## 4 Results and Discussion
Moreover, raising the side air flow rate converts the flow in the right branch of the U-tube to bubbly flow which is found to break down the entrainment process and siphon the flow of the U-tube by raising the static pressure in the tube upper part. The water vapor contours are seen in Figures 19-22. Lower values of water flow rates even at higher values of the side water  
Figure 6.0 Pressure contours at different flow ratios and \(X_{w}=662.96\), \(\alpha_{m}=0.7\) and \(X_{v}=0.5\). vapor flow decrease the pressures in the U-tube upper part. This is attributed to the instantaneous local condensation of water vapor in the upper part which enhances the continuous entrainment of the side mixture. Additionally, the water vapor can be seen at the right branch of the U-tube exit without condensation at higher values of water and side mixture flow rates. This process with time breaks the siphon flow in the proposed system. Figure 6.1 Air volume fraction contours at different flow ratios and \(X_{\mathrm{w}}=461.42\), \(\alpha_{\mathrm{m}}=0.7\) and \(X_{\mathrm{v}}=0.1\). Figure 6.2 Air volume fraction contours at different flow ratios and \(X_{\mathrm{w}}=4306.59\), \(\alpha_{\mathrm{m}}=0.2\) and \(X_{\mathrm{v}}=0.1\). Figure 6.3 Air volume fraction contours at different flow ratios and \(\mathrm{X_{w}}=6187.64\), \(\alpha_{\mathrm{m}}=0.2\) and \(\mathrm{X_{v}}=0.5\). Figure 6.4 Air volume fraction contours at different flow ratios and \(\mathrm{X_{w}}=662.96\), \(\alpha_{\mathrm{m}}=0.7\) and \(\mathrm{X_{v}}=0.5\). Figure 6.5 Vapor volume fraction contours at different flow ratios and \(\mathrm{X_{w}}=4306.59\), \(\mathrm{\alpha_{m}}=0.2\) and \(\mathrm{X_{v}}=0.1\). Generally, in mixing two different flows, the turbulent Reynolds number is computed to capture the degree of interaction and turbulence due to mixing. This number is a relation between the turbulent kinetic energies to the dissipation rates and is defined as \((Re_{\rm t}=k^{2}/(\varepsilon\delta))\). Moreover, the turbulent Reynolds number clarifies the mixing shear layers of the flow. The turbulent Reynolds number contours at different values of flow mass ratios are depicted in Figures 23-26. It is noticed that at a water flow rate of 2 and 4 kg/s and side mixture volume ratio of 0.7, higher values of turbulent Reynolds number and flow eddies occur. This ensures, better entrainment, and mixing can be satisfied with the flow conditions of 2-4 kg/s with a mass ratio in the range of 461-662 or less. Acceptable entrainment can work until a mass ratio of 1000 at \(\dot{m}_{\rm w}=2\) kg/s, as predicted previously in Figure 6.6  
Figure 6.7 Vapor volume fraction contours at different flow ratios and \(X_{\rm w}=6187.64\), \(\alpha_{\rm m}=0.2\) and \(X_{\rm v}=0.5\). Figure 6.8 Vapor volume fraction contours at different flow ratios and \(X_{\rm w}=662.96\), \(\alpha_{\rm m}=0.7\) and \(X_{\rm v}=0.5\). Figure 6.9 Turbulent Reynolds number contours at different flow ratios and \(\rm X_{w}=4306.59\), \(\rm\alpha_{m}=0.2\) and \(\rm X_{v}=0.1\). Figure 10.0 Turbulent Reynolds number contours at different flow ratios and \(\rm X_{w}=461.42\), \(\rm\alpha_{m}=0.7\) and \(\rm X_{v}=0.1\). The radial distribution of air and vapor volume fraction contours at different mass ratios and positions (L/d = 10, 25, 50, and 100) are shown in Figures 27 and 28. In these Figures, L represents the measured downward distance on the tube from the side pipe centerline, while d is the tube diameter. Air is flowing near the side mixture inlet at closer positions of the side pipe due to the water steam inertia. On the other side, the vapor is instantaneously condensed after mixing with the tube water stream at lower values of water mass flow rate. Increasing the tube water flow rate makes the vapor continuing downward in the tube without condensation and in some extreme cases, the vapor may exit the inverted U-tube in the lower water tank without condensation.