Simulation of interface and free surface flows in a viscous fluid using adapting quadtree grids

A new adaptive quadtree method for simulating laminar viscous fluid problems with free surfaces and interfaces is presented in this paper. The Navier–Stokes equations are solved with a SIMPLE‐type scheme coupled with the Compressive Interface Capturing Scheme for Arbitrary Meshes (CICSAM) (Numerical prediction of two fluid systems with sharp interfaces, Ph.D. Thesis, Imperial College of Science, Technology and Medicine, London, 1997) volume of fluid (VoF) method and PLIC reconstruction of the volume fraction field during refinement and derefinement processes. The method is demonstrated for interface advection cases in translating and shearing flow fields and found to provide high interface resolution at low computational cost. The new method is also applied to simulation of the collapse of a water column and the results are in excellent agreement with other published data. The quadtree grids adapt to follow the movement of the free surface, whilst maintaining a band of the smallest cells surrounding the surface. The calculation is made on uniform and adapting quadtree grids and the accuracy of the quadtree calculation is shown to be the same as that made on the equivalent uniform grid. Copyright © 2004 John Wiley & Sons, Ltd.     

Simulation of viscous water column collapse using adapting hierarchical grids

An adaptive hierarchical grid‐based method for predicting complex free surface flows is used to simulate collapse of a water column. Adapting quadtree grids are combined with a high‐resolution interface‐capturing approach and pressure‐based coupling of the Navier–Stokes equations. The Navier–Stokes flow solution scheme is verified for simulation of flow in a lid‐driven cavity at Re=1000. Two approaches to the coupling of the Navier–Stokes equations are investigated as are alternative face velocity and hanging node interpolations. Collapse of a water column as well as collapse of a water column and its subsequent interaction with an obstacle are simulated. The calculations are made on uniform and adapting quadtree grids, and the accuracy of the quadtree calculations is shown to be the same as those made on the equivalent uniform grids. Results are in excellent agreement with experimental and other numerical data. A sharp interface is maintained at the free surface. The new adapting quadtree‐based method achieves a considerable saving in the size of the computational grid and CPU time in comparison with calculations made on equivalent uniform grids. Copyright © 2005 John Wiley & Sons, Ltd.     

Exact pressure integrations on submerged bodies in waves using a quadtree adaptive mesh algorithm

The development of an adaptive free surface, mesh cutting, methodology, in order to analytically integrate pressures on varying wet parts of partially submerged surfaces in the presence of waves, is presented. Given a function of free‐surface elevation, the algorithm checks for the intersection of the body with the free surface and, based on user‐defined parameters, modifies the initial mesh, by subdividing the elements where necessary and eliminating others, via a quadtree approach. Redundant sub‐divisions, generated in the quad‐division process, are partially eliminated, but the quadrilateral nature of the elements is always kept. The free‐surface function must be single‐valued and its definition domain simply connected. Hydrostatic and Froude–Krylov forces are computed exactly on each panel by means of analytical formulations, which are derived and presented, based on the theory of linear gravity waves and from applying Green's theorem. Copyright © 2014 John Wiley & Sons, Ltd.     

Non-linear hydrodynamics of thin laminae undergoing large harmonic oscillations in a viscous fluid

Smoothed Particle Hydrodynamics is implemented to study the motion of a thin rigid lamina undergoing large harmonic oscillations in a viscous fluid. Particularly, the flow physics in the proximity of the lamina is resolved and contours of non-dimensional velocity, vorticity and pressure are presented for selected oscillation regimes. The computation of the hydrodynamic load due to the fluid–structure interaction is carried out using Fourier decomposition to express the total fluid force in terms of a non-dimensional complex-valued hydrodynamic function, whose real and imaginary parts identify added mass and damping coefficients, respectively. For small oscillations, the hydrodynamic force reflects the harmonic nature of the displacement, whereas multiple harmonics are observed as both the amplitude and frequency of oscillation increase. We propose a novel formulation of hydrodynamic function that incorporates added mass and damping coefficients for a thin rigid lamina spanning large amplitudes in viscous fluids in a broad range of the oscillation frequencies. Results of the simulations are validated against numerical and experimental works available in the literature in addition to theoretical predictions for the limit case of zero-amplitude oscillations.     

Dynamic coupling of fluid and structural mechanics for simulating particle motion and interaction in high speed compressible gas particle laden flow

In this work, structural finite element analyses of particles moving and interacting within high speed compressible flow are directly coupled to computational fluid dynamics and heat transfer analyses to provide more detailed and improved simulations of particle laden flow under these operating conditions. For a given solid material model, stresses and displacements throughout the solid body are determined with the particle–particle contact following an element to element local spring force model and local fluid induced forces directly calculated from the finite volume flow solution. Plasticity and particle deformation common in such a flow regime can be incorporated in a more rigorous manner than typical discrete element models where structural conditions are not directly modeled. Using the developed techniques, simulations of normal collisions between two 1 mm radius particles with initial particle velocities of 50–150 m/s are conducted with different levels of pressure driven gas flow moving normal to the initial particle motion for elastic and elastic–plastic with strain hardening based solid material models. In this manner, the relationships between the collision velocity, the material behavior models, and the fluid flow and the particle motion and deformation can be investigated. The elastic–plastic material behavior results in post collision velocities 16–50% of their pre-collision values while the elastic-based particle collisions nearly regained their initial velocity upon rebound. The elastic–plastic material models produce contact forces less than half of those for elastic collisions, longer contact times, and greater particle deformation. Fluid flow forces affect the particle motion even at high collision speeds regardless of the solid material behavior model. With the elastic models, the collision force varied little with the strength of the gas flow driver. For the elastic–plastic models, the larger particle deformation and the resulting increasingly asymmetric loading lead to growing differences in the collision force magnitudes and directions as the gas flow strength increased. The coupled finite volume flow and finite element structural analyses provide a capability to capture the interdependencies between the interaction of the particles, the particle deformation, the fluid flow and the particle motion.     

The interaction between shock waves and foam in a shock tube

An experimental study and a numerical simulation were conducted to investigate the mechanical and thermodynamic processes involved in the interaction between shock waves and low density foam. The experiment was done in a stainless shock tube (80 mm in inner diameter, 10 mm in wall thickness and 5 360 mm in length). The velocities of the incident and reflected compression waves in the foam were measured by using piezo-ceramic pressure sensors. The end-wall peak pressure behind the reflected wave in the foam was measured by using a crystal piezoelectric sensor. It is suggested that the high end-wall pressure may be caused by a rapid contact between the foam and the end-wall surface. Both open-cell and closed-cell foams with different length and density were tested. Through comparing the numerical and experimental end-wall pressure, the permeability coefficients α and β are quantitatively determined.     

土中爆炸波与地下结构相互作用计算方法研究综述

土中爆炸波与结构相互作用是地下工程结构抗爆计算的理论基础,理论研究中通常在宏观试验基础上,引入合理的介质动力本构模型分析波动问题。针对工程防护中的计算模型和解析方法,综述了岩土介质中爆炸波与结构相互作用的现状和研究进展,内容包括土的动力本构模型,自由场中爆炸波的传播、爆炸波与箱型、圆柱形和直墙圆拱型等地下结构的相互作用等。重点阐述了常用的非饱和土和饱和土的动力本构模型、考虑松弛效应的土的综合弹塑性模型,一维平面波在不均匀介质和分层介质中的传播及地下结构爆炸荷载计算方面的研究成果,分析了各种模型和计算方法的适用范围和存在问题。

     

A numerical investigation of waves propagating in the spinal cord and subarachnoid space in the presence of a syrinx

The term syringomyelia describes fluid-filled cavities in the spinal cord, which can interfere with normal nerve signal transmission. The finite-element code ADINA was used to construct an axisymmetric fluid/structure-interaction model of the tapered spinal cord and subarachnoid space (SAS), bounded by the dura mater. A syrinx was simulated, of corresponding dimensions to one shown by magnetic resonance imaging data of a patient with syringomyelia. The model was used to investigate the clinical hypothesis that SAS pressure waves move fluid along a syrinx and can thus lengthen it over time by tissue dissection. Simplified versions of the model were used to examine in detail the waves excited, and their reflection and refraction at sites of property discontinuity in the system. Comparison was made with wave predictions based on an analytical model, and excellent agreement was found. The results suggest that, under the circumstances modelled, pressure wave-induced motion of syrinx fluid is unlikely to lengthen such cavities, unless the transverse tensile strength of cord tissue is even smaller than has been appreciated so far.