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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.
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