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Heat transfer augmentation by swirl generators inserted into a tube with constant heat flux
International Communications in Heat and Mass Transfer 36 (2009) 865–871
Contents lists available at ScienceDirect
International Communications in Heat and Mass Transfer j o u r n a l h o m e p a g e : w w w. e l s ev i e r. c o m / l o c a t e / i c h m t
Heat transfer augmentation by swirl generators inserted into a tube with constant heat flux☆ İrfan Kurtbaş a,⁎, Fevzi Gülçimen b, Abdullah Akbulut c, Dinçer Buran d a
Hitit University, Mechanical Engineering Department, 19030 Çorum, Turkey Tunceli University, Mechanical Engineering Department, 62000 Tunceli, Turkey Dumlupinar University, Mechanical Engineering Department, 43000 Kutahya, Turkey d Dumlupinar University, Mechanical Education Department, 43500 Simav, Kutahya, Turkey b c
a r t i c l e
i n f o
Available online 6 June 2009 Keywords: Swirl generator Decaying flow Turbulator Pipe flow
a b s t r a c t A novel conical injector type swirl generator (CITSG) is devised in this study. Performances of heat transfer and pressure drop in a pipe with the CITSG are experimentally examined for the CITSGs' angle (α) of 30°, 45° and 60° in Reynolds number (Re) range of 10,000–35,000. Moreover, circular holes with different numbers (N) and cross-section areas (Ah) are drilled on the CITSG. In this way, total areas (At = N · Ah) of the holes on the CITSG are equaled each other. Besides, flow directors having three different angles (β = 30°, 60° and 90°) to radial direction are attached to every one of the holes. This study is a typical example for decaying flow. All experiments were conduced with air accordingly; Prandtl number was approximately fixed at 0.71. The local Nusselt number (Nux), heat transfer enhancement ratio (NuER) and heat transfer performance ratio (NuPR) are calculated and discussed in this paper. It is found that the NuER decreases with increase in Reynolds number, the director angle (β), the director diameter (d), and with decrease in the CITSG angle (α). Likewise, variation of NuPR and NuER is also essentially similar for the same independent parameters. © 2009 Elsevier Ltd. All rights reserved.
1. Introduction The use of turbulators in pipes or channels is one of the commonly used passive heat transfer enhancement strategies in single-phase internal flows. Accordingly, detailed investigation of the effect of twisted tape and wire coil turbulators on heat transfer augmentation has received considerable attention [1–3]. This passive heat transfer enhancement strategy has been used for various types of industrial applications such as shell-and-tube type heat exchangers, electronic cooling devices, thermal regenerators, internal cooling systems of gas turbine blades, and labyrinth seals for turbo-machines. Periodically positioned baffles in baffled channels and periodic turns in serpentine channels periodically interrupt hydrodynamic and thermal boundary layers [4]. The effect of conical-ring turbulators on the turbulent heat transfer, pressure drop and flow-induced vibrations is experimentally investigated. Their experiments are analyzed and presented in terms of the thermal performances of the heat-transfer promoters with respect to their heat-transfer
☆ Communicated by W.J. Minkowycz. ⁎ Corresponding author. E-mail addresses: [email protected] (İ. Kurtbaş), [email protected] (F. Gülçimen), aakbulut@firat.edu.tr (A. Akbulut), [email protected] (D. Buran). 0735-1933/$ – see front matter © 2009 Elsevier Ltd. All rights reserved. doi:10.1016/j.icheatmasstransfer.2009.04.011
enhancement efficiencies for a constant pumping power [5,6]. An experimental study on the heat transfer and friction loss characteristics of a surface with cylindrical fins in a rectangular cross-section channel with large diameter fins and different channel geometries is carried out by Bilen et al. [7]. Also, the pipe flow with various grooves (circular, trapezoidal and rectangular) at constant wall heat flux condition, and hollow rectangular fins surface is studied experimentally [8,9]. Co-axis free rotating propeller type turbulators are devised by Kurtbaş et al. [10,11]. The effect of the turbulators on heat transfer and exergy loss is investigated experimentally. Cakmak and Yildiz [12] performed a similar study and investigated the influence of the injectors with swirling flow generating on the heat transfer in the concentric heat exchanger. Moreover, many researchers have endeavored to construct compact and energy-efficient heat exchangers with swirl generator and finned tube [13–20]. Many numerical studies on swirl generators and fin- and tube heat exchangers are also performed and discussed [20–24]. The objective of the present work is to conduct experiments to measure local-mean Nusselt number (Nu x − Nu), heat transfer enhancement ratio (NuER) and heat transfer performance ratio (NuPR) for flow in a uniform heat flux pipe with conical injector type swirl generator (CITSG) inserts. This study also analyzes the effect of the CITSG angle, flow director angle (FDA), flow director diameter (FDD) on the heat transfer enhancement ratio (NuER) and heat transfer performance ratio (NuPR) for turbulence regime.
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Nomenclature A Ah As cp d D Dh f h hx I k L ṁ N Nu NuER NuPR P Pr q Q R2 Re T V V′
cross-sectional area of pipe, m2 cross-sectional area of hole m2 heating surface area of pipe, m2 specific heat, J/kg K the flow director diameter, m pipe inner diameter, m channel hydraulic diameter, m friction factor mean heat transfer coefficient, W/m2 K local heat transfer coefficient, W/m2 K current, Amp thermal conductivity, W/mK length, m mass flow rate of air, kg/s hole number mean Nusselt number the heat transfer enhancement ratio the heat transfer performance ratio pressure, Pa Prandtl number heat flux, W/m2 heat transfer rate, W regression coefficient Reynolds number temperature, K velocity, m/s voltage, V
Greek symbols α the CITSG angle β the flow director angle µ dynamic viscosity ρ density
Subscripts b bulk fd flow director in inlet out outlet p pipe sg swirl generator t total w wall
2. Experimental setup 2.1. Test section and apparatus Fig. 1 presents the schematic view of whole setup with each element. The experimental setup is divided into three main parts; named as (i) air supply system, (ii) test section and test specimens, and (iii) data acquisition system. The working fluid is air and it is sucked by a centrifugal fan. The propellers of the fan can turn up to 1500 rpm with the aid of an AC electric motor (1.1 kW). The speed of the fan can be adjusted and controlled by an AC inverter with accuracy of 1%. The fan is connected to a damping chamber (200 × 200 × 200 mm dimensions) which is made of 0.35 mm thickness galvanized plate. The damping chamber is stated between flow channel and fan, and can turn the flow 90-deg as shown in Fig. 1. To have more accurate measurements, a digital flow meter (measurement range: 0.6 to
40 m/s) is also setup between the flow channel and damping chamber. The test section (copper pipe) whole length is 1.2 m. The temperature of the heated surface is measured by 9 calibrated and electrically insulated 0.5 mm diameter T-type copper-constantan thermocouples. Two thermocouples are used to measure inlet and outlet flow temperature too. Also, one thermocouple is used to measure the ambient temperature. The thermocouple voltages were collected by ALMEMO 5990-0 datalogger and transmitted directly to a personal computer. Pressure drops throughout the test section were measured using a calibrated U-manometer. Fig. 2 depicts the geometrical details of the CITSG. The CITSG's are made of galvanized sheet. The CITSG has an angle (α) of 30°, 45° and 60° as seen in Fig. 2(a). The flow directors having three different angles (β = 30°, 60° and 90°) to radial direction are attached to every one of the holes (Fig. 2(b)). The FDD is changed as 4, 7 and 10 mm. Dimensions of the test section and the CITSG are given in Table 1. A silicone rubber heater is fixed to the outer surface of the copper pipe to provide the uniform heat flux. Electric current was supplied to the heater (test section) by an AC variable electric power supply (DELORENZO, with accuracy of ±1–1.5% for voltage (V′) and current (I)). To minimize the heat losses from the test section to the environment, the test section is wrapped with glass wool insulating material of 100 mm thickness. Reynolds number (Re) is varied from 10,000 to 35,000 (6 different values of air flow mass rates are tested). The up limit is considered as 35,000, due to the excessive pumping power requirement for the aluminum foam case experiments. The kinematic viscosity, specific heat and density of the fluid are also changed because of the temperature differences in the experiments. Therefore, Reynolds numbers are slightly changed in the same air flow mass rate. These little deviations in Reynolds number are not considered in the figures. As for Prandtl number, it is varied from 0.7 to 0.72. 2.2. Data reduction The average frontal velocity (V) was calculated by dividing the measured volumetric flow rate by the inlet cross-section area. The Reynolds number is based on the hydraulic diameter (Dh). The sensible heat transfer rate of air is calculated from the inlet and outlet temperatures across the test section, namely; Q = ṁ CpðTout − Tin Þ:
ð1Þ
Determination of the sensible heat transfer coefficient (h) is as follows: Q = hAs ðTw − Tb Þ
ð2Þ
where Q is net convective heat flux, Tw is average wall temperature of the plate surface adjacent to the fluid, Tb is average fluid bulk temperature in the pipe, and As is heating surface area. The physical properties (k, μ, ρ, cp) appearing in the dimensionless numbers (Nu, Re, Pr) are all evaluated at the bulk fluid temperature (Tb). Nusselt number is equal to the dimensionless temperature gradient at surface, and it provides to denote the convection heat transfer occurred at surfaces. Hence, local Nusselt number can be written as: Nux =
hx Dh k
ð3Þ
where hx is local sensible heat transfer coefficient, k is thermal conductivity of the air. The local heat transfer coefficient can then be calculated from
hx =
Q Q − Q loss = t : As Tw;x − Tb As Tw;x − Tb
ð4Þ
İ. Kurtbaş et al. / International Communications in Heat and Mass Transfer 36 (2009) 865–871
Fig. 1. Schematic diagram of experimental setup.
Fig. 2. The test section (a) detailed figure of the CITSG, (b) flow pipe with the CITSG.
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and Reynolds number is estimated to be 4.2% and 3.8%, respectively. Likewise, the uncertainty for friction factor is 5.8%.
Table 1 Dimensions of the independent parameters (mm). Lp
Lsg
1200
60 78.4 116
Lfd
d
6
4 7 10
D
α (deg)
β (deg)
60
30 45 60
30 60 90
3. Results and discussion
The mean heat transfer coefficient and Nusselt number can be written as follows: h=
1 Lp
Z
Lp 0
0:8
hx dx
hDh : Nu = k
ð5Þ
ρVDh : μ
2ρΔP Dh V 2 LP
Pr
0:76
0:4
Pr
0:4
ð9Þ
2
R = 0:99
ð10Þ
ð6Þ
ð7Þ
The friction coefficient ( f ) in a channel flow can be determined by measuring the pressure drop across the flow channel and average velocity of the air. Average friction coefficient can, therefore, be calculated from f =
Nu = 0:023Re
Nu∞ = 0:035Re
The subscripts x show the measurement point of temperatures on heated surfaces (x = 1–9). The total heat flux (Q t =V′ ·I/As) generated by silicone rubber heater. The heat losses from the insulation of the heated plates and the conduction are calculated to be 2.4% of the total heat flux. The most important parametric value, Reynolds number, depends strongly on hydraulic diameter and written as Re =
The convection heat transfer in an empty pipe without the CITSG was measured before measuring on the convection heat transfer in the pipe with the CITSG. The heat transfer coefficient inside the pipe can be calculated with the Dittus–Boelter as given below.
ð8Þ
where ΔP is pressure drop in the channel.
Eq. (9) is considered to be the most accurate in the range 0.6 ≤ Pr ≤ 160 and Re ≥ 10,000. As indicated in Fig. 3, the experimental results for empty pipe are found to agree within 6.8%. The mean Nusselt number for fully developed flow in an empty pipe is compared with results obtained from correlation of Dittus–Boelter [27]. Fig. 4 displays the local Nusselt number (Nux) as a function of the x/Lp for maximum and minimum Re values, α = 30°, DR = 0.166 and various β. As seen from the figure, Nux is relatively less at the beginning of the test section (x/Lp ≅ 0). Then, it increases rapidly up to x/Lp ≅ 0.4. The Nux is maximal at x/Lp ≅ 0.4 and slowly decreases in the direction of the flow for both Re ≅ 9700 and Re ≅ 33,700. It is seen that when Re increases, the effect of the FDA (β) on the Nux decreases. In other words, when the lower Re is, the effect of β on the Nux becomes more apparent. At the end of the pipe, the effect of β on the Nux is insignificant for all Reynolds numbers. Furthermore, when Re increases, the effect of the β on the Nux becomes weaker. Fig. 5 shows the variation of the Nux versus x/Lp with respect to various DR and Re values for α = 30° and β = 90°. Herein, the DR is defined as the ratio of the flow director diameter (FDD) to inner diameter of the pipe (D = Dh), namely DR = ðd = DÞ = ðd = Dh Þ:
ð11Þ
2.3. Uncertainty analysis Uncertainties in Reynolds number and other independent parameters are calculated according to the standard procedures established by Kline and McClintock [26]. The experimental uncertainty in convective heat flux (Q) was estimated to be 2.1%. The analysis shows that the maximum uncertainty associated with the Nusselt number
The FDD yields considerable heat transfer enhancements with a similar trend approximately in comparison with each other and the Nux increases with increase in Re and DR. In the meantime, the maximum value of Nux obtained from using Re ≅ 34,000 and Re ≅ 9800 for DR = 0.166 are found to be 307 and 226, respectively. In addition, the Nux decreases with decrease in DR. The effect of the CITSG angle
Fig. 3. Comparison of theoretical Nusselt number with Re for empty pipe.
Fig. 4. Comparison of Nux with varieties of x/Lp for α = 30° and DR = 0.166.
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Fig. 5. Comparison of Nux with varieties of x/Lp for α = 30° and β = 90°.
Fig. 7. Comparison of Nu with Re having DR and β as parameter for α = 30°.
(α) on the Nux for β = 90° and DR = 0.166 is given in Fig. 6. It is shown that Nux increases with decrease in α value. When Fig. 6 is examined together with Figs. 4 and 5, it is observed that Fig. 6 is different from the others. In other words, the effect of β and DR on the Nux is insignificant at the beginning of the pipe (x/Lp ≅ 0.01) as seen in Figs. 4 and 5. However, at both the beginning and the end of the pipe, the Nux changes depending on the α (Fig. 6). These differences can be attributed to the decrease of the swirl intensity throughout the pipe. In addition, the heat transfer results show the possibility of a dead zone called as “plug flow” in this short distance between the beginning of the pipe and the flow directors. The Nux does not change with β and DR in the dead zone, but changes with α and Re. In addition, the results indicate that the β and DR initially increase the swirl intensity up to x/Lp ≅ 0.4. However, after x/Lp ≅ 0.4, the effect of β and DR on swirl intensity decreases, especially x/Lp N 0.75. On the other hand, effect of α on swirl intensity goes on throughout the pipe. It is seen from Fig. 7 that the effect of the CITSG on heat transfer is significant for all Reynolds numbers used due to the induction of high reverse flow. In all cases of the CITSG inserts, the swirl flow gives higher
values of the Nu than that for fully developed flow. The CITSG turbulators yield considerable heat transfer enhancements with a similar trend approximately in comparison with the smooth tube and the Nusselt number increases with the rise of Reynolds number. The use of the CITSG shows a higher heat transfer rate than that of the empty pipe at around 61–80% depending on the Re, the FDA (β) and the DR values for α = 30°. Also, it is evident that the effect of both the DR and β on the Nu is more dominant in the lower Reynolds number range. When Re and α are constant, Nu increases with increase in DR, but Nu increases with decrease in β. Along with the increasing of Re, the effect of DR and β on Nu decreases. Fig. 7 clearly reveals that the effect of α on Nu is significant, which finding is consistent with the results herein. The figure indicates that the effect of DR on Nu becomes serious, especially at low Reynolds number. In the meantime, the increasing trend of Nu is falling depending on Reynolds number when α value is increased. Along with the increasing of Re, the increasing trend of Nu becomes weaker. In addition, the α value is larger, the increasing trend of Nu is smaller. The highest Nu value is approximately obtained as 265 for minimum α (30°) and β (30°), but maximum DR and Re value.
Fig. 6. Comparison of Nux with varieties of x/Lp for β = 90° and DR = 0.166.
Fig. 8. Comparison of NuER with varieties of Re for α = 30°.
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The effectiveness of using the CITSG is evaluated by studying ratio of mean Nusselt number (Nu) and the mean Nusselt number (Nu∞) for fully developed flow in an empty pipe. NuER = Nu = Nu∞
ð12Þ
Henceforth, this ratio will be referred to as the heat transfer enhancement ratio (NuER). The variation of this heat transfer enhancement ratio (NuER) with Reynolds number for various cases is shown in Fig. 8 for a fixed value of α = 30°.For the case of α = 30°, the heat transfer enhancement ratio (NuER) is quite great signifying that the use of the CITSG in a pipe with uniform heat flux is advantageous. The heat transfer enhancement ratio decreases with increase in Reynolds number. This is attributed to the fact that at higher Re values the turbulent effects play much more dominant role than the CITSG effects [4]. With developed turbulent flows of 10,000 ≤ Re b 35,000, the NuER decreases with the increase of Re in the present test section. The different decreasing rates of NuER versus Re according to the β and DR as indicated in Fig. 7 reflect a result of different Nu values. The decreasing rate of NuER depicted in Fig. 8 is clearly distinguishable. This situation shows that the effect of each independent parameter on heat transfer becomes apparent. If Fig. 8 is considered together with Fig. 9, the effect of α on the NuER will also be seen clearly. Fig. 8 reveals that the effect of β and DR on NuER becomes serious, especially at low Reynolds number. Contrary to β, the effect of α on NuER becomes serious at high Reynolds number. The effectiveness of using the CITSG can also be studied evaluating the heat transfer performance ratio. The heat transfer performance ratio is defined as the ratio of heat transfer enhancement to unit increase in pumping power 1=3
NuPR = NuER = ð f =f∞ Þ
:
ð13Þ
Fig. 10. Comparison of NuPR with varieties of Re for α = 30°.
Re ≅ 20,000. In addition, the unit increase in pumping power is higher than that of heat transfer enhancement ratio (NuER) at higher Re values. The empirical correlations for NuER, NuPR and f are derived using the software program Statistica 5.0. NuER, NuPR and f are correlated with the Re, Pr, α, β and DR. The correlations have a mean absolute deviation of 20% to that of the experimental data. NuER =28:46ðRe + 9140Þ 2 R = 0:96
− 0:09
Pr
0:4
ð1 + sin α Þ − 1:12 ð1 + sin βÞ − 0:43 DR0:24 ð14Þ
In this ratio, the friction factors are raised to the one-third power as the pumping power is proportional to the one-third power of the friction factor [4,25]. It is a common trend that the NuPR decreases as Re increases for turbulent flows. As expected the heat transfer ratio (NuPR) decreases with increase in Re. This behavior is attributed to the fact that at higher Reynolds number turbulent effects prevail over enhancement due to the CITSG. Fig. 10 shows the NuPR as a function of Re with β and DR as parameters for α = 30°. As seen from the figure, the effect of all parameters on NuPR is rather insufficient after Re ≅ 20,000. Figs. 10 and 11 indicate that the turbulent effects play much more dominant role than the CITSG effects at higher values than
The main objective of the present investigation is to determine the optimum values of dependent and independent parameters for a
Fig. 9. Comparison of NuER with varieties of Re for β = 30°.
Fig. 11. Comparison of NuPR with varieties of Re for β = 30°.
NuPR = 1:18 + ð0:16ðRe + 4656Þ − 0:84 Pr 0:4 ð1 + sin α Þ − 1:14 ð1 + sin βÞ − 1:58 ð1:96 + DRÞ1:24 Þ R2 = 0:95 0:4 − 3:88 ð1 + sin βÞ − 0:16 DR0:26 f =26:69Re − 0:24 Pr ð1 + sin α Þ 2 R = 0:98
ð15Þ
ð16Þ
İ. Kurtbaş et al. / International Communications in Heat and Mass Transfer 36 (2009) 865–871
uniform heat flux pipe with the conical injector type swirl generator (CITSG) inserts using heat transfer enhancement ratio (NuER) and heat transfer performance ratio (NuPR). The second objective is to develop an effective heat exchanger using the conical injector type swirl generator turbulators. 4. Conclusions This investigation experimentally studies the convective heat transfer and pressure drop in uniform heat flux pipe. The conical injector type swirl generators are employed. The coolant fluid is air. The variable parameters are the ratio of flow director diameter (d) to pipe inner diameter (D), the CITSG angle (α), the flow director angle (FDA(β)) and the Reynolds number (Re). In this work, the CITSG angles are 30°, 45° and 60°; the flow director angles are 30°, 60° and 90°, and Re varies from 9400 to 35,000. What follows is a brief summary: • The heat transfer and pressure drop are affected considerably by the CITSG angle (α), the flow director angle (FDA(β)) and the flow director diameter (DR), especially at lower Reynolds numbers. • Better heat transfer rates are found for a pipe with lower CITSG angle (α) and the flow director angle (β) or a higher value of the flow director diameter (DR). • The heat transfer enhancement ratio (NuER) decreases with increase in Re and increases with increase in the β and DR. • The effect of the β on Nux is at negligible level for higher Reynolds number. • The effect of the α on Nux is significant and goes on throughout the pipe. • The heat transfer ratio (NuPR) decreases with increase in Re. • The effect of all parameters on NuPR is rather insufficient after Re ≅ 20,000 and the unit increase in pumping power is higher than that of heat transfer enhancement ratio (NuER) at higher Re values. References [1] P. Promvonge, Thermal performance in circular tube fitted with coiled square wires, Energy Convers. Manag. 49 (2008) 980–987. [2] P. Promvonge, S. Eiamsa-ard, Heat transfer augmentation in a circular tube using V-nozzle turbulator inserts and snail entry, Exp. Ther. Fluid Sci. 32 (2007) 332–340. [3] P. Promvonge, S. Eiamsa-ard, Heat transfer behaviors in a tube with combined conical-ring and twisted-tape insert, Int. Commun. Heat Mass Transf. 34 (2007) 849–859. [4] K.H. Ko, N.K. Anand, Use of porous baffles to enhance heat transfer in a rectangular channel, Int. J. Heat Mass Transf. 46 (2003) 4191–4199. [5] K. Yakut, B. Sahin, S. Canbazoglu, Performance and flow-induced vibration characteristics for conical-ring turbulators, Appl. Energy 79 (2004) 65–76. [6] K. Yakut, B. Sahin, Flow-induced vibration analysis of conical rings used of heat transfer enhancement in heat exchanger, Appl. Energy 78 (2004) 273–288.
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Contents lists available at ScienceDirect
International Communications in Heat and Mass Transfer j o u r n a l h o m e p a g e : w w w. e l s ev i e r. c o m / l o c a t e / i c h m t
Heat transfer augmentation by swirl generators inserted into a tube with constant heat flux☆ İrfan Kurtbaş a,⁎, Fevzi Gülçimen b, Abdullah Akbulut c, Dinçer Buran d a
Hitit University, Mechanical Engineering Department, 19030 Çorum, Turkey Tunceli University, Mechanical Engineering Department, 62000 Tunceli, Turkey Dumlupinar University, Mechanical Engineering Department, 43000 Kutahya, Turkey d Dumlupinar University, Mechanical Education Department, 43500 Simav, Kutahya, Turkey b c
a r t i c l e
i n f o
Available online 6 June 2009 Keywords: Swirl generator Decaying flow Turbulator Pipe flow
a b s t r a c t A novel conical injector type swirl generator (CITSG) is devised in this study. Performances of heat transfer and pressure drop in a pipe with the CITSG are experimentally examined for the CITSGs' angle (α) of 30°, 45° and 60° in Reynolds number (Re) range of 10,000–35,000. Moreover, circular holes with different numbers (N) and cross-section areas (Ah) are drilled on the CITSG. In this way, total areas (At = N · Ah) of the holes on the CITSG are equaled each other. Besides, flow directors having three different angles (β = 30°, 60° and 90°) to radial direction are attached to every one of the holes. This study is a typical example for decaying flow. All experiments were conduced with air accordingly; Prandtl number was approximately fixed at 0.71. The local Nusselt number (Nux), heat transfer enhancement ratio (NuER) and heat transfer performance ratio (NuPR) are calculated and discussed in this paper. It is found that the NuER decreases with increase in Reynolds number, the director angle (β), the director diameter (d), and with decrease in the CITSG angle (α). Likewise, variation of NuPR and NuER is also essentially similar for the same independent parameters. © 2009 Elsevier Ltd. All rights reserved.
1. Introduction The use of turbulators in pipes or channels is one of the commonly used passive heat transfer enhancement strategies in single-phase internal flows. Accordingly, detailed investigation of the effect of twisted tape and wire coil turbulators on heat transfer augmentation has received considerable attention [1–3]. This passive heat transfer enhancement strategy has been used for various types of industrial applications such as shell-and-tube type heat exchangers, electronic cooling devices, thermal regenerators, internal cooling systems of gas turbine blades, and labyrinth seals for turbo-machines. Periodically positioned baffles in baffled channels and periodic turns in serpentine channels periodically interrupt hydrodynamic and thermal boundary layers [4]. The effect of conical-ring turbulators on the turbulent heat transfer, pressure drop and flow-induced vibrations is experimentally investigated. Their experiments are analyzed and presented in terms of the thermal performances of the heat-transfer promoters with respect to their heat-transfer
☆ Communicated by W.J. Minkowycz. ⁎ Corresponding author. E-mail addresses: [email protected] (İ. Kurtbaş), [email protected] (F. Gülçimen), aakbulut@firat.edu.tr (A. Akbulut), [email protected] (D. Buran). 0735-1933/$ – see front matter © 2009 Elsevier Ltd. All rights reserved. doi:10.1016/j.icheatmasstransfer.2009.04.011
enhancement efficiencies for a constant pumping power [5,6]. An experimental study on the heat transfer and friction loss characteristics of a surface with cylindrical fins in a rectangular cross-section channel with large diameter fins and different channel geometries is carried out by Bilen et al. [7]. Also, the pipe flow with various grooves (circular, trapezoidal and rectangular) at constant wall heat flux condition, and hollow rectangular fins surface is studied experimentally [8,9]. Co-axis free rotating propeller type turbulators are devised by Kurtbaş et al. [10,11]. The effect of the turbulators on heat transfer and exergy loss is investigated experimentally. Cakmak and Yildiz [12] performed a similar study and investigated the influence of the injectors with swirling flow generating on the heat transfer in the concentric heat exchanger. Moreover, many researchers have endeavored to construct compact and energy-efficient heat exchangers with swirl generator and finned tube [13–20]. Many numerical studies on swirl generators and fin- and tube heat exchangers are also performed and discussed [20–24]. The objective of the present work is to conduct experiments to measure local-mean Nusselt number (Nu x − Nu), heat transfer enhancement ratio (NuER) and heat transfer performance ratio (NuPR) for flow in a uniform heat flux pipe with conical injector type swirl generator (CITSG) inserts. This study also analyzes the effect of the CITSG angle, flow director angle (FDA), flow director diameter (FDD) on the heat transfer enhancement ratio (NuER) and heat transfer performance ratio (NuPR) for turbulence regime.
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Nomenclature A Ah As cp d D Dh f h hx I k L ṁ N Nu NuER NuPR P Pr q Q R2 Re T V V′
cross-sectional area of pipe, m2 cross-sectional area of hole m2 heating surface area of pipe, m2 specific heat, J/kg K the flow director diameter, m pipe inner diameter, m channel hydraulic diameter, m friction factor mean heat transfer coefficient, W/m2 K local heat transfer coefficient, W/m2 K current, Amp thermal conductivity, W/mK length, m mass flow rate of air, kg/s hole number mean Nusselt number the heat transfer enhancement ratio the heat transfer performance ratio pressure, Pa Prandtl number heat flux, W/m2 heat transfer rate, W regression coefficient Reynolds number temperature, K velocity, m/s voltage, V
Greek symbols α the CITSG angle β the flow director angle µ dynamic viscosity ρ density
Subscripts b bulk fd flow director in inlet out outlet p pipe sg swirl generator t total w wall
2. Experimental setup 2.1. Test section and apparatus Fig. 1 presents the schematic view of whole setup with each element. The experimental setup is divided into three main parts; named as (i) air supply system, (ii) test section and test specimens, and (iii) data acquisition system. The working fluid is air and it is sucked by a centrifugal fan. The propellers of the fan can turn up to 1500 rpm with the aid of an AC electric motor (1.1 kW). The speed of the fan can be adjusted and controlled by an AC inverter with accuracy of 1%. The fan is connected to a damping chamber (200 × 200 × 200 mm dimensions) which is made of 0.35 mm thickness galvanized plate. The damping chamber is stated between flow channel and fan, and can turn the flow 90-deg as shown in Fig. 1. To have more accurate measurements, a digital flow meter (measurement range: 0.6 to
40 m/s) is also setup between the flow channel and damping chamber. The test section (copper pipe) whole length is 1.2 m. The temperature of the heated surface is measured by 9 calibrated and electrically insulated 0.5 mm diameter T-type copper-constantan thermocouples. Two thermocouples are used to measure inlet and outlet flow temperature too. Also, one thermocouple is used to measure the ambient temperature. The thermocouple voltages were collected by ALMEMO 5990-0 datalogger and transmitted directly to a personal computer. Pressure drops throughout the test section were measured using a calibrated U-manometer. Fig. 2 depicts the geometrical details of the CITSG. The CITSG's are made of galvanized sheet. The CITSG has an angle (α) of 30°, 45° and 60° as seen in Fig. 2(a). The flow directors having three different angles (β = 30°, 60° and 90°) to radial direction are attached to every one of the holes (Fig. 2(b)). The FDD is changed as 4, 7 and 10 mm. Dimensions of the test section and the CITSG are given in Table 1. A silicone rubber heater is fixed to the outer surface of the copper pipe to provide the uniform heat flux. Electric current was supplied to the heater (test section) by an AC variable electric power supply (DELORENZO, with accuracy of ±1–1.5% for voltage (V′) and current (I)). To minimize the heat losses from the test section to the environment, the test section is wrapped with glass wool insulating material of 100 mm thickness. Reynolds number (Re) is varied from 10,000 to 35,000 (6 different values of air flow mass rates are tested). The up limit is considered as 35,000, due to the excessive pumping power requirement for the aluminum foam case experiments. The kinematic viscosity, specific heat and density of the fluid are also changed because of the temperature differences in the experiments. Therefore, Reynolds numbers are slightly changed in the same air flow mass rate. These little deviations in Reynolds number are not considered in the figures. As for Prandtl number, it is varied from 0.7 to 0.72. 2.2. Data reduction The average frontal velocity (V) was calculated by dividing the measured volumetric flow rate by the inlet cross-section area. The Reynolds number is based on the hydraulic diameter (Dh). The sensible heat transfer rate of air is calculated from the inlet and outlet temperatures across the test section, namely; Q = ṁ CpðTout − Tin Þ:
ð1Þ
Determination of the sensible heat transfer coefficient (h) is as follows: Q = hAs ðTw − Tb Þ
ð2Þ
where Q is net convective heat flux, Tw is average wall temperature of the plate surface adjacent to the fluid, Tb is average fluid bulk temperature in the pipe, and As is heating surface area. The physical properties (k, μ, ρ, cp) appearing in the dimensionless numbers (Nu, Re, Pr) are all evaluated at the bulk fluid temperature (Tb). Nusselt number is equal to the dimensionless temperature gradient at surface, and it provides to denote the convection heat transfer occurred at surfaces. Hence, local Nusselt number can be written as: Nux =
hx Dh k
ð3Þ
where hx is local sensible heat transfer coefficient, k is thermal conductivity of the air. The local heat transfer coefficient can then be calculated from
hx =
Q Q − Q loss = t : As Tw;x − Tb As Tw;x − Tb
ð4Þ
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Fig. 1. Schematic diagram of experimental setup.
Fig. 2. The test section (a) detailed figure of the CITSG, (b) flow pipe with the CITSG.
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and Reynolds number is estimated to be 4.2% and 3.8%, respectively. Likewise, the uncertainty for friction factor is 5.8%.
Table 1 Dimensions of the independent parameters (mm). Lp
Lsg
1200
60 78.4 116
Lfd
d
6
4 7 10
D
α (deg)
β (deg)
60
30 45 60
30 60 90
3. Results and discussion
The mean heat transfer coefficient and Nusselt number can be written as follows: h=
1 Lp
Z
Lp 0
0:8
hx dx
hDh : Nu = k
ð5Þ
ρVDh : μ
2ρΔP Dh V 2 LP
Pr
0:76
0:4
Pr
0:4
ð9Þ
2
R = 0:99
ð10Þ
ð6Þ
ð7Þ
The friction coefficient ( f ) in a channel flow can be determined by measuring the pressure drop across the flow channel and average velocity of the air. Average friction coefficient can, therefore, be calculated from f =
Nu = 0:023Re
Nu∞ = 0:035Re
The subscripts x show the measurement point of temperatures on heated surfaces (x = 1–9). The total heat flux (Q t =V′ ·I/As) generated by silicone rubber heater. The heat losses from the insulation of the heated plates and the conduction are calculated to be 2.4% of the total heat flux. The most important parametric value, Reynolds number, depends strongly on hydraulic diameter and written as Re =
The convection heat transfer in an empty pipe without the CITSG was measured before measuring on the convection heat transfer in the pipe with the CITSG. The heat transfer coefficient inside the pipe can be calculated with the Dittus–Boelter as given below.
ð8Þ
where ΔP is pressure drop in the channel.
Eq. (9) is considered to be the most accurate in the range 0.6 ≤ Pr ≤ 160 and Re ≥ 10,000. As indicated in Fig. 3, the experimental results for empty pipe are found to agree within 6.8%. The mean Nusselt number for fully developed flow in an empty pipe is compared with results obtained from correlation of Dittus–Boelter [27]. Fig. 4 displays the local Nusselt number (Nux) as a function of the x/Lp for maximum and minimum Re values, α = 30°, DR = 0.166 and various β. As seen from the figure, Nux is relatively less at the beginning of the test section (x/Lp ≅ 0). Then, it increases rapidly up to x/Lp ≅ 0.4. The Nux is maximal at x/Lp ≅ 0.4 and slowly decreases in the direction of the flow for both Re ≅ 9700 and Re ≅ 33,700. It is seen that when Re increases, the effect of the FDA (β) on the Nux decreases. In other words, when the lower Re is, the effect of β on the Nux becomes more apparent. At the end of the pipe, the effect of β on the Nux is insignificant for all Reynolds numbers. Furthermore, when Re increases, the effect of the β on the Nux becomes weaker. Fig. 5 shows the variation of the Nux versus x/Lp with respect to various DR and Re values for α = 30° and β = 90°. Herein, the DR is defined as the ratio of the flow director diameter (FDD) to inner diameter of the pipe (D = Dh), namely DR = ðd = DÞ = ðd = Dh Þ:
ð11Þ
2.3. Uncertainty analysis Uncertainties in Reynolds number and other independent parameters are calculated according to the standard procedures established by Kline and McClintock [26]. The experimental uncertainty in convective heat flux (Q) was estimated to be 2.1%. The analysis shows that the maximum uncertainty associated with the Nusselt number
The FDD yields considerable heat transfer enhancements with a similar trend approximately in comparison with each other and the Nux increases with increase in Re and DR. In the meantime, the maximum value of Nux obtained from using Re ≅ 34,000 and Re ≅ 9800 for DR = 0.166 are found to be 307 and 226, respectively. In addition, the Nux decreases with decrease in DR. The effect of the CITSG angle
Fig. 3. Comparison of theoretical Nusselt number with Re for empty pipe.
Fig. 4. Comparison of Nux with varieties of x/Lp for α = 30° and DR = 0.166.
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Fig. 5. Comparison of Nux with varieties of x/Lp for α = 30° and β = 90°.
Fig. 7. Comparison of Nu with Re having DR and β as parameter for α = 30°.
(α) on the Nux for β = 90° and DR = 0.166 is given in Fig. 6. It is shown that Nux increases with decrease in α value. When Fig. 6 is examined together with Figs. 4 and 5, it is observed that Fig. 6 is different from the others. In other words, the effect of β and DR on the Nux is insignificant at the beginning of the pipe (x/Lp ≅ 0.01) as seen in Figs. 4 and 5. However, at both the beginning and the end of the pipe, the Nux changes depending on the α (Fig. 6). These differences can be attributed to the decrease of the swirl intensity throughout the pipe. In addition, the heat transfer results show the possibility of a dead zone called as “plug flow” in this short distance between the beginning of the pipe and the flow directors. The Nux does not change with β and DR in the dead zone, but changes with α and Re. In addition, the results indicate that the β and DR initially increase the swirl intensity up to x/Lp ≅ 0.4. However, after x/Lp ≅ 0.4, the effect of β and DR on swirl intensity decreases, especially x/Lp N 0.75. On the other hand, effect of α on swirl intensity goes on throughout the pipe. It is seen from Fig. 7 that the effect of the CITSG on heat transfer is significant for all Reynolds numbers used due to the induction of high reverse flow. In all cases of the CITSG inserts, the swirl flow gives higher
values of the Nu than that for fully developed flow. The CITSG turbulators yield considerable heat transfer enhancements with a similar trend approximately in comparison with the smooth tube and the Nusselt number increases with the rise of Reynolds number. The use of the CITSG shows a higher heat transfer rate than that of the empty pipe at around 61–80% depending on the Re, the FDA (β) and the DR values for α = 30°. Also, it is evident that the effect of both the DR and β on the Nu is more dominant in the lower Reynolds number range. When Re and α are constant, Nu increases with increase in DR, but Nu increases with decrease in β. Along with the increasing of Re, the effect of DR and β on Nu decreases. Fig. 7 clearly reveals that the effect of α on Nu is significant, which finding is consistent with the results herein. The figure indicates that the effect of DR on Nu becomes serious, especially at low Reynolds number. In the meantime, the increasing trend of Nu is falling depending on Reynolds number when α value is increased. Along with the increasing of Re, the increasing trend of Nu becomes weaker. In addition, the α value is larger, the increasing trend of Nu is smaller. The highest Nu value is approximately obtained as 265 for minimum α (30°) and β (30°), but maximum DR and Re value.
Fig. 6. Comparison of Nux with varieties of x/Lp for β = 90° and DR = 0.166.
Fig. 8. Comparison of NuER with varieties of Re for α = 30°.
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The effectiveness of using the CITSG is evaluated by studying ratio of mean Nusselt number (Nu) and the mean Nusselt number (Nu∞) for fully developed flow in an empty pipe. NuER = Nu = Nu∞
ð12Þ
Henceforth, this ratio will be referred to as the heat transfer enhancement ratio (NuER). The variation of this heat transfer enhancement ratio (NuER) with Reynolds number for various cases is shown in Fig. 8 for a fixed value of α = 30°.For the case of α = 30°, the heat transfer enhancement ratio (NuER) is quite great signifying that the use of the CITSG in a pipe with uniform heat flux is advantageous. The heat transfer enhancement ratio decreases with increase in Reynolds number. This is attributed to the fact that at higher Re values the turbulent effects play much more dominant role than the CITSG effects [4]. With developed turbulent flows of 10,000 ≤ Re b 35,000, the NuER decreases with the increase of Re in the present test section. The different decreasing rates of NuER versus Re according to the β and DR as indicated in Fig. 7 reflect a result of different Nu values. The decreasing rate of NuER depicted in Fig. 8 is clearly distinguishable. This situation shows that the effect of each independent parameter on heat transfer becomes apparent. If Fig. 8 is considered together with Fig. 9, the effect of α on the NuER will also be seen clearly. Fig. 8 reveals that the effect of β and DR on NuER becomes serious, especially at low Reynolds number. Contrary to β, the effect of α on NuER becomes serious at high Reynolds number. The effectiveness of using the CITSG can also be studied evaluating the heat transfer performance ratio. The heat transfer performance ratio is defined as the ratio of heat transfer enhancement to unit increase in pumping power 1=3
NuPR = NuER = ð f =f∞ Þ
:
ð13Þ
Fig. 10. Comparison of NuPR with varieties of Re for α = 30°.
Re ≅ 20,000. In addition, the unit increase in pumping power is higher than that of heat transfer enhancement ratio (NuER) at higher Re values. The empirical correlations for NuER, NuPR and f are derived using the software program Statistica 5.0. NuER, NuPR and f are correlated with the Re, Pr, α, β and DR. The correlations have a mean absolute deviation of 20% to that of the experimental data. NuER =28:46ðRe + 9140Þ 2 R = 0:96
− 0:09
Pr
0:4
ð1 + sin α Þ − 1:12 ð1 + sin βÞ − 0:43 DR0:24 ð14Þ
In this ratio, the friction factors are raised to the one-third power as the pumping power is proportional to the one-third power of the friction factor [4,25]. It is a common trend that the NuPR decreases as Re increases for turbulent flows. As expected the heat transfer ratio (NuPR) decreases with increase in Re. This behavior is attributed to the fact that at higher Reynolds number turbulent effects prevail over enhancement due to the CITSG. Fig. 10 shows the NuPR as a function of Re with β and DR as parameters for α = 30°. As seen from the figure, the effect of all parameters on NuPR is rather insufficient after Re ≅ 20,000. Figs. 10 and 11 indicate that the turbulent effects play much more dominant role than the CITSG effects at higher values than
The main objective of the present investigation is to determine the optimum values of dependent and independent parameters for a
Fig. 9. Comparison of NuER with varieties of Re for β = 30°.
Fig. 11. Comparison of NuPR with varieties of Re for β = 30°.
NuPR = 1:18 + ð0:16ðRe + 4656Þ − 0:84 Pr 0:4 ð1 + sin α Þ − 1:14 ð1 + sin βÞ − 1:58 ð1:96 + DRÞ1:24 Þ R2 = 0:95 0:4 − 3:88 ð1 + sin βÞ − 0:16 DR0:26 f =26:69Re − 0:24 Pr ð1 + sin α Þ 2 R = 0:98
ð15Þ
ð16Þ
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uniform heat flux pipe with the conical injector type swirl generator (CITSG) inserts using heat transfer enhancement ratio (NuER) and heat transfer performance ratio (NuPR). The second objective is to develop an effective heat exchanger using the conical injector type swirl generator turbulators. 4. Conclusions This investigation experimentally studies the convective heat transfer and pressure drop in uniform heat flux pipe. The conical injector type swirl generators are employed. The coolant fluid is air. The variable parameters are the ratio of flow director diameter (d) to pipe inner diameter (D), the CITSG angle (α), the flow director angle (FDA(β)) and the Reynolds number (Re). In this work, the CITSG angles are 30°, 45° and 60°; the flow director angles are 30°, 60° and 90°, and Re varies from 9400 to 35,000. What follows is a brief summary: • The heat transfer and pressure drop are affected considerably by the CITSG angle (α), the flow director angle (FDA(β)) and the flow director diameter (DR), especially at lower Reynolds numbers. • Better heat transfer rates are found for a pipe with lower CITSG angle (α) and the flow director angle (β) or a higher value of the flow director diameter (DR). • The heat transfer enhancement ratio (NuER) decreases with increase in Re and increases with increase in the β and DR. • The effect of the β on Nux is at negligible level for higher Reynolds number. • The effect of the α on Nux is significant and goes on throughout the pipe. • The heat transfer ratio (NuPR) decreases with increase in Re. • The effect of all parameters on NuPR is rather insufficient after Re ≅ 20,000 and the unit increase in pumping power is higher than that of heat transfer enhancement ratio (NuER) at higher Re values. References [1] P. Promvonge, Thermal performance in circular tube fitted with coiled square wires, Energy Convers. Manag. 49 (2008) 980–987. [2] P. Promvonge, S. Eiamsa-ard, Heat transfer augmentation in a circular tube using V-nozzle turbulator inserts and snail entry, Exp. Ther. Fluid Sci. 32 (2007) 332–340. [3] P. Promvonge, S. Eiamsa-ard, Heat transfer behaviors in a tube with combined conical-ring and twisted-tape insert, Int. Commun. Heat Mass Transf. 34 (2007) 849–859. [4] K.H. Ko, N.K. Anand, Use of porous baffles to enhance heat transfer in a rectangular channel, Int. J. Heat Mass Transf. 46 (2003) 4191–4199. [5] K. Yakut, B. Sahin, S. Canbazoglu, Performance and flow-induced vibration characteristics for conical-ring turbulators, Appl. Energy 79 (2004) 65–76. [6] K. Yakut, B. Sahin, Flow-induced vibration analysis of conical rings used of heat transfer enhancement in heat exchanger, Appl. Energy 78 (2004) 273–288.
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