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Experimental investigation for optimization of design parameters in a rectangular duct with plate-fins heat exchanger by Taguchi method
Applied Thermal Engineering 50 (2013) 604e613
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Applied Thermal Engineering journal homepage: www.elsevier.com/locate/apthermeng
Experimental investigation for optimization of design parameters in a rectangular duct with plate-fins heat exchanger by Taguchi method Isak Kotcioglu a, *, Ahmet Cansiz b, Mansour Nasiri Khalaji a a b
Department of Mechanical Engineering, University of Atatürk, 25240 Erzurum, Turkey Department of ElectricaleElectronics Engineering, University of Atatürk, 25240 Erzurum, Turkey
h i g h l i g h t s < This study presents an optimization of heat exchangers by using Taguchi method. < The optimization includes the effects of the six different design parameters. < Effective design parameters are Re number, height of duct and length of winglet. < Aim of Taguchi analysis is to reach minimum pressure drop and maximum heat transfer.
a r t i c l e i n f o
a b s t r a c t
Article history: Received 27 January 2012 Accepted 22 May 2012 Available online 31 May 2012
This study presents the determination of optimum values of the design parameters in a heat exchanger with a rectangular duct by using Taguchi method. The heat exchanger has plate-fins containing periodically interrupted diverging and converging channel flow domains. The experimental investigation for the established heat exchanger involves short rectangular fins attached in 8 8 arrays to a surface having various inclination angles. The effects of the six design parameters such as the ratio of the duct channel width to height, the ratio of the winglets length to the duct channel length, inclination angles of winglets, Reynolds number, flow velocity and pressure drop are investigated. In the Taguchi experimental design method, Nusselt number and friction factor are considered as performance parameters. An L25 (56) orthogonal array is chosen as an experimental plan for the design parameters. The analysis of Taguchi method conducted with an optimization process to reach minimum pressure drop (friction factor) and maximum heat transfer (Nusselt number) for the designed heat exchanger. Experimental results validated the suitability of the proposed approach. Ó 2012 Elsevier Ltd. All rights reserved.
Keywords: Heat transfer Vortex generator Taguchi method
1. Introduction Thermal processes have practical importance in the heat exchangers from the heat transfer point of view. Plate-fin type heat exchangers are widely used in heating and cooling applications. Heat transfer, pressure losses, weight and price should be taken into account while designing the heat exchangers. Obtaining high heat transfer rates through various enhancement techniques can lead to substantial energy savings. Heat transfer processes in a heat exchanger are significantly improved by turbulence promoters via providing optimum flow condition having different geometrical features and orientations. Consequently, the effects of the sizes and orientations of these geometries are closely related to the * Corresponding author. Tel.: þ90 4422314867; fax: þ90 4422360957. E-mail address: [email protected] (I. Kotcioglu). 1359-4311/$ e see front matter Ó 2012 Elsevier Ltd. All rights reserved. doi:10.1016/j.applthermaleng.2012.05.036
performance of the heat transfer process. Plate-fin type heat exchangers are ones of the many heat exchanger forms described in the literature, which is the objective of this study. In this study a heat exchanger manufactured in a way that the flow is directed by extending surface structure with plate-fins periodically longitudinal interrupted diverging and converging in a duct channel. Goal of designing such geometry is to have a pin-fin arrangement constructed as a diffuserenozzle couple which provides a promoted turbulence in the channel. A literature survey of divergent and convergent channel arrays indicates that the heat transfer and friction characteristics are generally determined on the basis of maximum heat transfer rate. In such arrays the optimum parameters are the inter-fin spacing in both the stream-wise and span-wise directions. It is well known that increasing heat transfer occurs at the expense of increasing the friction factor. In this study, the investigations related to heat transfer enhancement include
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various heat exchanger types having different geometries and associated parameters. Bergles [1e3] prepared a number of survey articles dealing with the heat transfer for different applications. Experimental investigations by Russels et al. [4] and Deb et al. [5] demonstrated the augmentation of heat transfer by means of wing-type vortices. Fuji et al. [6] proposed new enhanced surfaces for forced convection heat transfer at low Reynolds numbers. Channels constructed with these surfaces experience alternate diverging-converging along with the flow passage allowing substantial heat transfer enhancement. Garg and Maji [7] reported the results of a numerical analysis of diverging-converging channels. These results indicate that such channel configuration is an effective technique for enhancing the heat transfer. In addition, Mendes and Sparrow [8] performed an experimental study to determine pressure distribution and friction factor at various taper angles of the diverging-converging tubes. The second law analysis of heat exchangers has been conducted by Bejan [9]. Kobus and Oshio [10] studied a theoretical and experimental study on the thermal performance of a pin-fin heat sink. A theoretical model was formulated to predict the influence of various geometrical, thermal and flow parameters of the effective thermal resistance of the heat sink. Chein and Huang [11] evaluated thermoelectric cooler applications in the electronic cooling. Arslanturk [12] investigated the efficiency of straight fins with temperature-dependent thermal conductivity and determined the temperature distribution within the fins. The studies of El-Saed and Tahat et al. [13,14] observed the optimal spacing of the fins in the span-wise and stream-wise directions for both in-line and staggered arrangements. Tahat et al. [15] also studied the effects of height, inter-fin spaces, thickness and tip-shroud clearance of fins on the heat transfer, fluid flow and pressure drop. Sahin et al. [16] experimentally investigated the effects of the longitudinal fin pairs and lateral separations of consecutively on the heat transfer and pressure drop characteristics by using the Taguchi method. Yakut et al. [17] investigated the efficiency of the hexagonal fins, stream-wise and span-wise distances between fins and flow velocity on thermal resistance and pressure drop characteristics using Taguchi experimental design method. Also the temperature distribution within the selected pin-fins was determined. Kotcioglu et al. [18] investigated a cross-flow heat exchanger in the presence of a balance between the entropy generation due to heat transfer and fluid friction with the second law analysis. Kotcioglu et al. [19] also examined experimentally the convective heat transfer and pressure drop in a cross-flow heat exchanger with hexagonal, square and circular pin-fin arrays. In that study, for the applied conditions, the optimal spacing of the pin-fin in the span-wise and stream-wise directions has been determined. In addition to above mentioned studies, Kotcioglu et al. [20] studied a cross-flow heat recovery-exchanger system operating with unmixed fluids. The thermodynamic analysis of the system was presented via determining the variations of exergy loss with Reynolds number. The effects of inlet conditions of the working fluids on the heat transfer characteristics were correlated via entropy generation number and exergy loss. Gunes et al. [21] investigated the determination of the optimum values of the design parameters in a tube with equilateral triangular crosssectioned coiled wire inserts. Kackar [22] reported that Taguchi method has developed more than 60 performance statistics which can be used depending on the problem being investigated. Experiments by Didarul and Islam et al. [23e27] were performed to investigate the effect of duct height on heat transfer enhancement. Considering the existing studies, all of the parameters affecting the heat transfer and pressure drop processes have not been investigated in detail. This requires a vast number of experiments together with the experimental cost and time consumption. In order to avoid such problems, an optimization criterion is useful to
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determine the quantitative estimate of the various parameters affecting the performance of the heat exchanger and main factors for the optimum design. Within this context, the required information about the behavior of a process is obtained by Taguchi method. Besides reducing the experimental cost, one of the advantages of the Taguchi method over the conventional experimental methods is to minimize the variability around the target when bringing the performance value to the target value. Because of the high cost, instead of determining uncontrollable parameters and removing them, values of controllable parameters which remove or reduce the negative effects of uncontrollable parameters should be investigated. Another advantage of this method is that the optimum working conditions determined from the laboratory study can be reproduced in real applications. For the optimum criteria in a successful application of Taguchi method, a systematic approach covering the necessary steps is very beneficial. In this paper, in addition to above given studies [16e20] an experimental investigation is described by Taguchi methods, which include the enhancement of forced convection heat transfer in a rectangular channel using inclined thin plates as wing-type vortex generators. The channels are constructed with the plates having diverging and converging sections along with the main flow direction. The heat transfer coefficients and pressure drops are measured for air flow with various arrangements of the plates and Reynolds numbers. From the experimental results, the usefulness of the design is determined and the most effective plate angle for heat transfer enhancement is established. Following, the performance of such heat transfer enhancement technique is evaluated and it is proposed that a channel with slits as well as enlargements of the winglet channel decreases the pressure drop. 2. Experimental apparatus and procedure In this experimental study, the tests are constructed in a heat exchanger based on the particular design parameters. The main features of the experimental setup are given elsewhere [28]. The experimental apparatus mainly consists of a settling chamber, the hydrodynamic entrance and test sections. The test section is constructed with stainless steel plates and the fins are arranged as shown in Fig. 1a and b. The inclination angle of the fins are fixed at various angles of b ¼ 7e20 respect to the direction of main flow. According to the tests, the inclination angle of fins with 20 appears to be maximum for the enhancement in the heat transfer. The fins are manufactured in a way that they are attached to the inner side of the bottom and top plates of the duct as shown in Fig. 1b. The dimensions of the designed fin parameters are given in Table 1, where the strong mixing occurs in a buffer region between divergent and convergent channel. In order to obtain a uniform heat flux the heating of the test section is provided by using a Nichrome resistance wire spirally wound over the outer periphery of the rectangular channel. The outer surface of the test section is covered with a layer of glass wool to prevent the heat loss. The cross-sectional areas (a b L) of the rectangular duct for this particular geometry are given in Table 1. The circular duct section is made of a PVC pipe of a 100-mm diameter and a 2040-mm length, which is connected to the convergent section through a flexible pipe. A set of PVC companion flanges is used to house the orifice plate. Air flows from settling chamber to inlet section of the duct where the velocity is fully developed. In order to measure the pressure difference the pressure taps are mounted on the top plate of the rectangular duct. The pressure taps are positioned on the centerlines and mid points between the fins. In order to measure the variation of temperature, the thermocouples are placed at equal intervals along the x and z directions in the duct, as shown in Fig. 1a. The thermocouples are
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Fig. 1. (a) Top view of the geometry and placement of winglets (b) in rectangular test channel.
inserted in holes drilled in the top wall. To measure the outlet and inlet temperatures of the air additional thermocouples are also placed on the downstream face of the orifice plate. The mass flow rate is calculated from the pressure drop across the orifice plate obstruction meter, which is constructed from brass and machined in terms of ASME standards [29]. The centrifugal blower fan is equipped with a 2.5-kW motor to supply the air for the duct. During the course of the experiments, the temperature difference between the mainstream and the heating surface is kept constant at various Reynolds numbers between 3000 and 30,000. At a fixed value of heat input for the given Reynolds number, the variations of the temperature along and transverse the duct at different locations are measured at the duct inlet and outlet, and before and after the orifice plate. 2.1. Flow visualization Flow visualization tests are used to explain the heat transfer features for the various channel geometries of the divergente convergent fin. In order to visualize the flow the Hele-Shaw apparatus is used as a smoke generator. Stream lines inside the channel are shown in Fig. 2, where the air is used as working fluid. From the flow in air channel it is seen that a weak horse shoe vortex appears in front of the fin. The longitudinal strong vortices are generated by the side top edges. The partial differential equations governing the forced convection of the fluid being compressed and heated in a rectangular duct are NaviereStokes and energy equations. As the pressure and temperature changes during study, the computational program calculates the various values of physical properties, with the aid of FORTRAN statements written with finite difference method for solving heat transfer and fluid flow problems. The CFD package code is used to simulate the fluid flow and temperature field, which is based on a finite difference method of solution. Once generating required mesh for the solver the discretization algorithm is used for the convective terms in the solution equations.
The length of fins and angles of inclination are kept constant during any particular test. In the cases where the fin angles are greater than 7, a back-flow region forms just downstream the end of the diverging section, indicating the occurrence of flow separation and the presence of a recirculation zone (shown as A in Fig. 2). In addition, there is a region situated between the diverging and converging channels (regions between A and B, in Fig. 2) where the velocity is not high enough to provide resolution of the flow direction. Due to the pressure rise at the end of the diverging channel (region A) and the pressure drop at the neighboring converging channel (region B), the velocities are high enough to cause turbulence. This region seems to be the mixing zone caused by the split between the divergent and convergent channel pairs. In the representative region between the fins, especially at third, fourth and fifth rows renewal of boundary layer formation is observed. The film patterned flow behavior around the fins is also observed via smoke generator. The present arrangement of the fins diverts the flow direction and the generated longitudinal vortex between the fins promotes the heat transfer from the surface. The heat transfer in the region between the fins in the span-wise direction is also enhanced due to lateral mixing and secondary flow. The results are well fit with those explained by Herman and Kang [30]. The vortex and boundary layer formation around the fin
Table 1 Coefficients for the friction factor correlations and characteristic parameters in the rectangular channel with a wing-type vortex generator. Note that the dimensions of b, a, l, g, s, W, e, c and L are in mm and b is in degree. Channel
b
a
l
g
s
W
b
e
c
L
f ¼ C0Rem
Type1 Type 2 Type 3 Type 4 Type 5 Type 6
10 15 18 20 20 10
202 206 215 226 210 210
60 60 60 60 60 60
10 10 10 10 10 10
9 11 10 12 13 10
23 28 33 55 48 10
7 9 11 15 20 pa
68 64 69 71 80 70
59.6 59.3 58.9 59.7 56.4 60
655 675 660 640 650 660
2.8Re0.166 7.06Re0.221 11.08Re0.242 74.27Re0.165 77.82Re0.116 4.00Re0.224
Fig. 2. Stream lines inside the channel: flow visualization of periodically interrupted diverging-converging adjacent on the channel floor and fin surfaces.
I. Kotcioglu et al. / Applied Thermal Engineering 50 (2013) 604e613
walls are very strong which result in a heat transfer enhancement. The strong attachment of the flow to both sides of the fins plays important role on the heat transfer. The mixing effect of secondary flows is observed in the intermediate region between wing cascades. This is due to the pressure and velocity differences across the passage between the converging and diverging fin pairs. 3. Experimental design and Taguchi method The Taguchi method is being extensively used in industry and engineering analyses due to its wide range of applications. Literature on the methodology is full of case studies from the automobile, plastics, electronics and process industries. The Taguchi’s method of quality engineering can be very effective when it is used properly [31]. The methodology developed by Taguchi for the process or product quality improvement depends on the statistical concepts and tools. This methodology is based on two fundamental concepts: First, the quality losses must be defined as deviations from targets, not conformance to arbitrary specifications, and the second, achieving high system-quality levels economically requires quality to be designed into the product. In order to have a robust system, the parameters are chosen in a way that the sensitivity of the system to the variance is minimum. For this purpose the Taguchi method provides a quality control to optimize the process of engineering experiments. This method helps the researcher to determine the possible combinations of factors and thereby identify the best condition. The Taguchi approach develops rules to carry out experiments, which further simplifies and standardizes the design of the experiment, along with minimizing the required number of factor combinations to test the factor effects. The Taguchi Method is a multi-stage process which consists of three design stages, namely system, parameter and tolerance. In this study, the parameter design stage is used. In the system design, the focus is on the determination of suitable working levels of design factors. The system design also involves the innovation and knowledge from applicable fields of sciences and technology. Once the levels are taken with careful understanding six parameters and five levels are used for the established experiments. The studied factors of the six parameters and five levels are given in Table 2. In the parameter design stage, the factor levels are determined in a way that they produce best performance of the product/process. The optimal condition is selected so that the influence of uncontrollable factors (noise factors) causes minimum variation of system performance. Therefore, the goal of parameter design is to identify the settings which minimize the variation in the performance characteristic and adjust its mean to an ideal value. The tolerance design stage is a procedure of fine tune the results of the parameter design by tightening the tolerance of factors with significant influence on the product. The use of Taguchi method is to demonstrate the large scale effect which is obtainable through a small scale execution (or experiment) using an orthogonal array (OA) and a signal-to-noise ratio (SNR) [31e33]. The procedure is performed with a lower Table 2 The parameters and their corresponding levels. Parameters
Level 1
2
3
4
5
A: Reynolds number () 5000 10,000 15,000 20,000 25,000 B: Width of the duct (mm) 202 206 215 226 210 C: Height of the duct (mm) 10 15 15 20 20 D: Length of the test section (mm) 665 675 660 640 650 E: Length of winglet y-direction (mm) 9 11 10 12 13 F: Inclination angle (b ) 7 9 11 15 20
607
cost, a higher quality, a quick delivery and a desired function. The Noise-Performance Statistics (NPS) are measures of process variability and they are used to identify the control factors and the combined optimal levels, which minimize the process variability. The Signal-to-Noise ratios are also used to measure the effect of the noise on the system. In this system while the signal is defined as the mean the noise is defined as the standard deviation. Such steps usually identify the need of innovation and identification of better materials, parts and machinery. In the Taguchi method the orthogonal array facilitates the experimental design process and provides a recipe for fractional factorial experiments. The choice of a suitable orthogonal array is critical for the success of an experiment and depends on the total degrees of freedom required to study the main and interaction effects, goal of experiment, resources and budget available and time constraints. Consequently, the orthogonal array allows computing the main and interaction effects via a minimizing number of experimental trials. The Taguchi analysis is performed with Minitab 15.0 software package, a computer program designed to perform the statistical functions. The software package generates the orthogonal array designs, where the degrees of freedom for the array design should be greater than or at least equal to those for the design parameters. For this reason L25 are suitable for the considered design. For six parameters at five levels each, the traditional full factorial design would require 56 experiments. Before selecting the orthogonal array, the minimum number of conducted experiments (Nt) can be fixed by using the following relation,
Nt ¼ 1 þ Nv ½Ln 1
(1)
where Nv is the number of fin channels and Ln is the number of levels. In this analysis, Nv ¼ 6 and Ln ¼ 5 are taken for fin channel and Nv ¼ 3 and Ln ¼ 5 are taken for the empty channel. Hence a minimum of 25 experiments are to be conducted. The available standard orthogonal arrays are L4, L8, L9, L12, L16, L18 etc. According to the Taguchi design concept L25 orthogonal array is chosen for the experiments as shown in Tables 3 and 4. As indicated in these tables, the observed values of the Reynolds number (A), width of
Table 3 Experimental plan of L25 (56) for friction factor and Nusselt number with their SNR values for winglet system. Experiment
A
B
C
D
E
F
f
SeN
Nu
SeN
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
1 1 1 1 1 2 2 2 2 2 3 3 3 3 3 4 4 4 4 4 5 5 5 5 5
1 2 3 4 5 1 2 3 4 5 1 2 3 4 5 1 2 3 4 5 1 2 3 4 5
1 2 3 4 5 2 3 4 5 1 3 4 5 1 2 4 5 1 2 3 5 1 2 3 4
1 2 3 4 5 3 4 5 1 2 5 1 2 3 4 2 3 4 5 1 4 5 1 2 3
1 2 3 4 5 4 5 1 2 3 2 3 4 5 1 5 1 2 3 4 3 4 5 1 2
1 2 3 4 5 5 1 2 3 4 4 5 1 2 3 3 4 5 1 2 2 3 4 5 1
1.15 1.76 2.14 2.23 2.27 1.46 1.67 2.04 1.97 0.85 1.77 1.97 1.73 0.60 1.33 1.63 1.93 0.68 1.05 1.42 1.63 0.62 1.02 1.36 1.67
1.22 4.93 6.61 6.97 7.13 3.33 4.49 6.21 5.88 1.32 4.96 5.90 4.77 4.35 2.48 4.28 5.73 3.25 0.45 3.07 4.28 4.13 0.24 2.71 4.50
15.2 18.4 23.9 32.6 39.7 47.8 61.2 21.6 32.4 36.4 35.9 47.9 63.1 85.0 28.6 94.2 36.4 45.5 56.1 75.5 59.7 81.4 118 43.1 53.7
23.6 25.3 27.5 30.2 31.9 33.6 35.7 26.7 30.2 31.2 31.1 33.6 36.0 38.5 29.1 39.4 31.2 33.1 34.9 37.5 35.5 38.2 41.5 32.6 34.6
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Table 4 Experimental plan of L25 (53) orthogonal array and SNR values for without winglet system. Experiment
A
B
C
f
SeN
Nu
SeN
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
1 1 1 1 1 2 2 2 2 2 3 3 3 3 3 4 4 4 4 4 5 5 5 5 5
1 2 3 4 5 1 2 3 4 5 1 2 3 4 5 1 2 3 4 5 1 2 3 4 5
1 2 3 4 5 2 3 4 5 1 3 4 5 1 2 4 5 1 2 3 5 1 2 3 4
0.131 0.065 0.051 0.046 0.040 0.032 0.024 0.021 0.023 0.071 0.015 0.013 0.014 0.054 0.023 0.009 0.010 0.037 0.019 0.012 0.007 0.027 0.014 0.011 0.008
17.63 23.61 25.78 26.64 27.78 29.84 32.36 33.33 32.56 22.95 36.13 37.46 36.80 25.27 32.70 40.22 39.92 28.50 34.02 37.98 42.13 31.07 36.70 38.75 41.52
38.62 50.60 55.79 58.00 61.06 49.39 88.97 92.95 89.76 58.17 116.4 123.6 120.0 71.33 99.74 150.2 148.2 88.55 113.5 135.8 172.9 105.0 135.3 148.5 168.3
31.73 34.08 34.93 35.36 35.71 37.99 38.98 39.36 39.06 35.29 41.32 41.84 41.58 37.06 39.97 43.53 43.41 38.94 41.10 42.66 44.75 40.42 42.63 43.43 44.52
the duct (B), height of the duct (C), length of the test section (D), length of winglet in y-direction (E) and inclination angle (F) are set at maximum level. Each experimental trail is performed as per L25. The optimization of the observed values is determined by comparing the standard method and Analysis of Variance (ANOVA).
Table 6 Factorial effect and contribution ratio for friction factor for winglet system.
SNR
The Analysis of Variance is used to analyze the results of the orthogonal array experiment in product design and to determine how much variation each quality-influencing factor contributes [34]. Table 3 shows the experimental design for L25 orthogonal array. All of the observed values are calculated based on the concept of higher the better and smaller the better. In this analysis, the observed values of efficiency, friction factor and Nusselt number are set to be maximum and minimum, respectively. Following, the ANOVA is used to analyze the experimental data. The control factors which may contribute to reduced variation can be quickly identified by looking at the amount of variation present as a response. The method significantly reduces the time required for experimental investigation [31,32]. In the Taguchi analysis, there exist three types of quality characteristics concerning the target design considered as SNR values. These are “higher is the better”, “nominal is the best” and “lower is the better”. As SNR value gets higher, the quality of product improves. The principal aim is to
Table 5 Factorial effect and contribution ratio for Nusselt number for winglet system. Level SNR
1 2 3 4 5 R (maxemin) Rank Contribution ratio (%)
A
B
C
D
E
F
27.7 31.5 33.6 35.2 36.5 8.74 2 44.49
32.6 32.8 32.9 33.3 32.9 0.67 4 3.42
32.9 32.9 32.9 32.9 33.0 0.09 6 1.77
33.3 32.9 33.1 32.9 32.6 0.71 3 3.6
28.6 30.8 32.5 35.1 37.4 8.78 1 44.67
32.9 32.7 32.9 33.0 33.0 0.33 5 2.09
A
B
C
D
E
F
5.3 3.7 2.7 2.0 1.5 3.8 2 22.8
3.6 3.3 2.9 2.3 3.1 1.2 4 4.6
2.3 2.2 4.3 5.5 5.5 7.9 1 47.0
3.2 3.0 3.1 2.9 2.9 0.3 6 2.0
3.6 3.4 3.1 2.8 2.3 1.3 3 13.2
3.0 2.8 3.0 3.3 3.1 0.4 5 7.2
R (maxemin) Rank Contribution ratio (%)
maximize the SNR value. Thus minimizing the effect of random noise factors has significant impact on the process performance. The SNR value, which condenses the multiple data points within a trial, depends on the type of characteristic being evaluated. All of the experiments are listed in a plan given in Tables 3 and 4. Contribution ratios of all factors on the performance criteria depending on the SNR values are given in Tables 5 and 6. Using these tables the optimal combination of the process parameters can be predicted. In order to execute the confirmation procedure of reproducibility, the difference of the S/N ratio between the optimum and current conditions in relation to estimation is obtained. From the SNR differences, the optimal process parameters obtained from the parameter design is verified. The optimal values of the factors are determined by maximizing the Nusselt number and minimizing the pressure loss, given in Table 7. The performance statistics (SNR) are selected as the optimization criteria and used as “the higher is the better” (Nusselt number) and “the lower is the better” (friction factor) situations and are evaluated by,
"
ZH 3.1. Analysis of variance (ANOVA)
Level 1 2 3 4 5
n 1X 1 ¼ 10 log n i ¼ 1 Yi2
#
"
n 1X Y2 ZL ¼ 10 log n i¼1 i
# (2)
where Z indicates performance statistic, n is the number of repetitions in confirmation experiments and Y is the performance value of the experiment.
3.2. Experimental plan for the optimization The heat transfer and pressure drop characteristics are generally used to describe the performance of a heat exchanger. In the Taguchi method, the experiment corresponding to the optimum working conditions may not be considered during the experiments. In such cases, the performance value corresponding to optimum working conditions can be predicted by utilizing the balanced characteristic of the orthogonal array. The planned experimental objective based on the Taguchi method is to determine the main effects of the working parameters of heat exchanger, to perform the analysis of variance and to establish the optimum conditions. The effects of each design parameter on the
Table 7 Optimum conditions and performance values of tested models for winglet system, where superscripts a, b, c, d, e and f are the sequence of effective parameters. Parameters A
B
C
D
E
F
Re
E
H
P
q
L
Nu
Optimum level Optimum value
5b 25000
5d 210
5e 20
5c 67.5
5a 20
5f 655
f
Optimum level Optimum value
2e 10000
4d 210
1a 10
5f 70
3a 11
5e 660
Real value
110.5 1.458
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609
Fig. 3. The effects of design parameters of A, B, C, D, E and F on Nusselt number.
Nusselt number and friction factor are shown in Figs. 3 and 4, respectively. The results indicate that the pressure drop increases with increasing the heat transfer. The performances of the heat exchanger can be calculated for each experiment of the L25 by using the observed values of the efficiency, friction factor and overall Nusselt number from Tables 5, 6, 8 and 9, which lists the ANOVA test results for efficiency, thermal resistance and overall heat transfer coefficient, respectively. The optimum operating conditions of heat exchanger for each of the observed values are illustrated in Tables 7 and 10.
3.3. Data reduction and uncertainty analysis In order to calculate the external free convection occurring between the outer surface of the insulated heat exchanger and the surroundings in flow direction the outer surface temperature of insulation must be known. The power supply provides a heating power (Q) of
Q ¼
ks A½Tw Tm L
(3)
where ks is the thermal conductivity of shell of stainless steel, Tw is the heated surface temperature and Tm is the bulk temperature. In this system L donates the distance traveled by air flow in the heat exchanger and A is the cross-sectional heat transfer area of the heating element. Therefore, the heat transfer area is given by
A ¼ aL þ 2Nw b½W þ L
(4)
where the values of parameters Nw, a, L, b and W are given in Fig. 1a. In Eq. (4), the first term on the right hand side of the equation represents area of the plate on the single layer and second term represents the cross-sectional area with the winglets. The thermal resistance (Rth) is defined as
Rth ¼
1 Tave TN ¼ KA Q
Fig. 4. The effects of design parameters of A, B, C, D, E and F on friction factor.
(5)
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Table 8 Factorial effect and contribution ratio for Nusselt number for without winglet system.
SNR
Level
A
B
C
1 2 3 4 5
34.3 37.3 40.3 41.9 43.1 8.8 1 64.1
39.0 39.7 39.4 39.1 39.6 0.71 3 5.1
36.6 38.3 40.2 40.9 40.9 4.2 2 30.6
R (maxemin) Rank Contribution ratio (%)
Parameters
where Tave is the average temperature of the base of the heat exchanger and TN is the temperature of the fluid flow. The local heat transfer coefficient is calculated from the following equation.
h ¼
q_ Tw Tm
(6)
where q_ is the heat flux. Tm is evaluated by energy balance calculation at a given cross section such that it is defined in term of the thermal energy transported by the fluid as it moves past the cross _ mC _ p, where Cp is section based on the equation given by Tm ¼ E= _ is the mass flow rate (m _ ¼ ruA) and the specific heat of the fluid, m E_ is the thermal energy balances. Consequently, by using the local heat transfer coefficient in Eq. (6) the local Nusselt number (Nu) is defined as,
Nu ¼
hDh ka
(7)
where ka is the thermal conductivity of air and Dh is the duck hydraulic diameter of the test section. The local Nusselt number is evaluated at points along the test section in terms of the local heat flux, local difference between the wall and bulk coolant temperatures and the properties evaluated at the bulk temperature of the fluid. The friction factor (f), which is evaluated from the pressure difference between the points just upstream and downstream of the fins attached to the heating surface is defined as,
f ¼
Dp 1 2 rU ½L=Dh 2
(8)
where U is the average flow velocity in the test section and r is the density. Reynolds numbers based on the mean velocity and the duct hydraulic diameter can be expressed as
Re ¼
UDh v
(9)
where v is the kinematic viscosity of air. The uncertainties associated with the measured and calculated values in a given experimental setup are analyzed to report the results with the highest
Table 9 Factorial effect and contribution ratio for friction factor for without winglet system.
SNR
Level
A
B
C
1 2 3 4 5
24.3 30.2 33.6 36.1 38.0 13.7 1 52.5
33.1 32.8 32.2 31.4 32.6 1.74 3 6.6
25.0 31.3 34.2 35.8 35.8 10.6 2 40.74
R (maxemin) Rank Contribution ratio (%)
Table 10 Optimum conditions and performance values for tested models for without winglet system, where superscripts a, b and c are the sequence of effective parameters.
A
B
C
Real value
Re
E
H
L
Nu
Optimum level Optimum value
5a 25000
4b 210
5c 20
110.5
f
Optimum level Optimum value
5a 25000
5c 210
5b 20
1.458
accuracy. The percentage relative uncertainty in the measured temperature for the thermocouples and the infrared camera are 0.25%. This value is applicable when the temperature measurements are within 0e100 C temperature range. The total uncertainty associated with the mass flow rate and Reynolds number is found to be 4% in the turbulent flow regime. The percentage relative uncertainty varies from 2.5% to 1.8% both for the heat transfer coefficient and Nusselt number. The uncertainties of experimental measurements are determined by using the method introduced by Kline and McClintock [35]. 4. Results and discussion It is not easy to simultaneously increase the heat transfer and decrease the pressure drop in a heat exchanger. With this respect the friction factor and the heat transfer coefficients for the divergingeconverging fin pattern and various duct heights need to be explored. For the experimental analysis regarding the constructed heat exchanger the considered parameters are the ratio of the duct channel width to height, the ratio of the fins length to the duct channel length, inclination angles of fins, Reynolds number, flow velocity and pressure drop. As it is stated in previous section each parameter has five levels, given in Table 2. A systematic approach is used to plan and analyze the results by establishing particular objectives such as the optimal condition for the product or process, the contribution of individual factors and the response under optimal conditions. In order to establish these conditions, the collected experimental data are analyzed for determination of the effects of each design parameter on heat transfer and friction factor. The effects of each design parameter on Nusselt number and friction factor are plotted in Figs. 3 and 4, respectively. The effects of the optimum performance statistics (SNR) values of each design parameter A, B, C, D, E and F on the heat transfer and friction factor are given in Table 2. The factor response table and graphs of the noise factors (N) are obtained from their computed SNR values given in Tables 5, 6, 8 and 9. Testing the combination of processing conditions through numerical simulation experiment produced the response diagram for the design factors, as shown in Figs. 3e6. Considering these tables and figures, the six noise factors by the standard L25 orthogonal array are configured. The larger slope in figures means that the effect of its noise factors is greater on the performance characteristic. This indicates that designing such element can achieve the lower-the-better property of performance characteristic. Because the variable factors have the greater effect on the performance characteristic, its deviation ratio will be greater. Since the effect of the SNR values is highest on the temperature, its contribution ratio shows six noticeable variable factors according to the sequence of Reynolds number, width of the duct, height of the duct, length of fin in y-direction, length of the test section and inclination angle. The test samples are designed by combining the six factors (A, B, C, D, E and F) and three factors (A, C and E)
I. Kotcioglu et al. / Applied Thermal Engineering 50 (2013) 604e613
611
Fig. 5. The effects of design parameters of A, B and C on friction factor.
which are selected to be the optimal conditions. The confirmation tests are performed by using these samples to confirm the reproducibility of the obtained results. The test samples are then divided into two methods regarded as presumed and confirmed tests of SNR values for optimal conditions in the cases of with and without the fins. After determining the optimum working parameters of heat exchanger the experiments are conducted and their values are provided in Tables 7 and 10. The experimental results give the optimum performance of heat exchanger and these values are found to be better than that of the previous observations. The certain typical models are calculated according to the orthogonal array and then the relatively better one could be obtained through the performance statistic analysis. In this calculation, the parameter R is the difference of maximum and minimum of the SNR value for every factor. The contribution ratio is equal to the ratio of the R values of each factor to the total R value of all factors as presented in Tables 5, 6, 8 and 9. The rank row is the order of factors according to the effectiveness. The contribution ratio of each parameter to Nusselt number and to friction factor is shown in Figs. 7 and 8, respectively. As can be seen from these figures, the pitch ratio has 60% of the total effect. This means that the parameter E is the most effective one on heat transfer. Considering the parameters of A, B, C, D, E and F in Fig. 7A and E are the most effective parameters on the Nusselt number with a contribution ratio of 47% of the total effect, while A, C and E are the most effective parameters on friction factor with a contribution ratio of 22e50% of the total effect as seen from Fig. 8. It is easy to evaluate the effects of optimum design parameters separately. In order to obtain an idea over the total optimization by making a reasonable comparison of each goal the combination of these effects is required. To combine the separate effects of each goal for general optimization, the importance of the levels of each parameter is defined firstly. Consequently, the final step is to control whether the real values obtained by the confirmation tests are in the confidence interval or not. According to the above arguments, the results prove that the Taguchi method is a reliable and easily applicable optimization tool for studying heat transfer enhancement. Since the essential quantities regarding the heat transfer are the friction factor and the heat transfer coefficients for the heat exchanger under consideration, it is important to determine these parameters. In order to estimate the pressure drop as well as thermal performance together with the insertion of the fins, the friction factor is measured for different duct size and dimensions.
The results are presented in Fig. 9. Pressure drop measurements for the six arrangements are converted to the friction factors, which are defined as,
f ¼
DP f ¼ a Reb ½a=bc ½s=bd ½e=Le ½tan b rU 2
(10)
where a ¼ 3915.91, b ¼ 0.286, c ¼ 1.317, d ¼ 0.156, e ¼ 1.059 and f ¼ 0.196. This friction occurs due to the turbulence and flow interactions caused by the diverging-converging fin pattern. In addition, for the empty channel configuration, where the fins are not placed on, the pressure drop measurements for the three arrangements tested in this study are converted to friction factors, defined as,
f ¼ a Reb ½a=bc
(11)
where a ¼ 2.663, b ¼ 0.98348 and c ¼ 1.785. Due to the effect of the inclined fins in the channel, the pressure drop also increases with increasing inclination angle. As also seen in Fig. 9, for all types of channel geometries, the dependence on the Reynolds number is pronounced and the value of the friction factor decreases with increasing the Reynolds number. This is due to the fact that the divergenteconvergent fin pattern vortex generated by the first row fin strikes the large side wall of the following fin as well as the surface. Consequently, a large drag force is developed and a higher pressure drop occurs. The large pressure drops are attributed to flow separation in diverging parts of the channel. Hence, by narrowing the separation zone a decrease in pressure drop is expected. The effect of the particular design of plate-fin heat exchanger on the Nusselt number is investigated in according with the Reynolds number. The mean Nusselt number (Num) is defined in terms of the mean flux and the mean difference between wall and fluid temperatures. The mean Nusselt number is expressed with the DittuseBoelter correlation, given by the following equation,
Num ¼ 0:023 Re0:8 Pr0:4
(12)
where Pr is the Prandtl number of air. As can be seen in Fig. 10, the average Nusselt number is a function of the Reynolds number. It is also seen from this figure that there is a good agreement between the results for the rectangular channel [28] and these correlations are observed over a wide range of the Reynolds number. This result suggests that the experimental apparatus used in this study is adequate.
Fig. 6. The effects of design parameters of A, B and C on Nusselt number.
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200 Dittus Boelter Correlation Experimental Data (Eq.)
Nusselt Number
160
120
80
40 Fig. 7. The contribution ratio of parameters of A, B, C, D, E and F to Nusselt number.
0
5000
10000
15000
20000
25000
Reynold Number Fig. 10. Effect of diverging-converging plate-fins on the average Nusselt number.
(E) are much effective on the Nusselt number, as shown in Figs. 3 and 7. The average Nusselt number increases with increasing the inclination angle. This result agrees with those given for the same type of the heat exchanger in literature [35]. 5. Conclusion
Fig. 8. The contribution ratio of parameters of A, B, C, D, E and F to friction factor.
2.5 General Correlation Experimental Data (Eq.)
Friction Factor
2
1.5
1
0.5
0 0
5000
10000
15000 20000 Reynolds Number
25000
30000
Fig. 9. Effect of diverging-converging plate-fins on friction factors.
Finally, the effects of the fin geometry on the heat transfer and pressure drop characteristics of rectangular channels are analyzed with the following equation.
Nu ¼ 1:48 Re0:63 ½a=b0:70 ½c=L0:65 ½tan b
1:4
(13)
From the point of the heat transfer enhancement view the parameters of Reynolds number (A) and length of fin in y-direction
The work described in this study is believed to be one of the first fundamental-level studies of the periodically interrupted divergingeconverging plate-fin heat exchangers. Within this context, an experimental investigation of designed fin patterns via considering the heat transfer and flow characteristics was described. Following the effects of fin height, inclination angle, fin pattern model and Reynolds number were examined with the Taguchi method. The optimal parameters have been designed to maximize the heat transfer and minimize the pressure drop in the heat exchanger. The selected parameters for the heat exchanger are Reynolds number, width of the duct, height of the duct, length of the test section, length of the fin, and inclination angle. The performance of this particular heat transfer enhancement technique was evaluated and it was proposed that a channel with slits as well as enlargements of the winglet channel decreases the pressure drop. From the results of flow visualization, the mixing effect of secondary flows is seen in the intermediate region between wing cascades. This was due to the pressure and velocity differences across the passage between the converging and diverging pairs of fins. A boundary layer develops at each contraction part and a flow separation occurs at the end of the enlargement part. The heat transfer is high around the fin rows for diverging and converging fin patterns. The heat transfer in the region between fins in the spanwise direction is also enhanced due to lateral mixing and secondary flow. In the diverging and converging fin pattern, the horseshoe vortexes as well as the vortexes generated by the side top and corner edges strongly touch the alternately angled plate-fin surfaces and end-wall, which significantly enhances the heat transfer. The level of heat transfer increases in a narrow width duct compared to a flat plate because the upper wall induces the flow vortex to attach to the end-wall and fin surface more strongly. The inclination angle of fins has a great influence on the heat transfer enhancement. The inclination angle of 20 appears to be
I. Kotcioglu et al. / Applied Thermal Engineering 50 (2013) 604e613
maximum for enhancement in the heat transfer. It can be concluded that the flow is turbulent in the intermediate regions. Thus, the heat transfer enhancement of the introduced rectangular channel geometries can be attributed to the secondary flow caused by the tabulator type flow effect and the frequent boundary layer interruptions at each enlargement part. As the inclination angle of the fin increases the mixing effect in the intermediate region between fins cascades improves the heat transfer characteristics. Nomenclature A a b c Cp Dh E_ f g h K ka ks l L Ln _ m Nu Nt Nv Nw n Pr Re Rth Q q_ Tave Tm Tw TN DP U W Y Z
cross-sectional heat transfer area of the heating element (m2) width of the duct (m) height of the duct in y-direction (m) length of winglet in x-direction (m) specific heat of the fluid (kJ/kg K) hydraulic diameter (m) thermal energy balances (W) friction factor distance between wing corners in narrow configuration (m) local heat transfer coefficient (W/m2 K) overall heat transfer coefficient (W/m2 K) thermal conductivity of air (W/m K) thermal conductivity of steel (W/m K) length of a winglet (m) length of the test section (duct, m) number of levels mass flow rate (kg/s) Nusselt number minimum number of conducted experiments number of variables number of winglets number of repetitions in confirmation experiments Prandtl number Reynolds number thermal resistance heating power (W) heat flux (W/m2) average temperature of the base of the heat exchanger (K) bulk temperature in the heating element (K) heated surface temperature (K) temperature of the fluid flow (K) pressure drop (Pa) average velocity (m/s) distance between wing corners in wide configuration performance value of the experiment performance statistic
Greek symbols inclination angle kinematic viscosity of air (m2/s) density (kg/m3)
b n r
References [1] A.E. Bergles, Enhancement of heat transfer, Int. J. Heat Transfer 6 (1978) 89e168. [2] A.E. Bergles, Augmentation of Heat Transfer, Heat Exchanger Design Handbook, Hemisphere Publ. Corp, Washington, D.C, 1983. [3] A.E. Bergles, Techniques to Augment Heat Transfer, Handbook of Heat Transfer Applications, McGraw-Hill, New York, 1985. [4] C.M. Russels, B.T.V. Jones, G.H. Lee, Heat transfer enhancement using vortex generators, Proc. 7th Int. Heat Transfer Conf., Munich 3 (1982) 283e288.
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[5] P. Deb, G. Biswas, N.K. Mitra, Heat transfer and fluid structure in laminar and turbulent flows in a rectangular channel with longitudinal vortices, Int. J. Heat Mass Transfer 38 (1995) 2427e2444. [6] M. Fuji, Y. Sensimo, G. Yamanaka, Heat transfer and pressure drop of perforated surface heat exchanger with passage enlargement and contraction, Int. J. Heat Mass Transfer 31 (1988) 135e142. [7] V.K. Garg, P.K. Maji, Laminar flow and heat transfer in a periodically convergingediverging channel, Int. J. Numer. Methods Fluids 8 (1988) 579e597. [8] P.S. Mendes, E.M. Sparrow, Periodically convergingediverging tubes and their turbulent heat transfer, pressure drop, fluid flow and enhancement characteristics, Int. J. Heat Transfer 106 (1984) 55e63. [9] A. Bejan, Entropy Generation through Fluid Flow, Wiley, New York, 1982. [10] C.J. Kobus, T. Oshio, Development of a theoretical model for predicting the thermal performance characteristics of a vertical pin-fin array heat sink under combined forced and natural convection with impinging flow, Int. J. Heat Mass Transfer 48 (2005) 1053e1063. [11] R. Chein, G. Huang, Thermoelectric cooler application in electronic cooling, Appl. Thermal Eng. 24 (2004) 2207e2217. [12] C. Arslanturk, A decomposition method for fin efficiency of convective straight fins with temperature-dependent thermal conductivity, Int. Commun. Heat Mass Transfer 32 (2005) 831e841. [13] S.A. El-Saed, S.M. Mohamed, A.M. Abdel-Latif, A.E. Abouda, Investigation of turbulent heat transfer and fluid flow in longitudinal rectangular-fin arrays of different geometries and shrouded fin array, Exp. Therm. Fluid Sci. 26 (2002) 879e900. [14] M.A. Tahat, R.F. Babushaq, S.D. Probert, Forced steady-state convection from pin-fin arrays, Appl. Energy 48 (1994) 335e351. [15] M.A. Tahat, Z.H. Kodah, B.A. Jarrah, S.D. Probert, Heat transfers from pinfin arrays experiencing forced convection, Appl. Energy 67 (2000) 419e442. [16] B. Sahin, K. Yakut, I. Kotcioglu, C. Celik, Optimum design parameters of a heat exchanger, Appl. Energy 82 (2005) 90e106. [17] K. Yakut, N. Alemdaroglu, I. Kotcioglu, C. Celik, Experimental investigation of thermal resistance of a heat sink with hexagonal fins, Appl. Thermal Eng. 26 (2006) 2262e2271. [18] I. Kotcioglu, S. Caliskan, A. Cansiz, S. Baskaya, Second law analysis and heat transfer in a cross-flow heat exchanger with a new winglet-type vortex generator, Energy 35 (2010) 3686e3695. [19] I. Kotcioglu, S. Caliskan, S. Baskaya, Experimental study on the heat transfer and pressure drop of a cross-flow heat exchanger with different pin-fin arrays, Heat Mass Transfer 47 (9) (2011) 1133e1142. [20] I. Kotcioglu, A. Cansiz, Heat transfer properties and energy-exergy efficiency in a finned cross-flow heat recovery unit, J. Heat Transfer 133 (4) (2011) 044503e044504. [21] S. Günes, E. Manay, E. Senyigit, V. Ozceyhan, A Taguchi approach for optimization of design parameters in a tube with coiled wire inserts, Appl. Thermal Eng. 31 (2011) 2568e2577. [22] R.N. Kackar, Off-line quality control, parameter design and Taguchi methods, J. Qual. Technol. 17 (1985) 176e209. [23] I.M. Didarul, K. Oyakawa, M. Yaga, Enhancement of heat transfer from a surface with rectangular fins of different patterns and arrangements in a duct flow, J. Enhanc. Heat Transfer 15 (2008). [24] M.D. Islam, K. Oyakawa, M. Yaga, I. Kubo, The effects of duct height on heat transfer enhancement of a co-rotating type rectangular finned surface in duct, Exp. Therm. Fluid Sci. 33 (2009) 348e356. [25] M.D. Islam, K. Oyakawa, I. Kubo, Comparative studies on the effect of duct height on heat transfer and flow behavior between co-angular and co-rotating type finned surface, Heat Mass Transfer 46 (2009) 245e253. [26] M.D. Islam, K. Oyakawa, I. Kubo, Visualization of flow pattern and thermal image analysis of enhanced heat transfer surface, Heat Mass Transfer 45 (2009) 511e517. [27] M.D. Islam, K. Oyakawa, M. Yaga, I. Senaha, Study on heat transfer and fluid flow characteristics with short rectangular plate fin of different pattern, Exp. Therm. Fluid Sci. 31 (2007) 367e379. [28] I. Kotcioglu, S. Caliskan, T. Ayhan, S. Baskaya, An experimental investigation of heat transfer enhancement in a rectangular duct with plate fins, Heat Transfer Res. 40 (2009) 263e280. [29] Measurement of Fluid Flow in Pipes Using Orifice, Nozzle and Venture, ASME Standard, MFC-3M, 1984. [30] C. Herman, E. Kang, Experimental visualization of temperature fields and study of heat transfer enhancement in oscillatory flow in a grooved channel, J. Heat Mass Transfer 37 (2001) 87e99. [31] G. Taguchi, Taguchi Techniques for Quality Engineering, Quality Resources, New York, 1987. [32] Bendell, Disney, Pridmore, Taguchi Methods e Applications in World Industry , In: IFS Series (1989). [33] P.J. Ross, Taguchi Techniques for Quality Engineering, McGraw-Hill, New York, 1996. [34] R.K. Roy, Design of Experiments Using the Taguchi Approach, John Wiley & Sons Inc, 2001. [35] S.J. Kline, F.A. McClintock, Describing uncertainties in single sample experiments, Mech. Eng. 75 (1955) 3e8.
Contents lists available at SciVerse ScienceDirect
Applied Thermal Engineering journal homepage: www.elsevier.com/locate/apthermeng
Experimental investigation for optimization of design parameters in a rectangular duct with plate-fins heat exchanger by Taguchi method Isak Kotcioglu a, *, Ahmet Cansiz b, Mansour Nasiri Khalaji a a b
Department of Mechanical Engineering, University of Atatürk, 25240 Erzurum, Turkey Department of ElectricaleElectronics Engineering, University of Atatürk, 25240 Erzurum, Turkey
h i g h l i g h t s < This study presents an optimization of heat exchangers by using Taguchi method. < The optimization includes the effects of the six different design parameters. < Effective design parameters are Re number, height of duct and length of winglet. < Aim of Taguchi analysis is to reach minimum pressure drop and maximum heat transfer.
a r t i c l e i n f o
a b s t r a c t
Article history: Received 27 January 2012 Accepted 22 May 2012 Available online 31 May 2012
This study presents the determination of optimum values of the design parameters in a heat exchanger with a rectangular duct by using Taguchi method. The heat exchanger has plate-fins containing periodically interrupted diverging and converging channel flow domains. The experimental investigation for the established heat exchanger involves short rectangular fins attached in 8 8 arrays to a surface having various inclination angles. The effects of the six design parameters such as the ratio of the duct channel width to height, the ratio of the winglets length to the duct channel length, inclination angles of winglets, Reynolds number, flow velocity and pressure drop are investigated. In the Taguchi experimental design method, Nusselt number and friction factor are considered as performance parameters. An L25 (56) orthogonal array is chosen as an experimental plan for the design parameters. The analysis of Taguchi method conducted with an optimization process to reach minimum pressure drop (friction factor) and maximum heat transfer (Nusselt number) for the designed heat exchanger. Experimental results validated the suitability of the proposed approach. Ó 2012 Elsevier Ltd. All rights reserved.
Keywords: Heat transfer Vortex generator Taguchi method
1. Introduction Thermal processes have practical importance in the heat exchangers from the heat transfer point of view. Plate-fin type heat exchangers are widely used in heating and cooling applications. Heat transfer, pressure losses, weight and price should be taken into account while designing the heat exchangers. Obtaining high heat transfer rates through various enhancement techniques can lead to substantial energy savings. Heat transfer processes in a heat exchanger are significantly improved by turbulence promoters via providing optimum flow condition having different geometrical features and orientations. Consequently, the effects of the sizes and orientations of these geometries are closely related to the * Corresponding author. Tel.: þ90 4422314867; fax: þ90 4422360957. E-mail address: [email protected] (I. Kotcioglu). 1359-4311/$ e see front matter Ó 2012 Elsevier Ltd. All rights reserved. doi:10.1016/j.applthermaleng.2012.05.036
performance of the heat transfer process. Plate-fin type heat exchangers are ones of the many heat exchanger forms described in the literature, which is the objective of this study. In this study a heat exchanger manufactured in a way that the flow is directed by extending surface structure with plate-fins periodically longitudinal interrupted diverging and converging in a duct channel. Goal of designing such geometry is to have a pin-fin arrangement constructed as a diffuserenozzle couple which provides a promoted turbulence in the channel. A literature survey of divergent and convergent channel arrays indicates that the heat transfer and friction characteristics are generally determined on the basis of maximum heat transfer rate. In such arrays the optimum parameters are the inter-fin spacing in both the stream-wise and span-wise directions. It is well known that increasing heat transfer occurs at the expense of increasing the friction factor. In this study, the investigations related to heat transfer enhancement include
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various heat exchanger types having different geometries and associated parameters. Bergles [1e3] prepared a number of survey articles dealing with the heat transfer for different applications. Experimental investigations by Russels et al. [4] and Deb et al. [5] demonstrated the augmentation of heat transfer by means of wing-type vortices. Fuji et al. [6] proposed new enhanced surfaces for forced convection heat transfer at low Reynolds numbers. Channels constructed with these surfaces experience alternate diverging-converging along with the flow passage allowing substantial heat transfer enhancement. Garg and Maji [7] reported the results of a numerical analysis of diverging-converging channels. These results indicate that such channel configuration is an effective technique for enhancing the heat transfer. In addition, Mendes and Sparrow [8] performed an experimental study to determine pressure distribution and friction factor at various taper angles of the diverging-converging tubes. The second law analysis of heat exchangers has been conducted by Bejan [9]. Kobus and Oshio [10] studied a theoretical and experimental study on the thermal performance of a pin-fin heat sink. A theoretical model was formulated to predict the influence of various geometrical, thermal and flow parameters of the effective thermal resistance of the heat sink. Chein and Huang [11] evaluated thermoelectric cooler applications in the electronic cooling. Arslanturk [12] investigated the efficiency of straight fins with temperature-dependent thermal conductivity and determined the temperature distribution within the fins. The studies of El-Saed and Tahat et al. [13,14] observed the optimal spacing of the fins in the span-wise and stream-wise directions for both in-line and staggered arrangements. Tahat et al. [15] also studied the effects of height, inter-fin spaces, thickness and tip-shroud clearance of fins on the heat transfer, fluid flow and pressure drop. Sahin et al. [16] experimentally investigated the effects of the longitudinal fin pairs and lateral separations of consecutively on the heat transfer and pressure drop characteristics by using the Taguchi method. Yakut et al. [17] investigated the efficiency of the hexagonal fins, stream-wise and span-wise distances between fins and flow velocity on thermal resistance and pressure drop characteristics using Taguchi experimental design method. Also the temperature distribution within the selected pin-fins was determined. Kotcioglu et al. [18] investigated a cross-flow heat exchanger in the presence of a balance between the entropy generation due to heat transfer and fluid friction with the second law analysis. Kotcioglu et al. [19] also examined experimentally the convective heat transfer and pressure drop in a cross-flow heat exchanger with hexagonal, square and circular pin-fin arrays. In that study, for the applied conditions, the optimal spacing of the pin-fin in the span-wise and stream-wise directions has been determined. In addition to above mentioned studies, Kotcioglu et al. [20] studied a cross-flow heat recovery-exchanger system operating with unmixed fluids. The thermodynamic analysis of the system was presented via determining the variations of exergy loss with Reynolds number. The effects of inlet conditions of the working fluids on the heat transfer characteristics were correlated via entropy generation number and exergy loss. Gunes et al. [21] investigated the determination of the optimum values of the design parameters in a tube with equilateral triangular crosssectioned coiled wire inserts. Kackar [22] reported that Taguchi method has developed more than 60 performance statistics which can be used depending on the problem being investigated. Experiments by Didarul and Islam et al. [23e27] were performed to investigate the effect of duct height on heat transfer enhancement. Considering the existing studies, all of the parameters affecting the heat transfer and pressure drop processes have not been investigated in detail. This requires a vast number of experiments together with the experimental cost and time consumption. In order to avoid such problems, an optimization criterion is useful to
605
determine the quantitative estimate of the various parameters affecting the performance of the heat exchanger and main factors for the optimum design. Within this context, the required information about the behavior of a process is obtained by Taguchi method. Besides reducing the experimental cost, one of the advantages of the Taguchi method over the conventional experimental methods is to minimize the variability around the target when bringing the performance value to the target value. Because of the high cost, instead of determining uncontrollable parameters and removing them, values of controllable parameters which remove or reduce the negative effects of uncontrollable parameters should be investigated. Another advantage of this method is that the optimum working conditions determined from the laboratory study can be reproduced in real applications. For the optimum criteria in a successful application of Taguchi method, a systematic approach covering the necessary steps is very beneficial. In this paper, in addition to above given studies [16e20] an experimental investigation is described by Taguchi methods, which include the enhancement of forced convection heat transfer in a rectangular channel using inclined thin plates as wing-type vortex generators. The channels are constructed with the plates having diverging and converging sections along with the main flow direction. The heat transfer coefficients and pressure drops are measured for air flow with various arrangements of the plates and Reynolds numbers. From the experimental results, the usefulness of the design is determined and the most effective plate angle for heat transfer enhancement is established. Following, the performance of such heat transfer enhancement technique is evaluated and it is proposed that a channel with slits as well as enlargements of the winglet channel decreases the pressure drop. 2. Experimental apparatus and procedure In this experimental study, the tests are constructed in a heat exchanger based on the particular design parameters. The main features of the experimental setup are given elsewhere [28]. The experimental apparatus mainly consists of a settling chamber, the hydrodynamic entrance and test sections. The test section is constructed with stainless steel plates and the fins are arranged as shown in Fig. 1a and b. The inclination angle of the fins are fixed at various angles of b ¼ 7e20 respect to the direction of main flow. According to the tests, the inclination angle of fins with 20 appears to be maximum for the enhancement in the heat transfer. The fins are manufactured in a way that they are attached to the inner side of the bottom and top plates of the duct as shown in Fig. 1b. The dimensions of the designed fin parameters are given in Table 1, where the strong mixing occurs in a buffer region between divergent and convergent channel. In order to obtain a uniform heat flux the heating of the test section is provided by using a Nichrome resistance wire spirally wound over the outer periphery of the rectangular channel. The outer surface of the test section is covered with a layer of glass wool to prevent the heat loss. The cross-sectional areas (a b L) of the rectangular duct for this particular geometry are given in Table 1. The circular duct section is made of a PVC pipe of a 100-mm diameter and a 2040-mm length, which is connected to the convergent section through a flexible pipe. A set of PVC companion flanges is used to house the orifice plate. Air flows from settling chamber to inlet section of the duct where the velocity is fully developed. In order to measure the pressure difference the pressure taps are mounted on the top plate of the rectangular duct. The pressure taps are positioned on the centerlines and mid points between the fins. In order to measure the variation of temperature, the thermocouples are placed at equal intervals along the x and z directions in the duct, as shown in Fig. 1a. The thermocouples are
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Fig. 1. (a) Top view of the geometry and placement of winglets (b) in rectangular test channel.
inserted in holes drilled in the top wall. To measure the outlet and inlet temperatures of the air additional thermocouples are also placed on the downstream face of the orifice plate. The mass flow rate is calculated from the pressure drop across the orifice plate obstruction meter, which is constructed from brass and machined in terms of ASME standards [29]. The centrifugal blower fan is equipped with a 2.5-kW motor to supply the air for the duct. During the course of the experiments, the temperature difference between the mainstream and the heating surface is kept constant at various Reynolds numbers between 3000 and 30,000. At a fixed value of heat input for the given Reynolds number, the variations of the temperature along and transverse the duct at different locations are measured at the duct inlet and outlet, and before and after the orifice plate. 2.1. Flow visualization Flow visualization tests are used to explain the heat transfer features for the various channel geometries of the divergente convergent fin. In order to visualize the flow the Hele-Shaw apparatus is used as a smoke generator. Stream lines inside the channel are shown in Fig. 2, where the air is used as working fluid. From the flow in air channel it is seen that a weak horse shoe vortex appears in front of the fin. The longitudinal strong vortices are generated by the side top edges. The partial differential equations governing the forced convection of the fluid being compressed and heated in a rectangular duct are NaviereStokes and energy equations. As the pressure and temperature changes during study, the computational program calculates the various values of physical properties, with the aid of FORTRAN statements written with finite difference method for solving heat transfer and fluid flow problems. The CFD package code is used to simulate the fluid flow and temperature field, which is based on a finite difference method of solution. Once generating required mesh for the solver the discretization algorithm is used for the convective terms in the solution equations.
The length of fins and angles of inclination are kept constant during any particular test. In the cases where the fin angles are greater than 7, a back-flow region forms just downstream the end of the diverging section, indicating the occurrence of flow separation and the presence of a recirculation zone (shown as A in Fig. 2). In addition, there is a region situated between the diverging and converging channels (regions between A and B, in Fig. 2) where the velocity is not high enough to provide resolution of the flow direction. Due to the pressure rise at the end of the diverging channel (region A) and the pressure drop at the neighboring converging channel (region B), the velocities are high enough to cause turbulence. This region seems to be the mixing zone caused by the split between the divergent and convergent channel pairs. In the representative region between the fins, especially at third, fourth and fifth rows renewal of boundary layer formation is observed. The film patterned flow behavior around the fins is also observed via smoke generator. The present arrangement of the fins diverts the flow direction and the generated longitudinal vortex between the fins promotes the heat transfer from the surface. The heat transfer in the region between the fins in the span-wise direction is also enhanced due to lateral mixing and secondary flow. The results are well fit with those explained by Herman and Kang [30]. The vortex and boundary layer formation around the fin
Table 1 Coefficients for the friction factor correlations and characteristic parameters in the rectangular channel with a wing-type vortex generator. Note that the dimensions of b, a, l, g, s, W, e, c and L are in mm and b is in degree. Channel
b
a
l
g
s
W
b
e
c
L
f ¼ C0Rem
Type1 Type 2 Type 3 Type 4 Type 5 Type 6
10 15 18 20 20 10
202 206 215 226 210 210
60 60 60 60 60 60
10 10 10 10 10 10
9 11 10 12 13 10
23 28 33 55 48 10
7 9 11 15 20 pa
68 64 69 71 80 70
59.6 59.3 58.9 59.7 56.4 60
655 675 660 640 650 660
2.8Re0.166 7.06Re0.221 11.08Re0.242 74.27Re0.165 77.82Re0.116 4.00Re0.224
Fig. 2. Stream lines inside the channel: flow visualization of periodically interrupted diverging-converging adjacent on the channel floor and fin surfaces.
I. Kotcioglu et al. / Applied Thermal Engineering 50 (2013) 604e613
walls are very strong which result in a heat transfer enhancement. The strong attachment of the flow to both sides of the fins plays important role on the heat transfer. The mixing effect of secondary flows is observed in the intermediate region between wing cascades. This is due to the pressure and velocity differences across the passage between the converging and diverging fin pairs. 3. Experimental design and Taguchi method The Taguchi method is being extensively used in industry and engineering analyses due to its wide range of applications. Literature on the methodology is full of case studies from the automobile, plastics, electronics and process industries. The Taguchi’s method of quality engineering can be very effective when it is used properly [31]. The methodology developed by Taguchi for the process or product quality improvement depends on the statistical concepts and tools. This methodology is based on two fundamental concepts: First, the quality losses must be defined as deviations from targets, not conformance to arbitrary specifications, and the second, achieving high system-quality levels economically requires quality to be designed into the product. In order to have a robust system, the parameters are chosen in a way that the sensitivity of the system to the variance is minimum. For this purpose the Taguchi method provides a quality control to optimize the process of engineering experiments. This method helps the researcher to determine the possible combinations of factors and thereby identify the best condition. The Taguchi approach develops rules to carry out experiments, which further simplifies and standardizes the design of the experiment, along with minimizing the required number of factor combinations to test the factor effects. The Taguchi Method is a multi-stage process which consists of three design stages, namely system, parameter and tolerance. In this study, the parameter design stage is used. In the system design, the focus is on the determination of suitable working levels of design factors. The system design also involves the innovation and knowledge from applicable fields of sciences and technology. Once the levels are taken with careful understanding six parameters and five levels are used for the established experiments. The studied factors of the six parameters and five levels are given in Table 2. In the parameter design stage, the factor levels are determined in a way that they produce best performance of the product/process. The optimal condition is selected so that the influence of uncontrollable factors (noise factors) causes minimum variation of system performance. Therefore, the goal of parameter design is to identify the settings which minimize the variation in the performance characteristic and adjust its mean to an ideal value. The tolerance design stage is a procedure of fine tune the results of the parameter design by tightening the tolerance of factors with significant influence on the product. The use of Taguchi method is to demonstrate the large scale effect which is obtainable through a small scale execution (or experiment) using an orthogonal array (OA) and a signal-to-noise ratio (SNR) [31e33]. The procedure is performed with a lower Table 2 The parameters and their corresponding levels. Parameters
Level 1
2
3
4
5
A: Reynolds number () 5000 10,000 15,000 20,000 25,000 B: Width of the duct (mm) 202 206 215 226 210 C: Height of the duct (mm) 10 15 15 20 20 D: Length of the test section (mm) 665 675 660 640 650 E: Length of winglet y-direction (mm) 9 11 10 12 13 F: Inclination angle (b ) 7 9 11 15 20
607
cost, a higher quality, a quick delivery and a desired function. The Noise-Performance Statistics (NPS) are measures of process variability and they are used to identify the control factors and the combined optimal levels, which minimize the process variability. The Signal-to-Noise ratios are also used to measure the effect of the noise on the system. In this system while the signal is defined as the mean the noise is defined as the standard deviation. Such steps usually identify the need of innovation and identification of better materials, parts and machinery. In the Taguchi method the orthogonal array facilitates the experimental design process and provides a recipe for fractional factorial experiments. The choice of a suitable orthogonal array is critical for the success of an experiment and depends on the total degrees of freedom required to study the main and interaction effects, goal of experiment, resources and budget available and time constraints. Consequently, the orthogonal array allows computing the main and interaction effects via a minimizing number of experimental trials. The Taguchi analysis is performed with Minitab 15.0 software package, a computer program designed to perform the statistical functions. The software package generates the orthogonal array designs, where the degrees of freedom for the array design should be greater than or at least equal to those for the design parameters. For this reason L25 are suitable for the considered design. For six parameters at five levels each, the traditional full factorial design would require 56 experiments. Before selecting the orthogonal array, the minimum number of conducted experiments (Nt) can be fixed by using the following relation,
Nt ¼ 1 þ Nv ½Ln 1
(1)
where Nv is the number of fin channels and Ln is the number of levels. In this analysis, Nv ¼ 6 and Ln ¼ 5 are taken for fin channel and Nv ¼ 3 and Ln ¼ 5 are taken for the empty channel. Hence a minimum of 25 experiments are to be conducted. The available standard orthogonal arrays are L4, L8, L9, L12, L16, L18 etc. According to the Taguchi design concept L25 orthogonal array is chosen for the experiments as shown in Tables 3 and 4. As indicated in these tables, the observed values of the Reynolds number (A), width of
Table 3 Experimental plan of L25 (56) for friction factor and Nusselt number with their SNR values for winglet system. Experiment
A
B
C
D
E
F
f
SeN
Nu
SeN
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
1 1 1 1 1 2 2 2 2 2 3 3 3 3 3 4 4 4 4 4 5 5 5 5 5
1 2 3 4 5 1 2 3 4 5 1 2 3 4 5 1 2 3 4 5 1 2 3 4 5
1 2 3 4 5 2 3 4 5 1 3 4 5 1 2 4 5 1 2 3 5 1 2 3 4
1 2 3 4 5 3 4 5 1 2 5 1 2 3 4 2 3 4 5 1 4 5 1 2 3
1 2 3 4 5 4 5 1 2 3 2 3 4 5 1 5 1 2 3 4 3 4 5 1 2
1 2 3 4 5 5 1 2 3 4 4 5 1 2 3 3 4 5 1 2 2 3 4 5 1
1.15 1.76 2.14 2.23 2.27 1.46 1.67 2.04 1.97 0.85 1.77 1.97 1.73 0.60 1.33 1.63 1.93 0.68 1.05 1.42 1.63 0.62 1.02 1.36 1.67
1.22 4.93 6.61 6.97 7.13 3.33 4.49 6.21 5.88 1.32 4.96 5.90 4.77 4.35 2.48 4.28 5.73 3.25 0.45 3.07 4.28 4.13 0.24 2.71 4.50
15.2 18.4 23.9 32.6 39.7 47.8 61.2 21.6 32.4 36.4 35.9 47.9 63.1 85.0 28.6 94.2 36.4 45.5 56.1 75.5 59.7 81.4 118 43.1 53.7
23.6 25.3 27.5 30.2 31.9 33.6 35.7 26.7 30.2 31.2 31.1 33.6 36.0 38.5 29.1 39.4 31.2 33.1 34.9 37.5 35.5 38.2 41.5 32.6 34.6
608
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Table 4 Experimental plan of L25 (53) orthogonal array and SNR values for without winglet system. Experiment
A
B
C
f
SeN
Nu
SeN
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
1 1 1 1 1 2 2 2 2 2 3 3 3 3 3 4 4 4 4 4 5 5 5 5 5
1 2 3 4 5 1 2 3 4 5 1 2 3 4 5 1 2 3 4 5 1 2 3 4 5
1 2 3 4 5 2 3 4 5 1 3 4 5 1 2 4 5 1 2 3 5 1 2 3 4
0.131 0.065 0.051 0.046 0.040 0.032 0.024 0.021 0.023 0.071 0.015 0.013 0.014 0.054 0.023 0.009 0.010 0.037 0.019 0.012 0.007 0.027 0.014 0.011 0.008
17.63 23.61 25.78 26.64 27.78 29.84 32.36 33.33 32.56 22.95 36.13 37.46 36.80 25.27 32.70 40.22 39.92 28.50 34.02 37.98 42.13 31.07 36.70 38.75 41.52
38.62 50.60 55.79 58.00 61.06 49.39 88.97 92.95 89.76 58.17 116.4 123.6 120.0 71.33 99.74 150.2 148.2 88.55 113.5 135.8 172.9 105.0 135.3 148.5 168.3
31.73 34.08 34.93 35.36 35.71 37.99 38.98 39.36 39.06 35.29 41.32 41.84 41.58 37.06 39.97 43.53 43.41 38.94 41.10 42.66 44.75 40.42 42.63 43.43 44.52
the duct (B), height of the duct (C), length of the test section (D), length of winglet in y-direction (E) and inclination angle (F) are set at maximum level. Each experimental trail is performed as per L25. The optimization of the observed values is determined by comparing the standard method and Analysis of Variance (ANOVA).
Table 6 Factorial effect and contribution ratio for friction factor for winglet system.
SNR
The Analysis of Variance is used to analyze the results of the orthogonal array experiment in product design and to determine how much variation each quality-influencing factor contributes [34]. Table 3 shows the experimental design for L25 orthogonal array. All of the observed values are calculated based on the concept of higher the better and smaller the better. In this analysis, the observed values of efficiency, friction factor and Nusselt number are set to be maximum and minimum, respectively. Following, the ANOVA is used to analyze the experimental data. The control factors which may contribute to reduced variation can be quickly identified by looking at the amount of variation present as a response. The method significantly reduces the time required for experimental investigation [31,32]. In the Taguchi analysis, there exist three types of quality characteristics concerning the target design considered as SNR values. These are “higher is the better”, “nominal is the best” and “lower is the better”. As SNR value gets higher, the quality of product improves. The principal aim is to
Table 5 Factorial effect and contribution ratio for Nusselt number for winglet system. Level SNR
1 2 3 4 5 R (maxemin) Rank Contribution ratio (%)
A
B
C
D
E
F
27.7 31.5 33.6 35.2 36.5 8.74 2 44.49
32.6 32.8 32.9 33.3 32.9 0.67 4 3.42
32.9 32.9 32.9 32.9 33.0 0.09 6 1.77
33.3 32.9 33.1 32.9 32.6 0.71 3 3.6
28.6 30.8 32.5 35.1 37.4 8.78 1 44.67
32.9 32.7 32.9 33.0 33.0 0.33 5 2.09
A
B
C
D
E
F
5.3 3.7 2.7 2.0 1.5 3.8 2 22.8
3.6 3.3 2.9 2.3 3.1 1.2 4 4.6
2.3 2.2 4.3 5.5 5.5 7.9 1 47.0
3.2 3.0 3.1 2.9 2.9 0.3 6 2.0
3.6 3.4 3.1 2.8 2.3 1.3 3 13.2
3.0 2.8 3.0 3.3 3.1 0.4 5 7.2
R (maxemin) Rank Contribution ratio (%)
maximize the SNR value. Thus minimizing the effect of random noise factors has significant impact on the process performance. The SNR value, which condenses the multiple data points within a trial, depends on the type of characteristic being evaluated. All of the experiments are listed in a plan given in Tables 3 and 4. Contribution ratios of all factors on the performance criteria depending on the SNR values are given in Tables 5 and 6. Using these tables the optimal combination of the process parameters can be predicted. In order to execute the confirmation procedure of reproducibility, the difference of the S/N ratio between the optimum and current conditions in relation to estimation is obtained. From the SNR differences, the optimal process parameters obtained from the parameter design is verified. The optimal values of the factors are determined by maximizing the Nusselt number and minimizing the pressure loss, given in Table 7. The performance statistics (SNR) are selected as the optimization criteria and used as “the higher is the better” (Nusselt number) and “the lower is the better” (friction factor) situations and are evaluated by,
"
ZH 3.1. Analysis of variance (ANOVA)
Level 1 2 3 4 5
n 1X 1 ¼ 10 log n i ¼ 1 Yi2
#
"
n 1X Y2 ZL ¼ 10 log n i¼1 i
# (2)
where Z indicates performance statistic, n is the number of repetitions in confirmation experiments and Y is the performance value of the experiment.
3.2. Experimental plan for the optimization The heat transfer and pressure drop characteristics are generally used to describe the performance of a heat exchanger. In the Taguchi method, the experiment corresponding to the optimum working conditions may not be considered during the experiments. In such cases, the performance value corresponding to optimum working conditions can be predicted by utilizing the balanced characteristic of the orthogonal array. The planned experimental objective based on the Taguchi method is to determine the main effects of the working parameters of heat exchanger, to perform the analysis of variance and to establish the optimum conditions. The effects of each design parameter on the
Table 7 Optimum conditions and performance values of tested models for winglet system, where superscripts a, b, c, d, e and f are the sequence of effective parameters. Parameters A
B
C
D
E
F
Re
E
H
P
q
L
Nu
Optimum level Optimum value
5b 25000
5d 210
5e 20
5c 67.5
5a 20
5f 655
f
Optimum level Optimum value
2e 10000
4d 210
1a 10
5f 70
3a 11
5e 660
Real value
110.5 1.458
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609
Fig. 3. The effects of design parameters of A, B, C, D, E and F on Nusselt number.
Nusselt number and friction factor are shown in Figs. 3 and 4, respectively. The results indicate that the pressure drop increases with increasing the heat transfer. The performances of the heat exchanger can be calculated for each experiment of the L25 by using the observed values of the efficiency, friction factor and overall Nusselt number from Tables 5, 6, 8 and 9, which lists the ANOVA test results for efficiency, thermal resistance and overall heat transfer coefficient, respectively. The optimum operating conditions of heat exchanger for each of the observed values are illustrated in Tables 7 and 10.
3.3. Data reduction and uncertainty analysis In order to calculate the external free convection occurring between the outer surface of the insulated heat exchanger and the surroundings in flow direction the outer surface temperature of insulation must be known. The power supply provides a heating power (Q) of
Q ¼
ks A½Tw Tm L
(3)
where ks is the thermal conductivity of shell of stainless steel, Tw is the heated surface temperature and Tm is the bulk temperature. In this system L donates the distance traveled by air flow in the heat exchanger and A is the cross-sectional heat transfer area of the heating element. Therefore, the heat transfer area is given by
A ¼ aL þ 2Nw b½W þ L
(4)
where the values of parameters Nw, a, L, b and W are given in Fig. 1a. In Eq. (4), the first term on the right hand side of the equation represents area of the plate on the single layer and second term represents the cross-sectional area with the winglets. The thermal resistance (Rth) is defined as
Rth ¼
1 Tave TN ¼ KA Q
Fig. 4. The effects of design parameters of A, B, C, D, E and F on friction factor.
(5)
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Table 8 Factorial effect and contribution ratio for Nusselt number for without winglet system.
SNR
Level
A
B
C
1 2 3 4 5
34.3 37.3 40.3 41.9 43.1 8.8 1 64.1
39.0 39.7 39.4 39.1 39.6 0.71 3 5.1
36.6 38.3 40.2 40.9 40.9 4.2 2 30.6
R (maxemin) Rank Contribution ratio (%)
Parameters
where Tave is the average temperature of the base of the heat exchanger and TN is the temperature of the fluid flow. The local heat transfer coefficient is calculated from the following equation.
h ¼
q_ Tw Tm
(6)
where q_ is the heat flux. Tm is evaluated by energy balance calculation at a given cross section such that it is defined in term of the thermal energy transported by the fluid as it moves past the cross _ mC _ p, where Cp is section based on the equation given by Tm ¼ E= _ is the mass flow rate (m _ ¼ ruA) and the specific heat of the fluid, m E_ is the thermal energy balances. Consequently, by using the local heat transfer coefficient in Eq. (6) the local Nusselt number (Nu) is defined as,
Nu ¼
hDh ka
(7)
where ka is the thermal conductivity of air and Dh is the duck hydraulic diameter of the test section. The local Nusselt number is evaluated at points along the test section in terms of the local heat flux, local difference between the wall and bulk coolant temperatures and the properties evaluated at the bulk temperature of the fluid. The friction factor (f), which is evaluated from the pressure difference between the points just upstream and downstream of the fins attached to the heating surface is defined as,
f ¼
Dp 1 2 rU ½L=Dh 2
(8)
where U is the average flow velocity in the test section and r is the density. Reynolds numbers based on the mean velocity and the duct hydraulic diameter can be expressed as
Re ¼
UDh v
(9)
where v is the kinematic viscosity of air. The uncertainties associated with the measured and calculated values in a given experimental setup are analyzed to report the results with the highest
Table 9 Factorial effect and contribution ratio for friction factor for without winglet system.
SNR
Level
A
B
C
1 2 3 4 5
24.3 30.2 33.6 36.1 38.0 13.7 1 52.5
33.1 32.8 32.2 31.4 32.6 1.74 3 6.6
25.0 31.3 34.2 35.8 35.8 10.6 2 40.74
R (maxemin) Rank Contribution ratio (%)
Table 10 Optimum conditions and performance values for tested models for without winglet system, where superscripts a, b and c are the sequence of effective parameters.
A
B
C
Real value
Re
E
H
L
Nu
Optimum level Optimum value
5a 25000
4b 210
5c 20
110.5
f
Optimum level Optimum value
5a 25000
5c 210
5b 20
1.458
accuracy. The percentage relative uncertainty in the measured temperature for the thermocouples and the infrared camera are 0.25%. This value is applicable when the temperature measurements are within 0e100 C temperature range. The total uncertainty associated with the mass flow rate and Reynolds number is found to be 4% in the turbulent flow regime. The percentage relative uncertainty varies from 2.5% to 1.8% both for the heat transfer coefficient and Nusselt number. The uncertainties of experimental measurements are determined by using the method introduced by Kline and McClintock [35]. 4. Results and discussion It is not easy to simultaneously increase the heat transfer and decrease the pressure drop in a heat exchanger. With this respect the friction factor and the heat transfer coefficients for the divergingeconverging fin pattern and various duct heights need to be explored. For the experimental analysis regarding the constructed heat exchanger the considered parameters are the ratio of the duct channel width to height, the ratio of the fins length to the duct channel length, inclination angles of fins, Reynolds number, flow velocity and pressure drop. As it is stated in previous section each parameter has five levels, given in Table 2. A systematic approach is used to plan and analyze the results by establishing particular objectives such as the optimal condition for the product or process, the contribution of individual factors and the response under optimal conditions. In order to establish these conditions, the collected experimental data are analyzed for determination of the effects of each design parameter on heat transfer and friction factor. The effects of each design parameter on Nusselt number and friction factor are plotted in Figs. 3 and 4, respectively. The effects of the optimum performance statistics (SNR) values of each design parameter A, B, C, D, E and F on the heat transfer and friction factor are given in Table 2. The factor response table and graphs of the noise factors (N) are obtained from their computed SNR values given in Tables 5, 6, 8 and 9. Testing the combination of processing conditions through numerical simulation experiment produced the response diagram for the design factors, as shown in Figs. 3e6. Considering these tables and figures, the six noise factors by the standard L25 orthogonal array are configured. The larger slope in figures means that the effect of its noise factors is greater on the performance characteristic. This indicates that designing such element can achieve the lower-the-better property of performance characteristic. Because the variable factors have the greater effect on the performance characteristic, its deviation ratio will be greater. Since the effect of the SNR values is highest on the temperature, its contribution ratio shows six noticeable variable factors according to the sequence of Reynolds number, width of the duct, height of the duct, length of fin in y-direction, length of the test section and inclination angle. The test samples are designed by combining the six factors (A, B, C, D, E and F) and three factors (A, C and E)
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611
Fig. 5. The effects of design parameters of A, B and C on friction factor.
which are selected to be the optimal conditions. The confirmation tests are performed by using these samples to confirm the reproducibility of the obtained results. The test samples are then divided into two methods regarded as presumed and confirmed tests of SNR values for optimal conditions in the cases of with and without the fins. After determining the optimum working parameters of heat exchanger the experiments are conducted and their values are provided in Tables 7 and 10. The experimental results give the optimum performance of heat exchanger and these values are found to be better than that of the previous observations. The certain typical models are calculated according to the orthogonal array and then the relatively better one could be obtained through the performance statistic analysis. In this calculation, the parameter R is the difference of maximum and minimum of the SNR value for every factor. The contribution ratio is equal to the ratio of the R values of each factor to the total R value of all factors as presented in Tables 5, 6, 8 and 9. The rank row is the order of factors according to the effectiveness. The contribution ratio of each parameter to Nusselt number and to friction factor is shown in Figs. 7 and 8, respectively. As can be seen from these figures, the pitch ratio has 60% of the total effect. This means that the parameter E is the most effective one on heat transfer. Considering the parameters of A, B, C, D, E and F in Fig. 7A and E are the most effective parameters on the Nusselt number with a contribution ratio of 47% of the total effect, while A, C and E are the most effective parameters on friction factor with a contribution ratio of 22e50% of the total effect as seen from Fig. 8. It is easy to evaluate the effects of optimum design parameters separately. In order to obtain an idea over the total optimization by making a reasonable comparison of each goal the combination of these effects is required. To combine the separate effects of each goal for general optimization, the importance of the levels of each parameter is defined firstly. Consequently, the final step is to control whether the real values obtained by the confirmation tests are in the confidence interval or not. According to the above arguments, the results prove that the Taguchi method is a reliable and easily applicable optimization tool for studying heat transfer enhancement. Since the essential quantities regarding the heat transfer are the friction factor and the heat transfer coefficients for the heat exchanger under consideration, it is important to determine these parameters. In order to estimate the pressure drop as well as thermal performance together with the insertion of the fins, the friction factor is measured for different duct size and dimensions.
The results are presented in Fig. 9. Pressure drop measurements for the six arrangements are converted to the friction factors, which are defined as,
f ¼
DP f ¼ a Reb ½a=bc ½s=bd ½e=Le ½tan b rU 2
(10)
where a ¼ 3915.91, b ¼ 0.286, c ¼ 1.317, d ¼ 0.156, e ¼ 1.059 and f ¼ 0.196. This friction occurs due to the turbulence and flow interactions caused by the diverging-converging fin pattern. In addition, for the empty channel configuration, where the fins are not placed on, the pressure drop measurements for the three arrangements tested in this study are converted to friction factors, defined as,
f ¼ a Reb ½a=bc
(11)
where a ¼ 2.663, b ¼ 0.98348 and c ¼ 1.785. Due to the effect of the inclined fins in the channel, the pressure drop also increases with increasing inclination angle. As also seen in Fig. 9, for all types of channel geometries, the dependence on the Reynolds number is pronounced and the value of the friction factor decreases with increasing the Reynolds number. This is due to the fact that the divergenteconvergent fin pattern vortex generated by the first row fin strikes the large side wall of the following fin as well as the surface. Consequently, a large drag force is developed and a higher pressure drop occurs. The large pressure drops are attributed to flow separation in diverging parts of the channel. Hence, by narrowing the separation zone a decrease in pressure drop is expected. The effect of the particular design of plate-fin heat exchanger on the Nusselt number is investigated in according with the Reynolds number. The mean Nusselt number (Num) is defined in terms of the mean flux and the mean difference between wall and fluid temperatures. The mean Nusselt number is expressed with the DittuseBoelter correlation, given by the following equation,
Num ¼ 0:023 Re0:8 Pr0:4
(12)
where Pr is the Prandtl number of air. As can be seen in Fig. 10, the average Nusselt number is a function of the Reynolds number. It is also seen from this figure that there is a good agreement between the results for the rectangular channel [28] and these correlations are observed over a wide range of the Reynolds number. This result suggests that the experimental apparatus used in this study is adequate.
Fig. 6. The effects of design parameters of A, B and C on Nusselt number.
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200 Dittus Boelter Correlation Experimental Data (Eq.)
Nusselt Number
160
120
80
40 Fig. 7. The contribution ratio of parameters of A, B, C, D, E and F to Nusselt number.
0
5000
10000
15000
20000
25000
Reynold Number Fig. 10. Effect of diverging-converging plate-fins on the average Nusselt number.
(E) are much effective on the Nusselt number, as shown in Figs. 3 and 7. The average Nusselt number increases with increasing the inclination angle. This result agrees with those given for the same type of the heat exchanger in literature [35]. 5. Conclusion
Fig. 8. The contribution ratio of parameters of A, B, C, D, E and F to friction factor.
2.5 General Correlation Experimental Data (Eq.)
Friction Factor
2
1.5
1
0.5
0 0
5000
10000
15000 20000 Reynolds Number
25000
30000
Fig. 9. Effect of diverging-converging plate-fins on friction factors.
Finally, the effects of the fin geometry on the heat transfer and pressure drop characteristics of rectangular channels are analyzed with the following equation.
Nu ¼ 1:48 Re0:63 ½a=b0:70 ½c=L0:65 ½tan b
1:4
(13)
From the point of the heat transfer enhancement view the parameters of Reynolds number (A) and length of fin in y-direction
The work described in this study is believed to be one of the first fundamental-level studies of the periodically interrupted divergingeconverging plate-fin heat exchangers. Within this context, an experimental investigation of designed fin patterns via considering the heat transfer and flow characteristics was described. Following the effects of fin height, inclination angle, fin pattern model and Reynolds number were examined with the Taguchi method. The optimal parameters have been designed to maximize the heat transfer and minimize the pressure drop in the heat exchanger. The selected parameters for the heat exchanger are Reynolds number, width of the duct, height of the duct, length of the test section, length of the fin, and inclination angle. The performance of this particular heat transfer enhancement technique was evaluated and it was proposed that a channel with slits as well as enlargements of the winglet channel decreases the pressure drop. From the results of flow visualization, the mixing effect of secondary flows is seen in the intermediate region between wing cascades. This was due to the pressure and velocity differences across the passage between the converging and diverging pairs of fins. A boundary layer develops at each contraction part and a flow separation occurs at the end of the enlargement part. The heat transfer is high around the fin rows for diverging and converging fin patterns. The heat transfer in the region between fins in the spanwise direction is also enhanced due to lateral mixing and secondary flow. In the diverging and converging fin pattern, the horseshoe vortexes as well as the vortexes generated by the side top and corner edges strongly touch the alternately angled plate-fin surfaces and end-wall, which significantly enhances the heat transfer. The level of heat transfer increases in a narrow width duct compared to a flat plate because the upper wall induces the flow vortex to attach to the end-wall and fin surface more strongly. The inclination angle of fins has a great influence on the heat transfer enhancement. The inclination angle of 20 appears to be
I. Kotcioglu et al. / Applied Thermal Engineering 50 (2013) 604e613
maximum for enhancement in the heat transfer. It can be concluded that the flow is turbulent in the intermediate regions. Thus, the heat transfer enhancement of the introduced rectangular channel geometries can be attributed to the secondary flow caused by the tabulator type flow effect and the frequent boundary layer interruptions at each enlargement part. As the inclination angle of the fin increases the mixing effect in the intermediate region between fins cascades improves the heat transfer characteristics. Nomenclature A a b c Cp Dh E_ f g h K ka ks l L Ln _ m Nu Nt Nv Nw n Pr Re Rth Q q_ Tave Tm Tw TN DP U W Y Z
cross-sectional heat transfer area of the heating element (m2) width of the duct (m) height of the duct in y-direction (m) length of winglet in x-direction (m) specific heat of the fluid (kJ/kg K) hydraulic diameter (m) thermal energy balances (W) friction factor distance between wing corners in narrow configuration (m) local heat transfer coefficient (W/m2 K) overall heat transfer coefficient (W/m2 K) thermal conductivity of air (W/m K) thermal conductivity of steel (W/m K) length of a winglet (m) length of the test section (duct, m) number of levels mass flow rate (kg/s) Nusselt number minimum number of conducted experiments number of variables number of winglets number of repetitions in confirmation experiments Prandtl number Reynolds number thermal resistance heating power (W) heat flux (W/m2) average temperature of the base of the heat exchanger (K) bulk temperature in the heating element (K) heated surface temperature (K) temperature of the fluid flow (K) pressure drop (Pa) average velocity (m/s) distance between wing corners in wide configuration performance value of the experiment performance statistic
Greek symbols inclination angle kinematic viscosity of air (m2/s) density (kg/m3)
b n r
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