# Flow Analysis of a Novel, Three-Way Cartridge Flow Control Valve
## 6 Discussion  
The results show that the flow control valve is able to maintain the required flow rate regardless of the load pressure value. Figures 13 and 14 show the possibility of adjusting the flow rate to a certain extent by changing the initial spring tension. If it is necessary to change the adjustment range more significantly, a spring with a different spring rate can be applied. The use of a stiffer spring allows a greater flow to be obtained; however, at the same time, energy losses rise due to the increase in pressure drop across the valve. According to the obtained \(p\)-\(Q\) characteristic (Figure 15), the flow rate deviation in the entire considered load range does not exceed \(\Delta Q_{A}=9\,\%\) for the low flow rate setting (\(Q=6.0\,\mathrm{dm}^{3}\,\mathrm{min}^{-1}\)) or \(\Delta Q_{A}=4\%\) for a high flow rate (\(Q=22\,\mathrm{dm}^{3}\,\mathrm{min}^{-1}\)). In general, at a given setting, the flow through the valve rises as the pressure in the load line increases. This is due to the influence of the hydrodynamic force (Equation (9)), which was estimated with the help of velocity distributions obtained from CFD studies (Figures 9 and 11). In subsequent simulations, the ability of the flow control valve to compensate for the varying pressure in the load line was tested. For this purpose, the load line was assigned a sinusoidal \(p_{2}\) pressure of average value \(10\,\mathrm{MPa}\), amplitude \(2.5\,\mathrm{MPa}\) and period \(2\,\mathrm{s}\) (Figure 16). The use of a flexible spring (\(k_{spr}=10\,\mathrm{N}\,\mathrm{mm}^{-1}\)) resulted in a maximum flow rate deviation not exceeding \(5\,\%\), with a maximum pressure drop across the valve \(\Delta p_{1}=0.7\,\mathrm{MPa}\). A stiffer spring that allows higher regulated flow rates to be obtained provides a more even flow where the maximum flow rate deviation does not exceed \(3\%\). However, the pressure drop is significantly higher, reaching the value of about \(1.9\,\mathrm{MPa}\). Laboratory tests were aimed at confirming the correctness of mathematical and simulation models and verifying the actual flow characteristics of the valve. In the first experiment, the flow rate through the \(A\) channel of the valve was measured at fixed valve settings, ensuring the nominal flow \(Q_{A}=10\,\mathrm{dm}^{3}\,\mathrm{min}^{-1}\) and \(Q_{A}=22\,\mathrm{dm}^{3}\,\mathrm{min}^{-1}\). Fixed pump flow rate \(Q_{0}=30\,\mathrm{dm}^{3}\,\mathrm{min}^{-1}\) and pressure in the load line varying in the range of \(p_{2}=2\)-\(30\,\mathrm{MPa}\) were assumed. The measurement uncertainties estimated by means of the standard deviation factor are equal to \(\Delta Q_{0}=\pm 0.38\,\mathrm{dm}^{3}\,\mathrm{min}^{-1}\), \(\Delta Q_{A}=\pm 0.60\,\mathrm{dm}^{3}\,\mathrm{min}^{-1}\) and \(\Delta p_{A}=\pm 0.37\,\mathrm{MPa}\). The results shown in Figure 19 indicate a high level of agreement. The correlation coefficient for the low and high flow rate settings was \(0.99\) and \(0.96\), respectively. As part of the second experiment, the value of the obtained flow rate \(Q_{A}\) was tested at a constant load of the supply line \(p_{2}=10\,\mathrm{MPa}\) and a variable pump flow \(Q_{0}=3-30\,\mathrm{dm}^{3}\,\mathrm{min}^{-1}\). As shown in Figure 21, also in this case, the results of simulations and laboratory experiments show a high degree of correlation, except for the lowest values of pump flow \(Q_{0}<4\,\mathrm{dm}^{3}\,\mathrm{min}^{-1}\). The results also showed that the regulated flow rate, provided that the pump capacity is sufficiently high (\(Q_{0}>Q_{A}\)), is almost constant over the entire range, with a deviation not exceeding \(\Delta Q_{A}<1\%\). laboratory experiments to determine operational range and flow characteristics. The proposed solution is particularly significant from an economic point of view because the valve has a relatively simple structure, does not require any advanced electronic control systems and can reduce power consumption compared to standard two-way flow control valves.