The authors previously described a new method [based on the new discrete vapor cavity model (new DVCM)] for numerical prediction of pressure changes during the water hammer with liquid column separation together with results of preliminary experimental verification of this method. This paper is a continuation of the research and includes results of additional laboratory tests and visualization of the cavitation zones generated during transient flow with liquid column separation. The results of these studies provide a better understanding of the phenomenon. It is shown that the phenomenon can have a distributed nature, which means that gas-vapor zones may be observed not only locally, in the vicinity of the shutoff valve, but may be spread along the pipeline length, and the intensity of this phenomenon decreases with distance from the valve. Laboratory test results were also used for further verification of the new DVCM. This verification shows that agreement between calculated and experimental res...

The paper presents the results of calculations of the water-hammer course accompanied by the column separation caused by a rapid closure of the butterfly valve. The computational method takes into account the cavitation characteristics of the valve that has been determined on the special laboratory stand in the Szewalski Institute of Fluid-Flow Machinery in Gdansk, Poland. In addition, calculations have been conducted using authors’ own discrete-vapour-cavity-model (the New Single-Zone DVCM). The paper presents also a comparison between these calculation results and the experimental ones obtained at the own laboratory stand for investigation of the water-hammer phenomenon in the pump discharge pipeline. The comparison of the numerical and empirical results is a basis for the verification process and assessment of the computational method that has been developed

This article presents the original procedures for measuring the flow rate using the pressure-time and the volumetric gauging method in the case of performance tests of a reversible hydraulic machine in either turbine or pump modes of operation. Achieving the lowest possible measurement uncertainty was one of the basic conditions during implemented machine tests. It was met using appropriate measuring procedures and high-class measuring equipment. Estimation of the uncertainty for both methods was made on the basis of an analysis consistent with current requirements in this respect. The pressure-time method was supplemented by the computational fluid dynamics (CFD) analysis that allowed reducing the impact of the pipeline complex irregular geometry on the uncertainty of flow measurement. Appropriate modifications of the calculation procedure enabled accurate measurements of flow during the pump mode of operation of the tested machine as well. The volumetric gauging method, thanks to a special procedure used for accurate measurement of the water level in the upper reservoir of the power plant, allowed measuring the discharge through the tested reversible machine with very low uncertainty. The obtained results allowed for a detailed comparison and mutual verification of the methods used to measure the discharge of the tested reversible machine in both modes of its operation. The most possible causes of obtained results are discussed and summarized in the paper. The need for further research was pointed out to explain the differences obtained and their influence on the accuracy of discharge measurement using the pressure-time method in pump operation mode.

This paper presents the results of laboratory tests of water hammer phenomenon induced in two series-connected copper pipes with different diameters (a diameter ratio of 1:1.25) by a quick-closing valve installed at the end of the simple upstream tank–pipeline–valve system. Test results were compared with calculations made with the use of various friction loss models incorporated in a one-dimensional model based on a method of characteristics. The calculation takes into consideration quasi-steady and unsteady friction models as well as a special discretization procedure of the solution domain that ensures the elimination of numerical diffusion in the numerical scheme. The main attention was paid to determining the value of the pressure wave speed in the pipes, which has a significant influence on the compliance between the calculations and the experimental results of the pressure amplitudes and wave frequencies. Two methods of determining the wave speed were proposed and evaluated based on the measurements. The results presented in this article indicate that the use of the proposed procedure instead of the classic formulas for determining the pressure wave speed gives the desired correspondence between the frequencies of the measured and calculated waves. Calculation examples made with the use of different friction models showed that application of the developed procedure for discretization of the solution domain and the method used for determining the wave speed opened the possibility of reliable verification of these models, free of numerical errors and frequency discrepancies between the computational and measured wave.

The work presented in this article concerns numerical studies on optimization methods used for the sustainable utilization of the energy potential of water, converting it into electricity in a hydropower plant equipped with more than one unit. These methods allow for maximization of production in given hydrological conditions, leading to the balanced, lossless, and environmentally friendly use of the renewable energy source that is water. Methods are selected from three groups, i.e., analytical, enumeration, and randomized. The results of calculations of optimal points of selected test functions carried out using the Broyden–Fletcher–Goldfarb–Shanno Limited-Memory Version (L-BFGS-B), Explicit Complete Enumeration (ECE), and Genetic Algorithm (GA) methods provided basic information on the features of these methods. Based on these tests, the GA method was selected to solve the problem of the optimal load distribution in a hydropower plant equipped with three identical hydro units. The defined optimization problem consisted of finding a configuration of hydro units in operation that would guarantee the maximum efficiency of the power plant under the imposed hydrological conditions. During the numerical studies, a number of calculations were performed to identify the impact of procedures and parameters characteristic of the optimization methods on the obtained results. Particular attention was paid to the GA method and penalty functions, enabling the elimination of results from the area of prohibited solutions.