Density-stratified Liquid Research Articles

Experimental and Numerical Study of Stratified Sloshing in a Tank under Horizontal Excitation

The density-stratified liquids horizontal sloshing was tested on a vibration table, and a series of laboratory experiments have been performed to analyze the influence of the excitation frequency on density-stratified liquids sloshing in a partially filled rectangular tank. The MultiphaseInterFOAM solver in OpenFOAM was employed to simulate two-layer fluids sloshing problems. The numerical results of dynamic pressure were validated against the experimental data, showing that the employed model can accurately simulate the stratified liquids sloshing phenomenon. Effects of two-layer fluids liquid depth ratio and total liquid depth on stratified sloshing characteristics were discussed in detail. The response law of the maximum interfacial wave elevation to external excitation frequency was presented in this study. The evolution of the velocity field of density-stratified liquids sloshing is also studied.

Laboratory and Computational Fluid Dynamics Investigation of Homogenization in a Tank Stirred by External Pump

The scope of this study was to investigate the homogenization of a two-layer stratified liquid in a tank where liquid stirring was achieved by carrying out external recirculation. Furthermore, the aim of the research was to observe the effect of the height of the outlet during the time of mixing one. The experimental fluid was two-layer, density stratified liquid. From the perspective of homogeneity, the effect of the height of the outlet was investigated in laboratory. Moreover, the experimental device was modeled in CFD. In simulation examination, laminar - and k-ε-model were used, and the influence of the outlet position was observed. The difference was remarkable in the first part of the measurement caused by the presence of sharp concentration variation in the tank. After the operating time, the expected homogeneity was fulfilled at the outlet in all cases. Regarding of CFD research, the results suggest that the laminar model is more effective to describe the concentration changes at the sampling point in the tank investigated.

Mathematical modeling of free-surface flows using multiprocessor computing systems

In this article the results of series of works concerning free-surface flows in liquid medium. Two models were considered: free-surface flows of homogeneous liquid and flows in density stratified liquid. For first model two problems were solved: fluid fluctuations in the container and the occurrence of an undular bore upon collision of a one-way flow with a wall. For second model also was performed test: collapse of homogeneously mixed spot of fluid in the stratified medium. For every test examples satisfactory results were obtained, comparable analysis was carried out whether it corresponds to analytic results.

Stability of a velocity field tangential discontinuity in a three-layer density-stratified liquid with a moving middle layer

A dispersion relation is analytically derived for gravitational waves in an ideal incompressible threelayer liquid with a free surface in the presence of a velocity field tangential discontinuity between the layers. The discontinuity results from the motion of the middle layer. The instability of the tangential discontinuity is shown to depend on the relative velocity of contacting layers, which, in turn, depends on the ratio of their densities. The closer the density ratio to unity, the lower the moving layer velocity causing instability. In the given case, instability involves internal waves arising at the second and third interfaces in accordance with the Kelvin–Helmholtz concept of instability development. Internal waves with wavelengths far exceeding the thickness of the middle layer are found to interact with each other. Surface waves only change their frequencies.

Method of controlling selective withdrawl through a hole in a vertical wall

This paper gives the results of experimental validation of a method of controlling selective withdrawl from the required layer of a stably density-stratified liquid which differs from traditional methods. The efficiency of the method is confirmed, and its advantages and drawbacks are noted.

Gas-dynamic analogy in the theory of stratified liquid flows with a free boundary

Novel approximate mathematical models of long-wave theory describing flows of a density-stratified liquid with a free boundary are proposed. It is shown that in certain cases the equations of the novel models coincide with either the equations of nonisentropic gas dynamics with a polytropic equation of state for γ = 2 or the equations describing the dynamics of a mixture of two perfect gases.

Numerical Investigation of Two-Dimensional Sloshing: Nonlinear Internal Waves

In this paper we examine internal sloshing motions in 2-D numerical wave tanks subjected to horizontal excitation. In all of the cases studied, the rectangular tank of liquid has a width-to-depth ratio of 2. The results presented are from simulations of internal waves induced by sloshing a density-stratified liquid. Nonlinear, viscous flow equations of a Newtonian, Boussinesq liquid are solved. Some of the features of the evolution of sloshing in nearly two-layer and three-layer fluid systems are described. Initially, the middle of the two layers and the center of the middle layer of the three layers are horizontal and located at the center of the tank. The two-layer cases are forced at resonance. The evolution of sloshing from rest is examined. The maximum amplitude of sloshing occurs during the initial transient. If breaking occurs, it is at the center of the container in the two-layer cases. The subharmonic forcing of a three-layer case induces a resonant response with the middle layer moving in such a way that motion is perpendicular to the isopycnals within this layer. These model problems provide some insights into the relatively complex sloshing that can occur in density-stratified liquids.

Nonlinear Free-Surface and Viscous-Internal Sloshing

This paper examines free-surface and internal-pycnocline sloshing motions in two-dimensional numerical wave tanks subjected to horizontal excitation. In all of the cases studied, the rectangular tank of liquid has a width-to-depth ratio of 2. The first set of results are based on an inviscid, fully nonlinear finite difference free-surface model. The model equations are mapped from the physical domain onto a rectangular domain. Case studies at and off resonance are presented illustrating when linear theory is inadequate. The next set of results are concerned with analyzing internal waves induced by sloshing a density-stratified liquid. Nonlinear, viscous flow equations are solved. Two types of breaking are discussed. One is associated with a shear instability which causes overturning on the lee side of a wave that moves towards the center of the container; this wave is generated as the dominant sloshing mode recedes from the sidewall towards the end of the first sloshing cycle. The other is associated with the growth of a convective instability that initiates the formation of a lip of heavier fluid above lighter fluid behind the crest of the primary wave as it moves up the sidewall. The lip grows into a bore-like structure as it plunges downward. It falls downward behind the primary wave as the primary wave moves up the sidewall and ahead of the primary wave as this wave recedes from the sidewall. This breaking event occurs near the end of the first cycle of sloshing, which is initiated from a state of rest by sinusoidal forcing.

Propagation of plane surface waves over an underwater obstacle and a submerged plate

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Schlieren interferometry applied to a gravity wave in a density-stratified liquid

A stably density-stratified liquid is produced in a rectangular glass tank by variation of the concentration of salt in water as a function of height. The glass tank is placed into the parallel beam of a schlieren interferometer with Wollaston prism adjusted to produce straight vertical fringes. A gravity wave of the cross wave type is excited and the resulting periodically deforming fringes are recorded by taking photographs. A method is developed to obtain from the fringe patterns results about propagation of the wave in space and time and about amplitude attenuation. The results are compared with the linear theory of Thomas and Stevenson (1972) and excellent agreement is found within the limits of the linear approach.

An interferometer to study density stratified flows

The conventional four-mirror interferometer is inconvenient for the study of density stratified liquids because of the refractive index gradient in the undisturbed state. It is found that a symmetrical six-mirror system is ideal for stratified liquids. The paths of the light rays through the system are analysed and experiments are described which verify that accurate quantitative results can be obtained.

Measurements of turbulence in a zero-mean-shear mixed layer

This paper is concerned with laboratory measurements of turbulence in a mixed layer and through a density interface, in the absence of a mean flow. The present results confirm the conclusion of Hopfinger & Toly (1976) that the turbulence in a mixed layer is not significantly affected by the slow entrainment of fluid across the bounding density interface. In a homogeneous fluid the turbulence intensity is found to be surprisingly non-uniform, even two grid mesh distances away from the grid. Velocity measurements have also been taken through a density interface (at the entraining boundary of a mixed layer) and the turbulence here varies in a manner that bears some resemblance to the theory of Hunt & Graham (1978). These velocity measurements were taken with a laser-Doppler anemometer and they were made possible by a novel experimental technique which eliminates the refractive index variations which normally occur in a turbulent, density-stratified liquid flow.

On the elimination of refractive-index variations in turbulent density-stratified liquid flows

The variations in refractive index in stratified liquid flows have been a major impediment to the use of laser-Doppler anemometry in these situations. This paper describes a method whereby these refractive-index variations can be drastically reduced while retaining the dynamically important density differences. The method uses two solutes to produce the density differences and it is shown that double-diffusive convection (of the salt-finger type) can be avoided by using a suitable pair of solutes. A theoretical model of the lateral wander of a single laser beam propagating through a turbulent medium is developed and this explains the success of the method.

Wave motions produced in a stratified liquid from flow past a submerged body

The integral-transform method is used to solve the linearized two- and three-dimensional problems of the wave motions produced by the flow of a density-stratified liquid past a submerged source and sink of equal intensity.

Numerical study of the behavior of a uniform “spot” in an ideal density-stratified liquid

A numerical analysis of the flow arising as a result of the collapse of a uniform spot in a heavy ideal liquid linearly stratified with respect to density is presented. The nonlinear model of the phenomenon is employed. The numerical results are compared with experiment.

Two automatic systems to generate gravitationally stable density stratifications in bodies of liquid at rest

Two automatic control systems for filling large tanks with gravitationally stable density stratified liquids are described. They are: (i) an analogue method using gate and mixture control valves operated through servomechanisms by rotating cams; (ii) a digital method with a numerically controlled metering-type pump. Measurements taken of a typical stratification showed that the actual density distribution was within 0?02% of that expected using the analogue method and within 0?01% using the digital method.

The internal wave pattern produced by a sphere moving vertically in a density stratified liquid

Experiments were conducted to test the linear theory of internal gravity waves produced in a stably stratified liquid by the steady vertical motion of a sphere. The measurements of the phase configuration in a medium whose density increased linearly with depth were made by means of a Toepler-schlieren system. The agreement between observation and prediction was found to be good.

The two-dimensional wave pattern produced by a disturbance moving in an arbitrary direction in a density stratified liquid

The two-dimensional internal wave pattern produced by a small disturbance moving with constant velocity along a line of arbitrary inclination in an inviscid, density stratified liquid is studied. It is shown how the far field wave pattern evolves as the inclination changes from the extreme of horizontal motion to that of vertical motion. It is found that, in general, waves propagate ahead of the disturbance.

A theoretical and experimental investigation of the phase configuration of internal waves of small amplitude in a density stratified liquid

Experiments were conducted to test the linear theory of internal gravity waves produced in a stably stratified liquid by the forced oscillations and the initial impulsive motion of a two-dimensional stationary disturbance. The measurements of the wave configuration in a medium whose density increased linearly with depth were made by means of a Toepler-schlieren system. The agreement between observation and prediction was found to be good.

The use of schlieren and shadowgraph techniques in the study of flow patterns in density stratified liquids

Various methods of establishing fluid media stably stratified in either temperature or the concentration of a foreign constituent are compared. A method used to construct a salt solution with precisely predetermined stratification is described. The Euler-Lagrange equations are solved exactly for a medium whose refractive index varies linearly in one dimension; the solution shows that a schlieren system may be used. For media with non-linear one-dimensional variation of refractive index, a modified shadowgraph technique may be employed. A device for the quantitative evaluation of a one-dimensional stratification is outlined and an example of its use is given.