On the Hydraulics of Two-layer Flows through the Gradual Constriction in Open-channel

Abstract

The main concern of this paper is to review the new theoretical and experimental treatments in this decade on the internal hydraulics of two-layer flows over a sill, through a contraction and the combination of a sill and contraction in a channel.By means of three approach methods as to the flow, which two layers are flowing in the same or opposite direction, the conditions for critical flow have been studied to define all of the essential characteristics of internal hydraulics.
First, “minimal approach”assumes Boussinesq approximation. Two-layer flow can be described in dimensionless parameter, known as Internal Froude Number (F_i²). Once the numbers are known, the flow condition through?out the channel can be drawn in Froude Number (FN)-plane.Hence, additional information of channel geometry and discharge relation should be known, in terms of parameters q₂/b, q_r and Y₂'.By then, a virtual control position of internal surface is explained by the FN-plane.This method also can be applied to moderate exchange flow with barotropic flow (U₀) known as Bernoulli potential problems.Using this concept, the characteristics of the flow can be figured such as two examples.
Second, “Characteristic function approach”uses the eigenvalue of two-layer flow matrix equation based on the equations of both continuity and motion.Two set characteristic velocities are obtained as the solution of quartic equation approximation. Based on this, Stability Froude Number (F_s²) facilitated a comprehensive understanding of the hydraulics of two-layer flows.
Third method is “Functional approach”.This is applied to explain an exchange flow in closed channel by Dalziel.Energy difference between two layers is converted into an implicit function in terms of several parameters.Developing these parameter relation, the interface can be determined at certain constriction of the channel geometry.
Further, Lawrence extended Bernoulli potential equation into other dimensionless one in terms of parameters, related to interface position (β_m) and the composite Froude number (G₀²).Both explanations about approach control and a classification scheme to predict the regime of flow is shown with experimental confirmation, provided the values of open-channel geometry, flow rate and lower layer height are given.
Finally, from the point of view of the tidal river flow analysis flow, the applicability of the above three methods are considered.