. C M. Yılmaz, O ¸ omaklı, S. Yapıcı, O.N. Sara, Heat transfer and friction characteristics in decaying swirl flow generated by different
[13]
[14]
[15] [16] [17]
radial guide vane swirl generators, Energy Conversion and Management 44 (2003) 283–300. 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. ASME Standard, Measurement of fluid flow in pipes using orifice, nozzle and venturi, ASME MFC-3M-1984, United Engineering Center 345 East 47th Street, New York, 1984. ANSI/ASME, Measurement Uncertainty, PTC 19, 1-1985, Part I, 1986. F. Incropera, P.D. Dewitt, Introduction to Heat Transfer, third ed., Wiley, 1996. T. Adachi, S. Hasegawa, Transition of the flow in a symmetric channel with periodically expanded grooves, Chemical Engineering Science 61 (2006) 2721–2729.
Heat transfer augmentation in a circular tube using V-nozzle turbulator inserts and snail entry Pongjet Promvonge a
a,*
, Smith Eiamsa-ard
b,1
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 Received 16 July 2006; received in revised form 24 February 2007; accepted 22 April 2007
Abstract Influences of V-nozzle turbulator inserts in conjunction with a snail entry on heat transfer and friction loss characteristics in a circular tube are experimentally investigated in this paper. In the present work, a set of converging-diverging nozzles like a venturi structure (referred to as V-nozzle) used as a turbulator/reverse-flow generator is placed inside the test tube through which air as the test fluid is passed. Also, the snail is mounted at the tube entrance to create a decaying swirl flow. The effects of the snail entry and insertion of V-nozzles with three different pitch ratios, PR = 2.0, 4.0, and 7.0 on heat transfer rate in the tube are examined for the Reynolds number ranging from 8000 to 18,000. The experimental results are displayed in terms of Nusselt number (Nu) and friction factor (f) as a function of Reynolds number (Re). The values of Nusselt number and friction factor for utilizing both the V-nozzle and the snail entry are found to be considerably higher than that for using the V-nozzle alone or the plain tube. The use of PR = 2.0 leads to higher Nusselt number and friction factor values than that of PR = 4.0 or 7.0. To assess the real benefits in using the turbulator and the swirl generator of the enhanced tube, empirical correlations in terms of Re and PR for Nusselt number, friction factor and performance evaluation criteria are also determined. Ó 2007 Elsevier Inc. All rights reserved. Keywords: Heat transfer enhancement; Swirl flow; Reverse flow; Turbulator; V-nozzle; Snail; Pitch ratio (PR=1 + S)
1. Introduction The need for high-performance thermal systems in many engineering applications has stimulated considerable interest in finding various methods to improve heat transfer in the system. The conventional heat exchangers are generally 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) interruption of boundary layer development *
Corresponding author. Tel.: +662 3264197; fax: +662 3264198. E-mail addresses: [email protected] (P. Promvonge), smith@ mut.ac.th (S. Eiamsa-ard). 1 Tel./fax: +662 9883666x241. 0894-1777/$ - see front matter Ó 2007 Elsevier Inc. All rights reserved. doi:10.1016/j.expthermflusci.2007.04.010
and increasing turbulence intensity; (2) increase in heat transfer area; and (3) generating of swirling and/or secondary flows. To date, many studies have been emphasized on passive heat-transfer enhancement methods and the fluid flow. Reverse/swirl flow devices form an important group of the passive augmentation techniques. The reverse flow, sometimes called ‘‘recirculation flow’’, device or the turbulator is widely employed in heat transfer engineering applications. This is because the convection heat transfer along the tube wall can be improved significantly by introducing the reverse/re-circulation flow to increase the effective axial Reynolds number and decrease the cross-sectional area of flow, leading to an increase in the mean velocity and temperature gradient. The reverse flow cannot only induce the higher heat fluxes and momentum transfer due to the large effective driving potential force but also the higher pressure drop. The strength of reverse flow and the
P. Promvonge, S. Eiamsa-ard / Experimental Thermal and Fluid Science 32 (2007) 332–340
333
Nomenclature A Cp D f h I k L m_ Nu DP PR Pr Q Re t T Te s S
heat transfer surface area of test tube [m2] specific heat [J/kg K] inner diameter of test tube [m] friction factor heat transfer coefficient [W/m2K] current [A] thermal conductivity of air [W/m K] length of the test section [m] mass flow rate [kg/s] Nusselt number pressure drop [Pa] pitch ratio [1 + S] Prandtl number heat transfer rate [W] Reynolds number thickness of test tube [m] temperature [°C] average temperature [°C] space length [m] space ratio [s/D]
reattached position are the main interest in many heat transfer applications such as heat exchangers, combustion chambers, gas turbine blades, and electronic devices. Yakut et al. [1] experimentally investigated the effect of conicalring turbulators on the turbulent heat transfer, pressure drop and flow-induced vibrations. Their experiments were analyzed and presented in terms of the thermal performances of the heat-transfer promoters with respect to their heat-transfer enhancement efficiencies for a constant pumping power. Yakut and Sahin [2] again reported the flow-induced vibration characteristics of conical-ring turbulators used for heat transfer enhancement in heat exchangers. They found that the Nusselt number increases with the rise of Reynolds number and the maximum heat transfer is obtained for the smallest pitch arrangement. Durmus [3] also studied the effect of cutting out conical turbulators, placed in a heat exchange tube, on the heat transfer rate with four different types of turbulators and different conical-angles and reported that the heat transfer improvement depends on the type and the angle of the turbulators. Ayhan et al. [4] numerically and experimentally examined the heat transfer augmentation in a tube by means of truncated hollow cone inserts. Eiamsa-ard and Promvonge [5] reported an effect of the V-nozzle turbulators on heat transfer rate in a circular tube and suggested that the nozzles has a significant effect on heat transfer enhancement. This indicates the crucial effect of the reverse/re-circulation flow can promote the heat transfer rate in tubes. Promvonge and Eiamsa-ard [6] again investigated the effect of conical-nozzle and snail entrance on heat transfer and friction characteristics in a uniform heat flux tube and found that the heat
U V V_
average axial velocity of test tube [m/s] voltage [volt] volume flow rate [m3/s]
Greek symbols g enhancement efficiency q density [kg/m3] l dynamic viscosity [Ns/m2] Subscripts a air b bulk conv convection in inlet o outer out outlet p plain tube pp pumping work t turbulator w wall
transfer rate increases considerably for using both enhancement devices. In general, the swirl flow generator is used in augmentative heat transfer in several engineering applications to enhance the rate of the heat and mass transfer equipment such as heat exchanger, vortex combustor, drying process, etc. The methods of generating swirl can be classified into three main categories. The first is the tangential flow injection to induce a swirling fluid motion along the tube [7– 10]. The second is the guide vanes swirl generators [11,12] classified into two types: the radial guide vane and the axial guide vane. The last one is the direct rotation of the tube. The above literature review indicates that both enhancement devices, the conical-nozzle turbulator and the snail swirl generator, are among the most effective and practical methods for augmenting heat transfer in tubes. The purpose of this study is to investigate the heat transfer and flow friction characteristics in a circular tube equipped with both the V-nozzle turbulator and the snail swirl generator. In the present study, the snail/swirl generator (tangential flow injection) [6,13] is fitted at the entrance of the tube and is expected to increase the tangential flow velocity, prolong the residence time of the flow in the tube and thin the boundary layer. The V-nozzles are placed inside the test tube at three pitch ratios (PR), defined as a ratio of pitch length to tube diameter; PR = 2.0, 4.0, and 7.0. The present experimental results are also compared with the results from using the V-nozzle turbulator or the snail swirl generator alone in another work [5,6]. All of the experiments are carried out at the same inlet conditions with the Reynolds
334
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number, based on the test tube diameter, in a range of 8000–18,000. 2. Experimental description 2.1. Experimental setup The experiments were conducted to examine the effect of using snail entry and V-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 7.5 kW blower, orifice meter to measure the flow rate, the 2200 mm calming section tube and the heat transfer test section. The copper test tube has a length of L = 1250 mm, with 47.5 mm inner diameter (D), 50.5 mm outer diameter (Do), and 1.5 mm tube thickness (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 A. The outer surface of the test tube was well insulated to minimize convective heat loss to 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 as can be seen in Fig. 2. In the experiment, two thermocouples were placed at 1860 mm (40D) upstream of the test section for measuring inlet air temperature while at 93 mm downstream of the test section for measuring outlet air temperature. Fifteen thermocouples were lined up along the test
tube wall surfaces (embedded in v-groove tube surfaces) and the thermocouples were placed round the tube to measure the circumferential temperature variation, which was found to be negligible. The mean wall temperature was determined by means of calculations based on the reading of the type-K thermocouples. Fig. 2 represented the V-nozzle arrangement used in the present work. The V-nozzle made of aluminum is 95 mm (2.0D) long and its end and throat diameters were 46 mm and 26 mm, respectively. The V-nozzles were placed with three different free-space lengths, s of arrangements, having s = 47.5 mm (PR = 2.0), s = 142.5 mm (PR = 4.0), and s = 205 mm (PR = 7.0), for each experiment. The test tube was fitted tightly with the V-nozzle turbulator by compression to prevent its movement and to reduce thermal contact resistance between the turbulator and the tube surface. For all cases of test runs, a snail type swirl generator was mounted at the entrance of the test tube to create swirling flow as seen in Fig. 2. In this experiment, the combination of the two phenomena: (1) the re-circulating flow induced by the Vnozzles and (2) the swirling flow created by the snail, are supposed to be effective in the vicinity of the tube wall, where thermal resistance is high. Furthermore, the combined techniques are expected to provide better chaotic mixing and rotating of the fluid in this region as well as causing increased viscous dissipation, thereby enhancing the heat transfer rate. 2.2. Experimental procedure In the apparatus setting above, the inlet bulk air at 25 °C from a 7.5 kW blower was directed through the orifice meter and passed to the heat transfer test section. The air
Fig. 1. Schematic diagram of experimental heat transfer setup.
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335
Fig. 2. Test tube fitted with V-nozzle turbulators and snail entry.
flow rate was measured by an orifice meter, built according to ASME standard [14]. Manometric fluid was used in Utube 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 drops across the heat transfer test tube and across the snail were measured with inclined U-tube manometers. The volumetric air flow rates from the blower were adjusted by varying motor speed through an inverter, situated before the inlet of test tube. 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 surface of the heat transfer test pipe for finding out the average Nusselt number. For each test run, it was necessary to record the data of temperature, volumetric flow rate and pressure drop of the bulk air at steady state conditions in which the inlet air temperature was maintained at 25 °C. 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 the heated tube with combined V-nozzles and snail entrance. The average Nusselt number and friction factor were calculated and discussed where all fluid properties were determined at the overall bulk mean temperature. In order to quantify the uncertainties of measurements, the reduced data obtained experimentally were determined. The uncertainty in the data calculation was based on Ref. [15]. 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 by a hot wire anemometer 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 In the present work, the air is used as a working 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
ð1Þ
where _ p;a ðT out T in Þ Qa ¼ mC
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 for internal convective heat transfer coefficient calculation. The convection heat transfer from the test section can be written by: Qconv ¼ hAð Te w T b Þ
ð3Þ
where T b ¼ ðT out þ T in Þ=2 and Te w ¼
X
T w =15
ð4Þ
ð5Þ
in which Tw is the local wall temperature and evaluated at the outer wall surface of the inner tube (thermocouples embedded in v-groove outer surfaces). In case of a copper tube, the thermal resistance of the tube wall can be neglected and therefore the measured Tw can be approximated to be the same as the inner wall surface temperature.
P. Promvonge, S. Eiamsa-ard / Experimental Thermal and Fluid Science 32 (2007) 332–340
The average wall temperatures are calculated from 15 points, lined between the inlet and the exit of the test pipe. The heating surface area, A based on the inner tube diameter (D) was used in all calculations for tube with/without turbulators. The average heat transfer coefficient, h and the average Nusselt number, Nu are estimated as follows: _ p;a ðT out T in Þ=Að Te w T b Þ h ¼ mC
ð6Þ
Nu ¼ hD=k
ð7Þ
The Reynolds number is given by Re ¼ UD=m
200
160
Plain tube
140 120 100
ð8Þ
DP ðL=DÞðqU 2 =2Þ
80 60
Friction factor, f can be written as: f ¼
V-nozzle and Snail, PR=2.0 V-nozzle and Snail, PR=4.0 V-nozzle and Snail, PR=7.0 Dittus-Boelter equation
180
Nusselt number
336
40 20
ð9Þ
0
in which U is mean velocity of the tube. All of thermal properties of the tested fluid are determined at the overall bulk air temperature, (Tout + Tin)/2.
8000
10000
12000
14000
16000
18000
Reynolds number Fig. 3. Effect of pitch ratio on Nusselt number for V-nozzle inserts and snail entry.
4. Experimental results and discussion 10
4.1. Verification of plain tube
Nu ¼ 0:023Re
4=5
Pr
0:4
for Re > 10; 000
ð10Þ
for Re 6 20; 000
f ¼ 0:423Re
0:275
6 5 4 3 2 1 0
8000
10000
12000
14000
16000
18000
Reynolds number
ð11Þ
In the figures, results of the present work reasonably agree well with the mentioned correlations with error limits of ±12% for friction factor and of ±7% for Nusselt number. The present Nusselt number and friction factor for the plain tube are correlated as follows: Nu ¼ 0:0135Re0:85 Pr0:4
Plain tube
7
Fig. 4. Effect of pitch ratio on friction factor for V-nozzle inserts and snail entry.
Friction factor correlation of Blasius [16]: f ¼ 0:316Re0:25
8
Friction factor
The present experimental results on Nusselt number and friction factor values in the plain tube without the V-nozzle inserts and snail entrance are first reported. The plain tube data are obtained to provide a reference against which the reverse/swirl data can be compared and to ensure that the plain tube data obtained from this system agree with predictions obtained from correlations in the open literature [16]. Verifications for this plain tube can be also found in another work [5]. The Nusselt number and the friction factor for the plain tube in the present work are compared with the previous correlations of Dittus-Boelter and of Blasius for the fully developed turbulent flow in circular tubes, as can be seen in Figs. 3 and 4, respectively. Nusselt number correlation of Dittus-Boelter [16]:
V-nozzle and Snail, PR=2.0 V-nozzle and Snail, PR=4.0 V-nozzle and Snail, PR=7.0 Blasius equation
9
ð12Þ ð13Þ
4.2. Effect of pitch ratio The present results on heat and fluid flow characteristics in a uniform heat flux tube with V-nozzle inserts together
with a snail entry of various pitch ratios (PR) are presented in the form of Nusselt number, Nu and friction factor, f. The results obtained under turbulent flow conditions for three pitch ratios are also presented in Figs. 3 and 4. Fig. 3 illustrates the variation of the average Nusselt number with Reynolds number for three pitch ratios (PR = 2.0, 4.0, and 7.0) using the V-nozzle turbulators along with the snail entry. In the figure, the heat transfer rate tends to increase considerably with the rise of Reynolds number for employing both enhancement devices. A close examination reveals that the heat transfer rate at the smaller pitch ratio is higher than that at the greater one over the Reynolds number range studied. This can be
P. Promvonge, S. Eiamsa-ard / Experimental Thermal and Fluid Science 32 (2007) 332–340
0:22
ð14Þ
The effect of using the V-nozzle turbulator in common with the snail entrance on the total pressure drop that includes the pressure drop across the test pipe and across the snail is presented in Fig. 4. The variation of the total pressure drop is shown in terms of friction factor with Reynolds number for various pitch ratios. 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 ones. The average increases in pressure losses of using the V-nozzles with the snail entry for PR = 2.0, 4.0, and 7.0 are around 61, 40, 22 times the plain tube, respectively. The losses mainly come from: (1) higher friction of increasing surface area and the blockage because of the presence of the nozzles and (2) the dissipation of the dynamical pressure of the air due to high viscous losses near the pipe wall, and to the extra forces exerted by rotation. Moreover, the increase in pressure drop is probably due to the secondary flows occurring as a result of the interaction of pressure forces with inertial forces in the boundary layer. The correlation for the friction factor can be written as follows: f ¼ 59Re0:29 ðPRÞ0:48
ð15Þ
The present results are compared with earlier published measurements for using the V-nozzle turbulators alone deduced from [5], conical-ring turbulator obtained from [1], and using the snail entry alone taken from [6]. Comparisons of the heat transfer and friction loss in: (1) tube with V-nozzle turbulator alone; (2) tube with conical-ring turbulator; (3) tube with snail entry and (4) tube with combined V-nozzle turbulator and snail entry are depicted in Figs. 5 and 6, respectively. It is visible in Fig. 5 that the tube with a combination of V-nozzles and snail entrance provides higher heat transfer rate than the tube fitted with either the V-nozzle or the snail alone. This can be attributed to 260 Conical-ring, PR=2.0 [1]
240
V-nozzle and Snail, PR=2.0 V-nozzle and Snail, PR=4.0 V-nozzle and Snail, PR=7.0 V-nozzle, PR=2.0 [5] V-nozzle, PR=4.0 [5] V-nozzle, PR=7.0 [5] Plain tube Snail [6]
220 200 180
Nusselt number
Nu ¼ 0:37Re0:635 Pr0:4 ðPRÞ
4.3. Influence of snail entry
160 140 120 100 80 60 40 20 0
8000
10000
12000
14000
16000
18000
Reynolds number Fig. 5. Variation of Nusselt number with Reynolds number for various enhancement devices.
12 Conical-ring, PR=2.0 [1]
11
V-nozzle and Snail, PR=2.0 V-nozzle and Snail, PR=4.0 V-nozzle and Snail, PR=7.0 V-nozzle, PR=2.0 [5] V-nozzle, PR=4.0 [5] V-nozzle, PR=7.0 [5] Plain tube Snail [6]
10 9
Friction factor
explained that the turbulence intensity and the flow path obtained from utilizing the smaller pitch ratio are greater and longer than that at the larger one and the appearance of reverse flow between two adjacent V-nozzle elements, leading to higher temperature gradients. In addition, due to the swirl/reverse flow and lower flow cross-sectional area, the better chaotic 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. It is worth noting that the tube fitted with the turbulators and the swirl generator can promote more heat transfer rate than the plain tube around 294%, 258% and 244% for PR = 2.0, 4.0 and 7.0, respectively. For the lowest pitch ratio (PR = 2.0), the increase in heat transfer rate is in the range of 229–294% over the plain tube for the Reynolds number ranging from 8000 to 18,000. Also, similar trends are found for other pitch ratios and the improvement for using PR = 2.0 is seen to be about 12–15% and 17–23% higher than for using PR = 4.0 and PR = 7.0, respectively. The result of the Nusselt number for utilizing V-nozzle turbulators and the snail entry is correlated as follows:
337
8 7 6 5 4 3 2 1 0
8000
10000
12000
14000
16000
18000
Reynolds number Fig. 6. Variation of friction factor with Reynolds number for various enhancement devices.
P. Promvonge, S. Eiamsa-ard / Experimental Thermal and Fluid Science 32 (2007) 332–340
better and fast mixing of the two flow phenomena: (1) the reverse flow from the V-nozzle and (2) swirling flow from the snail. The presence of V-nozzles in the test tube can be presumed to be a ribbed or grooved tube that can induce reverse flows inside [17]. Further, a close inspection reveals that the heat transfer augmentation from the V-nozzle alone with PR = 4.0 is slightly higher than that from the snail entrance. The heat transfer rate obtained from the V-nozzle together with the snail entry is around 2–10% and 5–12% over that from the V-nozzle alone and from the snail entry, respectively, depending on the Reynolds number interval. Variation of friction factor with Reynolds number for using various enhancement devices with PR = 2.0, 4.0, and 7.0 is displayed in Fig. 6. In the figure, the friction factor tends to reduce with the increase in Reynolds number and PR values for all device arrangements. The friction factor value for both the V-nozzle and the snail entry is around 80–110% higher than that for the V-nozzle alone, depending on PR used or about 250–300% over the snail. This indicates that the presence of the snail and the V-nozzle leads to a substantial increase in friction losses in the tube. It is worth noting that the friction factor value for the V-nozzle alone with PR = 4.0 and 7.0 is lower than that for the snail. The reduction of friction factor for the V-nozzle and snail entry with PR = 4.0 and 7.0 can be attributed to the decrease in surface area from using less V-nozzle number, leading to lower friction loss in the tube. In addition, it can be observed that the conical-ring with PR = 2.0 deduced from [1] provides higher heat transfer rate and friction factor than the V-nozzle alone or together with the snail entry. This is not surprising because the V-nozzle is basically come from the same root as the conical-ring. The V-nozzle is a compromise between the converging and diverging conical-rings in order to reduce high friction loss of the ring. It should be noted that the V-nozzle was built in a similar form of using two conicalnozzles mounted each other and thus, the V-nozzle is longer twice of the conical-ring. As can be seen in Figs. 5 and 6, the heat transfer rates obtained from using the conical-ring with PR = 2.0 (S = 1.0) are found to be higher than that from the present work around 22% for Nusselt number and 58% for friction factor. This indicates the merit of the V-nozzle in friction loss reduction, compared with the conical-ring. 4.4. Enhancement evaluation 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 constant pumping power, ðV_ DP Þp ¼ ðV_ DP Þt
ð16Þ
and the relationship between friction and Reynolds number can be expressed as:
ðfRe3 Þp ¼ ðfRe3 Þt
ð17Þ
The enhancement efficiency, g at constant pumping power is the ratio of the convective heat transfer coefficient of the tube with turbulators and the snail to the plain tube which can be written as follows: ht g ¼ ð18Þ h p pp
Using Eqs. (13), (15) and (17), the Reynolds number for the plain tube (Rep) can be written as a function of the Reynolds number for the V-nozzle turbulator and snail (Ret): Rep ¼ 5:63Re1:014 ðPRÞ t
0:26
ð19Þ
Employing Eqs. (12), (14), (18) and (19), the enhancement efficiency for the V-nozzle turbulator and the snail can be written as: ht 0:0012 g ¼ ¼ 6:31Re0:227 ðPRÞ ð20Þ t h p pp
The enhancement efficiencies of enhancement devices for PR = 2.0, 4.0, and 7.0, including those taken from [1,5,6] along with Reynolds number values are depicted in Fig. 7. In the figure, it is interesting to note that the enhancement efficiency shows a trend to reduce with the rise of Reynolds number for all pitch ratios. The enhancement efficiencies of the V-nozzle alone are found to be the highest and the conical-ring provides higher enhancement efficiency than the combined V-nozzle and snail entry. The enhancement efficiencies of the V-nozzle and snail entry for all pitch ratios having nearly the same values, are peak at the lowest Reynolds number and lower than those of the V-nozzle alone and the conical-ring. The efficiency of the V-nozzle and snail entry is also less than that of the snail except for Reynolds number less than 6000.
1.4 1.2
Enhancement efficiency
338
1 0.8 0.6 0.4 0.2 0 4000
Conical-ring, PR=2.0 [1] V-nozzle and Snail, PR=2.0 V-nozzie and Snail, PR=4.0 V-nozzle and Snail, PR=7.0 V-nozzle, PR=2.0 [5] V-nozzle, PR=4.0 [5] V-nozzle, PR=7.0 [5] Snail [6]
8000
12000
16000
20000
Reynolds number Fig. 7. Variation of enhancement efficiency with Reynolds number for various enhancement devices.
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339
lated by the present correlations are portrayed in Figs. 8 and 9. In the figures, the majority of the measured data falls within ±10% and ±15% for the present correlations of the Nusselt number and the friction factor, respectively.
150
120 +10%
Predicted Nu
5. Conclusions -10%
90
60
30 Nu=0.37Re0.635 Pr0.4(PR)-0.22 0
0
30
60
90
120
150
Experimental Nu Fig. 8. Nusselt numbers obtained from the present correlation and experimental data.
Enhancement efficiencies for Reynolds number ranging from 5000 to 18,000 vary between 0.71 and 0.91; 0.70 and 0.90; and 0.69 and 0.89 at PR = 2.0, 4.0, and 7.0, respectively. This means that the combined V-nozzle turbulators and snail entry are not feasible in terms of energy saving. Though, the devices of V-nozzle turbulators and the snail entry can be used effectively at very low Reynolds number or in places where pumping power is not important but compact sizes and ease of manufacture are needed. Comparison between the Nusselt number and the friction factor obtained from the present data with those calcu-
Experimental investigations have been conducted to examine the effect of V-nozzle turbulator inserts together with a snail 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 V-nozzles and snail entry results in a considerable increase in heat transfer rate and friction loss, especially at smaller pitch ratio. Depending on the flow conditions and pitch ratios, the maximum improvements of heat transfer rate over the corresponding plain tube are found to be about 294%, 258% and 244%, for PR = 2.0, 4.0, and 7.0, respectively. The enhancement efficiencies for all pitch ratios having nearly the same values, are found to be peak at the lowest Reynolds number and lower than those of the V-nozzle alone. Except for Reynolds number below 6000, the efficiency of both the V-nozzle and the snail entry is also lower than that of the snail. Enhancement efficiencies for Reynolds number ranging from 5000 to 18000 vary between 0.71 and 0.91; 0.70 and 0.90; and 0.69 and 0.89 for PR = 2.0, 4.0 and 7.0, respectively. In addition, the V-nozzle alone provides the best thermal performance over other turbulator devices. Acknowledgements The author gratefully acknowledges Prof. Kulthorn Silapabanleng for valuable discussion and the Thailand Research Fund (TRF) for the financial support of this research.
5
References 4
Predicted f
+15% 3 -15%
2
1 f=46.9Re-0.237 Pr-0.79 0
0
1
2 3 Experimental f
4
5
Fig. 9. Friction factors obtained from the present correlation and experimental data.
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