Analytical Solution of the Task of Boundary Determining of Flow Spreading

Abstract

A mathematical model of a two-dimensional high-speed flow in terms of justification and taking into account several physical assumptions is formulated. The problem is solved analytically in the plane of the velocity hodograph and in the physical plane to determine all parameters in terms of flow flow. The coupling of a uniform flow with a general flow in the form of a "simple wave" made it possible to achieve a reduction in the error of the mathematical model. The adequacy of the pre-sented method is shown. The existing models are described that are insufficiently acceptable and adequate in terms of the geometry of the flow boundary, but with a large mismatch in local depths and velocities. The adequacy of the new model as a whole is characterized by the convergence of the model parameters both in geometry (flow spreading boundaries) and kinematics (depth and flow velocity) increased to 18% in both directions. The section of the "simple wave" should be well combined with the real flow, taking into ac-count the forces of resistance to the flow. The boundaries of the use of the proposed model belong to the section of the expansion of the flow in 3-7 b as required in the reference literature, and have been clarified in earlier works. The proposed model, as shown in the article, takes into account real (experimental) flow spreading and is consistent with previously performed theoretical studies. An important conclusion in the article is that the values of the Froude criterion in the new model can be any in the range from 1 to infinity, and at the same time the section "$X_D^I$" can increase with in-creasing Froude number.