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Performance evaluation of wire mesh heat exchangers
Journal Pre-proofs Performance evaluation of Wire Mesh Heat Exchangers M.A. Sayed, A.M.T.A. ELdein Hussin, W. Aboelsoud, N.A. Mahmoud PII: DOI: Reference:
S1359-4311(19)35553-X https://doi.org/10.1016/j.applthermaleng.2019.114891 ATE 114891
To appear in:
Applied Thermal Engineering
Received Date: Revised Date: Accepted Date:
8 August 2019 27 December 2019 30 December 2019
Please cite this article as: M.A. Sayed, A.M.T.A. ELdein Hussin, W. Aboelsoud, N.A. Mahmoud, Performance evaluation of Wire Mesh Heat Exchangers, Applied Thermal Engineering (2019), doi: https://doi.org/10.1016/ j.applthermaleng.2019.114891
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Performance evaluation of Wire Mesh Heat Exchangers M. A. Sayed 1, A. M.T. A. ELdein Hussin 1, W. Aboelsoud 1, 2, N. A. Mahmoud 1 ____________________________________________________________________________________
Abstract Liquid-to-air cross-flow heat exchangers have a low heat transfer coefficient on the gas side due to poor thermal characteristics of air. One of the promising solutions is to attach extended surfaces on the gas side, thus increase the surface area of heat to transfer by convection. In this study, the experiment was carried out to evaluate the thermal and hydraulic performance of four modules of cross flow heat exchangers. One is bare copper tubes and three wire mesh heat exchangers with different mesh spacing. Hot distilled water was pumped into copper tubes at a constant flow rate of 9 l/min and inlet temperature of 80oC. The heat exchanger subjected to external cross airflow inside an air duct of 20 cm x 20 cm crosssectional area with an average air velocity of 2.8 m/s up to 14.9 m/s. Results showed an enhancement of Nusselt number for all wire mesh modules that is an increase of the volumetric heat transfer coefficient of up to 113.9% among the three tested modules compared to the bare module. The significance of this study is to use reasonably-priced wire mesh and maintain enhancement in the rate of heat transfer.
Keywords: Cross flow heat exchanger, wire mesh heat exchanger, and porous structure.
1. Department of Mechanical Power Engineering, Ain Shams University, Cairo, Egypt, 11517. 2. Corresponding author: E-mail address: [email protected] 1
Nomenclature Ain Inside tube surface area [m2] Aout Outer tube surface area [m2] Ac Cross-sectional area of flow [m2] AU cp Dh D out Dw F H in Ho H out Hv K air K Pipe lP ṁ Nu o Pt ∆P PPI P/V 𝑄̇ Red, ∞
R tot S ∆TLM
Overall heat transfer conductance [W/K] Specific heat at constant pressure [J/kg.K] Hydraulic diameter = 4Ac /Pt [m] Tube outside diameter [m] Wire diameter [mm] Correction factor Tube inside heat transfer coefficient [W/m2.K] Outer convection heat transfer coefficient [W/m2.K] Outer air convection heat transfer coefficient, [W/m2.K] Volumetric convective heat transfer coefficient [W/m3.K] Thermal conductivity of air [W/m.K] Thermal conductivity of pipe material [W/m.K] Copper pipe length [m] Mass flow rate [kg/s]
T U V∞ (or U∞) V̇
Temperature [ºC] Overall heat transfer coefficient [W/m2.K] Average air velocity in the free cross-sectional area of the air duct [m/s] Volume flow rate [m3/s]
XT
Transversal tube pitch [m]
Xt Wire mesh transversal pitch [mm] Overall surface efficiency ηo Greek Symbols ν Kinematic viscosity [m2/s] µ Dynamic viscosity [N.s/m2] ρ
Density [kg/m3]
ψ
Void fraction
ɳ
Efficiency
Subscripts a
Air
d out
Based on outer pipe diameter Outlet
Nusselt number based on the outer tube diameter Wetted perimeter [m] Air pressure drop across heat exchanger module [Pa] Pore per inch
w
Water
in p
Inlet Pipe
tot
Total
Pumping power per unit volume of heat exchanger module (W/m3) Hot water heat transfer rate [W] Reynold’s number based on outer pipe diameter and air velocity Total heat transfer resistance [K/W] Spacing between woven wire mesh sheet layers [mm] Logarithmic mean temperature difference [ºC or K]
v
Volumetric
avg lam
Average Laminar
turb t
Turbulent Wetted
2
Performance Evaluation of Wire Mesh Heat Exchangers M. A. Sayed 3, A. M.T. A. ELdein Hussin 1, W. Aboelsoud 1, 4, N. A. Mahmoud 1 ____________________________________________________________________________________
Abstract Liquid-to-air cross flow heat exchangers have low heat transfer coefficient on the gas side due to poor thermal characteristics of air. One of the promising solutions is to attach extended surfaces on the gas side, thus increase the surface area of heat to transfer by convection. In this study, experiment was carried out to evaluate thermal and hydraulic performance of four modules of cross flow heat exchangers. One is bare copper tubes and three wire mesh heat exchanger with different mesh spacing. Hot distilled water was pumped into copper tubes at constant flow rate of 9 l/min and inlet temperature of 80oC. The heat exchanger was subjected to external cross air flow inside an air duct of 20 cm x 20 cm cross sectional area with an average air velocities of 2.8 m/s up to 14.9 m/s. Results show an enhancement of
Nusselt number for all wire mesh modules that is an increase of the volumetric heat transfer coefficient of up to 113.9% among the three tested modules compared to the bare module. The significance of this study is to use reasonably-priced wire mesh and maintain enhancement
in the rate of heat transfer.
3. Department of Mechanical Power Engineering, Ain Shams University, Cairo, Egypt, 11517. 4. Corresponding author: E-mail address: [email protected] 3
1. Introduction Many industrial and domestic applications involve heat exchange processes, which if developed, can significantly provide savings in energy utilization and cost. Such applications are heat exchangers, which are used in air conditioning equipment, cooling the electrical components and waste heat recovery [1]. The desire of reducing energy consumption by more efficient energy usage has led to the development of more energy-efficient compact heat exchangers [1]. Compact heat exchangers have a large area density, usually of more than 700 (m2/m3) [2, 3]. Also, compact heat exchangers usually have a small hydraulic diameter of Dh ≤ 6 mm [4]. To improve the heat transfer performance of heat exchangers, active and passive techniques are used. One of the most commonly used passive techniques is extended surfaces [1, 5]. Examples of finned surfaces application are shell and tube heat exchanger, plate finned heat exchangers, finned tubes in air conditioning systems, and even in heat sinks used for cooling of electronic devices [1, 2, 6]. In single-pass liquid-to-air heat exchangers, fins are usually attached on the gas side. This is because air has a lower heat transfer coefficient, poor thermal characteristics and conventionally flows outside across the liquid tubes [3, 5]. Fins of many different configurations can be used for heat transfer augmentation on the gas side like plain fins, wavy fins, and louvered fins. However, such types of fins have different manufacturing complexities, high cost, maintenance issues, and they also have low mechanical strength for structural integrity because they are fabricated from thin material sheets [7]. More efficient types of extended surfaces are greatly required. Therefore, the need to develop and use the porous matrix is one of the most promising solutions in that field. Porous media can be defined as a solid matrix that is formed by a solid structure with interconnected void spaces [8]. Different porous inserts like metal foams and wire mesh blocks in channel flows have been investigated experimentally. Many studies were also conducted to assess heat transfer and fluid flow behavior through porous material [9] like metal foam, fins, and wire mesh screen inserts used in the internal flow. Metal foams have been extensively investigated for enhancing the heat removal rate in different configurations of heat exchangers. Nawaz, et al. [10], conducted an experimental study to assess the thermal and fluid flow performance of aluminum foam sheets attached to 4
cross flow water-to-air heat exchanger used in air conditioning applications. Chumpia and Hooman [11, 12], experimentally examined the heat transfer and fluid flow friction of water-to-air single pipe and single row heat exchanger subjected to cross airflow. The pipes were covered with a layer of aluminum foam. They concluded that with higher foam thickness and smaller transversal pitch between foam covered tubes, the rate of heat transfer was higher. Rezaey, [13], compared the effect of using copper metal foam and copper wire screens as extended surfaces attached to the surface of the heat exchanger. The highest heat transfer to water was achieved using wire mesh screens. T’Joen, et al. [14], experimentally evaluated the heat transfer and pressure drop performance of a single row, aluminum foamwrapped pipes, and cross flow heat exchanger. They concluded that the outer convection resistance was reduced with the increase in foam layer thickness, but the pressure drop also increased significantly. Extended surfaces like fins of various shapes attached to heat exchanger pipes were used in different studies. Huisseune, et al. [15], studied the heat transfer and fluid flow behavior for a single row cross flow heat exchanger using helically-finned round pipes. Empirical correlations were developed to predict the friction factor and Nusselt number. Wang et al., and Wang and Chi. [16, 17], experimentally studied the thermal and hydraulic performance of a cross flow heat exchanger. Heat exchanger tubes were attached with flat plain fins and louvered fins, respectively. Results showed that the friction factor is observed to be rather independent of the number of tube rows. They also reported that for the one and two tube rows, the heat transfer increases by the reduction of fin pitch. Yu Jin et al. [18], conducted a CFD numerical study of a 3-D cross flow heat exchanger to assess its heat transfer and pressure loss performance. The 3-D model consisted of ten rows of H-type finned tubes. Sparrow and Samie [19], conducted an experimental work to assess the thermal and pressure drop performance of one and two tube rows cross flow heat exchanger. The heat exchanger consisted of electrically heated rods, attached with integral annular fins. Because the wire-mesh screen is easy to manufacture and costs less than other porous materials, it is considered as an excellent candidate to enhance heat transfer. Fugmann et al. [20], carried out heat transfer and pressure drop experiments on two new proposed manufactured wire mesh heat exchangers. They also compared these wire mesh heat exchangers with other finned modules. Results showed that the wire mesh heat exchanger has the lower weight for a specific required heat transfer surface area as compared to the 5
finned types, despite having a lower heat transfer performance. Pavel, and Mohamad [21], inserted a matrix of aluminum circular wire screens inside a heated copper pipe. The highest increase in Nusselt number was about 5.2 times compared to the bare pipe flow case. Dyga and Płaczek [22], conducted an experimental work to assess the fluid flow characteristics and heat transfer performance of cylindrical multi-layered wrapped wire mesh packing. Xing, et al. [23], experimentally examined the heat transfer characteristics by inserting a cylindrical wire mesh suspended in the water flow stream inside a pipe. Hong et al. [24] experimentally investigated the effect of inserting wire coils inside air pipe flow, on the heat transfer and pressure drop performance. Carmer, et al. [25], conducted experiments to assess heat transfer enhancement achieved by attaching sinusoidally-shaped wire screens between two plate heaters which were then subjected to air flow in a rectangular channel. They reported an increase in heat removal rate and Nusselt number for tested samples having different spacing and porosity values. The highest enhancement in heat transfer was achieved with the screen sample of 12 mm spacing and 48% porosity. In addition, they developed correlations to predict the Nusselt number as a function of the Reynold’s number based on channel hydraulic diameter. Yanchen Fu et al. [26], experimentally assessed the thermal characteristics of air-to-air cross-flow wire mesh heat exchanger. Wang et al. [27], conducted an experimental study to estimate the heat transfer and fluid friction performance of a cross flow water-to-air heat exchanger having bare pipes. In the current study, the cross flow water-to-air heat exchanger consisting of ten equallyspaced wire meshed copper tubes, was tested under the steady-state conditions. Three modules having different layer-to-layer spacings of the wire mesh were tested and compared to the bare tube module. Hot distilled water was allowed to flow inside the heat exchanger tubes with outer air cross flow over the tube row. The experiments conducted on the four heat exchanger modules, covered a wide range of average cross air flow velocities which varied from 2.8 up to 14.9 m/s and covered a broad range of turbulent flow regimes. Experimental setup, fabrication of wire mesh heat exchangers, and procedure of the experiment are explained in the next section.
6
2. Experiment 2.1. Experimental setup The heat exchanger module in the current study consisting of ten equally-spaced copper tubes between two water heaters was bonded. The internal diameter of water tubes is 8.1 mm with a wall thickness of 0.7 mm. Water tubes were subjected to air flow passing through 20 cm x 20 cm air duct. Three of the heat exchanger modules were press-fitted with woven wire meshes, and a fourth bare module was also fabricated for comparison purposes. The woven wire mesh screens used in the heat exchangers have a wire diameter of 0.15 mm with a square opening of 0.3 mm x 0.3 mm, 57 PPI, and a porosity of 73.8%. The porosity of the wire woven mesh is calculated using a formula in [28], which is the function of wire diameter and mesh transverse pitch, equation 1.
α=1−(
π.dw 4.xt
)
(1)
Those copper alloy mesh screens were cut into three sheets of different lengths, all having the same width as the air duct, 20 cm. Each piece of the three cut sheets was shaped with rectangular corrugations and then drilled with ten holes of 9.25 mm in diameter (0.25 mm less than the outer pipe diameter). The ten copper tubes of the heat exchanger were then press-fitted into the drilled sheets, to ensure perfect contact, with a different layer-to-layer spacing of 4, 3, and 2 mm as shown in Figure 1. That is there are three values of the spacings between the layers of corrugated wire mesh heat exchangers of 4, 3, and 2 mm. The four heat exchanger modules tested in this study are shown in Figure 1.
7
(a) Bare heat exchanger module
(b) Wire mesh 4 mm spaced, finned heat exchanger module
(c) Wire mesh 3 mm spaced,
(d) Wire mesh 2 mm spaced,
finned heat exchanger module
finned heat exchanger module
Figure 1: Pictures of the different heat exchanger modules
8
(A)
(B)
Figure 2: Wire mesh corrugated sheet (A) Corrugated sheet press-fitted onto pipes, (B) Microscopic view of the woven wire mesh fibers’ size and pores.
The woven wire mesh screens are illustrated in Figure 2 using an electronic microscope. The temperature of inlet air was measured with a K-type thermocouple, and two calibrated RTDs were installed to measure the inlet and exit temperatures of the hot water. Corrugated wire mesh screens were attached to the one-row heat exchanger modules by press-fitting. Air duct was insulated during experiments using a 5cm-thick, glass wool sheet to minimize the thermal losses to the surroundings. The test rig as shown in Figure 3 consisted of hot water closed cycle and an open-circuit air duct.
9
Figure 3: Single line diagram of the heat exchanger experimental setup
10
The heat exchanger test section is located downstream of the inlet section of the air duct at a distance of 2.3 m to ensure a fully developed flow of air across copper tubes. The air enters through the duct at room temperature using a 5.5 hp, 3-phase centrifugal blower (Y112M - 4) that is located at the end of the outlet section of the air duct after the test section (suction side). The average air velocity and thus the volume flow rate were changed by air damper which was installed at the outlet of centrifugal blower. The air centerline velocity at the inlet to heat exchanger was measured by a hot wire anemometer (Testo-425) having an uncertainty of ±0.01 m/s. The pressure drop of air flow across each heat exchanger module was measured using a water U-tube manometer and an uncertainty value of ± 1 mm. Air inlet temperature at the centerline of air duct was measured by a K-type (24 AWG) thermocouple. Distilled water was heated in a stainless-steel tank by a 4-kW electric heater. Heater’s electrical power supply was controlled by an AC-voltage regulator to ensure constant inlet hot water temperature (± 0.1oC) to the heat exchanger module when either the air flow velocity or the water flow rate varies. The water flow rate to the heat exchanger pipes was changed by a flow control valve with the aid of a by-bass line valve in order to maintain a constant water flow rate. The water flow rate was measured by a turbine flow meter (Gems FT-110 Series) with the uncertainty of ± 0.01 l/min, which was installed downstream of the outlet of the heat exchanger module. Calibrated digital temperature reader, with the uncertainty of ± 0.1oC, was used to measure the inlet and exit water temperatures.
2.2. Experimental procedure Steady-state forced convection heat transfer experiments were conducted for each module of the heat exchangers at different air velocities and water flow rates. The procedure of the experiments has started by turning the centrifugal blower on, water heater, and hot water circulating pump. The air flow rate was adjusted by varying the opening of the volume air damper installed at the exit of the centrifugal blower. At each air volume damper opening, the water inlet temperature was adjusted using the AC-voltage regulator to maintain the desired temperature. Once the steady-state conditions are reached, the inlet air temperature, inlet and exit water temperatures, air velocity, hot water flow rate, and the pressure drop measurements were recorded. 11
The steady-state conditions were considered to be achieved when the measured temperature values were varied by ±0.1oC. All these measurements were taken at a fixed water flow rate of 9 L/min and a temperature of 80oC. All experiments were conducted for the four heat exchanger modules at varying air velocity range between 2.8 and 14.9 m/s. The following section, describes experimental results, its representation of the experimental data, along with analysis and discussion.
3. Results and discussion 3.1. Thermal performance The steady-state heat transfer tests were carried out for the four heat exchanger modules at the same operating conditions for comparison purposes. For each of the heat exchangers, the air flow velocity varied between 2.8 and 14.9 m/s. This velocity range involves a broad range of turbulent flow conditions. A thermal analysis was conducted, based on the logarithmic mean temperature difference, to assess the performance of each of the heat exchangers using the heat transfer rate calculated from the hot water side. The total heat transfer rate can be calculated using the energy balance equation 2, [2, 5]. Q̇w = ṁw ∗ cp,w ∗ (Tw,in − Tw,out )
(2)
Logarithmic mean temperature difference can then be calculated by equation 3, [1, 2, 5, 29]. ∆TLM =
(Tw,in − Ta,out ) − (Tw,out − Ta,in ) T − Ta,out ln( Tw,in − T ) w,out a,in
(3)
Then the overall heat transfer conductance (AU) can be estimated from equation 4, [1, 2, 5]. Q̇w = F . A. U. ∆TLM
(4)
where (F) is a correction factor related to the cross-flow heat exchanger type and to be calculated as elaborated in [30]. However, since the calculated value of the correction factor, F was so close to unity in most cases in this study, it was taken as one in all thermal calculations. The correction factor, F depends on the type of heat exchanger and water inlet
12
and water exit temperatures of the one-row finned tube heat exchanger tested by Lapin and Schurig [31]. The total resistance of heat transfer can then be determined from equation 5.
R tot
d ln( out ) 1 1 1 din = = + + AU hin Ain 2πk pipe lp hout Aout ɳ𝑜
(5)
where ηo , overall surface efficiency, is considered as one, since its value is usually very close to unity, Chumpia and Hooman [12]. Equation 5 can be rearranged to calculate the convective heat transfer coefficient based on the outside surface area of the water tube as illustrated in equation 6. d ln( out ) 1 1 1 din = − − hout Aout AU hin Ain 2πk pipe lp
(6)
The internal convection heat transfer coefficient on the waterside hin is calculated from Gnielinski formula [32], having an uncertainty value of 10%. The third term on the righthand side of the equation 6 is the conduction heat transfer resistance of the copper pipe wall with inner and outer diameters of 8.1 and 9.5 mm respectively. The thermal conductivity of copper is 380 W/m.K [33], and the pipe length is 20 cm. The external convection heat transfer coefficient is calculated based on the copper tube outer surface area (Ao) which is identical for all the heat exchanger modules. Results show that the heat transfer coefficient of the bare module changes with Reynold’s number and reaches a maximum of 303 W/m2.K at a Reynold’s number of 8142. For the 2, 3, and 4 mm wire mesh heat exchangers, the outer heat transfer coefficient reaches a maximum value of 467 W/m2.K at a Reynold’s number of 6339. The outer average Nusselt number based on the outer copper pipe diameter (dout) and the outer convective heat transfer coefficient can be calculated from equation 7, [1, 2]. Nuo =
ho dout k air
(7)
where kair is the thermal conductivity of air at the air inlet temperature. Equation 8, is to define Reynold’s number based on the outside diameter of the pipe. On the other hand, Reynold’s number is also defined based on the hydraulic diameter of the channel for comparison reasons, equation 9.
13
Red,∞ =
ρair . dout . V∞ µair
(8)
ReDh =
ρair . Dh . V∞ µair
(9)
The amount of heat transferred from hot water, at 80oC, and flow rate of 9 L/min, to external air flow is higher than that of bare module for all wire mesh heat exchangers as shown in Figure (4.A). Almost identical thermal performance was observed for the 2 mm, and 3 mm spacing of the finned modules over the entire tested range of Reynold’s number. Figure (4.B), shows an increase in the heat transfer rate up to 4 times that of the bare heat exchanger module. This increase of heat transfer rate in wire mesh heat exchangers was attributed to the larger heat transfer surface area provided by wire mesh sheet to the tubes. (A)
(B)
(B)
Figure 4: (A) Total heat transfer rate variation with average air inlet velocity, (B) The enhancement ratio of heat rate for the 3 wire heat exchanger modules. 14
Figure 5: Nusselt number variation with Reynold’s number.
Figure 5 shows that, the Nusselt number increases with the increase in Reynold’s number, due to the increase of flow turbulence. In addition, Nusselt number for all the wire mesh heat exchangers outperformed that of the bare heat exchanger module. Among the three tested wire mesh heat exchanger modules, there are little differences in the enhancement achieved of Nusselt number values which were attributed to the proximity of their layer-to-layer spacing. Moreover, an empirical correlation was obtained for the wire mesh heat exchangers in terms of Nusselt number, Reynold’s number and the layerto-layer spacing value (S), which is presented in equation 10. NuO = 9.0427. (Red,∞ )0.307 . (
S dout
)−0.128
(10)
For each of the wire heat exchanger modules, a correlation was fitted from experimental data illustrating the relationship between Nusselt number and Reynold’s number based on outer tube diameter and air average velocity. These empirical correlations for the bare heat exchanger module and the other 3 wire mesh heat exchanger samples have the form shown in equation 11, and the coefficients a, and b are listed in Table 1. NuO = a . Reb
15
(11)
Table 1: Curve fit coefficients for the experimental data of outer Nusselt number and Reynold’s number HE module Bare module 4 mm, spaced, finned module 3 mm, spaced, finned module 2 mm, spaced, finned module
a 0.4817 10.107 9.7073 11.904
b 0.5961 0.3068 0.3155 0.2974
Figure 6 illustrates the variation of the Nusselt number enhancement ratio with Reynold’s number. The wire mesh heat exchanger module of 2 mm layer-to-layer spacing achieves the highest Nusselt enhancement ratio with an average value of 2.3 over the entire range of Reynold’s number. A very close thermal performance was observed between all wire mesh heat exchangers, due to the close values of wire mesh layer-to-layer spacings. The decrease of the Nusselt enhancement ratio at higher Reynold numbers having the same trend as [24] is due to the deficiency of heat to transfer at higher air velocities.
Figure 6: the Nusselt number enhancement ratio variation with the Reynold’s number.
16
Experimental results of the bare heat exchanger were compared, as shown in Figure 7, with an experimental study by Wang, Lee, and Sheu [27], and some other empirical formula obtained for the single row, cross flow, heat exchanger by Gnielinski [34]. This comparison shows a good agreement of the experimental data obtained from this study and single row heat exchanger data of [27, 34]. V. Gnielinski's correlation is shown in equations 12 through 15. Nuo,one row = 0.3 + √(Nulam )2 + (Nuturb )2
(12)
where, NuL,lam = 0.664. √Reψ,L . (Pr) NuL,turb =
1⁄ 3
(13)
0.037. (Reψ,L )0.8 . Pr 1 + 2.443(Reψ,L ) Reψ,L =
−0.1
((Pr)
2⁄ 3
− 1)
V. lP ψ. νair
(14)
(15)
Where, the void fraction ψ, depends on the dimensionless transversal pitch (X T/dout), as illustrated in equation 16. ψ=1−(
π. dout ) 4. X T
(16)
Figure 7: Comparison of Nusselt number from experimental data of bare HE module with empirical correlations.
17
The variation of the outer Nusselt number with the Reynold’s number (based on the hydraulic diameter of the channel) is shown in Figure 8. The Nusselt number of the wire mesh heat exchangers always is increased with the increase of Reynold’s number with the same monotonic increase behavior as other enhanced heat exchangers from literature, Figure 8. The 2 mm wire heat exchanger has Nusselt number values higher than that of many other finned heat exchangers at the same Reynold’s number of [10, 16-19]. The higher values of the Nusselt number achieved with the 2 mm wire mesh heat exchanger is due to the highest surface area density of this module.
The correlation of Carmer et al. [25], was experimentally developed for a sinusoidallycorrugated wire mesh contained within two plate heaters. This correlation has been extrapolated for the best performing heat exchanger in order of comparison with the current study. The predicted performance in higher Reynolds number range shows that the proposed heat exchanger in the current study performs better than that of Carmer et al.[25]. This is attributed to the different spacing and the porosity of the two models. Carmer et al. [25] best model had porosity of 48% and spacing of 12 mm while the current model had porosity of 73.8% and spacing of 2, 3 and 4 mm.
Figure 8: Nusselt number variation with Reynold’s number (based on the channel hydraulic diameter) 18
3.2. Pressure drop Air-side pressure drop measurements were carried out for the four tested heat exchanger modules. Figure 9 shows the variation of pressure drop of the air-across different heat exchanger modules by varying the average air velocity. The relationship between the pressure drop for all heat exchanger modules and average air velocity is parabolic as depicted in [4, 11].
The pressure drop measurements of the bare heat exchanger module were also compared with the experimental results obtained for single row bare heat exchanger tested by [27]. It is clear that a good agreement of the experimental data for pressure measurements for both bare single row heat exchangers. It is also observed, that for the 3 mm, and 4 mm spaced finned heat exchanger modules, and the variation in pressure drop is negligible. A maximum pressure drop of 598 Pa was measured for the 2 mm spaced at an air velocity of 10.5 m/s.
Figure 9: Pressure drop variation with average air velocity
19
Figure 10 shows the variation of the air pressure drop with the inlet air velocity of tested wire heat exchanger compared to other enhanced heat exchangers.
Figure 10: Pressure drop variation with average air velocity
3.3. Combined performance Different combined performance criteria could be proposed. We find the most relevant is to define the volumetric efficiency or volumetric heat transfer coefficient was also proposed by [20], and is defined as in equation 17 and the pumping power per unit volume equation 18. hV =
hO . A O V
̇ P⁄ = Vair . ∆P V V
(17) (18)
Where, V is the gross volume occupied by the wire mesh heat exchanger, and Ao is the outer heat transfer surface area of all bare copper pipes. The experimental result of this study is also compared with data of earlier studies of different cross flow heat exchangers with enhancing techniques such as; metal foam, wire mesh, annular fins, flat plain-finned tubes, and louvered fin and tube heat exchangers. The variation of the outer volumetric convective heat transfer coefficient against the external air flow pumping power per unit volume of different heat exchangers is illustrated in Figure 11. 20
Figure 11: Variation of volumetric heat transfer coefficient with fluid pumping power per unit volume of different thermally-enhanced modules.
In Figure 11, the volumetric heat transfer coefficient always increases with the increase in fluid pumping power. This is due to the associated increase in cross flow air velocity. Results also show that at an average value of the pumping power per unit volume, the 3, 4, and 2 mm wire mesh finned modules achieved an increase in the volumetric convective coefficient of 113.9%, 91.5%, and 81.4% as compared to the bare heat exchanger. The single row heat exchanger of T’Joen [14], achieves higher volumetric convection heat transfer coefficients than that for all wire heat exchanger tested samples. This single row heat exchanger consisted of aluminum foam-wrapped pipes. The higher thermal performance could be attributed to better bonding using thermal glue between foam and pipes. Furthermore, another wire heat exchanger experimentally-investigated by Fugmann, Laurenz, and Schnabel [20], performed better than the tested samples of this study from the heat transfer point of view. This could be attributed to that this wire heat exchanger sample consisting of double row of 18, 10 mm outer diameter, copper pipes positioned in a staggered arrangement. Also, the woven wire sheet that was interconnected between these pipes has a wire diameter of 0.1 mm which is smaller than the wire mesh diameter used in this study of 0.15 mm and this magnifies the fin effect.
21
In addition, this wire mesh sheet was fitted into pipes by soldering which has lower contact resistance than press-fitting, despite the press-fitting is much cheaper. The variation of outer convective heat transfer coefficient with the pressure drop of air across each heat exchanger module is depicted in Figure 12. The outer convection coefficient always increases with the increase in pressure drop of air due to the increased turbulence and fluid mixing resulted in higher air velocities. The 3 mm wire mesh heat exchanger gives the highest convective heat transfer coefficients compared to other wire mesh modules at the same pressure drop. Compared to other heat exchangers, the proposed set of heat exchangers under study offer great improvement of thermal performance at a low cost.
Figure 12: Variation of outer convection heat transfer coefficient with pressure drop of air flow
22
4. Uncertainty analysis The uncertainty values of the measured parameters are listed in Table 2. The error propagation due to uncertainty in measured variables is estimated using equation 19, [35]. N
δR = {∑ ( i=1
2
∂R . δX i ) } ∂X i
1⁄ 2
(19)
Where, R represents the primary measured parameter, and δR is the corresponding uncertainty. Uncertainty results are tabulated in Table 3. Table 2: Uncertainty of measured variables Parameter
Uncertainty
Temperature
± 0.1 oC
Pressure head loss
± 1 mm
Velocity
± 0.01 m/s
Water flow rate
± 0.01 l/min
Pipe length
± 0.1 mm
Pipe diameter
± 0.1 mm
Table 3: Maximum relative uncertainty Physical parameter 𝑚̇𝑤 𝑄̇𝑤 ∆TLM ho Nuo
23
Calculated uncertainty ±0.11 % ±11.8 % ±0.9 % ±13.3 % ±13.4 %
5. Conclusion and discussion In this study, the heat transfer and pressure drop performance of the single row waterto-air cross flow heat exchanger were experimentally investigated. The heat exchanger consists of ten equally spaced copper pipes. A rectangular corrugated copper alloy woven wire mesh (40% copper content) is press-fitted to the heat exchanger pipes. Three modules of wire mesh heat exchangers were manufactured of 2, 3 and 4 mm layer-to-layer spacing. The fourth bare tube heat exchanger module is manufactured. The steady-state forced convection experiments were conducted and the conclusions obtained as follow:
Wire mesh heat exchangers are promising for enhancing the heat transfer rate at lower cost and simpler manufacturing, when compared to other enhanced heat exchangers, using metal foams and finned tubes.
Thermal performance: a comparison of Nusselt number ratio (which is the ratio of the Nusselt number of wire mesh heat exchanger to that of the bare module) is made between different wire mesh heat exchanger modules. Maximum average increase of 2.3 times Nusselt number ratio is achieved by the 2 mm spaced finned heat exchanger.
An empirical correlation is developed for the tested wire mesh heat exchanger which shows the dependence of the Nusselt number on the wire mesh heat exchanger dimensionless layer-to-layer spacing and Reynold’s number.
The 3 mm spaced finned wire mesh heat exchanger module gives the highest convection heat transfer coefficient at constant pumping power.
A Comparison between experimental data of the current study with other enhanced cross flow heat exchangers data obtained from open literature is made. Current study results show the same trend as that of other enhanced heat exchangers from literature for the Nusselt number and pressure drop plots. Wire mesh heat exchangers of this study show the comparable thermal performance of other finned tubes cross flow heat exchangers at a low cost.
Pressure drop measurements reveal that all wire mesh heat exchanger modules have higher pressure drop values than the bare heat exchanger. A maximum pressure drop of 598 Pa is measured for the 2 mm spacing at air velocity of 10.5 m/s.
24
References 1. 2. 3. 4. 5. 6. 7. 8. 9. 10. 11. 12. 13. 14. 15. 16. 17. 18. 19. 20. 21. 22. 23. 24. 25. 26. 27. 28. 29. 30. 31. 32. 33.
Bejan, A. and A.D. Kraus, Heat transfer handbook. Vol. 1. 2003: John Wiley & Sons. Bergman, T.L., et al., Fundamentals of heat and mass transfer. 2011: John Wiley & Sons. Thulukkanam, K., Heat exchanger design handbook. 2013: CRC press. Kurian, R., C. Balaji, and S. Venkateshan, Experimental investigation of near compact wire mesh heat exchangers. Applied Thermal Engineering, 2016. 108: p. 1158-1167. Kakaç, S., H. Liu, and A. Pramuanjaroenkij, Heat exchangers: selection, rating, and thermal design. 2002: CRC press. Li, Q., et al., Compact heat exchangers: A review and future applications for a new generation of high temperature solar receivers. Renewable and Sustainable Energy Reviews, 2011. 15(9): p. 4855-4875. Kim, S., J. Paek, and B. Kang, Flow and heat transfer correlations for porous fin in a plate-fin heat exchanger. Journal of heat transfer, 2000. 122(3): p. 572-578. Delgado, J.M.P.Q., Heat and Mass Transfer in Porous Media. 2012: p. 169-171. Rashidi, S., et al., Potentials of porous materials for energy management in heat exchangers–A comprehensive review. Applied energy, 2019. 243: p. 206-232. Nawaz, K., et al., Experimental studies to evaluate the use of metal foams in highly compact air-cooling heat exchangers. 2010. Chumpia, A. and K. Hooman, Performance evaluation of single tubular aluminium foam heat exchangers. Applied Thermal Engineering, 2014. 66(1-2): p. 266-273. Chumpia, A. and K. Hooman, Performance evaluation of tubular aluminum foam heat exchangers in single row arrays. Applied Thermal Engineering, 2015. 83: p. 121-130. Rezaey, R., High temperature gas to liquid metal foam and wire mesh heat exchangers. 2012. T’Joen, C., et al., Thermo-hydraulic study of a single row heat exchanger consisting of metal foam covered round tubes. International Journal of Heat and Mass Transfer, 2010. 53(15-16): p. 3262-3274. Huisseune, H., et al., Thermal hydraulic study of a single row heat exchanger with helically finned tubes. Journal of Heat transfer, 2010. 132(6): p. 061801. Wang, C.-C. and K.-Y. Chi, Heat transfer and friction characteristics of plain fin-and-tube heat exchangers, part I: new experimental data. International Journal of Heat and Mass Transfer, 2000. 43(15): p. 2681-2691. Wang, C.-C., et al., An experimental study of heat transfer and friction characteristics of typical louver fin-and-tube heat exchangers. International journal of heat and mass transfer, 1998. 41(4-5): p. 817-822. Jin, Y., et al., Parametric study and field synergy principle analysis of H-type finned tube bank with 10 rows. International Journal of Heat and Mass Transfer, 2013. 60: p. 241-251. Sparrow, E. and F. Samie, Heat transfer and pressure drop results for one-and two-row arrays of finned tubes. International journal of heat and mass transfer, 1985. 28(12): p. 2247-2259. Fugmann, H., E. Laurenz, and L. Schnabel, Wire Structure Heat Exchangers—New Designs for Efficient Heat Transfer. Energies, 2017. 10(9): p. 1341. Pavel, B.I. and A.A. Mohamad, Experimental investigation of the potential of metallic porous inserts in enhancing forced convective heat transfer. Journal of heat transfer, 2004. 126(4): p. 540-545. Dyga, R. and M. Płaczek, Efficiency of heat transfer in heat exchangers with wire mesh packing. Vol. 53. 2010. 54995508. Xing, F., J. Xie, and J. Xu, Modulated heat transfer tube with mesh cylinder inserted. International Communications in Heat and Mass Transfer, 2014. 56: p. 15-24. Hong, Y., et al., Heat transfer and fluid flow behaviors in a tube with modified wire coils. International Journal of Heat and Mass Transfer, 2018. 124: p. 1347-1360. Cramer, L., G.I. Mahmood, and J.P. Meyer, Thermohydraulic performance of a channel employing wavy porous screens. Heat Transfer Research, 2018. 49(18). Fu, Y., J. Wen, and C. Zhang, An experimental investigation on heat transfer enhancement of sprayed wire-mesh heat exchangers. International Journal of Heat and Mass Transfer, 2017. 112: p. 699-708. WANG, C.-C., W.-S. LEE, and W.-J. SHEU, Airside performance of staggered tube bundle having shallow tube rows. Chemical Engineering Communications, 2001. 187(1): p. 129-147. Ackermann, R.A., Cryogenic regenerative heat exchangers. 2013: Springer Science & Business Media. Schlunder, E.U., Heat Exchanger Design Handbook. 1983: Taylor & Francis Inc. Bowman, R.A., A.C. Mueller, and W.M. Nagle, Mean Temperature Difference in Design. Transactions of the ASME, 1940. 62: p. 283-294. Lapin, A. and W.F. Schurig, Heat Transfer Coefficients for Finned Exchangers. Industrial & Engineering Chemistry, 1959. 51(8): p. 941-944. Gnielinski, V., New equations for heat and mass transfer in turbulent pipe and channel flow. Int. Chem. Eng., 1976. 16(2): p. 359-368. Holman, J., Heat transfer, 1997. P rocess E fficiency [%], 1998. 20: p. 40-60. 25
34. 35.
Gnielinski, V., Gleichungen zur Berechnung des Wärmeübergangs in querdurchströmten einzelnen Rohrreihen und Rohrbündeln. Forschung im Ingenieurwesen A, 1978. 44(1): p. 15-25. Moffat, R.J., Describing the uncertainties in experimental results. Experimental thermal and fluid science, 1988. 1(1): p. 3-17.
26
Highlights
Nu of the wire mesh HX increases on average 2.3 times that of the bare module.
Correlation is developed to express Nu, Re and the dimensionless spacing.
The 3 mm spacing module gives the highest Nu at constant pumping power.
Mesh HX shows promising thermal performance at low cost.
27
Declaration of interests ☒ The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.
☐The authors declare the following financial interests/personal relationships which may be considered as potential competing interests:
28
S1359-4311(19)35553-X https://doi.org/10.1016/j.applthermaleng.2019.114891 ATE 114891
To appear in:
Applied Thermal Engineering
Received Date: Revised Date: Accepted Date:
8 August 2019 27 December 2019 30 December 2019
Please cite this article as: M.A. Sayed, A.M.T.A. ELdein Hussin, W. Aboelsoud, N.A. Mahmoud, Performance evaluation of Wire Mesh Heat Exchangers, Applied Thermal Engineering (2019), doi: https://doi.org/10.1016/ j.applthermaleng.2019.114891
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Performance evaluation of Wire Mesh Heat Exchangers M. A. Sayed 1, A. M.T. A. ELdein Hussin 1, W. Aboelsoud 1, 2, N. A. Mahmoud 1 ____________________________________________________________________________________
Abstract Liquid-to-air cross-flow heat exchangers have a low heat transfer coefficient on the gas side due to poor thermal characteristics of air. One of the promising solutions is to attach extended surfaces on the gas side, thus increase the surface area of heat to transfer by convection. In this study, the experiment was carried out to evaluate the thermal and hydraulic performance of four modules of cross flow heat exchangers. One is bare copper tubes and three wire mesh heat exchangers with different mesh spacing. Hot distilled water was pumped into copper tubes at a constant flow rate of 9 l/min and inlet temperature of 80oC. The heat exchanger subjected to external cross airflow inside an air duct of 20 cm x 20 cm crosssectional area with an average air velocity of 2.8 m/s up to 14.9 m/s. Results showed an enhancement of Nusselt number for all wire mesh modules that is an increase of the volumetric heat transfer coefficient of up to 113.9% among the three tested modules compared to the bare module. The significance of this study is to use reasonably-priced wire mesh and maintain enhancement in the rate of heat transfer.
Keywords: Cross flow heat exchanger, wire mesh heat exchanger, and porous structure.
1. Department of Mechanical Power Engineering, Ain Shams University, Cairo, Egypt, 11517. 2. Corresponding author: E-mail address: [email protected] 1
Nomenclature Ain Inside tube surface area [m2] Aout Outer tube surface area [m2] Ac Cross-sectional area of flow [m2] AU cp Dh D out Dw F H in Ho H out Hv K air K Pipe lP ṁ Nu o Pt ∆P PPI P/V 𝑄̇ Red, ∞
R tot S ∆TLM
Overall heat transfer conductance [W/K] Specific heat at constant pressure [J/kg.K] Hydraulic diameter = 4Ac /Pt [m] Tube outside diameter [m] Wire diameter [mm] Correction factor Tube inside heat transfer coefficient [W/m2.K] Outer convection heat transfer coefficient [W/m2.K] Outer air convection heat transfer coefficient, [W/m2.K] Volumetric convective heat transfer coefficient [W/m3.K] Thermal conductivity of air [W/m.K] Thermal conductivity of pipe material [W/m.K] Copper pipe length [m] Mass flow rate [kg/s]
T U V∞ (or U∞) V̇
Temperature [ºC] Overall heat transfer coefficient [W/m2.K] Average air velocity in the free cross-sectional area of the air duct [m/s] Volume flow rate [m3/s]
XT
Transversal tube pitch [m]
Xt Wire mesh transversal pitch [mm] Overall surface efficiency ηo Greek Symbols ν Kinematic viscosity [m2/s] µ Dynamic viscosity [N.s/m2] ρ
Density [kg/m3]
ψ
Void fraction
ɳ
Efficiency
Subscripts a
Air
d out
Based on outer pipe diameter Outlet
Nusselt number based on the outer tube diameter Wetted perimeter [m] Air pressure drop across heat exchanger module [Pa] Pore per inch
w
Water
in p
Inlet Pipe
tot
Total
Pumping power per unit volume of heat exchanger module (W/m3) Hot water heat transfer rate [W] Reynold’s number based on outer pipe diameter and air velocity Total heat transfer resistance [K/W] Spacing between woven wire mesh sheet layers [mm] Logarithmic mean temperature difference [ºC or K]
v
Volumetric
avg lam
Average Laminar
turb t
Turbulent Wetted
2
Performance Evaluation of Wire Mesh Heat Exchangers M. A. Sayed 3, A. M.T. A. ELdein Hussin 1, W. Aboelsoud 1, 4, N. A. Mahmoud 1 ____________________________________________________________________________________
Abstract Liquid-to-air cross flow heat exchangers have low heat transfer coefficient on the gas side due to poor thermal characteristics of air. One of the promising solutions is to attach extended surfaces on the gas side, thus increase the surface area of heat to transfer by convection. In this study, experiment was carried out to evaluate thermal and hydraulic performance of four modules of cross flow heat exchangers. One is bare copper tubes and three wire mesh heat exchanger with different mesh spacing. Hot distilled water was pumped into copper tubes at constant flow rate of 9 l/min and inlet temperature of 80oC. The heat exchanger was subjected to external cross air flow inside an air duct of 20 cm x 20 cm cross sectional area with an average air velocities of 2.8 m/s up to 14.9 m/s. Results show an enhancement of
Nusselt number for all wire mesh modules that is an increase of the volumetric heat transfer coefficient of up to 113.9% among the three tested modules compared to the bare module. The significance of this study is to use reasonably-priced wire mesh and maintain enhancement
in the rate of heat transfer.
3. Department of Mechanical Power Engineering, Ain Shams University, Cairo, Egypt, 11517. 4. Corresponding author: E-mail address: [email protected] 3
1. Introduction Many industrial and domestic applications involve heat exchange processes, which if developed, can significantly provide savings in energy utilization and cost. Such applications are heat exchangers, which are used in air conditioning equipment, cooling the electrical components and waste heat recovery [1]. The desire of reducing energy consumption by more efficient energy usage has led to the development of more energy-efficient compact heat exchangers [1]. Compact heat exchangers have a large area density, usually of more than 700 (m2/m3) [2, 3]. Also, compact heat exchangers usually have a small hydraulic diameter of Dh ≤ 6 mm [4]. To improve the heat transfer performance of heat exchangers, active and passive techniques are used. One of the most commonly used passive techniques is extended surfaces [1, 5]. Examples of finned surfaces application are shell and tube heat exchanger, plate finned heat exchangers, finned tubes in air conditioning systems, and even in heat sinks used for cooling of electronic devices [1, 2, 6]. In single-pass liquid-to-air heat exchangers, fins are usually attached on the gas side. This is because air has a lower heat transfer coefficient, poor thermal characteristics and conventionally flows outside across the liquid tubes [3, 5]. Fins of many different configurations can be used for heat transfer augmentation on the gas side like plain fins, wavy fins, and louvered fins. However, such types of fins have different manufacturing complexities, high cost, maintenance issues, and they also have low mechanical strength for structural integrity because they are fabricated from thin material sheets [7]. More efficient types of extended surfaces are greatly required. Therefore, the need to develop and use the porous matrix is one of the most promising solutions in that field. Porous media can be defined as a solid matrix that is formed by a solid structure with interconnected void spaces [8]. Different porous inserts like metal foams and wire mesh blocks in channel flows have been investigated experimentally. Many studies were also conducted to assess heat transfer and fluid flow behavior through porous material [9] like metal foam, fins, and wire mesh screen inserts used in the internal flow. Metal foams have been extensively investigated for enhancing the heat removal rate in different configurations of heat exchangers. Nawaz, et al. [10], conducted an experimental study to assess the thermal and fluid flow performance of aluminum foam sheets attached to 4
cross flow water-to-air heat exchanger used in air conditioning applications. Chumpia and Hooman [11, 12], experimentally examined the heat transfer and fluid flow friction of water-to-air single pipe and single row heat exchanger subjected to cross airflow. The pipes were covered with a layer of aluminum foam. They concluded that with higher foam thickness and smaller transversal pitch between foam covered tubes, the rate of heat transfer was higher. Rezaey, [13], compared the effect of using copper metal foam and copper wire screens as extended surfaces attached to the surface of the heat exchanger. The highest heat transfer to water was achieved using wire mesh screens. T’Joen, et al. [14], experimentally evaluated the heat transfer and pressure drop performance of a single row, aluminum foamwrapped pipes, and cross flow heat exchanger. They concluded that the outer convection resistance was reduced with the increase in foam layer thickness, but the pressure drop also increased significantly. Extended surfaces like fins of various shapes attached to heat exchanger pipes were used in different studies. Huisseune, et al. [15], studied the heat transfer and fluid flow behavior for a single row cross flow heat exchanger using helically-finned round pipes. Empirical correlations were developed to predict the friction factor and Nusselt number. Wang et al., and Wang and Chi. [16, 17], experimentally studied the thermal and hydraulic performance of a cross flow heat exchanger. Heat exchanger tubes were attached with flat plain fins and louvered fins, respectively. Results showed that the friction factor is observed to be rather independent of the number of tube rows. They also reported that for the one and two tube rows, the heat transfer increases by the reduction of fin pitch. Yu Jin et al. [18], conducted a CFD numerical study of a 3-D cross flow heat exchanger to assess its heat transfer and pressure loss performance. The 3-D model consisted of ten rows of H-type finned tubes. Sparrow and Samie [19], conducted an experimental work to assess the thermal and pressure drop performance of one and two tube rows cross flow heat exchanger. The heat exchanger consisted of electrically heated rods, attached with integral annular fins. Because the wire-mesh screen is easy to manufacture and costs less than other porous materials, it is considered as an excellent candidate to enhance heat transfer. Fugmann et al. [20], carried out heat transfer and pressure drop experiments on two new proposed manufactured wire mesh heat exchangers. They also compared these wire mesh heat exchangers with other finned modules. Results showed that the wire mesh heat exchanger has the lower weight for a specific required heat transfer surface area as compared to the 5
finned types, despite having a lower heat transfer performance. Pavel, and Mohamad [21], inserted a matrix of aluminum circular wire screens inside a heated copper pipe. The highest increase in Nusselt number was about 5.2 times compared to the bare pipe flow case. Dyga and Płaczek [22], conducted an experimental work to assess the fluid flow characteristics and heat transfer performance of cylindrical multi-layered wrapped wire mesh packing. Xing, et al. [23], experimentally examined the heat transfer characteristics by inserting a cylindrical wire mesh suspended in the water flow stream inside a pipe. Hong et al. [24] experimentally investigated the effect of inserting wire coils inside air pipe flow, on the heat transfer and pressure drop performance. Carmer, et al. [25], conducted experiments to assess heat transfer enhancement achieved by attaching sinusoidally-shaped wire screens between two plate heaters which were then subjected to air flow in a rectangular channel. They reported an increase in heat removal rate and Nusselt number for tested samples having different spacing and porosity values. The highest enhancement in heat transfer was achieved with the screen sample of 12 mm spacing and 48% porosity. In addition, they developed correlations to predict the Nusselt number as a function of the Reynold’s number based on channel hydraulic diameter. Yanchen Fu et al. [26], experimentally assessed the thermal characteristics of air-to-air cross-flow wire mesh heat exchanger. Wang et al. [27], conducted an experimental study to estimate the heat transfer and fluid friction performance of a cross flow water-to-air heat exchanger having bare pipes. In the current study, the cross flow water-to-air heat exchanger consisting of ten equallyspaced wire meshed copper tubes, was tested under the steady-state conditions. Three modules having different layer-to-layer spacings of the wire mesh were tested and compared to the bare tube module. Hot distilled water was allowed to flow inside the heat exchanger tubes with outer air cross flow over the tube row. The experiments conducted on the four heat exchanger modules, covered a wide range of average cross air flow velocities which varied from 2.8 up to 14.9 m/s and covered a broad range of turbulent flow regimes. Experimental setup, fabrication of wire mesh heat exchangers, and procedure of the experiment are explained in the next section.
6
2. Experiment 2.1. Experimental setup The heat exchanger module in the current study consisting of ten equally-spaced copper tubes between two water heaters was bonded. The internal diameter of water tubes is 8.1 mm with a wall thickness of 0.7 mm. Water tubes were subjected to air flow passing through 20 cm x 20 cm air duct. Three of the heat exchanger modules were press-fitted with woven wire meshes, and a fourth bare module was also fabricated for comparison purposes. The woven wire mesh screens used in the heat exchangers have a wire diameter of 0.15 mm with a square opening of 0.3 mm x 0.3 mm, 57 PPI, and a porosity of 73.8%. The porosity of the wire woven mesh is calculated using a formula in [28], which is the function of wire diameter and mesh transverse pitch, equation 1.
α=1−(
π.dw 4.xt
)
(1)
Those copper alloy mesh screens were cut into three sheets of different lengths, all having the same width as the air duct, 20 cm. Each piece of the three cut sheets was shaped with rectangular corrugations and then drilled with ten holes of 9.25 mm in diameter (0.25 mm less than the outer pipe diameter). The ten copper tubes of the heat exchanger were then press-fitted into the drilled sheets, to ensure perfect contact, with a different layer-to-layer spacing of 4, 3, and 2 mm as shown in Figure 1. That is there are three values of the spacings between the layers of corrugated wire mesh heat exchangers of 4, 3, and 2 mm. The four heat exchanger modules tested in this study are shown in Figure 1.
7
(a) Bare heat exchanger module
(b) Wire mesh 4 mm spaced, finned heat exchanger module
(c) Wire mesh 3 mm spaced,
(d) Wire mesh 2 mm spaced,
finned heat exchanger module
finned heat exchanger module
Figure 1: Pictures of the different heat exchanger modules
8
(A)
(B)
Figure 2: Wire mesh corrugated sheet (A) Corrugated sheet press-fitted onto pipes, (B) Microscopic view of the woven wire mesh fibers’ size and pores.
The woven wire mesh screens are illustrated in Figure 2 using an electronic microscope. The temperature of inlet air was measured with a K-type thermocouple, and two calibrated RTDs were installed to measure the inlet and exit temperatures of the hot water. Corrugated wire mesh screens were attached to the one-row heat exchanger modules by press-fitting. Air duct was insulated during experiments using a 5cm-thick, glass wool sheet to minimize the thermal losses to the surroundings. The test rig as shown in Figure 3 consisted of hot water closed cycle and an open-circuit air duct.
9
Figure 3: Single line diagram of the heat exchanger experimental setup
10
The heat exchanger test section is located downstream of the inlet section of the air duct at a distance of 2.3 m to ensure a fully developed flow of air across copper tubes. The air enters through the duct at room temperature using a 5.5 hp, 3-phase centrifugal blower (Y112M - 4) that is located at the end of the outlet section of the air duct after the test section (suction side). The average air velocity and thus the volume flow rate were changed by air damper which was installed at the outlet of centrifugal blower. The air centerline velocity at the inlet to heat exchanger was measured by a hot wire anemometer (Testo-425) having an uncertainty of ±0.01 m/s. The pressure drop of air flow across each heat exchanger module was measured using a water U-tube manometer and an uncertainty value of ± 1 mm. Air inlet temperature at the centerline of air duct was measured by a K-type (24 AWG) thermocouple. Distilled water was heated in a stainless-steel tank by a 4-kW electric heater. Heater’s electrical power supply was controlled by an AC-voltage regulator to ensure constant inlet hot water temperature (± 0.1oC) to the heat exchanger module when either the air flow velocity or the water flow rate varies. The water flow rate to the heat exchanger pipes was changed by a flow control valve with the aid of a by-bass line valve in order to maintain a constant water flow rate. The water flow rate was measured by a turbine flow meter (Gems FT-110 Series) with the uncertainty of ± 0.01 l/min, which was installed downstream of the outlet of the heat exchanger module. Calibrated digital temperature reader, with the uncertainty of ± 0.1oC, was used to measure the inlet and exit water temperatures.
2.2. Experimental procedure Steady-state forced convection heat transfer experiments were conducted for each module of the heat exchangers at different air velocities and water flow rates. The procedure of the experiments has started by turning the centrifugal blower on, water heater, and hot water circulating pump. The air flow rate was adjusted by varying the opening of the volume air damper installed at the exit of the centrifugal blower. At each air volume damper opening, the water inlet temperature was adjusted using the AC-voltage regulator to maintain the desired temperature. Once the steady-state conditions are reached, the inlet air temperature, inlet and exit water temperatures, air velocity, hot water flow rate, and the pressure drop measurements were recorded. 11
The steady-state conditions were considered to be achieved when the measured temperature values were varied by ±0.1oC. All these measurements were taken at a fixed water flow rate of 9 L/min and a temperature of 80oC. All experiments were conducted for the four heat exchanger modules at varying air velocity range between 2.8 and 14.9 m/s. The following section, describes experimental results, its representation of the experimental data, along with analysis and discussion.
3. Results and discussion 3.1. Thermal performance The steady-state heat transfer tests were carried out for the four heat exchanger modules at the same operating conditions for comparison purposes. For each of the heat exchangers, the air flow velocity varied between 2.8 and 14.9 m/s. This velocity range involves a broad range of turbulent flow conditions. A thermal analysis was conducted, based on the logarithmic mean temperature difference, to assess the performance of each of the heat exchangers using the heat transfer rate calculated from the hot water side. The total heat transfer rate can be calculated using the energy balance equation 2, [2, 5]. Q̇w = ṁw ∗ cp,w ∗ (Tw,in − Tw,out )
(2)
Logarithmic mean temperature difference can then be calculated by equation 3, [1, 2, 5, 29]. ∆TLM =
(Tw,in − Ta,out ) − (Tw,out − Ta,in ) T − Ta,out ln( Tw,in − T ) w,out a,in
(3)
Then the overall heat transfer conductance (AU) can be estimated from equation 4, [1, 2, 5]. Q̇w = F . A. U. ∆TLM
(4)
where (F) is a correction factor related to the cross-flow heat exchanger type and to be calculated as elaborated in [30]. However, since the calculated value of the correction factor, F was so close to unity in most cases in this study, it was taken as one in all thermal calculations. The correction factor, F depends on the type of heat exchanger and water inlet
12
and water exit temperatures of the one-row finned tube heat exchanger tested by Lapin and Schurig [31]. The total resistance of heat transfer can then be determined from equation 5.
R tot
d ln( out ) 1 1 1 din = = + + AU hin Ain 2πk pipe lp hout Aout ɳ𝑜
(5)
where ηo , overall surface efficiency, is considered as one, since its value is usually very close to unity, Chumpia and Hooman [12]. Equation 5 can be rearranged to calculate the convective heat transfer coefficient based on the outside surface area of the water tube as illustrated in equation 6. d ln( out ) 1 1 1 din = − − hout Aout AU hin Ain 2πk pipe lp
(6)
The internal convection heat transfer coefficient on the waterside hin is calculated from Gnielinski formula [32], having an uncertainty value of 10%. The third term on the righthand side of the equation 6 is the conduction heat transfer resistance of the copper pipe wall with inner and outer diameters of 8.1 and 9.5 mm respectively. The thermal conductivity of copper is 380 W/m.K [33], and the pipe length is 20 cm. The external convection heat transfer coefficient is calculated based on the copper tube outer surface area (Ao) which is identical for all the heat exchanger modules. Results show that the heat transfer coefficient of the bare module changes with Reynold’s number and reaches a maximum of 303 W/m2.K at a Reynold’s number of 8142. For the 2, 3, and 4 mm wire mesh heat exchangers, the outer heat transfer coefficient reaches a maximum value of 467 W/m2.K at a Reynold’s number of 6339. The outer average Nusselt number based on the outer copper pipe diameter (dout) and the outer convective heat transfer coefficient can be calculated from equation 7, [1, 2]. Nuo =
ho dout k air
(7)
where kair is the thermal conductivity of air at the air inlet temperature. Equation 8, is to define Reynold’s number based on the outside diameter of the pipe. On the other hand, Reynold’s number is also defined based on the hydraulic diameter of the channel for comparison reasons, equation 9.
13
Red,∞ =
ρair . dout . V∞ µair
(8)
ReDh =
ρair . Dh . V∞ µair
(9)
The amount of heat transferred from hot water, at 80oC, and flow rate of 9 L/min, to external air flow is higher than that of bare module for all wire mesh heat exchangers as shown in Figure (4.A). Almost identical thermal performance was observed for the 2 mm, and 3 mm spacing of the finned modules over the entire tested range of Reynold’s number. Figure (4.B), shows an increase in the heat transfer rate up to 4 times that of the bare heat exchanger module. This increase of heat transfer rate in wire mesh heat exchangers was attributed to the larger heat transfer surface area provided by wire mesh sheet to the tubes. (A)
(B)
(B)
Figure 4: (A) Total heat transfer rate variation with average air inlet velocity, (B) The enhancement ratio of heat rate for the 3 wire heat exchanger modules. 14
Figure 5: Nusselt number variation with Reynold’s number.
Figure 5 shows that, the Nusselt number increases with the increase in Reynold’s number, due to the increase of flow turbulence. In addition, Nusselt number for all the wire mesh heat exchangers outperformed that of the bare heat exchanger module. Among the three tested wire mesh heat exchanger modules, there are little differences in the enhancement achieved of Nusselt number values which were attributed to the proximity of their layer-to-layer spacing. Moreover, an empirical correlation was obtained for the wire mesh heat exchangers in terms of Nusselt number, Reynold’s number and the layerto-layer spacing value (S), which is presented in equation 10. NuO = 9.0427. (Red,∞ )0.307 . (
S dout
)−0.128
(10)
For each of the wire heat exchanger modules, a correlation was fitted from experimental data illustrating the relationship between Nusselt number and Reynold’s number based on outer tube diameter and air average velocity. These empirical correlations for the bare heat exchanger module and the other 3 wire mesh heat exchanger samples have the form shown in equation 11, and the coefficients a, and b are listed in Table 1. NuO = a . Reb
15
(11)
Table 1: Curve fit coefficients for the experimental data of outer Nusselt number and Reynold’s number HE module Bare module 4 mm, spaced, finned module 3 mm, spaced, finned module 2 mm, spaced, finned module
a 0.4817 10.107 9.7073 11.904
b 0.5961 0.3068 0.3155 0.2974
Figure 6 illustrates the variation of the Nusselt number enhancement ratio with Reynold’s number. The wire mesh heat exchanger module of 2 mm layer-to-layer spacing achieves the highest Nusselt enhancement ratio with an average value of 2.3 over the entire range of Reynold’s number. A very close thermal performance was observed between all wire mesh heat exchangers, due to the close values of wire mesh layer-to-layer spacings. The decrease of the Nusselt enhancement ratio at higher Reynold numbers having the same trend as [24] is due to the deficiency of heat to transfer at higher air velocities.
Figure 6: the Nusselt number enhancement ratio variation with the Reynold’s number.
16
Experimental results of the bare heat exchanger were compared, as shown in Figure 7, with an experimental study by Wang, Lee, and Sheu [27], and some other empirical formula obtained for the single row, cross flow, heat exchanger by Gnielinski [34]. This comparison shows a good agreement of the experimental data obtained from this study and single row heat exchanger data of [27, 34]. V. Gnielinski's correlation is shown in equations 12 through 15. Nuo,one row = 0.3 + √(Nulam )2 + (Nuturb )2
(12)
where, NuL,lam = 0.664. √Reψ,L . (Pr) NuL,turb =
1⁄ 3
(13)
0.037. (Reψ,L )0.8 . Pr 1 + 2.443(Reψ,L ) Reψ,L =
−0.1
((Pr)
2⁄ 3
− 1)
V. lP ψ. νair
(14)
(15)
Where, the void fraction ψ, depends on the dimensionless transversal pitch (X T/dout), as illustrated in equation 16. ψ=1−(
π. dout ) 4. X T
(16)
Figure 7: Comparison of Nusselt number from experimental data of bare HE module with empirical correlations.
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The variation of the outer Nusselt number with the Reynold’s number (based on the hydraulic diameter of the channel) is shown in Figure 8. The Nusselt number of the wire mesh heat exchangers always is increased with the increase of Reynold’s number with the same monotonic increase behavior as other enhanced heat exchangers from literature, Figure 8. The 2 mm wire heat exchanger has Nusselt number values higher than that of many other finned heat exchangers at the same Reynold’s number of [10, 16-19]. The higher values of the Nusselt number achieved with the 2 mm wire mesh heat exchanger is due to the highest surface area density of this module.
The correlation of Carmer et al. [25], was experimentally developed for a sinusoidallycorrugated wire mesh contained within two plate heaters. This correlation has been extrapolated for the best performing heat exchanger in order of comparison with the current study. The predicted performance in higher Reynolds number range shows that the proposed heat exchanger in the current study performs better than that of Carmer et al.[25]. This is attributed to the different spacing and the porosity of the two models. Carmer et al. [25] best model had porosity of 48% and spacing of 12 mm while the current model had porosity of 73.8% and spacing of 2, 3 and 4 mm.
Figure 8: Nusselt number variation with Reynold’s number (based on the channel hydraulic diameter) 18
3.2. Pressure drop Air-side pressure drop measurements were carried out for the four tested heat exchanger modules. Figure 9 shows the variation of pressure drop of the air-across different heat exchanger modules by varying the average air velocity. The relationship between the pressure drop for all heat exchanger modules and average air velocity is parabolic as depicted in [4, 11].
The pressure drop measurements of the bare heat exchanger module were also compared with the experimental results obtained for single row bare heat exchanger tested by [27]. It is clear that a good agreement of the experimental data for pressure measurements for both bare single row heat exchangers. It is also observed, that for the 3 mm, and 4 mm spaced finned heat exchanger modules, and the variation in pressure drop is negligible. A maximum pressure drop of 598 Pa was measured for the 2 mm spaced at an air velocity of 10.5 m/s.
Figure 9: Pressure drop variation with average air velocity
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Figure 10 shows the variation of the air pressure drop with the inlet air velocity of tested wire heat exchanger compared to other enhanced heat exchangers.
Figure 10: Pressure drop variation with average air velocity
3.3. Combined performance Different combined performance criteria could be proposed. We find the most relevant is to define the volumetric efficiency or volumetric heat transfer coefficient was also proposed by [20], and is defined as in equation 17 and the pumping power per unit volume equation 18. hV =
hO . A O V
̇ P⁄ = Vair . ∆P V V
(17) (18)
Where, V is the gross volume occupied by the wire mesh heat exchanger, and Ao is the outer heat transfer surface area of all bare copper pipes. The experimental result of this study is also compared with data of earlier studies of different cross flow heat exchangers with enhancing techniques such as; metal foam, wire mesh, annular fins, flat plain-finned tubes, and louvered fin and tube heat exchangers. The variation of the outer volumetric convective heat transfer coefficient against the external air flow pumping power per unit volume of different heat exchangers is illustrated in Figure 11. 20
Figure 11: Variation of volumetric heat transfer coefficient with fluid pumping power per unit volume of different thermally-enhanced modules.
In Figure 11, the volumetric heat transfer coefficient always increases with the increase in fluid pumping power. This is due to the associated increase in cross flow air velocity. Results also show that at an average value of the pumping power per unit volume, the 3, 4, and 2 mm wire mesh finned modules achieved an increase in the volumetric convective coefficient of 113.9%, 91.5%, and 81.4% as compared to the bare heat exchanger. The single row heat exchanger of T’Joen [14], achieves higher volumetric convection heat transfer coefficients than that for all wire heat exchanger tested samples. This single row heat exchanger consisted of aluminum foam-wrapped pipes. The higher thermal performance could be attributed to better bonding using thermal glue between foam and pipes. Furthermore, another wire heat exchanger experimentally-investigated by Fugmann, Laurenz, and Schnabel [20], performed better than the tested samples of this study from the heat transfer point of view. This could be attributed to that this wire heat exchanger sample consisting of double row of 18, 10 mm outer diameter, copper pipes positioned in a staggered arrangement. Also, the woven wire sheet that was interconnected between these pipes has a wire diameter of 0.1 mm which is smaller than the wire mesh diameter used in this study of 0.15 mm and this magnifies the fin effect.
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In addition, this wire mesh sheet was fitted into pipes by soldering which has lower contact resistance than press-fitting, despite the press-fitting is much cheaper. The variation of outer convective heat transfer coefficient with the pressure drop of air across each heat exchanger module is depicted in Figure 12. The outer convection coefficient always increases with the increase in pressure drop of air due to the increased turbulence and fluid mixing resulted in higher air velocities. The 3 mm wire mesh heat exchanger gives the highest convective heat transfer coefficients compared to other wire mesh modules at the same pressure drop. Compared to other heat exchangers, the proposed set of heat exchangers under study offer great improvement of thermal performance at a low cost.
Figure 12: Variation of outer convection heat transfer coefficient with pressure drop of air flow
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4. Uncertainty analysis The uncertainty values of the measured parameters are listed in Table 2. The error propagation due to uncertainty in measured variables is estimated using equation 19, [35]. N
δR = {∑ ( i=1
2
∂R . δX i ) } ∂X i
1⁄ 2
(19)
Where, R represents the primary measured parameter, and δR is the corresponding uncertainty. Uncertainty results are tabulated in Table 3. Table 2: Uncertainty of measured variables Parameter
Uncertainty
Temperature
± 0.1 oC
Pressure head loss
± 1 mm
Velocity
± 0.01 m/s
Water flow rate
± 0.01 l/min
Pipe length
± 0.1 mm
Pipe diameter
± 0.1 mm
Table 3: Maximum relative uncertainty Physical parameter 𝑚̇𝑤 𝑄̇𝑤 ∆TLM ho Nuo
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Calculated uncertainty ±0.11 % ±11.8 % ±0.9 % ±13.3 % ±13.4 %
5. Conclusion and discussion In this study, the heat transfer and pressure drop performance of the single row waterto-air cross flow heat exchanger were experimentally investigated. The heat exchanger consists of ten equally spaced copper pipes. A rectangular corrugated copper alloy woven wire mesh (40% copper content) is press-fitted to the heat exchanger pipes. Three modules of wire mesh heat exchangers were manufactured of 2, 3 and 4 mm layer-to-layer spacing. The fourth bare tube heat exchanger module is manufactured. The steady-state forced convection experiments were conducted and the conclusions obtained as follow:
Wire mesh heat exchangers are promising for enhancing the heat transfer rate at lower cost and simpler manufacturing, when compared to other enhanced heat exchangers, using metal foams and finned tubes.
Thermal performance: a comparison of Nusselt number ratio (which is the ratio of the Nusselt number of wire mesh heat exchanger to that of the bare module) is made between different wire mesh heat exchanger modules. Maximum average increase of 2.3 times Nusselt number ratio is achieved by the 2 mm spaced finned heat exchanger.
An empirical correlation is developed for the tested wire mesh heat exchanger which shows the dependence of the Nusselt number on the wire mesh heat exchanger dimensionless layer-to-layer spacing and Reynold’s number.
The 3 mm spaced finned wire mesh heat exchanger module gives the highest convection heat transfer coefficient at constant pumping power.
A Comparison between experimental data of the current study with other enhanced cross flow heat exchangers data obtained from open literature is made. Current study results show the same trend as that of other enhanced heat exchangers from literature for the Nusselt number and pressure drop plots. Wire mesh heat exchangers of this study show the comparable thermal performance of other finned tubes cross flow heat exchangers at a low cost.
Pressure drop measurements reveal that all wire mesh heat exchanger modules have higher pressure drop values than the bare heat exchanger. A maximum pressure drop of 598 Pa is measured for the 2 mm spacing at air velocity of 10.5 m/s.
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Highlights
Nu of the wire mesh HX increases on average 2.3 times that of the bare module.
Correlation is developed to express Nu, Re and the dimensionless spacing.
The 3 mm spacing module gives the highest Nu at constant pumping power.
Mesh HX shows promising thermal performance at low cost.
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Declaration of interests ☒ The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.
☐The authors declare the following financial interests/personal relationships which may be considered as potential competing interests:
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