PREDICTION OF FLUID FLOW AND HEAT TRANSFER THROUGH SQUARE DUCT WITH TWISTED TAPE INSERT AND INTERRUPTED RIB

Transcription

1 PREDICTION OF FLUID FLOW AND HEAT TRANSFER THROUGH SQUARE DUCT WITH TWISTED TAPE INSERT AND INTERRUPTED RIB Ho Keun Kang 1, Soo Whan Ahn 2, Myung Sung Lee 2 and Dae Hee Lee 3 1 Division of Marine System Engineering, Korea Maritime and Ocean University, Busan , South Korea 2 Department of Mechanical and System Engineering, Institute of Marine Industry, Gyeongsang National University, Tongyeong , South Korea 3 School of Mechanical and Automotive Engineering, High Safety Vehicle Core Technology Center, Gimhae , South Korea ahn9294@gnu.ac.kr ICETI 2012-J27001_SCI No. 13-CSME-79, E.I.C. Accession 3537 ABSTRACT Numerical predictions of characteristics of turbulent flows through a square duct (30 30 mm) with twisted tape inserts and with twisted tape inserts plus interrupted ribs are conducted to investigate regionally averaged heat transfer and friction factors. The twisted tape is a 0.1 mm thick carbon steel sheet with a diameter of 28 mm, length of 900 mm and 2.5 turns. The present study demonstrates that the twisted tape with interrupted ribs provides a greater overall heat transfer performance over the twisted tape with no ribs in the square duct. Keywords: heat transfer; friction factor; twisted tape; ribbed square duct; flow pattern. PRÉDICTION D ÉCOULEMENT DES FLUIDES ET LE TRANSFERT ÉNERGÉTIQUE À TRAVERS UN CONDUIT CARRÉ AVEC INSERTION DE BANDES TORSADÉES ET CÔTES INTERROMPUES RÉSUMÉ Des prédictions numériques des caractéristiques des fluides turbulents développés à travers un conduit carré (30 30 mm) avec des insertions de bandes torsadées, et avec insertion de bandes torsadées plus des côtes interrompues, sont menées pour étudier le transfert de chaleur moyen et le coefficient de frottement. La bande torsadée d une feuille d acier au carbone est d une épaisseur de 0,1 mm avec un diamètre de 28 mm, d une longueur de 900 mm et 2,5 tours. Les résultats démontrent que l insertion de bandes torsadées plus des côtes interrompues procure en général un plus grand transfert énergétique que la bande torsadée sans côtes dans le conduit carré. Mots-clés : transfert énergétique ; coefficient de frottement ; bande torsadée ; conduit carré avec côtes ; patron d écoulement. 917

2 1. INTRODUCTION Heat transfer augmentation techniques find application mainly in the design of more compact heat exchangers. Among the various augmentation techniques, the use of twisted tape inserts is an effective method to improve the thermo-hydraulic performance of turbulent flow heat exchangers [1], since it offers an increase in heat transfer as compared to the pressure drops. Significant investigations on pressure drop and heat transfer characteristics of the fully developed flow in circular tubes containing twisted tape inserts can be found in the literature [1 3]. These studies show that twisted tape inserts achieve sizable heat transfer enhancement with a significant pressure loss penalty. Considering the increasing effects of both a twisted tape and rib turbulators on heat transfer, Zhang et al. [4] used a compound technique(a twisted tape insert plus rib turbulators) to enhance heat transfer in tube flows. Their results show that heat transfer is enhanced by combining twisted tape and interrupted ribs rather than twisted-tape or interrupted ribs only. Several questions still remain unsolved that must be analyzed systematically since previous results are for flow in circular tubes. In reality, square channels are more common than circular tubes in most applications. It is questionable whether the twisted tape can provide the same heat transfer performance in a square channel as in a circular tube. The question arises because the secondary flow generated by the swirling motion due to the twisted tape is different in square channels than in circular tubes. Moreover, heat transfer performance from the combined use of a twisted tape and interrupted ribs in a square should also be of interest. The objective of the present study is therefore to investigate experimentally as well as numerically the effect of the twisted tape and combined effect of the twisted tape and interrupted ribs on heat transfer distribution and friction in square channels. Furthermore, the flow patterns are also numerically checked. 2. EXPERIMENTAL APPARATUS The experimental apparatus is shown in Fig. 1. The main components of the facility consist of a blower, an orifice flow meter, an entrance channel, and a test section. A 0.86 kw blower forces air into the pipe and the orifice meter and then through the straightener, entrance channel, and test section. The square duct test section used with only twisted tape inserts and twisted tapes plus interrupted ribs have a cross section of mm. The twisted tape inserts and axial interrupted ribs are placed inside the test section square channels with length L = 90 cm as shown in Fig. 2. And the smooth channel with length of 90 cm is also located before the test section. The twisted tape is 0.1 mm thickness carbon steel with a diameter D of 2.8 cm and length L of 90 cm. It has 2.5 turns throughout the entire duct length. The twisted tape is thermally insulated from the four side walls of the square duct to reduce heat conduction between tape rims and the aluminum duct. The dimension of an axial interrupted rib is mm as shown in Fig. 1. The gaps between the ribs are 23 mm in the axial direction and 15mm in the traverse direction. Test channels with the twisted tape plus interrupted ribs have aluminum ribs glued periodically on the inner bottom wall of the test section. The thin wood strips (0.2 mm thickness) are placed between the aluminum plates in the axial direction. The thin stainless foil heater(0.1 mm thickness) is installed at the backside of the aluminum plates. Five pressure taps were installed along the axial centerline of the walls to determine the pressure drop. A micro-manometer was used to measure the pressure differential over the specified channel length. An 8.16-cm-diameter pipe, equipped with an orifice plate, was used to measure the mass flow rate. Two heating conditions are investigated for test channels with twisted tape inserts and rib turbulators: (i) electric heat uniformly applied to the four side walls of the square duct, and (ii) electric heat uniformly applied to two opposite (top and bottom) walls of the square channel. The local surface temperatures of the test section are measured by copper-constantant thermocouples distributed along the length in the centerline and placed at each aluminum plate of each wall. These thermo- 918

3 Fig. 1. Schematics of experimental setup (1) and square test duct with a twisted tape (2). Fig. 2. Details of cross test section. couples are embedded into the pre-drilled holes on the outer surface of each aluminum plate. Thermocouples inserted and suspended in the center of the duct measure the bulk mean air temperature entering and leaving the test section. The bulk temperature is calculated by averaging the local temperatures in vertical direction from bottom to top of the channel. A 48-channel Hybrid Data Logger and a computer are used for data acquisition and reduction. 3. MATHEMATICAL MODEL The numerical simulations of the fluid flow and heat transfer in the analyzed square duct geometries are conducted with the CFX 11.0 commercial code. For the working fluid, material properties of air are taken. The turbulence stresses and the turbulence viscosity were calculated with the transient shear stress transport model, which was developed and improved by Menter [5]. It is a combination of the k ε and the k ω model of Wilcox [6], where the turbulence eddy frequency is used as ω = ρk µ t (1) At the wall, the turbulence frequency ω is much more precisely defined than the turbulence dissipation rate ε. Therefore, the SST model activates the Wilcox model in the near-wall region by setting the blending function F 1 = 1.0. Far away from the wall, F 1 = 0.0, thus activating the model for the rest of the flow fields: SST model = F1(k ω) model + (1 F 1 )(k ε) model (2) where F 1 = tanh(arg 4 ). Using Eq. (2), the transport equation for turbulence kinetic energy k has been formulated as [( (ρk) + (ρ νk) = µ + µ ) ] t k + P k β ρκω (3) t σ k 919

4 And for the turbulence eddy frequency ω as (ρω) t + (ρ νω) = [( µ + µ t σ ω ) ] ω ω + α 3 κ P k + (1 F 1 ) 2ρ ω βρω 2 (4) σ ω Based on turbulence kinetic energy κ and turbulence eddy frequency ω, eddy viscosity µ t has been defined as follows: α 1 k µ t = ρ (5) max(α 1 ω;sf 2 ) The SST model requires the distance of a node to the nearest wall for performing the blending between k ε and k ω. The wall scale equation is the equation solved to obtain the wall distance, or simply: 2 φ = 1 (6) where φ is the value of the wall scale. The wall distance can be calculated from the wall scale through wall distance = φ + φ 2 + 2φ (7) Since φ is always positive, the wall distance is also always positive. The dimensions of computational domain are idealized to reveal the fundamental issues and enable validation with available experimental model (L = 900 mm, W = 30 mm, and H = 30 mm). The total number of nodes in those domains is more than 500,000. A uniform heat flux is specified on all the walls, and the twisted taper is defined to be adiabatic. 4. DATA REDUCTION The regional heat transfer coefficient (h) is calculated from the regional heat transfer rate unit surface area from the inner wall to the cooling air, the local wall temperature (T w ) on each aluminum plate, and the local bulk mean air temperature (T b ) as h = (q q loss )/[A(T w T b )] (8) The regional total heat transfer rate (q) generated from the stainless thin heaters is determined from the measured resistance and current (q = I 2 R) on each side of the test channel. The heat loss (q loss ) is determined experimentally by supplying electrical power to the test section until a steady condition is achieved for a no flow condition. The heat loss is 5% of the power inputs for a Reynolds number of 10,000. It is found that the foil provides nearly uniformly heat flux on the entire test section channel. The local bulk mean air temperature in Eq. (8) is also calculated by energy conservation as T b, j = T in + (q q loss )/mc p (9) with the measured inlet air temperature (T in ) and the accumulated net heat input from the test duct inlet to the ith position. Eq. (9) is calculated from the local bulk mean air temperature (T b ) at the ith position. The calculated outlet bulk mean air temperature agrees with the measured values within 5%. The inlet bulk mean temperature is C and the wall temperature is C, depending on the test section conditions. The local Nusselt number is normalized by the Nusselt number for a fully developed turbulent flow in smooth circular tubes correlated by Dittus Boelter [7] as Nu r hd h /k = Nu s 0.023Re 0.8 Pr 0.4 (10) 920

5 Fig. 3. Local Nu numbers: (1) a twisted tape insert only; (2) a twisted tape insert+rib turbulators. Fig. 4. Flow patterns (x/d h = 14.0, Re = 22,300): (1) a twisted tape insert; (2) a twisted tape insert+rib turbulators. A manometer measures the pressure drop across the square channel. The local friction factor f for fully developed flow in a rectangular channel is defined in terms of the dimensionless channel length normalized by hydraulic diameter D h, pressure drop p on the local wall, and bulk mean air velocity u b as follows: f = p 4(L/D h )(ρu 2 b /2) (11) The weighted channel average friction factor f ra is the average of top wall friction factor f t1, side wall friction factor f s, and bottom wall friction factor f b, in the square channel as shown as f ra = f t + f b + 2 f s 4 Each friction factor was obtained from the pressure drop difference along axial distance in the centered line on the corresponding wall. The uncertainty associated with the length scale used in the data reduction was ±3.0%, based on the observed variations in the reported values in the literature. The standard deviation in the air bulk velocities was found to be within ±4.0%, and the maximum uncertainty in the heat transfer rate (Q) was estimated to be ±6.2%. These uncertainties would result in the maximum uncertainty of the convective heat transfer coefficient of ±8.9% at Re = 19,000 [8]. (12) 921

6 Fig. 5. Streamlines along axial direction (x/d h = 13.3, 15 and 16.7, Re = 22,300). 5. RESULTS AND DISCUSSION Figure 3(1) represents the local Nusselt numbers in the smooth channel with twisted tape inserts in the twosided heating and four-heating conditions, respectively. The results show that the local Nusselt numbers in the two-sided heating case (open symbols) are slightly higher than the four-sided heating case (solid symbols). This occurs because the colder fluid moves from the two unheating walls toward the two heating walls, which results in a higher heat transfer coefficient. Values of the fully developed Nusselt numbers with heating applied to two opposite walls were 1.08 to 1.19 times greater than those obtained with heating applied to all four walls at the same Reynolds number. Thus, the effect of the Reynolds number was more prominent in the two-sided heating condition than in the four-sided heating condition. The local Nusselt number decreases as the x/d k increases, and maintains a nearly constant value after x/d h = 7. Figure 3(2) shows the streamwise Nusselt number distributions based on the top wall temperature, and bottom wall temperature for the test section with the addition of ribs with twisted tape, respectively. The Nusselt numbers based on the bottom wall were 16 and 27% greater than those on the adjacent smooth sides and opposite smooth side at a Re = 29,000. The higher Nusselt numbers on the ribbed bottom wall were due to the increased level of turbulence generated by the ribs, which broke up the growth of the thermal boundary layer. The numerical values by using CFX commercial code are compared with the experimental data. The present experimental data do not precisely match the numerical results. It is not surprising because between calculated and measured results may be attributed to the variable fluid properties and the possible influence of buoyancy in the experimental system. Figure 4 shows a swirling motion created by the twisted tape in the cross-sectional area of the square channel at x/d h = A centrifugal force is superimposed over the main longitudinal flow that produces a secondary motion in the channel. The net effect of this change in the flow field increases the pressure drop and heat transfer enhancement. Interrupted ribs also act as turbulence promoters in the main flow field (Fig. 4(2)). Thus, the addition of ribs with the twisted tape increases local turbulence and secondary motion. It can be also seen from Fig. 4 that there is a stream of secondary flow behind the twisted tape. This is because a negative pressure gradient along the orientation of the rib exists behind the twisted tape. Figure 5 represents the twisted streamlines along the axial orientation. The main stream flows near the twisted tape surface are moving in helical vortices along axial orientation. The main stream flows near the twisted tape surface are moving in helical vortices along axial orientation. The vigorous twisting of the flowing air greatly may enhance the heat transfer to the air flow. The validity of the predicted patterns in Figs. 4 and 5 may be indirectly confirmed by comparing with the measurements in Fig. 7(2). 922

7 Fig. 6. Thermal contours (x/d h = 14.0, Re = 22,300: (1) 2-sided heating (no rib); (2) 4-sided heating (no rib); (3) 2-sided heating (rib); (4) 4-sided heating (ribs). Fig. 7. Average Nusselt number (1) and friction factor (2). Figure 6 shows the comparisons of thermal contours for the combination of the twisted tape with ribs or with no rib on the bottom walls, at which two different heating conditions; two opposite sided heating (bottom and top) and four sided heating, are applied. Thermal contours are basically symmetrical about the alignment of the twisted tape in the four sided heating channel with no rib. It might be attributed to the fact that the main stream flows would be split and skewed along the twisted tape as shown in Fig. 4(1). The thermal contour around the bottom of channel with no rib has the smaller thermal boundary thickness than with ribs, and the Nusselt numbers also become lower in the channel with no rib as shown in Fig. 7. It is due to the fact that because there is less air turbulence around the bottom wall in the channel with no rib, the temperature difference between bottom wall and bulk air is greater. Figure 7(1) shows the average Nusselt numbers for the fully developed flow in the smooth channel only, in the smooth channel with the twisted tape, and in the bottom ribbed channel with the twisted tape, respectively. The test section with the twisted tape plus the ribbed wall has the greatest Nusselt number. The empirical correlation by Dittus and Boelter [7] for a smooth channel is also plotted for a comparison. It is evident from Fig. 7(1) that there is a reasonably good agreement between the existing correlation and our results on the condition that the entire channel walls are heated. Figure 7(2) shows the average channel friction factors by obtaining from experimental and numerical data for the smooth channel, the channel with the twisted tape, and the channel with the twisted tape and ribs on the bottom wall, respectively. The empirical equation by Blasius for a smooth circular tube is included for a comparison. The present results for a smooth channel agreed with Blasius correlation within 3.5%. The results also showed that the 923

8 Fig. 8. Heat transfer performance under a constant pumping power. friction factor decreased with increasing Reynolds number since the relative increase in the magnitude of the fluid velocity squared was greater than the increase in the wall shear stress with increasing Reynolds number. The channel with the twisted tape and ribs on the bottom wall has the maximum friction factor in the present work. This was due to the greater flow resistance experienced with additional turbulators, leading to higher friction factor values. The experimental data by Zhang et al. [4] for the ribbed tube with the twisted tape is included for a comparison. The friction factor by Zhang et al. [4] was nearly 3.6 times greater than our present work at a Reynolds number of 29,000. The results may occur from the edge or corner effect in square channels. The flow field in a square channel with the twisted tape is more complicated than that in a circular tube because the secondary flow entrains in the four corners and creates corner vortices. This reduces a greater pressure drop in the square channels compared to the circular tubes. The interrupted ribs induce flow separation and reattachment, resulting in a secondary flow relative to the swirl flow generated by the twisted tape. This combined effect of swirl flow and turbulent secondary flow produces a higher pressure drop penalty. Figure 8 shows the performance curve, (Nu r /Nu s )/( f r / f s ) 1/3 as a function of the Reynolds number, where f s is the friction factor for the smooth tube without a tape obtained from the following Blasius empirical correlation [9]. This curve reflects the overall heat transfer performance of a channel taking the friction factor effect into account. The results show that the two-sided heating condition provides better overall heat transfer performance than the four-sided heating condition. In addition, the twisted tape with interrupted ribs provides a higher overall heat transfer performance over the twisted tape with no ribs. f s = Re 0.25 (13) This is because the ribs give a better increment in heat transfer than in friction factor. For a comparison, the results obtained by Zhang et al. [10] in a 4-side heated square channel with the twisted tape only were included. A duct of square cross-section provides higher surface to volume ratio than a circular tube. Further, if a square duct is inserted with a twisted tape, whose width equals the side of the duct, the flow and heat transfer become periodically fully developed with the distance of periodicality equals to a 90 rotation of the tape. Both the flow and heat transfer are experienced under continuous state of periodic development. Therefore, compared to a circular tube with a twisted tape, a higher thermal hydraulic performance can be expected from a square duct with a twisted tape. However, the twisted tape in a channel produces higher pressure drop. Due to this high pressure drop, the use of tape may be limited and worse than some existing technology for heat exchanger cooling. In this paper, we presented the results and it will be available in the 924

9 literature. The thermal system designer can decide whether or not they can use the results for any specific needs. 6. CONCLUSIONS 1. In the smooth channel with twisted tape inserts, values of the fully developed Nusselt numbers with heating applied to two opposite walls were 1.08 to 1.19 times greater than those obtained with heating applied all four walls at the same Reynolds number. 2. For the test section with the addition of ribs with twisted tape, the Nusselt numbers based on the bottom wall were 16 and 27% greater than those on the adjacent smooth sides and opposite smooth side at a Reynolds number of 29, The friction factor in the ribbed circular tube with twisted tape was nearly 3.6 times greater than in the ribbed square channel with a twisted tape at a Reynolds number of 29, The twisted tape with interrupted ribs provides a greater overall heat transfer performance over the twisted tape with no ribs. ACKNOWLEDGEMENT This research was supported by Basic Science Research Program through the National Research Foundation of Korea (NRF) funded by the Ministry of Education, Science and Technology (grant number ). REFERENCES 1. Manglik, R.M. and Bergles, A.E., Heat transfer and pressure drop correlations for twisted tape inserts in isothermal tubes: Part II Transition and turbulent flows, ASME Journal of Heat Transfer, Vol. 115, pp , Eiamsa-ard, S., Thianpong, C. and Promvonge, P., Experimental investigation of heat transfer and flow friction in a circular tube fitted with regularly spaced twisted tape elements, International Communications in Heat and Mass Transfer, Vol. 33, pp , Chang, S.W., Jan, Y.J. and Liou, J.S., Turbulent heat transfer and pressure drop in tube fitted with serrated twisted tape, International Journal of Thermal Science, Vol. 28, pp , Zhang, Y.M., Han, J.C. and Lee, C.P., Enhanced heat transfer and friction characteristics of turbulent flow in circular tubes with twisted tape inserts and axial interrupted ribs, Journal of Enhanced Heat Transfer, Vol. 4, pp , Menter, F.R., Zonal two equation k ω turbulence models for aerodynamic flows, AIAA (American Institute of Aeronautics and Astronautics) Paper , Wilcox, D., Turbulence Modelling for CFD, DCW Industries Inc., La Canada, California, Dittus, F.W. and Boelter, L.M.K., Publications in Engineering, University of California, Berkeley, California, Vol. 2, pp , Kline, S.J. and McClintock, F.A., Describing uncertainties in single sample experiments, Mechanical Engineering, Vol. 75, pp. 3 8, Kays, W.M. and Crawford, M.E., Convective Heat and Mass Transfer, 2nd edn., McGraw-Hill, Zhang, Y.M., Azad, G.M., Han, J.C. and Lee, C.P., Turbulent heat transfer enhancement and surface heating effect in square channels with wavy and twisted tape inserts with interrupted ribs, Journal of Enhanced Heat Transfer, Vol. 7, pp ,