Numerical modeling of the flow over the spillway using the weakly compressible moving particles semi-implicit method (WCMPS) (case study of Dehn Qala dam)

Introduction
Numerical simulation has increasingly become a very important tool for solving complex phenomena in fluid mechanics. Today, computational fluid dynamics (CFD), which uses numerical simulation to solve fluid flow problems, has become a major tool in many scientific and engineering studies. So far, most simulations have been performed using network-based Euler methods. The main problem with using such methods is the presence of sharp and mobile joints as well as free surface cells that require complex behaviors. In recent years, a new generation of numerical methods called mesh-free particle methods (Lagrangian) has been developed to solve computational fluid dynamics (CFD) problems. In these methods, the domain of the fluid is represented by a set of moving particles in the Lagrangian system. Mesh-free Lagrangian methods, including SPH and MPS, allow numerical modeling of flow in the face of large deformations or Discontinuity of boundaries. Due to the importance of the subject, the purpose of this study is to simulate the hydrodynamics of flow on the overflow of Dahan Ghaleh dam using a mesh-free Lagrangian method based on weakly compressible moving particle semi-implicit formulation (WC-MPS).

Methodology
In Lagrangian methods, unlike the Eulerian method, instead of networking the solution field and discrete the equations on the nodes, the solution field is divided into a number of particles and the discrete equations are solved on these particles. In fact, the governing equations are transformed into particle interaction equations using different operators. In the WC-MPS method, the system is considered as a system with weakly compressibility and calculates the pressure of each particle using the state equation. The MPS method uses particle density to track the free surface. Because there are no particles outside the free surface, the density of the particles on the free surface decreases severely. A particle is known as a free surface particle whose density is somewhat lower than the standard particle density. The value of this limit may be selected from 80% to 99% depending on the problem. Therefore, the pressure of this particle on the free surface will be set to zero in each time step and there is no need to apply any additional conditions for the free surface. For solid (impermeable) boundaries, such as walls or beds, In the vicinity of solid boundaries, the particle density decreases, which can lead to computational disturbances. Therefore, a number of ghost particles are located outside the boundaries to prevent this density reduction. In order to model the inlet and outlet flow, the particle recycling method at the inlet and outlet boundaries, which was developed by Jafari Nodoushan et al. (2016) was used.


Results and Discussion
In this study hydraulic parameters of the flow on the broad crested weirs, chute, and flip bucket of Dahan Ghaleh dam are investigated. At first, the free surface profile was compared at times t = 1, 5, 10, 15, 30 seconds for three flow rates of 461, 600, and 904 m3/s. when the discharge is 600 m3/s, the depth and velocity of the flow at the beginning of the channel will be 1.1 m and 9.1 m/s, respectively. The value of the depth and velocity of the flow at the beginning of the channel in WCMPS modeling is 1.191 m and 8.420 m/s, respectively, which shows the accuracy of the model in predicting the depth and velocity of the flow. In this research, the pressure is simulated in the form of pressure contour at different points in terms (pa) for three different flow rates. The highest pressure is near the bed in the approach channel and no part of the broad crested weirs, chute, and flip bucket is under negative pressure. Simulation of cavitation index has been done in broad crested weirs, chute, and flip bucket. the results showed that the cavitation index in the range of 110m to 140m has approached the critical value and the possibility of creating cavitation phenomenon in this area is more than in other places, but considering the cavitation index value in this area is greater than 1.8, according to the recommendation Falvey (1990) it does not need to be protected against cavitation. At the end, the height and length of the jump from the edge of the bucket for different discharges have been investigated.

Conclusion
In this study, the hydraulic parameters of the flow on the broad crested weirs, chute, and flip bucket of Dahan Ghaleh dam are investigated. The desired model has simulated the depth and velocity of the flow at the beginning of the channel after of the overflow, depth, velocity, and Froude number of the flow in the bucket floor with an error of less than 10%, and the jump length per discharge 600 (m3/s) with a maximum error of 12% has simulated. The comparison of the results indicates the accuracy and reliability of the results of the developed model.