Iterative Solution for Ideal Fluid Jets

Abstract

Free jets are important flow phenomena from outflow structures of dams and reservoirs. The basic case of jet flow originates from a free overfall with upstream critical flow conditions and a fully ventilated nappe. In this paper, a two-dimensional potential flow model has been developed. Semiinverse mapping of the Laplace equation has been employed in conjunction with an analytical solution of the Boussinesq equations to initiate iterations for locating the free streamlines under atmospheric pressure. A systematic iteration method is proposed using the squaring technique for solving the Laplacian field, a computation of the free streamlines using the curvilinear formulation of velocity at boundary streamlines in the energy equation, and an iteration of the position of the terminal jet section versus the brink section conditions. The model permits a convergent numerical solution, which was verified against experimental data, thereby indicating that the proposed ideal fluid flow model can be applied to predict the shape of free jets by simple computations.