Effect of flow field on open channel flow properties using numerical investigation and experimental comparison

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1 INTERNATIONAL JOURNAL OF ENERGY AND ENVIRONMENT Volme 3, Isse 4, 2012 pp Jornal homepage: Effect of flow field on open channel flow properties sing nmerical investigation and eperimental comparison I. Khazaee 1, M. Mohammadin 2 1 Department of Mechanical Engineering, Torbat-e- am branch, Islamic Azad University, Torbat-e- am, Iran. 2 Department of Mechanical Engineering, Shahrood branch, Islamic Azad University, Shahrood, Iran. Abstract In this paper a complete three-dimensional and two phase CFD model for flow distribtion in an open channel investigated. The finite volme method (FVM) with a dynamic Sb grid-scale was carried ot for seven cases of different aspect ratios, different inclination angles or slopes and convergencedivergence condition. The volme of flid (VOF) method was sed to allow the free-srface to deform freely with the nderlying trblence. The discharge throgh open channel flow is often evalated by velocity-area integration method from the measrement of velocity at discrete locations in the measring section. The variation of velocity along horizontal and vertical directions is ths very important to decide the location of the sensors. The aspect ratio of the channel, slope of the channel and divergenceconvergence of the channel have investigated and the reslts show that the depth of water at the end of the channel is higher at AR=0.8 against the AR=0.4 and AR=1.2. Also it is clear that by increasing the inclination angle or slope of the channel in case1, case4 and case5 the depth of the water increases. Also it is clear that the otlet mass flow rate is at a minimm vale at a range of inclination angle of the channel. Copyright 2012 International Energy and Environment Fondation - All rights reserved. Keywords: VOF model; Channel aspect ratio; Open channel; Velocity distribtion. 1. Introdction Open channel flows are fond in Natre as well as in man-made strctres. In Natre, tranqil flows are observed in large rivers near their estaries: e.g. the Nile River between Aleandria and Cairo, the Brisbane River in Brisbane. Rshing waters are encontered in montain rivers, river rapids and torrents. Classical eamples inclde the cataracts of the Nile River, the Zambesi rapids in Africa and the Rhine waterfalls[1]. In contrast to empirical stdies, nmerical investigations of open channels are limited becase it is mch more difficlt to model flow in open channels than in closed condits. This is becase flow conditions in open channels are complicated by the fact that the position of the free srface is liely to change with respect to time and space. Recently Direct Nmerical Simlation (DNS) for open channel flows have been reported, bt most of these simlations assme (1) that the free srface is a rigid slip srface and its vertical movement is neglected, as was the case in Nagaosa [2], or (2) simply apply the linearized freesrface bondary conditions, as in the case of Bore et al. [3].

2 618 International Jornal of Energy and Environment (IJEE), Volme 3, Isse 4, 2012, pp Mathematical models of the velocity profile in circlar pipes are available [4] and have been sed for determining the most appropriate locations of crrent meters/acostic transdcers for minimizing the systematic error in discharge measrement in circlar penstocs. However, to the best of athors nowledge, sch mathematical models are not available for open channels. In the open channel flow, the velocity distribtion along the vertical direction (depth) is theoretically represented by a logarithmic fnction of the depth of flow [5]. It is very difficlt to describe the velocity distribtion along the width theoretically. However, some of the investigators have proposed empirical eqations for the velocity distribtion based on eperimental and field data [6-9]. In this wor a three-dimensional and two phase CFD model for an open channel flow has investigated to stdy the flow distribtion for different open channels with different aspect ratios and convergencedivergence geometries. This CFD model developed for a real open-channel was first validated by comparing the velocity profile obtained from it with that obtained by actal measrement in the same channel. All the geometries are modeled with similar operating and bondary conditions. Flent , a finite volme comptational flid dynamics pacage, was sed to solve the non-linear system of eqations. 2. Nmerical model The three dimensional eqations together with the continity are solved sing the finite volme method with implicit formlation and first order discrete method that the relation of the pressre and velocity is with the simple algorithm. Transport eqations for trblence inetic energy and its dissipation are solved for closing the system of eqations. In addition a modified volme of Flid (VOF) method was employed for compting the free srface. The model was implemented into the commercial CFD code FLUENT with cstom developed ser-define fnctions (UDF) The VOF formlation relies on the fact that two or more flids are not interpenetrating. For each additional phase a variable is introdced, the volme fraction of the phase in the comptational cell. In each control volme, the volme fractions of all phases sm to nity. The fields for all variables and properties are shared by the faces and represent volme averaged vales. Ths the variables and properties in any given cell are either representative of one of the faces, or representative of a mitre of the faces, depending pon the volme fraction vales. The flow involves eistence of a free srface between the flowing flid and the atmospheric air above it. The flow is generally governed by the forces of gravity and inertia. In VOF model, a single set of momentm eqations is solved for two or more immiscible flids by tracing the volme fraction of each of the flids throghot the domain. The mathematical formlation adopted is described briefly below. In the crrent stdy, it is assmed that the density of water is constant throgh the comptational domain. The governing differential eqations of mass and momentm balance for nsteady free srface flow can be epressed as: ρ.( ρ) = 0 t 1.( ) = p.( ν ) g t ρ (1) (2) where is the velocity vector in the three directions; P is the pressre; ν is the moleclar viscosity; g is the gravitational acceleration in the three directions, and ρ is the density of flow. Small high-freqency flctations are present even in steady flow and, to accont for these, time averaging procedre is employed, which reslts in additional terms. These additional terms need to be epressed as calclable qantities for closre soltions. The standard κ- model has been sed in the present case. It is a semi-empirical model based on model transport eqations for the trblent-inetic energy κ and its dissipation rate, and is epressed by the following eqations:

3 International Jornal of Energy and Environment (IJEE), Volme 3, Isse 4, 2012, pp ν σ ν = i i T T t (3) 2 ν µ c T = (4) The dissipation of is denoted, and modeled as: C C t i i T T ν σ ν = (5) The constants in the - model have the following vales: µ c =0.09, 1 C =1.44, 2 C =1.92, σ =1.0 and σ =1.30. The properties appearing in the transport eqations are determined by the presence of the component phases in each control volme. For a N-phase system, the volme fraction-averaged density taes the following form: = q α q ρ ρ (6) For tracing the free srface the continity eqation for the volme fraction is sed. For the qth phase, this eqation has the following form: = 0 i q i q t α α (7) The volme fraction eqation is solved for each phase ecept the one that is defined as primary. For the primary phase the volme fraction is compted based on the following constraint: = = n q q 1 1 α (8) The physical problem considered in this paper is the three dimensional model of the open channel as shown in Figre 1 that the dimensionless parameter in this paper named aspect ratio, H W AR =,is defined to characterize the geometric effect of the channels. In Table 1 the characteristics of the channels sch as depth, width, length and slope are shown.

4 620 International Jornal of Energy and Environment (IJEE), Volme 3, Isse 4, 2012, pp Figre 1. The simlation domain Table 1. Detail of the different cases Case H(cm) W(cm) L(cm) Slope(deg) (convergence) (divergence) Bondary condition Appropriate condition mst be specified at domain bondaries depending on the natre of the flow. In the present stdy, pressre inlet bondary condition for the inlet of the channel and pressre otlet bondary condition for the otlet of the channel is specified, and the reslts of wall shear stress across the main channel and branch compared corresponding to the Knight et al. Eperiments in case1 at Table 1 [10]. The no-slip bondary condition is specified to set the velocity to be zero at the solid bondaries and walls and bed assmed to be rogh. At the top srface above the air, the pressre otlet bondary condition is specified. A mesh with nodes was fond to provide reqired spatial resoltion for different channel geometry. The soltion is considered to be converged when the difference between 7 sccessive iterations is less than 10 for all variables. 3. Reslts and discssion In order to show that the program in this stdy can handle the revene of the channel, we apply the present method to solve the whole domain of an open channel as described in the Knight et al. Eperiments [10]. The mesh employed for the comparison with the reference was The steadystate soltion is obtained by the nmerical procedre as mentioned in the previos section. As shown in Table 2, the reslt of the present predictions of the wall shear stress agreeing fairly closely with Knight et al. [10] gives one confidence in the se of the present program. Table 2. Comparison between eperimental reslts [10] and present stdy Inlet Velocity (m/s) 2 Shear Stress( N / m ) Knight et al Case 1 Present stdy Knight et al Case 2 Present stdy

5 International Jornal of Energy and Environment (IJEE), Volme 3, Isse 4, 2012, pp Figre 2 shows the effect of aspect ratio of the channel on the otlet mass flow rate for case1 (AR=1.2), case2 (AR=0.8) and case3 (AR=0.4). It is clear that by increasing the aspect ratio of the channel the mass flow rate increases that this is de to the velocity of the water at the otlet of the channel that this is becase of the low depth of water against the width of it Mass flow rate (g/s) Aspect Ratio Figre 2. Effect of aspect ratio of channel on otlet mass flow rate Figre 3 shows the effect of inclination angle (slope) of the channel on the otlet mass flow rate for case1 (θ=0.057 ), case4 (θ= ) and case5 (θ=0.573 ). It is clear that by increasing the inclination angle from θ=0.057 to θ= the otlet mass flow rate decreases bt when it increases to θ=0.573 the mass flow rate increases. Therefore it is clear that the otlet mass flow rate is at a minimm vale at a range of inclination angle of the channel. Velocity profile is considerably affected by a change in the width and slope of the channel. The effect of slope, aspect ratio of the channel and divergence and convergence of it de to change in channel width is investigated in Figre 4 at Z=0.55m and at the middle of the channel. It is seen that by increasing the aspect ratio from 0.4 to 1.2 for case1, case2 and case3 the maimm of velocity in the channel increases and is near the bed of the channel. Also it is clear that by increasing the slope of the channel from θ=0.057 to θ= for case1 and case4 the maimm velocity of the flow decreases bt when the slope increases from θ= to θ=0.573 the maimm velocity increases and the location of the maimm velocity moves to near the free srface of the flow that it is de to this may be attribted to accelerating flow in the channel. Also it is clear that the velocity profile is flat when the slope of the channel decreases. A very interesting reslt of this section is the effect of convergence and divergence channel on the velocity profile in case6 and case7. It is clear that the difference between maimm velocity at the convergence and divergence channel is very high and the velocity is at higher vale for divergence channel against the convergence channel. Also it is clear that the location of maimm velocity is nearer the bed for the convergence channel Mass flow rate (g/s) inclination angle (degree) Figre 3. Effect of inclination angle of channel on otlet mass flow rate

6 622 International Jornal of Energy and Environment (IJEE), Volme 3, Isse 4, 2012, pp Depth (m) Case 1 Case 2 Case 3 Case 4 Case 5 Case 6 Case velocity (m/s) Figre 4. Velocity profiles along vertical direction Figre 5 shows the volme fraction of the air at the otlet of the channel (Z=0.6m) for case1 to case7. It is clear that the depth of water at the end of the channel is higher at AR=0.8 against the AR=0.4 and AR=1.2 for case1, case2 and case3. Also it is clear that by increasing the inclination angle or slope of the channel in case1, case4 and case5 the depth of the water increases. Also a very interesting reslt of this section is the effect of convergence and divergence channel on the depth of water at the end of channel. It is clear that the depth of water is at lower vale when the channel is divergence and it is at higher vale when the channel is convergence that it is de to volme of the water at the end of channel. 1 Volme fraction of air case 1 case 2 case 3 case 4 case 5 case 6 case Depth (m) Figre 5. Volme fraction of air along vertical direction at otlet of channel Figre 6 shows the contors of volme fraction of air for case1 to case7. It is evident that the water srface is different for different aspect ratios, different inclination angles and convergence-divergence state even in a channel with the same water depth (h =0.11 m) in the inlet. It is clear that the srface tension is moderate and allows the water srface to deform freely in space for AR=1.2 and AR=0.8. The water srface has limited freedom to deform in space when the AR=0.4, becase of the strength of the inertia force. This condition is also confirmed for slope of the channel becase with increasing the slope in case5 the water srface has limited freedom to deform in space. In case6 and case7 for convergence and divergence channel it is clear that the water srface has the higher vale for convergence and lower vale for divergence condition.

7 International Jornal of Energy and Environment (IJEE), Volme 3, Isse 4, 2012, pp Figre 6. (Contined)

8 624 International Jornal of Energy and Environment (IJEE), Volme 3, Isse 4, 2012, pp Figre 6. (Contined)

9 International Jornal of Energy and Environment (IJEE), Volme 3, Isse 4, 2012, pp Figre 6. (Contined)

10 626 International Jornal of Energy and Environment (IJEE), Volme 3, Isse 4, 2012, pp Figre 6. Contor of volme fraction of air at middle of the channel for (a) case 1, (b) case 2, (c) case 3, (d) case 4, (e) case 5, (f) case 6 and (g) case 7 4. Conclsion A complete three-dimensional and two phase CFD model with finite volme method (FVM) and a dynamic Sb grid-scale for prediction of flow distribtion in an open channel investigated. The reslts of this paper are in good agreement with eperimental reslts of Knight et al.[10]. The reslts show that by increasing the aspect ratio of the channel the mass flow rate increases bt by increasing the inclination angle from θ=0.057 to θ= the otlet mass flow rate decreases and when it increases to θ=0.573 the mass flow rate increases. Also it is clear that the difference between maimm velocity at the convergence and divergence channel is very high and the velocity is at higher vale for divergence channel against the convergence channel. References [1] Hbert, C., The Hydralics of Open Channel Flow: An Introdction, Elsevier Btterworth- Heinemann, 2nd ed., [2] R. Nagaosa. Direct nmerical simlation of vorte strctres and trblent scalar transfer across a free srface in a flly developed trblence. Physics of Flids, 11(6): , 1999 [3] V. Bore, S.A. Orszag and I. Staroselsy. Interaction of srface waves with trblence: direct nmerical simlations of trblent open channel flow. Jornal of Flid Mechanics, 286(1): 1-23, 1995 [4] Salami L.A., On velocity-area methods for asymmetric profiles, University of Sothampton Interim Report V, [5] Schlichting, H., Bondary Layer Theory, McGraw Hill, [6] Sooy, A. A., Longitdinal dispersion in Open Channels, Jornal of Hydralic Division of American Society of Civil Engineering, Engineering Vol. 95, No. 4, 1969, pp [7] Bogle, G. V., Stream Velocity Profiles and Longitdinal Dispersion, Jornal of Hydralic Engineering-Trans ASCE, Vol. 123, No. 9, 1997, pp

11 International Jornal of Energy and Environment (IJEE), Volme 3, Isse 4, 2012, pp [8] Deng, Z., Singh, V. P. and Bengtsson, L., Longitdinal Dispersion Coefficient in Straight Rivers, Jornal of Hydralic Engineering-Trans ASCE, Vol. 127, No. 1, 2004 pp [9] Seo, Won II and Bae, K.O., Estimation of the longitdinal dispersion coefficient sing the velocity profiles in natral streams, Jornal of Hydralic Engineering-Trans ASCE, Vol. 130, No. 3, 2004, pp [10] D. W. Knight. Bondary shear in smooth and rogh channels. ASCE, Jornal of Hydralic Engineering, Hydrologic Science Division, 107(7): , 1981 Iman Khazaee was born in mashhad, iran, in He received his B.S. degree in mechanical engineering from Ferdowsi niversity of mashhad in 2006 and his master s degree at mechanical engineering department, Amirabir University of Technology in 2008 and a PhD degree from Ferdowsi University of Mashhad in Crrently, he is woring on PEM fel cells and their optimization. address: [email protected] Mohammad Mohammadin was born in Shahrood, Iran, in He received his B.S. degree in Mechanical Engineering from Khaeh Nasir Toosi University, Tehran, in 2001 and his M.S. degree in Bio-mechanics from Amir Kabir University in He has been a doctoral stdent in the Department of Mechanical Engineering at Ferdowsi University of Mashhad since address: [email protected]

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