Numerical Modeling of Supercritical Waves in Bends with the Finite Volume Method of Roe-TVD and Appraisal of Analytical Assumptions

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Abstract

In this research, using the finite volume method of Roe-TVD, supercritical flow in the curved channel of Reinauer and Hager was studied and the results were compared with the analytical method of Knapp-Ippen, the numerical method of HLL and the available experimental data of Reinauer and Hager. Then, using the numerical results, the accuracy of the assumptions of the analytical method was evaluated. It was observed that the super-critical oblique standing waves are diffused along the bend way. With an inlet Froude number, Fr0<4.2, the assumptions of constant average cross-sectional velocity along the bend and frictionless flow or constant specific energy is acceptable with an error of around one percent and the velocity variation at the external wall is tolerable with a maximum error of four percent. By increasing the inlet Froude number, flow at the internal wall dries up and the above assumptions are invalidated.

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References

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