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The article provides concise details about a hydraulic phenomenon known as the undular jump, that occurs under different conditions within different hydraulic constructions and can negatively influence on their operation and conditions. Therefore, the methods of modelling undular jump characteristics using physical and mathematical model are presented. Based on physical model of undular jump, the experimental data were obtained. Moreover, three mathematical models were considered and analyzed. The article gives the comparison of experimental data and data obtained by mathematical models. The advantages and disadvantages of considered mathematical models were specified. The novelty of work was in developing and improving mathematical model with taking into account the energy losses that are allowed to obtain the characteristics of undular jump with high accuracy.

The share of electricity generation by small hydropower plants is the least among other renewable energy sources in Ukraine, although the SHPPs were widely operated in the past. The aim of the article is to analyse the hydropotential of Ukrainian rivers and review the past and present states of small hydropower engineering in Ukraine. Moreover, the article emphasizes the main directions and gives recommendations for hydropower development in Ukraine considering ecological, economic, energy and legal issues.

Discharge measurement is the base of proper water management. The effective design and operation of hydraulic structures under both normal and extreme flow conditions depend on the quality of hydrological data. Understanding the water system requires consistent and long-term measurement. Despite that, the gauging station network is sparse, and its numbers are declining worldwide. This article aims to draw attention to the possibility of accurate flow measurement using existing hydraulic structures. Flow over a hydraulic structure profile is a physically well-defined phenomenon as the construction shape is fixed and simple compared to river profiles. The discharge can be derived from rating curves, turbine characteristics, and several easily measured variables. That allows continuous discharge measurement. The accuracy is compared with the gauging station on the river. Suitable technical solutions for ensuring and monitoring ecological flow are discussed.

The design of the elbow draft tubes is challenging due to the complexity of the flow. The whole turbine unit's power output strongly depends on the draft tube function, especially for the low-head turbines. The article presents a novel approach to optimizing elbow draft tubes for a variable-speed propeller turbine designed for low-head applications. First, the study addresses the specifics of the propeller variable speed turbine by comparing the classical Kaplan turbine. Then, the grid scaling test is conducted to evaluate the uncertainty of the pressure regeneration. Further, a new approach to parameterising the elbow draft tube geometry is introduced. The study employs ANSYS CFX 2021 R1 software for numerical simulation to optimise the elbow draft tube geometry in the CAESES environment. After the sensitivity test and deselecting the non-sensitive parameters, we perform multi-objective genetic algorithm (MOGA) optimization. The optimization process results in a Pareto front of optimised elbow draft tube shapes with the best pressure regeneration for different draft tube construction heights, enabling the selection of suitable candidates for various locations. Minimal difference in the performance of the selected elbow draft tube shapes with the simple straight draft tube confirms a high-quality draft tube optimization achievement. [ABSTRACT FROM AUTHOR]