Experimental investigation of pressure d

International Journal of Thermal Sciences 50 (2011) 361e368 Contents lists available at ScienceDirect International Journal of Thermal Sciences journal homepage: www.elsevier.com/locate/ijts Experimental investigation of pressure drop and friction factor for water flow in microtubes S Barlak a, S Yapıcı a, O.N Sara b, * a b Department of Chemical Engineering, Faculty of Engineering, Atatürk University, 25240 Erzurum, Turkey Department of Chemical Engineering, Faculty of Engineering, Çankırı Karatekin University, 18200 Çankırı, Turkey a r t i c l e i n f o a b s t r a c t Article history: Received May 2010 Received in revised form 16 August 2010 Accepted 17 August 2010 Available online October 2010 The pressure drop and friction factor for the flow distilled water in microtubes with the diameters ranging from 0.20 mm to 0.589 mm were investigated experimentally The experiments were carried out in the Reynolds number range of approximately 100e10000 and the length-to-diameter ratios (L/d) in the range of 16e265 It was observed that two different mechanisms of transition from laminar to turbulent flow occurred as smooth and abrupt The pressure drop and friction factor values agreed with the values of classical channel flow theory The L/d ratio had an important effect on the apparent friction factor in case of L/d < 100 It was found that the critical Reynolds number for the transition was between 2000 and 2500 Ó 2010 Elsevier Masson SAS All rights reserved Keywords: Microchannel Microtube Pressure drop Friction factor Laminar flow Introduction With development of the microsystem technology, the investigation of the flow phenomena in microtube and channels has been one of the most important subjects There are several studies, experimental or theoretical, on the heat transfer and the pressure drop for laminar and turbulent liquid or gas flow in microchannels The reviews of these studies are given by several researchers [1e5] The effects of the surface roughness, geometry of channel, type of fluid (gas or liquid, single or two phase), flow rate, surface fluid interaction, have been the major parameters, which were considered in the studies on the fluid flow in the microchannel In general, the experimental data have been compared with the conventional theories, and in many cases contradictory results have been reported The first diversity between studies is that the fact that there are three different results of the friction factor values; that is, the results smaller than, higher than and similar to the friction factor values predicted by classical theory These results have been reviewed by several researchers [1e4,6] The second is related to the critical value of Reynolds number at which the flow regime changes from laminar-to-turbulent For the transition from the * Corresponding author E-mail addresses: onuri@rocketmail.com, onurisara@karatekin.edu.tr (O.N Sara) 1290-0729/$ e see front matter Ó 2010 Elsevier Masson SAS All rights reserved doi:10.1016/j.ijthermalsci.2010.08.018 laminar to turbulent flow, different Reynolds numbers have been reported for very similar conditions It was also reported very early transition Reynolds numbers such as, in the range of 200e700 for water flowing through rectangular channels having hydraulic diameters of 0.133e0.367 mm [7], and of 300e900 for water flowing in microtubes with the diameters ranging from 0.050 to 0.245 mm [8], and 240 for water flowing through a rectangular channel with the hydraulic diameter of 0.146 mm [9] Vijayalakshmi et al [10] investigated the effect of compressibility, and the transition to turbulence flow through microchannels of hydraulic diameter ranging from 0.0605 mm to 0.211 mm, employing nitrogen as the working fluid They reported that the transition to turbulent occurred in the Reynolds number range of 1600e2300 They claimed that the slight decrease in the transition range may be due to the relative roughness or the edge effects of the trapezoidal channel geometry Morini et al [11] studied the laminar to turbulent transition in the fused silica and stainless steel microtubes having the diameters ranging from 0.125 to 0.180 mm, using nitrogen as working fluid They reported that the transitional regime started at the Reynolds numbers around 1800e2000, and the surface roughness had no effect on the hydraulic resistance in the laminar region for a relative roughness lower than 4.4%, taking compressibility into account Lorenzini et al [12] investigated the flow of nitrogen inside circular microchannels having the diameters ranging from 26 mm to 508 mm with different surface roughness values and L/d ratios in the range of 591e1689 362 S Barlak et al / International Journal of Thermal Sciences 50 (2011) 361e368 microtubes with the diameters in the range of 337 mme2083 mm They reported that the decrease in the tube diameter and increase in the relative roughness affected friction factor, even in the laminar flow, and that the Reynolds number range for the transition flow became narrower with decreasing tube diameter It was also reported that when the diameter of the tube changed from 2083 mm to 667 mm, the onset of transition region delayed at Reynolds number from 1500 to 2200 Although there are several studies on pressure drop and friction factor characteristics of the microchannel, because of the diversities between results, it can be said that further investigation is required in order to verify if the classical correlations can predict friction factor in laminar, transition and turbulent regimes Moreover, in many of the studies, the length-to-diameter ratio of the channel has been selected higher than 100 to provide fully developed condition [11,12] However, in some practical applications such as microexchangers, micro-reactors etc, it can be difficult to establish a flow length for hydrodynamically fully developed flow Therefore, the entrance effect, L/d ratio should be taken into account for pressure drop and friction factor characteristics of the fluid flow in microtubes In this study, it was aimed to investigate the pressure drop and friction factor of water flowing through microtubes with different diameters and L/d ratios for the cases of laminar, transition and turbulent flow conditions Nomenclature d f K L DP Re u r m tube diameter (m) friction factor (À) loss coefficient tube length (m) pressure drop (Pa) Reynolds number (À) mean velocity (m sÀ1) density (kg mÀ3) viscosity (kg mÀ1 sÀ1) Subscripts app apparent d developing e exit i inlet m miscellaneous net net o outlet t total In macro channel flow, the effect of inlet configuration, namely squared-edged, re-entrant and bell-mouth, of the circular straight horizontal tube on the transition to turbulence was investigated by Ghajar and Madon [13] under isothermal flow conditions, by Tam and Ghajar [14] for non-isothermal flow conditions They used 316 stainless steel tubes with an inside diameter of 1.58 cm and lengthto-diameter ratio (L/d) of 386 to provide fully developed flow condition It is reported that the transition occurred in the Reynolds number range of 1980e2600 for the re-entrant inlet, 2070e2800 for the square-edged inlet and 2125e3200 for the bell-mouth inlet for isothermal conditions, and it changed depending on heat flux in the case of non-isothermal flow On the other hand, several investigators remarked the dependence of critical Reynolds number on the surface roughness and geometry [11,15,16] In microchannel flow, the flow regime is often in laminar or transition region, especially, in the case of liquid flow Therefore, the pressure drop and friction factor characteristic of fluid flow under transition condition is important Recently, Ghajar et al [17] performed an experimental investigation for friction factor in the transition region for water flow in stainless steel minitubes and Experimental set up and data reduction Experimental set up adapted from our previous study [18,19] is shown schematically in Fig It consists of mainly a high-pressure nitrogen gas tube, a micro filter, a digital balance, a circulated water bath and the test section including micro-tube The flow to the test section was provided by high-pressure nitrogen gas and the flow rates were adjusted by a two-stage gas regulator The fluid passed through a micro filter before entering test section and was collected after the test section to be weighed Distilled water was used as working fluid and its temperature was kept at 25 Æ 0.2  C by circulated bath Five stainless steal tubes, produced for the purpose of the medical treatment, with diameter in range of 0.200 mme0.589 mm were used as test channel The geometrical dimensions of the channels used in the experiments are given in _ Table The dimension of the tubes was measured by NIKON MM 400 L video measuring microscope The pressure difference in the test section was measured by pressure transmitter (KELLER) in range 0e6 bar Æ 0.5% FS 10 P N2 Filter Pressure vessel Thermostat G as regulator Test tube Balance Fluid collection tank Flowmeter pressure drop measurement 10 Pressure measurement Fig Experimental set up S Barlak et al / International Journal of Thermal Sciences 50 (2011) 361e368 Table Geometrical and flow characteristic of tested tubes a Tube Diameter (mm) L/d A1 A2 A3 A4 200 200 200 200 265.90 215.90 163.70 104.85 75e1476 106e1666 159e1904 214e2391 B1 B2 250 250 65.32 48.74 437e3780 467e3305 C1 C2 C3 C4 400 400 400 400 79.19 56.93 41.00 31.13 587e4796 915e5432 1128e5850 1294e6234 D1 D2 D3 D4 505 505 505 505 69.64 46.20 31.21 18.30 918e6544 1600e7350 1651e7827 1888e8875 E1 E2 E3 E4 589 589 589 589 66.03 46.99 33.14 16.00 1283e8000 1693e8662 2000e9400 2512e10461 Re Parameter Uncertainty Diameter Density Viscosity Pressure Mass Time Reynolds number Friction factor Ỉ5 mm Ỉ1.0% Ỉ1.0% Ỉ0.5% FS Ỉ0.01 g Æ2 s Æ2.95% Æ12.92%e19.76% depending on the measured pressure value 300 A1 250 Δ P (kPa) A2 200 A3 150 A4 100 50 300 600 900 1200 1500 1800 2100 2400 2700 Re b 250 C1 200 C2 Δ P (kPa) Table Uncertainties of major parameters 363 150 C3 C4 100 50 1000 2000 3000 4000 5000 Re Fig Pressure drop versus Reynolds number Fig Pictures of cross-section of tubes before and after shortening a: tube-A, b: tube C 6000 7000 364 S Barlak et al / International Journal of Thermal Sciences 50 (2011) 361e368 b a 10.00 1.00 A1 B1 A2 B2 A3 64/Re f A4 f 1.00 0.10 Blasius 64/Re 0.10 0.01 100 1000 0.01 100 10000 1000 c d 1.00 1.00 C1 D1 C2 D2 D3 C3 D4 64/Re 0.10 f f C4 64/Re 0.10 Blasius Blasius 0.01 100 10000 Re Re 1000 10000 0.01 100 1000 Re 10000 Re e 1.00 E1 E2 E3 f E4 64/Re 0.10 Blasius 0.01 100 1000 10000 Re Fig Fully developed friction factor as function of Reynolds number The measured pressure drop, DPt, includes minor loss contributions, DPm, and the net pressure drop in the test tube can be calculated by: DPnet ¼ DPt À DPm (1) The minor losses consist of the contributions of the inlet, the exit and the developing flow pressure drops, and can be calculated by the following equation DPm ẳ Ki ỵ Ke ỵ Kxịị ru2 (2) where Ki and Ke are the loss coefficients for inlet and exit, respectively, and can be calculated by using the procedure given in classical textbooks [20,21] In this study, Ki is taken equal to 0.2 calculated by the equation given by [20] while Ke is equal because the outlet of the tube is open to the atmosphere K(x) is the incremental pressure drop number due to the entrance region effect, and for the L > Lhy it is called K(N) and is given as 1.20 ỵ 38/ Re by Chen (1972) for laminar flow [21] In the turbulent region, the effect of the entrance region on the pressure drop is relatively lower than that of laminar flow and the entrance length is shorter The L/ d ratio required for a fully turbulent flow changes in the range of 10e60 [22] For turbulent flow in the hydrodynamic entrance S Barlak et al / International Journal of Thermal Sciences 50 (2011) 361e368 b 200 180 A1 160 A2 B1 200 B2 A3 140 fRe 250 A4 120 150 64 100 64 fRe a 365 Blasius 100 80 60 50 40 20 400 800 1200 1600 2000 2400 2800 Re c d 500 500 C2 C3 300 fRe fRe D2 D3 400 C4 64 200 600 D1 C1 400 500 1000 1500 2000 2500 3000 3500 4000 4500 5000 Re Blasius D4 Blasius 300 64 200 100 100 0 1000 2000 3000 4000 5000 6000 7000 2000 4000 Re e Re 6000 8000 10000 700 E1 600 E2 fRe 500 E3 E4 400 64 300 Blasius 200 100 0 2000 4000 6000 8000 10000 12000 14000 Re Fig fRe as function of Reynolds number region of a smooth circular duct, the K(x) values are given as function of (L/d)/Re1/4 by Bhatti and Shah [23] For (L/d)/Re1/ > 1.067, it reaches a constant value of 0.070 The friction factor is expressed as follow: f ¼ 2DPnet ðL=dÞru2 (3) The friction factor f, calculated from Eq (3), refers to fully developed friction factor The friction factor calculated from Eq (3) with using DPm without K(x), called apparent friction factor and denoted by fapp, which reflects pressure drop arising from both momentum flux during the velocity profile development and the shear stress at the wall [13] The experimental uncertainties of the parameters were determined using the method described by Holman [24], and the uncertainties of the major parameters are given in Table Results and discussion Pressure drop measurements were conducted with the tubes having different diameter and length at various flow rates The Reynolds numbers employed in the experiments are given in Table For each tube, the pressure measurement was performed by beginning with the longest tube and then the length of the same tube was shortened mechanically to obtain the other length Therefore, for a tube of any length, the inlet geometry and surface condition remained the same As an example, Fig shows the pictures of the cross-sections of the tubes before and after shortening for the two different lengths of the tubes A and C In Fig 3, the net pressure drop (DPnet), which is determined by Eq (1), is plotted as a function of Reynolds number for the tubes A and C As can be seen from this figure, DPeRe relation is linear for Re < 2000 This behaviour can be clearly seen for tubes having the diameter of 366 S Barlak et al / International Journal of Thermal Sciences 50 (2011) 361e368 a b 0.5 0.4 A2 A3 A4 64/Re Blasius 0.16 B1 B2 64/Re Blasius 0.12 fapp fapp 0.3 A1 0.20 0.2 0.08 0.1 0.04 100 600 1100 1600 2100 0.00 500 2600 1500 2500 Re c d 0.20 0.16 C1 C2 C3 C4 4500 0.24 0.20 0.16 Blasius fa p p fapp 0.08 D1 D2 D3 D4 Blasius 0.12 0.12 0.08 0.04 0.00 1000 3500 Re 0.04 2000 3000 4000 Re e 5000 6000 0.00 1000 3000 5000 Re 7000 9000 0.24 0.20 0.16 fapp 7000 E1 E2 E3 E4 Blasius 0.12 0.08 0.04 0.00 1000 3000 5000 7000 Re 9000 11000 13000 Fig Apparent friction factor as function of Reynolds number 0.20 mm in Fig 3(a) This relation shows a non-linear behaviour for Re > 2000 The power of the Re changes in the range of 1e1.13 for Re < 2000 (Fig 3(a)), which is close to 1, showing that the HagenePoiseuille type flow prevails, and for Re > 2000 in the range of 1.56e2.18 for the other tubes of CeE The measured pressure values were converted to the fully developed friction factor values (f) by using Eq (3) The friction factor data for all channel configurations are plotted in Fig as a function of Reynolds number, known as Moody diagram To compare with the experimental data, the friction factor values were calculated from classical theory of macro channels, by using the equations of f ¼ 64/Re for fully developed laminar flow, and f ¼ 0.316ReÀ0.25, known as Blasius equation, for fully developed turbulent flow, which were presented graphically in Fig Fig (a) shows the experimental data for the tube having 0.20 mm diameter As seen from this figure, the experimental friction factor values agree with HagenePoiseuille flow The values for Re < 200 are lower than those predicted from 64/Re; however, the deviation is in the range of experimental uncertainty For this tube no distinguished transition form laminar to turbulent flow was observed at the Reynolds numbers in the range of 100e2300 In the case of the other tubes, namely, BeE, the Reynolds numbers are in the range of 500e10000, as shown from Fig (b)e(e) At the Reynolds number greater than about 2000, the deviation from the laminar flow was observed, which means the transition from laminar to turbulent flow started To determine the critical Reynolds number at which S Barlak et al / International Journal of Thermal Sciences 50 (2011) 361e368 1400 1200 Experimental fappRe 1000 Blasius (L/d=80) 800 600 400 200 0 0.01 0.02 0.03 0.04 0.05 (L/d)/Re Fig fappRe as function (L/d)/Re the transition flow starts, fRe product was plotted as function of the Reynolds number for all the tested tubes in Fig For the comparison purpose, the values of fRe predicted from 64/Re for fully developed laminar flow and from Blasius equation for turbulent flow are also given in this figure Fig 5(a) shows the results of the tube-A As seen from this figure, fRe products agree with the theoretical value within the range of the experimental uncertainty for the investigated Reynolds number in the range of 75e2390 It is also shown that even at the maximum Reynolds number of 2390 for this tube, the flow maintained its laminar flow character; no transition was observed The experimental results of the tube-B are shown in Fig 5(b) For the Reynolds numbers in the range of 2000e2500, the fRe value deviated from the behaviour of the laminar flow, and a transition from laminar to turbulent flow was observed for this tube Fig (c)e(e) shows the fRe relation versus Re for the other test tubes used in this study, namely C, D and E From these figure, at a Reynolds number around 2000, the occurrence of the transition can be clearly seen An imported result pointed out from Figs and 5, the transition from laminar to turbulent flow occurs with two different mechanisms as abrupt transition for the tube-B and smooth transition for the tubes-CeE Similar results have been observed by Lorenzi et al [12] for flow through circular microtubes The fact that for the tube-B the critical Reynolds number is higher than that for the tubes of C, D and E can be attributed to the geometry and condition Ghajar and Madon [13] investigated the effect of the channel inlet geometry on the transition Reynolds number for three different inlet geometries, namely re-entrant, square-edged and bell-mouth It was reported that the critical Reynolds number for bell-mouth was higher than the other inlet geometries in the range of 2125 < Re < 3200 The inlet geometry of the tubes A and B is closer to the bell-mouth geometry than that for other tubes This can be the reason that no transition occurs at Re ¼ 2390 for the tube-A Although, for the circular macro channels, the upper limit of the critical Reynolds number is undefined; however, for practical applications, the flow in range of 2300 Re 104 is accepted as transition flow [23] In general, in the studies of the pressure drop and friction factor in microchannels, higher L/d ratio was selected as emphasized before The L/d ratio used in this study changes in range of 16e265 To see the entrance length effect on the friction factor, the apparent friction factor for all tested tubes were plotted as function of the Reynolds number in Fig 6, which reflects both the surface friction and the developing flow effects Fig (a) shows the results of the tube-A having the L/d ratio in the range 105e265 Although the apparent friction factor values for L/d ¼ 105 are slightly higher, no 367 important effect of the L/d ratio was observed in the investigated range For hydrodynamically developing laminar flow in circular duct, the relation for the hydrodynamic entrance length, Lhy, was given by Bhatti and Shah [23] as Lhy/d ¼ 0.056 Re When this equation is used for the tube-A of the present work, the Lhy/d ratio was found to be in the range of 4e133 depending upon Re, which constitutes as much as % 4e127 of the minimum L/d ratio (¼105) used for the tube-A It is claimed that the effect of the entrance length can be ignored for the L/d value above 300 for laminar flow [25] The results of this study show that the L/d has no important affect on the friction factor fort the L/d ratios in range of 105e265 However, for the other test tubes of BeE, the L/d ratio affects seriously the values of the friction factor, as seen from Fig 6(b)e(e) Decreasing L/d increases the friction factor For the flow through macro circular pipes, the fully developed length for turbulent flow was given by the equation of Lhy/d¼1.3590Re1/4 [23] For the Reynolds number range of 2000e10000, Lhy/d values lay in the range of 8.4e12 fappRe products were plotted versus (L/d)/Re values for Re > 2000 in Fig Since the Reynolds number for the flow in the tube-A remains below this value, this figure does not include the results for the tube-A The results calculated from the Blasius equation were also included in this figure for L/d ¼ 80, for comparison Conclusion An experimental investigation of the water flow through the microtubes made of stainless steel with the diameters ranging from 0.200 to 0.589 mm and the values of the length-to-diameter ratio from 16 to 265 was performed The major findings obtained from the experimental results can be summarized as follows: It was observed that two different mechanisms of transition from laminar to turbulent flow occurred; smooth and abrupt The pressure drop and friction factor values agreed with the values of classical channel flow theory within the experimental uncertainty The L/d ratio had an important effect on the apparent friction factor in the case of L/ d < 100 It was found that the critical Reynolds number for the transition was between 2000 and 2500 Acknowledgements _ This study was funded by (TÜBITAK-MAG) under the grant number of 106M304, and their support is gratefully acknowledged References [1] C.B Sobhan, S.V Garimella, A comparative analysis of studies on heat transfer and fluid flow in 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Fully developed friction factor as function of Reynolds number The measured pressure drop, DPt, includes minor loss contributions, DPm, and the net pressure drop in the test tube can be calculated... Tam and Ghajar [14] for non-isothermal flow conditions They used 316 stainless steel tubes with an inside diameter of 1.58 cm and lengthto-diameter ratio (L /d) of 386 to provide fully developed flow... isothermal conditions, and it changed depending on heat flux in the case of non-isothermal flow On the other hand, several investigators remarked the dependence of critical Reynolds number on the