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Übungsaufgaben und Berechnungen für den Baubetrieb: Klausurvorbereitung mit ausführlichen Lösungen
(2019)
Kalkulation
(2019)
Baumaschinen
(2019)
Accurate determination of free-surface dynamics has attracted much research attention during the past decade and has important applications in many environmental and water related areas. In this study, the free-surface dynamics in several turbulent flows commonly found in nature were investigated using a synchronised setup consisting of an ultrasonic sensor and a high-speed video camera. Basic sensor capabilities were examined in dry conditions to allow for a better characterisation of the present sensor model. The ultrasonic sensor was found to adequately reproduce free-surface dynamics up to the second order, especially in two-dimensional scenarios with the most energetic modes in the low frequency range. The sensor frequency response was satisfactory in the sub-20 Hz band, and its signal quality may be further improved by low-pass filtering prior to digitisation. The application of the USS to characterise entrapped air in high-velocity flows is also discussed.
A new formulation for the prediction of free surface dynamics related to the turbulence occurring nearby is proposed. This formulation, altogether with a breakup criterion, can be used to compute the inception of self-aeration in high velocity flows like those occurring in hydraulic structures. Assuming a simple perturbation geometry, a kinematic and a non-linear momentum-based dynamic equation are formulated and forces acting on a control volume are approximated. Limiting steepness is proposed as an adequate breakup criterion. Role of the velocity fluctuations normal to the free surface is shown to be the main turbulence quantity related to self-aeration and the role of the scales contained in the turbulence spectrum are depicted. Surface tension force is integrated accounting for large displacements by using differential geometry for the curvature estimation. Gravity and pressure effects are also contemplated in the proposed formulation. The obtained equations can be numerically integrated for each wavelength, hence resulting in different growth rates and allowing computation of the free surface roughness wavelength distribution. Application to a prototype scale spillway (at the Aviemore dam) revealed that most unstable wavelength was close to the Taylor lengthscale. Amplitude distributions have been also obtained observing different scaling for perturbations stabilized by gravity or surface tension. The proposed theoretical framework represents a new conceptualization of self-aeration which explains the characteristic rough surface at the non-aerated region as well as other previous experimental observations which remained unresolved for several decades.
As with most high-velocity free-surface flows, stepped spillway flows become self-aerated when the drop height exceeds a critical value. Due to the step-induced macro-roughness, the flow field becomes more turbulent than on a similar smooth-invert chute. For this reason, cascades are oftentimes used as re-aeration structures in wastewater treatment. However, for stepped spillways as flood release structures downstream of deoxygenated reservoirs, gas transfer is also of crucial significance to meet ecological requirements. Prediction of mass transfer velocities becomes challenging, as the flow regime differs from typical previously studied flow conditions. In this paper, detailed air-water flow measurements are conducted on stepped spillway models with different geometry, with the aim to estimate the specific air-water interface. Re-aeration performances are determined by applying the absorption method. In contrast to earlier studies, the aerated water body is considered a continuous mixture up to a level where 75% air concentration is reached. Above this level, a homogenous surface wave field is considered, which is found to significantly affect the total air-water interface available for mass transfer. Geometrical characteristics of these surface waves are obtained from high-speed camera investigations. The results show that both the mean air concentration and the mean flow velocity have influence on the mass transfer. Finally, an empirical relationship for the mass transfer on stepped spillway models is proposed.