NUMERICAL SIMULATION OF STEADY CURRENT BELOW OFFSHORE PIPELINE NEAR PLANE BOUNDARY

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1 NMERICAL SIMLATION OF STEADY CRRENT BELOW OFFSHORE PIPELINE NEAR PLANE BONDARY Mani Golparvar Fard 1, Abbas Yeganeh-Bahiar and Liang Cheng 3 1 Posgraduae Suden, College of Civil Engineering, Iran niversi of Science and Technolog, Tehran 16844, Iran Hdro-Srucure and Srucure Research Cener, College of Civil Engineering, Iran niversi of Science and Technolog, Tehran 16844, Iran 3 School of Civil and Resource Engineering, The niversi of Wesern Ausralia, Perh, Ausralia eganeh@.ius.ac.ir Absrac: This paper presens a - urbulence model for simulaion of sead curren and is induced vore shedding caused b he presence of an offshore pipeline. Performance of he model around a circular clinder above a wall wih gap o diameer raios of 0.1, 0.35 and 0.5 under differen flow regimes wih Renolds numbers of 1500, 500 and 7000 is sudied. The flow field is compued wih solving he Renolds Averaged Navier-Soes equaions (RANS); he seabed under pipeline is reaed as a plane boundar wih no-slip boundar condiion on pipe surface. The governing equaions are solved using Finie olume Mehod in a Caresian coordinae ssem. Based on he numerical soluions, he flow field, vore shedding and disribuion of shear sress due o he presence of he pipeline near seabed are sudied. In addiion he mechanism of vore shedding wih differen gap o diameer raios is eamined wih focusing on he effec of vore shedding on bed shear sress. I is found ha he - urbulence model can well predic he flow field and is induced vore shedding around a pipeline; hence i can be easil applied for simulaion of scour below an offshore pipeline. Kewords: Renolds averaged navier soes equaions (RANS), - urbulence model, ore shedding and local scouring. 1. INTRODCTION Offshore pipelines insalled on seabed, have been eensivel used as he criical lins beween offshore fields and sorage unis. These pipelines disurb he flow field and produce imbalance in local sedimen ranspor ha leads o scouring of seabed. As pical cos of offshore pipelines sabilizaion is in order of millions of S dollars per ilomeer in Persian Gulf and Ausralian Wes Shelf; hence, he consequences of pipeline failure, would be ver sever economicall. On he oher hand, he flow field and is induced local scour involve a comple urbulen shear flow, which usuall ineracs wih is surrounding bed forms. Therefore, accurae simulaion of flow field around a pipeline o accoun for hdrodnamics forces is ver essenial. Wih hese obvious significances, local scour and flow below a pipeline have been subjecs of invesigaion over he las hree decades. A series of phsical and numerical sudies (e.g. Kjeldsen e al. [1]; Mao []; Brørs [3]; Sumer and Fredsøe [4, 5, 6], Li and Cheng [7, 8, 9], among ohers) has been done on local scour below a pipeline. In he numerical sudies, i has been found ha using differen flow models have disinguished effecs on he numerical resuls. Mainl wo ind of numerical models for fluid phase in scour predicion below a pipeline have been developed: Former approach is based on he poenial flow heor, (see Li and Cheng [10] and Hansen e al. [11]), while he laer one is based on - urbulence model (See Leeuwesein and Wind [1], Brørs [3] and Li and Cheng [8, 9]). I is eviden ha none of 46 Inernaional Journal of Civil Engineering, ol. 3, No. 1, March 005

2 he sudies based on he poenial flow models can eplain he genle slope of scour hole formed downsream of a pipeline. This is primaril because he poenial flow model is no able o simulae he vore shedding process associaed wih he flow around a pipeline. The genle slope of scour hole is mainl caused b vore shedding downsream of he pipeline and generaes a flucuaing shear sress field on he seabed. The scouring process downsream of pipeline is hen affeced b he flucuaing shear sress eperienced b seabed. As he poenial flow model is no capable of simulaing his flucuaing sress field; herefore, i canno simulae he downsream par of he scour hole, (see Sumer e al. [4]). Earl numerical eperimens based on he - urbulence model seem o have difficulies wih handling seabed deformaion caused b scouring. For insance Leeuwesein e al. [1] developed a single-phase numerical model based on - urbulence model. In heir numerical par of he invesigaion, he so-called Cloud in Cell (CIC) mehod is emploed o simulae he flow. I is repored ha CIC mehod generall gives good predicion for he gross characerisics of he organized wae, bu he imporan conclusion is drown ha he organized wae behind he pipeline has srong effecs on he profile of scour hole; while, ime-averaged bed shear sress is no a suiable parameer o use in predicing he Lee-wae scour behind a pipeline. Laer on, an Bee and Wind [13] proposed an improved - urbulence model. In his model, he flow field is obained b solving he RANS equaions wih a sandard - model. The comparison of he calculaion resuls wih he eperimenal ones is encouraging. Brørs [14] presened a model ha includes he descripion of fluid flow b a sandard - urbulence model. Flow around a surface mouned clinder is prediced in good agreemen wih he eperimens. However, in scour calculaions he model does no predic periodic vore shedding, even during he laer sages of scour developmen. Li and Cheng [9] developed a numerical model for local scour around pipelines emploing a slighl differen approach. The flow around he pipeline is solved using a Large Edd Simulaion (LES) model. The resuls in predicion of seabed shear sress are more accurae han radiional he - urbulence models. Alhough numerical modeling of flow around an isolaed clinder has been carried ou eensivel, onl a few sudies have considered he flow over a circular clinder near a plane bed. Lee e al. [15] presened a finie difference soluion o D Navier- Soes equaions wih a Smagorins's Subgrid Scale (SGS) urbulence model. In heir sud, qualiaive comparisons show favorable agreemen wih he eperimenal measuremen of Bearman and Zdravovich [16], bu i is found ha he model overpredics he scour downsream a pipeline, possibl because he D-SGS model over predics he ineracions beween he vorices shed from he clinder pipe and seabed. Laer, Lei e al. [17] carried ou a D Direc Numerical Simulaion (DNS) in suding wall effec on flow over a circular clinder for a relaivel low Renolds number; however heir sud does no conain high Renolds number in subcriical flow regimes, which induce periodic vore shedding. The over predicion of ineracions beween he vorices shed from pipeline and seabed in previous numerical models, and he lac of numerical models in suding he wall boundar effec on flow for high Renolds numbers (subcriical regimes of flow) moivaed he curren research. Therefore, o have more accurae suding of flow field around a pipeline near a plane boundar and o predic ineracions among vorices in subcriical regimes of flow, a sandard - urbulence model (Launder and Spalding, [0]) is presened. Flow around a circular Inernaional Journal of Civil Engineering, ol. 3, No. 1, March

3 48 Inernaional Journal of Civil Engineering, ol. 3, No. 1, March 005 clinder above a wall wih gap o diameer raio of 0.1, 0.35 and 0.5 for differen flow regimes wih Renolds numbers (1500, 500 and 7000) is simulaed and he performance of he sandard - urbulence model is eamined on differen sead curren moions wih differen gap raios.. NMERICAL MODEL.1. Governing Equaions The governing equaions of he fluid flow are implemened wih a vericall wodimensional urbulence model, as follows: 0 = (1) Γ Γ ρ = P 1 () Γ Γ ρ = P 1 (3) = ν ν Γ (4) in which, are mean flow veloci componens in sreamwise () and upward verical () direcion, respecivel; P is pressure; is ime; Г is effecive viscosi; ν is molecular ineic viscosi and ν is he edd viscosi. σ ν ν σ ν ν = r p (5) ( ) σ ν ν σ ν ν = r 1 c p c (6) = ν r p (7) = ν µ C (8) in which is urbulen ineic energ; is dissipaion of urbulen ineic energ; r p is producion of urbulen ineic energ due o shear sress and µ C, σ, σ, 1 C and C are consans for he sandard - urbulence model. Table 1 presens he recommended values for he model consans according o Launder and Spalding [0]. Table1. Consans for he sandard - urbulence model. c µ σ σ c 1 c Compuaional Domain Fig. 1 gives a sech of he compuaional domain. The waer deph is considered equal o 3.5D, which is chosen on he fac ha vore shedding in his case, is no as crucial as ha of he behind an isolaed clinder while he gap raio (e/d) is small. Horizonal disances are se o 10D for he upsream and 0D for he downsream laeral boundaries. These disances are chosen on he basis ha less disance ma cause he ouflow and inflow boundar condiions o highl affeced b boh vore shedding and sream races of he fluid phase. I is nown ha while he gap raio is less han 0.3, vore shedding would be oall suppressed; herefore o have a precise sud of gap raio effecs on vore shedding, differen gap o

4 diameer raio has been used in his sud. Hence he compuaion domain would cover from /D=-10 o /D=0 in he horizonal direcion and from /D=0 o /D=3.5 in he verical direcion. The clinder is placed wih is cener in (, )=(10D, e); while "e" is 0.1D, 0.35D or 0.5D. in which κ is von-kármán consan (=0.41) and * is shear veloci. An addiional assumpion of he local equilibrium beween generaion and dissipaion of urbulen energ is made a he grid poin in he vicini of boom wall, hence and a he firs grid are calculaed b = * C µ ; = κ * p (1) 3. NMERICAL EXPERIMENTS AND DISCSSION: Fig. 1. Sech of flow domain and is boundar condiions..3. Boundar Condiions A he waer surface, a smmeric boundar condiion is applied as follows: = 0, = 0 (9) A solid boundar (i.e. pipe surface), he noslip boundar condiion normal o is surface is emploed: = 0 or = 0 (10) For seabed boundar, he wall funcion is implemened, namel he logarihmic law holds beween solid wall and is adjacen grid poin. On laer sages of scour simulaion, for proper fiing of logarihmic veloci disribuion, he heoreical bed level would be se below he average heigh of he paricles surface, (see Yeganeh e al. [1]). The boundar condiion for sreamwise veloci, a he grid poin (= p ) in he vicini of boom is epressed as: ( p,) p* = ν * ( p,) 1 p * = ln(9.793 ) κ ν * p ν p ν * * > (11) To demonsrae he effec of vore shedding on bed shear sress and is effec on local scour, flow around a circular clinder above a fied plane is simulaed using a sandard - urbulence model. I is apparenl eviden ha he flucuaing shear sress due o vore shedding around a pipe has a e effec in he local scour around i as hrough using phsical model ess, Sumer e al. [4] observed ha he near-bed veloci flucuaes significanl downsream of he model pipe. Therefore, i is suggesed ha he flucuaing seabed shear sress has a phsicall powerful effec on he local scouring downsream of he pipe and consequenl, in his sud, i has been considered for modeling of flow below a pipeline and is induced local scour. When a clinder is locaed near a wall, i is epeced ha vore shedding depends on he Renolds number (Re), he gap raio (e/d) and he characerisics of wall boundar laer. Generall, vore shedding occurs when he Renolds number, Re, based on he clinder diameer (D) and he free-sream veloci () is above 40. For he Renolds numbers up o above 150, he vore shedding flow remains laminar (See Beaudan and Moin [3]). Transiion o hreedimensional flow sars a a Renolds number of abou depending on eperimenal condiions, and ends a abou Re= 60, a which fine scale hree- Inernaional Journal of Civil Engineering, ol. 3, No. 1, March

5 dimensional eddies appear (See Williamson [4]). Furhermore he flow is classified as subcriical regime for Renolds number from 300 o (see Niemann and Hölscher [5]). I is in his subcriical regime of flow ha he boundar laer along he clinder surface is laminar hroughou he circumference unil separaion and periodic vore shedding would be induced. Therefore in his sud, o insure he vore shedding siuaions horoughl esed, he Renolds numbers are aen in he range of he subcriical regime values (1500, 500 and 7000). To diminish he effec of mesh size on numerical soluion and o brace he Caresian coordinae ssem, a careful meshindependence sud has been done, and as a resul a 60 7 mesh wih grid poins being concenraed oward flow direcion and he seabed is emploed for cases sudied, (Fig. ). vorices wih he seabed are clearl displaed b he veloci vecors depiced in hese figures. Fig.. Compuaional Mesh for e/d= 0.35 and e/d= Observing Flow Field To undersand he flow field characerisics and he mechanism of vore shedding due o he presence of pipe near seabed, Figs. 3 and 4 are presened. The process of vore shedding around pipe and he ineracion of Fig. 3. Flow paern during vore shedding process (e/d = 0.35, Re=1500). Two differen gap raio parameers (0.35 and 0.5) for Renolds number of 1500 are 50 Inernaional Journal of Civil Engineering, ol. 3, No. 1, March 005

6 presened. I is readil seen ha: (i) vorices are shed alernaivel from he op and boom, forming a vore sree downsream of he pipe; and (ii) here are clearl ineracions beween seabed and vorices shed from he pipe especiall when he gap raio is 0.35, which allows more ineracion beween pipe and seabed. Fig. 4. Flow paern during vore shedding process (e/d = 0.5, Re=1500). 3.. Mechanism of ore Shedding To undersand he mechanism of vore shedding a differen gap raios, i is useful o loo a he vore shedding formaions firs. Figs. 5, 6 and 7 presen he insananeous vorici conours calculaed in one shedding ccle a Re= 1500 and e/d= 0.1, 0.35 or 0.5, respecivel. In he vicini of clinder and wall, here are hree laers of veloci, wo shear laers ha develop along on he op and boom surface of he clinder, and a shear laer develops along he wall. These hree laers are clearl visible in Figs. 5, 6 and 7. Boh he op shear laer on he clinder and he shear laer on he wall induce a srong vorici, while he vorici changes sign from negaive o posiive as he laer is changed. The formaion or suppression of he vore shedding resuls from he ineracion of hese hree laers, can be described as follows: A Fig. 5a, he ail of a posiive vore is being formed and i is being fed b he lower shear laer a he boom of clinder. In he meanime, a negaive vore is forming from he upper shear laer. For he ime being, in Fig.5b, he feeding of negaive vore from he upper shear laer is cu off b growing posiive vore; while, he newl formed negaive vore downsream of he pipe coninues o grow and pushes he posiive vore downsream. This process is quie significan as i passes hrough Fig. 5c and coninues hrough Fig. 5d. I is due o insabili in he lower free shear laer resuling from a high concenraion of posiive vorici ha he lower shear laer rolls up o form a posiive vore. The formaion procedure of vore coninues, so ha i reaches o a sead periodic vore shedding process. As he gap o diameer raio (e/d) is changed o 0.5, he wall shear laer a he clinder locaion places far from he lower shear laer on he clinder surface (Fig. 6). Therefore in he vore formaion area, hese wo shear Inernaional Journal of Civil Engineering, ol. 3, No. 1, March

7 Fig. 5. Insananeous vorici around a pipeline, (D= 100 mm, e/d= 0.35, = 150 mm/s). Fig. 6. Insananeous vorici around a pipeline, (D= 100 mm, e/d= 0.50, = 150 mm/s). laers do no inerac on he clinder surface. As he wall shear laer grows, i separaes from wall a a locaion downsream of he pipe and forms a negaive vore. This negaive vore ges ogeher wih a vore pair resuled from he vore shedding and mies he negaive vore originaing from he op of he clinder in far wae, while he are ransporing downsream. I is concluded ha due o he significan disance beween he pipe and seabed, he vore shedding does no ge affeced b he shear wall laer a his gap raio. The siuaion changes considerabl a ver small gap raios. Fig. 7 demonsraes he insananeous vorici conours for he same 5 Inernaional Journal of Civil Engineering, ol. 3, No. 1, March 005

8 Renolds number. Due o he small gap beween he pipe and seabed (e/d= 0.1), vorici in he separaed free shear laer ges ver wee; herefore, he upper shear laer coninues o grow and affec downsream, wihou forming an vorices in he near wae of he pipe. In his condiion, he near wae is quie sable since no vore shedding is formed Effecs of Renolds Number Figs. 6, 8 and also 9 presen he insananeous vorici conours obained a Renolds numbers (Re= 500 and 7000). Fig. 7. Insananeous vorici around a pipeline, (D= 100 mm, e/d= 0.10, = 150 mm/s). Fig. 8. Insananeous vorici around pipeline, (e/d= 0.50, = 50 mm/s, Re=500). Inernaional Journal of Civil Engineering, ol. 3, No. 1, March

9 To minimize he effec of gap o diameer raio, e/d is se o 0.5. In his gap o diameer raio, he wall shear laer a he clinder locaion places far from he lower shear laer on clinder surface and i would be possible o observe he effec of Renolds numbers apar of gap o diameer raio. Comparing o low Renolds numbers regimes of flow repored b Lei e al. [17], he overall vorici level in shear laers in high Renolds numbers are higher and hree shear laers are hinner ha hose a low Renolds numbers. The effec of differen high Renolds numbers can be observed hrough Figs. 6, 8 and 9 as Re increases from 1500 o When Re reaches 7000, wall shear laer a he clinder is almos annihilaed and due o is wea performance, i is no able o roll up and form vorices; consequenl, i would no inerac wih oher wo laers. A pair vore resuled from he clinder is observed in all siuaions. This pair vore would no inerac on he clinder surface bu i would mi he negaive vore originaing from he op of he clinder in far wae; while, he are ransporing downsream. Consequenl, hese upper and he lower free shear laers forming he pair vore are ranspored downsream; hus, he wae developmen can be easil seen Characerisic of Bed Shear Sress Ampliude of shear sress oscillaion and he mean values of shear sress var a differen locaions along seabed. To observe such variaions, Fig. 10 gives he disribuion of he values of he seabed shear sress along seabed downsream of pipeline. I can be easil seen ha he maimum shear sress aes place direcl underneah of pipe wih large ampliude of oscillaion as Renolds number changes. I can also be observed ha he maimum boom shear sress reaches is second pea a disance almos equal 5-7 pipe diameers downsream of he pipe and decreases again as i moves downward, especiall when gap o diameer raio (e/d) is 0.1. The similar phenomenon was observed b Sumer e al. [4] in heir phsical eperimens, where he veloci oscillaions near he seabed were emploed o discuss he effec of vore shedding on he local scour. The second pea in seabed shear sress is due o small gap raio beween he clinder and he seabed and i is significan as normall i Fig. 9. Insananeous vorici around pipeline, (e/d= 0.50, = 700 mm/s, Re=7000). 54 Inernaional Journal of Civil Engineering, ol. 3, No. 1, March 005

10 Fig. 10. Characerisic Bed shear sresses (D=100 mm, Fied Fla Bed). is in his region ha srong scouring can be observed. I is concluded ha a domain of a leas 7 diameers downsream of he pipe is needed o model local scour under offshore pipeline. 4. CONCLSIONS The following conclusions can be drawn: A sandard - urbulence model wih he so-called wall funcion boundar condiion is compuaionall affordable and relaivel well calibraed for differen Renolds- Number engineering flows, in addiion comparing o eperimenal visualizaions, numerical visualizaion can provide more deails abou he flow field, Thus he mechanism of vore shedding in sead curren due o he presence of pipe near seabed can be easil observed. Renolds number has a significan effec on vore shedding caused b he presence of he pipe. Onl in subcriical regime, he boundar laer along he surface of he clinder is laminar hroughou he circumference unil separaion. A small e/d, as a resul of he conac of hese shear laers, he posiive vorici in he lower shear laer is cancelled b he negaive vore forming a he wall shear laer. Consequenl, he lower shear laer is suppressed and i would no be srong enough o roll up and form vorices; herefore i would no have an significan effec on he upper shear laer. As e/d increases, he vore shedding is more observable and he vorici phenomena would be enhanced b increase in Renolds number. Compared o he low Renolds number flows, he overall vorici level in shear laers in high Renolds numbers are higher and hree shear laers are hinner ha hose a low Renolds numbers. Whereas in high Renolds numbers, he wall shear laer a clinder is almos defeaed and i would no Inernaional Journal of Civil Engineering, ol. 3, No. 1, March

11 able o roll up and form vorices; consequenl, i would no inerac wih oher wo shear laers. The pair vore resuled from he clinder would no inerac on he clinder surface bu while ransporing downsream, he would mi he negaive vore originaing from he op of he clinder in far wae, herefore, he wae developmen can be easil seen. Seabed shear sress has a significan effec on local scour under offshore pipelines and i is easil seen ha due o he presence of pipe, he scour hole caused b he vore shedding can be enlarged even o 5-7 diameers downsream of he pipe. Insead of using curvilinear coordinae ssems, he presen sud uses a Caresian coordinae ssem for simulaion of flow field around he pipe. In order o have a precise sud, a mesh-independence sud has been done, and a dense mesh wih grid poins being concenraed oward flow direcion and he seabed is emploed for cases sudied. This coordinae ssem suffers from heav load of numerical calculaions; even hough he level of precision is no significanl changed. sing curvilinear coordinae ssems wih grid poins being concenraed oward pipe surface and he seabed would lessen he amoun of numerical soluions. REFRENCES [1]. Kjeldsen, S.P., Gjørsvi, O., Bringaer, K.G. and Jacobsen, J., Local scour near offshore pipelines. Proceeding of Second Inernaional Conference on Pors and Ocean Engineering under Arcic Condiions, niversi of Iceland, pp []. Mao, Y., The ineracion beween a pipeline and erodible bed. PhD Disseraion, Technical niversi of Denmar, Lngb, Denmar. [3]. Brørs, B., Modeling of flow and scour a pipelines. Journal of Hdraulic Engineering 15 (5), pp [4]. Sumer, B.M. and Fredsøe, J., Ineracion beween vibraing pipe and erodible bed. Journal of Waerwa, Por, Coasal and Ocean Engineering. ASCE 114, 5, pp [5]. Sumer, B.M. and Fredsøe, J., 199. A review of wave/curren-induced scour around pipelines. Proceeding of 3 rd In. Conference on Coasal Eng. (ICCE 199), Chaper 17, pp [6]. Sumer, B.M. and Fredsøe, J., Wave scour around srucures. Advanced Coasal and Ocean Engineering, Edior Philip, L.-F., Liu, (4), pp [7]. Li, F. and Cheng, L Numerical simulaion of local scour under offshore pipelines. Proceeding of 8h Inernaional Conference on Offshore and Polar Eng., ISOPE`98, ol., pp [8]. Li, F. and Cheng, L., A numerical model for local scour under offshore pipelines. Journal of Hdraulic Engineering, ASCE 15, 4, pp [9]. Li, F. and Cheng, L., 000. Towards predicion ime developmen of local scour around offshore pipelines. Inernaional Smposium on scour of foundaions, The inernaional Socie on Soil Mechanics and Geoechnical Engineering (ISSMEG), Melbourne, Ausralia, pp [10]. Li, F. and Cheng, L., 001. Predicion of lee-wae scouring of pipelines in currens. Journal of Waerwa, Por, Coasal and Ocean Engineering, ASCE 17, pp [11]. Hansen, E. A., Fredsøe, J., and Ye, M Two-dimensional scour below pipelines. Proc. of 5h In. smposium on offshore mechanics and arcic eng, ASCE, New Yor, pp [1]. Leeuwesein, W., Bijer, E. A., 56 Inernaional Journal of Civil Engineering, ol. 3, No. 1, March 005

12 Peerbole, E. B., and Wind, H. G The Naural self burial of submarine pipelines. Proceeding 4h Inernaional Conference on behavior of Offshore srucures (BOSS), Elsevier Science, New Yor, pp [13]. an Bee, F. A., and Wind, H. G Numerical modeling of erosion and sedimenaion around pipelines. Journal of Coasal Engineering. ol. 14, pp [14]. Brørs, B., 1999.Numerical Modeling of Flow and Scour a Pipelines. Journal of Hdraulic Engineering, ol. 15, No. 5, pp [15]. Lee, Y. G., Hong S. W., Kang, K. J., A numerical simulaion of vore moion behind a circular clinder above a horizonal plane boundar. Proceeding of he Fourh Inernaional Offshore and Polar Engineering Conference, Osaa, Japan, ol.3, pp [16]. Bearman, P. W., Zdravovich, M. M., Flow around a circular clinder near a plane boundar. Journal of Fluid Mechanics 89 (1), pp [17]. Lei, C., Cheng, L., Kavanagh, K., 1999a. A finie difference soluion of he shear flow over a circular clinder. Ocean Engineering 7 (3), pp [18]. [18] Lei, C., Cheng, L., Kavanagh, K., 1999b. Reeaminaion of he effec of a plane boundar on force and vore shedding of a circular clinder. Journal of Wind Engineering and Indusrial Aerodnamics 80 (3), pp [19]. Jensen, B. L Large-scale vorices in he wae of a clinder placed near a wall. Proceeding of Second Inernaional conference on laser anemomer-advanced and applicaions, Srahcde, K, pp [0]. Launder, B. E., Spalding, D. B., The numerical compuaion of urbulen flows. Compuer Mehods in Applied Mechanics and Engineering (3), pp [1]. Yeganeh-Bahiar, A., Gooh, H. and Saai, T. 000a. Numerical Sud of he Euler-Lagrange coupling muliphase flow model o he bed-load ranspor a high shear sress. Journal of Hdraulic Research, IAHR, ol. 38, 5, pp []. Grass, A. J., Raven P. W. J., Suar, R. J., Bra, J. A, The influence of boundar laer veloci gradiens and bed proimi on vore shedding from free span pipelines. Journal of Energ Resources Technolog, 106, pp [3]. Beaudan, P. and Moin, P., Numerical eperimens on he flow pas a circular clinder a subcriical Renolds number, Repor No.TF-6, Thermosciences Division, Deparmen of Mechanical Engineering, Sanford niversi, Sanford, California, SA. [4]. Williamson, C. H. K., ore dnamics in he clinder wae. Annual Review of Fluid Mechanics 8, pp [5]. Niemann, H. J., Hölscher, N., A review of recen eperimens on he flow pas circular clinders. Journal of Wind Engineering and Indusrial Aerodnamics 33, pp Inernaional Journal of Civil Engineering, ol. 3, No. 1, March