CFD Simulation of Open Channel Flooding Flows and ... - Kostic

Proceedings of the 6th WSEAS International Conference on FLUID MECHANICS (FLUIDS'09)CFD Simulation of Open Channel Flooding Flowsand Scouring Around Bridge StructuresB. D. ADHIKARY, P. MAJUMDAR, and M. KOSTICDepartment of Mechanical EngineeringNorthern Illinois UniversityDeKalb, IL 60115U.S.A.Email: kostic@niu.edu; Web: http://www.kostic.niu.eduAbstract: - Simulation of scour-pit formations under the bridge decks and around the bridge piers, due to sedimentsuspension and transport caused by flooding and pressure flow conditions, is of significant interest nowadays tocomputational fluid dynamics (CFD) and hydraulic researchers. From CFD perspective, analysis of bridge undervarious flooding conditions and impact of the drag and lift forces on it, are necessary to determine bridge stability.This study is focused on the simulation of open channel turbulent flows over inundated bridge deck and evolution ofscour pit under various flooding conditions. Solutions for flow field and turbulence, using a representative bedroughness value, are based on Reynolds Averaged Navier-Stokes (RANS) equations, and turbulence closure modelusing a commercial CFD code. An iterative computational methodology is developed for the evolution of scour-pitprofile using the single-phase slip-flat-top surface with (re)moving boundary formulation, based on an empiricalcorrelation for critical shear stress to characterize initiation of sediment removal. The computational model hasdemonstrated stable and converged solution for the evolution of the scour-pit shape and size using a constant criticalshear stress value. The success of the simulation model can be substantially improved with development of afunctional critical shear stress by taking into account solid-fluid interactions, scour bed profile and slope, as well asmore extensive validation with experimental data.Key-Words: - Bridge structures, CFD simulation, Computational fluid dynamics, Flooding flows, Flow scouring,Turbulence modeling.1. IntroductionDesign and construction of bridges needs reevaluationas it has raised considerable safety concern in recenttimes. Some recent bridge failures increase thisapprehension to such a level that extensive researchwork is going on nation-wide to prevent these kindsof damages. Due to the flood or increased water flow,the downward movements of the bed or an increaseddrag and lift forces on the bridge decks and piers aresome very common reasons for bridge failures.Under the flooded condition, formation of scour-pit atthe water channel bottom weakens the strength of thebridge piers, which eventually damages the bridge.The accurate estimation of this kind of scour dependson the flow field and turbulence conditions, sedimentbed forms, sediment transport and suspensionphenomena, along with the interaction between thesediments and the water. Analysis of scour-pitdevelopment under the bridge decks and around thebridge piers due to sediment transport caused byflooding and pressure flow conditions, is importantfor the design, construction and maintenance ofbridges.Smith [1] presented the modeling technique of acontraction scour around a horizontal stationarycylinder by using two-phase volume-of-fraction(VOF) methodology available in FLOW-3Dcommercial CFD code. Guo [2] adapted the Shields-Rouse equation for the calculation of critical shearstress based on the experimental results and itsapplication to sediment transport. This equationprovides the way to correlate the critical shear stressfor the initiation of sediment movement to thedimensionless sediment diameter. Singh [3]ISSN: 1790-5095 106 ISBN: 978-960-474-40-6

Proceedings of the 6th WSEAS International Conference on FLUID MECHANICS (FLUIDS'09)developed an integrated 2-D numerical sedimenttransport model to simulate the sediment transport inwater medium. Both the suspended load and bed loadhave been taken into account in this study. Camenenet al. [4] proposed a new empirical correlationbetween the roughness height and some of theimportant hydrodynamic and sediment parameters forplane beds, under steady flow conditions. Zhao andFernando [5] performed CFD simulation using Fluentcommercial code for the evolution of scour aroundpipelines, using Eulerian-Eulerian coupled two-phasemodel for fluid and solid phases. They investigatedthe effect of different sediment transport modes, suchas bed-load, suspended-load, and laminated-load, onthe development of scour.The objective of this study is to develop asimulation model to predict the shape and size of ascour-pit under the inundated bridge deck. The scourevolution under a flooded bridge deck due to theaccelerated turbulent flow has been studied and acomputational methodology has been developed usingthe single-phase (re)moving boundary formulation foropen channel flows over flooded bridge deck. This isdone based on the computational fluid dynamicsanalysis of the flow fields around the bridge deck andcomputation of shear stress over the stream scour bedcontour.2. Description of the Physical ProblemIn this section, a description of the physical probleminvolving open channel flow over an inundated bridgedeck, along with all physical parameters ofimportance and range of operating conditions underconsideration, are presented. A schematic of the flowchannel configuration for flow over a six-girderbridge and the bridge dimensions are shown in Fig. 1.The characteristic dimensions, shown in Fig. 1are as follows: hu= water height from free-surface tothe bottom of the channel or channel bed, hb= waterdepth from bridge-bottom to channel-bottom ands = bridge height.This study is primarily concerned with a twodimensional(2-D) model and neglecting the presenceof openings in the bridge-deck side walls.Dimensionless parameters, used to characterizeopen channel flow over an inundated bridge deck, aredescribed below.Froude Number (Fr): The Froude number is animportant parameter that governs characteristics ofthe open channel flow. Froude number is defined asthe ratio of flow velocity to the velocity of freesurfacewave at a particular location. It could beconsidered as a ratio of inertial forces to the gravityforces, and is expressed as:VuFr = (1)gLcWhere, Vu= upstream velocity and Lc=characteristics length for the channel flow.Reynolds Number (Re): The Reynolds number is alsoconsidered as a very important parameter for openchannel flow analysis which defines the level of flowinertia and turbulence, and is the ratio of inertia forcesto the viscous forces, given as:V uDRe = h(2)νWhere, Vu= upstream velocity; Dh= hydraulicdiameter; ν = kinematic viscosity of the water.In calculating the Reynolds number based on theupstream flow, water height ( hu) is considered as thehydraulic radius, resulting in hydraulic diameter Dh=4 h u. For open channel flows the Re numbers areusually very high and flows are turbulent.WV uYsh uZxh bFig. 1: Schematic and characteristic dimensions of the computational domain:water channel with bridge deck modelISSN: 1790-5095 107 ISBN: 978-960-474-40-6

Proceedings of the 6th WSEAS International Conference on FLUID MECHANICS (FLUIDS'09)Inlet velocity, thus, the mass flow-rate, isassigned as a boundary condition, whereas the socalled standard outlet boundary condition is assumed.He AMG solver is used here in an iterative way tocalculate the minimum mass, velocity and pressureresiduals. As only 2-D simulations have beenperformed so far in this research, requiring only onecell thickness along the third Z-direction, the frontand rear wall of the computational domain have beentaken as the symmetry boundary walls, since theSTAR-CD code is based on the 3-D simulationconcept and does not have special 2-D mode. For allthe simulations presented in this study, the inlet isdefined as the velocity inlet; the outlet condition hasbeen set as the standard outlet which indicates theconstant pressure gradient in flow direction at theoutlet. The top wall is defined as the slip-wall tosimulate the free-surface open-channel flow, whereasthe bottom wall is the no-slip boundary.In this study an iterative procedure is used toestablish the appropriate fully-developed inletvelocity profile and turbulence conditions. Theiterative procedure starts with an average uniformvelocity and specified turbulence conditions at theinlet and ends with determination of the (fully)established exit velocity profile and turbulenceconditions. The process is repeated until the solutionis converged. These exit profiles are then used as inletconditions in the subsequent iterations.3.2. Computational Methodology for the Evolutionof Scour ProfileAs stated above, the scouring computationalmethodology is based on the fact that the scouring isdue to induced local shearing stresses at the sedimentsurface, thus requiring the CFD analysis of the flowfield around the bridge deck and computation of shearstress over the bed contour. An iterativecomputational methodology is developed forevolution of scour-pit profile using the single-phaseturbulent flow modeling (based on a representativebed roughness value) with slip-flat-top surface, by(re)moving boundary formulation and use of anempirical correlation for critical shear stress tocharacterize initiation of sediment removal. Use ofsuch a correlation significantly simplifies themathematical and computational difficultiesassociated with such a two-phase fluid-solid coupledtransport process. One of the main challenges is todevelop the apparent critical-scouring shearing stresscorrelations to account for all the complexities ofsolid material resistance to flow scouring. Additionalconsideration must me given to the characterization ofthe scour-bed surface roughness, which dependsconsiderably on the type of bed forms and flowconditions.3.3. Empirical Correlation for Critical Shear Stressat Channel Bottom:In general, the apparent critical shearing stress is notconstant, but a local function of other flow-andmaterialproperties, like fluid-solid surfaceinteractions, downgrade and upgrade slope scouring,where gravity has opposite contribution to grainremoval and deposition, for example. Additionalconsideration must be given to the characterization ofthe scour-bed surface roughness, as stated above.However, since such a correlation depends on numberof key parameters, such as, fluid and sedimentparticle’s type and size, type of obstacles, and flowcondition, it has to be determined by experiments fora specific application [6].A comprehensive review of various approaches tofind out the critical shear stress at the bottom wall ofan open channel flow, is given by Singh [3]. One ofthe critical shear stress correlations for sedimenttransport used in this simulation study is given byGuo [2], and is based on the Shields-Rouse equationwith fitted parameters to match existing experimentaldata, i.e.:τc0.850.23 ⎡ ⎛ d ⎞⎤= + 0.054⎢1− exp⎜−*⎟⎣(4)density of sediment; g = acceleration( ρ − ) ⎜ ⎟⎢ ⎝ 23 ⎠⎥ ⎥ sρ gd50d*⎦Where, ρs=due to gravity; d50 = median size of the bedsediment;d*= d50⎡⎢⎣τ c*uc= critical velocity; and;ρ( ρ ρ −1)s2νg⎤⎥⎦1 3= dimensionless diameter(5)Our computational methodology is developed andimplemented based on a constant critical shear stressvalue which is estimated using the above correlationfor shear stress value over a bottom boundary surface.ISSN: 1790-5095 109 ISBN: 978-960-474-40-6

Proceedings of the 6th WSEAS International Conference on FLUID MECHANICS (FLUIDS'09)(a)(b)(c)Fig. 3: Scour formation: white box represents flooded bridge, while black area is fluidcomputational domain with scouring at the bottom, layer-by-layer.From top-down: after (a) 5 iterations, (b) 10 iterations, and (c) 24 iterations.is represented by a smoother scoured bottomgeometry using a spline interpolation function. Thenew bed geometry contour is re-meshed, and thesimulation is repeated to determine a new bed shearstress distribution.Initial sets of results are obtained by removing thebottom boundary with layers of 2 mm thickness (4-cell thick layer with a cell size of 0.5 mm). Figure 3shows iterative evolution of scour-pit profile atseveral selected iterations, while Fig. 4 shows thecorresponding shear stress distribution, including thescour-pit surface.Results show continuous decrease in shear stressdistribution with the evolving scour bottom surfacewith increasing number of iterations. The scour shapeand size reach a steady equilibrium state by about 24iterations. As shown, the local shear stress values atthe scoured surface are reduced progressively as thescour-pit deepens with iterations and reaches belowthe critical shear stress value of 0.58 N/m 2 . In thescour-pit surface regions near the sharp corners edges,a considerable jumps and discontinuities can beobserved. This is primarily caused by sharp corners ofthe stair-case-like scour-bottom geometry. This is nota physical phenomenon, but rather, they are purelycomputational artifacts and may lead to themisleading conclusion that scour profile andmaximum scour depth have not reached anequilibrium state. This discrepancy can be eliminatedby making the scoured bottom smoother, using thespline interpolation function to replace the stair-casescour-pit profile obtained after each iteration step.This procedure is currently being implemented. Otherimportant factors, that may cause errors in thesimulation results, are the selection of bed roughnessvalues and the assumption of constant critical shearstress values at the scoured surface. Further workaims to improve the simulation model by evaluatingresults with additional experimental data andimplementing more realistic representative bedroughness.ISSN: 1790-5095 111 ISBN: 978-960-474-40-6

Proceedings of the 6th WSEAS International Conference on FLUID MECHANICS (FLUIDS'09)(a)(b)Fig. 4: Shear stress distribution along bottom boundary at different iterations:(a) along the bottom of whole domain, and (b) along the scoured bottom.5. ConclusionsAn iterative computational methodology is developedfor the evolution of scour-pit profile using the singlephaseturbulent flow model with (re)movingboundary formulation by means of an empiricalcorrelation for critical shear stress and using arepresentative bed roughness value. The simulationmodel is based on the computational fluid dynamicssolution for velocity, stresses and turbulence flowISSN: 1790-5095 112 ISBN: 978-960-474-40-6

Proceedings of the 6th WSEAS International Conference on FLUID MECHANICS (FLUIDS'09)fields, and resulting stresses around the bridge deckand flow bottom surface. The single-phase, slip-flattopsteady-state model was chosen over the transientVOF two-phase model, considering improvedstability and convergence, and shorter computationaltime, while achieving similar accuracy of obtainedresults. The computational model demonstrated stableand converged solutions for the evolution of thescour-pit shape and size using a constant, empiricalcritical-shear-stress value. Use of the constant criticalshear stress value over the entire scour pit rather thanthe functional critical shear stress profile is one of themain deficiencies of this methodology. Additionally,there is considerable uncertainty in the use of therepresentative bed roughness value. Further numericalstudies need to be performed to optimize criticalsimulation parameters while validating the resultswith available experimental data.Acknowledgments:The authors like to acknowledge support by DeanPromod Vohra, College of Engineering andEngineering Technology of Northern IllinoisUniversity (NIU), and Dr. David P. Weber ofArgonne National Laboratory (ANL); and especiallythe contributions by Dr. Tanju Sofu, and Dr. StevenA. Lottes of ANL, as well as financial support byU.S. Department of Transportation (USDOT) andcomputational support by ANL’s TransportationResearch and Analysis Computing Center (TRACC).References:[1] Smith, Heather D., Modeling the flow and scouraround an immovable cylinder, M.S. Thesis, OhioState University, 2004.[2] Guo, J., Hunter Rouse and Shields Diagram,Advances in Hydraulic and Water Engineering,Vol. 2, 2002, pp. 1096-1098.[3] Singh, Vikas, Two dimensional sedimenttransport model using parallel computers, M.S.Thesis, Banaras Hindu University, 2005.[4] Camenen, Benoit, Bayram, Atilla, Larson,Magnus, Equivalent Roughness Height for PlaneBed under Steady Flow, Journal of HydraulicEngineering, Vol. 132, No. 11, November 1,2006.[5] Zhao, Zhihe, Fernedo, H. J. S., NumericalSimulation of Scour around Pipelines Using anEulerian-Eulerian Coupled Two-phase Model,Journal of Fluid Mechanics, Vol. 7, 2007, pp.121-142.[6] Van Rijn, L. C., Sediment transport I: Bed loadtransport, Journal of Hydraulic Engineering, Vol.110, No. 10, 1984, pp. 1431-1456.[7] Adhikary, B. D., Flow and Pressure ScourAnalysis of an Open Channel Flow Having anInundated Bridge Deck Under Various FloodingCondition, M. S. Thesis, Northern IllinoisUniversity, 2008.ISSN: 1790-5095 113 ISBN: 978-960-474-40-6