# Numerical Analysis of Fluid Stream Division to Supply Multiple Hydraulic Receivers
###### Abstract  
This article presents a proposal and a numerical analysis of a hydraulic system consisting of one constant capacity pump supplying multiple receivers in the form of hydraulic motors, based on the example of a rail grinder. The proposed approach requires splitting the stream of the working fluid, which was achieved using 2-way flow control valves. As part of the preliminary CFD studies, the pressure and velocity distributions of the flow control valve were obtained, and the discharge coefficient of the valve nozzles was determined as a function of the valve spool position. Then, a mathematical model of the system was formulated, which was used to build a simulation model in the Matlab/Simulink environment. Next, the ability of the system to achieve the assumed operating parameters and its energy efficiency in a given load range were tested. The results indicate that the system can effectively perform the required work cycles with sufficient accuracy. hydraulic system; fluid stream split numerical analysis; CFD; simulation; Simulink +
Footnote †: journal: Applied sciences  
multiple hydraulic actuators powered by a single pump was the subject of two publications by [PERSON] et al. First, a leader-following control system with lumped uncertainties involving uncertain hydraulic parameters and unknown external load was developed [4]. Next, feedback linearization was applied to guarantee the control system stability under nonlinear dynamics and unknown load circumstances [5]. The authors verified the effectiveness of the controller by both simulations and test bench experiments. Similar problems also appear in vehicles' hydraulic control systems, which usually include multiple actuators [6; 7]. The crucial elements of the developed system are flow control valves. Valves of this type provide a constant output flow rate independent of the pressure drop. Research on the development of flow control valves mainly concerns the modifications in the structure or design of new control systems. A flow control valve with a digital flow compensator was proposed by [PERSON] et al. [8]. The compensator provided reasonable static control characteristics with a significantly reduced dead zone. In turn, [PERSON] et al. [9] presented a novel design of a rotary hydraulic flow control valve operating at high flow rates above 150 liters per minute. Similarly, [PERSON] and [PERSON] in [10] analyzed the flow characteristics of a proportional flow control valve and made some modifications to the spool geometry to improve its characteristics. Some studies focus on flow rate control in specific practical applications, such as the electro-hydraulic hitch control valve of an agricultural tractor [11] or a flow control valve for stroke speed adjustment of a robotic lifting device [12]. Regarding research on advanced control techniques of flow control valves, there are also publications on using artificial intelligence methods, such as genetic algorithms [13; 14] and neural networks [15; 16; 17]. This article analyzes the operation of a grinding machine intended for railway rails or other similar elements. A characteristic feature of this device is that, due to the complex profile of the rail, it is necessary to use multiple grinding wheels, all of which must be driven simultaneously and at a similar rotational speed, regardless of the actual load. Due to the high temperature at the grinding site, the potential use of electrical equipment also poses significant problems. Therefore, after the analysis, it was decided that using a hydraulic system could be much more advantageous. This solution is beneficial because it does not require electricity. Furthermore, while using hydraulic oil as the working medium, it is possible to dissipate heat from the hydraulic motor to the cooling system, even in a distant location. The article proposes a solution in which one pump supplies at least four receivers simultaneously.