# Discharge Coefficients of a Heavy Suspension Nozzle
## 5 Results and Discussion
Such relatively small discrepancies are understandable when considering that, in the CFD simulations, the process is considered as adiabatic, the fluid is considered as ideal, and the large volume remains constant. Figure 5 presents the fluid temperature evolution in both reservoirs and for the four cases numerically evaluated. When the discharge is from the large to the small reservoir, as in Figure 5a, the fluid temperature on the large reservoir suffers a decrease of less than 20\({}^{\circ}\), and the increase of the fluid temperature in the small reservoir lies between 55\({}^{\circ}\) and 85\({}^{\circ}\); such a large increase is perfectly understandable when considering the reduced volume of this particular reservoir and that the walls are considered adiabatic. Notice, as well, that the temperature decrease and increase are directly dependent on the pressure ratio between reservoirs. When the flow goes from the small to the large reservoir, as in Figure 5b, the temperature decrease in the small tank oscillates between 50\({}^{\circ}\) and 70\({}^{\circ}\), and a maximum temperature rise of around 30\({}^{\circ}\) is observed in the large reservoir. A point which needs to be considered, and which could help to explain why the discharge from the small to the large reservoir takes longer than the one in the opposite direction, is that, regardless of the flow direction, the temperature variation at the small reservoir is several times larger than the one observed at the large one. Another possible explanation needs to be found in the possible existence of a flow restriction under these conditions, therefore reducing the effective flow section. In fact, the most plausible explanation is likely to be the different nozzle resistance the fluid is facing when flowing in opposite directions. These hypotheses will be analyzed in the remaining part of the paper. Figure 6 introduces the experimentally-based fluid temperature temporal variation on both reservoirs for the two flow directions and for all pressure differentials evaluated; see Table 1. Figure 5(a,b) characterize the temperature decrease in the large and small reservoirs when the flow goes from the large to the small and from the small to the large reservoirs, respectively. The fluid temperature evolution in both reservoirs obtained from the CFD simulations is also presented for comparison. Figure 4: Measured temporal pressure variation in both reservoirs, comparison between experimental and CFD results. (**a**) Flow from large to small reservoir. (**b**) Flow from small to large reservoir. Five different pressure decays are considered for each flow direction; see Table 1.  
Figure 5: Numerical temperature evolution in the upstream and downstream reservoirs. (**a**) The flow goes from the large to the small reservoir. (**b**) The flow goes from the small to the large reservoir. The first thing to be observed is that the fluid temperature decay is proportional to the initial pressure ratio between reservoirs, and the higher the pressure ratio, the higher the fluid temperature decay in the upstream reservoir. As previously observed, the temperature drop is particularly high in the small reservoir. Temperature decreases of over \(50^{\circ}\) are observed in the small reservoir, and such decrease is of less than \(20^{\circ}\) in the large one. When comparing the temperature evolution experimentally-based with the CFD one, a particularly good agreement is observed in the large reservoir, and a maximum difference between experimental and numerical results of about 3.3% is observed in the small reservoir when the discharge is from 0.6 to 0.1 MPa. The experimentally-based results generate final temperatures slightly lower than the ones obtained via CFD simulations. As the walls were assumed adiabatic in the CFD simulations, Figure 6 confirms this assumption; then, the heat transferred through the walls appears to be negligible.