Al-Qadisiya Journal For Engineering Sciences Vol. 3 No. 2 Year 2010 161 EXPERIMENTAL STUDY OF THE FRICTION FACTOR IN EQUILATERAL TRIANGULAR DUCT WITH DIFFERENT TYPES OF VOREX GENERATORS (OBSTACLES) Mohammed Ghanem Jehad University of Anbar, Mech. Eng. Dept. Abstract: Friction factors for fully developed flow in an equilateral triangular duct containing built-in vortex generators of delta wing, rectangular wing, pair of delta winglets, and pair of rectangular winglets have been investigated experimentally for Reynolds numbers ranging from (24 500) to (75 750). The ratio of the cross- sectional area of the test duct to that of the vortex generator (AD/AVG) was remaining constant during experiments. The variable parameters were; type of vortex generator, vortex generator angle of attack, and Reynolds number. The friction factor values for the smooth triangular duct are in good agreement with the existing data. The present results show that the friction factor is affected strongly by the wing greater than the winglet pair of vortex generators. The delta wing causes flow loss greater than the rectangular wing, while the flow loss accompany with the existence of the pair of delta- winglets is less than that of the pair of rectangular winglet. It is also observed that the friction factor is affected remarkably by the angle of attack of vortex generator. Keyword: Triangular Duct, Fully Developed, Friction Factor, Obstacle. أنواع مختلفة من النمو في مجرى مثلث المقطع باستخدام تجريبية لمعامل ا�حتكاك كاملدراسة )عوائق(مولدات الدوامية محمد غانم جھاد قسم الھندسة الميكانيكية، كلية الھندسة- جامعة ا�نبار :الخالصة ثلث، والجناح المستطيل، والجنيح تم اجراء دراسة تجريبية لبيان تاثير غرز مولدات الدوامية نوع الجناح الم 500(عدد رينولدز تراوح بين المثلث، والجنيح المستطيل على جريان الهواء داخل مجرى مثلث المقطع ولقيم تم تثبيت نسبة مساحة المقطع العرضي للمجرى الى مساحة مولد الدوامية خالل التجارب، ). 75 750(و ) 24 كانت نتائج . نوع مولد الدوامية، وزاية ميل مولد الدوامية، وعدد رينولدز: وكانت المتغيرات في هذا البحث هي بينت النتائج الحالية ان . االختبارات للجهاز بدون وجود مولدات الدوامية جيدة مقارنة مع نتائج البحوث السابقة كما وان المولد نوع .معامل االحتكاك يكون متاثرًا بشكل كبير بالمولدات نوع الجناح اكثر منه من نوع الجنيح Al-Qadisiya Journal For Engineering Sciences Vol. 3 No. 2 Year 2010 162 الجناح المثلث يولد هبوط ضغط اقل من الجناح المستطيل، في حين ان خسائر الجريان المرافقة لوجود الجنيح كما ولوحظ ان تغيير زاوية ميالن مولد الدوامية تؤثر . المثلث هي اقل من تلك المرافقة لوجود الجنيح المستطيل .بشكل واضح على معامل االحتكاك .، عائقمعامل االحتكاكمجرى مثلث، تام النمو، : مات المفتاحيةالكل NOMENCLATURE Lest of symbols A Internal cross-sectional area of the orifice plate (m2). DA Internal cross-sectional area of the test duct (m 2). VGA Vortex generator area (m 2). C Constant. d Constant. hD Hydraulic diameter (m). f Darcy’s friction factor. of Standard friction factor(without obstacle). h Height of the vortex generator (m). L Distance between two tandem static pressure taps (m). l Length of the vortex generator (m). •m Air mass flow rate (kg/s). p Wetted perimeter of the walls of the duct (m). ∆∆∆∆ P Pressure drop between the static pressure taps (pa). Re Reynolds number. S Distance between tips of winglet pair (m). inTb Inlet air bulk temperature ( oK). outTb Outlet air bulk temperature ( oK). fT Air bulk film temperature ( oK). U Mean velocity of the air (m/s). Al-Qadisiya Journal For Engineering Sciences Vol. 3 No. 2 Year 2010 163 W Length of the side of the test duct (m). zX Distance of wingtip from the leading edge of the test section (m). Greek symbols ββββ Angle of attack of vortex generator (degree). ρρρρ Air density (kg/m3 ) µµµµ Absolute viscosity (pa.s). υυυυ Kinematic viscosity (m/s2) Introduction: In the development of recent industrial world, the reduction in the heat exchanger size and enhancement in their performance for heat transfer had a great interest of investigators. But there are always economical factors to reduce the costs of heat transfer process. The need for high performance thermal systems due to study the increase in the pressure drop associated with the augmentation operations in heat transfer. Use of vortex generators for heat transfer enhancement is one passive method that generates vortices which creates high turbulence in fluid flow over heat transfer surfaces. Aly et al. (1978) performed a numerical and experimental study for fully developed airflows through an equilateral triangular duct for high values of Reynolds number. They have found that the measured and predicted friction factor have a good agreement with the Blasius1 equation for friction factor in smooth circular tubes. An experimental study was performed by Altemani et. al. (1980) to determine the entrance region, fully developed heat transfer and fluid flow characteristics for turbulent airflow in an unsymmetrical heated equilateral triangular duct. They have found that the circular –tube friction factor results deviate from those of equilateral triangular duct, even when the hydraulic diameter is employ. In (1986) Chegini et. al. studied theoretically and experimentally the friction factors for fully developed flow in triangular duct for two apex- angles with and without fins for a wide range of Re number. This study showed that the equilateral triangular duct has smaller scatter of friction factor data compared with the isosceles. A numerical and experimental study of flow and heat transfer characteristics in a rectangular channel with built-in wing vortex generator was investigated by Biswas et. al. (1992) and Laith (2008). Biswas et. al. have seen that the combined spanwise average friction factor (fxRe) increases approximately linearly with the angle of attack of generator, and more affected with Re number. Laith found that the friction factor changes significantly when Re numbers increased. As an extension of the work of Biswas et. al. (1992), Dep et al. (1995) and Biswas et al. (1994) studied the effect of the delta-wing and winglet- pair type vortex generator on a fluid flow and heat transfer characteristics through a rectangular channel. Biswas et al. (1994) have found that the loss (corresponding to the combined spanwise average friction factor coefficient) due to the winglet-pair is less than that due to the wing. Kotcioglu et al. (1998) investigated the rectangular-wing in the rectangular channel as in a way of divergent and convergent arrays. They observed that the pressure drop is influenced strongly by the inclination angle of vortex generator. Sabah et. al. (2007) studied numerically the effect of exist of 1 f = 0.316/Re0.25 Al-Qadisiya Journal For Engineering Sciences Vol. 3 No. 2 Year 2010 164 multi–types of turbulators on the fluid flow and temperature distribution for laminar and turbulent flow in a rectangular duct. The influence of vortex generators angle and louver angle on heat transfer and flow loss in laminar channel flows was numerically studied by Chung (2003). The purpose of this paper is to highlight the effect of the four basic types of the vortex generators experimentally on the pressure drop gradient in a triangular duct. These four basic types of the vortex generators are shown in Figure (1). Experimental apparatus: The experiments were performed in an open–loop airflow circuit. The first air is encountered of regulator valve upstream wise of the blower, and then ducted to a circular tube which is provided by an orifice plate flowmeter in the axial mid-length to measure the air flow rate. The upstream end of the circular tube is coupled with the blower by using a flexible tube to minimize the vibration that occurs during blower operation and the downstream end mated with a hydrodynamic development section. The hydrodynamic development duct has an equilateral triangular cross section. A convergent contraction aluminum part was used to transit from circular tubing of the upstream piping system to the downstream triangular cross-section. The air exiting the hydraulic development section passes through the test section which they mated together at the same horizontal straight line and have an identical cross-section. The scheme of the current experimental apparatus is shown in Figure (2). During a course of experiments, Reynolds number was varied between (24 500) and (75 750). The development and test section were of identical internal dimensions; side of triangle=15 (cm), and hydraulic diameter=8.66 (cm). The respective axial lengths of the development and test sections were (24 hD ) and (15 hD ). The experiments tests were performed in the fluid laboratory, engineering college, university of Anbar. The volumetric flow rate of air was measured by an orifice plate meter whose pressure taps were located one diameter upstream and half-diameter downstream as published in Roberson et. al. (1997) and Spencer et. al. (1982). The internal diameter ratio of the orifice plate and the tube is (0.7). Some parameters were to be constant during the experimental apparatus design. These parameters are; the ratio of the cross-sectional area of the test duct to that of the vortex generators (AD/AVG), the distance of the wingtip from the leading edge of the test duct (Xz), the number of the VG punched in the duct, and the distance between the tips of winglet pairs (S). The geometry of the vortex generator was dependent upon the inclination angle (β) to keep the ratio (AD/AVG) is to be constant. This can be seen clearly in Table (1) and Figure (3), (4), and (5). The variable parameters are; the type of the vortex generator, the vortex generator angle of attack which is (20, 30, and 40) degree, and Reynolds number varying from (24 500) to (75 750). The vortex generator thickness is assumed negligible. The test section has seven static pressure taps located at various positions along the axial direction. At any given axial location, the taps were also located in the circumferential direction to sense any pressure variation in that direction. The three taps at any given location jointed together to form one end. The difference in pressure was measured by connecting the inclined manometer two ends to each tandem two measuring points by PVC tubes. A mercury thermometer is used to measure the input and output temperature of the test section. The air properties were estimated at the air bulk film temperature that is defined as follows, Al-Qadisiya Journal For Engineering Sciences Vol. 3 No. 2 Year 2010 165 Holman (1976): 2 outin bTbT fT + = …(1) The mass flow rate can be computed by the following equation: UAm ρ=. … (2) The experimental data are represented in the standard form of friction factor as a function of Reynolds number defined as follows. Streeter (1979): P mhDU µν .4 Re == …(3) The symbol ( hD ) is the hydraulic diameter of the triangular duct that can be defined as follows, Streeter (1979): P A D Dh 4= …(4) The friction factor f, known as Darcy friction factor in the literature, is defined as, Streeter (1979): ] 2 [ 2U D L P f h ρ × ∆ = …(5) Results And Discussion: For checking the velocity of the experimental apparatus, Figure (6) shows the comparison between the current data without any obstacle and the literature experimental data. The results of Petukhov-Popov, Prandtl, and Blasius were developed for circular tubes, while the data of Altemani Al-Qadisiya Journal For Engineering Sciences Vol. 3 No. 2 Year 2010 166 was for triangular duct as published in research of Altemani et. al.(1980). As shown in Figure (6), the present data over predicts that of Altemani by about (4.5) percent, whereas it is lower than that of Blasius, Petukhov-Popov, and Blasius by about (5, 6.86, and 8) percent respectively. This comparison indicates that the experimental rig is satisfactory. Figure (7) shows the axial distribution of the (f x Re) along the test section for Re=24500 while keeping the angle of attack of vortex generator constant. It is apparent that the flow loss associated the existence of the wing-type is greater than that associated the winglet pair of VGs. This is because the wing-type causes a pressure drop region behind the trailing end of the vortex generator greater than that it is caused by the winglet pairs of vortex generators, and the air flow is circulated smoothly with the existence of winglet-pair type while if the wing-type is existence the air flow is circulated strongly. The pressure drop caused by RW is larger than that of DW. Also, we obtain a (f x Re) for the case of RWP greater than that of DWP. This performance gives a behavior similar to that of the rectangular channel as investigated by Tiggelback (1994). As expected, the friction factor value remains unchanged throughout in the duct for the flow without any obstacle. For example, at β=20 deg the (fxRe) for the case of DW at a location (X/Dh=2), is about (93.9%) more than that for the plane duct flow, while for the case of DWP over the (f x Re) value for plane channel about (57.4%). This behavior can also be clearly remarked in the Figure (8) when Re=75750 and β=40 degree. Figure (9) shows the effect of the varying of the vortex generator angle of attack while keeping the ratio of (AD/AVG) constant. It is observed clearly that the friction factor increases monotonically with (β) because the vortex circulation increases which increases resistance and a higher value of friction is obtained. For example, at β=30o, the friction factor for the case RW promotes by about (24.7) percent more than that for β=20o as shown in Figure (9-a). Figure (10) exhibits the effect of Re number on the average friction factor through the test section. It seems that the friction factor is reversely proportion with Reynolds number. For example, in the case of RWP the ( f ) is about (56.7%) when Re=24 500 and β=40o greater than that for Re=75 750 as shown in Figure (10-d). A correlation of the friction factor is determined as a function of Reynolds number to compare the fourth cases data. The correlation obtained from the current experimental data is: 2Re π β d C f = …(6) The values of the variables C and d in Eq.(6) are tabulated in Table (2). Concluding Remarks: Depending on the results presented and discussed, the main conclusions of this study can be summarized as follows: 1. The flow loss in a triangular duct (corresponding to the friction factor) due to the Al-Qadisiya Journal For Engineering Sciences Vol. 3 No. 2 Year 2010 167 winglet-pair is less than that due to the wing. 2. The pressure drop increases strongly with the angle of attack of vortex generator (> 30 degree). 3. The difference in the pressure drop caused by the delta-winglet pair and rectangular – winglet pair is very slightly. 4. The friction factor changes significantly when the Reynolds numbers increased. References: 1. Altemani, C.A.C., & Sparrow, E.M., November 1980,“Turbulent Heat Transfer in an Unsymmetrically Heated Triangular Duct”, ASME Journal of Heat Transfer, Vol. 102, pp. (590–597). 2. Aly, A.M.M., Trupp, C. & Gerrard A.D., 1978,“Measurements and Prediction of Fully Developed Turbulent Flow in an Equilateral Triangular Duct” J. of fluid Mech. Vol.85, part 1, pp. (57–83). 3. Biswas, G., and Chattopadhyay, H., 1992,“Heat Transfer in a Channel with Built–in Wing– Type Vortex Generators”, Int. J. Heat Mass Transfer. Vol. 35, No. 4, pp. (803–814). 4. Biswas, G., Dep, P., and Biswas, S., August 1994,“Generation of Longitudinal Streamwise Vortices–A Device for Improving Heat Exchanger Design”, ASME Journal of Heat Transfer, Vol. 116, pp. (588–597). 5. Chegini, H. & Chaturvedi, S.K., August 1986,“an Experimental and Analytical Investigation of Friction Factors for Fully Developed Flow in Internally Finned Triangular Ducts”, Journal of Heat Transfer, Vol. 108, pp. (507– 512). 6. Chung, J.D., Park, B.K., and Lee, J.S., 2003 ,“The Compined Effects of Angle of Attack and Louver Angle of a Winglet Pairon Heat Transfer Enhancemet”, J. Enhanced Heat Transfer, Vol.10, Number.1, PP(31-43). 7. Dep, P., Biswas, G., and Mitra, N. K., 1995,“Heat Transfer and Flow Structure in Laminar and Turbulent Flows in a Rectangular Channel with Longitudinal Vortices”, Int. J. Heat Mass Transfer, Vol. 38, No. 13, pp. (2427–2444). 8. Holman. J. P., 1976,”Heat Transfer”, 4th Edition, McGraw–Hill, Inc. 9. Kotcioglu, I., Ayhan,T., Olgun, H., and Ayhan, B., “Heat Transfer and Flow Structure in a Rectangular Channel with Wing – Type Vortex Generator”, Tr. J. of Engineering and Environmental Science, 22, 1998, pp. (185–195). 10. Laith. J.H., 2008,“Numerical and Experimental Investigation of Heat Transfer Augmentation using Vortex Generators”, Ph.D. Thesis, University of Technology. 11. Ligrani, P. M., Ortiz, A., Joseph, S. L., and Evans, D. L., January 1989,“Effects of Embedded Vortices on Film – Cooled Turbulent Boundary Layers”, Journal of Turbomachinery, Vol. 111, , pp. (71–77). 12. Roberson, John A., and Crowe, Clayton T., 1997,“Engineering Fluid Mechanics “, 6th Edition, Jone Wiley and Sons Inc., USA. 13. Sabah, T.A., Waheed, S.M., & Laith, J.H., 2007,“Numerical Investigation into Velocity and Temperature Fields Over Smooth and Rough Ducts for Several Types of Turbulators” Eng. And Technology, Vol.25, No.10. 14. Spencer, E.A., June 1982,“Progress on International Standardization of Orifice Plates for Flow Measurement”, Int. J. Heat & Fluid Flow, Vol. 3, No.2, pp. (59 – 66). 15. Streeter Victor L. & Wylie E. Benjamin, 1979,“Fluid Mechanics “, 7th Edition, McGRAW– Al-Qadisiya Journal For Engineering Sciences Vol. 3 No. 2 Year 2010 168 HIL, Inc. 16. Tiggelbeck, St., Mitra, N.K., & Feibig, M., November 1994,“Comparison of Wing Type Vortex Generators for Heat Transfer Enhancement in Channel Flows”, ASME Journal of Heat Transfer, Vol. 116, pp. (880 – 885). Table (1) Test model geometry, all values in mm. 20 degree 30 degree 40 degree RW DW RWP DWP RW DW RWP DWP RW DW RWP DWP Vortex height (h) 16 23 20 31 23 30 16 23 32 44 11 16 Vortex length (l) 46 65 33 46 44 63 32 44 50 70 35 50 Area AVG(mm 2) 500 500 500 500 500 500 500 500 500 500 500 500 AD/AVG 20 20 20 20 20 20 20 20 20 20 20 20 Distance of the wingtip from leading edge (Xz) 1Dh 1Dh 1Dh 1Dh 1Dh 1Dh 1Dh 1Dh 1Dh 1Dh 1Dh 1Dh Distance between tips of winglet pairs (S) 20 20 20 20 20 20 Table (2) Values of the variables C and d in Eq.(6) case var β C d DW 20 0.723 0.549 30 2.036 0.668 40 1.762 0.666 RW 20 0.798 0.564 30 1.254 0.612 40 2.466 0.680 DWP 20 0.161 0.427 Al-Qadisiya Journal For Engineering Sciences Vol. 3 No. 2 Year 2010 169 30 0.408 0.538 40 0.614 0.587 RWP 20 0.203 0.443 30 0.367 0.523 40 1.103 0.635 Figure (1) Schematic of longitudinal vortex generators types; a-delta wing, b- rectangular wing, c-delta winglet pair, d–rectangular winglet pair. RW DW RWP DWP Xz S l β W h Figure (3) Schematic of the geometry of the duct with the delta-winglet pair. Figure (4) Shows the ratio of (AD/AVG) that is equal to 20. Al-Qadisiya Journal For Engineering Sciences Vol. 3 No. 2 Year 2010 170 Figure ( 6 ) Friction Factor results Re x 10-3 20 30 40 50 60 70 80 f x 1 0 2 1.4 1.6 1.8 2.0 2.2 2.4 2.6 Current data Petukhov-popov [2] Blasius [2] Altemani [2] RW RWP DW DWP h s/ 2 l Figure (5) Shows elevation and plan view of different VGs. β W/2 β Al-Qadisiya Journal For Engineering Sciences Vol. 3 No. 2 Year 2010 171 Figure ( 8 ) Axial Distribution (fxRe) along the Test Section at ββββ =40o and Re=75 500. X/D h 0 2 4 6 8 10 12 14 16 f x R e 0 10000 20000 30000 40000 RW DW DWP RWP without obstacle Location of the obstacle Figure ( 7 ) Axial Distribution of (fxRe) along the Test Section at β=40o and Re=24500. X/D h 0 2 4 6 8 10 12 14 16 f x R e 0 3000 6000 9000 12000 15000 without obstacle RW DW DWP RWP Location of the obstacle Al-Qadisiya Journal For Engineering Sciences Vol. 3 No. 2 Year 2010 172 (a) (b) 15 20 25 30 35 40 45 f x 1 0 2 6 8 10 12 14 16 RW DW RWP DWP 15 20 25 30 35 40 45 f x 1 0 2 2 4 6 8 10 12 14 16 RW DW RWP DWP β β (a) (b) Figure ( 9 ) Effect of the Angle of Attack of Vortex Generators on the Average Friction Factor. (a) Re=24500, (b)Re=75750. Fig ( 10 ) Effect of Reynolds Number on the Average Friction Factor in the Duct. (a)DW, (b)RW, (c) DWP and (d)RWP. Re x 10-3 20 30 40 50 60 70 80 f x 10 2 1 2 3 4 5 6 without obstacle 20 deg 30 deg 40 deg Re x 10-3 20 30 40 50 60 70 80 f x 1 0 2 1 2 3 4 5 6 7 without obstacle 20 deg 30 deg 40 deg Re x10-3 20 30 40 50 60 70 80 f x 10 2 1 2 3 4 5 without obstacle 20 deg 30 deg 40 deg ( d ) ( b ) Re x 10-3 20 30 40 50 60 70 80 f x 10 2 1 2 3 4 5 without obstacle 20 deg 30 deg 40 deg ( a ) ( c )