Inhomogeneous wave reflection from the surface of a partially saturated thermoelastic porous media

2021 ◽  
Vol ahead-of-print (ahead-of-print) ◽  
Author(s):  
Manjeet Kumar ◽  
Xu Liu ◽  
Kapil Kumar Kalkal ◽  
Virender Dalal ◽  
Manjeet Kumari
Keyword(s):  
Free Surface ◽  
Phase Shift ◽  
Incident Wave ◽  
Decomposition Theorem ◽  
Inhomogeneous Wave ◽  
Content Type ◽  
Reflected Waves ◽  
Partially Saturated ◽  
Inhomogeneous Waves ◽  
Bulk Waves

Purpose The purpose of this paper is to study the propagation of inhomogeneous waves in a partially saturated poro-thermoelastic media through the examples of the free surface of such media.. Design/methodology/approach The mathematical model evolved by Zhou et al. (2019) is solved through the Helmholtz decomposition theorem. The propagation velocities of bulk waves in partially saturated poro-thermoelastic media are derived by using the potential functions. The phase velocities and attenuation coefficients are expressed in terms of inhomogeneity angle. Reflection characteristics (phase shift, loci of vertical slowness, amplitude, energy) of elastic waves are investigated at the stress-free thermally insulated boundary of a considered medium. The boundary can be permeable or impermeable. The incident wave is portrayed with both attenuation and propagation directions (i.e. inhomogeneous wave). Numerical computations are executed by using MATLAB. Findings In this medium, the permanence of five inhomogeneous waves is found. Incidence of the inhomogeneous wave at the thermally insulated stress-free surface results in five reflected inhomogeneous waves in a partially saturated poro-thermoelastic media. The reflection coefficients and splitting of incident energy are obtained as a function of propagation direction, inhomogeneity angle, wave frequency and numerous thermophysical features of the partially saturated poro-thermoelastic media. The energy of distinct waves (incident wave, reflected waves) accompanying interference energies between distinct pairs of waves have been exhibited in the form of an energy matrix. Originality/value The sensitivity of propagation characteristics (velocity, attenuation, phase shift, loci of vertical slowness, energy) to numerous aspects of the physical model is analyzed graphically through a particular numerical example. The balance of energy is substantiated by virtue of the interaction energies at the thermally insulated stress-free surface (opened/sealed pores) of unsaturated poro-thermoelastic media through the bulk waves energy shares and interaction energy.

Prediction of Ship Motions Via a Three-Dimensional Time-Domain Method Following a Quad-Tree Adaptive Mesh Technique

2020 ◽  
Vol 27 (1) ◽  
pp. 29-38
Author(s):  
Teng Zhang ◽  
Junsheng Ren ◽  
Lu Liu
Keyword(s):  
Free Surface ◽  
Incident Wave ◽  
Time Domain ◽  
Three Dimensional ◽  
Adaptive Mesh ◽  
Wave Profile ◽  
Time Domain Method ◽  
Ship Motions ◽  
Quad Tree ◽  
Mesh Technique

AbstractA three-dimensional (3D) time-domain method is developed to predict ship motions in waves. To evaluate the Froude-Krylov (F-K) forces and hydrostatic forces under the instantaneous incident wave profile, an adaptive mesh technique based on a quad-tree subdivision is adopted to generate instantaneous wet meshes for ship. For quadrilateral panels under both mean free surface and instantaneous incident wave profiles, Froude-Krylov forces and hydrostatic forces are computed by analytical exact pressure integration expressions, allowing for considerably coarse meshes without loss of accuracy. And for quadrilateral panels interacting with the wave profile, F-K and hydrostatic forces are evaluated following a quad-tree subdivision. The transient free surface Green function (TFSGF) is essential to evaluate radiation and diffraction forces based on linear theory. To reduce the numerical error due to unclear partition, a precise integration method is applied to solve the TFSGF in the partition computation time domain. Computations are carried out for a Wigley hull form and S175 container ship, and the results show good agreement with both experimental results and published results.

scholarly journals Effect of Modelling Inhomogeneous Wave Conditions on Structural Responses of a Very Long Floating Bridge

2021 ◽  
Vol 9 (5) ◽  
pp. 548
Author(s):  
Jian Dai ◽  
Christos Stefanakos ◽  
Bernt J. Leira ◽  
Hagbart Skage Alsos
Keyword(s):  
Water Environment ◽  
Bridge Structure ◽  
Inhomogeneous Wave ◽  
Wave Condition ◽  
Analysis And Design ◽  
Inhomogeneous Waves ◽  
Modelling Analysis ◽  
Structural Responses ◽  
Floating Bridge ◽  
Wave Conditions

Floating bridges are suitable for connecting land parcels separated by wide and deep waterbodies. However, when the span of the crossing becomes very long, the water environment exhibits inhomogeneities which introduce difficulties to the modelling, analysis and design of the bridge structure. The wave inhomogeneity may be described by means of field measurement and/or numerical simulations. Both approaches face complications when the resolution is much refined. It is thus important to examine the effect of the resolution related to the modelling of inhomogeneous waves on the global structural responses. In this study, a hypothetical crossing at the Sulafjord is chosen, and the wave environment in the year 2015 at 10 positions along the crossing is numerically computed. Next, different inhomogeneous wave conditions are established based on the wave data at 3, 5, and 10 positions, respectively. Time-domain simulations are conducted to examine the effect of different modelling approaches of the inhomogeneous wave condition on the global responses of a long, straight and side-anchored floating bridge.

Numerical study for the improvement of bead spreading architecture with modified nozzle geometries in additive manufacturing of polymers

2021 ◽  
Vol ahead-of-print (ahead-of-print) ◽  
Author(s):  
Easir Arafat Papon ◽  
Anwarul Haque ◽  
Muhammad Ali Rob Sharif
Keyword(s):  
Free Surface ◽  
Numerical Model ◽  
3D Printing ◽  
Cross Section ◽  
Nozzle Exit ◽  
Cross Sectional ◽  
Content Type ◽  
The Cross ◽  
Viscous Polymer ◽  
Sectional Shape

Purpose This paper aims to develop a numerical model of bead spreading architecture of a viscous polymer in fused filament fabrication (FFF) process with different nozzle geometry. This paper also focuses on the manufacturing feasibility of the nozzles and 3D printing of the molten beads using the developed nozzles. Design/methodology/approach The flow of a highly viscous polymer from a nozzle, the melt expansion in free space and the deposition of the melt on a moving platform are captured using the FLUENT volume of fluid (VOF) method based computational fluid dynamics code. The free surface motion of the material is captured in VOF, which is governed by the hydrodynamics of the two-phase flow. The phases involved in the numerical model are liquid polymer and air. A laminar, non-Newtonian and non-isothermal flow is assumed. Under such assumptions, the spreading characteristic of the polymer is simulated with different nozzle-exit geometries. The governing equations are solved on a regular stationary grid following a transient algorithm, where the boundary between the polymer and the air is tracked by piecewise linear interface construction (PLIC) to reconstruct the free surface. The prototype nozzles were also manufactured, and the deposition of the molten beads on a flatbed was performed using a commercial 3D printer. The deposited bead cross-sections were examined through optical microscopic examination, and the cross-sectional profiles were compared with those obtained in the numerical simulations. Findings The numerical model successfully predicted the spreading characteristics and the cross-sectional shape of the extruded bead. The cross-sectional shape of the bead varied from elliptical (with circular nozzle) to trapezoidal (with square and star nozzles) where the top and bottom surfaces are significantly flattened (which is desirable to reduce the void spaces in the cross-section). The numerical model yielded a good approximation of the bead cross-section, capturing most of the geometric features of the bead with a reasonable qualitative agreement compared to the experiment. The quantitative comparison of the cross-sectional profiles against experimental observation also indicated a favorable agreement. The significant improvement observed in the bead cross-section with the square and star nozzles is the flattening of the surfaces. Originality/value The developed numerical algorithm attempts to address the fundamental challenge of voids and bonding in the FFF process. It presents a new approach to increase the inter-bead bonding and reduce the inter-bead voids in 3D printing of polymers by modifying the bead cross-sectional shape through the modification of nozzle exit-geometry. The change in bead cross-sectional shape from elliptical (circular) to trapezoidal (square and star) cross-section is supposed to increase the contact surface area and inter-bead bonding while in contact with adjacent beads.

Bedforms in a turbulent stream: formation of ripples by primary linear instability and of dunes by nonlinear pattern coarsening

2010 ◽  
Vol 649 ◽  
pp. 287-328 ◽  
Author(s):  
ANTOINE FOURRIÈRE ◽  
PHILIPPE CLAUDIN ◽  
BRUNO ANDREOTTI
Keyword(s):  
Grain Size ◽  
Shear Stress ◽  
Free Surface ◽  
Stability Analysis ◽  
Sediment Transport ◽  
Phase Shift ◽  
Linear Instability ◽  
Basal Shear ◽  
Flat Sand ◽  
Nonlinear Pattern

It is widely accepted that both ripples and dunes form in rivers by primary linear instability; the wavelength of the former scaling on the grain size and that of the latter being controlled by the water depth. We revisit here this problem in a theoretical framework that allows to give a clear picture of the instability in terms of dynamical mechanisms. A multi-scale description of the problem is proposed, in which the details of the different mechanisms controlling sediment transport are encoded into three quantities: the saturated flux, the saturation length and the threshold shear stress. Hydrodynamics is linearized with respect to the bedform aspect ratio. We show that the phase shift of the basal shear stress with respect to the topography, responsible for the formation of bedforms, appears in an inner boundary layer where shear stress and pressure gradients balance. This phase shift is sensitive to the presence of the free surface, and the related effects can be interpreted in terms of standing gravity waves excited by topography. The basal shear stress is dominated by this finite depth effect in two ranges of wavelength: when the wavelength is large compared to the flow depth, so that the inner layer extends throughout the flow, and in the resonant conditions, when the downstream material velocity balances the upstream wave propagation. Performing the linear stability analysis of a flat sand bed, the relation between the wavelength at which ripples form and the flux saturation length is quantitatively derived. It explains the discrepancy between measured initial wavelengths and predictions that do not take this lag between flow velocity and sediment transport into account. Experimental data are used to determine the saturation length as a function of grain size and shear velocity. Taking the free surface into account, we show that the excitation of standing waves has a stabilizing effect, independent of the details of the flow and sediment transport models. Consequently, the shape of the dispersion relation obtained from the linear stability analysis of a flat sand bed is such that dunes cannot result from a primary linear instability. We present the results of field experiments performed in the natural sandy Leyre river, which show the formation of ripples by a linear instability and the formation of dunes by a nonlinear pattern coarsening limited by the free surface. Finally, we show that mega-dunes form when the sand bed presents heterogeneities such as a wide distribution of grain sizes.

Adaptive simulation of free surface flows with discrete least squares meshless (DLSM) method using a posteriori error estimator

2012 ◽  
Vol 29 (8) ◽  
pp. 794-813 ◽  
Author(s):  
G. Shobeyri ◽  
M.H. Afshar
Keyword(s):  
Free Surface ◽  
Posteriori Error ◽  
Free Surface Flows ◽  
Error Estimator ◽  
A Posteriori ◽  
Posteriori Error Estimator ◽  
A Posteriori Error ◽  
Content Type ◽  
Adaptive Simulation ◽  
Refinement Strategy

PurposeThe purpose of this paper is to propose an adaptive refinement strategy based on a posteriori error estimate for the efficient simulation of free surface flows using discrete least squares meshless (DLSM) method.Design/methodology/approachA pressure projection method is employed to discretize the governing equations of mass and momentum conservation in a Lagrangian form. The semi‐discretized equations are then discretized in space using the DLSM method, in which the sum of squared residual of the governing equations and their boundary conditions are minimized with respect to the unknown nodal parameters.FindingsSince the position of the free surface is of great significant in free surface problems, a posteriori error estimator which automatically associates higher error to the nodes near the free surface is proposed and used along with a node moving refinement strategy to simulate the free surface problems more efficiently. To test the ability and efficiency of the proposed adaptive simulation method, two test problems, namely dam break and evolution of a water bubble, are solved and the results are presented and compared to those of analytical and experimental results.Originality/valueError estimate and adaptive refinement have been mostly used in confined and steady‐state flow. Here in this paper, a new attempt has been made to use these concepts in moving boundary problem.

Modeling the sloshing problem in a rectangular tank with submerged incomplete baffles

2016 ◽  
Vol 26 (3/4) ◽  
pp. 722-744 ◽  
Author(s):  
Marcela A. Cruchaga ◽  
Carlos Ferrada ◽  
Nicolás Márquez ◽  
Sebastián Osses ◽  
Mario Storti ◽  
...  
Keyword(s):  
Experimental Data ◽  
Free Surface ◽  
Wave Height ◽  
Numerical Study ◽  
Free Surface Flows ◽  
Numerical Results ◽  
Surface Evolution ◽  
Content Type ◽  
Near Resonance ◽  
Wave Heights

Purpose – The present work is an experimental and numerical study of a sloshing problem including baffle effects. The purpose of this paper is to assess the numerical behavior of a Lagrangian technique to track free surface flows by comparison with experiments, to report experimental data for sloshing at different conditions and to evaluate the effectiveness of baffles in limiting the wave height and the wave propagation. Design/methodology/approach – Finite element simulations performed with a fixed mesh technique able to describe the free surface evolution are contrasted with experimental data. The experiments consist of an acrylic tank of rectangular section designed to attach baffles of different sizes at different distance from the bottom. The tank is filled with water and mounted on a shake table able to move under controlled horizontal motion. The free surface evolution is measured with ultrasonic sensors. The numerical results computed for different sloshing conditions are compared with the experimental data. Findings – The reported numerical results are in general in good agreement with the experiments. In particular, wave heights and frequencies response satisfactorily compared with the experimental data for the several cases analyzed during steady state forced sloshing and free sloshing. The effectiveness of the baffles increases near resonance conditions. From the set of experiments studied, the major reduction of the wave height was obtained when larger baffles were positioned closer to the water level at rest. Practical implications – Model validation: evaluation of the effectiveness of non-massive immersed baffles during sloshing. Originality/value – The value of the present work encompass the numerical and experimental study of the effect of immersed baffles during sloshing under different imposed conditions and the comparison of numerical results with the experimental data. Also, the results shown in the present work are a contribution to the understanding of the role in the analysis of the proposed problem of some specific aspects of the geometry and the imposed motion.

Kelvin wave attenuation along nearly straight boundaries

1972 ◽  
Vol 53 (2) ◽  
pp. 273-286 ◽  
Author(s):  
H. G. Pinsent
Keyword(s):  
Incident Wave ◽  
Wave Attenuation ◽  
Plane Waves ◽  
Kelvin Waves ◽  
Kelvin Wave ◽  
Incident Wavelength ◽  
Reflected Waves ◽  
Linearized Theory ◽  
Coastal Boundary ◽  
Wave Problems

Two related wave problems are considered for a rotating sea of nearly uniform depth bounded by a coastline which is nearly straight. The depth changes are assumed to be independent of the distance from the coastline. The first problem, which is concerned with the origin of Kelvin waves in a coastal wave record, deals with a system of plane waves incident on the coastline and giving rise, in addition to reflected waves, to a Kelvin wave moving along the coast. Linearized theory is used to obtain details of the Kelvin wave for arbitrary perturbations in coastline and depth. Results suggest that the depth changes have their greatest effect in producing Kelvin waves if the incident wave crests are nearly parallel, but not exactly so, to the line of the depth changes. On the other hand when the wave crests are parallel to the coast, Kelvin waves are produced only by changes in the coastal boundary. In the second problem a Kelvin waye is assumed to be the incident wave. To find the energy propagated away from the coastline it is necessary to extend the theory to second order in the perturbations. It is shown that for a fixed wave period less than a pendulum day this energy has a maximum for a perturbation whose length is of comparable magnitude to the incident wavelength. Finally, the theory is applied to Kelvin waves propagating along the Californian coastline. Results obtained tend to confirm the suspicion that coastal irregularities are responsible for certain anomalies detected in tidal wave constituents by Munk, Snodgrass & Wimbush (1970).

Numerical Simulation of Fluid Resonance in Narrow Gap of Two Bodies in Close Proximity

2014 ◽  
Author(s):  
Nima Moradi ◽  
Tongming Zhou ◽  
Liang Cheng
Keyword(s):  
Free Surface ◽  
Wave Height ◽  
Incident Wave ◽  
Flow Theory ◽  
Wave Generation ◽  
Numerical Results ◽  
Wave Frequency ◽  
Computational Domain ◽  
Narrow Gap ◽  
Wave Flume

The resonant behavior of the fluid trapped in the narrow gap between a floating LNG and an LNG carrier in a side-by-side offloading operation is investigated in this study employing a numerical wave flume. The wave flume is based on the finite volume solution of the Navier-Stokes equations to account for the viscous dissipation. The waveFoam toolbox, a modified version of the standard OpenFOAM multiphase flow solver interFoam developed by Jacobson et al (2011) has been used for the purpose of wave generation and relaxation inside the computational domain. This method has a quite high efficiency as it takes advantage of the potential flow theory for wave generation purpose and the viscous flow theory for inside the wave tank, respectively. The volume of fluid (VOF) method first introduced by Hirt and Nichols (1981) is used to capture the free surface oscillations at the air and water interface. Water waves are generated at a reasonable distance from the inlet boundary and two rectangular relaxation zones at the inlet and outlet boundaries of the domain have been implemented to suppress wave reflection at the outer boundaries as well as waves reflected internally in the computational domain. The influence of incident wave frequency on resonance wave height and frequency is examined. Numerical results of free surface evolution at different incident wave frequency seem to agree well with the experimental results of Saitoh et al (2006) and numerical results of Lu et al (2008). In order to justify the effect of bilge keels on flow separation at the bottom corner of the ship, four different corner configurations have been investigated and compared to the base sharp edged case. It is observed that the magnitude of the free surface elevation at the resonance frequency increases significantly by about 10 times the incoming wave height while the peak of resonant frequency curves shifts to higher frequencies in the higher curvature modes compared with the base case.

Effect of Free Surface Nonlinear and Fluid Viscosity on Fluid Resonance in the Narrow Gap

2017 ◽  
Author(s):  
Sheng-chao Jiang ◽  
Li Zou ◽  
Tie-zhi Sun ◽  
Chang-feng Liu
Keyword(s):  
Free Surface ◽  
Energy Dissipation ◽  
Resonant Frequency ◽  
Incident Wave ◽  
Wave Amplitude ◽  
Relative Energy ◽  
Dominant Factor ◽  
Fluid Viscosity ◽  
Narrow Gap ◽  
Resonant Amplitude

Numerical simulations are carried out for gap resonance problem between two side-by-side non-identical boxes. The linear potential model over-predicts the resonant amplitude in the narrow gap because it not only neglects the energy dissipation due to vortical motion, but also neglect the nonlinearity due to free surface. More relative energy are reflected with the increase of incident wave amplitude, leading to the decrease of relative resonant amplitude and relative energy dissipation in the narrow gap at resonant frequency. When the incident wave frequency is outside a little band to resonant frequency, relative energy dissipation becomes the dominant factor for the decrease of relative wave amplitude in the narrow gap with the increase of incident wave amplitudes. In a word, both the free surface nonlinearity and fluid viscosity play the important, but different, roles on wave resonances in the narrow gap.

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