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Experimental testing of the heat exchanger with star-shaped fins
International Journal of Heat and Mass Transfer 149 (2019) 119190
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International Journal of Heat and Mass Transfer journal homepage: www.elsevier.com/locate/hmt
Experimental testing of the heat exchanger with star-shaped fins ˇ c´ c Mladen Bošnjakovic´ a,∗, Simon Muhicˇ b, Ante Ciki a
Technical Department, College of Slavonski Brod, Dr. M. Budaka 1, 35000 Slavonski Brod, Croatia Faculty of Mechanical Engineering, University of Novo mesto, Na Loko 2, 8000 Novo mesto, Slovenia c Department of Mechanical Engineering, University North, 104. brigade 3, 42000 Varaždin, Croatia b
a r t i c l e
i n f o
Article history: Received 31 July 2019 Revised 10 November 2019 Accepted 7 December 2019
Keywords: Heat exchanger Experimental testing Enhanced heat transfer Star-shaped fin
a b s t r a c t Increase of the heat flow rate by applying finned surfaces is common in gas-liquid heat exchangers. Thereby, devices with annular fins are frequently used. Demands for higher capacity lead to size and mass increase of heat exchangers which over time becomes a significant problem, especially if the application of stainless steel is required. The solution to this problem is in a more efficient heat exchange on the gas side. This paper analyses the application of stainless steel star-shaped fins which increase the turbulence of fluid flow with their shape and in that way the heat exchange. For this purpose, two heat exchangers of identical size were made: one with annular fins and one with star-shaped fins. Both heat exchangers were experimentally tested with the same equipment and under identical conditions in the Reynolds number range from 20 0 0 to 13,0 0 0. The test results indicate an increase in the heat flux by 39.3% when applying the star-shaped fins relative to annular fins, with the reduction of the heat exchanger mass by 23.8%. © 2019 Elsevier Ltd. All rights reserved.
1. Introduction The construction of smaller, lighter and more energy efficient heat exchangers have always presented a challenge for engineers. Heat transfer on the air side in this context represents the key factor. In order to increase the heat transfer, it is necessary to know the influence of the heat exchanger geometry on the heat transfer and the pressure drop. The most frequently analysed parameters are the tube outer diameter, the transverse and longitudinal tube pitch and tubes arrangement. When applying fins, the effect of the fin thickness, fins step, fin outer diameter and fin shape on heat transfer is analysed. In the last century, numerous studies have been carried out on the influence of the parameters of the heat exchanger on the heat transfer based primarily on experimental examinations. Studies show correlations for heat transfer and pressure drops most often in the form of non-dimensional numbers Nu and Eu. Correlations of Ward and Yang were used for the purpose of this study [1], ESDU company correlations (Engineering Sciences Data Unit) [2], correlation according VDI-Wärmeatlas [3] and according to Briggs [4], which includes the same tube arrangement, the same area of
∗
Corresponding author. ´ E-mail address: [email protected] (M. Bošnjakovic).
https://doi.org/10.1016/j.ijheatmasstransfer.2019.119190 0017-9310/© 2019 Elsevier Ltd. All rights reserved.
the tube and fins pitch and the same interval of Re numbers as in the experimental test. Due to the complex physical processes in heat exchangers, this topic is still very actual, and various studies are still being conducted. For example, Lee et al. [5] investigated the heat transfer coefficient on the airside in a heat exchanger with spiral fins. The influence of the flow rate and the fin pitch on the heat transfer coefficient were investigated by Watel et al. [6] and Pongsoi and Wongwises [7]. A study was conducted for Reynolds numbers (based on the outer diameter of the tube and the inlet air velocity) between 2550 and 42,0 0 0. Hofmann et al. [8] have examined heat transfer and pressure drop at different serrated and annular finned-tubes in cross-flow with aim of optimizing heat exchanger performance. The height of the fins of U and L forms, fin thickness, fin pitch and the width of the fin segment were varied. Tubes had staggered arrangement with an equal longitudinal and transverse pitch. Anoop, Balaji and Velusamy [9] investigated the heat transfer on one tube with serrated fins combining the experimental approach and numerical calculation. Lindqvist et al. [10] used ALAMO software, data from literature and Computational Fluid Dynamics to obtain increased accuracy and validity range of heat transfer and pressure drop correlations. Naess [11] experimentally tested heat transfer and pressure drop on ten geometries, with each having 32 active tubes with the
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Nomenclature A d g Eu F L Nt Nu m˙ q˙ Q˙ p R Re s t Tln T u u uA uB U x¯
λ α β η ε ρ
surface area on the air side [m2 ] diameter [m] gravity of Earth [ms−2 ] Euler numbercorrection factor [-] tube length [m] total number of tubes [-] Nusselt numbermass flux [kg/s] heat flux [W/m2 ] heat transfer rate [W] pressure [bar] thermal contact resistance [m2 K/W] Reynolds numberpitch [m] thickness [m] the logarithmic mean temperature difference [K] the average temperature [K] velocity [m/s] combined standard uncertainty random standard uncertainty of mean the systematic standard uncertainty the 95 percent confidence uncertainty the sample average the thermal conductivity [W/(m·K)] average convective heat transfer coefficient [W/(m2 ·K)] coefficient of thermal expansion of the fluid [m3 /(m3 K)] efficiency / dynamic viscosity [-] / [Pas] effectiveness [-] density [kg/m3 ]
Subscripts a air b fin base av average bl boundary layer c contact cd conduction cv convection e effective / equivalent f fin i inside l longitudinal max maximal (for ideal fin) o outside / overall r root t tube / finless tube surface area TB tube bundle tr transversal tot total uf unfinned part of tube 1 air inlet 2 air outlet
Subodh Kr. Sharma et al. [13] experimentally examined the temperature profile on fins of rectangular, trapezoidal and triangular shape. They involved four different materials: aluminium, copper, bronze and mild steel. Fins were welded to a plate which they heated to a certain temperature. The temperature was measured at predetermined fins locations. They concluded that the triangular shape of the fin was most effective for heat dissipation. Numerous methods used in computational fluid dynamics have been developed today. A review of all the methods applied today in computer fluid dynamics was given by Lokman and Fdhil [14]. Nemati [15] numerically analysed fluid flow in the annular-finned tube heat exchangers by different turbulent models. Tahrour et al. [16] experimentally and numerically compared the heat transfer characteristics and pressure drops of eccentric and concentric annular-finned tube bundles. Karl Lindqvist and Erling Næss [17] have created a heat exchanger model with four rows of serrated tubes and tested it numerically. They found that numerical simulation yields similar results as experimentally obtained and can be used to analysing the thermal performance of the heat exchangers. Bošnjakovic´ et al. [18] numerically analysed fluid flow in the heat exchangers with star-shaped fins and with annular fins. The results of the numerical analysis for star shaped fins in range 2200
l-shaped fins. Mobtil at al. [12] used infrared thermography system to experimentally determine the transient heat transfer coefficient distribution over the fin of the second row of a staggered finned tube assembly. The results of the above studies were considered in selecting the geometry of the heat exchanger that is the subject matter.
The experimentally tested tube heat exchanger consists of a total of 13 staggered tubes arranged longitudinally in five, and transversally in three rows. Thirty five fins are mechanically set on each tube. Between the tubes and fins is achieved interference fit (tight mechanical joint). Fins are very thin and are placed longitudinally to the direction of the airflow, and perpendicularly to the
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Fig. 1. The characteristic cross-section of the heat exchanger (fins in the second row of tubes are not shown). Table 1 Geometric data of fins and tubes. Fins df,o (mm) 40
Tubes df,r (mm) 27
df,i (mm) 20
tf (mm) 0.5
sf (mm) 4.5
do (mm) 20
di (mm) 17
Arrangement – Staggered
sl (mm) 40
str (mm) 50
Fig. 3. Tube with star-shaped fins. Fig. 2. Annular fin geometry (left) and innovative star-shaped fin (right).
direction of water flow. The sizes of the exchanger are selected to fit into the equipment of the test lab. Internal dimensions of the finned tube heat exchanger are 240 × 160 × 162 mm. Fig. 1 shows the characteristic cross-section of the heat exchanger. For this research, the stainless steel tube Ø20 × 1.5 mm was chosen. As a reference geometry, a stainless annular fin Ø40/Ø20 with thickness of 0.5 mm is chosen (Fig. 2, left). The innovative star-shaped fin has eight vertices uniformly distributed over the circumference (Fig. 2, right). Initial diameter, the fin thickness, and pitch were selected according to literature recommendations [1, 5, 22] and the possibilities of testing in the laboratory. Geometric data are given in Table 1. The heat exchanger prototype with star-shaped fins was first made. It was decided to fix fins to the tube by tight mechanical I-joint because hard brazing or welding requires much more time and resources (Fig. 3).
Fins were laser cutted. In order to achieve an interference fit, several test fins with an inner diameter from 0.01 to 0.06 mm smaller than the measured tube outer diameter were made. From these fins, a fin with inner diameter that provided a tight joint without the fin buckling was chosen. In this case, the fin diameter was about 0.02 mm smaller than the outer diameter of the tube. The interference fit is produced by mechanically developing contact pressure through elastic deformation of the fin. The quality of the cutted surface is good although a certain surface roughness exists. As seen from Fig. 4 on the right (annular fin) on the left part of the tube circumference the joint is good, while on the right side it is slightly worse. Fig. 5 shows the heat exchanger housing in the welded form. The water inlet and water outlet chamber can be seen on the top and bottom of housing. 2.2. Experimental facility Experimental testing of the heat exchanger prototype was carried out in the laboratory of the Faculty of Mechanical Engineering
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Fig. 4. Detail of the tight mechanical joint of the star-shaped fin (left) and the annular fin (right).
Fig. 5. Heat exchanger prototype with annular fins (left) and with star-shaped fins (right).
in Novo mesto. Fig. 6 shows a schematic diagram of a measurement line. The air and water temperatures at the inlet into the heat exchanger were measured using Pt100 platinum resistance thermometers connected to the data acquisition system and the data storage computer. The inlet and outlet air temperature were measured with one thermometer placed in the middle of the channel where the temperature of the channel cross-section was uniform. The temperature measurement point of the hot air was located 1 m away from the heat exchanger output. The measurement uncertainty of the Pt100 thermometer is ±0.01 °C in the measuring range from −200 °C to +400 °C (model ZA9030FS2). The air pressure drop was measured with a pressure transducer ALMEMO FDA602S1K. Measuring range is ±1250 Pa. The device accuracy is ± 0.5% of the measured value. For measuring the water pressure drop pressure transducer FDA 602 L was used, which works on the piezo principle. The accuracy of the device is ± 1.5% of the measured value in the range from 10 °C to 80 °C. The water flow rate was measured by the multifunctional CF Echo II instrument (Fig. 8). This is, in fact, an ultrasonic metre of heat energy, which measures temperature and flow. The measuring range of the device is from 0.6 m3 /h to 15 m3 /h, with accuracy class 2.0 according to. EN 1434. Mass airflow was determined by measuring the static pressure drop in the measuring nozzle located in the air channel upstream of the heat exchanger. A measuring nozzle was made according to VDI/VDE 2041
standard. Fig. 7 and 8 show the details of experimental measurements. All measuring instruments were pre-calibrated before application. 2.3. Experimental procedure The test was carried out on two heat exchangers: one with starshaped fins and one with annular fins with geometry as described in the previous section. The conditions in the laboratory were controlled in terms of measuring atmospheric pressure, air temperature and humidity. The first heat exchanger was placed in the test line, and measurements were made for the predefined input parameters. After that another heat exchanger was placed in the test line and measurements were made with approximately the same input parameters. The input parameters were the water and air temperature and the air velocity at the inlet to the heat exchanger. The water flow was regulated so that the water temperature difference at the inlet and outlet of heat exchanger was within the range of 3 °C to 5 °C. The experimental data were obtained for five different air-flow rates (Table 2).where umax is the air velocity in narrowest cross-section of the tube bundle. Each individual measurement was performed when a steadystate equilibrium (stationarity) of heat transfer was achieved. Temperatures, pressures and flow rates were measured each second; sampling at this rate is called instantaneous or second by second sampling. All measurement data were recorded on the computer.
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Fig. 6. Schematic diagram of the measurement line.
Fig. 7. Measurement of temperature and air pressure drop (left) and data acquisition system (right).
Fig. 8. Airflow measurement (left), flowmeter and water temperature measurement (right).
From the total time of the test (1 h), a 30-min interval is selected in which the air and water temperature oscillations are minimal, that is, the steady-state equilibrium is best achieved. To achieve repeatable data points and sets, a series of criteria for steady state equilibrium was established. Based on the propos-
als of Tartar Lupia [23] and Taylor [24], the following requirements on the stationarity are: •
changes in the air temperature at the entrance of heat exchanger during the test < 0.5 °C,
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Fig. 9. Water and air temperatures sampling data.
Table 2 Measured air-flow rates. Measurement No. Star-shaped fins Annular fins
•
•
umax (m/s) Re umax (m/s) Re
1
2
3
4
5
1.29 1493 1.28 1505
3.00 3618 2.98 3639
4.62 5575 4.55 5580
6.70 8164 6,57 8159
8.59 10,521 7.68 9496
change in the water temperature at the entrance of heat exchanger during the test < 1 °C, deviation in the heat flux during the measurement does not exceed 5%.
Furthermore, in order to be valid results, the requirement is that the difference between heat fluxes on the air side and on the water side is less than 8% (acc. ASME standard [25] proposed is less than 15%). The deviation of the water mass flow and air mass flow should be less than 5% [25]. These requirements are checked by statistical analysis of measured data. If the data do not meet the requirements, the measurement should be repeated. The objective of the experiment is to obtain relevant data to thermally and hydraulically compare two prototypes of heat exchangers. Therefore, in that way the same test conditions for both heat exchangers should be provided. Measurement results always include a certain error or a measurement uncertainty. However, as testing is carried out on the same equipment and in (approximately) the same conditions, it could be assumed that errors are of the same size and the same sign. Errors in measurement results nonlinearly affect the air and water physical properties and the calculation of the Nu number. However, if errors are kept in a sufficiently small interval, the result of the comparison of the two heat exchangers should be the same regardless of the presence of the measurement error. Therefore, in this case, it is not of the primary goal to determine the true value of the measured quantities but to ensure that they meet previously described stationarity requirements as well as additional relevance requirements based on statistical analysis. 2.4. Overview of measurement results In accordance with the methodology described in Section 2.3, measurements were performed. Fig. 9 shows the example of the
water and air temperature sampling data at the inlet and outlet of the heat exchanger for star-shaped fins at Re=10,521. Fig. 10 shows the example of the water and air flux sampling data for the same experiment. From Figs. 9 and 10, it is clear that steady state equilibrium has been achieved. Statistically processed data is presented in Table 3. U is the overall or expanded uncertainty at 95% confidence level, u is combined standard uncertainty, uA is random standard uncertainty of mean and uB is the standard uncertainty of instruments. Data for other tested air speeds for annular and star-shaped fins was processed in the same way. Input data was analysed according to the criteria set out in Section 2.3 and with regard to the measurement uncertainty. All input data met the criteria in Section 2.3. As it can be seen from the Table 3, the measurement uncertainty uA is very small. However, the measurement uncertainty of the instruments (uB ) on the air side is relatively high and has a dominant influence on the overall measurement uncertainty. The measurement uncertainty of air and water temperatures is typically ±0.1%. The measurement uncertainty of water mass flux is typically ±2%, the measurement uncertainty of air mass flux is from ±2.0% to ±2.7% for air velocities greater than 2 m/s and about ±10% for air velocity less than 2 m/s. The highest uncertainty is related to the measurement of air pressure at the outlet of tube bundle and ranges from ±0.1% to ±30%. The greatest impact on the thermal calculation results is the measurement uncertainty of the air mass. The impact of measurement uncertainty on the calculation result of the Nu and Eu numbers is analysed in Section 4.
3. Physical model of heat transfer for the analysed heat exchanger prototype The physical model of the heat transfer consists of a tube bundle through which cold air flows, input chamber in which hot water is supplied and output chamber (Fig. 11). The space of the tube bundle is bounded to the left and right sides by a 2 mm tube sheet over which convective heat transfer is performed. The space of the tube bundle is bounded from the top and bottom side by sheets of 2 mm thickness. On the outside of the housing, there is insulation (shown in Fig. 7). The tube sheets and housing sides are welded which provides good heat conductivity and heat transfer to the air. The water enters the chamber from the bottom and exits on the upper side. The water flow in the chambers is very complex
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Fig. 10. Water and air temperatures sampling data. Table 3 Measurement results for star-shaped fins (Re=10,521).
x¯ uA uB u U U (%)
Ta,1 °C
Ta,2 °C
pa,1 Pa
pa,2 Pa
ma kg/s
Tw,1 °C
Tw,2 °C
mw kg/s
19.07 0.002 0.01 0.01 0.02 0.10
26.89 0.002 0.01 0.01 0.02 0.08
194.1 0.047 0.134 0.143 0.285 0.15
10.96 0.070 0.970 0.973 1.946 17.75
0.2251 2.6E-05 0.0024 0.0024 0.0047 2.09
80.06 0.003 0.01 0.01 0.02 0.03
75.35 0.003 0.01 0.01 0.02 0.03
0.0879 2.1E-05 0.0009 0.0009 0.0018 2.00
Table 4 Correlations for local and average Nu numbers for q = const. [27]. Flow type
Local Nux number
Average Nu number
Interval of validity
Laminar Turbulent
0.453 · Re0L .5 · P r 1/3 0.0308 · Re0L .8 · P r 1/3
0.906 · Re0L .5 · P r 1/3 0.0385 · Re0L .8 · P r 1/3
Pr > 0.6 Re <5ˑ105 0.6 ≤ Pr < 60 5ˑ105 ≤ Re ≤ 107
Fig. 12. Fluids flow scheme.
Fig. 11. Physical model of heat exchanger.
and vortexing, which causes uneven flow distribution in particular tubes. The cold air passing through the heat exchanger is heated which causes the uneven temperature of the housing walls. Due to the intense mixing of water in the chambers, a constant thermal flow is assumed through the wall of the housing. Some heat
Fig. 13. Thermal resistance concept.
fluxes from the water and the housing to the air are appropriately marked. Total energy balance for the entire heat exchanger is calculated on the basis of measured data (Fig. 12). Ideally, it is valid:
Q˙ a = Q˙ w .
(1)
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Fig. 14. Resistance network representing finned tube.
According to ASHRAE 33-78, Wang et al. [26] suggest that the deviation of heat fluxes calculated on the basis of measured temperatures of air and water should not be greater than 5.0%. Also, they suggest that the experiment should be conducted at a sufficient water velocity so that water resistance is less than 15% of the total heat transfer resistance, thus ensuring accurate results for the air side heat transfer coefficient. If it is analysed the heat flux on each heat exchanger surface (Fig. 11), it can be written:
Q˙ a,K1 + Q˙ a,K2 + Q˙ a,K3 + Q˙ a,TB = Q˙ w,K1 + Q˙ w,K2 + Q˙ w,K3 + Q˙ w,TB .
(2)
The primary interest is to determine the heat flux that air receives through the tube bundle, in order to thermally compare two different fins geometries. Therefore, it is first necessary to calculate the heat flux that the air receives from the casing walls.
Q˙ a,TB = Q˙ a − Q˙ a,K1 − Q˙ a,K2 − Q˙ a,K3 .
(3)
The model of fluid flow over the flat plate is used for heat transfer on casing walls. For the calculation of the heat transfer in this experiment, the equation for the constant thermal flow is taken. It is clear that this condition is not fulfilled on all the housing plates, but the condition of the constant wall temperature is also not fulfilled, so it is estimated that the condition of the constant thermal flux gives realistic results for the concrete case. For the Re numbers up to 4·103 , the assumption of laminar flow is applied because the Re number is far below the critical. For Re numbers greater than 4·103 , which is also somewhat lower than the critical Re number, due to fins impact, it is assumed mixing of air layers and turbulent flow, so appropriate equation for turbulent flow is applied. For the calculation of the total thermal resistance, it is necessary to calculate the heat transfer coefficient inside the tubes. Tube flow analysis led to the conclusion of the equal importance of natural and forced convection. For this case correlation according to Depew and August were applied [27]:
Nu = 1.75 · Gz + 0.12 · Gz · Gr
1/3
· Pr
0.36 0.88
1/3 η 0.14 w,av · . ηw , t (4)
In equitation (4) Graetz number is defined by:
Gz =
π
,
(5)
g · β · (Tt,i − Tw,av ) · di3
(6)
4
· Re · P r ·
dt,i L
and Grasshoff number by:
Gr =
2 νav
,
where g represents acceleration of Earth’s gravity and β coefficient of thermal expansion of the fluid. After calculating the heat transfer rate in the tube bundle, in order to calculate the heat transfer coefficient at the air side, the logarithmic mean temperature difference is calculated according to the Eq. (7):
Tln = F ·
(Tw,1 − Ta,2 ) − (Tw,2 − Ta,1 ) T
−T
ln Tww,,12 −Taa,,21
.
(7)
The correction factor F corrects temperature related to the heat exchanger with counter-current flow of the fluids when applied to the heat exchanger with cross-flow of fluids and can be determined from appropriate literature, e.g. Çengel [28]. In the analysis of finned heat exchangers, several modes of heat transfer occur simultaneously. Such problems can be solved easily by the introduction of thermal resistance concepts in an analogous manner to the concept of electric circuits. In this case, the thermal resistance (R) corresponds to electrical resistance; temperature difference corresponds to voltage, and the heat transfer rate corresponds to electric current. The resistance network includes convection to the inner surface of the tube (Rw,cv )
Rw,cv =
1
αw · π · di · L · Nt
,
(8)
the conduction through the tube (Rcd )
ln
Rcd =
do di
,
2 · π · L · Nt · λt
(9)
the resistance associated with the convection from the unfinned portion of the tube
Ruf,cv =
1
αo · π · do · L · Nt ·
sf −tf sf
,
(10)
the resistance associated with the convection from the fins
Rf,cv =
1
αo · π · ηf · Af · Nf · Nt
,
(11)
and the contact resistance
Rc =
Rc
π · do · L · Nt ·
tf sf
.
(12)
The total network resistance is
Rtot = Rw,cv + Rcd +
1 Ruf,cv
1 + . Rc + Rf,cv
(13)
Also, the total network resistance can be calculated according equitation (14):
Rtot =
Tln Q˙ a,TB
.
(14)
Thermal contact resistance between fins and tube is a source of insecurity. By putting fins on the tubes mechanically, it is not possible to achieve an ideal contact between the tube and fin surface. A large number of parameters affect the amount of thermal contact resistance and no unique analytical expression that would involve different types of joints was suggested. The contact resistance depends on the initial contact pressure between the tube and fin surface, tube and fin surface roughness, the coefficient of thermal expansion of tube and fin materials, the fluid temperature inside and outside the tube, the length of the circle at which full contact was achieved and micro hardness of softer material, interface interstitial material properties and surfaces coatings. The influence of the previously mentioned parameters according to available literature was systematically investigated by H. Abdollahi et al. [29]. Seshimo [30] states that the contact resistance is usually in the range from 6·10−5 to 1·10−4 m2 K/W. Çengel [28] thinks that the most experimentally determined values of the thermal contact resistance fall between 5·10−6 and 5·10−4 m2 K/W. During the heat exchanger operation hot water flows through the tube, and cold air around the tube. Therefore, there is a certain degree of temperature difference between the tubes and fins, so the linear expansion of the tube is greater than the linear expansion of fins. As a result, the initial contact pressure between tubes and fins increases and the contact resistance decreases.
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In practice it is very difficult to accurately predict the contact resistance and most of the published works on the airside absorbed contact resistance into the airside performance. In this paper, for both heat exchangers, the same contact resistance of 1·10−4 m2 K/W is assumed. This is accordance with the assumption of Seshimo and Çengel. To calculate the actual average coefficient of heat transfer on the air side α o from equitation (13) and (14), it is necessary to know the fin efficiency ηf . The calculation of the values α o and ηf has been done iteratively in MS Excel since both variables are interrelated. Calculation method for ηf is defined by Bošnjakovic´ et al. [18] [31].. The average efficiency of the heat exchanger tube bundle is calculated according to the Eq. (15):
ηTB = 1 −
Af η 1− f . Atot C1
C1 = 1 − ηf · α0 · Af
Rc d0 · π · tf
(15)
.
(16)
Fig. 15. Comparison of the Nu number obtained by experimental testing and calculated using the literature correlation.
The effectiveness of the fin is calculated according to Eq. (17) [28].:
εf =
Af · ηf , Ab
(17)
where Ab is the cross-sectional area of the fin at the base. The efficiency of the entire tube bundle surface is calculated according to Eq. (18) [28]:
εtot =
At,uf · Nt + Af,tot · ηf . L · do · π · Nt
(18)
where Af,tot is the total surface area of all fins on the one tube, At,uf is the area of the unfinned portion of the tube outside surface and L is the tube length. Dimensionless numbers Re, Nu and Eu were calculated for the properties of the fluid at a boundary layer temperature. Nusselt number (Nu) is defined by the Eq. (19).
Nu =
αo · do . λa,bl
(19)
Fig. 16. Comparison of the Eu number obtained experimentally and calculated using the literature correlation.
Euler number (Eu) is defined by the Eq. (20).
Eu =
p , Nl · ρa,bl · u2max
(20)
where Nl is a number of tube rows in the longitudinal direction, and ρ a,bl air density at the boundary layer temperature, and λa,bl thermal conductivity of the air at the temperature of the boundary layer. The heat flux is calculated according to the expression:
q˙ A =
Q˙ a . Atot
(21)
The heat flow per unit mass of the tube bundle is equal to:
q˙ m =
Q˙ a . mtot
(22) Fig. 17. Fins efficiency.
4. Results The results obtained by experimental testing were compared with ordinary literature correlations [1], [2], [3], [4]. From Fig. 15 it can be seen that the Nu number for heat exchanger with annular fins matches literature correlations. As expected, Nu number for heat exchanger with star-shaped fins is higher than for annular fins. For Re=1500 the difference is about 16.5%, and for Re=10,500 the difference is about 18.6%. From Fig. 16 it can be seen that the Eu number for heat exchanger with annular fins matches literature correlations. The
value of the Eu number for star-shaped fins is lower by 13% to 14% compared to annular fins. The fin efficiency depends on the conduction in the fin, convention to the fin, shape of the fin and the sizes of the fin. The fin efficiency decreases with Re increase. Fig. 17 shows fins efficiency for star-shaped fins and annular fins. Distance between curves increases slightly with increasing Re. The efficiency of star-shaped fins compared to annular fins is greater from 5.7% to 16.1% regarding to the Re number.
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Fig. 18. Fins effectiveness.
Fig. 21. Comparison of the heat flux for annular and star-shaped fins.
Fig. 19. The efficiency of the tube bundle surface area.
Fig. 22. Comparison of the heat flow rate per kg of tube bundle for annular and star-shaped fins.
Fig. 20. The tube bundle effectiveness for annular and star-shaped fins.
The effectiveness of the annular fin (Fig. 18) is greater than the star-shaped fin due to the larger surface of annular fins. By increasing the Re number, the fin’s effectiveness decreases due to the fin’s efficiency decreases. The effectiveness of annular fins compared to star-shaped fins rises up from 32% to 38% regarding to the Re number. An illustration of the efficiency of the tube bundle surface is given in Fig. 19. However, the tube bundle surface effectiveness of annular fins compared to star-shaped fins is greater from 24.5% to 32.5% regarding to the Re number.
The heat exchanger with star-shaped fins has a thermal flux greater from 35.5% to 55.8% compared to the heat exchanger with annular fins (Fig. 21). This means that for the same materials, operating conditions and the same heat flux heat exchanger with starshaped fins can have up to 55.8% less surface area in observed range of Re numbers and for stainless steel fins. The star-shaped fins heat exchanger has a heat flow rate per unit of mass greater than 12.2% for lower Re and 29% for higher Re compared to the annular finned heat exchanger (Fig. 22). This is a relative indicator of reducing the mass of the tube bundle because it depends on the ratio of the fin and tube mass. For example, if the tube had a wall thickness of 0.5 mm instead of a wall thickness of 1.5 mm, for Re=1500 the heat flow rate per mass unit would be 372 W/kg for star-shaped fins and 286 W/kg for annular fins (if ignored change of heat resistance through the tube wall). In this case, the difference of the heat flows rate per kg of the tube bundle is 30%. For all tested variants, the weight of the star-shaped fin compared to the mass of the annular fin is 43.5% lower. The tube bundle includes tubes and fins. In this sense, the mass reduction is 23.5%. The share of the heat flow through the heat exchanger casing is about 15% of the total heat flow. The influence of measurement uncertainty on the calculation of Nu and Eu was made by incorporating the upper or lower limits of measured temperature (T ± U), mass flux (m ± U) and pressure (p ± U) in the thermal calculation. The sensitivity of the calculation results to the measurement uncertainty is shown in Figs. 23 and 24.
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tube bundle mass by 23.5% compared to the heat exchanger with annular fins. For applications were it is important that the heat exchanger has small mass and size, the application of star-shaped fins may be good choice. Further research related to optimization of geometry of star-shaped fins is needed to obtain a final evolution of the starshaped fins. This research did not receive any specific grant from funding agencies in the public, commercial, or not-for-profit sectors. Declaration Competing Interest
Fig. 23. The influence of measurement uncertainty on the calculation of Nu.
We wish to confirm that there are no known conflicts of interest associated with this publication and there has been no significant financial support for this work that could have influenced its outcome. We confirm that the manuscript has been read and approved by all named authors and that there are no other persons who satisfied the criteria for authorship but are not listed. We further confirm that the order of authors listed in the manuscript has been approved by all of us. We confirm that we have given due consideration to the protection of intellectual property associated with this work and that there are no impediments to publication, including the timing of publication, with respect to intellectual property. In so doing we confirm that we have followed the regulations of our institutions concerning intellectual property. References
Fig. 24. The influence of measurement uncertainty on the calculation of Eu.
The deviation of Nu for the star-shaped fins is from −5.6% to +6.1%, and for the annular fins the deviation is from −6.2% to 7.1%. The deviation of the Eu for the star-shaped fins is from +3.3% to −4.1%, and the Eu deviation for the annular fins is from +2.8% to −4.1% (Fig. 24). Since measurements are carried out with the same equipment, it can be assumed that the deviations of the measured values is in the same direction. In that sense, it can be said that the impact of measurement uncertainty is up to 1% related to the Nu number and about 0.5% related to the Eu number. 5. Conclusions Two finned heat exchanger of the same sizes and construction, made from stainless steel, were tested experimentally. One heat exchanger had annular fins and the other had star-shaped fins. The testing of both heat exchangers was carried out at almost the same input parameters. The defined stationary conditions for this type of testing were met. In this way, the same conditions of fluid flow and heat exchange in the tested heat exchangers are created, so it is possible to compare the obtained results. The annular heat exchanger was used as a standard heat exchanger and the results of its testing were compared with the corresponding results from the literature. The obtained test results are well-aligned with the literature results, so it can be concluded that the test was performed correctly. A comparison of annular and star-shaped finned tubes revealed a general increase in the air-side heat transfer coefficient within the investigated Reynolds numbers range. The experimental results indicate that the heat exchanger with star-shaped fins has an increase in heat transfer coefficient from 16.5% to 18.5%, and the increase in the heat flux from 35.5% to 55.8% with a reduction of the
[1] D.J. Ward, E.H. Young, Heat transfer and pressure drop of air in forced convection across triangular pitch banks of finned tubes, Chem. Eng. Progr. Symp. Ser. 55 (1959) 37–44. [2] ESDU, High-fin staggered tube banks: heat transfer and pressure drop for turbulent single phase gas flow, 1986. [3] S. Kabelac, M. Kind, H. Martin, D. Mewes, K. Schaber, P. Stephan, VDIWärmeatlas, 11. Auflage, 2013. doi:10.1007/978-3-642-19981-3. [4] D.E. Briggs, E.H. Young, Convection heat transfer and pressure drop of air flowing across triangular pitch banks of finned tubes, Chem. Eng. Progr. Symp. 59 (1963) 1–10. [5] M. Lee, T. Kang, Y. Kim, Air-side heat transfer characteristics of spiral-type circular fin-tube heat exchangers, Int. J. Refrig. 33 (2010) 313–320, doi:10.1016/j. ijrefrig.2009.09.019. [6] B. Watel, S. Harmand, B. Desmet, Influence of flow velocity and influence of flow velocity and fin spacing on the forced convective heat transfer from an annular-finned tube, JSME Int. J. Ser. B 42 (1999) 56–64, doi:10.1299/jsmeb.42. 56. [7] P. Pongsoi, S. Wongwises, Determination of Fin Pitches for Maximum Performance Index of L-Footed Spiral Fin-and-Tube Heat Exchangers, J. Therm. Eng. 1 (1) (2015) 251–262. [8] R. Hofmann, F. Frasz, K. Ponweiser, Heat transfer and pressure drop performance comparison of finned-tube bundles in forced convection, WSEAS Trans. Heat Mass Transf. 2 (2007) 72–88 http://www.wseas.us/e-library/transactions/ heat/2007/25-669N.pdf. [9] B. Anoop, C. Balaji, K. Velusamy, A characteristic correlation for heat transfer over serrated finned tubes, Ann. Nuclear Energy 85 (2015) 1052–1065, doi:10. 1016/j.anucene.2015.07.025. [10] K. Lindqvist, Z.T. Wilson, E. Næss, N.V. Sahinidis, A machine learning approach to correlation development applied to fin-tube bundle heat exchangers, Energies 11 (2018) 1–16, doi:10.3390/en11123450. [11] E. Næss, Experimental investigation of heat transfer and pressure drop in serrated-fin tube bundles with staggered tube layouts, Appl. Therm. Eng. 30 (2010) 1531–1537. [12] M. Mobtil, D. Bougeard, S. Russeil, Experimental study of inverse identification of unsteady heat transfer coefficient in a fin and tube heat exchanger assembly, Int. J. Heat Mass Transf. 125 (2018) 17–31, doi:10.1016/j.ijheatmasstransfer. 2018.04.028. [13] S.K. Sharma, A. Kumar, P. Kumari, Experimental investigation of temperature in fins, Int. J. Appl. Eng. Res. 13 (2018) 354–357 http://www.ripublication.com. [14] M.L. Hosain, R.B. Fdhila, Literature review of accelerated cfd simulation methods towards online application, Energy Procedia 75 (2015) 3307–3314, doi:10. 1016/j.egypro.2015.07.714. [15] H. Nemati, S. Samivand, Numerical study of flow over annular-finned tube heat exchangers by different turbulent models, CFD Lett. 6 (2014) 101–112. [16] F. Tahrour, A.H. Benmachiche, M. Aksas, C. Bougriou, 3-D Numerical study and comparison of eccentric and concentric annular-finned tube heat exchangers, J. Eng. Sci. Technol. 10 (2015) 1508–1524.
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[17] K. Lindqvist, E. Næss, A validated cfd model of plain and serrated fin-tube bundles, Appl. Therm. Eng. 143 (2018) 72–79, doi:10.1016/J.APPLTHERMALENG. 2018.07.060. ˇ c, ´ A. Ciki ´ S. Muhicˇ , M. Stojkov, Development of a new [18] M. Bošnjakovic, type of finned heat exchanger, Tehnical Gazette (2017) 24, doi:10.17559/ TV-20171011071711. [19] H.J. Lee, J. Ryu, S.H. Lee, Influence of perforated fin on flow characteristics and thermal performance in spiral finned-tube heat exchanger, Energies (2019) 12, doi:10.3390/en12030556. [20] X. Liu, J. Yu, G. Yan, A numerical study on the air-side heat transfer of perforated finned-tube heat exchangers with large fin pitches, Int. J. Heat Mass Transf. 100 (2016) 199–207, doi:10.1016/j.ijheatmasstransfer.2016.04.081. [21] I. Fourar, A.H. Benmachiche, S. Abboudi, Effect of material and geometric parameters on natural convection heat transfer over an eccentric annularfinned tube, Int. J. Ambient Energy 0 (2019) 1–19, doi:10.1080/01430750.2019. 1573757. [22] G. Xie, Q. Wang, B. Sunden, Parametric study and multiple correlations on airside heat transfer and friction characteristics of fin-and-tube heat exchangers with large number of large-diameter tube rows, Appl. Therm. Eng. 29 (2009) 1–16, doi:10.1016/j.applthermaleng.2008.01.014. [23] R. Tatara, G. Lupia, Assessing heat exchanger performance data using temperature measurement uncertainty, Int. J. Eng. Sci. Technol. 3 (2011) 1–12 http://dx.doi.org/10.4314/ijest.v3i8.1.
[24] C. Taylor, Measurement of finned-tube heat exchanger performance measurement of finned-tube heat exchanger, Georgia Institute of Technology, 2004. [25] ASME PTC 30-1991, ASME performance test codes - Code on air cooled heat exchangers, (1991). [26] C.C. Wang, R.L. Webb, K.Y. Chi, Data reduction for air-side performance of finand-tube heat exchangers, Exp. Thermal Fluid Sci. 21 (20 0 0) 218–226, doi:10. 1016/S0894-1777(0 0)0 0 0 05-4. [27] C.A. Depew, S.E. August, Heat transfer due to combined, J. Heat Transf. 93 (1971) 380–384, doi:10.1115/1.3449834. [28] Y.A. Çengel, Heat Transfer: A Practical Approach, McGraw-Hill, New York, 2003, doi:10.1017/CBO9781107415324.004. [29] H. Abdollahi, S. Shahraki, M. Motahari-Nezhad, A review on the effects of different parameters on contact heat transfer, Thermophys. Aeromech. 24 (2017) 499–512, doi:10.1134/s0869864317040011. [30] M. Seshimo, Y.i Fujii, An experimental study of the performance of plate fin and tube heat exchangers at low Reynolds number, in: Proceedings of the Third ASME/JSME Thermal Engineering Joint Conference, 1991, p. 449. ˇ c, ´ A. Ciki ´ S. Muhicˇ , M. Stojkov, Tube heat exchanger with new [31] M. Bošnjakovic, star shaped fins, in: Proceedings of the IOP Conference Series: Materials Science and Engineering, 2018, doi:10.1088/1757-899X/393/1/012071.
Contents lists available at ScienceDirect
International Journal of Heat and Mass Transfer journal homepage: www.elsevier.com/locate/hmt
Experimental testing of the heat exchanger with star-shaped fins ˇ c´ c Mladen Bošnjakovic´ a,∗, Simon Muhicˇ b, Ante Ciki a
Technical Department, College of Slavonski Brod, Dr. M. Budaka 1, 35000 Slavonski Brod, Croatia Faculty of Mechanical Engineering, University of Novo mesto, Na Loko 2, 8000 Novo mesto, Slovenia c Department of Mechanical Engineering, University North, 104. brigade 3, 42000 Varaždin, Croatia b
a r t i c l e
i n f o
Article history: Received 31 July 2019 Revised 10 November 2019 Accepted 7 December 2019
Keywords: Heat exchanger Experimental testing Enhanced heat transfer Star-shaped fin
a b s t r a c t Increase of the heat flow rate by applying finned surfaces is common in gas-liquid heat exchangers. Thereby, devices with annular fins are frequently used. Demands for higher capacity lead to size and mass increase of heat exchangers which over time becomes a significant problem, especially if the application of stainless steel is required. The solution to this problem is in a more efficient heat exchange on the gas side. This paper analyses the application of stainless steel star-shaped fins which increase the turbulence of fluid flow with their shape and in that way the heat exchange. For this purpose, two heat exchangers of identical size were made: one with annular fins and one with star-shaped fins. Both heat exchangers were experimentally tested with the same equipment and under identical conditions in the Reynolds number range from 20 0 0 to 13,0 0 0. The test results indicate an increase in the heat flux by 39.3% when applying the star-shaped fins relative to annular fins, with the reduction of the heat exchanger mass by 23.8%. © 2019 Elsevier Ltd. All rights reserved.
1. Introduction The construction of smaller, lighter and more energy efficient heat exchangers have always presented a challenge for engineers. Heat transfer on the air side in this context represents the key factor. In order to increase the heat transfer, it is necessary to know the influence of the heat exchanger geometry on the heat transfer and the pressure drop. The most frequently analysed parameters are the tube outer diameter, the transverse and longitudinal tube pitch and tubes arrangement. When applying fins, the effect of the fin thickness, fins step, fin outer diameter and fin shape on heat transfer is analysed. In the last century, numerous studies have been carried out on the influence of the parameters of the heat exchanger on the heat transfer based primarily on experimental examinations. Studies show correlations for heat transfer and pressure drops most often in the form of non-dimensional numbers Nu and Eu. Correlations of Ward and Yang were used for the purpose of this study [1], ESDU company correlations (Engineering Sciences Data Unit) [2], correlation according VDI-Wärmeatlas [3] and according to Briggs [4], which includes the same tube arrangement, the same area of
∗
Corresponding author. ´ E-mail address: [email protected] (M. Bošnjakovic).
https://doi.org/10.1016/j.ijheatmasstransfer.2019.119190 0017-9310/© 2019 Elsevier Ltd. All rights reserved.
the tube and fins pitch and the same interval of Re numbers as in the experimental test. Due to the complex physical processes in heat exchangers, this topic is still very actual, and various studies are still being conducted. For example, Lee et al. [5] investigated the heat transfer coefficient on the airside in a heat exchanger with spiral fins. The influence of the flow rate and the fin pitch on the heat transfer coefficient were investigated by Watel et al. [6] and Pongsoi and Wongwises [7]. A study was conducted for Reynolds numbers (based on the outer diameter of the tube and the inlet air velocity) between 2550 and 42,0 0 0. Hofmann et al. [8] have examined heat transfer and pressure drop at different serrated and annular finned-tubes in cross-flow with aim of optimizing heat exchanger performance. The height of the fins of U and L forms, fin thickness, fin pitch and the width of the fin segment were varied. Tubes had staggered arrangement with an equal longitudinal and transverse pitch. Anoop, Balaji and Velusamy [9] investigated the heat transfer on one tube with serrated fins combining the experimental approach and numerical calculation. Lindqvist et al. [10] used ALAMO software, data from literature and Computational Fluid Dynamics to obtain increased accuracy and validity range of heat transfer and pressure drop correlations. Naess [11] experimentally tested heat transfer and pressure drop on ten geometries, with each having 32 active tubes with the
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Nomenclature A d g Eu F L Nt Nu m˙ q˙ Q˙ p R Re s t Tln T u u uA uB U x¯
λ α β η ε ρ
surface area on the air side [m2 ] diameter [m] gravity of Earth [ms−2 ] Euler numbercorrection factor [-] tube length [m] total number of tubes [-] Nusselt numbermass flux [kg/s] heat flux [W/m2 ] heat transfer rate [W] pressure [bar] thermal contact resistance [m2 K/W] Reynolds numberpitch [m] thickness [m] the logarithmic mean temperature difference [K] the average temperature [K] velocity [m/s] combined standard uncertainty random standard uncertainty of mean the systematic standard uncertainty the 95 percent confidence uncertainty the sample average the thermal conductivity [W/(m·K)] average convective heat transfer coefficient [W/(m2 ·K)] coefficient of thermal expansion of the fluid [m3 /(m3 K)] efficiency / dynamic viscosity [-] / [Pas] effectiveness [-] density [kg/m3 ]
Subscripts a air b fin base av average bl boundary layer c contact cd conduction cv convection e effective / equivalent f fin i inside l longitudinal max maximal (for ideal fin) o outside / overall r root t tube / finless tube surface area TB tube bundle tr transversal tot total uf unfinned part of tube 1 air inlet 2 air outlet
Subodh Kr. Sharma et al. [13] experimentally examined the temperature profile on fins of rectangular, trapezoidal and triangular shape. They involved four different materials: aluminium, copper, bronze and mild steel. Fins were welded to a plate which they heated to a certain temperature. The temperature was measured at predetermined fins locations. They concluded that the triangular shape of the fin was most effective for heat dissipation. Numerous methods used in computational fluid dynamics have been developed today. A review of all the methods applied today in computer fluid dynamics was given by Lokman and Fdhil [14]. Nemati [15] numerically analysed fluid flow in the annular-finned tube heat exchangers by different turbulent models. Tahrour et al. [16] experimentally and numerically compared the heat transfer characteristics and pressure drops of eccentric and concentric annular-finned tube bundles. Karl Lindqvist and Erling Næss [17] have created a heat exchanger model with four rows of serrated tubes and tested it numerically. They found that numerical simulation yields similar results as experimentally obtained and can be used to analysing the thermal performance of the heat exchangers. Bošnjakovic´ et al. [18] numerically analysed fluid flow in the heat exchangers with star-shaped fins and with annular fins. The results of the numerical analysis for star shaped fins in range 2200
l-shaped fins. Mobtil at al. [12] used infrared thermography system to experimentally determine the transient heat transfer coefficient distribution over the fin of the second row of a staggered finned tube assembly. The results of the above studies were considered in selecting the geometry of the heat exchanger that is the subject matter.
The experimentally tested tube heat exchanger consists of a total of 13 staggered tubes arranged longitudinally in five, and transversally in three rows. Thirty five fins are mechanically set on each tube. Between the tubes and fins is achieved interference fit (tight mechanical joint). Fins are very thin and are placed longitudinally to the direction of the airflow, and perpendicularly to the
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Fig. 1. The characteristic cross-section of the heat exchanger (fins in the second row of tubes are not shown). Table 1 Geometric data of fins and tubes. Fins df,o (mm) 40
Tubes df,r (mm) 27
df,i (mm) 20
tf (mm) 0.5
sf (mm) 4.5
do (mm) 20
di (mm) 17
Arrangement – Staggered
sl (mm) 40
str (mm) 50
Fig. 3. Tube with star-shaped fins. Fig. 2. Annular fin geometry (left) and innovative star-shaped fin (right).
direction of water flow. The sizes of the exchanger are selected to fit into the equipment of the test lab. Internal dimensions of the finned tube heat exchanger are 240 × 160 × 162 mm. Fig. 1 shows the characteristic cross-section of the heat exchanger. For this research, the stainless steel tube Ø20 × 1.5 mm was chosen. As a reference geometry, a stainless annular fin Ø40/Ø20 with thickness of 0.5 mm is chosen (Fig. 2, left). The innovative star-shaped fin has eight vertices uniformly distributed over the circumference (Fig. 2, right). Initial diameter, the fin thickness, and pitch were selected according to literature recommendations [1, 5, 22] and the possibilities of testing in the laboratory. Geometric data are given in Table 1. The heat exchanger prototype with star-shaped fins was first made. It was decided to fix fins to the tube by tight mechanical I-joint because hard brazing or welding requires much more time and resources (Fig. 3).
Fins were laser cutted. In order to achieve an interference fit, several test fins with an inner diameter from 0.01 to 0.06 mm smaller than the measured tube outer diameter were made. From these fins, a fin with inner diameter that provided a tight joint without the fin buckling was chosen. In this case, the fin diameter was about 0.02 mm smaller than the outer diameter of the tube. The interference fit is produced by mechanically developing contact pressure through elastic deformation of the fin. The quality of the cutted surface is good although a certain surface roughness exists. As seen from Fig. 4 on the right (annular fin) on the left part of the tube circumference the joint is good, while on the right side it is slightly worse. Fig. 5 shows the heat exchanger housing in the welded form. The water inlet and water outlet chamber can be seen on the top and bottom of housing. 2.2. Experimental facility Experimental testing of the heat exchanger prototype was carried out in the laboratory of the Faculty of Mechanical Engineering
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Fig. 4. Detail of the tight mechanical joint of the star-shaped fin (left) and the annular fin (right).
Fig. 5. Heat exchanger prototype with annular fins (left) and with star-shaped fins (right).
in Novo mesto. Fig. 6 shows a schematic diagram of a measurement line. The air and water temperatures at the inlet into the heat exchanger were measured using Pt100 platinum resistance thermometers connected to the data acquisition system and the data storage computer. The inlet and outlet air temperature were measured with one thermometer placed in the middle of the channel where the temperature of the channel cross-section was uniform. The temperature measurement point of the hot air was located 1 m away from the heat exchanger output. The measurement uncertainty of the Pt100 thermometer is ±0.01 °C in the measuring range from −200 °C to +400 °C (model ZA9030FS2). The air pressure drop was measured with a pressure transducer ALMEMO FDA602S1K. Measuring range is ±1250 Pa. The device accuracy is ± 0.5% of the measured value. For measuring the water pressure drop pressure transducer FDA 602 L was used, which works on the piezo principle. The accuracy of the device is ± 1.5% of the measured value in the range from 10 °C to 80 °C. The water flow rate was measured by the multifunctional CF Echo II instrument (Fig. 8). This is, in fact, an ultrasonic metre of heat energy, which measures temperature and flow. The measuring range of the device is from 0.6 m3 /h to 15 m3 /h, with accuracy class 2.0 according to. EN 1434. Mass airflow was determined by measuring the static pressure drop in the measuring nozzle located in the air channel upstream of the heat exchanger. A measuring nozzle was made according to VDI/VDE 2041
standard. Fig. 7 and 8 show the details of experimental measurements. All measuring instruments were pre-calibrated before application. 2.3. Experimental procedure The test was carried out on two heat exchangers: one with starshaped fins and one with annular fins with geometry as described in the previous section. The conditions in the laboratory were controlled in terms of measuring atmospheric pressure, air temperature and humidity. The first heat exchanger was placed in the test line, and measurements were made for the predefined input parameters. After that another heat exchanger was placed in the test line and measurements were made with approximately the same input parameters. The input parameters were the water and air temperature and the air velocity at the inlet to the heat exchanger. The water flow was regulated so that the water temperature difference at the inlet and outlet of heat exchanger was within the range of 3 °C to 5 °C. The experimental data were obtained for five different air-flow rates (Table 2).where umax is the air velocity in narrowest cross-section of the tube bundle. Each individual measurement was performed when a steadystate equilibrium (stationarity) of heat transfer was achieved. Temperatures, pressures and flow rates were measured each second; sampling at this rate is called instantaneous or second by second sampling. All measurement data were recorded on the computer.
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Fig. 6. Schematic diagram of the measurement line.
Fig. 7. Measurement of temperature and air pressure drop (left) and data acquisition system (right).
Fig. 8. Airflow measurement (left), flowmeter and water temperature measurement (right).
From the total time of the test (1 h), a 30-min interval is selected in which the air and water temperature oscillations are minimal, that is, the steady-state equilibrium is best achieved. To achieve repeatable data points and sets, a series of criteria for steady state equilibrium was established. Based on the propos-
als of Tartar Lupia [23] and Taylor [24], the following requirements on the stationarity are: •
changes in the air temperature at the entrance of heat exchanger during the test < 0.5 °C,
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Fig. 9. Water and air temperatures sampling data.
Table 2 Measured air-flow rates. Measurement No. Star-shaped fins Annular fins
•
•
umax (m/s) Re umax (m/s) Re
1
2
3
4
5
1.29 1493 1.28 1505
3.00 3618 2.98 3639
4.62 5575 4.55 5580
6.70 8164 6,57 8159
8.59 10,521 7.68 9496
change in the water temperature at the entrance of heat exchanger during the test < 1 °C, deviation in the heat flux during the measurement does not exceed 5%.
Furthermore, in order to be valid results, the requirement is that the difference between heat fluxes on the air side and on the water side is less than 8% (acc. ASME standard [25] proposed is less than 15%). The deviation of the water mass flow and air mass flow should be less than 5% [25]. These requirements are checked by statistical analysis of measured data. If the data do not meet the requirements, the measurement should be repeated. The objective of the experiment is to obtain relevant data to thermally and hydraulically compare two prototypes of heat exchangers. Therefore, in that way the same test conditions for both heat exchangers should be provided. Measurement results always include a certain error or a measurement uncertainty. However, as testing is carried out on the same equipment and in (approximately) the same conditions, it could be assumed that errors are of the same size and the same sign. Errors in measurement results nonlinearly affect the air and water physical properties and the calculation of the Nu number. However, if errors are kept in a sufficiently small interval, the result of the comparison of the two heat exchangers should be the same regardless of the presence of the measurement error. Therefore, in this case, it is not of the primary goal to determine the true value of the measured quantities but to ensure that they meet previously described stationarity requirements as well as additional relevance requirements based on statistical analysis. 2.4. Overview of measurement results In accordance with the methodology described in Section 2.3, measurements were performed. Fig. 9 shows the example of the
water and air temperature sampling data at the inlet and outlet of the heat exchanger for star-shaped fins at Re=10,521. Fig. 10 shows the example of the water and air flux sampling data for the same experiment. From Figs. 9 and 10, it is clear that steady state equilibrium has been achieved. Statistically processed data is presented in Table 3. U is the overall or expanded uncertainty at 95% confidence level, u is combined standard uncertainty, uA is random standard uncertainty of mean and uB is the standard uncertainty of instruments. Data for other tested air speeds for annular and star-shaped fins was processed in the same way. Input data was analysed according to the criteria set out in Section 2.3 and with regard to the measurement uncertainty. All input data met the criteria in Section 2.3. As it can be seen from the Table 3, the measurement uncertainty uA is very small. However, the measurement uncertainty of the instruments (uB ) on the air side is relatively high and has a dominant influence on the overall measurement uncertainty. The measurement uncertainty of air and water temperatures is typically ±0.1%. The measurement uncertainty of water mass flux is typically ±2%, the measurement uncertainty of air mass flux is from ±2.0% to ±2.7% for air velocities greater than 2 m/s and about ±10% for air velocity less than 2 m/s. The highest uncertainty is related to the measurement of air pressure at the outlet of tube bundle and ranges from ±0.1% to ±30%. The greatest impact on the thermal calculation results is the measurement uncertainty of the air mass. The impact of measurement uncertainty on the calculation result of the Nu and Eu numbers is analysed in Section 4.
3. Physical model of heat transfer for the analysed heat exchanger prototype The physical model of the heat transfer consists of a tube bundle through which cold air flows, input chamber in which hot water is supplied and output chamber (Fig. 11). The space of the tube bundle is bounded to the left and right sides by a 2 mm tube sheet over which convective heat transfer is performed. The space of the tube bundle is bounded from the top and bottom side by sheets of 2 mm thickness. On the outside of the housing, there is insulation (shown in Fig. 7). The tube sheets and housing sides are welded which provides good heat conductivity and heat transfer to the air. The water enters the chamber from the bottom and exits on the upper side. The water flow in the chambers is very complex
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Fig. 10. Water and air temperatures sampling data. Table 3 Measurement results for star-shaped fins (Re=10,521).
x¯ uA uB u U U (%)
Ta,1 °C
Ta,2 °C
pa,1 Pa
pa,2 Pa
ma kg/s
Tw,1 °C
Tw,2 °C
mw kg/s
19.07 0.002 0.01 0.01 0.02 0.10
26.89 0.002 0.01 0.01 0.02 0.08
194.1 0.047 0.134 0.143 0.285 0.15
10.96 0.070 0.970 0.973 1.946 17.75
0.2251 2.6E-05 0.0024 0.0024 0.0047 2.09
80.06 0.003 0.01 0.01 0.02 0.03
75.35 0.003 0.01 0.01 0.02 0.03
0.0879 2.1E-05 0.0009 0.0009 0.0018 2.00
Table 4 Correlations for local and average Nu numbers for q = const. [27]. Flow type
Local Nux number
Average Nu number
Interval of validity
Laminar Turbulent
0.453 · Re0L .5 · P r 1/3 0.0308 · Re0L .8 · P r 1/3
0.906 · Re0L .5 · P r 1/3 0.0385 · Re0L .8 · P r 1/3
Pr > 0.6 Re <5ˑ105 0.6 ≤ Pr < 60 5ˑ105 ≤ Re ≤ 107
Fig. 12. Fluids flow scheme.
Fig. 11. Physical model of heat exchanger.
and vortexing, which causes uneven flow distribution in particular tubes. The cold air passing through the heat exchanger is heated which causes the uneven temperature of the housing walls. Due to the intense mixing of water in the chambers, a constant thermal flow is assumed through the wall of the housing. Some heat
Fig. 13. Thermal resistance concept.
fluxes from the water and the housing to the air are appropriately marked. Total energy balance for the entire heat exchanger is calculated on the basis of measured data (Fig. 12). Ideally, it is valid:
Q˙ a = Q˙ w .
(1)
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Fig. 14. Resistance network representing finned tube.
According to ASHRAE 33-78, Wang et al. [26] suggest that the deviation of heat fluxes calculated on the basis of measured temperatures of air and water should not be greater than 5.0%. Also, they suggest that the experiment should be conducted at a sufficient water velocity so that water resistance is less than 15% of the total heat transfer resistance, thus ensuring accurate results for the air side heat transfer coefficient. If it is analysed the heat flux on each heat exchanger surface (Fig. 11), it can be written:
Q˙ a,K1 + Q˙ a,K2 + Q˙ a,K3 + Q˙ a,TB = Q˙ w,K1 + Q˙ w,K2 + Q˙ w,K3 + Q˙ w,TB .
(2)
The primary interest is to determine the heat flux that air receives through the tube bundle, in order to thermally compare two different fins geometries. Therefore, it is first necessary to calculate the heat flux that the air receives from the casing walls.
Q˙ a,TB = Q˙ a − Q˙ a,K1 − Q˙ a,K2 − Q˙ a,K3 .
(3)
The model of fluid flow over the flat plate is used for heat transfer on casing walls. For the calculation of the heat transfer in this experiment, the equation for the constant thermal flow is taken. It is clear that this condition is not fulfilled on all the housing plates, but the condition of the constant wall temperature is also not fulfilled, so it is estimated that the condition of the constant thermal flux gives realistic results for the concrete case. For the Re numbers up to 4·103 , the assumption of laminar flow is applied because the Re number is far below the critical. For Re numbers greater than 4·103 , which is also somewhat lower than the critical Re number, due to fins impact, it is assumed mixing of air layers and turbulent flow, so appropriate equation for turbulent flow is applied. For the calculation of the total thermal resistance, it is necessary to calculate the heat transfer coefficient inside the tubes. Tube flow analysis led to the conclusion of the equal importance of natural and forced convection. For this case correlation according to Depew and August were applied [27]:
Nu = 1.75 · Gz + 0.12 · Gz · Gr
1/3
· Pr
0.36 0.88
1/3 η 0.14 w,av · . ηw , t (4)
In equitation (4) Graetz number is defined by:
Gz =
π
,
(5)
g · β · (Tt,i − Tw,av ) · di3
(6)
4
· Re · P r ·
dt,i L
and Grasshoff number by:
Gr =
2 νav
,
where g represents acceleration of Earth’s gravity and β coefficient of thermal expansion of the fluid. After calculating the heat transfer rate in the tube bundle, in order to calculate the heat transfer coefficient at the air side, the logarithmic mean temperature difference is calculated according to the Eq. (7):
Tln = F ·
(Tw,1 − Ta,2 ) − (Tw,2 − Ta,1 ) T
−T
ln Tww,,12 −Taa,,21
.
(7)
The correction factor F corrects temperature related to the heat exchanger with counter-current flow of the fluids when applied to the heat exchanger with cross-flow of fluids and can be determined from appropriate literature, e.g. Çengel [28]. In the analysis of finned heat exchangers, several modes of heat transfer occur simultaneously. Such problems can be solved easily by the introduction of thermal resistance concepts in an analogous manner to the concept of electric circuits. In this case, the thermal resistance (R) corresponds to electrical resistance; temperature difference corresponds to voltage, and the heat transfer rate corresponds to electric current. The resistance network includes convection to the inner surface of the tube (Rw,cv )
Rw,cv =
1
αw · π · di · L · Nt
,
(8)
the conduction through the tube (Rcd )
ln
Rcd =
do di
,
2 · π · L · Nt · λt
(9)
the resistance associated with the convection from the unfinned portion of the tube
Ruf,cv =
1
αo · π · do · L · Nt ·
sf −tf sf
,
(10)
the resistance associated with the convection from the fins
Rf,cv =
1
αo · π · ηf · Af · Nf · Nt
,
(11)
and the contact resistance
Rc =
Rc
π · do · L · Nt ·
tf sf
.
(12)
The total network resistance is
Rtot = Rw,cv + Rcd +
1 Ruf,cv
1 + . Rc + Rf,cv
(13)
Also, the total network resistance can be calculated according equitation (14):
Rtot =
Tln Q˙ a,TB
.
(14)
Thermal contact resistance between fins and tube is a source of insecurity. By putting fins on the tubes mechanically, it is not possible to achieve an ideal contact between the tube and fin surface. A large number of parameters affect the amount of thermal contact resistance and no unique analytical expression that would involve different types of joints was suggested. The contact resistance depends on the initial contact pressure between the tube and fin surface, tube and fin surface roughness, the coefficient of thermal expansion of tube and fin materials, the fluid temperature inside and outside the tube, the length of the circle at which full contact was achieved and micro hardness of softer material, interface interstitial material properties and surfaces coatings. The influence of the previously mentioned parameters according to available literature was systematically investigated by H. Abdollahi et al. [29]. Seshimo [30] states that the contact resistance is usually in the range from 6·10−5 to 1·10−4 m2 K/W. Çengel [28] thinks that the most experimentally determined values of the thermal contact resistance fall between 5·10−6 and 5·10−4 m2 K/W. During the heat exchanger operation hot water flows through the tube, and cold air around the tube. Therefore, there is a certain degree of temperature difference between the tubes and fins, so the linear expansion of the tube is greater than the linear expansion of fins. As a result, the initial contact pressure between tubes and fins increases and the contact resistance decreases.
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In practice it is very difficult to accurately predict the contact resistance and most of the published works on the airside absorbed contact resistance into the airside performance. In this paper, for both heat exchangers, the same contact resistance of 1·10−4 m2 K/W is assumed. This is accordance with the assumption of Seshimo and Çengel. To calculate the actual average coefficient of heat transfer on the air side α o from equitation (13) and (14), it is necessary to know the fin efficiency ηf . The calculation of the values α o and ηf has been done iteratively in MS Excel since both variables are interrelated. Calculation method for ηf is defined by Bošnjakovic´ et al. [18] [31].. The average efficiency of the heat exchanger tube bundle is calculated according to the Eq. (15):
ηTB = 1 −
Af η 1− f . Atot C1
C1 = 1 − ηf · α0 · Af
Rc d0 · π · tf
(15)
.
(16)
Fig. 15. Comparison of the Nu number obtained by experimental testing and calculated using the literature correlation.
The effectiveness of the fin is calculated according to Eq. (17) [28].:
εf =
Af · ηf , Ab
(17)
where Ab is the cross-sectional area of the fin at the base. The efficiency of the entire tube bundle surface is calculated according to Eq. (18) [28]:
εtot =
At,uf · Nt + Af,tot · ηf . L · do · π · Nt
(18)
where Af,tot is the total surface area of all fins on the one tube, At,uf is the area of the unfinned portion of the tube outside surface and L is the tube length. Dimensionless numbers Re, Nu and Eu were calculated for the properties of the fluid at a boundary layer temperature. Nusselt number (Nu) is defined by the Eq. (19).
Nu =
αo · do . λa,bl
(19)
Fig. 16. Comparison of the Eu number obtained experimentally and calculated using the literature correlation.
Euler number (Eu) is defined by the Eq. (20).
Eu =
p , Nl · ρa,bl · u2max
(20)
where Nl is a number of tube rows in the longitudinal direction, and ρ a,bl air density at the boundary layer temperature, and λa,bl thermal conductivity of the air at the temperature of the boundary layer. The heat flux is calculated according to the expression:
q˙ A =
Q˙ a . Atot
(21)
The heat flow per unit mass of the tube bundle is equal to:
q˙ m =
Q˙ a . mtot
(22) Fig. 17. Fins efficiency.
4. Results The results obtained by experimental testing were compared with ordinary literature correlations [1], [2], [3], [4]. From Fig. 15 it can be seen that the Nu number for heat exchanger with annular fins matches literature correlations. As expected, Nu number for heat exchanger with star-shaped fins is higher than for annular fins. For Re=1500 the difference is about 16.5%, and for Re=10,500 the difference is about 18.6%. From Fig. 16 it can be seen that the Eu number for heat exchanger with annular fins matches literature correlations. The
value of the Eu number for star-shaped fins is lower by 13% to 14% compared to annular fins. The fin efficiency depends on the conduction in the fin, convention to the fin, shape of the fin and the sizes of the fin. The fin efficiency decreases with Re increase. Fig. 17 shows fins efficiency for star-shaped fins and annular fins. Distance between curves increases slightly with increasing Re. The efficiency of star-shaped fins compared to annular fins is greater from 5.7% to 16.1% regarding to the Re number.
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ˇ ´c / International Journal of Heat and Mass Transfer 149 (2019) 119190 M. Bošnjakovi´c, S. Muhicˇ and A. Ciki
Fig. 18. Fins effectiveness.
Fig. 21. Comparison of the heat flux for annular and star-shaped fins.
Fig. 19. The efficiency of the tube bundle surface area.
Fig. 22. Comparison of the heat flow rate per kg of tube bundle for annular and star-shaped fins.
Fig. 20. The tube bundle effectiveness for annular and star-shaped fins.
The effectiveness of the annular fin (Fig. 18) is greater than the star-shaped fin due to the larger surface of annular fins. By increasing the Re number, the fin’s effectiveness decreases due to the fin’s efficiency decreases. The effectiveness of annular fins compared to star-shaped fins rises up from 32% to 38% regarding to the Re number. An illustration of the efficiency of the tube bundle surface is given in Fig. 19. However, the tube bundle surface effectiveness of annular fins compared to star-shaped fins is greater from 24.5% to 32.5% regarding to the Re number.
The heat exchanger with star-shaped fins has a thermal flux greater from 35.5% to 55.8% compared to the heat exchanger with annular fins (Fig. 21). This means that for the same materials, operating conditions and the same heat flux heat exchanger with starshaped fins can have up to 55.8% less surface area in observed range of Re numbers and for stainless steel fins. The star-shaped fins heat exchanger has a heat flow rate per unit of mass greater than 12.2% for lower Re and 29% for higher Re compared to the annular finned heat exchanger (Fig. 22). This is a relative indicator of reducing the mass of the tube bundle because it depends on the ratio of the fin and tube mass. For example, if the tube had a wall thickness of 0.5 mm instead of a wall thickness of 1.5 mm, for Re=1500 the heat flow rate per mass unit would be 372 W/kg for star-shaped fins and 286 W/kg for annular fins (if ignored change of heat resistance through the tube wall). In this case, the difference of the heat flows rate per kg of the tube bundle is 30%. For all tested variants, the weight of the star-shaped fin compared to the mass of the annular fin is 43.5% lower. The tube bundle includes tubes and fins. In this sense, the mass reduction is 23.5%. The share of the heat flow through the heat exchanger casing is about 15% of the total heat flow. The influence of measurement uncertainty on the calculation of Nu and Eu was made by incorporating the upper or lower limits of measured temperature (T ± U), mass flux (m ± U) and pressure (p ± U) in the thermal calculation. The sensitivity of the calculation results to the measurement uncertainty is shown in Figs. 23 and 24.
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tube bundle mass by 23.5% compared to the heat exchanger with annular fins. For applications were it is important that the heat exchanger has small mass and size, the application of star-shaped fins may be good choice. Further research related to optimization of geometry of star-shaped fins is needed to obtain a final evolution of the starshaped fins. This research did not receive any specific grant from funding agencies in the public, commercial, or not-for-profit sectors. Declaration Competing Interest
Fig. 23. The influence of measurement uncertainty on the calculation of Nu.
We wish to confirm that there are no known conflicts of interest associated with this publication and there has been no significant financial support for this work that could have influenced its outcome. We confirm that the manuscript has been read and approved by all named authors and that there are no other persons who satisfied the criteria for authorship but are not listed. We further confirm that the order of authors listed in the manuscript has been approved by all of us. We confirm that we have given due consideration to the protection of intellectual property associated with this work and that there are no impediments to publication, including the timing of publication, with respect to intellectual property. In so doing we confirm that we have followed the regulations of our institutions concerning intellectual property. References
Fig. 24. The influence of measurement uncertainty on the calculation of Eu.
The deviation of Nu for the star-shaped fins is from −5.6% to +6.1%, and for the annular fins the deviation is from −6.2% to 7.1%. The deviation of the Eu for the star-shaped fins is from +3.3% to −4.1%, and the Eu deviation for the annular fins is from +2.8% to −4.1% (Fig. 24). Since measurements are carried out with the same equipment, it can be assumed that the deviations of the measured values is in the same direction. In that sense, it can be said that the impact of measurement uncertainty is up to 1% related to the Nu number and about 0.5% related to the Eu number. 5. Conclusions Two finned heat exchanger of the same sizes and construction, made from stainless steel, were tested experimentally. One heat exchanger had annular fins and the other had star-shaped fins. The testing of both heat exchangers was carried out at almost the same input parameters. The defined stationary conditions for this type of testing were met. In this way, the same conditions of fluid flow and heat exchange in the tested heat exchangers are created, so it is possible to compare the obtained results. The annular heat exchanger was used as a standard heat exchanger and the results of its testing were compared with the corresponding results from the literature. The obtained test results are well-aligned with the literature results, so it can be concluded that the test was performed correctly. A comparison of annular and star-shaped finned tubes revealed a general increase in the air-side heat transfer coefficient within the investigated Reynolds numbers range. The experimental results indicate that the heat exchanger with star-shaped fins has an increase in heat transfer coefficient from 16.5% to 18.5%, and the increase in the heat flux from 35.5% to 55.8% with a reduction of the
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