THE EFFECT OF TWISTED TAPE WIDTH ON HEAT TRANSFER AND PRESSURE DROP FOR FULLY DEVELOPED LAMINAR FLOW

Transcription

1 S 0 THE AMERICAN SOCIETY OF MECHANICAL ENGINEERS 345 E. 47th St., New York, N.Y The Society shall not be responsible for statements or opinions advanced in papers or discussion at meetings of the Society or of its Divisions or Sections, or printed in its publications. Discussion is printed only if the paper is published in an ASME Journal. Authorization to photocopy material for internal or personal use under circumstance not falling within the fair use provisions of the Copyright Act is granted by ASME to libraries and other users registered with the Copyright Clearance Center (CCC) Transactional Reporting Service provided that the base fee of $0.30 per page is paid directly to the GCC, 27 Congress Street, Salem MA Requests for special permission or bulk reproduction should be addressed to the ASME Technical Publishing Department. Copyright 1995 by ASME Al Rights Reserved Printed in U.S.A. 95-GT-42 THE EFFECT OF TWISTED TAPE WIDTH ON HEAT TRANSFER AND PRESSURE DROP FOR FULLY DEVELOPED LAMINAR FLOW Walid M. Chakroun and Sami F. AI-Fahed Center of Research for Experimental Thermal Sciences Mechanical Engineering Department Kuwait University KUWAIT ABSTRACT A series of experiments was conducted to study the effect of twisted-tape width on the heat transfer and pressure drop with laminar flow in tubes. Data for three twisted-tape wave lengths each with five different widths have been collected with constant wall temperature boundary condition. Correlations for the friction factor and Nusselt number are also available. The correlations predict the experimental data to within 10 % to 15 % for the heat transfer and friction factor, respectively. The presence of the twisted tape has caused the friction factor to increase by a factor of 3 to 7 depending on Reynolds number and the twisted-tape geometry. Heat-transfer results have shown an increase of 1.5 to 3 times that of plain tubes depending on the flow conditions and the twisted-tape geometry. The width shows no effect on friction factor and heat transfer in the low range of Reynolds number but have a more pronounced effect on heat transfer at the higher range of Reynolds number. It is recommended to use a loose-fit tapes for low Reynolds number flows instead of tight-fit in the design of heat exchangers because they are easier to install and remove for cleaning purposes. NOMENCLATURE A caxial cross sectional area Ai circumferential area based on the inside diameter Cp specific heat Di inside diameter f friction factor, Equation I fsw, swirl flow friction factor Gz Graetz number H twist wave length hi inside heat transfer coefficient k thermal conductivity of the fluid L length of the test section L smaximum helical flow length rh mass flow rate Num mean Nusselt number Pr Prandtl number Q heat gained by the oil Re Reynolds number ReSW Reynolds number based on swirl velocity Sw dimensionless swirl parameter Tooutlet oil temperature Ti inlet oil temperature Tw average wall temperature V average velocity Vsactual swirl velocity Vamean axial velocity W width of twisted tape Y twist ratio, H/D; 6 thickness of twisted tape Ap pressure drop t dynamic viscosity p fluid density subscript b at bulk fluid temperature w at tube wall temperature Presented at the International Gas Turbine and Aeroengine Congress & Exposition Houston, Texas - June 5-8, 1995 This paper has been accepted for publication in the Transactions of the ASME Discussion of it will be accepted at ASME Headquarters until September 30, 1995

2 INTRODUCTION Heat transfer can greatly be enhanced by the introduction of twisted-tape inserts. However, the increase of pressure drop affects the pumping power necessary to maintain the mass flow rate. Twisted-tape insert is a well established method for enhancing heat transfer characteristic of heat exchangers that can be used in oil coolers for gas turbines. Substantial cost savings can be achieved by employing twisted tapes to improve heat transfer in industrial heat exchangers. For a given thermal duty, a smaller heat exchanger can be obtained by inserting a twisted tape. Along with the heat transfer enhancement, however, there is an increase in the frictional resistance to flow. This paper examines and demonstrates the effectiveness of using a twisted tape as a heat transfer enhancement technique for laminar flow with a constant-wall-temperature boundary condition. The gap between the twisted tape and the internal diameter of the tube will also be investigated. The motivation of the work is the desire to use a loose-fit twisted tape that is easier to install and clean when compared to one with a tight-fit. The influence of the gap between the twisted tape and the tube wall on pressure drop and heat transfer will be analyzed. Several numerical and experimental studies have been reported on twisted tape inserts. However very few addressed the effect of the gap between the twisted tape and the internal diameter of the tube. Most of the early work was concerned with the effect of twisted tape in turbulent flow (Royds, 1921; Koch, 1958; and Lopina, 1969). Duplessis (1982) and Monheit (1987) conducted a numerical and experimental heat transfer study, respectively, for laminar isothermal boundary condition. Bandyopadhyay et al. (1991) also reported heat transfer data for laminar flow. Their experiments were performed for a constantheat-flux condition. Manglik and Bergles ( ) reported experimental data and correlations for heat transfer and pressure drop for twisted tape. Their experiments however were limited to twisted tapes that have the same width as the internal diameter of the tube. In their extensive work on twisted tapes, they did not address the effect of gap width between the twisted tape and the internal diameter of the tube. Ayub and Al-Fahed (1993) reported pressure drop measurement for different twisted tape inserts with different gap widths. Their results were limited however to turbulent water flow. The presence of the twisted tape affects the flow field inside the tube. The blockage of the tube flow by the tape increases the flow velocity. In addition, the twisted tape induces a secondary flow resulting in a swirl mixing. For a tight-fit twisted tape, the tape acts as a fin. This will not be the case for loose-fit twisted tape with a smaller width. The gap between the twisted tape and the wall of the tube will be investigated in the present work. The present study includes heat transfer and friction factor measurements. The data was collected for fully developed laminar flow and constant wall temperature where the working fluid is oil. Different twisted tapes with different Y and W were investigated (Y =H/Di, where H is the wavelength of the twisted tape, D; is the internal diameter of the tube, and W is the width of the twisted tape). Fifteen different arrangements were used in this study that are: three twist ratios, each with five different tape widths. The schematic drawing of the twisted tape insert is shown in Figure 1. The physical dimensions of the tapes are given below. Y= H/D 13.2 MM Twisted Tape Width 12.6 mm 12.0 am 11.4 mm 7.1 A B C D E 5.4 F G H I J 3.6 K L M N 0 EXPERIMENTAL PROCEDURE 10.8 The friction factor for the twisted tape experiments was calculated by measuring the pressure drop along the tube. The experimental set up to measure the pressure drop is shown in Figure 2. The apparatus is designed to permit a comprehensive study of flow in tubes. It consists of a circuit through which the fluid is circulated continuously by means of a gear pump. A high-viscosity fluid was selected (Shell Tellus R5) in order to give values of the Reynolds number well in the laminar region. The oil is drawn from the reservoir and delivered by way of a Rotameter flow meter to the perspex settling chamber. The oil passes from the chamber through a parabolic bell mouth into the upper horizontal pipe in which the measurements are taken. The tube is made of copper, of 15.9 mm outside diameter and 14.0 mm inside diameter. The total length of the tube is 4.4 m; however, the test section in which the twisted tape is inserted is 2 m long. The tube is adjusted on its supports to be straight and horizontal. The arrangement of smoothing screens in the settling chamber ensures that the oil enters the tube in an undisturbed condition. Pressures are measured with a digital transducer with a range from 0 to 3 bars. The friction factor is calculated by f= Lp (Di/L) (1) pv2 /2 A schematic diagram of the heat transfer facility is shown in Figure 3. The rig includes two test sections of a single tube-intube heat exchanger. One test section carries a smooth copper tube of 14.0 nun inside diameter and a wall thickness of 1.05 mm and the second contains the same tube with a twisted-tape insert. The twisted tape was fixed at both ends inside the tube by using strings to prevent it from slidding when the flow is passing through. In both sections, saturated steam is introduced n 2

3 into the annulus and is used as an isothermal heat source. Shell Tellus R5 oil is used as the test fluid. The other components include a flow meter, thermocouples and a data acquisition system. Each test section has a nominal length of 1 m, and both were preceded by a calming length of 3 m to eliminate any entrance effects. The system was insulated by wrapping insulation tape around the exposed portions of the tubes and the shells. The oil inlet temperature was controlled by means of a heat exchanger where chilled water is used for cooling. Annulus, wall, and test fluid temperatures were measured using gage copper-constantan thermocouples with a 273 K reference junction. Inlet and outlet fluid bulk temperatures were determined by using mixing cup technique. The wall temperature is obtained by taking the average of fifteen thermocouples installed in five axial locations along the wall of the tube. At each location three thermocouples are installed around the circumference of the tube. Each thermocouple is soldered in a groove (thermowell) inside the wall. The variation in the wall temperature axially and circonferentially was always less then 3 %. The inside heat transfer coefficient and Nusselt number are calculated as follows: Q = mcp(to Ti) (2) Q = hiai(tw Tb) (3) where To +Ti Tb = (4) hence hi and Nusselt number are calculated by mcp(to Ti) hl Ai(Tw Tb) (5) hidi Num= All fluid properties are evaluated at the mean bulk temperature, Tb. The uncertainty in the experimentally determined friction factor and Nusselt numbers were estimated based on the ANSUASME Standard on Measurement Uncertainty (1986) following the procedure of Coleman and Steele (1989). The bias limits for all variables involved in the calculations of friction factor and Nusselt numbers were estimated. Because all thermocouples used in the Nusselt number determination were calibrated against the same standard, some elemental contributions to the bias limits were correlated. The effects of correlated biases were to reduce the overall uncertainty in the Nusselt number. The correlated biases were also accounted for in the uncertainty analysis. For the friction factor and Nusselt (6) number data in this paper, the overall uncertainty ranges from 8 % to 13 % for the friction factor and from 5 % to 10 % for the Nusselt number depending on flow conditions. PLAIN TUBE QUALIFICATION Pressure drop and heat transfer data were collected first for the plain tube. The plain-tube data will serve as a validation of the facility and procedure over the range of Reynolds number anticipated in the twisted-tape testing. Figures 4 and 5 show the friction-factor and heat-transfer results plotted against known plain-tube correlations. Figure 4 presents the friction factor results that are calculated from the measured pressure drop using Equation 1. The friction-factor data are in excellent agreement with the 64/Re equation that is the analytical solution for laminar flow in plain tube. Figure 5 presents the heat transfer data plotted as Graetz number versus Num(lrb / lw) 0.14 The plain-tube data are found to be in good agreement with the Seider-Tate correlation: Num = 2.02Gz1/3(µb /pw)0.14 (7) where Gz = ReD Pr (8) LID This equation is valid over the range of parameters 4< Gz5 10,000 and ( /Jb /,u w ) <9.75 and is based on the mean bulk temperature. The range of Reynolds number and Graetz number for the twisted tape testing were from 230 to 2300 and from 300 to 4500 respectively. PRESSURE DROP AND HEAT TRANSFER RESULTS The experimental study provided pressure drop and heat transfer data for 15 different twisted tape arrangements. Three different wave lengths of H equal to 10, 7.5, and 5 cm were investigated. Data for five tape widths for every wavelength were collected. When a twisted tape is inserted inside a plain tube, it creates a swirl flow as a result, it is often refer to as swirling device. New flow characteristic will be created by introducing the twisted tape. Due to the helical rotating fluid flow, a centrifugal force is superimposed over the longitudinal flow, produces a secondary motion. The net effect of this change is the increase of pressure drop and heat transfer when a twisted tape is inserted into a plain tube. Figure 6 shows results for the friction factor versus Reynolds number. The friction factor for the twisted tape was 3 times larger at low range of Reynolds number and 7 times larger for the high range of Reynolds number than that of the plain tube. No substantial effect of the tape width was 3

4 noticed on the friction factor for the cases investigated in this work. In general, when the width of the twisted tape is decreased, the secondary motion will also decrease resulting in a friction-factor values closer to the plain-tube data. For the cases investigated here, the decrease in the twisted- tape width was not enough to show a substantial decrease in pressure drop. Figure 6 shows a small decrease in friction factor for smaller tape width, however no definite conclusion can be made since the change is within the uncertainty of the measurements. Manglik and Bergles (1992) have correlated friction factor and heat transfer data obtained with a swirl parameter that is similar to the Dean number for flow in curved tubes. The swirl parameter (Sw) describes the intensity of the secondary motion induced by the twisted tape, and it is defined as (centrifugal force)(convective inertia force) Sw = 2 (9) (viscous force) Sw = (PV 2 /H)(PV 2 /Di) Re2 (10) (µv / Di2 )2Y Because the square of Reynolds number becomes very large in magnitude, the swirl parameter was redefined as 1/2 Sw= ReSw' = Re [rz/(n-46/di)]11+(n/2y) 2 I (11) Where Re,w is based on the swirl velocity V, and internal diameter of the tube Di. The swirl parameter accounts for the tape thickness, its twist ratio, and the twisting velocity. The swirl velocity is defined as r1/2 Vs = Va [1+(n/2Y) 2 ] (12) where Va is the axial velocity and it is defined as Va =Ii1JPAc Ar is being the axial cross sectional area, A c = [(7tDi2 /4)-6W] The friction factor can be expressed in terms of swirl parameters as D fsw. = PVs2 /2 (Di / Ls ) (13) where L s is the maximum helical flow length and defined as r 1/2 Ls = L L l +( n / 2Y)2 ] (14) From these definitions 1 (fre)sw =(fre)[(n-46/di) /n][l+(n /2Y)2 j (15) Figure 7 shows that Equation 15 predicts the data obtained for all fifteen cases. The small fluctuation is due to the change in twisted tape width because Equation 15 is derived for tight-fit twisted tape where the width is essentially equal to the inside diameter. The correlation proposed by Manglik and Bergles (1992) predicts the experimental data within ± 15 %. The correlation, proposed for the friction factors for laminar swirl flow, is given by (f Re)Sw =15.767[( / Di) / (n 4S / Di )] 2 r Sw2 5511/6 (16) Figure 8 presents the experimental data and the correlation given in Equation 16. For the cases investigated in this paper, the width of the tape has no definite effect on the friction factor. The result is favorable because the aim was to justify the use of loose-fit twisted tape insert because of the ease in installing and cleaning. As mentioned before, the heat transfer increases with a twisted tape for a variety of reasons. The blockage of the flow due to the presence of the twisted tape increases the flow velocity. The hydraulic diameter is reduced and tends to increase the heat transfer coefficient. The helical motion of the fluid and the secondary flow induced by the presence of the twisted tape improves the mixing. If the width of the twisted tape is close to the inside diameter, the twisted tape will act as a fin and therfore aids in transfering heat. The Grashof number for the data collected here is smaller compared to the square of the swirl parameter. The effect of free convection is not important in this experiment and the dominant effect is the secondary motion caused by the swirl flow. Figures 9, 10, and 11 present the heat transfer data for the twisted tape inserts and with the plain tube. The same scale was used on all figures for ease in comparison. The heat transfer data were plotted as Graetz number versus Num(µb / µw) 0.14 The maximum heat transfer enhancement values for the twisted tapes are 3, 2.5, and 1.5 times for twist ratio of 3.6, 5.4, and 7.1, respectively. Figure 9 presents the data for twist ratio of 3.6. The results were for five twist widths of W equal to 13.2 mm, 12.6 mm, 12.0 mm, 11.6 mm, and 10.8 mm. Also the plain tube results were plotted on the same figure for comparison. The figure shows that the heat transfer performance gradually decreases with decreasing tape width until W equals about 11.6 mm. The data for W equal to 10.8 mm are higher than those of 11.6 mm. 4

5 Figure 10 presents the data for twist ratio of 5.4. At the highest Graetz number, the heat transfer decreases for this case by almost 15 % more than that obtained with Y=3.6. For this case, the heat transfer data for W= 12.6 mm are higher than those of 13.2 mm; however, the data decreases up to W equal 11.6 mm. Again for this case, the data for W equal of 10.8 mm are higher than those of 11.6 mm. Figure 11 contains the data for a twist ratio of 7.1. This tape processes the smallest swirl component in the flow field. As expected, the heat transfer decreases by 28 % from that obtained with Y equal to 3.6 at the highest value of Graetz number. For this case, the behavior of heat transfer with the width of the tape is similar to that obtained with Y equal to 5.4. The data for the case of 10.8 nun width are higher than all the others. Two competing physical effects cause the heat transfer data to behave as shown in Figures 9,10, and 11. The swirl flow and helical motion inside the tube tend to increase the heat transfer. Also, when the width of the twisted tape decreases, some of the fluid is forced to flow between the tape and the tube that increases the velocity and also increases the heat transfer. For Y equal to 3.6, the swirl effect is dominant and heat transfer decreases with a decreasing the width of the tape. For the other two cases, however the swirl effect is not as strong and the squeezed flow or the leakage effect becomes relatively important. The leakage effect for a width of 10.8 mm is more dominant than that obtained with W= 11.6 mm. These results indicate that more experimental and numerical work are needed where both the twist ratio and the width of the twisted tape are design parameters in achieving an optimum heat-exchanger performance. Since most of the uncertainties in the experiment are bias or systematic errors, the data can be compared with each other with a high degree of confidence. The heat transfer data for all cases were correlated as suggested by Manglik and Bergles (1992) to the swirl parameter Sw. The Swirl parameter (Sw) describes the intensity of the tape-twist induced secondary motion. The width of the tape is accounted for in the calculation of the swirl parameter. Figure 12 presents the experimental data and the correlation. The data is correlated by Num = 0.318Sw0.569 Pr0.3(4b / µw )0.14 (17) within ± 10 %, and the regression fit through the experimental data has a correlation coefficient of The swirl parameter used used here is defined in Equation 11. Equation 17 gives the correlation for laminar flow heat transfer in circular tube with twisted tape insert of different tape widths. CONCLUSION The effect of the twisted-tape width on the heat-transfer and friction-factor performance with laminar flow in circular tube has been studied. Heat transfer and pressure drop measurements for twisted tape ratio of 3.6, 5.4, and 7.1 were performed. Five different tape widths of W equal to 13.2 mm, 12.6 mm, 12.0 mm, 11.6 mm, and 10.8 mm for each twist ratio were investigated. The range of Reynolds number and Graetz number for the twisted tape testing are from 230 to 2300 and from 300 to 4500 respectively. A twisted tape causes the friction factor and heat transfer to increase by factor of 3 to 7 times and 1.5 to 3 times, respectively, compared to the plain-tube data. The magnitude depends upon the flow conditions and the twisted tape geometry. The data show that the width of the twisted tape has little effect on friction factor but more pronounced effect on heat transfer. For heat transfer, the effect of width is seen more in the high range of Reynolds number where the variation in the heat transfer to the change of width for the cases investigated in this work is about 20 %. When the twisted-tape width decreases, the swirl effect becomes smaller but the leakage of high velocity flow between the tape and the wall of the tube becomes more intense resulting in increase in heat transfer. So the idea that heat transfer always decreases with the decrease of the twistedtape width is not always true. Because of the effect of the width of the twisted tape is not seen for low Reynolds number flows, it is recommend to use loose-fit twisted tapes instead of tight-fit ones for low Reynolds number flows since it is easier for cleaning and installing. Correlations for both friction factor and heat transfer data are available. Such correlations are based on the work of Manglik and Bergles (1992). These correlations constitute good tools in the design of twisted tape insert heat exchangers. REFERENCES 1986, Measurement Uncertainty, ANSFASME PTC , Part 1. Ayub, Z.H., Al-Fahed, S. F., 1993, "The Effect of Gap Width Between Horizontal Tube and Twisted Tape on the Pressure Drop in Turbulent Water Flow," hit. Journal of Heat and Fluid Flow, Vol. 14, pp Bandyopadhyay, P. S., 1991, "Influence of Free Convection on Heat Transfer During Laminar Flow in Tubes with Twisted Tapes," Experimental Thermal and Fluid Science, Vol 4, pp Coleman, H. W., and Steele, W. G., 1989, "Experimental and Uncertainty Analysis for Engineers, " Wiley, New York. Du Plessis, J. P., 1982, "Laminar Flow and Heat Transfer in a Smooth Tube with a Twisted Tape Insert," Ph.D Thesis, Dept. of Mechanical Engineering, University of Stellnbosch, South Africa Koch, R., 1958, "Druckverlust and Warmeubergang bei verwirbelter Stromung," VDI-Forschungshefl 469, Series B, Vol. 24, pp

6 Lopina, R. F., and Bergles, A. E., 1969, "Heat Transfer and Pressure Drop in Tape Generated Swirl Flow of Single- Phase Water," Journal of Heat Transfer, Vol. 91, pp Manglik, R. M., and Bergles, A. E., 1987, "A Correlation for Laminar Flow Enhanced Heat Transfer in Uniform Wall Temperature Circular Tubes with Twisted-Tape Inserts," Advances in Heat Transfer- 1987, HTD-Vol. 68, ASME, New York, pp Manglik, R. M., Bergles, A. E., and Joshi, S. D., 1988, "Augmentation of Heat Transfer to Laminar Flow of Non Newtonian Fluids in Uniformly Heated Tubes with Twisted - Tape Inserts," Experimental Heat Transfer, Fluid Mechanics and Thermodynamics 1988, R. K. Shaba et al., Elsevier Science Publishing, New York, pp Manglik, R. M., and Bergles, A. E., 1992a, "Heat Transfer Enhancement and Pressure Drop in Viscous Liquid Flows in Isothermal Tubes with Twisted-Tape Inserts," Warme-und Stoffubertragung, Vol. 27, No.3. Manglik, R. M., and Bergles, A. E., 1992, "Heat Transfer and Pressure Drop Correlation for twisted-tape Inserts in Isothermal Tubes: Part I - Laminar Flows," Enhanced Heat Transfer, HTD- Vol. 68, ASME, pp Monheit, M., 1987, "Experimental Evaluation of the Convection Characteristics of Tubes with Twisted Tape Inserts," Advances in Enhanced Heat transfer, HTD Vol. 68, ASME New York, Royds, R., 1921, "Heat Transmission by Radiation Conduction and Convection," 1st Ed., Constable and Co., London, UK, pp mm DD H it O.5 mm Figurel Schematic drawing of twisted-tape insert. PITOT TUBE SETTLING DDOGER PRESSURE SENSING _ / WILT PERSPEX DEFLECTOR RESERVOIR liii II LIVERY PIPE Figure 2 Schematic diagram of the pressure drop facility. VALVE TWISTED TAPE LOOP STEAM IN CUPNC FLOW CONDENSATE OUT METER (LIQUID + VAPOUR) COLD FLUID OUT SMOOTH TUBE LOOP ]FLUID Figure 3 Schematic diagram of the heat transfer facility. 6

7 o Y= f=64/re Re Figure 4 Friction factor data and correlation for the plain tube Y= ` I E 0z Re GZ W=13.2 W=12.6 W=12.0 o W=11.4 0W=10.8 Smooth Figure 5 Heat transfer data and Sieder-Tate correlation for Figure 6 Comparison of friction factor data for twisted tape the plain tube. and plain tube laminar flow. 7

8 0) a ! Y=3.6 Y=5.4 Y= W=13.2 mm 90 W=12.6 mm A W=12.0 mm 80 V W=11.4 mm. t *v 70 W=10.8 mm 3 Plain Tube i X60 ;^ 50 '^ Z 40 v Sw GZ Figure 7 Variation of friction factor with swirl parameter, Sw. Figure 9 Heat Transfer data for different widths of the twisted tape for twist ratio of V G) V a 2 II f (Experimental) T7 100 W=13.2 mm 90 W=12.6 mm d' 80 W=12.0 mm W=11.4 mm 70 W=10.8 mm, 60 Plain Tube 50 E40 V) z 30 20, + ' 10 e GZ Figure 8 Comparison of the experimental data and prediction for the friction factor. Figure 10 Heat Transfer data for different widths of the twisted tape for twist ratio of

9 r 100 W=13.2 mm 90 W=12.6 mm 80 W=12.0 mm V W=11.4 mm 70 W=10.8 mm 60 Plain Tube 50.::,!e E40 Z ^^., GZ Figure 11 Heat Transfer data for different widths of the twisted tape for twist ratio of 7.1. M 0 10 a c Z E SW1000 Figure 12 Correlation for laminar flow heat transfer in tubes with twisted-tape inserts. 9