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The replacement of existing spillway crests or gates with labyrinth weirs is a proven techno-economical means to increase the discharge capacity when rehabilitating existing structures. However, additional information is needed regarding energy dissipation of such weirs, since due to the folded weir crest, a three-dimensional flow field is generated, yielding more complex overflow and energy dissipation processes. In this study, CFD simulations of labyrinth weirs were conducted 1) to analyze the discharge coefficients for different discharges to compare the Cd values to literature data and 2) to analyze and improve energy dissipation downstream of the structure. All tests were performed for a structure at laboratory scale with a height of approx. P = 30.5 cm, a ratio of the total crest length to the total width of 4.7, a sidewall angle of 10° and a quarter-round weir crest shape. Tested headwater ratios were 0.089 ≤ HT/P ≤ 0.817. For numerical simulations, FLOW-3D Hydro was employed, solving the RANS equations with use of finite-volume method and RNG k-ε turbulence closure. In terms of discharge capacity, results were compared to data from physical model tests performed at the Utah Water Research Laboratory (Utah State University), emphasizing higher discharge coefficients from CFD than from the physical model. For upstream heads, some discrepancy in the range of ± 1 cm between literature, CFD and physical model tests was identified with a discussion regarding differences included in the manuscript. For downstream energy dissipation, variable tailwater depths were considered to analyze the formation and sweep-out of a hydraulic jump. It was found that even for high discharges, relatively low downstream Froude numbers were obtained due to high energy dissipation involved by the three-dimensional flow between the sidewalls. The effects of some additional energy dissipation devices, e.g. baffle blocks or end sills, were also analyzed. End sills were found to be non-effective. However, baffle blocks with different locations may improve energy dissipation downstream of labyrinth weirs.
Non-intrusive measuring techniques have attained a lot of interest in relation to both hydraulic modeling and prototype applications. Complimenting acoustic techniques, significant progress has been made for the development of new optical methods. Computer vision techniques can help to extract new information, e. g. high-resolution velocity and depth data, from videos captured with relatively inexpensive, consumer-grade cameras. Depth cameras are sensors providing information on the distance between the camera and observed features. Currently, sensors with different working principles are available. Stereoscopic systems reference physical image features (passive system) from two perspectives; in order to enhance the number of features and improve the results, a sensor may also estimate the disparity from a detected light to its original projection (active stereo system). In the current study, the RGB-D camera Intel RealSense D435, working on such stereo vision principle, is used in different, typical hydraulic modeling applications. All tests have been conducted at the Utah Water Research Laboratory. This paper will demonstrate the performance and limitations of the RGB-D sensor, installed as a single camera and as camera arrays, applied to 1) detect the free surface for highly turbulent, aerated hydraulic jumps, for free-falling jets and for an energy dissipation basin downstream of a labyrinth weir and 2) to monitor local scours upstream and downstream of a Piano Key Weir. It is intended to share the authors’ experiences with respect to camera settings, calibration, lightning conditions and other requirements in order to promote this useful, easily accessible device. Results will be compared to data from classical instrumentation and the literature. It will be shown that even in difficult application, e. g. the detection of a highly turbulent, fluctuating free-surface, the RGB-D sensor may yield similar accuracy as classical, intrusive probes.
Using optimization to design a renewable energy system has become a computationally demanding task as the high temporal fluctuations of demand and supply arise within the considered time series. The aggregation of typical operation periods has become a popular method to reduce effort. These operation periods are modelled independently and cannot interact in most cases. Consequently, seasonal storage is not reproducible. This inability can lead to a significant error, especially for energy systems with a high share of fluctuating renewable energy. The previous paper, “Time series aggregation for energy system design: Modeling seasonal storage”, has developed a seasonal storage model to address this issue. Simultaneously, the paper “Optimal design of multi-energy systems with seasonal storage” has developed a different approach. This paper aims to review these models and extend the first model. The extension is a mathematical reformulation to decrease the number of variables and constraints. Furthermore, it aims to reduce the calculation time while achieving the same results.