Free Surface Level Research Articles

Laser Doppler Method for Measuring Oscillating Flow in Prismatic Tanks

THE flowfield inside a partially filled prismatic tank with a rectangular section which oscillates laterally has been analyzed using a laser Doppler velocimeter. The distribution of vertical velocity near the free surface, when the frequency of the acting force is equal to one of the natural frequencies of the liquid-tank system, shows that the maxima and the nodes are shifted toward the center of the tank in comparison with the positions computed using the linear theory. Considering the effective value of the horizontal velocity along a vertical line, it is possible to show a velocity out of phase at different points. This phenomenon is particularly noticeable for the vibration modes of higher order. Contents Experimental studies of the sloshing flow, which are needed essentially to determine the natural frequencies of the tankliquid system, have been carried out by flow visualization or by measuring the free surface levels, the accelerations, and the pressures.1 Few attempts have been made to analyze the velocity field instead. In fact, the particular characteristic that the velocity of the fluid motion oscillates near the zero value has made it difficult to analyze the fluid field experimentally. In the present paper good results are obtained using a laser Doppler velocimeter (LDV) to determine the velocity field inside the fluid in a tank laterally excited. The LDV method enables one to obtain very accurate velocity measurements with a good spatial resolution, without disturbing the field in any way. The tests have been carried out using a Plexiglas rectangular tank (30 X 15 cm) rigidly fixed to the oscillating table which is excited by a sinusoidal force of given amplitude and frequency supplied by an electromagnetic vibrator; the height of the liquid at rest was kept at h= 15 cm. The vibrator is controlled through an amplifier by a signal generator with a 0.01-Hz sensitivity in the low-frequency band (Fig. 1). The LDV is a one channel system and was used in the dual beam mode.2'3 The transparent walls of the tank permit the use of the forward-scattering method. The two beams are then led in the tank and allowed to cross at the point of interest. The LDV apparatus consists essentially of an-He-Ne laser of 5 mW power; an optical unit with a Bragg cell to shift the frequency, in order to measure negative velocities and those close to zero; a photomultiplie r; a series of filters, in order to reduce the noise-signal ratio; and a tracker, in order to measure the Doppler frequency. The output signal from either the accelerometer amplifier or the trackers are sent to an rms voltmeter which measures the effective value of acceleration and velocity. The vertical component of velocity is measured by the LDV at the point M which has been taken on the symmetry plane 2

Correlation between Schottky barrier heights on compound semiconductors and metal and semiconductor electronegativities

Examination of experimental results reveals a correlation between the free-surface band-bending and the value of the metal-semiconductor barrier extrapolated to zero electronegativity. Further, in materials with relatively high surface-state densities, the free-surface Fermi level Esf shows only a small variation for a range of semiconductors. It is proposed that this pinning is associated with the electronegativity of the anion. Formulas are presented for the prediction of barrier heights on a wide range of compound semiconductor alloys.

Shock wave diffraction at normal incidence on the free surface of liquid containing a wedge with its tip at the interface

Normal incidence of a plane shock wave in gas on the free surface of a compressible liquid, its reflection and diffraction are considered in the case when the liquid occupies a part of the lower half-plane, while the other is taken by a wedge whose tip is at the unperturbed interface. In a particular case one of the wedge sides can coincide with the free surface level line or be at a nearly straight angle to it. Owing to the problem linearity, the flows of liquid and gas are considered separately, viz. the flow of liquid is determined by the pressure behind the shock wave reflected from the solid /wedge/ wall, and the obtained form of the free surface determines the perturbed gas flow /1/.

Unsteady flow to a pumped well in a fissured aquifer with a free surface level maintained constant

New equations are derived for the drawdown in an aquifer consisting of two horizontal layers referred to as the block and the fissure, which have different hydraulic properties. The free water surface forming the upper aquifer boundary is located in the block. The water level is assumed to remain constant during pumping. The block and the fissure are compressible. The depth of the fissure is small in comparison with that of the block. The abstraction well, lined along the block, is pumped at a constant rate. The discharge per unit length of the unlined part in the fissure is constant, and the radius of the well is vanishingly small. Type curves for the drawdown in the fissure and the block are computed and plotted for some selected parameters involved. The effect of the block compressibility on the drawdown in the fissure is shown by comparing the type curves with the type A drawdown curves of Boulton (1963). The influence of the free surface compared with that of an impervious top layer on the drawdown in the fissure and the block is estimated by comparing the type curves with those of Boulton and Streltsova (1977a) found from the equations for a two‐layered formation, the top and bottom surfaces of which are impermeable.

Pompes primaires sodium à grandes dimensions

The primary pumps of high-speed reactors operate under a free sodium surface level and deliver the f1uid to the reactor core. This report describes a design study of a sodium pump from the following angles : a) Dimensions: Decreasing the diameter of a pump also decreases its weight (and therefore cost) and the diameter of the basic reactor unit. b) Technology : The aim is to achieve a simple design whilst ensuring technological continuity of the pumps in the system. The first design step was to determine reactor parameters to be considered in designing the pump. The most important of these are the following : a) Rate of flow b) Pressure drop across the reactor core, c) Available NPSH (here : pressure at the top of the reactor + head of sodium between a rotor and the free sodium surface). Design assumptions were 1 200 MW, four pumps, and all corresponding external parameters. The second step was to consider all potentially suitable hydraulic jet geometries associated with combinations of various rotor types (Fig. 1) and diffuser designs. The following were eliminated on initial analysis : a) Volute designs, as too bulky for a high-speed reactor. b) Crossf1ow designs, as involving excessively difficult design and manufacturing problems. This left the following designs for further consideration : a) Two-stage pumps with bottom intakes and non-dismantleable manifolds. b) Two-stage pumps with top intakes and non-dismantleable manifolds. c) Two-stage pumps with top intakes and dismantleable manifolds. d) Twin-rotor pumps with non-dismantleable manifolds. e) High-level intake pumps with dismantleable manifolds. f) High-level intake pumps with non-dismantleable manifolds. g) Low-level intake pumps with non-dismantleable manifolds. These designs were analysed, with the following results : a) Two-stage designs are very complicated and do not result in any substantial improvement as regards geometry. Hence, they were eliminated. b) Though twin-rotor designs are attractive as regards geometry, their bearings, overhung rotors and critical shaft speeds are major problems. They were therefore eliminated. c) High-level intake pumps require the largest amount of space and, in addition, have to be provided with an intake skirt. This resulted in their elimination. d) Axial low-level intake pumps (Fig. 9) combine simple design with optimal diameter. It was concluded that such pumps offered both optimal dimensions and a suitably simple overall design for the considered reactor parameters. The report ends with a brief review of specific hydraulic problems associated with these pumps, e.g. choice of diffuser design, inflow to the hydrostatic bearing, etc.

Three-dimensional theory on supercavitating hydrofoils near a free surface

Supercavitating hydrofoils of large aspect ratio operating near a free surface are investigated, assuming an inviscid and irrotational flow with the effects of gravity and surface tension neglected. The flow near the foil, treated as two-dimensional, is solved by a nonlinear free-streamline theory, then a three-dimensional ‘downwash’ correction is made using Prandtl's lifting-line theory. The strength of the lifting-line vortex is determined by information from the two-dimensional solution through a matching procedure, in which the inverse of aspect ratio is used as a small parameter for asymptotic expansions. The analysis incorporates a free-surface reference level to determine the submergence depth of the foil. The present method can be applied to any type of foil having an arbitrary planform or profile shape, including a rounded leading edge, a twist and even a small dihedral angle, within the assumption of large aspect ratio. Numerical computations made on rectangular flat-plate hydrofoils show excellent agreement of results with existing experimental data, even for large angles of attack and relatively low aspect ratios. The pressure distributions, shapes of the cavity and free surface are also calculated as a function of spanwise position.

Quelques aspects des écoulements presque horizontaux à deux dimensions en plan et non permanent, application aux estuaires

Quelques aspects des écoulements presque horizontaux à deux dimensions en plan et non permanent, application aux estuaires