Received: April 28, 2019; Revised: June 12, 2019; Accepted: June 22, 2019 Keywords and phrases: triangular tube bank, heat exchangers, cross flow, staggered tubes.
FORCED CONVECTION HEAT TRANSFER IN STAGGERED TRIANGULAR TUBES IN CROSS FLOW
M. A. Halim1, M. A. Omara1 and E. M. Elhefnawy2
1Mechanical Department Faculty of Industrial Education Suez University, Egypt
2HVAC Department Advanced Industrial Secondary School at Red Sea Governorate Ministry of Education, Egypt
Abstract
Forced convective heat transfer, friction factor, enhancement efficiency, and entropy generation characteristics past equilateral triangular tubes at rotational angles have been investigated experimentally. Utilizing air as an operating for wide ranges of the
Reynolds number (Re) ( )32 1032.10Re106.2 ×≤≤× and angle of
rotational ( ).900 ≤θ≤ The experimental results show that a
considerable increase in Nusslet number (Nu) for circular tubes than
equilateral triangular tubes at the vertex facing the flow ( ),0=θ
while the Nu for equilateral triangular tubes bundle increases than a
circular tube at rotational angles above ( ).0=θ Also, results
indicated that the best Nu and overall enhancement efficiency is
achieved for the flat surface facing the flow values of ( ).90=θ The
M. A. Halim, M. A. Omara and E. M. Elhefnawy 508
results obtained are correlated in the form of Nu, friction factor, and enhancement efficiency as a function of Re and angles of rotational.
Nomenclature
A heat transfer area ( )2m S entropy generation ( )KW
C characteristic length (m) T temperature (K)
h local heat transfer coefficient of air
( )KmW 2 V velocity ( )sm
mh average heat transfer coefficient of
air ( )KmW 2 υ kinematics viscosity of air ( )sm2
K thermal conductivity ( )KmW φ irreversibility distribution ratio
L length of triangle tube (m) cp Specific heat at constant pressure,
KkgJ
S local surface temperature Subscript
Nu local Nusselt number of air sm average surface temperature
mNu average Nusselt number of air g total rate of entropy generation
Q heat transfer rate (W) ∞ air inlet temperature
q heat flux ( )2mW Δp rate of entropy generation due to fluid
Re Reynolds number ΔT rate of entropy generation due to heat transfer
ε Effectiveness, ( ( )) PTTcq eip Δ−.
1. Introduction
A heat exchanger is a piece of equipment built for efficient heat transfer from one medium to another. A high performance heat exchanger for saving and making effective use of energy is a very important facility. Tube banks are widely employed in cross flow heat exchangers, the design of which is still based on empirical correlations of heat transfer and pressure drop, [1]. Using in a wide variety of applications includes power production process,
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commercial processes, house hold applications, refrigeration, ventilating, air-conditioning systems, power generation, food industries, electronics, manufacturing industries and environmental engineering. There are numerous studies which take into consideration the effect of tube shape and bundle geometry on the performance of heat exchangers, [1-4]. For example, Žukauskas and Ulinskas [5] suggested correlations for heat transfer and pressure drop for in-line and staggered banks of circular tubes. Their study
covered the range of ≤≤ Re1 ,102 6× and ,500Pr7.0 ≤≤ as well as a wide range of relative transverse and longitudinal pitches. They suggested an efficiency factor for the evaluation of heat transfer surfaces efficiency in further improvement of heat exchangers constructions. Comparisons of circular and elliptical tubes as the essential elements of heat exchangers have been reported in several studies. Brauer [6] reported 18% of relative reduction in the pressure drop for elliptical tubes compared to circular ones. Horvat et al. [7] studied the transient heat transfer and fluid flow for circular, elliptical, and wing-shaped tubes with the same cross sections. Comparing the three types of tubes, they reported that the values of the average drag coefficient were lower for the ellipsoidal and the wing-shaped tubes than those for the cylindrical ones. The effects of cylinders spacing and angles of attack on the drag coefficient for elliptical tubes in tandem arrangement were investigated by Nishiyama et al. [8]. They found that the angle of attack, as well as, the cylinders spacing influenced the drag coefficients. They concluded that the cylinders spacing and the angles of attack should be arranged as small as possible to minimize the drag and to achieve compactness of the system. Harris and Goldschmidt [9] investigated the effects of the variation of the tube axis ratios and angles of attack on the drag
coefficient for Re ranging from 3104.7 × to .104.7 4× Re was based on the length of the major axis. They concluded that an axis ratio of 0.30 or less must be achieved. Ibrahim and Gomma [10] have performed experimental and numerical studies of the turbulent flow over bundle of elliptical tubes.
Their investigation covered a range of Re from 3106.5 × to 31040 × with four axis ratios considered (0.25, 0.33, 0.5 and 1) and the flow angles of
M. A. Halim, M. A. Omara and E. M. Elhefnawy 510
attack were varied from 0 to .150 Their results showed that the best and
worst flow angles of attack were 0 and ,90 respectively for fixed pumping power. Ibrahim et al. [11], conducted an experimental investigation of the
performance of a bundle of semi-circular tubes. Re was ranged from 4102 ×
to ,105.16 4× the angles of attack were varied from 0 to 270 and the relative longitudinal pitch SL/d was at 1.35 and 2.69, while the relative transverse pitch was kept at ST/d = 1.35. They concluded that the best and
worst angles of attack were 270 and ,0 respectively. Fluid flow and heat transfer across a long equilateral triangular cylinder placed in a horizontal channel was studied by Srikanth at al. [12] for Re (Re) ranges from 1 to 80 (in the steps of 5) and Prandtl number of 0.71 for a fixed blockage ratio of 0.25, the results showed that. The mean drag coefficient decreases with increasing value of the Re; however, the wake length increases with Re for the range of conditions covered. The average Nu increases with increasing value of the Re. The maximum changes between the values for triangular and square obstacles are found to be about 25% for Re = 1 and 12.5% to 15% for
.45Re5 ≤≤ The values of the triangular cylinder case. An experimental investigation has been conducted by Ibrahim and Moawed [13] to clarify heat transfer characteristics and entropy generation for individual elliptical tubes with longitudinal fins. The investigated geometrical parameters included the placement of the fins at the frontal, the rear and both frontal and rear portions of the tubes. The results indicated that the use of fins affected the results of heat transfer coefficient, friction factor and irreversibility ratio. Sayed Ahmed et al. [14‐17], experimentally and numerically, studied the flow and heat transfer characteristics of a cross flow heat exchanger employing staggered wing-shaped tubes with zero angle of attack. Hot air was forced to flow over the external surfaces of the tubes and exchanged heat with the cold water flowing inside. The results indicated that, the bundle of wing-shaped tubes has better performance over other bundles for similar parameters and conditions. An experimental study of air cooling and dehumidification process around a bank of in-line elliptical tubes of cross flow heat exchanger
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was conducted by Ibrahiem et al. [18]. They concluded that; (a): The Colburn j-factor increases with the angle of attack θ for constant relative transverse pitch for the given range of relative longitudinal pitch, (b): the effectiveness ( )ε of the wet surfaces of the tested bundle increases with θ.
It appears from the previous works of the literature that there are only a few studies that considered triangle-shaped tubes. Therefore, the aim of the present study was to investigate the air flow characteristics and pressure contours through the triangle-shaped tubes bundle in cross-flow with various angles of attack. To achieve these goals, experimental studies have been conducted. Three cases of the tubes arrangements, with various angles of attack θ, row angles of attack θ with different Re.
2. Experimental Setup
The experiments are conducted in an open-circuit air flow horizontal wind tunnel operated in a suction mode with wind tunnel of 2780 mm length, as shown in Figure 1. The tunnel is capable of producing an air velocity up to
6 m/s. Plexiglas test section of ( ) ,mm305305 2× and 780 mm long is
mounted in the middle of the wind tunnel. The cross-sectional dimensions of triangle-shaped tubes, drawn from 0.5 mm thick, 22.5 mm outer diameter circular copper tube with 305 mm long, is shown in Figure 2(a). The tested tube bundle, shown in Figure 2(b), consists of 22 triangle-shaped tubes distributed through three successive rows in addition to four half dummy ones. The tubes of the bundle could be fixed in the test section with a special mechanism having the capability of changing the flow angle of attack θ while the longitudinal (SL) and transverse (ST) tube-pitches of 37 mm were kept constant. The air from the laboratory space passes through the bell mouth intake, the test section, and the centrifugal fan that discharges the air outside the laboratory. The fan runs at a constant speed, and the air flow rate is controlled by an adjustable iris in the fan discharge.
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Figure 1. Schematic diagram of experimental apparatus.
Figure 2. Arrangement of triangle tube array (a) and tube angle of attack (b).
3. Uncertainty Analysis
Generally, the accuracy of the experimental results depends upon the accuracy of the individual measuring instruments and the manufacture accuracy of the triangle tube. Also, the accuracy of an instrument is limited by its minimum division (its sensitivity). In the present work, the uncertainties in Nu and Re, f and irreversibility ratio ( )φ are estimated
following the differential approximation method. For a typical experiment, the total uncertainties in measuring the main heater input power, surface temperature, the heat transfer rate and the triangle tube surface area are
%22%,55%,2 ±±± and %,8.1± respectively. These are combined to
give maximum errors of %56.3and%28.2%,1.4%,86.2 ±±± in Nu, Re, f
and irreversibility ratio ( )φ respectively.
4. Data Reduction
The data reduction of the measured results is summarized in the
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following procedures:
The mean heat transfer coefficient for longitudinal triangle tube is calculated as:
( ).∞−= TTqh s (1)
Average heat transfer coefficient is computed in non-dimensional form by means of Nu:
.kchNu ×= (2)
The Re is defined in the conventional way as:
.Re υ×= cv (3)
The friction factor f can be calculated from:
.2 2∞ρΔ= VPf (4)
Effectiveness ( )ε represents the heat transfer per unit pumping power as
stated by Gomaa et al. as follows.
( ).
PTTc eipa
Δ
−ρ=ε (5)
The total rate of entropy generation due to heat transfer between a body and a flow that surrounds the body is:
( ) .2∞∞∞ +−= TVFTTTQS Dsmg (6)
In Eq. (6) the terms on the right hand side indicate, respectively, the entropy generation due to heat transfer ,TSΔ and the entropy generation due to fluid
friction ,pSΔ thus equation can be written as:
.TPg SSS ΔΔ += (7)
The irreversibility of the process is minimized when the entropy generation due to fluid friction, ,pSΔ is minimized. Eq. (7) can be non-
M. A. Halim, M. A. Omara and E. M. Elhefnawy 514
dimensionalized by dividing through by the constant ,TSΔ to get:
,1 φ+=ΔΔ TP SS (8)
where φ (the irreversibility distribution ratio) is a controlling parameter of the entropy minimization of heat exchange systems. In constant power input applications, the irreversibility distribution ratio φ is an inverse indication of efficiency, thus φ is defined by
( ).∞∞∞ΔΔ −==φ TTQTVFSS smDTP (9)
The drag force is expressed as:
.APFD ×Δ= (10)
5. Results and Discussions
Figure 3 shows how the variation of thermal resistance changes with Re at varying rotational angles. The thermal resistance decreases as the Re increases at all rotation angles of equilateral triangular tubes bundle. It is shown that the thermal resistance increases as the vertex facing the flow
( ),0=θ while the flat surface facing the flow ( ),90=θ the thermal
resistance decreases. The results are consistent with logical, since the decreasing Re means that the thermal conductivity increases.
Figure 4 shows the variation of Nu with rotational angles ( )θ for various
Re. For the case 0=θ the vertex is facing the flow, while for 90=θ the flat surface is facing the flow. The results showed that the Nu increases with increasing rotational angles, where the maximum Nu was obtained at
rotational angle ( )90=θ for all Re used. This is likely because of the
higher turbulence and better contact surface area between fluid and heating wall surface. Also, the results appear that the rear side of the internal tubes is affected by the high turbulence flow from the other upstream tubes, therefore higher level heat transfer is observed and a steady state heat transfer is established. This has been observed by Žukauskas and Ulinskas [5].
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Figure 5 presents the experimental of Stanton number (St) as a function of Re for varying rotational angles. The results show that the Stanton number always decreases with increasing Re. The Stanton number first rapidly decreases with increasing Re and then gradually decreases with Re. The
highest value of Stanton number is occurred at ,90=θ while the lowest
value of Stanton number is occurred at .0=θ
The intensity of turbulence depends on the bank arrangement and Re. The ratio of cNuNu of equilateral triangular tubes is demonstrated in Figure 6 at varying rotational angles. From this figure, it is clear that the ratio of
cNuNu decreases with increasing Re at all rotational angles. Also, the heat transfer enhancement increases with increasing rotational angles and reaches
a maximum at rotational angle equal ,90 at this angle of attack ( ),90 in which the flat surface of the tube faces the main stream, the intensity of turbulence is high through the tube array passage. This, in turn, enhances the convective heat transfer coefficient; however, a higher pressure drop is expected.
The variation of friction factor with Re for different cases of equilateral triangular tubes positions is shown in Figure 7. This figure shows that friction factor increases with decreasing Re for all rotational angles. At the same Re, the friction factor increases as rotational angles increase. Also, friction factor in the case of the flat surface facing the flow is greater than that of the vertex facing the flow for all values of Re. This may be attributed to the dissipation of the dynamic pressure of fluid due to good contact surface area and the action caused by the reverse flow.
Figure 8 shows the effect of the rotational angles ( )θ on the pumping power (pu) at different Re. At a certain Re, the pumping power increases
with rotational angles increasing from ( ).90to0 This is due to the fact that, the equilateral triangular tubes bundle arrangement promoted turbulent mixing and lengthened the air flow-path through the bundle. The size and the strength of the turbulence level, as well as the reversed flow region are affected by rotational angles and Re variations.
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Heat transfer enhancement obtained leads to increasing the pressure drop caused by bank tube arrangement. Therefore, a performance analysis is important for the evaluation of the net energy gain to determine if the method employed to increase the heat transfer is effective from energy point of view or not. The variation between the enhancement efficiency and Re at varies rotational angles is shown in Figure 9. From the figure, it can be seen that the overall enhancement ratio increases with increase in rotational angles. It is clear from Figure 9 that for all cases, the overall enhancement ratio is greater
than unity above rotational angle equal .0 The best overall enhancement
achieved for the flat surface facing the flow ( ).90=θ
The effect of rotational angles on the effectiveness at different values of Re is shown in Figure 10. It is clear from the figure that the rotational angles increases, the effectiveness increases at all values of Re. Also, it is clear from the figure that the highest and lowest values of effectiveness, are occurred at the lowest and highest values of Re at all the studied arrangements respectively.
The relation between entropy generations ( )gS and entropy generation
number ( )sN with the rotational angles of equilateral triangular tubes bundle
arrangement of different values of Re are shown in Figure 11 and Figure 12. These figures show that gS and sN for all cases increase with the increase
of Re and the values of rotational angles. The values of gS and sN of
equilateral triangular tubes bundle arrangement is minimum and maximum at
the vertex facing the flow ( )0=θ and the flat surface facing the flow
values of ( )90=θ respectively.
The irreversibility distribution ratio is a controlling parameter of the entropy generation of heat exchange systems, where ,1>φ the irreversibility
is dominated by losses due to fluid friction, and if ,1<φ the irreversibility is
dominated by losses due to heat transfer. The results of irreversibility distribution against rotational angles vary Re as shown in Figure 13. This
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figure indicates that 1<φ for all cases of the positions tubes bank. This
means that the entropy generation caused by heat transfer is greater than that caused by friction factor. Also, it is clear that the irreversibility distribution ratio increases with increases rotational angles and Re.
6. Validation with the Previous Work
Comparison between the Nu obtained from the present work with another research is shown in Figure 14. In the figure, the Nu for equilateral triangular tubes bundle increases than a circular tube at rotational angles varies from
30 to ,90 while the Nu for circular tube increases than a rotational angle
equal .0 The increases for Nu are between 30 % to 117 % than a circular
tube, for the flat surface facing the flow values of ( ).90=θ
7. General Correlations
The general correlation of the Nu as a function of Re and θ of the experimental results is expressed as follows:
.ReNCNu = (11)
The experimental data is fitted to get the constants obtained as:
[ ] 8756.08373.3773.107049.8 2 ++θ−θθ=C
[ ] .4459.02255.03533.00747.0 2 ++θ−θθ=N
The general correlation of the f as a function of Re and θ of the experimental results is expressed as follows:
.Re 21CCf = (12)
The experimental data is fitted to get the constants obtained as:
[ ] 581.13907.18346.191708.6 21 +−θ+θ−θ=C
[ ] .3189.03867.0385.01212.0 22 −+θ−θθ=C
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The general correlation of the η as a function of Re and θ of the experimental results is expressed as follows:
4Re3CC=η (13)
[ ] 3666.2905.16622.43605.33 23 +−θ−θθ=C
[ ] .1169.00814.02012.00231.0 24 −+θ−θθ=C
These equations are used in the case of ( )32 1032.10Re1026 ×≤≤× and
( ) ,1,57.10 =≤θ≤ LT SS where rotational angles ( )θ by rad.
8. Concluding Remarks
An experimental study was performed to determine the effect of rotational angles of equilateral triangular tubes bundles on heat transfer and
friction characteristics within the range of Re from 21026 × to 31032.10 × for a uniform heat flux in an equilateral triangular tubes bundle. In this study,
rotational angles vary from 0 to .90 The following conclusions were derived:
(a) The Nu and friction factor increase with increasing rotational angles.
(b) For all cases, Nu increases and friction factor decreases with increasing Re. The highest Nu and friction factors are obtained at the flat
surface facing the flow values of ( ).90=θ
(c) For rotational angles above ,0 the overall enhancement ratio is higher than unity for investigated cases.
(d) The best overall enhancement is achieved for the flat surface facing
the flow values of ( ).90=θ
(e) The Nu for equilateral triangular tubes bundles increases than a
circular tube at rotational angles varies from 30 to .90
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(f) The Nu for circular tubes increases than rotational angles for the
vertex facing the flow ( ).0=θ
(g) The increases from Nu are “between” 30 % to 117 % than a circular
tube, for the flat surface facing the flow values of ( ).90=θ
Figure 3. Variation of cR versus Re at different angles ( ).θ
Figure 4. Variation of Nu versus Re at different angles ( ).θ
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Figure 5. Variation of tS versus Re at different angles ( ).θ
Figure 6. Variation of cNuNu versus Re at different angles (θ).
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Figure 7. Variation of f versus angle θ at different Re.
Figure 8. Variation of Pu versus angle θ at different Re.
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Figure 9. Variation of η versus Re at different flow angles ( ).θ
Figure 10. Variation of 310×ε versus angle θ at different Re.
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Figure 11. Variation of gS versus angle θ at different Re.
Figure 12. Variation of 310×sN versus tilt angle θ at different Re.
M. A. Halim, M. A. Omara and E. M. Elhefnawy 524
Figure 13. Variation of 410×φ versus angle θ at different Re.
Figure 14. Validation of the present work with the results of Žukauskas and Ulinskas et al. [5].
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