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Performance characteristics of heat exchanger with internal turbulence generators under various blade configurations and operating conditions
Applied Thermal Engineering 123 (2017) 562–572
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Applied Thermal Engineering journal homepage: www.elsevier.com/locate/apthermeng
Research Paper
Performance characteristics of heat exchanger with internal turbulence generators under various blade configurations and operating conditions Dae-Hae Kim a, Edward Joshua T. Pialago b,⇑, Jai-Yoon Shin c, Oh Kyung Kwon d, Min-Soo Kim b, Chan Woo Park b,⇑ a
Thermalchemical Energy System R&D Group, Korea Institute of Industrial Technology, Cheonan, Chungcheongnam 31056, Republic of Korea Division of Mechanical Design Engineering, Chonbuk National University, Jeonju, Jeonbuk 54896, Republic of Korea Mechanical Technology Research Group, LS Mtron, Anyang, Gyeonggi 14119, Republic of Korea d Energy System Technology Center, Korea Institute of Industrial Technology, Cheonan, Chungcheongnam 31056, Republic of Korea b c
a r t i c l e
i n f o
Article history: Received 28 October 2016 Revised 28 April 2017 Accepted 22 May 2017 Available online 24 May 2017 Keywords: Heat transfer rate Friction factor Turbulence generator Heat exchanger Oil cooler
a b s t r a c t In this study, turbulence generators with rectangular geometry were designed to be fixed inside the tube of an oil cooler for the hydraulic steering of automobiles and their performance characteristics in the heat exchanger were investigated. The heat transfer rates, heat transfer coefficients, the coefficient of the pressure drop values, and friction factors were measured in accordance to the flow rates and inlet temperature of the oil. The resulting Nusselt numbers (Nu) increased when the angle of the turbulence generator wings was increased up to 45–65° but decreased when the angle was increased further up to 75°. On the hand, the friction factor (f) continued to increase as the angle configuration was increased. The highest value of the thermal performance enhancement factor (TEF), which was 6.46, was obtained from the turbulence generator angle of 45°, which could be considered as the optimum angle configuration. Lastly, the empirical correlations that were developed for the Nu and the f had good agreement with the experimental values and both had conservative error range of ±20%. Ó 2017 Elsevier Ltd. All rights reserved.
1. Introduction The performance of automobiles is directly influenced by the heat exchangers used in maintaining the temperatures of parts such as the engine and the automatic transmission. Among the heat exchangers used in cars such as the one for car air conditioning is the oil cooler that is used as a device for preventing the increase of the temperature of the oil circulating inside the automatic transmission. For smooth lubrication and power transmission, the temperature of the automatic transmission oil has be maintained at about 80–90 °C. If this is not done properly, the temperature of the oil will reach 110–130 °C. When the oil temperature increases like this, the oil density and viscosity rapidly changes. From this, the high pressure and the high speed of the transmission will cause oil cavitation to occur. This phenomenon in automatic transmissions can interfere with the smooth power delivery and can damage the automatic transmission parts. Therefore, in order to cool the automatic transmission
⇑ Corresponding authors. E-mail addresses: [email protected], [email protected] (E.J.T. Pialago), [email protected] (C.W. Park). http://dx.doi.org/10.1016/j.applthermaleng.2017.05.119 1359-4311/Ó 2017 Elsevier Ltd. All rights reserved.
fluid, a variety of oil coolers are installed. Accordingly, several studies have been conducted to improve the performance of the oil cooler heat exchanger [1,2]. Research for heat transfer enhancement is often applied to heat exchangers, air-conditioning and refrigeration systems, and heat recovery systems [3]. In particular, various methods have been considered and utilized for inducing turbulent flow in order to increase the heat transfer of heat exchangers [4–6]. The development and heat transfer performance studies of inserts for promoting turbulent flow in heat exchangers are not new. However, researchers are still looking for new geometries, approaches, and construction methods that are better than the already existing ones, especially those that are specific for certain applications. These inserts, also referred as vortex generators or turbulence generators, have various geometries with different heat transfer characteristics. Examples of these geometries are straight and twisted internal fin inserts [7], coiled wire inserts [8], delta-winglets with forward and backward arrangements [9,10], and corrugated/vortex-generator plate-fin in plate-fin heat exchangers [11]. The heat transfer performances as influenced by the inserts may be varied such as by modifying the width of the twisted tape tube inserts [12]. Other studies that used similar turbulence generators
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Nomenclature A CP Dh h k L Lh Lt _ m DP Q_ R T DT U UY V
flow area, m2 specific heat, J/kg K hydraulic diameter, m inlet heat transfer coefficient, W/m2 K thermal conductivity, W/m K length, m hydrodynamic fully developed entry length, m thermally fully developed entry length, m mass flow rate, kg/s pressure drop, Pa heat transfer rate, W thermal resistance, K/W temperature, °C or K temperature difference, K overall heat transfer coefficient, W/m K uncertainty of variable velocity, m/s
Greek symbols q density, kg/m3 l dynamic viscosity, Pa s g efficiency
examined the effects of the turbulence generator geometries such as twist and free space ratio of the inserted tapes on the heat transfer and the pressure drop [13]. Researchers also performed experimental investigation on shell and helically coiled tube heat exchangers [14]. In the study by Eiamsa-ard and Promvonge [15], they measured the heat transfer and pressure drop of heat exchanger, which was inserted with V-nozzle turbulence. In addition, it has been studied that the heat transfer coefficient can be increased by machining the inside wall of tubes to the generate of turbulence [16,17]. However, the existing turbulence generators are simply inserted in the tube. The movement of turbulence generators occurs along the flow. Sometimes, a thin aluminum tube is damaged due to its movement. Therefore a study of a type of turbulence generators that are fixed inside the tube is necessary. In this study, turbulence generators were designed to be fixed inside the tube of an oil cooler, and were investigated for their performance characteristics in the heat exchanger. An experimental study was carried out on the effects of the wing or blade angle configuration, the oil temperature, and the oil flowrate on the cooling heat transfer rate and the pressure drop of the oil cooler equipped with the fixed-type vortex or turbulence generators.
2. Experimental procedure 2.1. Experimental apparatus 2.1.1. Turbulence generators The general shape of the turbulence generators used in this study is shown in Fig. 1. These turbulence generators were made from 1-mm thick aluminum sheets. Each of them had a length and width of 205 mm and 10 mm, respectively. The wing blades of turbulence generators had a height of 4 mm and a width of 5 mm. To investigate their influence on heat transfer and on the performance of the oil cool, the angle configuration of the wing blades was varied from 25° to 75°. Unlike conventional turbulent flow generators, the turbulence generators in this study were inserted and fixed on the walls inside the tubes with two fixture blades as shown in the upper left of Fig. 1. These fixture blades also
Subscripts air, in air inlet air, out air outlet av average LMTD logarithmic mean temperature difference oil, in oil inlet oil, out oil outlet Dimensionless groups f friction factor fo friction factor of smooth tube Nu Nusselt number Nuo Nusselt number of smooth tube Pr Prandtl number Re Reynolds number Acronym TEF thermal performance enhancement factor
Fig. 1. Shape of the turbulence generator.
acted as fins through which heat conduction to the tube walls occurred. Forward or backward arrangements of winglets have been studied such as the ones in Ref. [18]. In the case of the present study, as shown in Fig. 2, the arrangements of the blades or winglets of the turbulence generators in this study are both forward and backward arrangements. As can be seen in Fig. 2b, the blades of the upper part of the turbulence generator of had forward arrangement while those of the lower part had backward arrangement. Fig. 2 also shows the expected fluid flow inside the tube when the turbulence generator is inserted. It can be seen in the figure that the flow is separated into two: one flow along the wings and another flow along the tube wall. The mixing of these two flows generates strong turbulence.
2.1.2. Fin-tube heat exchanger The oil cooler was a fin-tube type heat exchanger that consisted of external square aluminum fins and aluminum tubes inside which the turbulence generators were inserted. The dimensions of the heat exchanger are shown in Fig. 3. The exchanger had a four-pass set-up with a total tube length of 820 mm. The total tube
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was installed at the duct exit to induce the flow of air. The oil flow and the air flow were controlled by regulating the speed (i.e., rpm) of the pump and the blower, respectively. The oil (part no. 47390 52700L1, SK Lubricants Co.) and oil pump used in the experiments were actual products for automotive applications. The temperatures of the oil and the air were controlled by heaters in the oil bath and in the duct, respectively. Each of the heaters was precisely controlled by a PID control unit. The flow rates of the oil and the air were measured by an oil mass flow meter and an air mass flow meter, respectively. The temperatures of the oil and the air were measured by the RTDs. And lastly, the pressure drop of each side of the heat exchanger was also measured using differential pressure transmitters. In this work, an Agilent 34970A data acquisition system (Agilent Technologies) and a LabVIEW program (National Instruments Corp.) were used for recording the experimental data. The specifications of the measurement devices are listed in Table 1. 2.2. Experimental conditions
Fig. 2. Fluid flow inside the tube.
length involved in heat transfer was 760 mm. The outside and inside diameters of the tubes were 10 mm and 10.36 mm, respectively. The square fins outside the tubes had height, width, thickness, and pitch of 30 mm, 40 mm, 1 mm, and 2 mm, respectively. The U-tubes for connecting the oil flow from one tube to another were thermally insulated. With this thermal insulation, heat transfer occurred only through the fins and the outside surfaces of the tubes.
2.1.3. Heat transfer experimental set-up The experimental set-up for the evaluation of the heat transfer performance of the fin-tube type oil cooler is shown in Fig. 4. As shown in the figure, the oil cooler was installed inside a duct with an induced draft set-up. The external surfaces of this duct as well as those of the pipe lines connected to the oil cooler were thermally insulated to prevent heat loss. An appropriate oil pump was used for the circulation of the oil through the pipe lines from the oil bath to the oil cooler and back. For the duct side, a blower
The experimental parameter settings for this study were based on the operating condition of oil coolers in automotive vehicles. There were three main experimental parameters that were considered: (1) the flow conditions of the air, (2) the flow conditions of the oil, and (3) the wing blade angle configurations of the turbulence generator. Concerning the air, its flowrate was kept constant at 10 m3/min and its temperature was kept constant at 40 °C by the heater installed in the duct inlet. On the other hand, the flow conditions of the oil were varied with different parameter values (i.e., temperatures and flowrates). Considering that the temperature of the oil in the oil cooler of automotive vehicles generally ranges from 50 °C to 110 °C, the oil temperatures for the experiments were varied within this range. Similarly, based on actual operating conditions of oil coolers, the oil flowrates were varied from 1 L/min to 7 L/min. Lastly, the wing blade angle configurations were also varied as previously described in Section 2.1.1. The details of test conditions are listed in Table 2. The experiments were conducted to examine the characteristics of the heat transfer and the pressure drop of the heat exchanger when turbulence generators with different wing blade angles were inserted. We measured the oil and the air temperatures at the inlets and the outlets of the heat exchanger as well as the corresponding flowrates and calculated the heat transfer rates. The measured oil flowrates were also used to determine the inside and outside heat transfer coefficients of the oil cooling heat exchanger by following the Wilson plot method [19,20]. The Wilson plot
Fig. 3. Dimensions of the heat exchanger.
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Fig. 4. Schematic of the experimental set-up.
Table 1 Measurement devices. Instrument
Manufacturer
Specifications (Measuring range)
Accuracy
Air mass flow meter
SIERRA
Oil mass flow meter
KYONGIN
±1% of full scale ±0.1% of full scale
Differential pressure transmitter Turbo browser
SIEMENS
Temp: 14–176 °C Flow: 0–100 m/s Temp: 20 °C to 120 °C Flow: 0–500 m/s Temp: 0–125 °C Pressure: 0.05–5 bar 3.7 kW (5 HP)
RTD
MICROMENT
Heater
HEASUNG
KIJEONSA
Temp: 10 °C to 120 °C 20 kW, 15 kW, 10 kW
0.3% Efficiency: 82% 95% 95%
Reoil ¼
qoil V oil Dh loil
ð3Þ
Nuoil ¼
hin Dh koil
ð4Þ
The average heat transfer rate was calculated using Eq. (5) and the overall heat transfer coefficient of the heat exchanger was calculated using Eq. (6).
Q_ air þ Q_ oil Q_ av ¼ 2
ð5Þ
Q_ av ¼ UAF DT LMTD
ð6Þ
The total thermal resistance of the heat exchanger is expressed by Eq. (7) and the logarithmic mean temperature difference is expressed by Eq. (8) [22].
Table 2 Test conditions.
Rtot ¼
Parameters
Values
Air temperature (°C) Air flow (m3/min) Oil temperature (°C) Oil flow (L/min) Turbulizer angle
40 10 50, 70, 90, 110 1, 3, 5, 7 No turbulizer, 25°, 35°, 45°, 55°, 65°, 75°
method uses the variation of flow rate, specifically fluid velocity, to estimate heat transfer coefficients. The data reduction for these various heat transfer values are discussed with details in Section 2.3. 2.3. Data reduction The heat transfer rate in the heat exchanger was calculated from the temperature differences and flow rates of the air and the oil. The air and the oil heat transfer rates are expressed by Eqs. (1) and (2), respectively; while the Reynolds number and the Nusselt number of the oil are expressed by Eqs. (3) and (4), respectively [21]. For the credibility of the experiments, energy balance between the air and the oil sides was performed and, due to the thermal insulation, the error of the energy balance was only around 8%.
1 F DT LMTD ¼ UA Q_ av
DT LMTD ¼
ð7Þ
T oil;in T air;out T oil;out T air;in T T ln T oil;in Tair;out air;in
ð8Þ
oil;out
In Eqs. (6) and (7), F is the correction factor for the log mean temperature difference DTLMTD of cross-flow heat exchanger configurations. Considering the temperature ratios T⁄P and T⁄R defined as
T P ¼
T oil;out T oil;in T air;in T oil;in
ð9Þ
T R ¼
T air;in T air;out T oil;out T oil;in
ð10Þ
_ air C P;air T air;out T air;in Q_ air ¼ m
ð1Þ
the corresponding correction factors were determined to be approximately equal to one (F 1) based on the correction factor chart for cross-flow heat exchangers [23]. The total thermal resistance of the heat exchanger consisted of the inside and the outside thermal resistances of the tube, and the thermal resistance of the tube due to its thermal conductivity and thickness. The thermal resistance of the tube was much smaller than the other thermal resistances and was considered negligible. So, the overall thermal resistance was simplified as expressed by Eq. (11).
_ oil C P;oil T oil;out T oil;in Q_ oil ¼ m
ð2Þ
1 1 1 þ UA hin Ain gt hout Aout
ð11Þ
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The gt in Eq. (11) was the overall surface efficiency of the fins. The inside and outside heat transfer coefficients (hin and hout) were determined using the Wilson plot method [19,20]. Using this method for each angle configuration of turbulizer, Eq. (11) can be expressed as
1 1 þ C4 C C UA C 1 Re 2 Pr 3
ð12Þ
where
C 1 ReC 2 PrC3 ¼ hin Ain C1 ¼ C5
ð13Þ
koil Ain Dh
ð14Þ
C 2 ¼ 0:8
ð15Þ
C 3 ¼ 0:3
ð16Þ
C4 ¼
1
ð17Þ
gt hout Aout
It can be seen that the inside thermal resistance of the tube in Eq. (12) is expressed as a proportion of the inverse of Re and Pr. With constant air flowrate and varying oil flowrate inside the tubes during the experiments, Eq. (12) was simply plotted by having the experimental values of 1/(Re0.8Pr0.3) as the abscissa and those of 1/UA as the ordinate. The values of the slope and the y-intercept of this linear plot are equal to 1/C1 and C4, respectively. The value of C1 is determined from the slope. Using either C1 or C4, the values of hin and hout can be estimated. Moreover, the values of C1 were determined for the corresponding h values. With the available values of C1, the inside heat transfer coefficients hin were calculated using Eq. (13). Lastly, the pressure difference inside the heat exchanger is expressed by Eq. (18) from which the friction coefficient can be obtained.
DP ¼ f
L qV 2 Di 2
ð18Þ
where UY represents the uncertainty of the variable. The values of the calculated data uncertainties are listed in Table 3. 3. Results and discussion 3.1. Verification of the experiments Because of the influence of high viscosity, Reynolds number of the oil inside the tube was 279–1981, which was in the laminar flow region. On the other hand, the Pr number was 88–127. The lengths of the hydrodynamic and thermally fully developed entrance in the laminar region can be expressed by Eqs. (20) and (21), respectively [25,26].
Lh;laminar 0:05Re
ð20Þ
Lt;laminar 0:05RePrD ¼ Pr Lh;laminar
ð21Þ
The hydrodynamic fully developed entrance length was 0.14–1.0 m, depending on the Reynolds number. In the experiments, each tube of four-pass heat exchanger was mixed with an entrance region. Therefore, verification of the validity of the heat transfer experiments was done by using the correlation by Sieder and Tate [27,28] and the calculated results were compared with the heat transfer experimental results from the internally smooth tube. If the surface temperatures of both fluids were different, according to Sieder and Tate, the Nusselt number of the entrance of the laminar flow and fully developed region can be defined as Eq. (22).
1 0:14 RePrD 3 lb Nu ¼ 1:86 L lo
Fig. 5 shows the comparison of the Nusselt numbers according to the Reynolds numbers obtained from the experimental results and the Nusselt numbers calculated using Sieder and Tate’s correlation, Eq. (22), in smooth tubes without turbulence generator. Lastly, when the flow is a fully developed laminar flow, the tube inside friction coefficient (f) as influenced by the Reynolds number can be expressed by Eq. (23).
f ¼
2.4. Experimental uncertainty Table 1 shows the summary of the uncertainties of the measured raw data based on the information provided by the instrument manufacturers. Experimental uncertainty was calculated using Engineering Equation Solver (EES). The method for determining this uncertainty propagation is described in Ref. [24]. Assuming the individual measurements are uncorrelated and random, the uncertainty in the calculated quantity can be determined as
vffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi u n 2 uX @Y UY ¼ t U 2x @X i i
ð22Þ
64 Re
ð23Þ
In the experiments, the friction coefficient in the entry region was generally larger than that of the fully developed laminar flow. Thus, as shown in Fig. 6, the friction coefficients obtained from the experiments were larger than those obtained using Eq. (23) in the fully developed region. Similar results that showed the variation of the friction factor with Reynolds numbers at the entry region were reported in Refs. [29,30].
ð19Þ
Table 3 Uncertainties of the experimental data. Measured variables
Calculated variables
Variables
Uncertainty
Variables
Uncertainty (%)
Temperature Mass flow rate Diameter Length Differential pressure
0.1 K 0.1 kg/s 0.0005 m 0.01 m 2 Pa
Friction factor Nusselt number Reynolds number
6.1 4.96 6.21 Fig. 5. Comparison of the fully developed heat transfer data of the present work with the correlation by Sieder and Tate.
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Fig. 6. Comparison of the present work and f equation.
3.2. Reynolds number and wing angle effect 3.2.1. Nusselt number (Nu) Fig. 7 shows the variation of the Nu values as affected by the Re values of the flowing oil at 50 °C, 70 °C, 90 °C, and 110 °C. Based on the results, a general trend can be described as follows. First, with respect to the Re of each of the angle configurations, the Nu increased as the Re increased. Second, further increase of the Nu and Re values was observed with the increase of the oil temperature. And third, the Nu increased when the angle of the turbulence generator wings was increased up to 45° to 65° but decreased when the angle was increased further up to 75°. The influence of convective heat transfer became considerably greater than that of conductive heat transfer when the oil velocity was increased. The increase of the oil temperature caused the decrease of the viscosity and resulted in the further increase of the Reynolds number. The higher the wing angle of the turbulence generator became, the greater flow turbulence resulted. Consequently, the convective heat transfer in the tube was enhanced. However, the positive effect of the angle of the turbulence generator decreased when
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the angle was increased further. Fig. 8 presents the variation of the convection heat transfer enhancement expressed as the ratio of the turbulence generator Nu to the smooth tube Nuo as influenced by the Reynolds number of the oil and the angle of the turbulence generator. The trends of the values in Fig. 8 were the same as those of Fig. 7. In particular, the top Nu/Nuo values were observed from the turbulence generator angles of 45°, 55°, and 65° while the bottom values were observed from angles of 25°, 35°, and 75°. Fig. 9 shows the values of Nu/Nuo ratio according to the turbulence generator angles for each oil temperature. It can be clearly seen in the figure that the Nu/Nuo ratio increased as the oil temperature increased. On the other hand, it can also be observed that the Nu/Nuo ratio increased with the increased of the turbulence generator angle but only up to 45°, 55°, and 65°. Beyond these angles, Nu/Nuo ratio decreased. The highest three Nu/Nuo values were 10.41, 9.05, and 10.55 which were respectively obtained from the angles of 45°, 55°, and 65° at the oil temperature of 110 °C. These results indicate that the optimum enhancement in terms of the Nu values can be achieved from turbulence generators with wing angles of 45°, 55°, and 65°. Moreover, it can also be observed from the results in Figs. 7 and 8 as well as in Fig. 9 that the Nu values were considerably high despite the low range of Re values. The calculated values of Re were based on the measured oil flow rate and thermodynamic properties. Although the Re values were in the laminar range, turbulence was generated by the presence of the inserts in the tubes. This turbulence resulted in the enhancement of the forced convection similar to the results reported in Ref. [8].
3.2.2. Friction factor (f) Fig. 10 depicts the variation of the friction factor or coefficient with the change in Re and inclined wing angle for each oil temperature. The overall value of the friction coefficient diminished as the Reynolds number increased, but it increased as the angle of turbulence generators increased. As the temperature of the oil increased, the density and viscosity of the oil decreased and consequently
Fig. 7. Variation of Nu with Re and angle of inclined baffle.
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Fig. 8. Variation of Nu/Nuo with Re and angle of inclined baffle.
Fig. 9. Comparison of Nu/Nuo with angle.
resulted in the reduction of the flow differential pressure. By inducing a flow pressure drop by means of the increase of the turbulence generator wing angle, it was observed that the friction coefficient increased. Khoshvaght-Aliabadi et al. [31] investigated the performance of a plate-fin heat exchanger with vortex generator channels. They observed that when the wing attack angle was increased the heat transfer coefficient and pressure drop increased. Tamna et al. [32] also showed that a tube with twisted-tape inserts yielded considerably high heat transfer compared with a plain tube. The Nusselt number exhibited an uptrend with the rise of the Reynolds number. And in their study, they showed that the Nusselt number of the tube with insert was much higher than that of the plain tube. This was due to the strong vortex that helped in increasing the turbulence intensity and reducing the boundary layer that resulted in higher convection. The use of turbulence generator leads to substantial increase in friction factor above the plain tube but a downtrend of the friction factor occurs when the Reynolds number is increased. The higher friction loss is mainly the outcome from
the increased surface area and higher swirl intensity due to the inserts [32]. Muthusamy and Vivar [33], and Eiamsa-ard and Thianpong [13] observed similar results that showed the decrease of the fraction factor. Fig. 11 shows the variation of the relative friction coefficient (f/fo) with Reynolds number of each angle of the turbulence generator at different oil temperatures. The f/fo ratio fluctuated (i.e., decreased and increased) with Re, while it increased as the angle of the turbulence generator increased. This variation of the f/fo ratio according to the turbulence generator angles for each oil temperature can also be clearly observed in Fig. 12. As shown by the bar graph, the f/fo ratio increased as the angle of the turbulence generator and the oil temperature as well as the Re increased. These trends were slightly different compared with those of the Nu/Nuo. While the increase of Nu/Nuo was observed to peak at turbulence generator angles of 45°, 55° and 65°, f/fo kept on increasing as the angle increased. The rise of the f/fo was considerably smaller than the Nu/Nuo. In Ref. [34], Wu and Tao used longitudinal vortex generators that were similar to the ones in the present study. They calculated the heat transfer rate and the friction factor of the rectangular winglets along the fluid flow. Regardless of temperature, when the angle of winglet in longitudinal vortex generator increased the f/fo ratio also increased. Like other studies [8,10], the use of inserts in tubes in the present study yielded better heat transfer performance as compared with plain tubes. However, the inserts resulted in higher pressure drop due to the increased friction in the fluid flow.
3.3. Thermal performance enhancement factor (TEF) effect The thermal performance enhancement factor (TEF) is defined by considering Nu, Nuo, f, and fo; and is expressed as Eq. (24). The TEF, which represents the enhanced heat transfer performance through the experimental study, is defined by heat transfer performance efficiency [35,36].
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Fig. 10. Variation of f with Re and angle of inclined baffle.
Fig. 11. Variation of f/fo with Reynolds number and angle of inclined baffle.
Nu Nuo
TEF ¼ 1=3 f fo
ð24Þ
Fig. 13 shows the variation of the TEF values with change of the Reynolds number at different oil temperatures. As the Reynolds number increased, the values of TEF increased. This variation was similar to the change of Nu/Nuo at each oil temperature. At the oil temperature of 50 °C, the TEF was small when the Re was about
120. It significantly increased thereafter when the Re was increased to about 300, 450, and 600. Similar trends were observed for the TEF values at oil temperatures of 70 °C, 90 °C and 110 °C as shown in the figure. One particular observation from the variations of the TEF values was that the highest TEF values at all Re values and oil temperatures were obtained from the turbulence generator with a wing angle of 45°. Fig. 14 shows the summarized relationship between the average TEF values and the angles of the turbulence generator wings
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of the present study and those of the recently published ones is not ideal due to the difference in the fluid used and operating conditions (e.g., temperature and velocity). For example, the experiments reported in Refs. [7,9,10] had high Re and different fluid properties. Some studies that used viscous liquid and that are similar to the present study are those of Refs. [8,37]. The study by Akhavan-Behabadi et al. [8] had oil temperature and Re ranges that were similar to the ones in the present study. However, the inserts in their study were significantly different because they were using coiled wires. With the increase of Re, the TEF values of the present study increased while those of Ref. [8] decreased. 3.4. Empirical correlations
Fig. 12. Comparison of f/fo with angle.
or blades. As indicated in the figure, the TEF increased as the turbulence generator angle increased from 25° to 45°. Similar to what was mentioned in the previous paragraph, the highest value of TEF, which was 6.46, was obtained from the turbulence generator angle of 45°. However, the TEF decreased when the angle was increased further from 45° to 75°. This means that, although the pumping power rose up when the angle was increased up to 45°, the heat transfer performance enhancement ratios were still considerably higher than that of the pumping power. However, when the angle was higher than 45°, the heat transfer performance enhancement ratio decreased while the pumping power continued to rise up thereby resulting in the decrease of TEF. The top three average TEF values were obtained from angles of 45°, 55° and 65°. In the case of 55° and 65°, the difference between the corresponding TEF values was considerably small. The present study specifically intends to apply the inserts for the enhancement of cooling of oil in automotive vehicles. Recent studies about tube inserts for turbulence or vortex generation in the fluid flow, such as those of Refs. [9,10,31], used water as the main heat transfer medium. Direct comparison between the results
For every angle configuration of the turbulence generator in this study, the inside Nusselt number can be defined in the general form of Eq. (25).
Nu ¼ C 5 ReC 2 PrC3
ð25Þ
The exponents C2 and C3 are respectively equal to 0.8 and 0.3, which correspond to those used in the Wilson plot described in Section 2.3 of this article. The coefficient C5 can be considered as a geometrical coefficient that is a function of the turbulence generator angle, which can be expressed in dimensionless form as h/h90. By performing a regression analysis of the experiment values, the Nu can be empirically correlated to Re, Pr, and h/h90 as in Eq. (26).
Nu ¼ 1:069Re0:8 Pr0:3
h 0:137 1 0:874 h90 h90 h
ð26Þ
On the other hand, the values of the tube inside friction coefficient f obtained from Eq. (18) was correlated to the values of Re and h/h90° also by multiple regression analysis. The resulting correlation for f is expressed as Eq. (27).
f ¼ 4:202Re0:380
h
0:958
h90
ð27Þ
Figs. 15 and 16 respectively show the comparisons between the model and the experimental values of Nu and f. The calculated or
Fig. 13. Variation of thermal performance enhancement factor (TEF) with Re and angle of inclined baffle.
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their performance characteristics in the heat exchanger. The following are the conclusions.
Fig. 14. Variation of average thermal performance enhancement factor (TEF) with angle of inclined baffle.
(1) The Nu values increased when the angle of the turbulence generator wings was increased up to 45–65° but decreased when the angle was increased further up to 75°. As the temperature of the oil was increased, the density and the viscosity of the oil decreased and resulted in the reduction flow differential pressure and friction factors. (2) The turbulence generators with angles of 45°, 55° and 65° exhibited the highest three average Nu/Nuo values, which were equal to 10.41, 9.05, and 10.55, respectively. Concerning the average f/fo, the value kept increasing as the angle configuration was increased. (3) The TEF increased as the turbulence generator angle increased from 25° to 45°. The highest value of TEF, which was 6.46, was obtained from the turbulence generator angle of 45°. However, the TEF decreased when the angle was increased further from 45° to 75°. In the case of 55° and 65°, the difference between the corresponding TEF values was considerably small. So, the optimum angle configuration of the turbulence generator is 45°. (4) The experimental results of Nu and f can be expressed in the form of model equations. The calculated or predicted Nu values obtained using the model equations had good agreement with the experimental values and both had conservative error range of ±20%.
Acknowledgment
Fig. 15. Comparison between the measured Nu and the calculated Nu by the correlation.
This work was supported by a grant (No. 2015R1A2A2A01005693) from the National Research Foundation of Korea funded by the Korean Government. References
Fig. 16. Comparison between the measured f and calculated f by the correlation.
predicted Nu and f values of the oil cooler had good agreement with the experimental values and both had a conservative error range of ±20%. The oil cooler of this study is now in commercial use. The basic research results obtained under various experimental conditions are needed for more efficient heat transfer enhancement of the product. The proposed empirical correlations of Eqs. (26) and (27) above may be used for the specification of the product and its enhancement. 4. Conclusion In this study, the turbulence generators were designed to be fixed inside the tubes of an oil cooler, and were investigated for
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[26] R.K. Shah, M.S. Bhatti, Laminar Convective Heat Transfer in Ducts, in: S. Kakac, R.K. Shah, W. Aung (Eds.), Handbook of Single-Phase Convective Heat transfer, Wiley Interscience, New York, 1987. [27] E.N. Sieder, G.E. Tate, Heat Transfer and Pressure Drop of Liquids in Tubes, Ind. Eng. Chem. 28 (1936) 1429–1435. [28] H.K. Tam, L.M. Tam, A.J. Ghajar, Effect of inlet geometries and heating on the entrance and fully-developed friction factors in the laminar and transition regions of a horizontal tube, Exp. Thermal Fluid Sci. 44 (2013) 680–696. [29] S.A. Alnassri, T. Unny, Developing laminar-flow in the inlet length of a smooth pipe, Appl. Sci. Res. 36 (1980) 313–332. [30] S.G. Kandlikar, L.A. Campbell, Effect of Entrance Condition on Frictional Losses and Transition to Turbulence, in: ASME 2002 International Mechanical Engineering Congress and Exposition, Heat Transfer, Vol. 4, New Orleans, Louisiana, USA, 2002, pp. 131–136. [31] M. Khoshvaght-Aliabadi, S. Zangouei, F. Hormozi, Performance of a plate-fin heat exchanger with vortex-generator channels: 3D-CFD simulation and experimental validation, Int. J. Therm. Sci. 88 (2015) 180–192. [32] S. Tamna, Y. Kaewkohkiat, S. Skullong, P. Promvonge, Heat transfer enhancement in tubular heat exchanger with double V-ribbed twisted-tapes, Case Stud. Therm. Eng. 7 (2016) 14–24. [33] C. Muthusamy, M. Vivar, I. Skryabin, K. Srithar, Effect of conical cut-out turbulators with internal fins in a circular tube on heat transfer and friction factor, Int. Commun. Heat Mass Transfer 44 (2013) 64–68. [34] J.M. Wu, W.Q. Tao, Numerical study on laminar convection heat transfer in a rectangular channel with longitudinal vortex generator Part A: Verification of field synergy principle, Int. J. Heat Mass Transfer 51 (2008) 1179–1191. [35] D.L. Gee, R.L. Webb, Forced convection heat transfer in helically rib-roughened tubes, Int. J. Heat Mass Transfer 23 (1980) 1127–1136. [36] P. Promvonge, S. Pethkool, M. Pimsarn, C. Thianpong, Heat transfer augmentation in a helical-ribbed tube with double twisted tape inserts, Int. Commun. Heat Mass Transfer 39 (2012) 953–959. [37] S. Saha, S.K. Saha, Enhancement of heat transfer of laminar flow of viscous oil through a circular tube having integral helical rib roughness and fitted with helical screw-tapes, Exp. Therm. Fluid Sci. 47 (2013) 81–89.
Contents lists available at ScienceDirect
Applied Thermal Engineering journal homepage: www.elsevier.com/locate/apthermeng
Research Paper
Performance characteristics of heat exchanger with internal turbulence generators under various blade configurations and operating conditions Dae-Hae Kim a, Edward Joshua T. Pialago b,⇑, Jai-Yoon Shin c, Oh Kyung Kwon d, Min-Soo Kim b, Chan Woo Park b,⇑ a
Thermalchemical Energy System R&D Group, Korea Institute of Industrial Technology, Cheonan, Chungcheongnam 31056, Republic of Korea Division of Mechanical Design Engineering, Chonbuk National University, Jeonju, Jeonbuk 54896, Republic of Korea Mechanical Technology Research Group, LS Mtron, Anyang, Gyeonggi 14119, Republic of Korea d Energy System Technology Center, Korea Institute of Industrial Technology, Cheonan, Chungcheongnam 31056, Republic of Korea b c
a r t i c l e
i n f o
Article history: Received 28 October 2016 Revised 28 April 2017 Accepted 22 May 2017 Available online 24 May 2017 Keywords: Heat transfer rate Friction factor Turbulence generator Heat exchanger Oil cooler
a b s t r a c t In this study, turbulence generators with rectangular geometry were designed to be fixed inside the tube of an oil cooler for the hydraulic steering of automobiles and their performance characteristics in the heat exchanger were investigated. The heat transfer rates, heat transfer coefficients, the coefficient of the pressure drop values, and friction factors were measured in accordance to the flow rates and inlet temperature of the oil. The resulting Nusselt numbers (Nu) increased when the angle of the turbulence generator wings was increased up to 45–65° but decreased when the angle was increased further up to 75°. On the hand, the friction factor (f) continued to increase as the angle configuration was increased. The highest value of the thermal performance enhancement factor (TEF), which was 6.46, was obtained from the turbulence generator angle of 45°, which could be considered as the optimum angle configuration. Lastly, the empirical correlations that were developed for the Nu and the f had good agreement with the experimental values and both had conservative error range of ±20%. Ó 2017 Elsevier Ltd. All rights reserved.
1. Introduction The performance of automobiles is directly influenced by the heat exchangers used in maintaining the temperatures of parts such as the engine and the automatic transmission. Among the heat exchangers used in cars such as the one for car air conditioning is the oil cooler that is used as a device for preventing the increase of the temperature of the oil circulating inside the automatic transmission. For smooth lubrication and power transmission, the temperature of the automatic transmission oil has be maintained at about 80–90 °C. If this is not done properly, the temperature of the oil will reach 110–130 °C. When the oil temperature increases like this, the oil density and viscosity rapidly changes. From this, the high pressure and the high speed of the transmission will cause oil cavitation to occur. This phenomenon in automatic transmissions can interfere with the smooth power delivery and can damage the automatic transmission parts. Therefore, in order to cool the automatic transmission
⇑ Corresponding authors. E-mail addresses: [email protected], [email protected] (E.J.T. Pialago), [email protected] (C.W. Park). http://dx.doi.org/10.1016/j.applthermaleng.2017.05.119 1359-4311/Ó 2017 Elsevier Ltd. All rights reserved.
fluid, a variety of oil coolers are installed. Accordingly, several studies have been conducted to improve the performance of the oil cooler heat exchanger [1,2]. Research for heat transfer enhancement is often applied to heat exchangers, air-conditioning and refrigeration systems, and heat recovery systems [3]. In particular, various methods have been considered and utilized for inducing turbulent flow in order to increase the heat transfer of heat exchangers [4–6]. The development and heat transfer performance studies of inserts for promoting turbulent flow in heat exchangers are not new. However, researchers are still looking for new geometries, approaches, and construction methods that are better than the already existing ones, especially those that are specific for certain applications. These inserts, also referred as vortex generators or turbulence generators, have various geometries with different heat transfer characteristics. Examples of these geometries are straight and twisted internal fin inserts [7], coiled wire inserts [8], delta-winglets with forward and backward arrangements [9,10], and corrugated/vortex-generator plate-fin in plate-fin heat exchangers [11]. The heat transfer performances as influenced by the inserts may be varied such as by modifying the width of the twisted tape tube inserts [12]. Other studies that used similar turbulence generators
D.-H. Kim et al. / Applied Thermal Engineering 123 (2017) 562–572
563
Nomenclature A CP Dh h k L Lh Lt _ m DP Q_ R T DT U UY V
flow area, m2 specific heat, J/kg K hydraulic diameter, m inlet heat transfer coefficient, W/m2 K thermal conductivity, W/m K length, m hydrodynamic fully developed entry length, m thermally fully developed entry length, m mass flow rate, kg/s pressure drop, Pa heat transfer rate, W thermal resistance, K/W temperature, °C or K temperature difference, K overall heat transfer coefficient, W/m K uncertainty of variable velocity, m/s
Greek symbols q density, kg/m3 l dynamic viscosity, Pa s g efficiency
examined the effects of the turbulence generator geometries such as twist and free space ratio of the inserted tapes on the heat transfer and the pressure drop [13]. Researchers also performed experimental investigation on shell and helically coiled tube heat exchangers [14]. In the study by Eiamsa-ard and Promvonge [15], they measured the heat transfer and pressure drop of heat exchanger, which was inserted with V-nozzle turbulence. In addition, it has been studied that the heat transfer coefficient can be increased by machining the inside wall of tubes to the generate of turbulence [16,17]. However, the existing turbulence generators are simply inserted in the tube. The movement of turbulence generators occurs along the flow. Sometimes, a thin aluminum tube is damaged due to its movement. Therefore a study of a type of turbulence generators that are fixed inside the tube is necessary. In this study, turbulence generators were designed to be fixed inside the tube of an oil cooler, and were investigated for their performance characteristics in the heat exchanger. An experimental study was carried out on the effects of the wing or blade angle configuration, the oil temperature, and the oil flowrate on the cooling heat transfer rate and the pressure drop of the oil cooler equipped with the fixed-type vortex or turbulence generators.
2. Experimental procedure 2.1. Experimental apparatus 2.1.1. Turbulence generators The general shape of the turbulence generators used in this study is shown in Fig. 1. These turbulence generators were made from 1-mm thick aluminum sheets. Each of them had a length and width of 205 mm and 10 mm, respectively. The wing blades of turbulence generators had a height of 4 mm and a width of 5 mm. To investigate their influence on heat transfer and on the performance of the oil cool, the angle configuration of the wing blades was varied from 25° to 75°. Unlike conventional turbulent flow generators, the turbulence generators in this study were inserted and fixed on the walls inside the tubes with two fixture blades as shown in the upper left of Fig. 1. These fixture blades also
Subscripts air, in air inlet air, out air outlet av average LMTD logarithmic mean temperature difference oil, in oil inlet oil, out oil outlet Dimensionless groups f friction factor fo friction factor of smooth tube Nu Nusselt number Nuo Nusselt number of smooth tube Pr Prandtl number Re Reynolds number Acronym TEF thermal performance enhancement factor
Fig. 1. Shape of the turbulence generator.
acted as fins through which heat conduction to the tube walls occurred. Forward or backward arrangements of winglets have been studied such as the ones in Ref. [18]. In the case of the present study, as shown in Fig. 2, the arrangements of the blades or winglets of the turbulence generators in this study are both forward and backward arrangements. As can be seen in Fig. 2b, the blades of the upper part of the turbulence generator of had forward arrangement while those of the lower part had backward arrangement. Fig. 2 also shows the expected fluid flow inside the tube when the turbulence generator is inserted. It can be seen in the figure that the flow is separated into two: one flow along the wings and another flow along the tube wall. The mixing of these two flows generates strong turbulence.
2.1.2. Fin-tube heat exchanger The oil cooler was a fin-tube type heat exchanger that consisted of external square aluminum fins and aluminum tubes inside which the turbulence generators were inserted. The dimensions of the heat exchanger are shown in Fig. 3. The exchanger had a four-pass set-up with a total tube length of 820 mm. The total tube
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was installed at the duct exit to induce the flow of air. The oil flow and the air flow were controlled by regulating the speed (i.e., rpm) of the pump and the blower, respectively. The oil (part no. 47390 52700L1, SK Lubricants Co.) and oil pump used in the experiments were actual products for automotive applications. The temperatures of the oil and the air were controlled by heaters in the oil bath and in the duct, respectively. Each of the heaters was precisely controlled by a PID control unit. The flow rates of the oil and the air were measured by an oil mass flow meter and an air mass flow meter, respectively. The temperatures of the oil and the air were measured by the RTDs. And lastly, the pressure drop of each side of the heat exchanger was also measured using differential pressure transmitters. In this work, an Agilent 34970A data acquisition system (Agilent Technologies) and a LabVIEW program (National Instruments Corp.) were used for recording the experimental data. The specifications of the measurement devices are listed in Table 1. 2.2. Experimental conditions
Fig. 2. Fluid flow inside the tube.
length involved in heat transfer was 760 mm. The outside and inside diameters of the tubes were 10 mm and 10.36 mm, respectively. The square fins outside the tubes had height, width, thickness, and pitch of 30 mm, 40 mm, 1 mm, and 2 mm, respectively. The U-tubes for connecting the oil flow from one tube to another were thermally insulated. With this thermal insulation, heat transfer occurred only through the fins and the outside surfaces of the tubes.
2.1.3. Heat transfer experimental set-up The experimental set-up for the evaluation of the heat transfer performance of the fin-tube type oil cooler is shown in Fig. 4. As shown in the figure, the oil cooler was installed inside a duct with an induced draft set-up. The external surfaces of this duct as well as those of the pipe lines connected to the oil cooler were thermally insulated to prevent heat loss. An appropriate oil pump was used for the circulation of the oil through the pipe lines from the oil bath to the oil cooler and back. For the duct side, a blower
The experimental parameter settings for this study were based on the operating condition of oil coolers in automotive vehicles. There were three main experimental parameters that were considered: (1) the flow conditions of the air, (2) the flow conditions of the oil, and (3) the wing blade angle configurations of the turbulence generator. Concerning the air, its flowrate was kept constant at 10 m3/min and its temperature was kept constant at 40 °C by the heater installed in the duct inlet. On the other hand, the flow conditions of the oil were varied with different parameter values (i.e., temperatures and flowrates). Considering that the temperature of the oil in the oil cooler of automotive vehicles generally ranges from 50 °C to 110 °C, the oil temperatures for the experiments were varied within this range. Similarly, based on actual operating conditions of oil coolers, the oil flowrates were varied from 1 L/min to 7 L/min. Lastly, the wing blade angle configurations were also varied as previously described in Section 2.1.1. The details of test conditions are listed in Table 2. The experiments were conducted to examine the characteristics of the heat transfer and the pressure drop of the heat exchanger when turbulence generators with different wing blade angles were inserted. We measured the oil and the air temperatures at the inlets and the outlets of the heat exchanger as well as the corresponding flowrates and calculated the heat transfer rates. The measured oil flowrates were also used to determine the inside and outside heat transfer coefficients of the oil cooling heat exchanger by following the Wilson plot method [19,20]. The Wilson plot
Fig. 3. Dimensions of the heat exchanger.
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Fig. 4. Schematic of the experimental set-up.
Table 1 Measurement devices. Instrument
Manufacturer
Specifications (Measuring range)
Accuracy
Air mass flow meter
SIERRA
Oil mass flow meter
KYONGIN
±1% of full scale ±0.1% of full scale
Differential pressure transmitter Turbo browser
SIEMENS
Temp: 14–176 °C Flow: 0–100 m/s Temp: 20 °C to 120 °C Flow: 0–500 m/s Temp: 0–125 °C Pressure: 0.05–5 bar 3.7 kW (5 HP)
RTD
MICROMENT
Heater
HEASUNG
KIJEONSA
Temp: 10 °C to 120 °C 20 kW, 15 kW, 10 kW
0.3% Efficiency: 82% 95% 95%
Reoil ¼
qoil V oil Dh loil
ð3Þ
Nuoil ¼
hin Dh koil
ð4Þ
The average heat transfer rate was calculated using Eq. (5) and the overall heat transfer coefficient of the heat exchanger was calculated using Eq. (6).
Q_ air þ Q_ oil Q_ av ¼ 2
ð5Þ
Q_ av ¼ UAF DT LMTD
ð6Þ
The total thermal resistance of the heat exchanger is expressed by Eq. (7) and the logarithmic mean temperature difference is expressed by Eq. (8) [22].
Table 2 Test conditions.
Rtot ¼
Parameters
Values
Air temperature (°C) Air flow (m3/min) Oil temperature (°C) Oil flow (L/min) Turbulizer angle
40 10 50, 70, 90, 110 1, 3, 5, 7 No turbulizer, 25°, 35°, 45°, 55°, 65°, 75°
method uses the variation of flow rate, specifically fluid velocity, to estimate heat transfer coefficients. The data reduction for these various heat transfer values are discussed with details in Section 2.3. 2.3. Data reduction The heat transfer rate in the heat exchanger was calculated from the temperature differences and flow rates of the air and the oil. The air and the oil heat transfer rates are expressed by Eqs. (1) and (2), respectively; while the Reynolds number and the Nusselt number of the oil are expressed by Eqs. (3) and (4), respectively [21]. For the credibility of the experiments, energy balance between the air and the oil sides was performed and, due to the thermal insulation, the error of the energy balance was only around 8%.
1 F DT LMTD ¼ UA Q_ av
DT LMTD ¼
ð7Þ
T oil;in T air;out T oil;out T air;in T T ln T oil;in Tair;out air;in
ð8Þ
oil;out
In Eqs. (6) and (7), F is the correction factor for the log mean temperature difference DTLMTD of cross-flow heat exchanger configurations. Considering the temperature ratios T⁄P and T⁄R defined as
T P ¼
T oil;out T oil;in T air;in T oil;in
ð9Þ
T R ¼
T air;in T air;out T oil;out T oil;in
ð10Þ
_ air C P;air T air;out T air;in Q_ air ¼ m
ð1Þ
the corresponding correction factors were determined to be approximately equal to one (F 1) based on the correction factor chart for cross-flow heat exchangers [23]. The total thermal resistance of the heat exchanger consisted of the inside and the outside thermal resistances of the tube, and the thermal resistance of the tube due to its thermal conductivity and thickness. The thermal resistance of the tube was much smaller than the other thermal resistances and was considered negligible. So, the overall thermal resistance was simplified as expressed by Eq. (11).
_ oil C P;oil T oil;out T oil;in Q_ oil ¼ m
ð2Þ
1 1 1 þ UA hin Ain gt hout Aout
ð11Þ
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The gt in Eq. (11) was the overall surface efficiency of the fins. The inside and outside heat transfer coefficients (hin and hout) were determined using the Wilson plot method [19,20]. Using this method for each angle configuration of turbulizer, Eq. (11) can be expressed as
1 1 þ C4 C C UA C 1 Re 2 Pr 3
ð12Þ
where
C 1 ReC 2 PrC3 ¼ hin Ain C1 ¼ C5
ð13Þ
koil Ain Dh
ð14Þ
C 2 ¼ 0:8
ð15Þ
C 3 ¼ 0:3
ð16Þ
C4 ¼
1
ð17Þ
gt hout Aout
It can be seen that the inside thermal resistance of the tube in Eq. (12) is expressed as a proportion of the inverse of Re and Pr. With constant air flowrate and varying oil flowrate inside the tubes during the experiments, Eq. (12) was simply plotted by having the experimental values of 1/(Re0.8Pr0.3) as the abscissa and those of 1/UA as the ordinate. The values of the slope and the y-intercept of this linear plot are equal to 1/C1 and C4, respectively. The value of C1 is determined from the slope. Using either C1 or C4, the values of hin and hout can be estimated. Moreover, the values of C1 were determined for the corresponding h values. With the available values of C1, the inside heat transfer coefficients hin were calculated using Eq. (13). Lastly, the pressure difference inside the heat exchanger is expressed by Eq. (18) from which the friction coefficient can be obtained.
DP ¼ f
L qV 2 Di 2
ð18Þ
where UY represents the uncertainty of the variable. The values of the calculated data uncertainties are listed in Table 3. 3. Results and discussion 3.1. Verification of the experiments Because of the influence of high viscosity, Reynolds number of the oil inside the tube was 279–1981, which was in the laminar flow region. On the other hand, the Pr number was 88–127. The lengths of the hydrodynamic and thermally fully developed entrance in the laminar region can be expressed by Eqs. (20) and (21), respectively [25,26].
Lh;laminar 0:05Re
ð20Þ
Lt;laminar 0:05RePrD ¼ Pr Lh;laminar
ð21Þ
The hydrodynamic fully developed entrance length was 0.14–1.0 m, depending on the Reynolds number. In the experiments, each tube of four-pass heat exchanger was mixed with an entrance region. Therefore, verification of the validity of the heat transfer experiments was done by using the correlation by Sieder and Tate [27,28] and the calculated results were compared with the heat transfer experimental results from the internally smooth tube. If the surface temperatures of both fluids were different, according to Sieder and Tate, the Nusselt number of the entrance of the laminar flow and fully developed region can be defined as Eq. (22).
1 0:14 RePrD 3 lb Nu ¼ 1:86 L lo
Fig. 5 shows the comparison of the Nusselt numbers according to the Reynolds numbers obtained from the experimental results and the Nusselt numbers calculated using Sieder and Tate’s correlation, Eq. (22), in smooth tubes without turbulence generator. Lastly, when the flow is a fully developed laminar flow, the tube inside friction coefficient (f) as influenced by the Reynolds number can be expressed by Eq. (23).
f ¼
2.4. Experimental uncertainty Table 1 shows the summary of the uncertainties of the measured raw data based on the information provided by the instrument manufacturers. Experimental uncertainty was calculated using Engineering Equation Solver (EES). The method for determining this uncertainty propagation is described in Ref. [24]. Assuming the individual measurements are uncorrelated and random, the uncertainty in the calculated quantity can be determined as
vffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi u n 2 uX @Y UY ¼ t U 2x @X i i
ð22Þ
64 Re
ð23Þ
In the experiments, the friction coefficient in the entry region was generally larger than that of the fully developed laminar flow. Thus, as shown in Fig. 6, the friction coefficients obtained from the experiments were larger than those obtained using Eq. (23) in the fully developed region. Similar results that showed the variation of the friction factor with Reynolds numbers at the entry region were reported in Refs. [29,30].
ð19Þ
Table 3 Uncertainties of the experimental data. Measured variables
Calculated variables
Variables
Uncertainty
Variables
Uncertainty (%)
Temperature Mass flow rate Diameter Length Differential pressure
0.1 K 0.1 kg/s 0.0005 m 0.01 m 2 Pa
Friction factor Nusselt number Reynolds number
6.1 4.96 6.21 Fig. 5. Comparison of the fully developed heat transfer data of the present work with the correlation by Sieder and Tate.
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Fig. 6. Comparison of the present work and f equation.
3.2. Reynolds number and wing angle effect 3.2.1. Nusselt number (Nu) Fig. 7 shows the variation of the Nu values as affected by the Re values of the flowing oil at 50 °C, 70 °C, 90 °C, and 110 °C. Based on the results, a general trend can be described as follows. First, with respect to the Re of each of the angle configurations, the Nu increased as the Re increased. Second, further increase of the Nu and Re values was observed with the increase of the oil temperature. And third, the Nu increased when the angle of the turbulence generator wings was increased up to 45° to 65° but decreased when the angle was increased further up to 75°. The influence of convective heat transfer became considerably greater than that of conductive heat transfer when the oil velocity was increased. The increase of the oil temperature caused the decrease of the viscosity and resulted in the further increase of the Reynolds number. The higher the wing angle of the turbulence generator became, the greater flow turbulence resulted. Consequently, the convective heat transfer in the tube was enhanced. However, the positive effect of the angle of the turbulence generator decreased when
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the angle was increased further. Fig. 8 presents the variation of the convection heat transfer enhancement expressed as the ratio of the turbulence generator Nu to the smooth tube Nuo as influenced by the Reynolds number of the oil and the angle of the turbulence generator. The trends of the values in Fig. 8 were the same as those of Fig. 7. In particular, the top Nu/Nuo values were observed from the turbulence generator angles of 45°, 55°, and 65° while the bottom values were observed from angles of 25°, 35°, and 75°. Fig. 9 shows the values of Nu/Nuo ratio according to the turbulence generator angles for each oil temperature. It can be clearly seen in the figure that the Nu/Nuo ratio increased as the oil temperature increased. On the other hand, it can also be observed that the Nu/Nuo ratio increased with the increased of the turbulence generator angle but only up to 45°, 55°, and 65°. Beyond these angles, Nu/Nuo ratio decreased. The highest three Nu/Nuo values were 10.41, 9.05, and 10.55 which were respectively obtained from the angles of 45°, 55°, and 65° at the oil temperature of 110 °C. These results indicate that the optimum enhancement in terms of the Nu values can be achieved from turbulence generators with wing angles of 45°, 55°, and 65°. Moreover, it can also be observed from the results in Figs. 7 and 8 as well as in Fig. 9 that the Nu values were considerably high despite the low range of Re values. The calculated values of Re were based on the measured oil flow rate and thermodynamic properties. Although the Re values were in the laminar range, turbulence was generated by the presence of the inserts in the tubes. This turbulence resulted in the enhancement of the forced convection similar to the results reported in Ref. [8].
3.2.2. Friction factor (f) Fig. 10 depicts the variation of the friction factor or coefficient with the change in Re and inclined wing angle for each oil temperature. The overall value of the friction coefficient diminished as the Reynolds number increased, but it increased as the angle of turbulence generators increased. As the temperature of the oil increased, the density and viscosity of the oil decreased and consequently
Fig. 7. Variation of Nu with Re and angle of inclined baffle.
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Fig. 8. Variation of Nu/Nuo with Re and angle of inclined baffle.
Fig. 9. Comparison of Nu/Nuo with angle.
resulted in the reduction of the flow differential pressure. By inducing a flow pressure drop by means of the increase of the turbulence generator wing angle, it was observed that the friction coefficient increased. Khoshvaght-Aliabadi et al. [31] investigated the performance of a plate-fin heat exchanger with vortex generator channels. They observed that when the wing attack angle was increased the heat transfer coefficient and pressure drop increased. Tamna et al. [32] also showed that a tube with twisted-tape inserts yielded considerably high heat transfer compared with a plain tube. The Nusselt number exhibited an uptrend with the rise of the Reynolds number. And in their study, they showed that the Nusselt number of the tube with insert was much higher than that of the plain tube. This was due to the strong vortex that helped in increasing the turbulence intensity and reducing the boundary layer that resulted in higher convection. The use of turbulence generator leads to substantial increase in friction factor above the plain tube but a downtrend of the friction factor occurs when the Reynolds number is increased. The higher friction loss is mainly the outcome from
the increased surface area and higher swirl intensity due to the inserts [32]. Muthusamy and Vivar [33], and Eiamsa-ard and Thianpong [13] observed similar results that showed the decrease of the fraction factor. Fig. 11 shows the variation of the relative friction coefficient (f/fo) with Reynolds number of each angle of the turbulence generator at different oil temperatures. The f/fo ratio fluctuated (i.e., decreased and increased) with Re, while it increased as the angle of the turbulence generator increased. This variation of the f/fo ratio according to the turbulence generator angles for each oil temperature can also be clearly observed in Fig. 12. As shown by the bar graph, the f/fo ratio increased as the angle of the turbulence generator and the oil temperature as well as the Re increased. These trends were slightly different compared with those of the Nu/Nuo. While the increase of Nu/Nuo was observed to peak at turbulence generator angles of 45°, 55° and 65°, f/fo kept on increasing as the angle increased. The rise of the f/fo was considerably smaller than the Nu/Nuo. In Ref. [34], Wu and Tao used longitudinal vortex generators that were similar to the ones in the present study. They calculated the heat transfer rate and the friction factor of the rectangular winglets along the fluid flow. Regardless of temperature, when the angle of winglet in longitudinal vortex generator increased the f/fo ratio also increased. Like other studies [8,10], the use of inserts in tubes in the present study yielded better heat transfer performance as compared with plain tubes. However, the inserts resulted in higher pressure drop due to the increased friction in the fluid flow.
3.3. Thermal performance enhancement factor (TEF) effect The thermal performance enhancement factor (TEF) is defined by considering Nu, Nuo, f, and fo; and is expressed as Eq. (24). The TEF, which represents the enhanced heat transfer performance through the experimental study, is defined by heat transfer performance efficiency [35,36].
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Fig. 10. Variation of f with Re and angle of inclined baffle.
Fig. 11. Variation of f/fo with Reynolds number and angle of inclined baffle.
Nu Nuo
TEF ¼ 1=3 f fo
ð24Þ
Fig. 13 shows the variation of the TEF values with change of the Reynolds number at different oil temperatures. As the Reynolds number increased, the values of TEF increased. This variation was similar to the change of Nu/Nuo at each oil temperature. At the oil temperature of 50 °C, the TEF was small when the Re was about
120. It significantly increased thereafter when the Re was increased to about 300, 450, and 600. Similar trends were observed for the TEF values at oil temperatures of 70 °C, 90 °C and 110 °C as shown in the figure. One particular observation from the variations of the TEF values was that the highest TEF values at all Re values and oil temperatures were obtained from the turbulence generator with a wing angle of 45°. Fig. 14 shows the summarized relationship between the average TEF values and the angles of the turbulence generator wings
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of the present study and those of the recently published ones is not ideal due to the difference in the fluid used and operating conditions (e.g., temperature and velocity). For example, the experiments reported in Refs. [7,9,10] had high Re and different fluid properties. Some studies that used viscous liquid and that are similar to the present study are those of Refs. [8,37]. The study by Akhavan-Behabadi et al. [8] had oil temperature and Re ranges that were similar to the ones in the present study. However, the inserts in their study were significantly different because they were using coiled wires. With the increase of Re, the TEF values of the present study increased while those of Ref. [8] decreased. 3.4. Empirical correlations
Fig. 12. Comparison of f/fo with angle.
or blades. As indicated in the figure, the TEF increased as the turbulence generator angle increased from 25° to 45°. Similar to what was mentioned in the previous paragraph, the highest value of TEF, which was 6.46, was obtained from the turbulence generator angle of 45°. However, the TEF decreased when the angle was increased further from 45° to 75°. This means that, although the pumping power rose up when the angle was increased up to 45°, the heat transfer performance enhancement ratios were still considerably higher than that of the pumping power. However, when the angle was higher than 45°, the heat transfer performance enhancement ratio decreased while the pumping power continued to rise up thereby resulting in the decrease of TEF. The top three average TEF values were obtained from angles of 45°, 55° and 65°. In the case of 55° and 65°, the difference between the corresponding TEF values was considerably small. The present study specifically intends to apply the inserts for the enhancement of cooling of oil in automotive vehicles. Recent studies about tube inserts for turbulence or vortex generation in the fluid flow, such as those of Refs. [9,10,31], used water as the main heat transfer medium. Direct comparison between the results
For every angle configuration of the turbulence generator in this study, the inside Nusselt number can be defined in the general form of Eq. (25).
Nu ¼ C 5 ReC 2 PrC3
ð25Þ
The exponents C2 and C3 are respectively equal to 0.8 and 0.3, which correspond to those used in the Wilson plot described in Section 2.3 of this article. The coefficient C5 can be considered as a geometrical coefficient that is a function of the turbulence generator angle, which can be expressed in dimensionless form as h/h90. By performing a regression analysis of the experiment values, the Nu can be empirically correlated to Re, Pr, and h/h90 as in Eq. (26).
Nu ¼ 1:069Re0:8 Pr0:3
h 0:137 1 0:874 h90 h90 h
ð26Þ
On the other hand, the values of the tube inside friction coefficient f obtained from Eq. (18) was correlated to the values of Re and h/h90° also by multiple regression analysis. The resulting correlation for f is expressed as Eq. (27).
f ¼ 4:202Re0:380
h
0:958
h90
ð27Þ
Figs. 15 and 16 respectively show the comparisons between the model and the experimental values of Nu and f. The calculated or
Fig. 13. Variation of thermal performance enhancement factor (TEF) with Re and angle of inclined baffle.
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their performance characteristics in the heat exchanger. The following are the conclusions.
Fig. 14. Variation of average thermal performance enhancement factor (TEF) with angle of inclined baffle.
(1) The Nu values increased when the angle of the turbulence generator wings was increased up to 45–65° but decreased when the angle was increased further up to 75°. As the temperature of the oil was increased, the density and the viscosity of the oil decreased and resulted in the reduction flow differential pressure and friction factors. (2) The turbulence generators with angles of 45°, 55° and 65° exhibited the highest three average Nu/Nuo values, which were equal to 10.41, 9.05, and 10.55, respectively. Concerning the average f/fo, the value kept increasing as the angle configuration was increased. (3) The TEF increased as the turbulence generator angle increased from 25° to 45°. The highest value of TEF, which was 6.46, was obtained from the turbulence generator angle of 45°. However, the TEF decreased when the angle was increased further from 45° to 75°. In the case of 55° and 65°, the difference between the corresponding TEF values was considerably small. So, the optimum angle configuration of the turbulence generator is 45°. (4) The experimental results of Nu and f can be expressed in the form of model equations. The calculated or predicted Nu values obtained using the model equations had good agreement with the experimental values and both had conservative error range of ±20%.
Acknowledgment
Fig. 15. Comparison between the measured Nu and the calculated Nu by the correlation.
This work was supported by a grant (No. 2015R1A2A2A01005693) from the National Research Foundation of Korea funded by the Korean Government. References
Fig. 16. Comparison between the measured f and calculated f by the correlation.
predicted Nu and f values of the oil cooler had good agreement with the experimental values and both had a conservative error range of ±20%. The oil cooler of this study is now in commercial use. The basic research results obtained under various experimental conditions are needed for more efficient heat transfer enhancement of the product. The proposed empirical correlations of Eqs. (26) and (27) above may be used for the specification of the product and its enhancement. 4. Conclusion In this study, the turbulence generators were designed to be fixed inside the tubes of an oil cooler, and were investigated for
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