Most of today’s water supply systems are based on plastic pipes. They are characterized by the retarded strain (RS) that takes place in the walls of these pipes. The occurrence of RS increases energy losses and leads to a different form of the basic equations describing the transient pipe flow. In this paper, the RS is calculated with the use of convolution integral of the local derivative of pressure and creep function that describes the viscoelastic behavior of the pipe-wall material. The main equations of a discrete bubble cavity model (DBCM) are based on a momentum equation of two-phase vaporous cavitating flow and continuity equations written initially separately for the gas and liquid phase. In transient flows, another important source of pressure damping is skin friction. Accordingly, the wall shear stress model also required necessary modifications. The final partial derivative set of equations was solved with the use of the method of characteristics (MOC), which transforms the original set of partial differential equations (PDE) into a set of ordinary differential equations (ODE). The developed numerical solutions along with the appropriate boundary conditions formed a basis to write a computer program that was used in comparison analysis. The comparisons between computed and measured results showed that the novel modified DBCM predicts pressure and velocity waveforms including cavitation and retarded strain effects with an acceptable accuracy. It was noticed that the influence of unsteady friction on damping of pressure waves was much smaller than the influence of retarded strain.

This paper concerns the start-up process of a hydrostatic transmission with a fixed displacement pump, with particular emphasis on dynamic surplus pressure. A numerically controlled transmission using a proportional directional valve was analysed by simulation and experimental verification. The transmission is controlled by the throttle method, and the variable resistance is the throttling gap of the proportional spool valve. A mathematical description of the gear start-up process was obtained using a lumped-parameters model based on ordinary differential equations. The proportional spool valve was described using a modified model, which significantly improved the performance of the model in the closed-loop control process. After assuming the initial conditions and parameterization of the equation coefficients, a simulation of the transition start-up was performed in the MATLAB–Simulink environment. Simulations and experimental studies were carried out for control signals of various shapes and for various feedback from the hydraulic system. The pressure at the pump discharge port and the inlet port of the hydraulic motor, as well as the rotational speed of the hydraulic motor, were analysed in detail as functions of time. In the experimental verification, complete measuring lines for pressure, speed of the hydraulic motor, flow rate, and temperature of the working liquid were used.

In pressurised pipeline systems, various water hammer events commonly occur. This phenomenon can cause extensive damage or even lead to a failure of the pumping system. The aim of this work is to experimentally re-examine the possibility of using an additional polymeric pipe, installed at the downstream end of the main pipeline, to control water hammer. A previous study on this topic investigated additional polymeric pipes connected to the hydraulic system with a short joint section of the same diameter as the main pipeline. In the current research, a different method of including an additional pipe was considered which involved connecting it with a pipe of a smaller diameter than the main pipeline. Three additional HDPE pipes, with different volumes, were investigated. The performance of the devices was studied for hydraulic transients induced by both rapid and slow, manual valve closures. Experimental results show that the additional polymeric pipe can provide significant pressure surge damping during rapid water hammer events. As the valve closing time lengthens, the influence of the additional pipe on the maximum pressure increase is reduced. The additional HDPE pipe does not provide notable protection against hydraulic transients induced by slow valve closure in terms of reducing the first pressure peak. No relationship between the volume of the additional pipe and the damping properties was noticed. The observed pressure oscillations were used to evaluate a one-dimensional numerical model, in which an additional pipe is described as a lumped parameter of the system. The viscoelastic properties of the device were included using the one element Kelvin–Voigt model. Transient flow equations were solved with the implicit method of characteristics. Calculation results demonstrate that this approach allows one to reasonably reproduce unsteady flow oscillations registered during experiments in terms of the maximum pressure increase and pressure wave oscillation period.

Contractions and expansions are common features in various types of pipeline systems. The purpose of this study is to investigate the influence of a sudden cross section change on transient pressure waves. The paper presents laboratory data and numerical calculations of pressure oscillations during the valve-induced water hammer in serially connected steel pipes. Five different variants of experiments were conducted which included recording pressure changes at the downstream end of the pipeline system. The more sections with different diameters there are connected in series, the more complex the transient wave recorded is. Laboratory data indicate a significant influence of individual pipeline sections on the final course of pressure oscillations. Transient equations were solved using the explicit MacCormack scheme. In order to numerically simulate water hammers in pipe series, the improved junction boundary condition was established. It involves assigning two sets of values, which describe flow parameters, to the connection node thus causing it to act as two separate nodes. The numerical model was calibrated with the unsteady friction factor. The derivation of equations that take into account a sudden change in diameter in the connected pipes allowed the reproduction of the wave nature of the water hammer phenomenon, results were satisfactory as compared to experimental data. The numerical model correctly reproduced pressure wave interactions and pressure amplitudes.

It is well known that the water hammer phenomenon can lead to pipeline system failures. For this reason, there is an increased need for simulation of hydraulic transients. High-density polyethylene (HDPE) pipes are commonly used in various pressurised pipeline systems. Most studies have only focused on water hammer events in a single pipe. However, typical fluid distribution networks are composed of serially connected pipes with various inner diameters. The present paper aims to investigate the influence of sudden cross-section changes in an HDPE pipeline system on pressure oscillations during the water hammer phenomenon. Numerical and experimental studies have been conducted. In order to include the viscoelastic behaviour of the HDPE pipe wall, the generalised Kelvin–Voigt model was introduced into the continuity equation. Transient equations were numerically solved using the explicit MacCormack method. A numerical model that involves assigning two values of flow velocity to the connection node was used. The aim of the conducted experiments was to record pressure changes downstream of the pipeline system during valve-induced water hammer. In order to validate the numerical model, the simulation results were compared with experimental data. A satisfactory compliance between the results of the numerical calculations and laboratory data was obtained.

This paper experimentally and numerically investigates the water hammer phenomenon in serially connected steel and HDPE pipes with different diameters. The aim of the laboratory tests was to obtain the time history of the pressure head at the downstream end of the pipeline system. Transient tests were conducted on seven different pipeline system configurations. The experimental results show that despite the significantly smaller diameter of the HDPE pipe compared to the steel pipe, introducing an HDPE section makes it possible to suppress the valve-induced pressure surge. By referring to the results of the experimental tests conducted, the comparative numerical calculations were performed using the fixed-grid method of characteristics. To reproduce pressure wave attenuation in a steel pipe, Brunone-Vitkovský instant acceleration-based model of unsteady friction was used. To include the viscoelastic behavior of the HDPE pipe wall, the one-element Kelvin–Voigt model was applied. By calibrating the unsteady friction coefficient and creep parameters, satisfactory agreement between the calculated and observed data was obtained. The calibrated values of parameters for a single experimental test were introduced in a numerical model to simulate the remaining water hammer runs. It was demonstrated that using the same unsteady friction coefficient and creep parameters in slightly different configurations of pipe lengths can be effective. However, this approach fails to reliably reproduce the pressure oscillations in pipeline systems with sections of significantly different lengths.