Numerical Simulation and Geometric Optimization of the Stepped Spillway of Jare Dam Using a Multi Objective Genetic Algorithm

Concerning the importance of water saving in Iran, as an arid and semi-arid country, dam construction plays a crucial role in water resources management. Spillways are one of the most important components of a dam. They are different in shape and function. Stepped spillway is one of the most designed and operated ones. Numerical simulation of the stepped spillway of Jare dam using FLOW 3D software and the geometric optimization of the steps' dimension using the multi-objective genetic algorithm is investigated in this research. The idea of using stepped spillways goes back to 3500 years ago (James et al., 2001). The oldest stepped spillway built in Iran has been recorded from 600 years ago. Studying the geometric features of stepped spillways in order to optimize the size and dimension of steps has also been the issue of interest for researchers (Chanson, 1996 and 20021; Pegram et al., 1999; Ferrari, 2010).

An experimental model of Stepped spillway of Jare Dam has been set up first in order to calibrate and verify the numerical model. Flow 3D software is applied for numeric simulation of the spillway and the multi objective genetic algorithm (NSGAII) is implemented to optimize the geometric dimensions. Calibration of the model has done after introducing the experimental models' geometry to FLOW 3D. Comparing the velocity data recorded by the numerical model and the experimental velocity data, the software has been verified.Turbulence modeling is the construction and use of a mathematical model to predict the effects of turbulence. Turbulence models are simplified constitutive equations that predict the statistical evolution of turbulent flows. K-epsilon (k-ε) turbulence model is a practical model to simulate the mean flow characteristics for turbulent flow conditions. It is a two-equation model which gives a general description of turbulence condition of the ambient flow by means of two transport equations (PDEs). The RNG model was developed using Re-Normalisation Group (RNG) methods to renormalize the Navier-Stokes equations, to monitor the effects of smaller scales of motion especially those of vertex movements. In k-ε model the eddy viscosity is determined from a single turbulence length scale, so the diffusion seen in the calculated turbulence is that which occurs only at the specified scale, although in real physical situations, all scales of motion will contribute to the turbulent diffusion especially those with more curvature streams. RNG turbulent model, as mathematical method that can be utilized to extract turbulence similar to the k- ε, results in a modified form of the epsilon equation. We have implemented both methods to simulate the turbulancd in the flow over the stepped spillway and to compare the effectiveness of both models when flow is dealing with a complicated solid as the Jare Dam spillway. Five different types have been considered for the geometry of the stepped spillway. Numbers of steps are designated 3 to 7 steps and are earmarked as the algorithm constrains. The variables are then defined and the fitness function of the algorithm is extracted. The multi objective genetic algorithm is then coded in MATLAB. In optimization procedure the geometric features including width, height and the number of steps in each five discussed type are calculated.

Velocity results using two turbulent models, RNG and K-ε, have been calculated separately. The results of the RNG model depict better match in accordance to the physical model's velocity data with less than 10 percent error. In optimization procedure the stepped spillway with 4 steps, 0.072m width (1:5) and 0.0665m height (1:5), is considered as the most optimum choice regarding the economic and hydraulic concerns.

Flow 3D software simulated the flow over the stepped spillway of Jare Dam quite acceptable. The simulating model depicted the most accuracy using the RNG turbulent model and the multi objective genetic algorithm used (NSGAII) suggested the 4 steps spillway as the most economic and functional choice for Jare stepped spillway.