VOL. 16, NO. 14, JULY 2021 ISSN 1819-6608 ARPN Journal of Engineering and Applied Sciences ©2006-2021 Asian Research Publishing Network (ARPN). All rights reserved. www.arpnjournals.com EFFECTS OF ENTRY CONDITIONS ON CHANNEL FLOW CHARACTERICSTICS Oyewola O. M.1, Singh P.M.1, Odele R. P.2 and Petinrin M. O.2 1School of Mechanical Engineering, Fiji National University, Suva, Fiji 2Department of Mechanical Engineering, University of Ibadan, Ibadan, Nigeria E-Mail: oooyewola001@gmail.com ABSTRACT Y There have been various studies on channel flow due to its relevance in engineering applications, but Rthe effects of the entry conditions on its flow characteristics have not been given much attention. This 2-D numerical simulation studied how the initial velocity and tripping devices at the entrance of a channel affect the mean flow structure. TAhe CFD analysis is based on the use of COMSOL Multiphysics. The turbulent stresses in the RANS equation are closed using the k-ɛ turbulence model. Input parameters for the simulation are taken from experimental conditions Rin the literature, with Reynolds number ranging from 18,700 to 600, 000. The CFD strategy flow without tripping is validated against experimental results and a good agreement is achieved. The results show that the skin fLrictioIn B factor for the flow without tripping for Reynolds number 18,700 is 3.59x10-3. However, for the same Re, with tripping devices covering 15%, 30%, 45%, and 60% of the channel height, the skin friction factors are 3.68x10-3, 3.78x10-3, 3.82x10-3, and 3.98x10-3 respectively. Hence it has been shown the tripping devices placed at the entry of a channel increase the skin friction coefficient by values between 2% to 11% for the various conditions considered in Nthis work. Keywords: entry conditions, channel flow, skin friction, Reynolds number, tripping dAevices. 1. INTRODUCTION effects Dof secondary currents aren’t felt. Thus for channels Channel flow can be described as a three- with a smaller aspect ratio (B/H<5), the effects of free dimensional flow which is widely affected by the effects suArface currents and the side walls are predominant on the of free surface currents and the side walls. The velocity IBflow, and the maximum velocity on the channel centerline profiles of open channel flow are of great interest t o is observed to be below the surface - dip phenomenom engineers as it has practical consequences in the (Yang et al., 2004, Yan et al., 2011, Al Faruque et al., estimation of erosion effects and transportatioFn of 2014, Bonakdari et al., 2014). Hence, studies in open sediments in alluvial channels. Over the years mOuch work channel flow have also revealed that the classical log law has been done on studying channel flow. Tominaga et al. gives a good description of the velocity distribution in the (1989) noted, from their experimental stuYdies on the three- inner region (Yan et al., 2004, Nezu, 2005, Alfaz et al., dimensional turbulent structure of channel flow, that the 2009, Al Faruque et al., 2014) and the extent of collapse secondary currents observed in oIpeTn channel flows are of the mean velocity profile - in inner scaling - with the quite different from those in closed channel flows. log region is dependent on the Reynolds number (Alfaz et Cardoso et al. (1989) in their eSxperiments on uniform flow al., 2009, Al Faruque et al., 2004). in smooth open channel noted that a wide two-dimensional In the entrance and very close to the channel bed region existed in the cenRter, which was free of effects of in open channel flows, the velocity gradients are always secondary currents. This observation is in agreement with high as the boundary layer grows, laminar flow is hardly the results of KirkgEoz (1989), Tominaga et al. (1992), encountered in practice and so much more attention is Kirkgoz and AVrdichoglu (1997), and Nezu (2005). All being paid to turbulent flow (Bonakdari et al., 2014). these authorsI thus corroborate that for an aspect ratio However, there is a transition from laminar to turbulent (width to depth ratio of the flow, B/H) B/H≥5, there exists boundary layer near the leading edge (Figure-1). a predominant two-dimensional region for which the UN 1507 VOL. 16, NO. 14, JULY 2021 ISSN 1819-6608 ARPN Journal of Engineering and Applied Sciences ©2006-2021 Asian Research Publishing Network (ARPN). All rights reserved. www.arpnjournals.com RY Figure-1. Velocity profiles in developing and fully developed open channel A flow (Bonakdari et al., 2014; Kirkgoz and Ardichoglu, 1997). R Tripping devices are known to cause immediate 2. METHODOLOGY B transition from a laminar to a turbulent boundary layer, The present numeIrical study makes use of and cause a more fully developed flow sooner. A tripping COMSOL Multiphysics commercial CFD package. The device could be a ring, a cylinder, sandpaper, or some software is a finite-ele mLent method solver, and solves for rough element. Most channel flow experiments make use the velocity field across all sections. of tripping devices to cause immediate transition, however N much attention has not been paid to how tripping affects 2.1 Governing Fluid Flow Equations the characteristics of a flow. Al-Salaymeh and Bayoumi TheA two governing equations adopted for (2009) did an experimental investigation of tripping effect modeling the steady and incompressible flow in open on the friction factor in turbulent pipe flows by installing channelD are: tripping devices for different blocking areas: 10%, 20%, A 30% and 40%, at the pipe entrance. Their results suggested a) The law of conservation of mass that there is an insignificant effect on the friction factor as B the blocking area (dimension of trip device) increased, bu t I U j the centerline velocity decreased with an increase in the = 0 blocking area. F x j (1) In this present work, the effects of initOial velocity and tripping devices with blocking areas: 15%, 30%, 45%, b) The Reynolds time averaged Navier-Stokes (RANS) and 60%, of flow parameters in an open Ychan nel flow will equation. be solved numerically. T Ui Ui 1 SP I    U U  j+U j = − + ' ' i +  −u  iu j t x j R xi x j   x j x i   (2) where xi represents Ethe coordinate axis, Ui‘s represent the tensor in equation (2) is given as (Ferziger and Peric, stream velocitIieVs in the streamwise and vertical direction, z 2002; Wilcox, 2006) is the vertical elevation and ρ represents the density, P ' ' represenNts the pressure, and uiu j is the specific Reynolds  U U j 2−u 'u ' ii j =T  +  − k ijstreUss tensor.  x j xi  3 2.2 Turbulence Closure Applying the Boussinesq approximation to obtain Thus, the k-ε turbulence equations are employed the eddy viscosity model, the specific Reynolds stress to obtain the closed form solution of the eddy viscosity model and the equations are as given 1508 VOL. 16, NO. 14, JULY 2021 ISSN 1819-6608 ARPN Journal of Engineering and Applied Sciences ©2006-2021 Asian Research Publishing Network (ARPN). All rights reserved. www.arpnjournals.com k     k    U U   U =  + T +  i j 2 U + − k i     j T ij  − x x  j j   k  x j   x x 3 x  j i   j     T      U U  2 i j U  2 U ij =  +   +C1 T  +  − kij  −C 2 x j x j       x j  k   x j xi  3  x j k  k 2 d) The slip boundary condition is set at the free Ysurface where T = C of the domain  R The constants in the two-equation eddy-viscosity 2.4 Computational Grid model have values given below The computational domain isA made up of a Cε1 = 1.44, Cɛ2 = 1.92, Cφ = 0.09, σk = 1.0, σɛ = 1.3 rectangular channel of length 9.5m, and height 0.1m (Figure-2). The computational domRain is made up of a 2.3 Boundary Conditions hybrid of structured and unstructured meshes. A structured Boundary conditions are required in order to boundary layer mesh is requIireBd at the base of the domain solve the governing equations around the computational and around the trip c ylLinder. The domain contains very domain. large cell densities around the entry and at the free surface of the flow, and higher cell density around the bottom wall a) The velocity inlet condition is set at the inlet of the and the trip cyNlinder. Relatively fine triangular and domain quadrilateral elements are used in the rest of the flow b) The pressure outlet condition is set at the exit of the domain. FivAe different computational domains are set up domain i.e. gauge pressure = 0 to simulate the different trip conditions of the flow. c) The wall-function method is utilized at the bottom D wall and the walls of the trip devices, which assumes a predictable behavior of the viscous sub-layer IB A O F Y T Figure-2. TSwo-Idimensional computational domain in which the circle (trip cylinder) covers a certain percentage of the channel height. 2.5 Simulation ParametRers u 1 u *Data is taken from test conditions utilized in = ln y + B u *   experiments of VTomEinaga et al. (1989). The experimental study was caIrried out in smooth and rough rectangular open channels. The results were obtained in a channel with Where K = 0.39 (Von Karman constant) and B = 12.5 m lNength, and a square cross section (0.40 m × 0.40 5.5, and u is the velocity along the profile, and a vertical m). The experiments were performed with the Reynolds distance y. numUber equal to 19,000 and Froude number equal to 0.19 The skin-friction coefficient is calculated by for a depth of flow equal to 0.10 m and the mean velocity 2 equal to 0.187 m/s. Velocity measurements were  u *  performed using a hot-film anemometer. C f = 2   U e  2.6 The Friction Velocity and Skin Friction Factor Friction velocities are obtained at various where U* is the friction velocity and Ue is the free stream positions in the streamwise direction of the flow in both velocity. For comparison, the streamwise velocity profiles the trip and the no trip cases. The velocity profiles are are then obtained for the no-trip flow, 15% trip, 30% trip, obtained at the various positions. These profiles are 45% trip, and 60% trip at the fully developed section exported for post-processing. The friction velocity is x=6.5m obtained through the least-squares method, and comparing with prandtl-von-karman law of the wall equation 1509 VOL. 16, NO. 14, JULY 2021 ISSN 1819-6608 ARPN Journal of Engineering and Applied Sciences ©2006-2021 Asian Research Publishing Network (ARPN). All rights reserved. www.arpnjournals.com 3. RESULTS AND DISCUSSIONS experiments under various conditions, of Kirkgoz and Ardichoglu (1997). The simulation results compare well 3.1 Validation of Simulation Results with the experimental data. In Table-1, the simulation results for the flow without tripping are compared with data obtained in the Table-1. Comparison of experimental and simulation data. Test U* experimental U* simulation h Fr Re Number (mm/s) (mm/s) Y 1 0.05 0.3 10500 9.7 8.7 R 2 0.025 0.85 10500 21.2 22.1 3 0.075 0.67 20025 23.5 22 A 4 0.1 0.34 33300 16.5 B15R.3 5 0.08 0.68 48320 30.8 27 6 0.15 0.36 64950 20.8 I 18.9 7 0.12 0.5 65040 25.7 L 23.5 8 0.1 0.66 65000 29.8N 27.5 Hence in order to quantitatively compare the sublayer; in Athe simulation results the friction velocity are numerical model with the experimental results two obtained by estimating the logarithmic region of the wall. indicators, relative error (Rerr) and root-mean-square error D (RMSE) were used: 3.2A Flow Development B The developed section of a flow is very important n U −U I as that is where reasonable measurements of a flow’s 1 mo expR =  properties are taken. The flow is checked for full err n i=1 U exp F development by comparing the velocity profiles at various stream wise positions x = 1.1, 1.7, 2.5, 3.0, 3.5, 4.0, 4.5, 2 n U −U  O 5.0, 5.5, 6.5, 7.0. Full development of the flow was 1 mo expRMSE =   assumed to be achieved when the velocity profiles n  i=1  U exp  Y witnessed no significant changes. From Figure-3, the variation in velocity profiles can be noticed at various IT stream wise positions in the developing region of the flow. where Umo is the estimated friction velocity from the In Figure-4, the absolute collapse in velocity profiles can simulation, and Uexp is the estimated friction velocity from be seen which indicates a fully developed flow. Thus for the experiments. Values of ReSrr = 7.2% and RMSE = 8.6% this flow condition i.e. v = 0.187m/s and h = 0.10m, the show there is reasonRable agreement between the entry length is determined to be 6.5m or 65h. This experimental and the simulation results. Also, it should be E observation is in agreement with literature where it is noted that the friction velocity in the experiments was suggested that the development length is placed around obtained by point-wise measurements in the viscous V 50h-70h. NIU 1510 VOL. 16, NO. 14, JULY 2021 ISSN 1819-6608 ARPN Journal of Engineering and Applied Sciences ©2006-2021 Asian Research Publishing Network (ARPN). All rights reserved. www.arpnjournals.com 0.12 x = 1.1 0.1 x = 1.7 0.08 x = 2.5 x = 3.0 0.06 x RY= 3.5 0.04 Ax = 4.0R x = 4.50.02 IB x = 5.00 L x = 5.50.05 0.07 0.09 0.11 0.13 0.15 0.17 0.19 0.21 0.23 velocity N x = 6.5 Figure-3. Velocity profiles at different streamwDise poAsitions in the channel. 0.12 x = 6.5 Ax= 7.0 IB0.1 0.08 OF 0.06 Y 0.04 IT 0.02 S 0 0 ER 0.05 0.1 0.15 0.2 0.25 IV velocity N Figure-4. Velocity profiles at streamwise positions for x = 6.5m, and x=7.0m. 3.3 UVariation of Friction Velocity Along Channel gradually in the developing region, becoming constant in Length towards the end of the developing region and further The results of the simulation reveal that the downstream (Table-2, Figure-5). This is in agreement with friction velocity (and thus the bed shear stress) is the work of Ranga Raju et al. (2000) who made similar maximum near the entrance (i.e. at x=0), and it decreases observations in their experiments. 1511 channel height channel height VOL. 16, NO. 14, JULY 2021 ISSN 1819-6608 ARPN Journal of Engineering and Applied Sciences ©2006-2021 Asian Research Publishing Network (ARPN). All rights reserved. www.arpnjournals.com Table-2. Calculated shear velocities for flow without tripping. Re x = 1.1 x = 1.7 x = 2.5 x = 3.0 x = 4.0 x = 5.5 x = 6.5 18700 10 9.3 9.1 9 8.9 8.9 8.9 60000 28.5 26.9 26.2 26 25.9 25.5 25.5 131000 55.7 54.9 54 53.7 53.3 52.9 52.7 240000 96.3 94.9 93.9 93.7 93 92.2 91.9 330000 129 127 126 125 125 123 123 Y 420000 163 160 158 158 155 154 153 R 600000 225 224 219 218 216 214 RA 213 250 B 200 L I N Re = 18700150 A Re = 60000D Re = 131000100 A Re = 240000 50 IB Re = 330000 Re = 420000 0 Re = 600000 1.1 1.7 2.5 F3 4 5.5 6.5 strOeamwise distance Figure-5. TPlotY of variation of shear velocity with streamwise location. 3.4 Reynolds Number and SkSin FIriction Relationship there is an increase in the value of the skin friction The relationship mentioned in section 2.6 coefficient as the degree of tripping is increased. However, between skin friction coefficient and friction velocity, is this increase is negligible. The observed trend is in used to obtain the relaRtionship between the Reynolds agreement with observations made by Al-Salaymeh and number and skin frEiction coefficient for the various test Bayoumi (2009) in their experiments on the effects of conditions. entry conditions on friction factor in pipe flow. This is FiguIreV-6 shows the relationship between friction agreeable as pipe and channel flow have similar structures. factor and Reynolds number. The trend observed and It should as well thus be noted that the increase in skin results oNbtained are in good agreement with previous friction factor for the flow conditions in this numerical research works. From Figure-7, the effect of tripping on experiment range between 2 and 11%. skinU friction factor can be deduced. It can be seen that 1512 U* VOL. 16, NO. 14, JULY 2021 ISSN 1819-6608 ARPN Journal of Engineering and Applied Sciences ©2006-2021 Asian Research Publishing Network (ARPN). All rights reserved. www.arpnjournals.com 0.004 0.0035 0.003 0.0025 0.002 0.0015 AR Y 0.001 0.0005 R 0 B 0 100000 200000 300000 400000 50000L0 I 600000 700000Re Figure-6. Friction factor vs Reynolds AnumbNer. 0.0045 D 0.004 A 0.0035 0.003 IB 0.0025 OF 0.002 0.0015 TY 0.001 I 0.0005 S 0 0VE R 100000 200000 300000 400000 500000 600000 700000 I No trip 15% trip 30% trip 45% trip 60% trip UN Figure-7. Friction factor and Reynolds number for various degrees of tripping. 3.5 Mean Velocity Profile: Inner Scaling in Figure-8 and Figure-9, all data obtained in both the non- The distributions of the streamwise component of trip flow and the tripped flow show good agreement with the mean velocity in inner scaling for various flow the log law of the wall. It should be noted however that the conditions are shown below. Friction velocity was standard k-𝜖turbulence model with wall-functions which is calculated using least-squares method by fitting the utilized does not resolve the viscous sub-layer and is thus logarithmic law of the wall expression with a best fit line not represented in the chart. drawn in the inner region of the velocity profile. As shown 1513 Cf VOL. 16, NO. 14, JULY 2021 ISSN 1819-6608 ARPN Journal of Engineering and Applied Sciences ©2006-2021 Asian Research Publishing Network (ARPN). All rights reserved. www.arpnjournals.com 35 30 25 20 RY 15 A 10 R Re = 18700 Re= 600000 Re = 131000 ReB = 240000 5 Re = 330000 Re = 420000 Re = 600000 LI 0 1 10 100 1000 y+ AN 10000 100000 Figure-8. Normalized velocity distribution fDor flow without tripping. A 35 30 IB 25 O F Re = 18700 trip 15% Y Re = 18700 trip 30%20 T Re = 18700 trip 45%I Re = 18700 trip 60%S Re = 131000 trip 15%15 Re = 131000 trip 30% Re = 131000 trip 45% 10 ER Re = 131000 trip 60% IV Re = 420000 trip 15%5 Re = 420000 trip 30%N Re = 420000 trip 45%U Re = 420000 trip 60%0 1 10 100 1000 10000 100000 y+ . Figure-9. Normalized velocity distribution for flow with tripping. 4. CONCLUSIONS existing literature. It was discovered that tripping devices Numerical analysis has been performed using the placed at the entry of an open channel to cause immediate standard k-𝜖 turbulence model to study the effects of entry transition from laminar to turbulent boundary layer, cause conditions on the characteristics of channel flow. The flow an increase in the value of the skin friction coefficient by a is simulated for various degrees of tripping under the same factor between 2 and 11%. Thus the tripping devices could conditions. The trends observed are in agreement with be likened to roughness elements placed in the bed of a 1514 U+ U+ VOL. 16, NO. 14, JULY 2021 ISSN 1819-6608 ARPN Journal of Engineering and Applied Sciences ©2006-2021 Asian Research Publishing Network (ARPN). All rights reserved. www.arpnjournals.com channel which experimental works have reported to Channel Flows. Journal of Hydraulic Research. 27(1): increase the value of the skin friction coefficient. 149-173. Wilcox D. C. 2006. Turbulence modeling for CFD (3rd Declaration of Conflict of Interest ed.). California: DCW. The authors declare that there is no conflict of interest regarding the publication of this article. All Yan J., Tang H., Xiao Y., Li K. and Tian Z. 2011. authors read and contributes to this article. Experimental Study on Influence of Boundary on Location of Maximum Velocity in Open Channel Flows. Water REFERENCES Science and Engineering. 4(2): 185-191. Y Afzal B., Al Faruque M. and Balachandar R. 2009. Effects Yang S., Tan S. and Lim S. 2004. VelocityR Distribution of Reynolds Number, Near-Wall Perturbation and and Dip-Phenomenon in Smooth Uniform Open Channel Turbulence on Smooth Open-Channel Flows. Journal of Flows. Journal of Hydraulic EngineeringA. 130(12): 1179- Hydraulic Research. 47(1): 66-81. 1186. R Al Faruque M.D., Wolcott S., Goldowitz J. and Wolcott T. NOMENCLATURE 2014. Open Channel Flow Velocity Profiles for Different B Reynolds Numbers and Roughness Conditions. h channel height I International Journal of Research in Engineering and F Froude number L Technology. 3(1): 400-405. Re ReynoldNs num ber U* Friction velocity Al-Salaymeh A. and Bayoumi O.A. 2009. Investigations U mean flow velocity of Tripping Effect on the Friction Factor in Turbulent Pipe Ue freeA-stream velocity Flows. Journal of Fluids Engineering. 131, 3-10. Le DLength of flow developing zone ν kinematic viscosity Bonakdari, H., Lipeme-Kouyi, G. and Asawa, L.G. 2014. νT turbulent kinematic viscosity Developing Turbulent Flows in Rectangular Channels: A g A acceleration due to gravity parametric study. Journal of Applied Research in Water and Wastewater. 1(2): 53-58. IBρ density Cf skin friction coefficient K von-karman constant Cardoso A.H., Graf W.H. and Gust G. 1989. UniformF flow B width of channel in a Smooth Open Channel. Journal of Hydraulic U+ normalized velocity Research. 27(5): 603-616. O y+ normalized vertical height k turbulent kinetic energy Ferziger J. H. and Peric M. 2002. Computational methods ϵ rate of dissipation for fluids dynamics. (3rd ed.). BerliIn:T Spri Ynger. Kirkgoz S.M. 1989. TurbuSlent Velocity Profiles For Smooth and Rough Open Channel Flow. Journal of Hydraulic Engineering. 1R15(11): 1543-1561. Kirkoz S.M. and ArEdichoglu M. 1997.Velocity Profiles of Developing and Developed Open Channel Flow. Journal of Hydraulic EInVgineering. 123(12): 1099-1105. Nezu I. N2005. Open-Channel Flow Turbulence and Its ResUearch Prospect in the 21 st Century. Journal of Hydraulics Engineering. 131(4): 229-246. Ranga Raju K.G., Asawa G.L. and Mishra H.K. 2000. Flow-Establishment Length in Rectangular Channels and Ducts. Journal of Hydraulic Engineering. 126(7): 533-539. Tominaga A. and Nezu I. 1992. Velocity Profiles in Steep Open-Channel Flows. Journal of Hydraulic Engineering. 118(1): 73-90. Tominaga A., Nezu I., Ezaki K. and Nakagawa H. 1989. Three-dimensional Turbulent Structure in Straight Open 1515