Rodrigo de Melo Porto

Stepped and smooth spillways: resistance effects on stilling basin lengths

The Darcy–Weisbach equation was used in the analysis of flow over spillways, furnishing theoretical tools to design stilling basins. Predictions for the length of hydraulic jump stilling basins downstream of stepped and smooth spillways are presented, together with ranges of values for the Darcy–Weisbach friction factor of both spillways. The experimental data were compared with results of the theoretical solution of the gradually varied flow equation. All comparisons were made in non-dimensional form. The values of the Darcy–Weisbach friction factor were roughly five times smaller for smooth spillways than for stepped spillways. The theoretical predictions and the experimental data allow to present approximate equations for a preliminary evaluation of the length and the bed level of hydraulic jump stilling basins. In the same way, approximate equations were presented for the evaluation of the friction factor in smooth and stepped spillways, as a function of the Froude number at the downstream cross-section.

Transition length between water and air-water flows on stepped chutes

This study presents the steps followed to obtain mathematical models for the length of the transition region between the “full-water” and “full-mixed” flows in stepped spillways. This transition length is defined here as the distance along the flow, parallel to the pseudo-bottom, starting at the end of the “full-water” region and ending at the beginning of the “full-mixed” region. The definition is proposed based on experimental profiles of the surface obtained with an acoustic sensor in a stepped chute, which allows one to locate adequately the minima and maxima of the profile. A set of profiles obtained for different flow conditions is shown, and a comparison between predicted and calculated transition lengths is made. Experimental data and theoretical predictions superpose adequately for the present set of data.

Lower nappe aeration in smooth channels: experimental data and numerical simulation

Bed aerators designed to increase air void ratio are used to prevent cavitation and related damages in spillways. Air entrained in spillway discharges also increases the dissolved oxygen concentration of the water, which can be important for the downstream fishery. This study considers results from a systematic series of measurements along the jet formed by a bed aerator, involving concentration profiles, pressure profiles, velocity fields and corresponding air discharges. The experimental results are, then, compared, with results of computational fluid dynamics (CFD) simulations with the aim of predicting the air discharge numerically. Comparisons with jet lengths and the air entrainment coefficients from the literature are also made. It is shown that numerical predictive tools furnish air discharges comparable to measured values. However, if more detailed predictions are desired, verification experiments are still necessary.

Stepped Spillways: Theoretical, Experimental and Numerical Studies

Flows on stepped spillways have been widely studied in various research institutions motivated by the attractive low costs related to the dam construction using roller-compacted concrete and the high energy dissipations that are produced by such structures. This is a very rich field of study for researchers of Fluid Mechanics and Hydraulics, because of the complex flow characteristics, including turbulence, gas exchange derived from the twophase flow (air/water), cavitation, among other aspects. The most common type of flow in spillways is known as skimming flow and consists of: (1) main flow (with preferential direction imposed by the slope of the channel), (2) secondary flows of large eddies formed between steps and (3) biphasic flow, due to the mixture of air and water. The details of the three mentioned standards may vary depending on the size of the steps, the geometric conditions of entry into the canal, the channel length in the steps region and the flow rates. The second type of flow that was highlighted in the literature is called nappe flow. It occurs for specific conditions such as lower flows (relative to skimming flow) and long steps in relation to their height. In the region between these two “extreme” flows, a “transition flow” between nappe and skimming flows is also defined. Depending on the details that are relevant for each study, each of the three abovementioned types of flow may be still subdivided in more sub-types, which are mentioned but not detailed in the present chapter. Figure 1 is a sketch of the general appearance of the three mentioned flow regimes.

Details of Hydraulic Jumps for Design Criteria of Hydraulic Structures

The sudden transition from supercritical to subcritical flow, known as hydraulic jump, is a phenomenon that, although being studied along decades, still presents aspects that need better quantification. Geometrical characteristics, such as the length of the roller (or the jump itself), still have no definitive formulation for designers of hydraulic structures. Even predictions of the sequent depths, usually made considering no shear forces, may present deviations from the observed values.

Efeito da Turbulência na Determinação da Superfície Livre para o Cálculo da Resistência aos Escoamentos em Canais com Fundo em Degraus

The use of the Darcy-Weisbach equation involving research on smooth and stepped chutes developed over decades is presented in this work, looking at the wide variety of data and forecasts for the friction factor. The variations found for this dimensionless quantity are discussed with the help of experimental data measured in the physical model with 45o and step height of 5.0 cm. The results show that the turbulence near the free surface that prevents an accurate determination of the depth to be used, may be responsible for the dispersion in evaluating the resistance factor found in the literature. In addition, equations are presented that can help develop projects involving similar structures to those adopted in the tests performed.

Use of convolution and geotechnical rock properties to analyze free flowing discharge test

Discharge tests are conducted in order to determine aquifers transmissivity (T) and storage coefficient (S). However the interpretation of test data is not unique and the results may vary depending on adopted hypothesis. In this work, the convolution technique is applied for the reconstruction of observed drawdown curves aiming for the reduction of uncertainty. The interference between a flowing well and an observation well is evaluated in order to determine the hydrogeological parameters of the confined Guarani Aquifer System (Araujo et al. 1999). Discharge test data are analyzed according to the Jacob and Lohman (1952) method. The application of convolution enabled the determination of the most reliable solution. Obtained transmissivity (T = 411.0 m 2 /d) and storage coefficient (S = 2.75x10 -4 ) are close to values estimated by direct evaluation of the geotechnical sandstone properties.