Dynamics Of Free Surface Flows Research Articles

Free surface flow characteristics of multi-phase viscoplastic fluids on inclined flumes and planes

Laboratory experiments were conducted to understand the dynamics of gravity-driven free surface flow of multi-phase viscoplastic fluids. Foam and sand–foam mixtures were employed to represent multi-phase yield stress fluids. Two different foam–water ratios of 0.1 and 0.2 were used and a wide range of sand concentrations from 0 to 0.82 were selected. A series of flume tests were conducted to model the two-dimensional flow of sand–foam mixtures for two slopes of 10° and 15°. Effects of sand concentration co on the dynamics of free surface flow were investigated. Three-dimensional spreading tests were carried out using an inclined plane with four bed slopes of α = 10°, 12°, 15° and 18. Single and multi-discontinuity were observed in the spreading of foam mixtures. It was found that the number of discontinuities can be correlated with the bed slope and multi-discontinuity occurred for α ≥ 12°. Flow heights and frontal velocities were measured for different experimental conditions (slope angle, rheological parameter). The results of spreading tests were properly scaled using a non-dimensional time scale and Froude number. Experimental results were used to predict the rheological characteristics of sand–foam mixtures based on the Herschel–Bulkley constitutive law. Predictions were compared with independent measurements of the rheological parameter. The inclined plane test results showed that the shear stress predictions were independent of the bed slope and the uncertainty of the predictions was slightly higher than the rheometery results from the literature.

A non-invasive airborne wave monitor

This work presents a new acoustical method for remote measurement of the surface characteristics of the dynamic air–water interface in turbulent free-surface flows. The technique uses the reflection of a monochromatic ultrasonic wave by the dynamically rough air–water interface to measure the water surface position. It is found that with careful selection of the acoustical components and their configuration, the phase of the reflected signal responds to the local fluctuations in the fluid interface at the point of specular acoustic reflection. In order for the method to be applicable, three criteria must be satisfied: (1) the dominant wavelength of the surface under investigation must be greater than the first Fresnel zone corresponding to the wavelength and component geometry of the acoustical system; (2) the mean magnitude of the instantaneous local surface gradient must not exceed 0.025; and (3) the root-mean-square wave height must be greater than 1% of the acoustic wavelength. Under these conditions the mean error of the system is within 5% (and usually within 1%) of the acoustic wavelength, and is generally within 10% of the wave amplitude for turbulence generated waves, and 3% of the amplitude for gravity waves. This error may be reduced by optimising the acoustic wavelength for the surface of interest. For turbulent depth limited flows, the surface waves fall well within the criteria, and the absolute errors are independent of wave height, so for larger wave heights, the relative error can be considerably lower. The technique provides a robust system for monitoring the dynamics of free surface flows, which is non-invasive, low cost, and low power. The method has been tested on laboratory flows but should be applicable to remote sensing of free surface properties on a local scale in field environments where invasive techniques are difficult to implement such as might be found in coastal, river and wastewater environments.

Critical Flow: A Historical Perspective

The dynamics of free surface flows are strongly influenced by the so-called critical flow state. The critical flow theory is relevant from an engineering standpoint, allowing for the computation of the head-discharge relationship for weirs and flumes, or the identification of control sections from which a free surface profile may be computed both in the up- and downstream directions Montes 1998; Hager 1999; Chanson 2004. In what follows, the origins of the critical flow concept are reviewed. Its evolution from perspectives of both the specific energy and the specific momentum is then highlighted, involving applications both in parallel- and curvilinear-streamline flows.

Classical hydraulic jump: basic flow features

The dynamics of free surface flow is characterised by the so-called Froude number F, whose value F = 1 separates subcritical (F < 1) and supercritical (F > 1) flows. The transition from F < 1 to F > 1 is smooth and continuous, as observed in weir flow. However, the reverse transition from F > 1 to F < 1 is abrupt and discontinuous. In the present research the simplest approximation is proposed to describe hydraulic jump flow. The 2D flow features of the classical hydraulic jump are properly described and favorably compared with experimental data. Based on one-dimensional results, the hydraulic jump flow is rationally related to the critical flow condition and it is proved that the specific energy of the main flow reaches a minimum value at F = 1, whereas the total energy head decreases due to energy dissipation. Further results relate to the effects of air, and the non-uniform pressure and velocity distributions.

Flux-blending schemes for interface capture in two-fluid flows

This paper is aimed at developing a robust algorithm (FBICS) to capture the interface between two immiscible fluids without the need of interface reconstruction. The advection equation of the volume fraction is solved using the fully conservative finite volume method. Determination of the convective flux through each cell face is based on blending of high resolution schemes and compressive schemes to preserve the sharpness and boundedness of the interface. The flux-blending practice is fulfilled with the use of flux limiters. Test on simple advection flow problems indicates that the well-known CICSAM and HRIC schemes lose accuracy as the Courant number increases. In contrast, the present method maintains high-accuracy performance for Courant numbers up to one. The capability of the method to cope with the complicated dynamics of free surface flows is demonstrated via calculation of the collapsing flow of a water column with an obstacle.

Mean-field dynamics of free surface flows through obstacle arrays in a narrow passage: amendments of the Washburn model

This paper is devoted to a moving-boundary problem of the creeping flow of a Newtonian liquid in a narrow passage, driven by capillary action at a free liquid–gas interface. We are specifically interested in the effects of an array of cylindric obstacles on that flow, which is of direct relevance to electronics manufacturing applications. We solve the related hydrodynamic equations by the efficient Monte Carlo technique of random walk simulation, capturing the time evolution of a global shape of the liquid–gas interface and the corresponding mean-field (averaged) dynamics of the flow. This dynamics represents the known Washburn dependence amended by a certain factor that reflects geometric parameters of the obstacle array. As a main contribution of this investigation, we calculate Washburn's factor for a wide range of rectangular and rectangular centered arrays. The results of our calculations demonstrate good agreement with available experimental data.

Dynamics of Free-Surface Flows With Surfactants

There is ample quantitative evidence (through, for example, surface tension measurements) of the presence of surfactants at the air-sea interface in sufficient quantities to influence the sea surface dynamics and its interactions with ambient flow turbulence. The importance of the role of the surfactants can also be judged from independent observations of phenomena such as suppression of short wavelength capillary waves and the presence of long-lived slick structures at the ship wakes. Although there is consensus on the presence of surfactants as the underlying reason behind these phenomena, the capability of quantitative predictions is still lacking for most of them. The objective of the present work is to introduce to the general engineering mechanics community the governing equations and the relevant issues associated with the study of free surface flows with surfactants. In particular, we focus on the interactions between a high Reynolds number flow, interface deformation and surfactant distribution next to and at the water-air interface. In addition, recent progress is briefly reviewed. Then, the remaining outstanding issues to allow the understanding of the dynamics of nonlinear interactions between turbulent flow and surfactant structure and concentration at the air-water interface are outlined.