Performance of rectangular labyrinth weir- an experimental and numerical study

Labyrinth weirs are commonly used to increase the capacity of existing spillways and provide more efficient spillways for new dams due to their high specific discharge capacity compared to the linear weir. In the present study, experimental and numerical investigation was conducted to improve the rectangular labyrinth weir performance. In this context, four configurations were tested to evaluate the influence of the entrance shape and alveoli width on its discharge capacity. The experimental models, three models of rectangular labyrinth weir with rounded entrance and one with flat entrance, were tested in rectangular channel conditions for inlet width to outlet width ratios (a/b) equal to 0.67, 1 and 1.5. The results indicate that the rounded entrance increases the weir efficiency by up to 5%. A ratio a/b equal to 1.5 leads to an 8 and 18% increase in the discharge capacity compared to a/b ratio equal to 1 and 0.67, respectively. In addition, a numerical simulation was conducted using the opensource CFD OpenFOAM to analyze and provide more information about the flow behavior over the tested models. A comparison between the experimental and numerical discharge coefficient was performed and good agreement was found (Mean Absolute Relative Error of 4–6%).

Induced magnetic field and viscous dissipation on flows of two immiscible fluids in a rectangular channel

The unsteady, magneto-hydrodynamic generalized Couette flows of two immiscible fluids in a rectangular channel with isothermal walls under the influence of an inclined magnetic field and an axial electric field have been investigated. Both fluids are considered electrically conducting and the solid boundaries are electrically insulated. Approximate analytical solutions for the velocity, induced magnetic, and temperature fields have been determined using the Laplace transform method along with the numerical Stehfest's algorithm for the inversion of the Laplace transforms. Also, for the nonlinear differential equation of energy, a numerical scheme based on the finite differences has been developed. A particular case has been numerically and graphically studied to show the evolution of the fluid velocity, induced magnetic field, and viscous dissipation in both flow regions.

Wall Pressures In a Channel Flow Obstructed By a Line of Inclined Rods: Invariant Groups and Semi-Empirical Correlations

An experiment is conducted in a rectangular channel obstructed by a transverse line of four inclined cylindrical rods. The wall pressure around the perimeter of a central rod and the pressure drop through the channel are measured varying the inclination angle of the rods. Three assemblies of rods with different diameters are tested. The measurements were analyzed applying momentum conservation principles and semi-empirical considerations. Several invariant dimensionless groups of parameters relating the pressure at key locations of the system with characteristic dimensions of the rods are produced. It was found that the independence principle holds for most of the Euler numbers characterizing the pressure at different locations, that is, the group is independent of the inclination angle provided that the inlet velocity projection normal to the rods is used to non-dimensionalize the pressure. The resulting semi-empirical correlations can be useful for designing similar hydraulic units.

EIGENFREQUENCIES OF OSCILLATIONS OF A PLATE WHICH SEPARATES A TWO-LAYER IDEAL FLUID WITH A FREE SURFACE IN A RECTANGULAR CHANNEL

The frequency spectrum of plane vibrations of an elastic plate separating a two-layer ideal fluid with a free surface in a rectangular channel is investigated analytically and numerically. For an arbitrary fixing of the contours of a rectangular plate, it is shown that the frequency spectrum of the problem under consideration consists of two sets of frequencies describing the vibrations of the free surface of the liquid and the elastic plate. The equations of coupled vibrations of the plate and the fluid are presented using a system of integro-differential equations with the boundary conditions for fixing the contours of the plate and the condition for the conservation of the volume of the fluid. When solving a boundary value problem for eigenvalues, the shape of the plate deflection is represented by the sum of the fundamental solutions of a homogeneous equation for a loose plate and a partial solution of an inhomogeneous equation by expanding in terms of eigenfunctions of oscillations of an ideal fluid in a rectangular channel. The frequency equation of free compatible vibrations of a plate and a liquid is obtained in the form of a fourth-order determinant. In the case of a clamped plate, its simplification is made and detailed numerical studies of the first and second sets of frequencies from the main mechanical parameters of the system are carried out. A weak interaction of plate vibrations on vibrations of the free surface and vice versa is noted. It is shown that with a decrease in the mass of the plate, the frequencies of the second set increase and take the greatest value for inertialess plates or membranes. A decrease in the frequencies of the second set occurs with an increase in the filling depth of the upper liquid or a decrease in the filling depth of the lower liquid. Taking into account two terms of the series in the frequency equation, approximate formulas for the second set of frequencies are obtained and their efficiency is shown. With an increase in the number of terms in the series of the frequency equation, the previous roots of the first and second sets are refined and new ones appear.