Free-surface disturbances due to the submersion of a cylindrical obstacle

We explore the initial perturbations that form on a liquid free surface as a result of the submersion of a circular cylinder beneath the surface, a scenario that arises in a number of diverse applications. The behaviour of the free surface is determined by transforming the equations of motion of the system via the Wehausen scheme, to variables for the free surface. A small-time series expansion is utilized to construct a recursive scheme that can be implemented numerically, and the time frame over which this approximation is valid is analysed. The resulting numerical model allows one to extend the results in the literature to study arbitrary cylinder sizes, including those where the cylinder is close to the free surface, and arbitrary cylinder motions. Of particular interest in this study was identifying the conditions under which strong jets would appear, and those were the free surface exhibited gravity waves. The formation of a central jet is found to be related to the growth of secondary, nonlinear waves, which rapidly merge as the obstacle is submerged. Classification maps are presented as a function of obstacle size and submersion speed, to identify the conditions which lead to jetting. Furthermore, the acceleration profile of the cylinder is shown to significantly affect the conditions under which jets form, which we argue is due to the rate at which energy is injected into the system.

The influence of obliquely perforated dual-baffles on sway induced tank sloshing dynamics

This paper examines the influence of oblique perforated baffles on the sloshing dynamics of rectangular liquid storage tanks. The analysis presented accounts for sway induced hydrodynamic forces and entropy generation. Internal liquid free surface oscillation is modelled by the volume of fluid method. The effect of baffle geometric parameters, orientation and porosity on loads is examined and numerical results are compared against a set of experiments. Consequently, an engineering method suggesting the optimum size, angle of inclination and topology of baffles for the case of a rectangular tank is presented. It is shown that implementation of optimized oblique porous dual baffles may reduce sloshing loads by up to 15%.

CHARACTER OF MANIFESTATION OF NONLINEARITIES FOR VIBRATION DISTURBANCE OF MOTION OF ELLIPSOIDAL RESERVOIR WITH LIQUID WITH A FREE SURFACE

The problem with vibration disturbance of the reservoir of ellipsoidal shape, partially filled with a liquid, is under consideration. For the construction of the model, we use the before developed method, based on the use of non-Cartesian parametrization of the domain, occupied by a liquid. And the method of the auxiliary domain for satisfying boundary conditions on tank walls above the unperturbed free surface of a liquid, where the liquid can pass in its perturbed motion. The liquid is considered as ideal incompressible. The mathematical model of the system is constructed based on the variational formulation of the problem in the form of the Hamilton–Ostrogradskiy principle. The motion of a liquid free surface is given in the form of decomposition with respect to normal modes of oscillations. Amplitude parameters of oscillations of a liquid free surface together with parameters of the translational motion of the reservoir form a complete independent system of parameters, for which the resolving system of ordinary differential equations is constructed. The constructed model includes nonlinear properties of the system and corresponds to the model of the combined motion of the liquid with the reservoir. According to its structure, the model has considerable similarities with the case of the cylindrical reservoir. The practical implementation of the method is done for vibration disturbance of the system motion in the horizontal plane for the case of extended and compressed ellipsoidal reservoirs. The analysis of the character of manifestation of the dynamical behavior of the system in different ranges of frequencies of motion disturbance shows that mainly this system behaves as a system with the soft type of nonlinearities. The system output to the steady mode of oscillations is not observed. Modulation of oscillations of a liquid free surface is considerably manifested for most modes. Increased attention is paid to the study of regularities of variation of a period of the oscillation modulation. It was ascertained that due to compression of the spectrum of liquid oscillations with the increase of the wavenumber, the simultaneous considerable effect of several frequencies is manifested in the system reservoir–liquid, which leads to complex modulation envelope lines.

Acoustic radiation force effect on a spherical drop placed in the vicinity of an ideal liquid free surface

Acoustic radiation force effect on a liquid spherical drop placed in the vicinity of an ideal liquid free surface is studied. The problem of determination of the radiation forces acting on an obstacle in ideal liquid is formulated with respect to the Lagrange coordinate system. Thus, the radiation pressure is defined as time-averaged value of the acoustic pressure over the obstacle surface. This approach is adequate if, at determining of the acoustic pressure in a fluid, the deviation of the pressure from the harmonic law in time domain is taken into account in the obstacle vicinity. An action of the acoustic radiation force on a spherical drop of ideal liquid placed in turn in a liquid by its free plane surface is studied here for the case of the incident plane sound wave propagating perpendicularly to the liquid boundary. As a result, the liquid sphere is appeared to be located in the standing sound wave of pressure which has its displacement node at the free surface. Problem solution is obtained as a three step procedure. Initially, solution of the problem of an incident wave scattering at the drop is derived. With making use of the results obtained, the second step encompasses determining of hydrodynamic forces acting on the liquid spherical drop with their subsequent averaging over the suitable time interval at the third step. It is found there frequencies of the incident wave exist that provide zero radiation force acting on the drop which is immobile in this case. These equilibrium positions of the spherical drop could be stable or unstable with respect to the incident wave frequency variation.

Dimensioning of vortex storm overflows

Vortex storm overflow is an interesting and useful technical solution, especially important in storm and combined sewage systems. However, there are no methods of this device dimensioning, which would be mathematically simple and properly precise physically. Such a method has been proposed in this paper, on the basis of investigations performed for the vortex separators and vortex flow controls. The essence of this method relies on the kinematic model of the velocity field and energy balance of the inflowing stream and dissipation. The procedure enables specialists to calculate the rise of the liquid free surface caused by the inlet stream energy and the hydraulic resistance of the bottom outlet. These mathematical relations are completed by two formulae: for the bottom ‘morning glory’ sink and for the upper overflow. The model has been positively verified during the laboratory measurements, so can be used during the technical dimensioning of the vortex storm overflows.