Free Surface Variation Research Articles

ANALYSIS OF TURBULENT FLOW OVER ROUGHNESS BY LES AND PIV WITH WATER SURFACE FLUCTUATION

In the applications of the Large eddy simulation (LES) to open-channel flows with roughness, water surface is usually treated as a fixed boundary by neglecting the effects of surface fluctuation generated by boil vortices or relatively large surface variations caused by the drag force at each roughness element. In the present study, in order to expand the applicability of LES to such general conditions, the bottom topography is treated by introducing the immersed boundary method and the free surface variation is simulated by introducing a density function. It was made clear that the developed model is capable to represent relatively large surface variations in the strip-roughness flows with various roughness spacings. The numerical results agreed fairly well with those obtained by PIV.

Tracking the free surface of time-dependent flows: image processing for the dam-break problem

The dam-break problem (i.e., the sudden release of a given volume of fluid down a slope) has attracted a great deal of attention from mechanicians and physicists over the past few years, with particular interest devoted to the free-surface profile and the spreading rate. Experimentally, impediments to accurate measurements of the free-surface evolution are numerous because of the significant variations in its curvature and velocity. To accurately measure the surge’s free-surface variations with time, we have developed a new imaging system, consisting of a digital camera coupled with a synchronized micro-mirror projector. The object’s surface is imaged into a camera and patterns are projected onto the surface under an angle of incidence that differs from the imaging direction. From the deformed pattern recorded by the camera, the phase can be extracted and, by using unwrapping algorithms, the height can be computed and the free surface reconstructed. We were able to measure the free surface of the flow to within 1 mm over a surface of 1.8 × 1.1 m2. Although the techniques used in our system are not new when taken individually, the system in its entirety is innovative and more efficient than most methods used to-date in practical applications.

Viscous Fluid in Tank under Coupled Surge, Heave, and Pitch Motions

A tank might be simultaneously excited by surge, heave, and pitch ground motions during earthquakes. A time-independent finite-difference method is used to intensively study the combined effects of surge, heave, and pitch motions on sloshing viscous fluid in a rigid, rectangular tank. A complete fully nonlinear free-surface condition is used in the analysis. The numerical results are validated by the existing reported results. The evolution of the velocity vectors are described and discussed in detail. The coupled surge and heave and combined surge, heave, and pitch motions would enhance the free-surface stability during the transition period, during which the free surface variation ceases and sloshing begins in the opposite direction. No clear eddies are generated during a surge motion as they are during a heave motion. While the tank is experiencing pitch motion, a clear clockwise eddy occurs during the transition period, when the slope of the surface is negative. However, the eddy is counterclockwise when the slope is positive. A comparison between the surface elevation with combined surge, heave, and pitch motion and that of the superposition of separated excitation is made. The coupling effects are significant, and simultaneous surge and pitch motions should be included during a real earthquake analysis. The dominance of the frequency of excitation, ωx, on the frequency of the sloshing displacement is presented when ωx is less than the first fundamental frequency of water in tank, ω1. The first fundamental frequency dominates the frequency of the sloshing displacement throughout the sloshing when ωx is greater than ω1.

Three-dimensional modelling of free surface variation in a meandering channel

This paper presents a three-dimensional numerical study for the calculation of turbulent free surface flow in a meandering channel. The flow calculation is performed by solving the three-dimensional Reynolds-averaged continuity and Navier-Stokes equations with the k-ε turbulence model for steadystate flow. The model equations are solved numerically with a general-purpose finite-volume code. A free surface treatment for the spatial variation of the water surface in meandering open channel flow is employed. The effect of mesh resolution on the solution is also investigated. The performance of the model is assessed by comparing predicted results with the large-scale high-quality experimental data obtained from the UK Flood Channel Facility for inbank flow. The predicted distributions of water surface elevation, bed shear stress and streamwise and transverse velocities are used to investigate model performance. The predictive ability of the model is also assessed against the simulations with a planar surface assumption and use of the surface porosity method with regard to the distribution of bed shear stress. The results show that the free surface treatment for ihe spatial variation of the water surface is vital for the accurate prediction of bed shear stress.

Rescaled height coordinates for accurate representation of free-surface flows in ocean circulation models

Conventional height coordinate models have previously represented free-surface variations by a variable thickness upper layer. We present a rescaled height coordinate, which we call z ∗ , that treats the time-dependent free surface as a coordinate surface. This coordinate is isomorphic with the atmospheric η coordinate, sometimes known as the step-mountain coordinate. The z ∗ coordinate has also been used in a coastal ocean model. However, unlike both these implementations, here we use the finite volume method within the z ∗ coordinate framework, allowing an accurate representation of topography. The resulting scheme provides a very accurate representation of motions over steep topography in a three-dimensional general circulation model, even with fast and large amplitude free-surface variations.

CFD simulation of two‐ and three‐dimensional free‐surface flow

AbstractThe paper describes the implementation of moving‐mesh and free‐surface capabilities within a 3‐d finite‐volume Reynolds‐averaged‐Navier–Stokes solver, using surface‐conforming multi‐block structured meshes. The free‐surface kinematic condition can be applied in two ways: enforcing zero net mass flux or solving the kinematic equation by a finite‐difference method. The free surface is best defined by intermediate control points rather than the mesh vertices. Application of the dynamic boundary condition to the piezometric pressure at these points provides a hydrostatic restoring force which helps to eliminate any unnatural free‐surface undulations. The implementation of time‐marching methods on moving grids are described in some detail and it is shown that a second‐order scheme must be applied in both scalar‐transport and free‐surface equations if flows driven by free‐surface height variations are to be computed without significant wave attenuation using a modest number of time steps. Computations of five flows of theoretical and practical interest—forced motion in a pump, linear waves in a tank, quasi‐1d flow over a ramp, solitary wave interaction with a submerged obstacle and 3‐d flow about a surface‐penetrating cylinder—are described to illustrate the capabilities of our code and methods. Copyright © 2003 John Wiley & Sons, Ltd.

Application of two‐phase fluid approach for free‐surface ship flow simulation

Computational fluid dynamics methodology is applied to simulate the three‐dimensional free‐surface ship flow. Different from the widely used height function approach, a two‐phase fluid approach is adopted to capture the free surface variation generated by a ship with forward speed. The free surface is determined by the fluid concentration in a volume‐of‐fluid method. In the present study, the calculated results qualitatively match the measurements not only in the free‐surface wave system, but also in the total resistance prediction and the axial velocity distribution at the propeller plane.

Fundamental Properties of High Velocity Flows in a Continuously Meandering Channel

Fundamental properties of high velocity flows in a continuously meandering channel are studied analytically and experimentally. The linearized equations of the depth averaged flow model with the inertia term of momentum equation in the transverse direction, which is equivalent to Hasegawa's equation, is derived by use of the.power series expansion of transverse coordinate. Through the examination of the fundamental characteristics of the solution, it is shown that the resonance between the free surface variations and the channel meandering occurs with the increase of Froude number. The laboratory tests are carried out to verify the existence of resonance relation, changing the bottom slope of a channel. The comparisons of the analytical solution with the experimental results indicate that the resonance can be observed at the Froude number predicted by the theory and the amplitude of free surface variations in the experiments depends on the amplitude of the channel meandering.

Simultaneous measurements of water impact on a two-dimensional body

This study utilizes a high-speed charge coupled device (CCD) camera as the data acquisition system to simultaneously measure the pressure and flow field. The measurement system can be triggered by an external optical sensor, to obtain the free surface and pressure variations in each time step of the initial stage of water impact. The whole field image was observed by a high-speed area scan sensor camera. Almost no interval between photographing moving objects was allowed owing to the extremely short transfer time and high exposure sensitivity of the camera. Following image transfer, this characteristic and the hardware computational function of a video card not only allowed for binarization, accumulative addition but we could also quickly identify the track of a moving object and obtain the image and numerical data which we needed. Moreover, the flow characteristics are observed via a flow following “seeding” particles, and the digital particle tracking velocimeter (DPTV) so that the flow field velocity distribution can be measured.

Experimental Study on Sound Pressure Generated by Wave-Submerged Structure Interaction

This study is intended to discuss the sound pressure generated by the wave-submerged structure interaction, which is considered to play an important role on fish gathering function of an artificial fish reef. Laboratory experiments were carried out to measure a sound pressure as well as the velocity and free surface variation. In the experiments, idealized simple structures were employed and flow visualization was also conducted. It is confirmed that the installation of the submerged structure generates the sound pressure on several frequency domains. Moreover, it is revealed that the variation of sound pressure depends much on vortex formation and its behavior.

How to determine critical marangoni number in half floating zone convection

In the present paper, the coordinated measurements of the temperature profile inside the liquid bridge and the boundary variation of free surface, in addition to other quantities, were obtained in the same time for the half floating zone convection. The results show that the onset of free surface oscillation is earlier than the one of temperature oscillation during the increasing of applied temperature difference, and the critical Marangoni numbers, defined usually by temperature measurement, are larger than the one defined by free surface measurement, and the difference depends on the volume of liquid bridge. These results induce the question, “How to determine experimentally the critical Marangoni number?”

Vortex Formation with Free Surface Variation in Shear Layer of Open Channel Flows near Abrupt Expansion

The vortex formation with the free surface variation in the shear layer of open channel flows is investigated by means of the plane-2D-shallow water equations. The invisid instability analysis of the tanhtype velocity profile is firstly shown in order to make sure the applicability of the equations for the vortex formation in a free boundary layer. Then, the numerical simulation is made for the plane 2D-flow domain of open-channels with an abrupt expansion. Some numerical results conserning the vortex formation (velocity vectors, contour lines of depth etc.) are shown indicating the relation between the temporal velocity variations and the vortex shedding processes.

Unsteady thermocapillary flows and free surface oscillations

The unsteady thermocapillary flow and the free surface variation in a two-dimensional, thin liquid layer are investigated theoretically. The temperature is fixed at one end and sinusoidally varied at the other. By employing sine series expansions, the asymptotically oscillatory solutions of the u-velocity distribution and the free surface deformation are solved exactly. It is found that there exists an inversely proportional relation between τ u, the u-velocity time scale and τ s, the free-surface variation time scale, when the free surface has a maximum oscillation. Near the maximum oscillation conditions, the u-velocity may assume a uni-directional distribution across the layer depth. Furthermore, the deformation of the free surface becomes smaller when the gravity effect becomes more important.

An Explicit Finite Difference Model for Unconfined Aquifers

ABSTRACTMost of the current simulation models for unconfined aquifers are based on the assumption that the free surface variation is small so that it can be combined with permeability to reduce the nonlinear Boussinesq equation to a linear partial differential equation (PDE). One of the most obvious reasons for using the linearization assumption is for the ease of numerical solution. This work presents a simpler alternative which permits an easy direct solution of the Boussinesq equation. A forward in time, central in space (FTCS) explicit finite difference method is used in the simulation model. The model was first validated by comparing its results with known analytical solution. It was then applied to an actual situation in which the short‐term responses (from pumping) of an unconfined aquifer were simulated. The study shows that the stability of the model can be easily controlled, and because of the simple algorithm used, the code can be expeditiously developed and economically run on smaller machines. Due to the uncertainties in the calibration results, it is recommended here that more data be collected to improve the calibration before the model is used as a real‐time simulation tool.

Finite Element Analysis of a Nonsteady Seepage Problem

The finite element method has been applied to the analysis of seepage problem in steady state as well as the finite difference method, but rarely in nonsteady state. The aim of this study is to extend the application of the finite element method to the analysis of nonsteady seepage problem. Firstly, this paper describes the principle of the finite element method in nonsteady seepage problem and the procedure of the analysis, especially on the techniques for calculating the variation of free surface and for determining the position of seepage-out point. Secondly, an example is shown: the analysis of the seepage through an earth dam with a core and a horizontal drainage, in nonsteady state.