An engineering based approach for hydraulic computations in river flows S. Di Francesco, C. Biscarini, A. Pierleoni, and P. Manciola Citation: AIP Conference Proceedings 1738, 270012 (2016); View online: https://doi.org/10.1063/1.4952051 View Table of Contents: http://aip.scitation.org/toc/apc/1738/1 Published by the American Institute of Physics An Engineering Based Approach for Hydraulic Computations in River Flows S. Di Francescoa,1, C. Biscarinib, A. Pierleonia and P. Manciolac a b Niccolò Cusano University, Rome, via–don Gnocchi 3, 00166 Rome, Italy UNESCO WATER CHAIR, University for Foreigners of Perugia, Piazza Fortebraccio, 4 06100, Perugia, Italy c DICA, University of Perugia, Via G. Duranti 94, 06125, Perugia, Italy 1 Corresponding Author: silvia.difrancesco@unicusano.it Abstract. This paper presents an engineering based approach for hydraulic risk evaluation. The aim of the research is to identify a criteria for the choice of the simplest and appropriate model to use in different scenarios varying the characteristics of main river channel. The complete flow field, generally expressed in terms of pressure, velocities, accelerations can be described through a three dimensional approach that consider all the flow properties varying in all directions. In many practical applications for river flow studies, however, the greatest changes occur only in two dimensions or even only in one. In these cases the use of simplified approaches can lead to accurate results, with easy to build and faster simulations. The study has been conducted taking in account a dimensionless parameter of channels (ratio of curvature radius and width of the channel (R/B). Keywords: river, curvature, hydraulic model. PACS: 47.60.-I, 47.61.Jd, 47.11- j INTRODUCTION This paper presents a comparison of the simulation results of 1D, 2D and 3D model for flows in meandering channel. The inadequacy of a pure 1D model for the simulation of transient flows in valleys with abrupt changes in direction is a known issue in scientific community: the reflection process is completely ignored, with the consequence that the water level upstream from the bend is by far underestimated [1,2]. Momentum losses occurring in the bends, which are not taken into account by the one-dimensional model, were at the origin of the observed difference between 1D 2Dmodels [3]. 3D models based on continuum mathematical formulations [4,5] or innovative mesoscopic approach [6,7,8,9,10] have been already applied to river flow analyses, but hydraulic engineering projects are often still based on 1D [11] or at least 2D flow equations. Although in general all fluids flow are threedimensionally, in many cases the use of simplified models based on shallow water approaches [12] or Saint Venant equations [13] is allowed. The resultant numerical analyses is then much more simple, with less computational effort. The study has been conducted taking in account the dimensionless parameter of meandering channels (ratio of curvature radius and width of the channel (R/B)). Varying the parameter, the effect of curvature on hydraulic simulations is studied. Simple test cases, well known in literature, have been analysed through the three orders of model and suggestions about the use of simplified models are given. NUMERICAL SIMULATIONS Numerical simulations have been performed through the use of openSource or freeware tools, based on full Navier Stokes (NS) [14], Shallow Water (SWE)[12] and Saint Venant equations (SVE) [13]. The influence of geometric characteristics of channel (curvature an width ) on flow pattern is analysed, trying to define threshold values of R/B that lead to comparable results in 1D, 2D and 3D models. Numerical investigation are carried out starting with a rectilinear channel, with width B = 1m. At the inlet section a constant discharge (1mc/s) is applied, while at the outlet a water surface elevation is specified. At this stage results of 1D e 2D models are the same. The channel geometry is then modified, decreasing the value of curvature radius and the distribution of water surface elevation is studied (Figure 1). International Conference of Numerical Analysis and Applied Mathematics 2015 (ICNAAM 2015) AIP Conf. Proc. 1738, 270012-1–270012-4; doi: 10.1063/1.4952051 Published by AIP Publishing. 978-0-7354-1392-4/$30.00 270012-1 In order to evaluate the geometric characterization (at what R/B value ) that allows to switch from a detailed to a one-dimensional model with sufficient accuracy, the water surface variation along cross section, defined as hsv = %(hs, max –hs, min)/ hmax, as relevant parameter for this study, is considered. 1 (1) H sv R B For a straight channel Hsv =0. Assuming that the motion can be considered 1D if max( hsv , x ) 2 then it is easy to deduce the threshold value of R/B parameter (table 1). 0.72 0.7 0.7 0.68 0.68 0.66 0.66 0.64 0.64 0.62 0.62 0 10 20 X(m) 30 40 0 50 0.72 0.72 0.7 0.7 0.68 0.68 0.66 0.64 0.62 0.62 10 20 X(m) 30 20 X(m) 30 40 20 X(m) 30 40 0.66 0.64 0 10 R/B= 44.8 R/B= 3.7 h (m) h (m) R/B= 10.4 R/B= 3.4 h (m) h (m) 0.72 40 0 10 FIGURE 1. WS elevation in outer (green), internal (black) bank and stream midline (red) TABLE 1. Results of 2D simulations for different values of R/B R 5.850 6.325 7.250 17.740 46.950 76.160 R/B 3.441 3.721 4.265 10.435 27.618 44.800 Δhmean 0.017 0.016 0.013 0.005 0.003 0.001 Δhmax 0.038 0.036 0.035 0.011 0.007 0.003 hmax 0.718 0.705 0.690 0.680 0.682 0.683 Δhmax/hmax 0.053 0.051 0.050 0.015 0.010 0.005 Hsv 5.28 5.11 5.00 1.55 0.95 0.50 Thus, the use of 1D hydraulic model is acceptable if the curvature radius is at least 10 times greater than the width of the channel. This means that at a given transversal section of river reach, water surface elevation is constant throughout the section and flow is 1D. For value of R/B<10 water surface super elevation in external bank is evident, the components of velocity cannot be neglected and the use of 2D-3D model is necessary. Two channels with R/B=3 [15] and R/B=1 [16] are taken in account. The mean characteristics of experimental setups are reported in table 2. 270012-2 TABLE 2. Experimental test cases. Test Case De Vriend Rozoskii Width B (m) 1.7 0.8 Discharge Q (m3/s) 0.180 0.0124 houtlet (m) 0.1953 0.053 Velocity (m/s) 0.542 0.26 Roughness n Manning 0 0.0 For R/B=3 the results of simulations are in good agreement with experimental results (figure 2A). This means that at this stage of curvature the flow is mainly 2D. By increasing the value of curvature, the 3D effects of secondary flows become evident and the 2D modelling is not able to capture the real behaviour of flow. (figure 2B). A B FIGURE 2. Comparison of 2D-3D simulations with experimental data in a normalized channel: A) R/B=3, B) R/B=1. X axis: distance along the channel/total length, Y axis: Water surface elevation (h)/hmax. As evident by simulation results in this case the 2D model has difficulties in reproducing the water “super elevation” in the outer bank. Good results are provided by 3D model as reported in figure and table 3. Distance 4017 5110 6009 6517 6932 7451 8064 8562 9092 10514 TABLE 3: Comparison of experimental and simulated water surface elevation (mm) BANK Survey data 3D model 2D model BANK Survey data 3D model External 58.58 5.858 58.98 Internal 58.58 58.58 External 57.86 58.28 58.59 Internal 57.86 57.82 59.17 59.38 56.7 Internal 55.95 54.67 External External 60.42 60.58 59.5 Internal 53.52 53.53 60.61 60.78 59.51 Internal 52.93 53.27 External External 60.94 61.23 59.45 Internal 53.46 53.29 60.88 60.82 59.19 Internal 53.52 53.52 External External 59.1 59.74 59.04 Internal 54.57 54 56.28 57.61 58.84 Internal 56.28 54.92 External External 56.15 56.66 56.05 Internal 56.15 56.66 2D model 58.98 58.32 54.32 54.1 53.78 53.66 53.33 53.4 58.84 56.04 Numerical simulations carried out suggests the following preliminary considerations for hydraulic simulations in a river channel: if the R/B value is greater than 10, 1D hydraulic model well fit the real behaviour of flow pattern. For R/B in the range (1-10) flow is mainly 2D (velocity and acceleration in the Z-coordinate are almost negligible) and models based on Shallow Water are suitable. For low value of R/B the flow is fully 3D and the adoption of approximate models leads to errors in fluid flow pattern prediction. CONCLUSIONS The present paper addresses a relevant problem in hydraulic engineering: the selection of an appropriate model to undertake river flow routing. The type of flow model may be classified according to the number of spatial 270012-3 dimensions, to flow equations used and numerical system applied. In the present paper, a Saint Venant, a SW and a RANS-VOF model have been tested on different channel geometry characterizations. The capability of different model to correctly simulate free surface simulations has also been verified by comparing numerical results with the experimental data. The study has been conducted taking in account a dimensionless parameter of channels (ratio of curvature radius and width of the channel (R/B)). As result, suggestions of the three order models’ applicability are given. REFERENCES 1. C. Biscarini , Di Francesco S. and Manciola P., CFD modelling approach for dam break flow studies, Hydrology and Earth System Sciences,14,4,705-718, 2010,Copernicus GmbH 2. C. Biscarini., Di Francesco S., Nardi F., & Manciola P., Detailed Simulation of Complex Hydraulic Problems with Macroscopic and Mesoscopic Mathematical Methods, Mathematical Problems in Engineering, 2013. 3. Horritt, M. S., and P. D. Bates. "Evaluation of 1D and 2D numerical models for predicting river flood inundation." Journal of Hydrology 268.1 (2002): 87-99. 4. P. 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