On the discharge characteristic at the dam site after dam break

Abstract

UDC 532.532 + 532.59 V. I. BukreevA review of the information available in the literature is given, and new experimental data on the depth and discharge at the dam site after a total and a partial dam break are presented. It is shown that in the case of a partial dam break with the formation of a rectangular breach, the specific discharge per unit width of the breach is higher than the specific discharge in the case of a total dam break with the same excess initial energy in the headwater.Introduction. The solution of the hydrodynamic problem of dam break, which is of independent importance, can also be used to test methods for the calculation of catastrophic waves resulting, for example, from earthquakes, landslides, meteorite falls, strong explosions, shallow-water tsunami, quick stop of containers filled partially with a fluid, the striking of wind waves on a ship deck. At present, this problem has been solved using the model of potential fluid motion, in particular, the first approximation [1, 2] and higher approximation [3, 4] of shallow-water theory, Saint Venant equation [5,6], the Euler and Navier-Stokes equations [7], and the equations taking into account turbulent mixing [8] and the interaction of water and air [7].The dam break problem differs from the other problems of catastrophic waves in the clear formulation of the initial conditions. These conditions are only characterized by geometrical parameters L i , the acceleration of gravity g, and the physical properties of water (in some models, in addition, by the properties of air). In the ideal fluid model, the physical properties of water are ignored. In this case, which is degenerate from the viewpoint of dimension theory, the system has freedom in choosing the characteristic velocity. In other words, the characteristic Froude number in this formulation of the problem is uniquely determined by geometrical parameters. This simplifies not only the calculations but also physical modeling because experiments can be performed on fairly small setups. In the ideal fluid model, it suffices to observe geometrical similarity in order for the Froude number to be the same as under natural conditions. In a viscous fluid, the Froude number also depends on the Reynolds number. However, even for a small (about 10-cm) initial free-surface level difference, the Reynolds number Re > 10 4 and the flow at the dam site virtually does not depend on this parameter. For large initial differences between the headwater and tailwater levels, the water continuity may be interrupted, in which case the results of the classical theory and laboratory experiments, strictly speaking, are not applicable. This process, however, has a local nature. At fairly large distances from the dam site, its influence is manifested mainly in the fact that the initial potential energy stored in the dam is not entirely converted to the energy of wave motion. Quantitative information on such local energy losses is currently not available.Calculations of dam-break waves at large distances and times for...

Experimental verification of methods for calculating partial dam-break waves

“…The experiments performed in [8,9] and in the present study show that partial dam-break waves can be of the same types (A, B, and C) as those resulting from a dam break above a drop. Below, this is used in extension of theory [11,12].…”

“…Below, the dam-break wave is primarily considered. The upstream wave needs to be studied in greater detail because, according to experimental data [8,9], the shape of this wave is more complex than that in the first shallow-water approximation.…”

Discharge and energy-loss coefficients in flow through a breach in a trapezoidal dam

“…The theory of [1] assumes that after dam break, the flow in the vicinity of the breach rapidly becomes steady-state. Experiments [3,4] have supported this assumption. Therefore, in calculations using the method proposed in [1], it is sufficient to know the discharge coefficient for steady-state flow through a weir in the form of a breach.…”

“…Only the discharge and energy-loss coefficients are considered. Some information on the free-surface level established ahead of a rectangular breach after a partial dam break is given in [3,4]. Experimental data on the discharge coefficient of a rectangular weir is contained in [5].…”

“…In the experiments, the piezometers were placed so that, in the case of their displacement for a distance ±10H along the x axis, the changes in the values of m and ζ did not exceed the measurement error. This error can be judged from the scatter of the experimental points in Figs As is known, in a certain range of parameters of the problem, a critical depth is established in some cross section above the weirs [3][4][5], which is calculated by the formula h * = (q 2 /g) 1 If H 2 < h * + δ, the state of head and tail conjugation is invariably free. The influence of the submergence of the weir crest is characterized by the dimensionless parameter…”