OPTIMIZATION OF COMPOSITE PARABOLIC CHANNEL CROSS-SECTION BASED ON CHANGES IN DISCHARGE AND FREEBOARD

This paper presents an optimal cross-section of a composite parabolic channel by considering four models based on freeboard changes. In this research, four models were presented separately to present the optimal shape of the parabolic cross-section. In the first model, the freeboard was considered zero. In the second model, a freeboard of 0.5 m was considered. In the third model, the freeboard was considered as a function of the discharge according to the standard regulations of India; in the fourth model, the freeboard was considered as a function of the flow depth in the optimization process. The objective function is to minimize the cost of lining and excavation costs. Design variables include flow depth and side slopes. Constraints include the Manning equation constraint to maintain a uniform flow, the Froud number constraint to ensure subcritical flow in the channel, total top width, and the velocity constraint to control sedimentation and erosion. The above optimization problem is solved using the optimization algorithm and the method of simultaneous perturbation stochastic approximation (SPSA). The results show that increasing the discharge increases the flow depth, left and right side slopes, total top width and water surface width, channel cross-sectional area and flow area, the total channel perimeter and wetted perimeters, flow velocity, Froud number, and the cost. By examining the relationship between cost with design variables, constraints and geometric parameters of parabolic channel cross-section at different iterations, the characteristic of the model that won the most number of iterations is based on the increase in left and right side slopes, total top width and water surface width, the cross-sectional area of the canal and the flow area, the total channel perimeter and the wetted perimeters, the Froud number, the cost increase. In contrast, increasing the depth and flow velocity reduces the cost. Comparison of the results of the four models with each other shows that the cost values in the first model are lower than those in other models. In the third model, they are higher than all models.