3-D NUMERICAL SIMULATION OF FLOW AND CLEAR WATER SCOUR BY INTERACTION BETWEEN BRIDGE PIERS

Transcription

1 Tenth Internatonal Water Technology Conference, IWTC , Aleandra, Egypt D NMERICAL SIMLATION OF FLOW AND CLEAR WATER SCOR BY INTERACTION BETWEEN BRIDGE PIERS Gamal A. A. Abouzed, Hassan I. Mohamed and Shma M. Al Cvl Eng. Dept., Faculty of Eng., Assut nversty, Assut, 71516, Egypt ABSTRACT In ths paper, the flow and local scour varaton around sngle per and ntroducng nteracton effect between brdge pers were studed usng 3D flow model. The model used a fnte-volume method to solve the non-transent Naver-Stoes equatons for three dmensons on a general non-orthogonal grd. The turbulence model s used to solve the Reynolds-stress term. The numercal model solves the sedment contnuty equaton n conuncton wth van Rn s bed-load sedment transport formula to smulate the bed evoluton. The 3D flow model was verfed through epermental study n the non cohesve bed materal n an epermental flume. The dfferent causes of local scour around the per were smulated well, such as bow flow, down flow, horseshoe vorte, pressure varaton and lee-wae vorte. It was found from ths research study that the local scour depth by nteracton process between brdge pers depends on the Froude number, the dstance between pers and the dameter of pers. The mamum scour depth for double pers s hgher than that for sngle per. Furthermore, the effect of per shape on the scour process was studed and t was found that the mamum scour depth for crcular per s less than that for rectangular one for both sngle and double pers cases. The results show good agreement between smulaton and epermental results. Also, emprcal equaton was developed from the epermental data for computng the mamum scour depth due to the nteracton between brdge pers. Keywords: Numercal Modelng, Flow, Local Scour, Double Brdge Pers, Turbulence Model. INTRODCTION Local scour of alluval channel beds around obstructons s a problem of contnung nterest. The comple three-dmensonal flow and sedment transport around such structures have defed an analytcal soluton to the problem and there are wde dvergences n scour depths estmated through the avalable emprcal and sememprcal methods. The tme consumng and epensve nature of epermental research on scourng processes caused by flowng water maes t attractve to develop numercal tools for the predcton of the nteracton of the flud flow and the movable bed. The rapdly decreasng computer costs mae ths approach ncreasngly attractve.

2 900 Tenth Internatonal Water Technology Conference, IWTC , Aleandra, Egypt In the past, the researches on scour were manly focused on the constructon of sngle brdges. In the present tme, the long etended masonry pers are replaced wth multple small renforced concrete pers. In these cases, the dfferent scour patterns compared to that n the case of constructng the sngle per are observed, Cho et al. [1], Cho and Ahn [2] and Yasser [3]. In recent years, several numercal models were constructed for smulatng 3D flow feld and/or bed varatons around crcular pers. Rchardson and Panchang [4] used a 3D transent model to compute the flow feld around a per wthn a gven fed scour hole. Wthout modelng sedment transport, they estmated the depth of equlbrum scour smply by means of Lagrangan partcle-tracng analyss. By ncorporatng varous sedment transport models, few researchers developed scourng models wth varous features. Omttng the transent terms, Olsen and Melaaen [5] computed the scour hole development by solvng the 3D Naver-Stoes equatons wth the (turbulent netc energy and dsspaton rate) model for the Reynolds stresses, and the advecton-dffuson equaton for sedment transport. Olsen and Kellesvg [6] etended the aforementoned model of Olsen and Melaaen wth transent terms. Tseng et al. [7] nvestgated numercally the 3D turbulent flow feld around square and crcular pers. The smulated results they obtaned ndcated that the velocty and shear stress around the square per were sgnfcantly hgher than those around the crcular per. Yen et al. [8] developed a morphologcal model consstng of a 3D flow model and a scour model to smulate the bed evoluton around a crcular per. The large eddy smulaton approach was employed to compute 3D flow velocty and bed shear felds. Accordng to the aforementoned researches, local scour near cylnders was studed etensvely by many nvestgators where emphass was placed on the formulaton of mamum scour depth equatons from laboratory eperments and most papers were based on laboratory data. Numercal smulaton of flow and local scour around multple pers seems to have been pad lttle attenton. Ths paper presents the fndngs of numercal and epermental nvestgaton for the flow and local scour due to nteracton of multple crcular and rectangular for steady flow under a clear water scour condton. MODEL DESCRIPTION The computatonal flud dynamcs code used for ths nvestgaton was developed by Olsen [9]. The model was appled to number of engneerng stuatons ncludng flow modellng for estmaton of spllway capacty, (Olsen and Kellosvg [10]), smulaton of water and sedmentaton n a sand trap, (Olsen and Soglund [11]), smulaton of scour around a cylnder, (Olsen and Kellesvg [6]), and smulaton of flow dynamcs n a rver wth large roughness elements, (Olsen and Stoseth [12]). The code solves the Naver-Stoes equatons wth a - turbulence closure model on a three-

3 Tenth Internatonal Water Technology Conference, IWTC , Aleandra, Egypt 901 dmensonal non-orthogonal grd. Ths software employs the Naver-Stoes equatons for turbulent flow n a general three-dmensonal geometry: ) p ( 1 - u u t ρ δ ρ + = + (1) Where s the local velocty; s space dmenson; δ s Kronecer delta; ρ s flud densty; p s pressure; and u s the average velocty. A control-volume approach s used for dscretzaton of the equatons. The default mechansm for pressure correcton s the SIMPLE method, Patanar [13]. Ths s used for couplng of all cells ecept those closest to the surface and allows calculaton of a free water surface. For these cells, the contnuty of water was used to calculate movement of the water surface. The numercal models and the dscretzaton of the equatons are descrbed n more detals by Rod [14], Patanar [13], and Melaaen [15]. The - model s used to calculate the turbulent shear stress for three-dmensonal smulatons. The eddy-vscosty concept wth the - model s used to model the Reynolds stress term as llustrated n equaton (2) (where the frst term on the rghthand sde of the equaton forms the dffusve term n the Naver-Stoes equaton): ) ( u - δ ν u T + = (2) The - model smulates the eddy-vscosty as: ν µ 2 = C T (3) where s the netc energy as defned by: u u 2 1 = (4) s modelled as: σ ν - p ) ( ) ( + = + T t (5) where p s gven by: ) ( T + =ν p (6) and s modelled as p t T c - c ) ( σ ν + = + (7) The equatons contan fve constants. These constants are mpled n the used program as, (Olsen [9]):

4 902 Tenth Internatonal Water Technology Conference, IWTC , Aleandra, Egypt c 9; c 1 = 1.44; c 2 = 1.92; σ = 1.0; and = 1.3. µ = σ The nfluence of rough boundares on flud dynamcs s modelled through the ncluson of the wall law: 1 = K 30z ln * s (8) As t s gven by Schlchtng [16], The varable s equals to the roughness heght, K s von Karmen constant, s the mean velocty, * s the shear velocty and z s the heght above the bed. Boundary shear stress s calculated as: τ = 0.3 ρ (9) Ths approach s the one, whch was used by Olsen and Kellesvg [10] and Olsen and Soglund [11] and assume that turbulent netc energy s the drver for boundary shear stress. In open cells, turbulent netc energy can be advected wth the flow and dsspated to adacent cells. However, energy cannot pass through bed cells and s assumed to be transferred from netc energy to a force n the form of boundary shear stress. sng ths approach boundary shear stress s prncpally determned by shear near bed through equaton (5) and (6). Calculaton of Sedment Transport Sedment s transported as bed load and suspended load. The suspended load can be calculated wth the convecton-dffuson equaton, c c c = Γ + w (10) z n whch c = sedment concentraton and w = fall velocty of sedment partcles. The dffuson coeffcent Γ was obtaned from the - model: Τ Γ = ν S c (11) The Schmdt number S c s assumed to be unty n ths study. Eqn. (10) was dscretzed wth a control volume approach. The bed load can be smulated wth bed load equaton. However, the estng bed load equatons are developed for one-dmensonal unform flow. For a three-dmensonal flow stuaton, van Rn [17] developed a formula n whch the bed load was calculated as a concentraton n the elements closest to the bed. The suspended load calculaton also needs a formula for the concentraton at the bed. If ths formula s the same as the

5 Tenth Internatonal Water Technology Conference, IWTC , Aleandra, Egypt 903 formula for smulatng the bed load, t s possble to smulate both bed load and suspended load at the same tme. Then nteracton between bed load and suspended load s also smulated. Van Rn s [17] formula for bed concentraton s gven as c bed d = (12) a Τ D * n whch a = a reference level, set to 1.5 % of the water depth. τ 0 τ Τ = τ crtcal crtcal 1 ( ρ ρ ) g 3 s w D* = d 50 2 ν (13) (14) where τ 0 = bed shear stress; τ crtcal = crtcal bed shear stress; ρ w and ρ s = densty of water and sedment respectvely; ν = vscosty of the water, and g = acceleraton of gravty. Grd Constructon A structured grd mesh on the -y-z plane was generated. As shown n Fg. 1, a three dmensonal grd mesh wth 92 elements n the -drecton, 40 elements n the y- drecton and 14 elements n the z-drecton. An uneven dstrbuton of grd lnes n both horzontal and vertcal drectons was chosen n order to eep the total number of cells n an acceptable range and to get valuable results n the area around the cylnder. The followng grd lne dstrbutons were chosen: In X-drecton: 10 cells wth a 4 m, 5 cells wth a 1 m, 50 cells wth a 05 m and 26 cells wth a 5 m respectvely. In Y-drecton: 10 cells wth a 1 m, 20 cells wth a 05 m and 10 cells wth a 1 m respectvely. In z-drecton: 6 cells wth 5% heght of the water depth and 7 cells wth 10% of the water depth. The crcular per was generated by specfyng ts ordnates, and then the grd nterpolated usng the ellptc grd generaton method as shown n Fg. 2. However, the rectangular per was generated by blocng the area of the per.

6 904 Tenth Internatonal Water Technology Conference, IWTC , Aleandra, Egypt (a) z-plane for computatonal grd Fg. (1): (b) y-plane for computatonal grd Fg(2) detaled vew of the grd after per generaton The only boundary condtons, that were specfed, were the water dscharge, the geometry and the ntal water level, boundary roughness and sedment sze. The upstream boundary condton was gven by the mean approach flow velocty. Zero gradent boundary condtons at the downstream boundary had to be gven to prevent nstabltes. Ths meant that the water dscharge at the downstream boundary was not specfed. EXPERIMENTAL WORK Partcular eperments were conducted n an open rectangular tltng flume wth a length of 17.5 m, wdth of 0.3 m and depth of 0.5 m to verfy the numercal results. Eperments were carred out under the condton of clear water scour. Table (1) shows the range of varables used n the eperments. Where, three dfferent szes of

7 Tenth Internatonal Water Technology Conference, IWTC , Aleandra, Egypt 905 wooden pers, 30, 50 and 70 mm dameter respectvely, were used. The flume bed was covered by clean angular sand partcles wth d 50 = 0.9 mm for a thcness of 20 cm. The flow dscharge was changed two tmes (8.5 and 10.5 l/s). Test secton located 6 m away from the upstream end. A false floor was constructed along the length of the flume 0.20 m above the bottom. The eperment was started by carefully fllng the flume wth water to the requred flow depth. Ths was done wth great care so as not to cause too much dsturbance to the flow. Two pont gauges of 0.1 mm accuracy were used for measurng water depth n the longtudnal drecton and the profle of the scour hole. Each eperment was stopped after a perod from 3 to 4 hours. Table (1): Range of varables for laboratory eperments Parameter Symbol Value Range nts From To Per dameter D 30,50, mm Dscharge Q 8.5, L/s Mean water depth h 10.5,12,14, cm Froude number Fe vared Per spacng L/D vared Sedment sze d mm MODEL VERIFICATION A seres of tests was frst performed on a sngle per. Fgure (3) shows epermental values of mamum scour depth as a rato of mean water depth, (d s /h)ep, versus the numercal values, (d s /h)nu, predcted by the 3D numercal model for the dfferent three per dameters used n ths study. It was notceable that there were well agreement between the epermental and numercal values of mamum scour depth. The correlaton coeffcent between observed and predcted values was 0.9. Two pers of varous spacng and dfferent dameters were then nvestgated. Fgure (4) shows a comparson between the numercal values and the epermental values of mamum scour depth as a rato of the water depth at case of two pers for dfferent spacng and dameters. Well agreement was notceable between the numercal and the epermental values. The correlaton coeffcent between observed and predcted values was 0.92.

8 906 Tenth Internatonal Water Technology Conference, IWTC , Aleandra, Egypt (ds/h)ep Lne of best agreement D=3cm D=5cm D=7cm (d s /h)nu Fg. (3): Epermental values of mamum scour depth versus numercal values for sngle per and dfferent per dameters (ds/h)ep (d s /h)nu D=5cm L/D=1 D=5cm L/D=3 lne of best agreemen D=7cm L/D=1 D=7cm L/D=3 Fg. (4): Epermental values of mamum scour depth versus numercal values for double pers at dfferent dameters and spacng between the pers

9 Tenth Internatonal Water Technology Conference, IWTC , Aleandra, Egypt 907 RESLTS AND DISCSSIONS In the prevous secton, the numercal model was verfed usng the epermental data. Now, t s ready to analyss and dscusson of the numercal results. 1- Flow patterns and Local Scour around Sngle Per Some of the smulated results are plotted n Fgs Snce the flow feld at far dstance downstream s almost the same as that of the upstream nflow, the smulated results are only plotted wthn the range 2 / D 3 n the -drecton to clearly show the detaled flow feld around the per. Fg. 5 presents the smulated velocty feld on the horzontal plane at z/h=0.14. It clearly shows that reverse flow ests n front of the per and the horseshoe vorte around the cylnders. Furthermore, the plots clearly show the estence of a separaton zone behnd the cylnder. The locaton of the separaton pont etends further downstream at the surface than close to the bed. The wae regon n the numercal model results was defned as the regon n whch the longtudnal veloctes are n opposte drecton to the man flow drecton and ths n agreement wth Al and Karm [18]. In comparson between Fg. 5-a and 5-b, t was obvous to notce that reverse flow becomes stronger by ncreasng the dameter of the per. Longtudnal Sectonal elevaton Longtudnal Sectonal elevaton 3 m Fg. (5): Velocty vectors for per dameter = 30 and 70 mm respectvely at dscharge = 8.5 l/s and approach flow depth = 12cm

10 908 Tenth Internatonal Water Technology Conference, IWTC , Aleandra, Egypt In Fg. 6, the smulated scour hole bed contours for the flow cases shown n Fg. 5 s drawn. It s notceable from ths fgure that scour hole dmensons depend on the case of the flow around the per. Furthermore, the scour hole etends around the crcular per wth a deeper area at the upstream sde and a shallower one downstream and ths n well agreement wth the epermental observaton and prevous researches. Also, the scour depth ncreases wth the ncreasng of the cylnder dameter. Flow drecton Fg. (6): Smulated fnal bed elevaton contours for per dameter = 30 and 70 mm respectvely at dscharge = 8.5 l/s and approach flow depth = 12cm 2- Flow patterns and Local Scour around Double Pers Fgure (7) shows a comparson between the velocty vectors around sngle and double pers respectvely at z/h =0.14. It notceable the dfference n the flow felds between the two cases. In case of double cylnders, the reverse flow downstream the frst cylnder hts the second one whch maes dsspaton for the lee-wae vorte and at the same tme actvates the horseshoe vorte causng hgher local scour depth upstream of the frst cylnder.

11 Tenth Internatonal Water Technology Conference, IWTC , Aleandra, Egypt 909 Sngle ple double ple Fg. (7): Velocty vectors for sngle and double pers at per dameter= 50mm, dscharge=10.5l/s and upstream mean water depth= 14cm. Fgure (8) shows a comparson between the bed profles at case of sngle and double pers respectvely for the flow cases shown n Fg. 7. It s notceable the dfference between the two, where the scour hole at the double pers s deeper and at the same tme the scour depth at the sdes of the per s shallower Flow drecton Fg. (8): Bed profles for sngle and double pers at per dameter= 50mm, dscharge= 10.5l/s and mean upstream water depth= 14cm Fgure (9) shows the effect of the dstance between pers on the scour process. It s notceable that the scour hole area ncreases by ncreasng of the dstance between the

12 910 Tenth Internatonal Water Technology Conference, IWTC , Aleandra, Egypt pers. Furthermore, the scour depth s greater for L/D=1 than that for L/D=3.0. Fgure (10) shows the varaton of d s double / d s sngle wth Froude number at dfferent values of per spacng L/D Flow drecton Fg. (9): Bed profles for L/D=1, 3 respectvely at per dameter = 70 mm, dscharge = 8.5l/s and mean water depth = 14cm ds double/ds sngle D=5cm,L/D=1 D=5cm,L/D=3 D=7cm,L/D=1 D=7cm,L/D= F e Fg. (10): Values of d s double / d s sngle versus Froude number The presence of pers across a stream creates constrcted flow because of the reducton n the wdth of the stream. The correspondng afflu (rse n upstream water level) depends on the type of the flow. The establshment of afflu levels s etremely mportant not only for the desgn of safe brdge dec levels but also for local scour around the per. Fgure (11) shows the effect of afflu rato ( h / h) on the mamum scour depth. It s clearly shown that the mamum scour depth ncreases by ncreasng of afflu level for both sngle and double pers.

13 Tenth Internatonal Water Technology Conference, IWTC , Aleandra, Egypt 911 ds /h sngle ple D=7cm double ple L/D= h/h Fg. (11): Effect of afflu upstream the per on the mamum scour depth a. Effect of Per Shape on The Scour Process Fg. 12 llustrates the bed profles for rectangular and crcular pers respectvely. From that fgure one can fnd that the dmenson of the scour hole for crcular per s less than that for rectangular per. Ths due to that the as of the horseshoe vorte n the front of the crcular per s closer to the per than that n the case of the rectangular one because the veloctes of the down flow and reverse flow generated by the crcular per are smaller than those generated by the rectangular one. Fg. 13 shows a smlar trend for the case of double pers Fg. (12): Smulated fnal bed elevaton contours for rectangular and crcular sngle brdge pers respectvely at dscharge = 8.5 l/s and approach flow depth = 12cm

14 912 Tenth Internatonal Water Technology Conference, IWTC , Aleandra, Egypt Fg. (13): Smulated fnal bed elevaton contours for rectangular and crcular double brdge pers respectvely at dscharge = 8.5 l/s and approach flow depth = 12cm b. Emprcal Equaton for Mamum Scour Depth The mamum scour depth around double brdge pers s sgnfcantly dependent on Froude number as shown n Fg. (14), rato of per wdth to channel wdth, Fg. (15), spacng between pers, per wdth to mean water depth rato and per wdth to mean gran sze rato. A mult-lnear regresson analyss s used to correlate the dfferent parameters and deduce an emprcal equaton for computng the mamum scour depth (Eqn. 15) due to the nteracton between brdge pers, where the symbols as defned before. The correlaton coeffcent between observed and predcted values s d / h = 0.92D / h D / b + 01L / D + 4.2F 06D / d (15) s e + Fgure (16) shows a comparson between the mamum scour depths computed usng Eqn. 15 and epermental values. 50 ds/h F e Fg. (14): Effect of Froude number on the mamum scour depth

15 Tenth Internatonal Water Technology Conference, IWTC , Aleandra, Egypt 913 ds/h Q=10.5l/s,h=14cm 0.2 Q=8.5l/s,h=10.5cm D/b Fg. (15): Effect of per dameter to channel wdth rato (D/b) on the mamum scour depth (ds/h) Eqn (d s /h)ep Fg. (16) : Values of mamum scour depth computed by Eqn. 15 versus epermental values CONCLSIONS The man concluson drawn from ths study can be summarzed as follows: Flow and local scour around sngle and double pers were modeled usng 3D numercal model. Many parameters whch are very dffcult to be measured epermentally can be computed usng the model, such as the bed shear stress dstrbuton, velocty vectors, afflu upstream the per and pressure dstrbuton. There are many parameters, whch have a large effect on the mamum scour depth at multple brdge pers, these parameters are dameter of the per, spacng between pers, Froude number and bed sedment sze. The local scour depth at a per, when the nteracton between brdge pers ests, s severely affected by the scours at the other pers.

16 914 Tenth Internatonal Water Technology Conference, IWTC , Aleandra, Egypt The mamum scour depth for double pers s larger than that for sngle per. However, the mamum scour depth asde the per s shallower. The mamum scour depth for crcular pers s smaller than that of rectangular pers and ths s n agreement wth prevous researches. The model computatons compare well wth the epermental flume data. Emprcal equaton correlatng the dfferent parameters has been deduced for appromate computaton of mamum scour depth due to the nteracton between cylndrcal brdge pers. NOMENCLATRE The followng symbols are used n ths paper: b = channel wdth c 1, c 2 = constant n model c = constant n model µ D = per dameter d s = mamum scour depth d 50 = bed sedment gran sze at 50% passng F = water flu F e = Froude number g = acceleraton of gravty h = water depth = turbulent netc energy L= spacng between pers from centerlne to centerlne p = pressure p = producton of turbulent netc energy Q = dscharge = mean velocty u = fluctuatng velocty t = tme = length scale δ = Kronecer delta = turbulent dsspaton of ν T = turbulent eddy vscosty ρ = densty of water σ,σ = constant n model REFERENCES 1. Cho, G. W., Hahm, C. H., Jun, B. H. and Ahn S. J. (1998). The nfluence of the local scour by nteracton between brdge pers. ICHE conference, Seoul, South Korea.

17 Tenth Internatonal Water Technology Conference, IWTC , Aleandra, Egypt Cho, G. W. and Ahn, S. J. (2001). Mamum local scour depth varaton at prdge pers. IAHR conference, Beng, Chna. 3. Yasser, M. R. (1997). Local scour around brdge ples, M. Sc. Thess, Assut nversty, Assut, Egypt. 4. Rchardson, J. E. and Panchang, V. G. (1998). Three-dmensonal smulaton of scour-nduced flow at brdge pers. J. of Hydraulc Engneerng, ASCE, 124, Olsen, N. R. B. and Melaaen, M. C. (1993). Three-dmensonal calculaton of scour around cylnders. J. of Hydraulc Engneerng, ASCE, 119, Olsen, N. R. B. and Kellesvg, H. M. (1998). Three-dmensonal numercal flow modelng for estmaton of mamum local scour depth. J. of hydraulc Research, IAHR, 36, Tseng, M. H., Yen, C. L. and Song (2000). Computaton of three-dmensonal flow around square and crcular pers. Internatonal Journal for Numercal Methods n Fluds, 34, Yen C. L., La, J. S. and Chang, W. Y. (2001). Modellng of 3D flow and scourng around crcular pers. Proc. Natl. Sc. Counc., ROC (A), Vol. 25, No. 1, Olsen, N. R. B., (1996), A three-dmensonal numercal model for smulaton of sedment movement n water ntaes wth mult-bloc opton, SSIIM ser Manual Verson Olsen, N. R. B., and Kellesvg, H. M., (1998a), Three-dmensonal numercal flow modellng for estmaton of spllway capacty, J. of Hydraulc Research, Vol. 36, No Olsen, N. R. B., and Soglund, (1994), Three-dmensonal numercal modellng of water and sedment flow n a sand trap, J. of Hydraulc Research, 32, Olsen, N. R. B., and Stoseth, S., (1995), Three-dmensonal numercal modellng of water flow n a rver wth large bed roughness. J. of Hydraulc Research, 33, Patanar, S. V., (1980), Numercal heat transfer and flud flow, McGraw- Hll, New Yor. 14. Rod, W., (1980), Turbulence models and ther applcaton n hydraulcs- a state of the art revew, IAHR: Delft. 15. Melaaen, M. C., (1992), Calculaton of flud flows wth staggered and nonstaggered curvlnear non-orthogonal grds-the theory, Numercal Heat Transfer, Part B, 21, Schlchtng, H., (1960), Boundary layer theory, McGraw-Hll. 17. Van Rn, L. C. (1987). Mathematcal modelng of morphologcal processes n the case of suspended sedment transport. Ph.D. Thess, Delft nversty of Technology, Delft, the Netherlands. 18. Al, K. H. and Karm, O. (2002). Smulaton of flow around pers. J. of Hydraulc Research, 40(2),