Experimental Study of Shock Waves in Open-Channels Transition with Trapezoidal and Rectangular Sections

Background and objectives: Contractions have many uses in supercritical flows, such as flow conveyance from intake channels of dams to tunnel spillways, reduction of chutes width and reduction of flow conveyance time in the flood conduits. In supercritical flows studies, the formation of the shock waves has an important role. Technically, production and development of the mentioned waves are undesirable due to water depth increase because of several times increasing of inflow water depth, its spread at a wide range in downstream of channel and water surface roughness. Any weak design of channels under supercritical condition can cause to scour channel’s bed and walls, damage to equipment in the flow direction, raising maintenance costs and reduce water conveyance efficiency. In the present research, the formation of shock waves in converged transitions of open channel with rectangular and trapezoidal sections was investigated using laboratory and physical models.
Materials and methods: In order to investigate hydraulic parameters of shock waves in the converged transitions, twelve models with different geometries were used. In the present research, the studied geometric variables were the diagonal length of transition walls (0.5, 0.75 and 1m) and side wall angle (33.69º, 45º, 60º and 90º). In all used models, the convergence ratio was 0.5. The height and instantaneous velocity were measured in different points of formed shock waves in the mentioned models for four different Froude number in the range of 3.25 to 9.23.
Results: The measured values in the converged transitions showed that the velocity distribution was not uniform in the vertical direction of shock waves. Also, the results showed that by traveling wave front toward downstream cause to reduce wave velocity and increase wave height so that for various geometries, the changes trend was different. The results showed that on average, and for side slopes angels of 33.69º, 45º and 60º, the maximum height of shock waves was reduced 64.8%, 54.3% and 39.6% respectively in the comparison of trapezoidal and rectangular sections. Also, in the converged transitions and for the mentioned side slope angles, maximum shock wave velocity was reduced 39.1%, 31.6% and 16.5% respectively in the comparison of trapezoidal and rectangular sections. Increasing of side slope angle was accompanied with energy dissipation increment of shock waves for a constant Froude number and transition wall length. Also, maximum value of energy dissipation was seen for 0.5m of wall length. The values of energy dissipation for the mentioned length, Fr1=7.26 and side slopes angels of 33.69º, 45º, 60º and 90º were achieved 14.69%, 15.43%, 16.34% and 18.72%, respectively.
Conclusion: The analysis of the velocity profiles and free surface of shock waves showed that in general the reduction of side slope angle (increasing side slopes) of the transition wall, increase of diagonal wall length of the transition and reduction of Froude number have a direct relationship with the reduction of waves velocity and height. Since channels are constructed in the form of trapezoidal, the obtained results of the present research can be very useful for designer engineers.