# Impact of Mesh Resolution and Temperature Effects in Jet Ejector CFD Calculations
## 3 Results
### The Analysis for the Primary Temperature Variations Using the Refined Mesh  
The third study has the objective to analyze the differences when only the primary temperature changes and using the _refined_ mesh. The graph in Figure 11 shows the lines for the default primary temperature (T\({}_{\rm p}\) = 380 K), marked as \"T\" and represented with circular markers, and a case with this temperature increased by a factor of 1.2 (T\({}_{\rm p}\) = 456 K), marked as \"Tv\", with diamond shaped markers. In this case, by increasing only the temperature of the primary flow, only the stagnation conditions in the primary inlet are changed, without affecting the conditions at the secondary inlet, which remain constant. As can be seen in the figure, this produces an increase in the entrainment capacity of the primary flow (entrainment ratio) when the ejector is working in critical conditions. These differences between the two cases are maintained throughout the critical behavior zone.  
Figure 10: Mach number scenes comparison for three temperatures, at consecutive C, D, and E points from Figure 9.  
The difference in the entrainment ratio when the primary temperature increases by a factor of 1.2 is a variation from 1.17 to 1.28 in critical conditions. When dimensionless maps are used, the values obtained must be corrected with the temperatures and pressures used as reference. In this case, to correct the mass flow rates used in the map, they must be corrected with the square root of the temperature variation. In our case, the observed increase in the entrainment ratio coincides with the square root of the variation in the inlet primary temperatures, since \(\sqrt{1.2}\cdot 1.17=1.28\). However, when they are changed to subcritical conditions, the behavior in both cases is very similar, and no significant differences are observed.  
To check this, we corrected the results obtained from the case with the default primary temperature and compared it with the \"\(\mathrm{Tv}\)\" results (a case with a primary inlet temperature increased by a factor of 1.2).  
We can calculate the corrected entrainment ratio, as indicated in Equation (4):  
\[\omega^{*}=\frac{\dot{m_{s}^{*}}}{\dot{m_{p}^{*}}} \tag{4}\]  
And as the \(\dot{m_{s}^{*}}=const.\), we can focus on calculating the \(\dot{m_{p}^{*}}\) in the primary inlet as follows Equation (5):  
\[\dot{m_{p}^{*}}=\frac{\sqrt{\frac{\dot{T_{p}}/T}{\dot{p_{p}}/p}}}{\dot{p_{p}} /p} \tag{5}\]  
In our case, the pressures remain constant, and the proportions of primary temperatures were namely 1.2; therefore, we obtained the \"\(\mathrm{T}\) corrected\" entrainment ratio results as calculated in Equation (6):  
\[\omega^{*}=\sqrt{1.2}\cdot\omega_{v} \tag{6}\]  
Figure 12 below presents the graph of those plotted results, with the \"\(\mathrm{Tv}\)\" marked with diamonds and \"\(\mathrm{T}\) corrected\" with star symbols.  
Figure 11: Lines of \(\pi_{\mathrm{sp}}\) = 0.26 for case with higher primary inlet temperature ratio using _refined_ mesh.  
As can be seen, the curves fit. The critical operations zone values for the entrainment ratio overlap. After entering the subcritical operations zone, although the lines fluctuate, both cases seem to follow the same patterns. Then, towards the backflow operations regime they get closer again.