# Discharge Coefficients of a Heavy Suspension Nozzle
## 5 Results and Discussion  
In the present section, initially the measured temporal pressure evolution inside the reservoirs is compared with the ones obtained from the CFD simulations. The same is later being done with the temporal temperature at the upstream reservoirs. Next, the time-dependent mass at each reservoir is also compared between CFD and experimentally-based results, which is followed by the temporal mass flow comparison. The time-dependent  
Figure 3: (**a**) Reservoirs main mesh; (**b**) T shape nozzle section mesh; (**c**) T shape nozzle mesh general view. Mach numbers at the respective critical sections and the discharge coefficients versus the Reynolds number are presented next. At the end of this section, a figure showing the flow inside the nozzle and for both flow directions is introduced. In this figure, the critical sections where the flow becomes sonic and the locations where supersonic flow is to be expected are clearly stated. Figure 4 presents the temporal pressure variation measured in both reservoirs for the different initial pressure differentials introduced in Table 1. Each curve is, in reality, the average one obtained after performing each test ten times. Although not presented in Figure 4, the standard deviation of each point was smaller than 1% for all tests performed. From Figure 4a, it is observed the discharge lasts about two seconds, regardless of the initial pressure differential existing between the two reservoirs. In fact, the time needed to complete the discharge suffers an increase of about 22.5% when comparing the discharge from 0.4 to 0.1 MPa with the 1.1 to 0.1 MPa one. This phenomenon is clearly understandable then the higher the upstream pressure the higher is the mass to be transferred from one reservoir to the other. Notice that the initial mass of fluid in the downstream reservoir is the same for all cases presented in Figure 4a, except the case at which the initial downstream pressure is of 0.4 MPa, being the upstream pressure of 1.2 MPa. This case shows clear differences versus the rest of the discharges; then, the time required to complete the discharge is about 10% shorter than the one needed to complete the discharge when the upstream/downstream reservoir pressures were 0.4 and 0.1 MPa, respectively. In fact, the discharge time is directly related to the initial fluid density ratio \(\rho_{upstream}/\rho_{downstream}\) between reservoirs, given the rest of the parameters, reservoirs volumes, and initial fluid temperature as constant, the smaller the initial upstream/downstream density ratio \(\rho_{upstream}/\rho_{downstream}\), and the shorter the discharge time. From the observation of the temporal pressure decay when the flow goes from the small reservoir to the large one, as in Figure 4b, it is realized that the discharge time obeys to the same upstream/downstream density rule just presented. It is interesting, as well, to observe that, when comparing discharge times for the same pressure differential and opposite flow directions, the discharge time is larger when the fluid goes from the small to the large reservoir. This is likely linked to the resistance the T shape nozzle is presenting when the fluid flows in such direction. The time the flow remains under chocked conditions it is expected to depend on such resistance. This point is to be clarified in the remaining part of the paper. Figure 4 also compares the pressure decay and increase measured experimentally with the ones obtained from the CFD simulations, two cases are compared for each flow direction. The comparison shows a very good agreement, generating the same discharge times and final pressures as the ones measured experimentally. Small discrepancies are observed in the final pressure values when the flow goes from the small to the large reservoir, a discrepancy of 4.4% is observed for a discharge from 1.2 to 0.4 MPa, and the variation reaches 11.3% for a discharge from 0.6 to 0.1 MPa.