Gilles Belaud

Experimental and Numerical Investigation of Flow under Sluice Gates

AbstractThe flow characteristics upstream and downstream of sluice gates are studied experimentally and numerically using Reynolds averaged Navier-Stokes two-dimensional simulations with a volume of fluid method. Special attention was brought to large opening and submergence, a frequent situation in distribution canals that is little seldom addressed in the literature. Experimental results obtained by ADV measurements provide mean velocity distributions and turbulence characteristics. The flow is shown to be mostly two-dimensional. Velocity fields were simulated using renormalization group k-epsilon and Reynolds stress model turbulence models, leading to an estimation of energy and momentum correction coefficients, head loss, and bed friction. The contraction coefficient is also shown to increase with gate opening at large submergence, which is consistent with the energy-momentum balance. This result can be used to derive accurate discharge equations.

Calculation of Contraction Coefficient under Sluice Gates and Application to Discharge Measurement

The contraction coefficient under sluice gates on flat beds is studied for both free flow and submerged conditions based on the principle of momentum conservation, relying on an analytical determination of the pressure force exerted on the upstream face of the gate together with the energy equation. The contraction coefficient varies with the relative gate opening and the relative submergence, especially at large gate openings. The contraction coefficient may be similar in submerged flow and free flow at small openings but not at large openings, as shown by some experimental results. An application to discharge measurement is also presented.

Irrigated Grassland Monitoring Using a Time Series of TerraSAR-X and COSMO-SkyMed X-Band SAR Data

The objective of this study was to analyze the sensitivity of radar signals in the X-band in irrigated grassland conditions. The backscattered radar signals were analyzed according to soil moisture and vegetation parameters using linear regression models. A time series of radar (TerraSAR-X and COSMO-SkyMed) and optical (SPOT and LANDSAT) images was acquired at a high temporal frequency in 2013 over a small agricultural region in southeastern France. Ground measurements were conducted simultaneously with the satellite data acquisitions during several grassland growing cycles to monitor the evolution of the soil and vegetation characteristics. The comparison between the Normalized Difference Vegetation Index (NDVI) computed from optical images and the in situ Leaf Area Index (LAI) showed a logarithmic relationship with a greater scattering for the dates corresponding to vegetation well developed before the harvest. The correlation between the NDVI and the vegetation parameters (LAI, vegetation height, biomass, and vegetation water content) was high at the beginning of the growth cycle. This correlation became insensitive at a certain threshold corresponding to high vegetation (LAI ~2.5 m2/m2). Results showed that the radar signal depends on variations in soil moisture, with a higher sensitivity to soil moisture for biomass lower than 1 kg/m². HH and HV polarizations had approximately similar sensitivities to soil moisture. The penetration depth of the radar wave in the X-band was high, even for dense and high vegetation; flooded areas were visible in the images with higher detection potential in HH polarization than in HV polarization, even for vegetation heights reaching 1 m. Lower sensitivity was observed at the X-band between the radar signal and the vegetation parameters with very limited potential of the X-band to monitor grassland growth. These results showed that it is possible to track gravity irrigation and soil moisture variations from SAR X-band images acquired at high spatial resolution (an incidence angle near 30°).

Closed-form solution of the potential flow in a contracted flume

The potential flow upstream from a contraction in a rectangular flume is analysed. In order to calculate the potential function, the flow is considered as the superposition of sinks uniformly distributed in the contraction. The effect of boundaries is taken into account by introducing virtual sinks. The calculation is performed in the complex plane and provides a closed-form solution of the complex potential function. As an illustration, the effect of contraction size and position is analysed, and the solution is compared to experimental measurements and other numerical solutions for vertical sluice gates.

Discussion of “Revisiting the Energy-Momentum Method for Rating Vertical Sluice Gates under Submerged Flow Conditions” by Oscar Castro-Orgaz, Luciano Mateos, and Subhasish Dey

The discussers really appreciated the efforts to make more solid some usual assumptions used to derive reliable stage-discharge relationships, and the confrontation with field measurements. Energy and momentum equations are generally applied in their standard form, as presented in most hydraulic engineering books. The authors are right to point out that some of these assumptions are simplistic, which introduces biases in the derived relationships. Velocity distribution is one of these assumptions, and trying to improve this distribution is commendable. Head loss is another crucial issue, especially for submerged gates where the presence of the roller above the jet induced large dissipation. The authors also neglected the friction forces and assumed that contraction coefficient (Cc) is the same in submerged flow as in free flow. This assumption was questioned by Henderson (1989), and Belaud et al. (2009) showed how to derive a continuous relationship for Cc between low submergence (Cc about 0.61) and fully open gate (Cc ¼ 1). For submerged gates, there have been a limited number of experimental studies that explored the validity of the most sensitive assumptions. Compared to free flow, much more phenomena need to be quantified, such as head loss due to jet–roller interaction, velocity distributions at the contracted section and downstream measuring section, friction forces between these two sections. The effect of submergence introduces another dimension when trying to elaborate generic relationships. As the practical objectives are to obtain accurate discharge predictions, a common approach is to calibrate corrections using measured discharges, water levels, and openings. This may not be sufficient to validate physically based improvements since several phenomena compensate for each other. The pioneer experimental works used by the authors provided very useful data sets to perform this analysis. This discussion is based on recent experimental and numerical results presented by Cassan and Belaud (2012). Experiments used acoustic Doppler velocimetry at selected locations, for three configurations in free flow and three in submerged flow. Computational fluid dynamics was used in complement, with the objective to interpolate flow characteristics between measuring points and to explore other configurations than those measured. Experiments were essential to verify the validity of the numerical results, based on Reynolds–Average Navier–Stokes simulations with the volume-of-fluid method and Reynolds stress model as turbulence closure model. Notations are those of the discussed paper.

Signal Level Comparison Between TerraSAR-X and COSMO-SkyMed SAR Sensors

Soil and vegetation biophysical parameter retrieval using synthetic-aperture-radar images requires radiometrically well-calibrated sensors. In this letter, a comparison of signal levels between TerraSAR-X (TSX) and the COSMO-SkyMed (CSK) constellation (CSK1, CSK2, CSK3, and CSK4) was carried out in order to analyze the ability to use jointly all current X-band sensors. The analysis of the X-band signal over forest stands showed a stable signal (variation lower than 1 dB) over time for each of the studied sensors, but a significant difference was observed between the different X-band sensors. Differences between radar signals were higher in HH than in HV polarization. TSX and CSK4 showed similar backscatter signals, with signal level differences of 0.6 dB in HH and 1.4 dB in HV. The CSK3 signal was observed to be lower than those from TSX and CSK4 by about 2.1 dB and 1.5 dB in HH against 3.2 dB and 1.8 dB in HV, respectively. Moreover, CSK2 and CSK1 which showed slightly different backscatter signals (within 1.1 dB in HH and 1.9 dB in HV) had signal levels lower than those obtained from TSX (2.2-3.3 dB in HH and 3.2-5.1 dB in HV for about 29° incidence angle). These results show that it is currently difficult to use jointly the available X-band satellites (CSK and TSX) for estimating the biophysical parameters of soil or vegetation. This is due to the significant difference in the radar signal level between some of the analyzed satellites, which will cause a high overor underestimation of biophysical parameters.

Simulation study on the influence of roughness on the downstream automatic control of an irrigation canal

AbstractThe controllability of an irrigation canal depends on its physical characteristics, on the control algorithm used, and on the actual condition of the canal in relation to the algorithm tuning conditions. The flow conditions and controllability in an irrigation canal may change if the hydraulic friction changes. Great variations in friction were observed in an irrigation canal in Spain owing to the presence of Rhizoclonium hieroglyphicum, a type of algae that grows in clear water. Such large variations in friction may have a significant effect on the stability and performance of automatic canal controllers. Using the unsteady-state model Simulation of Irrigation Canal (SIC), the influence of roughness on the performance of the study canal under distant downstream control of its four coupled pools was investigated. A set of proportional-integral (PI) controllers was tuned for different values of Mannings n. The controller’s performance under real conditions is sensitive to the roughness conditions ...

ASSIMILATION OF DISCHARGE DATA INTO SEMI-DISTRIBUTED CATCHMENT MODELS FOR SHORT TERM FLOW FORECASTING: CASE STUDY OF THE SEINE RIVER BASIN

This study addresses the sensitivity of short-term flow forecasting in the Seine River basin (43,800 km2, France) to the spatial distribution using a semi-distributed model (Transfer with GR, TGR). The basin was decomposed into intermediate basins depending on the gauging stations selected for this study. A lumped hydrological model was applied on each intermediate basin and a routing model was used to propagate the discharge through the river network. Discharge data at the gauging stations were assimilated using a Kalman filter and tests for flow forecasting were performed with a lead time up to 72 h. Several spatial configurations, defined by a selection of one or several gauging stations, were tested and the performances were compared to a reference lumped model currently used operationally by the regional flood forecasting centre. Results showed that the forecasting performance improves with an increase in the degree of spatialization. Nevertheless this improvement was not systematic and the integration of some particular gauging stations degraded the model performance. In addition, it was shown that integrating some other stations (generally the most upstream) led to a negligible improvement. This suggests that in an operational context, where the model has to be robust and computationally efficient, some efforts should focus on finding the optimal spatial distribution, which is not necessarily the one using all the available stations.

Closed-form Expression of the Response-Time of an Open-Channel

Computing accurately the response time of an open channel is of extreme importance for management operations on canal networks, such as feed-forward control problems. The methods proposed in the literature to approximate the response time do not always account for the influence of a cross structure at the downstream end of a canal pool, which may have a significant impact on the response time. This paper proposes a new approach to compute the response time, accounting explicitly for the backwater and the feedback effects due to the downstream cross structure. The method provides a distributed analytical expression of the response time as a function of the characteristics of the canal (geometry, roughness) and of the downstream cross structure. A test canal with a weir or a gate at the downstream end is used to compare the new method with some of the others. Results show that the proposed expression accurately reproduces the response time for various backwater and downstream boundary conditions.

Parameter identification for the shallow water equation using modal decomposition

A parameter identification problem for systems governed by first-order, linear hyperbolic partial differential equations subjected to periodic forcing is investigated. The problem is posed as a PDE constrained optimization problem with data of the problem given by the measured input and output variables at the boundary of the domain. By using the governing equations in the frequency domain, a spatially dependent transfer matrix relating the input variables to the output variables is obtained. It is shown that by considering a finite number of dominant oscillatory modes of the input, an accurate representation of the output can be obtained. This converts the original PDE constrained optimization problem to one without any constraints. The optimal parameters can be identified using standard nonlinear programming. The utility of the proposed approach is illustrated by considering a river reach in the Sacramento-San-Joaquin Delta, California, that is subjected to tidal forcing. The dynamics of the reach are modeled by linearized Saint-Venant equations. The available data is the flow variables measured upstream and downstream of the reach. The parameter identification problem is to estimate the average free-surface width, the bed slope, the friction coefficient and the steady-state boundary conditions. It is shown that the estimated model gives an accurate prediction of the flow variables at an intermediate location within the reach.