Amyloid Beta-Peptide (1-40) Figure shows the free surface flow over the stepped

Figure 7 shows the free surface flow over the stepped spillway in experiments, VOF and mixture numerical models. It is apparent that the mixture model flow field shows a better agreement with experiments than the VOF model. The reason is that in the explicit VOF model, the air cannot diffuse to the water, and the boundaries of the water and air are separate. In the mixture model, no obvious boundary is apparent between the water and air phase, and the flow field shows the aeration. In this figure, the contour of the volume fraction is shown and the value of 0.5 can be assumed for the boundary between water and air.
Figure 8 shows the vortex generated in the steps with the mixture model and this vortex causes more dissipation of Amyloid Beta-Peptide (1-40) in each step. Figure 9 depicts the depth at which the air volume concentration is 0.9. The negative pressure positions on the steps in the mixture model are depicted in Figure 10. These positions are the critical positions where cavitating flow may be occurred, and should be analyzed for this phenomenon.
After deducing that the mixture model can predict results better than the VOF model, the above example, again, has been solved with various types of two-equation Eddy-Viscosity, such as Standard , Realizable , RNG (RENORMALIZED GROUP) , Standard –, SST (Shear Stress Transport) – models and also the RSM model, in order to achieve the best turbulence model.
The simplest and most complete scheme in turbulence models are two-equation models, in which two separate transport partial differential equations for the kinetic energy of turbulence and the length scale or turbulence dissipation rate are solved. In the RSM model, each term of Reynolds stress is calculated using a transport partial differential equation and one additional partial differential equation is used for solving the dissipation rate. The RSM model usually has more ability in modeling turbulent flow; however, it increases the computational time  [18].
In Table 3, the total velocity and head loss in all turbulence models are compared with the experiments and it is obvious that the minimum error belongs to the RSM (Low-Re Stress-Omega) model and that it is superior to other models. In Table 3, is the difference between the numerical and experimental results of each model.
In this part of the study, a new design for a step-pool spillway is numerically analyzed. Mardashti  [10] designed six types of new step-pool spillway and experimentally analyzed them. He has reported that among his models, types 4 and 5 are the optimal types. The basic difference between these two types is in the coefficient, , of the ogee spillway curve relation, which is as follows:
General principles of step-pool spillway architecture, which are depicted in Figure 11, are as follows:
In this research, in addition to analyzing types 4 and 5 with slopes of 18.8 and 28, which are reported experimentally  [10], some new step-pool spillways of type 4 with slopes of 35°, 40°, 45°and 50° have been designed and numerically analyzed. Table 4 shows the characteristics of different models of step-pool spillways that have been analyzed here.
Table 5 is the comparison of the presented results with Mardashti and Talebbeydokhti  [11]  experiments for the models of types 4 and 5 with 18.8°and 28° slopes. Amyloid Beta-Peptide (1-40) It should be mentioned that the meshing strategy and boundary conditions are the same as stepped-spillways in the previous sections.
Figure 12 shows the comparison of Table 5 graphically. As clear in this figure, in both cases, the relative error increases by increasing the discharge flow. These errors may be related to the formation of the calculated vortices in the pools (Figure 13), which are not exactly the same size and shape as the experimental vortices.
Figure 14 shows the formed vortices in the steps, which is the main reason for energy dissipation.
Figure 15 shows the free surface contour and there is no obvious boundary apparent between the water and air phase, and the flow field shows the aeration. Figure 16 depicts the location of the negative pressure on the steps for one kind of step-pool spillway. This position is the critical position where cavitating flow may be occurred and should be analyzed for this phenomenon.