Numerical investigation of the turbulent flow around a bridge abutment

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1 River Flow 2006 Ferreira, Alves, Leal & Cardoso (eds) 2006 Taylor & Francis Group, London, ISBN Numerical investigation of the turbulent flow around a bridge abutment A. Teruzzi & F. Ballio Politecnico di Milano, Milano, Italy S. Salon OGS, Trieste, Italy V. Armenio Università degli studi di Trieste, Trieste, Italy ABSTRACT: Bridge failures are frequently related to phenomena of local erosion at piers and abutments; literature on this topic does not provide fully satisfactory formulations to evaluate the scour depth. Since a detailed definition of the flow can improve the comprehension of the phenomenon, a numerical study on the turbulent flow around an obstacle archetypal of an abutment is presented. The turbulent flow characteristics are investigated by means of Large Eddy Simulation, obtaining results both on the averaged flow characteristics as on the instantaneous ones. The averaged flow around the obstacle is structured as a highly three-dimensional system of vortex structures; instantaneous structures are characterized by high vortex intermittency. The shear and normal stress distributions on the bottom-wall are analyzed in comparison with experimental observations relative to erosion phenomena. The numerical simulations are consistent with experimental observations on flow characteristics around an abutment in flat-bed condition and provide details on its three-dimensional features and instantaneous behavior. 1 INTRODUCTION As documented in literature works (see for example Cardoso & Bettess 1999) local scour at piers or abutments is one of the most frequent cause of bridge failure. The erosion phenomenon is the result of the interaction between a complex three-dimensional turbulent flow and the river bed; since the definition of the flow features can improve the comprehension of the localized erosion phenomenon, in this work a study on the flow around an obstacle archetypal of an abutment is presented. Several literature works on erosion problems propose various parametric formulas to evaluate maximum scour depth at bridge piers or abutments (see Melville & Coleman 2000 and literature therein cited), but the resulting values from the different formulations are very scattered, as showed in Cardoso & Bettes (1999), and therefore not really satisfactory in bridge design. In order to explain the dependency of the scour depth from the control parameters of the system, a comprehension of the erosion mechanism (the sediment-flow interaction) at the sediment scale could be useful. For such an approach it is relevant to define the flow field characteristics (in terms of velocities, vortexes, stresses, etc.) and the associated sediments motion features (as velocities, directions, mass-rate intensities, etc.). In this work the turbulent flow characteristic aspects are investigated, and particularly a Large Eddy Simulation study of the turbulent flow around a trapezoidal obstacle on a flat-bed is presented. Examples of literature experimental results for similar configurations can be found in Ahmed & Rajaratnam (2000) and in Barbhuiya & Dey (2003) with flat-bed condition and with developed scour hole respectively. The literature results from experiments around abutments are averaged in time and do not describe the turbulent nature of the flow. A general description of the principal (averaged) vortex structures can be found in Melville & Coleman (2000), where the principal vortex is identified as the main responsible for the erosion process. Numerical and experimental results of a turbulent flow field around an abutment in flat-bed configuration are presented in Chrisohoides et al. (2003) where a URANS model is used for numerical simulations. Their results are consistent with the description of an highly three-dimensional flow near the abutment, recognizing a complex system of multiple vortexes in front of the obstacle. 667

2 In this work the LES technique permits to define in details both the averaged flow characteristics as well as the instantaneous ones for the flow field around a trapezoidal obstacle; the attention is particularly focused on the area in front of the obstacle, correspondent to the region where the maximum scour depth is observed in erosion experiments. Results describing the three-dimensional flow structures are presented, as well as the shear and normal stress patterns on the walls. The latter variables are directly correlated to the scour process, and are therefore analyzed in comparison with observations of erosion experiments. 2 NUMERICAL MODEL The turbulent flow results presented in this work are obtained by means of Large Eddy Simulations (LES). LES method is intermediate between RANS and DNS; it resolves the large, energy carrying scales and models the dissipative small ones, supposed isotropic. The SGS stresses are evaluated by the generalized coordinates dynamic Lagrangian mixed model proposed in Armenio & Piomelli (2000), which in Cartesian frameworks can be written as: where the overbar indicates the filtering operation, ū are the velocity resolved components, S ij is the resolved strain-rate tensor, is a term related to the filtering dimension and C is the model coefficient. The first two terms and the last one in (1) represent respectively the scale similar (Bardina et al. 1980) and the eddy viscosity part (Smagorinsky 1963). In the used dynamic Lagrangian model the coefficient C is evaluated during the simulation, using the energy content of the small resolved scales (Germano et al. 1991), and averaged over flow path lines (Menevau et al. 1996), since in the presented geometry there is not homogeneity directions over which averaging can be operated. Particulars on the model implementation, specifically on the formulation in curvilinear coordinates, can be found in Armenio & Piomelli (2000). 3 GEOMETRY AND PARAMETERS The numerical simulations are carried out in a duct with rectangular cross-section and a near wall trapezoidal obstacle (representing an abutment). A sketch of the duct and obstacle geometry and of the coordinate system is presented in Figure 1. With reference to quantities indicated in Figure 1, the duct and obstacle dimension are: B = 2.5 h, L = 13.5 h, b = 0.5 h, and α = 45. The Large Eddy Simulations are carried out setting no-slip boundary condition on the duct and obstacle Figure 1. Sketch of duct geometry and coordinate system (not in scale). walls; the inlet condition is a series of cross-section velocity fields previously obtained from a developed and constant mass-rate turbulent flow in a straight rectangular duct, with same dimensions and flowrate of the present case, but without the obstacle. The Reynolds number based on the duct height and bulk velocity at the inlet cross-section is equal to The number of grid points is respectively in the x-, y- and z-direction. The grid points are clustered in the y- and z-direction near the walls in order to assure that the viscous sub-layer is directly resolved; moreover the grid spacing along the x-direction is reduced in the obstacle region, since the complexity of the flow field in this area requires a higher definition. The simulations are carried out with a constant time step corresponding to a Courant number close to 0.4. The mean quantities presented in section 4 are obtained by averaging on about 10 large eddy turn over time (LETOT) and over the two symmetric parts of the duct separated by the (x, z) half height plane, therefore all the averaged results are defined on the half duct. 4 RESULTS 4.1 Flow field around the obstacle The numerical simulations allow the definition of the flow field around the trapezoidal obstacle in detail, and specifically to obtain information on its complex three-dimensional and turbulent characteristics. The vortex structures are identified for the instantaneous and mean flow fields by the Q-criterion. In Figure 2 the results obtained for the averaged flow show a system of vortices in front of the obstacle and the vortex sheet detaching from the edge of the obstacle. Upstream the obstacle different structures can be identified: a corner vortex (indicated with I), with axis parallel to the y-direction, which is bended horizontally in proximity of the bottom wall and eventually joined to a horizontal vortex (II), thus creating a big structure rounding the obstacle (III), parallel to the (x, z)-wall; finally, a longitudinal vortex can 668

3 Figure 2. Vortex structures of the averaged flow (half duct). Figure 4. Sketch of topology (half duct). Figure 3. Stream-traces of the averaged flow on the (x, y)- and (x, z)-wall (half duct). be observed in the corner between the (x, y)- and (x, z)-wall (IV). In Figure 2 the directions of the vorticity vectors associated to the described structures are qualitatively shown. More details on the three-dimensional structures are provided by the shear stress traces on the walls. Figure 3 shows the stream-traces of the averaged flow on the (x, y)- and (x, z)-wall, revealing the flow topology resulting from the interaction between the incoming boundary layer and the adverse pressure gradient due to the obstacle. The averaged flow is probably affected by not fully developed statistics, since nonzero velocity component v on the symmetry plane are present. An enlarged schematic of shear lines topology is shown in Figure 4. The trace of the circulation in front of the obstacle due to the (main) horizontal vortex II is clearly detectable on the (x, y)-wall (focus/node C). On the upstream wall of the obstacle an attachment line exits from node B directed vertically downwards; it eventually continues upstream on the bottom, connecting node B to the saddle A. Node B, as well as its counterpart on the lateral wall, i.e. the saddle D, are the direct consequence of the presence of vertical vortex I. Notice that saddle D should lay on the symmetry plane: we already discussed that the incomplete symmetry of the flow is due to incomplete convergence of the mean values. The singular attachment line B-A (and its continuation A-C, partially not visible in the figures) delimitates the domain where the flow is pushed towards the lateral vertical wall by the vortices I and IV, while the outer streamlines directly follow the main path around the obstacle. Fluid particles within the inner domain enters either vortex I or vortex II, and are consequently transported in the outer region where the two vortices merge together and are stretched by the main flow. The vortex sheet detaching from the abutment edge is basically two-dimensional, coherent with a 2D separation reattachment pattern. The averaged flow results are coherent with classics literature schemes about flow around abutments, but add details in the description of the backflow in front of the obstacle, particularly on the near (x, y)- wall region (not experimentally easy to investigate). Indeed the corner vortices I and IV, associated to the specific topology of this flow, are a distinguishing element with respect to the flow over symmetrical bodies (see for example results around bridge piers). The analysis of the instantaneous values can provide significant additional information to be considered for the comprehension of the sediment-fluid interaction; indeed the river bed sediments interact with the intermittent turbulent flow, which characteristics are not necessarily revealed by the averaged features. The instantaneous stream-traces on the walls near the obstacle give qualitative information on the instantaneous flow, particularly they reveal that some highlighted elements of the mean flow are permanent in the instantaneous one, while others are very intermittent. On the (x, y)-wall the instantaneous flow fields are very complex and, as expected, there is not symmetry with respect to the duct center plane, so the flow topology is not easily readable and referable to the main characteristics highlighted in the averaged flow. On the (x, z)-wall the saddle is not easily recognizable and very intermittent in time and position. Figure 5a, b show an example of instantaneous stream-traces respectively on the (x, y)- and (x, z)-wall 669

4 Figure 5. Instantaneous stream-traces: a) on the (x, y)-wall, b) on the (x, z)-wall (half duct). (only the half part of the (x, y)-wall is reproduced).the position of the described singular points in the averaged flow are indicated, to highlight the differences between instantaneous and averaged topology. In the instantaneous fields, the vortex system is quite different from the averaged one (see some examples of instantaneous vortexes in front of the obstacle in Fig. 6); several elongated vortexes in the flow direction can be recognized in all the analyzed time steps, while a very intermittent corner structure parallel to the y-axis is sometime present (see Fig. 6b). Typical detaching rolls are always recognizable at the obstacle edge, while the upstream vortex organization change significantly in time, see Figure 6a, b, c. The evolution in time of the topological features and the differences between instantaneous and averaged flow emphasize the complexity in time and space of the flow obtained from simulations, which is representative of the one interacting with sediments around an abutment. 4.2 Stresses Large Eddy Simulations of this study are representative of the flow around an abutment in a flat-bed river, that is at the beginning of the scour processs. In Oliveto & Hager (2002) the scour maximum depth evolution in time is analyzed; the authors observe that at abutments the scour starts at the edge of the obstacle, progressively moving towards the vertical wall as scour develops, so that the erosion process tends to Figure 6. duct). Examples of instantaneous vortex structures (half interest all the region upstream the abutment. Similar consideration were made in Teruzzi (2002). The experimental works of Molinas et al. (1998) and of Rajaratnam & Nwachukwu (1983) indicate that the maximum shear stress at the bed lies near the abutment edge. In the numerical simulations of Chrisohodes et al. (2003) the maximum shear velocity is localized in a similar position (they used an abutment geometry without edge). The averaged results of stress distribution near the obstacle on the (x, z)-wall are presented in Figures 7, 8 and 9. Figure 7 shows the time-averaged shear stress module on the (x, z)-wall divided by τ, that is the mean shear stress in a straight duct with same dimension and Reynolds number of the present one; upstream and to the side of the obstacle there is a large region with shear stress higher than 3 τ, with a maximum of about 13 τ at the obstacle. Results of Figure 7 indicate that the region where the shear stresses exceed the mean value of the far field is concentrated in the edge region and in the wake, while no stress amplification is detectable in the proximity of the vertical wall. In a situation where the mean 670

5 Figure 7. Averaged shear stress module on the (x, z)-wall, normalized by τ. Figure 10. Shear stress module rms, normalized by τ Figure 8. by τ. Averaged pressure on the (x, z)-wall, normalized Figure 9. Averaged pressure gradient along the y-axis, normalized by τ and h (dashed lines when negative). value τ is close to the incipient condition for grain motion, this result would indicate that the sediment motion could commence at the abutment edge (consistently with literature observation) but at the same time that no sediment transport and therefore no scour could be expected close to the vertical wall. The mean Figure 11. Variation coefficient of shear stress module. shears are not able to explain the experimental experience of authors, which indicates that in the first instant of scour some sediment motion can be observed in the corner region. The pressure distribution can play a role in the erosion process; in Figures 8 and 9 the normalized averaged pressure and its gradient along y-direction on the (x, z)-wall are respectively presented. The pressure minimum in Figure 8 lies at the obstacle edge, coherently with the maximum shear in this position. Maximum pressure values are positioned on the vertical wall, in front of the abutment, as a result of the blocking effect of the obstacle. It is possible that the pressure gradient can be an additional active factor for the scour process in the proximity of the edge, but this is hardly true in proximity of the vertical wall. In this area, however, the averaged vertical pressure gradient (Fig. 9) is particularly intense, so that, depending on the grain size, an uplift pressure effect can play a significant role on particle entrainment. Due to the turbulent character of the flow, a relevant role in the erosion is played by the instantaneous quantities, specifically by the instantaneous shear stresses; indeed, in regions where the averaged shear stress module does not exceed the (average) critical value, grain 671

6 movements can be explained by fluctuating components, which as indicated by statistics are higher than those of a flow over the standard plane-bed configuration for which incipient motion conditions are defined. From the detailed data of the Large Eddy Simulations it is possible to obtain τ, the rms of the shear stress module on the (x, z)-wall, which is showed in Fig. 10, normalized by τ. In Figure 11 the variation coefficient is plotted, where τ values are normalized versus the local mean stress. Values of τ have the same order of magnitude of τ, with maxima of about 1.5 τ along the upstream face of the abutment; highest values of variation coefficient can be observed upstream the obstacle (in the corner and near the separation) revealing region where the instantaneous fluctuations of the shear stress module are of the same order of magnitude than the averaged ones. On the contrary near the obstacle edge the fluctuating terms are about 10% of the averaged shear stresses. Results for the fluctuating components of shear stresses together with those for vertical pressure gradients may explain the erosion capacity of the flow field in the corner region, where mean shear stresses do not exceed those in the far field; on the contrary, for flat-bed conditions (beginning of the erosion process), mean shear values can be easily pointed as the prevailing scour agent in the edge region, coherently with previous literature observations. 5 CONCLUSIONS In this work a Large Eddy Simulation study of the turbulent flow around an obstacle, archetypal of a bridge abutment, is presented, with aim to improve knowledge on the local scour phenomenon. Data from numerical simulations enables a detailed description of the turbulent flow field and stresses in the near obstacle region. The flow field results are consistent with previous literature description of a complex highly threedimensional system of vortex structures in front of the abutment. The instantaneous flow field analysis reveals high intermittency of the flow field characteristics and particularly of the flow structures organization in front of the obstacle. Maximum mean shear stress values are concentrated in a relatively small area at the abutment upstream edge, where the maximum scour capacity is typically located. Mean values alone are presumably not sufficient to explain the scour capacity in the corner region, close to the vertical wall: in this area fluctuating components as well as local pressure gradients may have an important role, so that standard sediment-fluid interaction models (incipient motion thresholds and transport equation) may be inadequate to describe the phenomenon. The coherence of our results with observations from flume experiments gives value to the hypothesis that the studied flow field is representative of the phenomenon in spite of the wall boundary condition on the upper surface. REFERENCES Ahmed, F. & Rajaratnam, N Observations on flow around bridge abutment. Journal of Engineering Mechanics 126(1): Armenio, V. & Piomelli, U A Lagrangian mixed subgrid-scale model in generalized coordinates. Flow, Turbulence and Combustion 65: Barbhuya, A.K. & Dey, S Vortex flow field in a scour hole around abutments. International Journal of Sediment Research 18(4): Bardina, J., Ferziger, J.H. & Reynolds, W.C Improved subgrid scale models for large eddy simulation. AIAA paper, 13th Fluid and Plasma Dynamics Conference, Snowmass, July New York: AIAA. Cardoso, A.H. & Bettess, R Effects of time and channel geometry on scour at bridge abutments. Journal of Hydraulic Engineering 125(4): Chrisohoides, A., Sotiropoulos, F. & Sturm, T.W Coherent structures in flat-bed abutment flow: computational fluid dynamics simulations and experiments. Journal of Hydraulic Engineering 129(3): Germano, M., Piomelli, U., Moin, P. & Vabot, W.H A dynamic subgrid-scale eddy viscosity model. Physics of Fluids A 3(7): Melville, B.W. & Coleman, S.E Bridge scour. Highlands Ranch, Colorado: Water Resources Publications. Menevau, C., Lund, T.S. & Cabot, W.H A Lagrangian dynamic subgrid-scale model of turbulence. Journal of Fluid Mechanics 319: Molinas, A., Kheireldin, K. & Wu, B Shear stress around vertical wall abutments. Journal of Hydraulic Engineering 124(8): Oliveto, G. & Hager, W.H Temporal evolution of clear-water pier and abutment scour. Journal of Hydraulic Engineering 128(9): Rajaratnam, N. & Nwachukwu, B.A Flow near groinlike structures. Journal of Hydraulic Engineering 109(3): Smagorinsky, J General circulation experiments with the primitive equations. I. The basic experiment. Monthly Weather Review Teruzzi, A Erosione localizzata e generalizzata in corrispondenza delle spalle dei ponti. Studio sperimentale. Degree thesis, Politecnico di Milano. 672