# Discharge Coefficients of a Heavy Suspension Nozzle
## 5 Results and Discussion
When comparing Figure 8a,b, for any given pressure differential, it is observed that, at time zero, the mass flow, when the fluid goes from L-to-S, is slightly larger than when the fluid goes from the S-to-L, indicating the flow is seeing a higher restriction when the fluid is going from S-to-L reservoir. Figure 9a,b introduce the Mach number temporal evolution at the nozzle minimum section as a function of the pressure differential and for the two flow directions, L-to-S and S-to-L reservoirs, respectively. The information presented obeys the cases where numerical and experimentally-based results can be compared. When the fluid goes from the large to the small reservoir, the flow is initially sonic, and the time during which the flow remains under sonic conditions increases with the pressure ratio increase, as in Figure 9a. When the fluid is flowing from the small to the large reservoir, and for initial respective pressures of 1.2 MPa and 0.4 MPa, the discharge is sonic during a very small time. But, when the initial reservoirs pressure is of 0.6 MPa and 0.1 MPa, respectively, the time at which the flow remains sonic is of nearly 1 s, which is almost the same time observed when the fluid goes from the large to the small reservoir, and, for a respective pressure of 1.1 MPa and 0.1 MPa, compare figures Figure 9a,b. The reason why the fluid remains sonic during a longer time, when the flow goes from S-to-L reservoirs, is likely to be caused by the sudden flow restriction the fluid is suffering when the flow enters the horizontal section of the nozzle and coming from the two T shape branches. The two T shape branches promote the existence of a flow restricted section at the horizontal nozzle inlet, restricting, as well, the entrance of the fluid from a vertical plane, the fluid can only move vertically in the two vertical branches of the T nozzle. In reality, this effect is creating a smaller effective section of the flow in this case than when flow goes from large to small reservoir. In other words, the nozzle resistance to the fluid is larger when the flow goes from the small to the large reservoir; therefore, the mass flow is also smaller. In fact, when comparing the mass flow curves for the same pressure drop presented in Figure 8a,b, it can be clearly seen that the mass flow is higher during the initial times when the fluid goes from the L-to-S reservoir. At this point, it must be highlighted that the location where the Mach number values are computed is always where the spatially averaged Mach number is maximum. Such location is at the end of the horizontal nozzle, beginning of the T junction, when the flow goes from L-to-S reservoir, and at the end of the horizontal nozzle and beginning of the large tank, when the flow goes from the S-to-L reservoir. Such different locations were expected; then, regardless of the  
Table 1.2 Temporal evolution of the maximum Mach number obtained at the nozzle separating the two reservoirs. Comparison between the numerical results and the experimentally-based ones. (**a**) Flow from large to small reservoir. (**b**) Flow from small to large reservoir. flow direction, the fluid at the entrance of the horizontal nozzle has to be subsonic and accelerates along it. The temporal discharge coefficients as a function of the Reynolds number, and for the four cases at which CFD and experimentally-based results are generated, is presented in Table 1.3 The variations of the discharge coefficient when the flow goes from the large to the small tank, and vice versa, is given in Figure 10a,b, respectively. For both flow directions, the numerical and experimentally-based results are presented for the pressure differentials studied using both methodologies. The first thing to notice is that, for a given flow direction, the discharge coefficient shows a very similar temporal trend, regardless of the pressure ratio evaluated. In fact, it is to be expected that the discharge coefficient depends on the Reynolds number but not on the pressure ratio between reservoirs.