Free Surface Variation Research Articles

Influence of free-surface variation on the repeatability of seismic data.

Influence of free-surface variation on the repeatability of seismic data.

Three‐dimensional modeling of non‐hydrostatic free‐surface flows on unstructured grids

SummaryA three‐dimensional numerical model is presented for the simulation of unsteady non‐hydrostatic shallow water flows on unstructured grids using the finite volume method. The free surface variations are modeled by a characteristics‐based scheme, which simulates sub‐critical and super‐critical flows. Three‐dimensional velocity components are considered in a collocated arrangement with a σ‐coordinate system. A special treatment of the pressure term is developed to avoid the water surface oscillations. Convective and diffusive terms are approximated explicitly, and an implicit discretization is used for the pressure term to ensure exact mass conservation. The unstructured grid in the horizontal direction and the σ coordinate in the vertical direction facilitate the use of the model in complicated geometries. Solution of the non‐hydrostatic equations enables the model to simulate short‐period waves and vertically circulating flows. Copyright © 2015 John Wiley & Sons, Ltd.

Discharge and flow field of the circular channel along the side weir

The side weir is one of the most important hydraulic structures that is used by hydraulic engineers for adjusting and controlling flow in urban waste collection systems, irrigation and drainage networks. In this study, an equation is proposed for computing side weir discharge located on circular channels. The equation computes the side weir discharge with sufficient accuracy. Then, the RNG k–ε turbulence model is used for simulating the turbulence of the flow field and the free surface flow variations are modeled using volume of fluid scheme. Comparing experimental results with numerical simulations indicates acceptable accuracy of the numerical model. Also, the side weir discharge coefficients, flow free surface variation, behavior of dividing stream surface and variations of stagnation point height for different discharges within a circular channel along a side weir were examined.

3D-CFD NUMERICAL MODELING OF IMPACTS FROM HORIZONTAL AXIS TIDAL TURBINES IN THE NEAR REGION

A Virtual Blade Model approach has been applied to simulate flows across a Horizontal Axis Tidal Turbine (HATT). The 3D-CFD Fluent 14.5 package was employed to solve the Reynolds Averaging Navier Stokes equations. A source term was added in the momentum equation as part of the solution developed through the Blade Element Momentum Theory for an incompressible flow in a open channel. The model was validated against experimental data of a 3 bladed 0.5m diameter turbine in a high speed re-circulating water flume in terms of velocity and Turbulent Kinetic Energy (TKE) profiles. The model results correlate well with the experimental data. The change of flow field and the variation of free surface can be clearly seen in the results.

Process Parameter Identification in Thin Film Flows Driven by a Stretching Surface

The flow of a thin liquid film over a heated stretching surface is considered in this study. Due to a potential nonuniform temperature distribution on the stretching sheet, a temperature gradient occurs in the fluid which produces surface tension gradient at the free surface of the thin film. As a result, the free surface deforms and these deformations are advected by the flow in the stretching direction. This work focuses on the inverse problem of reconstructing the sheet temperature distribution and the sheet stretch rate from observed free surface variations. This work builds on the analysis of Santra and Dandapat (2009) who, based on the long-wave expansion of the Navier-Stokes equations, formulate a partial differential equation which describes the evolution of the thickness of a film over a nonisothermal stretched surface. In this work, we show that after algebraic manipulation of a discrete form of the governing equations, it is possible to reconstruct either the unknown temperature field on the sheet and hence the resulting heat transfer or the stretching rate of the underlying surface. We illustrate the proposed methodology and test its applicability on a range of test problems.

Secondary current properties generated by wind-induced water waves in experimental conditions

Secondary currents such as the Langmuir circulation are of high interest in natural rivers and the ocean because they have striking impacts on scour, sedimentation, and mass transport. Basic characteristics have been well-studied in straight open-channel flows. However, little is known regarding secondary circulation induced by wind waves. The presented study describes the generation properties of wind waves observed in the laboratory tank. Wind-induced water waves are known to produce large scale circulations. The phenomenon is observed together with high-speed and low-speed streaks, convergence and divergence zones, respectively. Therefore, it is important to determine the hydrodynamic properties of secondary currents for wind-induced water waves within rivers and lakes. In this study, using two high-speed CMOS cameras, stereoscopic particle image velocimetry (PIV) measurements were conducted in order to reveal the distribution of all three components of velocity vectors. The experiments allowed us to investigate the three-dimensional turbulent structure under water waves and the generation mechanism of large-scale circulations. Additionally, a third CMOS camera was used to measure the spanwise profile of thefree-surface elevation. The time-series of velocity components and the free-surface were obtained simultaneously. From our experiments, free-surface variations were found to influence the instantaneous velocity distributions of the cross-sectional plane. We also considered thegeneration process by the phase analysis related to gravity waves and compared the contribution of the apparent stress.

Assessment of Turbulence Models for Prediction of Intermixed Amount with Free Surface Variation Using Coupled Level-Set Volume of Fluid Method

Assessment of Turbulence Models for Prediction of Intermixed Amount with Free Surface Variation Using Coupled Level-Set Volume of Fluid Method

3D numerical simulation of partial breach dam-break flow using the LES and k–ϵ turbulence models

The shallow water equations, also known as the Saint Venant equations, are commonly used to simulate transient free-surface flows including dam-break and levee-breach flows. However, these solutions give inaccurate results in the near-field of dam-break flow. In this paper, 3D numerical simulations of dam-break flow are done using the large eddy simulation (LES) and the k–ϵ turbulence models with tracking of the free surface by the volume-of-fluid model. A computational fluid dynamics solver is utilized for this. Results are compared with published experimental data on dam-break flow through a partial breach as well as with results obtained by others using a shallow water model. The results show that both the LES and the k–ϵ modelling satisfactorily reproduce the temporal variation of the measured bottom pressure. However, the LES model captures better the free surface and velocity variation with time.

Research on formation and stability of keyhole in stationary laser welding on aluminum MMCs reinforced with particles

The formation and stability of keyhole in stationary laser welding on aluminum metal matrix composites reinforced with particles are studied using a numerical simulation. The interaction between molten pool and reinforcement particles is evaluated by using the particle–fluid coupling model in the numerical simulation. In order to study the effect of different volume fractions of particles on the keyhole stability and fluid flow inside the molten pool, keyhole formation process, variation of free surface, temperature distribution, and fluid flow are calculated numerically, respectively. The calculation results show that the keyhole is stable at the beginning under different conditions and then the protrusion occurs inside the keyhole with increasing calculation time. The flow behavior of molten pool affected by particles and forces acting on the surface could explain the forming of humps inside the keyhole, which directly cause the variation of the keyhole. As the volume fraction of TiB2 particles increases, the keyhole is more likely to be instable and the oscillation occurs at an earlier time. Fluctuations of the surface tension and recoil pressure due to the uneven distribution play an important role in the instability of the keyhole.

2D numerical simulation of submerged hydraulic jumps

Hydraulic jumps are usually used to dissipate energy in hydraulic engineering. In this paper, the turbulent submerged hydraulic jumps are simulated by solving the unsteady Reynolds averaged Navier–Stokes equations along with the continuity equation and the standard k–ɛ equations for turbulence modeling. The Lagrangian moving grid method is employed for the simulation of the free surface. In the developed model, kinematic free-surface boundary condition is solved simultaneously with the momentum and continuity equations, so that the water elevation can be obtained along with velocity and pressure fields as part of the solution. Computational results are presented for Froude numbers ranging from 3.2 to 8.2 and submergence factors ranging from 0.24 to 0.85. Comparisons with experimental measurements show that numerical model can simulate the velocity field, variation of free surface, maximum velocity, Reynolds shear and normal stresses at various stations with reasonable accuracy.

Ejecta source and transport modeling in the FLAG hydrocode

We present the ongoing development and implementation of an ejecta model in the FLAG hydrocode. Ejecta is the term given to particulate matter that is produced at the free surface of a material subject to extreme shock loading. Following shock propagation into a material and reflection at its free surface, conditions may be sufficient to induce phase changes, damage, or fragmentation at the surface. The dynamics of the fragmentation may be such that a “cloud” of particulate matter forms and propagates away from the material.Modeling such phenomena in a continuum hydrodynamics code challenges the assumptions underlying the numerical approximations made in the hydrodynamics. The representative scales for the particulate matter are often much smaller than the representative scales for the bulk material producing the ejecta. However, this scale separation allows for statistical descriptions of ejecta that are compatible with continuum mechanics.Earlier work documents an initial effort in modeling ejecta in the FLAG hydrocode. The FLAG hydrocode computes continuum mechanics solutions for fluid and solid materials in an Arbitrary–Eulerian–Lagrangian (ALE) framework. To model ejecta in FLAG, a hybrid particle-continuum representation was defined that allows for coupling with continuum materials on large (bulk) scales. Numerical models were developed and implemented for particle production (sourcing) as well as for solving the particle equations of motion. The numerics were shown to conserve mass, momentum and energy, and preliminary results were given for modeling drag and volume effects.This work documents recent advances in source and transport models. Spatial and temporal dependencies have been added to the source models to account for geometric free-surface variations, mesh dependence, and shock loading. More physically relevant drag models have been implemented that include Reynolds number effects. These will be presented along with test results verifying the models. A FLAG model of an actual ejecta experiment will also be presented.

Three-Dimensional Simulation Parameters for 90° Open Channel Bend Flows

AbstractSharp open channel bend flows are highly three-dimensional because of the combined effects of secondary flow, large free-surface variations, and flow separation along the inner bend wall. A...

Surface temperature reconstruction based on the thermocapillary effect

A thin liquid film subject to a temperature gradient is known to deform under the action of thermocapillary stresses which induce convective cells. The free surface deformation can be thought of as the signature of the imposed temperature gradient, and this study investigates the inverse problem of trying to reconstruct the temperature field from known free surface variations. The present work builds on the analysis of Tan et al. [“Steady thermocapillary flows of thin liquid layers I. Theory”, Phys. Fluids A 2 (1990) 313–321, doi:10.1063/1.857781] which provides a long-wave evolution equation for the fluid film thickness variation on nonuniformly heated substrates and proposes a solution strategy for the planar flow version of this inverse problem. The present analysis reveals a particular case for which there exists an explicit, closed-form solution expressing the local substrate temperature in terms of the local film thickness and its spatial derivatives. With some simplifications, this analysis also shows that this solution applies to three-dimensional flows. The temperature reconstruction strategies are successfully tested against “artificial” experimental data (obtained by solving the direct problem for known temperature profiles) and actual experimental data. doi:10.1017/S1446181111000654

Evaluation of the influence of the time‐varying electromagnetic component in M‐EMS on flow at the free surface

AbstractIn the continuous casting process, the surface quality of the steel is as important as its productivity. The surface quality is mostly decided in the molten metal flow during the initial solidification stage, which progresses at the free surface of the molten steel. To improve the surface quality, this flow must be controlled. M‐EMS generates a time‐varying electromagnetic force, which helps to control the shape of the free surface. In this paper, we evaluate the possibility of controlling the flow at the free surface by MHD calculations. The results show a slight possibility for the flow at the free surface to be controlled. Although the free surface variation in a pulsed EMC process, which controls the shape of the free surface using the time‐varying electromagnetic force component, depends on electromagnetic force, the time‐varying component in the M‐EMS depends on the velocity of the molten metal. Since there is a first‐order lag between the electromagnetic force and this velocity, free surface variation in M‐EMS does not linearly depend on the time‐varying electromagnetic component. © 2011 Wiley Periodicals, Inc. Electr Eng Jpn, 177(3): 62–68, 2011; Published online in Wiley Online Library (wileyonlinelibrary.com). DOI 10.1002/eej.21167

Study of Solitary-Wave-Induced Fluid Motions and Vortices in a Cavity Using a Two-Dimensional Viscous Flow Model

This study presents a combined numerical and experimental investigation of the free-surface variation and induced fluid motion for a solitary wave propagating past a submerged cavity (or trench). The formation of vortices and the trajectories of fluid particles showing the transport of fluid content within the cavity zone are examined. A two-dimensional viscous flow is simulated by solving the stream function and vorticity equations using the finite-analytic method. Equations of free-surface boundary conditions are discretized by a two-step finite-difference scheme. To obtain more detailed motions in a cavity, a transient boundary-fitted grid system with locally refined grids is adopted. Experimental measurements of the free-surface elevations and the visual observations of the vortex motion were carried out to compare to the numerical solutions. The simulated free-surface elevations and fluid particle motion at various times are found to agree reasonably well with measurements and recorded observations. The formation and subsequent growth of a pair of recirculating vortices around the front corner of the cavity are clearly simulated by the present model. The effects of cavity size and incident-wave height on the flow patterns and the transport displacement of the fluid particles along the vertical and horizontal directions are analyzed. The results indicate that the greater the incident-wave height, the larger the values of the horizontal and vertical transporting distances. With an increase of cavity length, the strength of induced up-rolling vortices and the amount of downstream transporting fluid particles increases. However, the depth of the cavity has an insignificant influence on the height of the up-rolling vortices.

Three-dimensional modelling of flow in sharp open-channel bends with vanes

Flow around a sharp open-channel bend is highly three-dimensional (3D) due to the combined effects of secondary flow, a large free surface variation and flow separation along the inner wall. Continuous vanes often used in closed curved conduits to generate a more uniform downstream flow were tested in the open channel using a 3D finite-volume model with a Reynolds stress turbulence model and the volume of fluid method for free surface prediction. The velocity field, turbulent kinetic energy and the extent of the flow separation zone were successfully validated against laboratory measurements for the no-vane case. The 3D simulations for one-vane and three-vane configurations reveal that vertical vanes are effective to reduce the secondary flow intensity and flow separation along the inner wall. The energy loss for bends with vanes is further slightly reduced compared to the no-vane case. The three-vane configuration is particularly efficient at creating uniform downstream flow.

SURFACE TEMPERATURE RECONSTRUCTION BASED ON THE THERMOCAPILLARY EFFECT

AbstractA thin liquid film subject to a temperature gradient is known to deform under the action of thermocapillary stresses which induce convective cells. The free surface deformation can be thought of as the signature of the imposed temperature gradient, and this study investigates the inverse problem of trying to reconstruct the temperature field from known free surface variations. The present work builds on the analysis of Tan et al. [“Steady thermocapillary flows of thin liquid layers I. Theory”, Phys. Fluids A2 (1990) 313–321, doi:10.1063/1.857781] which provides a long-wave evolution equation for the fluid film thickness variation on nonuniformly heated substrates and proposes a solution strategy for the planar flow version of this inverse problem. The present analysis reveals a particular case for which there exists an explicit, closed-form solution expressing the local substrate temperature in terms of the local film thickness and its spatial derivatives. With some simplifications, this analysis also shows that this solution applies to three-dimensional flows. The temperature reconstruction strategies are successfully tested against “artificial” experimental data (obtained by solving the direct problem for known temperature profiles) and actual experimental data.

Nonlinear dynamics of phase separation in thin films

We present a long-wavelength approximation to the Navier–Stokes Cahn–Hilliard equations to describe phase separation in thin films. The equations we derive underscore the coupled behaviour of free-surface variations and phase separation. We introduce a repulsive substrate–film interaction potential and analyse the resulting fourth-order equations by constructing a Lyapunov functional, which, combined with the regularizing repulsive potential, gives rise to a positive lower bound for the free-surface height. The value of this lower bound depends on the parameters of the problem, a result which we compare with numerical simulations. While the theoretical lower bound is an obstacle to the rupture of a film that initially is everywhere of finite height, it is not sufficiently sharp to represent accurately the parametric dependence of the observed dips or ‘valleys’ in free-surface height. We observe these valleys across zones where the concentration of the binary mixture changes sharply, indicating the formation of bubbles. Finally, we carry out numerical simulations without the repulsive interaction, and find that the film ruptures in finite time, while the gradient of the Cahn–Hilliard concentration develops a singularity.

BEM-CADMAS-SURF 결합해석법에 기초한 수치조파수조의 응용

대수심의 유체운동을 포텐셜 운동으로 가정하여 자유수면의 거동을 신속히 해석하는 BEM 해석법과 구조물 근방에서 유체의 자유 수면 변화를 계산하기 위하여 NS방정식의 해석으로 CADMAS-SURF 기법을 결합하여 하이브리드 수치기법을 개발하였다. 하이브리드 해석법에서는 반사파를 고려해야 할 넓은 영역에서, 대수심의 영역은 BEM이, 천수역은 CADMAS-SURF가 계산하게 된다. 특히, 하이브리드 모델은 장시간에 걸친 불규칙파의 운동에 대해서는 단독의 CADMAS-SURF을 이용한 계산에 비해 거의 동일한 정확도로 월등히 신속하게 계산할 수 있다. 본 연구에서는 완경사 해저면을 가진 넓은 해역에서, 호안구조물에 내습하는 파랑의 처오름과 월파와 같은 강비선형 파랑장 계산에 결합해석모델을 적용하였다. 계산결과는 각각 토요시마(풍도(豊島))의 규칙과 처오름 실험과 고다(합전(合田))가 제안한 불규칙파의 월파량 산정도와 비교하였다. The hybrid numerical model is developed by combining BEM that can calculate the wave motion rapidly under the potential theory and CADMAS-SURF that solves Navier-Stokes equations for the free surface variation near the structure, In the hybrid model the calculation of wave motion in a wide field of wave reflection for deep water area is conducted by BEM but for shallow water area by CADMAS-SURF. Especially the hybrid model can calculate random wave motions for long term period more rapidly with almost similar accuracy than the calculation of wave motion which was carried out by CADMAS-SURF only. In this study the coupling model was applied to the calculation of the strong nonlinear wave motion such as wave runup and overtopping at the coastal structure on the mild-slope bottom and the results of numerical model were compared with the Toyosima's experiments of regular wave runup and Goda's design diagram of ramdom wave overtopping, respectively.

Evaluation of Influence of Time-Varying Electromagnetic Component in M-EMS on Flow at Free Surface

In the continuous casting process, surface quality of steel is as important as its productivity. The surface quality is mostly decided in the molten metal flow during initial solidification stage, which progresses at the free surface of the molten steel. To improve the surface quality, this flow must be controlled. M-EMS generates the time-varying electromagnetic force, which helps to control the shape of the free surface. In this paper, we evaluate the possibility of controlling the flow at the free surface by the MHD calculations. The result showed a little possibility of the flow at the free surface being controlled. Though the free surface variation in a pulsed EMC process, which controls the shape of the free surface using the time-varying electromagnetic force component, depends on electromagnetic force, the time-varying component in the M-EMS is decided by the velocity of the molten metal. Since there is a first-order lag between the electromagnetic force and this velocity, free surface variation in M-EMS does not linearly depend on the time-varying electromagnetic component.