Mean flow characteristics, vertical structures and bed shear stress at open channel bifurcation

Transcription

1 P a g e 99 Journal of Appled Research n Water and Wastewater 7(017) Orgnal paper Mean flow characterstcs, vertcal structures and bed shear stress at open channel bfurcaton Abar Safarzadeh 1,*, Baba Khaatrostam 1 Department of Engneerng, Unversty of Mohaghegh Ardabl, Iran. Research Department, Ardabl Regonal Water Co., Iran. ARTICLE INFO Artcle hstory: Receved 5 February 017 Receved n revsed form 9 March 017 Accepted 14 Aprl 017 Keywords: Dvdng flow CFD Secondary flow Turbulence model Sedment transport ABSTRACT Water supply from rvers s accomplshed wth flow dverson through an ntae structure. A lateral ntae le bfurcaton s the smplest method to wthdraw water. However, flow at a channel bfurcaton s turbulent, hghly three-dmensonal (3D) and so has many complex features. Ths paper reports a 3D numercal nvestgaton of these features n an open channel flow. Smulatons have been done on rectangular channel geometry, wth smooth bed and sdewalls. The standard -ɛ, -ω model of the Wlcox, and RSM turbulence models are compared usng the commercal code FLUENT. The smulaton results have been compared wth avalable expermental data. It was found that all of the turbulence models tested here accurately predcted velocty profles n the man channel but n the branch channel, the RSM model wth the -ω model performng better than the -ɛ model. Predcted flow physcs are n close agreement wth prevously reported expermental results. 017 Raz Unversty-All rghts reserved. 1. Introducton Rvers are a maor source of water for meetng varous demands. Usually, water supply from rvers s accomplshed wth flow dverson through an ntae structure. Rver flow often transports sedment and desgners are faced wth the problem of sedment enterng the canals and water conveyance systems. The art of the desgner s to eep the amount of sedment enterng the dverson system to a mnmum. A lateral ntae s the smplest method of flow wthdrawal. In spte of ts smple layout, usng ths system leads to complex flow patterns and sedmentaton problems at the uncton regon. Flow through lateral ntaes s turbulent and hghly three-dmensonal consstng of secondary vortces and flow separaton (Neary et al. 1996; Neary and Odgaard 1993). The complex flow patterns can lead to sedment deposton n the ntae channel (Bardoll 1997 and Abbas 003). The past numercal studes of dverson flows have been mostly two-dmensonal. Lepsch et al. (198); Hayes et al. (1989); and Lee and Chu (199) have reported lamnar flow calculatons. 3D numercal nvestgatons of lamnar flow through lateral ntaes have been reported by Neary and Sotropoulos (1996). They employed a fnte-volume method and used a non-staggered computatonal grd and demonstrated the relatonshp between sngular ponts n the wall shear stress feld and patterns of bed-load movement observed n the laboratory. Two-dmensonal turbulent flow smulatons have been reported by Shettar and Murthy (1996). They used depth-averaged mean flow equatons closed wth the -ɛ model wth standard wall functons. They are the only researchers that consdered the effect of water surface varatons on the flow characterstcs n the uncton regon. Issa and Olvera (1994) are the frst researchers that have reported a 3D turbulent flow smulaton for T-uncton flow. They employed the Reynolds-averaged Naver-Stoes equatons n conuncton wth the -ɛ turbulence model. Neary et al. (1999) conducted a 3D turbulent flow smulaton for ths problem. They employed 3D Reynolds-averaged equatons closed wth the -ω model. They used the expermental measurements of Bardoll (1997) for valdaton. None of the revewed studes have * Correspondng author E-mal: safarzadeh@uma.ac.r attempted to compare the results of dfferent turbulence models to dentfy the proper model for ths problem. In ths paper FLUENT, a commercally-avalable CFD software, has been used for smulatng the turbulent flow structure through a lateral ntae. The standard -ɛ, -ω model of Wlcox, and the Reynolds stress model (RSM) turbulence closure schemes are used to smulate the turbulent flow through lateral ntaes n open channels and the results are compared to publshed expermental data Obectves In ths study, a 3D numercal nvestgaton s carred out for turbulent ncompressble flows through a 90-degree rectangular dverson. The obectve of ths wor s twofold: () to dentfy the proper turbulence model for ths problem; and () to analyze the numercal soluton n order to now the complex physcs of dverson flows wth emphass on velocty profle varaton along the man channel and branch channel, flow topology patterns, and shear stress varatons on the sold boundares.. Test case As mentoned before, the expermental measurements of Bardoll,1997 are used to valdate the numercal results of the present study. The layout of the expermental flume s shown n Fg. 1. The experments were conducted n an open-channel flume consstng of a T-uncton of two straght rectangular channels wth Ar =. Flow depth was determned by the volume of water n the flume and otherwse not regulated. Dscharge was determned by Ventur meters on flume ppng for both the branch and man channels. The nlet dscharge was m 3 /sec. Velocty measurements were obtaned wth a Sonte Acoustc Doppler Velocmeter (ADV). A dscharge rato of 0.3 was used to comply wth the expermental results. The orgn of the coordnate axs s located at the outer wall of the man channel, n front of the ntae nlet. These axes are normalzed wth respect to the wdth of the channel (X* = X/b). Please cte ths artcle as: A. Safarzadeh, B. Khaatrostam, Mean flow characterstcs, vertcal structures and bed shear stress at open channel bfurcaton, Journal of Appled Research n Water and Wastewater, 4(1), 017,

2 P a g e 300 Safarzadeh and Khaatrostam / J. App. Res. Wat. Wast. 7(017) t c (6) The turbulence quanttes and ε are calculated by the followng transport equatons: v U t U U U vt (7) x x x x x x vt U c 1 P c x x x (8) G s the turbulence producton by mean shear modeled as follows: 3. Governng equatons 3.1. Mean flow equatons Fg. 1. Geometrcal propertes of the test case For an ncompressble flud flow, the equaton of contnuty and balance of momentum for the mean moton, n Cartesan coordnates are gven as (FLUENT, Inc., 1993): U 0 x U U R P U g x x x x x x where U s the mean velocty, X s the poston, P s the mean pressure, g s the gravty accelarton and μ s the dynamc vscosty. In ' ' Eq., R uu denotes the Reynolds stress tensor. Here u = u U, s the th flud fluctuaton velocty component. Ths parameter s modeled usng the Boussnesq s assumpton: ' ' u u t S (3) 3 where, μ t s the eddy vscosty. S and are mean rate of stran tensor and turbulent netc energy respectvely and are defned as follows: S 1 U U ( ) x x 1 ( ' ' u ) u (5) 3.. Turbulence closure equatons The standard -ɛ and the -ω model of Wlcox and Reynolds stress model (RSM) turbulence closure schemes are used for turbulence modelng. In ths research, these models are employed and the proper model s selected for further nvestgaton of flow structure at ths feld Standard -ε turbulence model Accordng to ths model, the eddy vscosty s related to the turbulence netc energy () and ts rate of dsspaton (ɛ) (Cel, 1999): (1) () (4) U U U G t ( ) x x x Closure coeffcents used at ths model are summarzed n Table 1 (Cel, 1999). Table 1. Closure coeffcents used n -ɛ model. C µ C ɛ1 C ɛ δ δ ɛ ω turbulence model Ths model has been gven by Wlcox (1988, 1994). In contrast to the -ɛ model, whch solves for the dsspaton (ɛ) or rate of destructon of turbulent netc energy, the -ω model solves for only the rate at whch the dsspaton occurs (the turbulent frequency, ω). Dmensonally ω can be related to ɛ by ω = ɛ / (Cel, 1999): t (10) The turbulence quanttes and ω are calculated by the followng transport equatons: 1 * * U ( t) G x x R x (9) (11) 1 U vt G (1) x x R x Closure coeffcents used at ths model are summarzed n Table (Cel, 1999). Table. Closure coeffcents used n -ω model. α Β * Β σ * σ 5/9 9/100 3/40 ½ ½ RSM turbulence model The Reynolds stress model (RSM) solves the Reynolds-averaged Naver-Stoes equatons by usng the Reynolds stresses transport equatons (seven-equatons for 3D flow) and an equaton for the dsspaton rate, ɛ. The RSM accounts for the effects of the streamlne curvature, vortcty, crculaton, and rapd changes n the stran rate n a more effcent way than the two-equaton models; however, t requres more computatonal effort and tme. The transport equaton n ths model s as Eq. 9 (Launder, 1989, a and b). Left hand sde terms of Eq. 9 are the local tme dervatves and convecton term (C ) respectvely. Terms of the rght hand sde are turbulent dffuson (D T,), molecular dffuson (D L,), stress producton (P ), pressure stran (Φ ), dsspaton (ɛ ) and producton by system rotaton (F ), respectvely. Most of the terms n ths transport equaton, ncludng C, D L,, P do not requre any modelng and are drectly Please cte ths artcle as: A. Safarzadeh, B. Khaatrostam, Mean flow characterstcs, vertcal structures and bed shear stress at open channel bfurcaton, Journal of Appled Research n Water and Wastewater, 4(1), 017,

3 P a g e 301 Safarzadeh and Khaatrostam / J. App. Res. Wat. Wast. 7(017) solved. However, D T, (Len and Leschzner, 1994), Φ and ɛ (Gbson and Launder, 1978; Launder, 1989a and b) need to be modeled to close the transport equaton. To smulaton the pressure stran the lnear pressure-stran method s used. ( u u ) ( u u u ) t x ( u u u ) p( u u ) x ( uu ) x x u u u u u u u u p( ) x x x x u u ( ) x x ( u um m u um m ) 4. Numercal soluton (13) The CFD code used n ths wor s verson of Fluent. Ths software allows the soluton of the three-dmensonal Naver-Stoes equatons n order to calculate the flow feld. Ths code uses a fntevolume dscretzaton method n conuncton wth dfferent turbulence models. Dfferent schemes such as Second Order Upwnd, SOU, Power Law and Quc may be used to dscretze the convecton terms of the transport equatons. Pressure and velocty feld couplng may be done by SIMPLE, SIMPLEC and PISO algorthms. Flow geometres are constructed usng Gambt Software. Flow feld boundary condtons and mesh generatons were done by ths software [8]. For ths study, due to exstence of crculaton and separaton zones n the flow feld, the convecton term has been dscretzed usng the SOU scheme. Staggered meshes n conuncton wth SIMPLE algorthm have been used for flow feld soluton. The convergence crteron s set to 10e-5. y y p w (14) where, Δy p s the dstance of the near-wall node to the sold surface and τ w s the wall shear stress. The dstance of the frst grd surface off the walls s mportant and depends on the flow condtons, wall roughness and the turbulence model that s used. The -ɛ model uses the wall functon to "brdge" the soluton varables at the near-wall cells and the correspondng quanttes on the wall but the -ω model resolves the near wall regon (lamnar sub layer regon). 4.. Materals and methods A three dmensonal vew of a typcal computatonal mesh for a rectangular dverson confguraton s shown n Fg.. The grd lnes were clustered near the sold walls and n the uncton regon. To ensure the valdty of the numercal soluton for each turbulence model, dfferent mesh szes were appled to each of the models, accordng to the recommended selecton of the near-wall cells (FLUENT 1993). Fg. 3 llustrates comparsons between measured and predcted velocty profles usng the RSM turbulence model wth dfferent mesh szes. A varety of mesh szes were employed. The coarsest of the mesh szes wth smlar results are shown. For the coarser of these two grd cases there were 198,60 total nodes and 0,45 for the fner grd case. The dfference between the coarse and the fne grd predctons at the man channel are small enough to conclude that the coarser of the meshes be selected for the remander of the analyss. For the -ɛ and RSM models the total nodes were thus 198,60 whle for -ω they were 5,41. Addtonally, t was found that usng 10 nodes n the boundary layer for the -ɛ and RSM turbulence models and nodes n the lamnar sub-layer for the -ω model s adequate. These were determned by the gudelnes n the FLUENT User s Manual (FLUENT Inc., 1993). Z Y X 4.1. Boundary condton At the man channel nlet, the Velocty Inlet boundary condton has been used. The flow propertes at the channel nlet are shown at Table 3 (Bardoll, 1996). The flow s subcrtcal and has a turbulent regme. The velocty feld and turbulence parameters (,ɛ and ω) are mposed from a separate smulaton of fully developed turbulent flow through a straght channel. At the exts of both the man and branch channels, the outflow boundary condton has been used. Ths condton states that the gradents of all varables (except pressure) are zero n the flow drecton. At these boundares, the flow often reaches a fully developed state. To ensure that ths condton was satsfed at the ext of the dverson (a fully developed separaton eddy); ths channel was lengthened to. meters. The expermental length of the man channel was recognzed to be adequate. Table 3. Flow propertes at nlet secton. Dscharge(Q 1) (lt/sec) Froude Number Reynolds Number The nlet dscharge has been apportoned between channels. The Dscharge rato (r = Q /Q 1= 0.3) was mposed to the ext of the dverson. Taylor showed that for dscharge ratos between 0 and 0.45 and Froude numbers n the man channel between 0 and 0.4, there s less than % varaton n flow depth n the vcnty of the dverson (Taylor, 1944). Usng these ponts, the Symmetry boundary condton has been used to model the free surface. At the sold boundares the Wall boundary condton was used. The walls were hydraulcally smooth and the no-slp and no-flux condtons dctated to them. The mplementaton of wall boundary condtons n turbulent flows starts wth the evaluaton of: Fg.. Computatonal mesh at dvdng zone. 5. Results and dscusson 5.1. Approprate turbulence model Comparsons between measured and predcted streamwse velocty profles near the free surface plane n both the man and branch channels for the two turbulence models employed are presented n Fg. 4. Ths Fgure shows that all of the turbulence models used accurately predct velocty profles n the man channel but n the branch channel, the RSM model performs very well and the -ω model performed better than the -ɛ turbulence model. Comparson between measured and predcted results n Fg. 6 show that the -ɛ model under-predcts the length of the separated flow n the ntae channel but the -ω and RSM model predctons show good agreement wth the expermental results. The predcton by the -ω model dffers slghtly from the expermental results, but the RSM model predcts the velocty profles very well. Please cte ths artcle as: A. Safarzadeh, B. Khaatrostam, Mean flow characterstcs, vertcal structures and bed shear stress at open channel bfurcaton, Journal of Appled Research n Water and Wastewater, 4(1), 017,

4 P a g e 30 Safarzadeh and Khaatrostam / J. App. Res. Wat. Wast. 7(017) Fg. 3. Grd senstvty results (only the coarsest two acceptable grd sze results shown)."fne grd" had 0,45 computatonal nodes and "Coarse grd" had 198,60. Re= Fg. 4. Comparson of turbulence model results (Near surface D velocty profles). Forward velocty maxmum shfts toward the nner ban as the flow enter the nlet regon (Sec. m ). As the flow enters nto the branch, the resultant velocty along the nlet reduces (Sec. m 3) and hence, at the downstream edge of the nlet, forward velocty maxmum shfts away from the nner wall (Sec. m 4). The small dscrepances at Sec. m 3 may be caused by the so-called velocty-dp phenomenon that cannot be smulated by sotropc models, whle RSM models predcts ths phenomenon well. The falure of the two-equaton models to accurately model the regons wth ansotropc turbulence, such as curved-surface secondary motons and separaton are the weaness of these models. In addton, the two equaton turbulence models are unable to predct certan flow features because of the assumpton that the flow does not depart far from local equlbrum, and that the Reynolds number s hgh enough that local sotropy of eddy vscosty s approxmately satsfed. 5.. Physcs of dvng flow Fg. 5 llustrates the D streamlne plots at three horzontal planes: near bed (Y/H=0.01), Md-depth (Y/H=0.5) and near free surface planes (Y/H=1). The most dstnct features n these plots are: 1- The dvdng streamlne. Ths lne denoted as SL n these fgures. Its locaton n the man channel changes over depth extendng out further near the bed than near the surface. - Fg. 5 (a) ndcates the separaton zone along the left wall of the ntae. The normalzed length of ths zone (L r=l s/b) s about 5.. The length of the separaton zone decreases by gong downwards. 3- In Fg. 5(c) there are streamlnes of flow that appear to emanate on the rght wall of the branch. These are streamlnes of flow that enter the branch at hgher elevaton, then mpnges on the rght wall and are deflected down ward toward the bed where they spread out n the drecton of the separaton zone. Interacton of deflected downward flow and cross sectonal secondary flows along the lateral ntae results n a tornado-le 3D moton (Fg. 7). 4- Fg. 5(c) contans many mportant features that may be used for sedment transport mplcatons. Ths fgure shows that the most of the bed flow reachng the uncton regon s dragged nto the ntae channel. There are some specal ponts that have mplcatons for sedmentatons. These are the ponts where the magntude of the shear stress vector goes to zero and ts drecton s ndetermnate. These are nown as sngular-ponts and the most sgnfcant among them are a focus of separaton (F s), located n the branch channel and a saddle pont (S), located ust off the downstream corner of the ntae. The focus of separaton n the branch channel s a pont where near-bottom partcles would tend to accumulate and corresponds wth the regon where sandbars are commonly nown to form at lateral ntaes. The saddle pont off the downstream corner of the ntae s the orgn of streamlnes that sweep the bed of the uncton regon and dvert them to the focus of the separaton regon (Neary et al., 1993). Fg.7 llustrates the bed-shear stress dstrbutons. Ths fgure can be used to dentfy lely regons of scour and deposton. The followng three regons are observed: 1- A crcular regon of low bed-shear stress, whch concdes wth focus pont (zone m), dscussed earler. - A hgh bed-shear stress zone that loos le a dagger (zone n) where bed-load transport s lely to occur. 3-A hgh shear stress zone off the downstream corner of the ntae (zone p). Downward flow and secondary moton at ths regon are the causes of ths scourng. 4- A low shear stress zone concdng wth the saddle pont (zone q). At ths regon, the sedmentaton may occur. 5- A hgh shear stress zone at the nlet of the dverson channel (zone I). Laterally accelerated flow due to transverse sucton pressure and secondary flow due to role of the dvdng surface as the outer ban of a vrtual bend and outer boundary of the separaton zone as the nner wall of a vrtual bend are the man causes of the scornng process at ths regon. Common sedment transport models use the so-called mean bed shear stress approach n whch bed-load transport occurs when the bed-shear stress exceeds a threshold level. Although the present smulatons were conducted wth a fxed bed, the bed shear stress approach can be used to nterpret the computed shear stress dstrbutons to gan qualtatve nsghts about the effects of the flow structure on sedmentaton processes n lateral ntaes. Comparson of Fgs. 7 and 8 shows that hgh and low shear stress zones predcted by current numercal smulatons perfectly concde wth scourng and deposton zones at dvdng zone of the channel whch are prevously reported n a movable bed expermental wor. Please cte ths artcle as: A. Safarzadeh, B. Khaatrostam, Mean flow characterstcs, vertcal structures and bed shear stress at open channel bfurcaton, Journal of Appled Research n Water and Wastewater, 4(1), 017,

5 P a g e 303 Safarzadeh and Khaatrostam / J. App. Res. Wat. Wast. 7(017) (a) (b) Fg. 7. Bed shear stress contour at dvdng flow zone. Dverson channel Scourng hole zone p Inlet Scourng Zone I (c) Sedment Deposton Zone q Fg. 8. Bed topography n a movable bed expermental dvdng flow test (Abbas, 003). 6. Conclusons Fg. 5. D streamlnes at horzontal planes: (a): Y/H=1, (b): Y/H=0.5 and (c): Y/H=0.01. A commercally avalable CFD code for the predcton of flow n the open channel dvson was used. Three turbulence closure schemes were employed and the performance of each model was evaluated usng expermental data. It was found that all of the turbulence models tested here accurately predcted velocty profles n the man channel but n the branch channel, the RSM model wth the -ω model performng better than the -ɛ model. D streamlne plot at near-bed surface exhbts a complex nature of flow at ths plane. At ths plane the sngular ponts was seen. The most sgnfcant among these ponts are a focus of separaton (F s), located n the branch channel and a saddle pont (S), located ust off the downstream corner of the ntae. These ponts have an mportant role n sedmentaton problem. The calculated bed-shear stress dstrbutons can be used to dentfy lely regons of scour and deposton. Due to presence of hghly turbulent dvdng surface along the man channel and the flow separaton zone along the dverson channel, nstablty of shear layers generated by these two flow mechansms nduce strong nstantaneous vertcal motons and consequently bed shear stresses. It s necessary to use sophstcated modelng approaches such as large eddy smulaton (LES) n order to nvestgate the unsteady nature of the turbulent flow at dvdng zone, especally at the near bed regon to mprove our nowledge about the sedment control at rver dverson proects. Fg. 6. 3D flow structure nsde of the branch channel. Please cte ths artcle as: A. Safarzadeh, B. Khaatrostam, Mean flow characterstcs, vertcal structures and bed shear stress at open channel bfurcaton, Journal of Appled Research n Water and Wastewater, 4(1), 017,

6 P a g e 304 Safarzadeh and Khaatrostam / J. App. Res. Wat. Wast. 7(017) References Abbas A., Expermental study of sedment control at lateral ntae n straght channel, PhD Thess, Tarbat Modares Unversty, (003). Bardoll B., Sedment control at lateral dverson, PhD dssertaton, Unversty of Iowa, (1997). Cel, I.B., Introductory turbulence modelng, Western Vrgna Unversty, (1999). Fluent Inc., FLUENT user s gude; Fluent, New Hampshre, (1993). Gbson M.M., Launder B.E., Ground effects on pressure fluctuatons n the atmospherc boundary layer, Journal of Flud Mechancs 86 (1978) Launder B.E., Spaldng D.B., Lectures n Mathematcal Models of Turbulence, Academa press, London, England, (197). Launder B.E., Second-moment closure and ts use n modelng turbulent ndustral flows, Internatonal Journal of Numercal Methods n Fluds 9 (1989a) Launder B.E., Second-moment closure: present and future?, Internatonal Journal of Heat Flud Flow 10 (1989b) Len F.S., Leschzner M.A., Assessment of turbulent transport models ncludng non-lnear RNG eddy-vscosty formulaton and secondmoment closure, Computers and Fluds 3 (1994) Neary V., Odgaard A.J., Three-dmensonal flow structure at open channel dversons", Journal of Hydraulc Engneerng 119 (1993) Neary V., Sotropoulos F., Numercal nvestgaton of lamnar flows through 90-degree dverson of rectangular cross-secton, Computer and Fluds 5 (1996) Shettar A., and Murthy K., A numercal study of dvson of flow n open channels, Journal of Hydraulc Research 34 (1996) Taylor E.H., Flow characterstcs at rectangular open-channel unctons, Transactons of the Amercan Socety of Cvl Engneers 109 (1944) Please cte ths artcle as: A. Safarzadeh, B. Khaatrostam, Mean flow characterstcs, vertcal structures and bed shear stress at open channel bfurcaton, Journal of Appled Research n Water and Wastewater, 4(1), 017,