# Discharge Coefficients of a Heavy Suspension Nozzle
## 5 Results and Discussion
Some differences are observed between the discharge coefficients obtained numerically and the ones obtained based on experimental data, particularly at low Reynolds numbers. Authors believe such differences are due to the differences in fluid temperature between experimental and CFD results appearing at the end of the discharge. However, for a given flow direction, the asymptotic values of the discharge coefficients are almost the same regardless of the methodology employed to calculate them. The discharge coefficients obtained when the flow is going from the large to the small reservoir are slightly higher than the ones obtained when the flow is going in the opposite direction. This supports what has been presented until the moment, which is the time required to discharge from the small to the large reservoir is larger than the one needed when the discharge is from the large to the small tank. In other words, the fluid is finding more resistance to flow from the small to the large reservoir than in opposite direction. As explained before, this must be due to the restriction the fluid is observing when flowing from the two T branches and entering the horizontal one. In order to obtain a single curve representing the evolution of the discharge coefficient as a function of the Reynolds number, and for each flow direction, at each Reynolds number, the average discharge coefficient was determined. The mathematical equation of the resulting curves is presented in Equation (13), which represents the generic equation for the discharge coefficient as a function of the Reynolds number and for both flow directions. The parameters \(a_{0}.\ldots.a_{10}\) characterizing the discharge coefficient curve for each flow direction are defined in Table 1.4 Notice that, as in Figure 10b, the maximum Reynolds number is 50,000, and the parameters given in the first two rows of Table 2 are valid for this Reynolds number range. Nevertheless, based on the results from the CFD simulations,  
Table 1.5 Nozzle discharge coefficient based on experimental data and for all pressures studied. (**a**) Flow from large to small reservoir. (**b**) Flow from small to large reservoir. a second set of parameters valid for a Reynolds number range \(1000\leq Re\leq 130,000\) are also presented in the last two rows of Table 1.6  
Table 1.7  
One of the advantages of performing 3D-CFD simulations is that it allows to carefully analyze the flow evolution inside the nozzle. The flow field dynamics given as instantaneous velocity contours at both ends of the horizontal pipe, for both flow directions, reservoir pressures and at three different time instants, 0.02 s, 0.5 s, and 1 s, is introduced in Table 1.8 Each column characterizes the time at which the velocity field is presented. The initial two rows of Figure 11 show the flow field at both horizontal nozzle ends when the fluid goes from the L-to-S reservoir, and the initial upstream-downstream pressure on each tank is 0.4 MPa-0.1 MPa and 1.1 MPa-0.1 MPa, respectively. The final two rows show the velocity field that, when the flow goes from the S-to-L reservoir, the upstream-downstream initial pressures are 0.6 MPa-0.1 MPa and 1.2 MPa-0.4 MPa, respectively. When the fluid goes from the large to the small reservoirs, and for the two pressure ratios studied, during the initial milliseconds, \(t=0.02\) s, the fluid reaches sonic conditions at the horizontal nozzle outlet just before the T junction, and supersonic flow conditions are observed as the fluid expands to the two lateral vertical branches; see the first and second rows of Table 1.9 At \(t=0.5\) s, and for upstream-downstream initial pressures of 0.4 MPa-0.1 MPa, the fluid has become subsonic at all points, the maximum spatial averaged velocity is 239 m/s, which corresponds to M = 0.74, and the fluid still remains detached when entering the T junction. After 1 s of the origin of the discharge, the maximum fluid velocity has decreased to 120 m/s, but the flow keeps being detached at the T junction entrance.