Claudio Zanzi

Simulation of high density ratio interfacial flows on cell vertex/edge-based staggered octree grids with second-order discretization at irregular nodes

Abstract A numerical code has been developed for the simulation of unsteady incompressible interfacial flows with large density ratios, based on discretizing the conservation equations on a rectangular adaptive grid with a graded octree data structure, in which the pressure and velocity components are stored at the cell vertices and edges, respectively. With this arrangement, which is novel for octree grids, node alignment simplifies the Poisson equation discretization at nodes common to cells with different refinement levels (irregular nodes), while the staggered storage of variables avoids the pressure–velocity coupling difficulties associated with collocated grids. Three different discretization approaches at irregular nodes are proposed: second- and first-order schemes, and an efficient scheme based on a linear interpolation from the surrounding nodes. A grid refinement test in two dimensions, and 3D deformation and static bubble tests were carried out to assess the accuracy and efficiency of the proposed discretization methods at irregular nodes, the performance of the different schemes used to solve the level set transport equation and the capability of the numerical code to reduce spurious currents. The results of the tests are discussed and compared with results available in the literature. Finally, the ability of the code to accurately simulate the complex phenomena involved in the impact of a water drop on a free surface is demonstrated by thoroughly comparing numerical and experimental results.

Application of Non-Convex Analytic and Geometric Tools to a PLIC-VOF Method

An efficient approach to handle either convex or non-convex arbitrary polytopes is applied to volume truncation and volume conservation enforcement operations involved in volume of fluid (VOF) methods. A comparison between the proposed approach and conventional procedures based on convex decomposition is carried out for different tests, demonstrating that the proposed tools represent a substantial improvement in computational efficiency. A speedup of around one order of magnitude is achieved for the reconstruction of several interfacial shapes. The non-convex tools have been used to implement a highly accurate volume of fluid (VOF) method based on a multidimensional advection scheme with edge-matched flux polyhedra and a piecewise linear interface calculation (PLIC) method. A preliminary analysis of the accuracy, computational efficiency and volume conservation properties of the implemented PLIC-VOF method is carried out.Copyright

Smoke and Heat Propagation Modeling in Transportation Interchange Stations Using LES and RANS Methods

A numerical study of smoke and heat transport from fires occurring in a large interchange bus station is presented. The ultimate goal of this type of study is to increase the fire safety level of the station by improving the design of fire protection systems and evacuation procedures. The phenomena involved in the fire are highly transient and three dimensional, and their modeling requires large computational resources. In the present work, we introduce several simplifications in the numerical model, mainly related to turbulence modeling and the boundary conditions used to reproduce the effects of the combustion process, which allow us capturing the essential features of the fire while keeping the memory requirements and the CPU time at a reasonable level. In particular, we are interested in describing in a realistic way the spread of smoke and heat in a typical fire scenario in the lobby of an interchange bus station. The numerical analysis is carried out with the aid of a general-purpose computer code, using two different approaches for turbulence modeling (RANS and LES) and several discretization schemes. The fire effects are reproduced in a simple way, describing the fire focus as a source of mass, heat and chemical species. Boundary conditions are imposed at the fire focus, by setting the inlet velocity, temperature and gas composition (combustion products) at a section of appropriate area. The values of these quantities are chosen to be consistent with the prescribed heat release rate, type of fuel (heptane) and fire spread area. A comparison of the results obtained with the different methods, along with the CPU time consumption and dependence on the computational mesh, is presented. The capabilities and limitations of unsteady RANS and LES methods to reproduce the main features of the smoke and heat propagation patterns are analyzed.Copyright

An Adaptive-Grid Projection Method for High Density Ratio Interfacial Flows

A graded-adaptive grid projection method to solve the Navier-Stokes equations for incompressible interfacial flows characterized by large density ratios is presented. The numerical model is similar to the one we proposed in [7] and extended to 3D problems in [8].The free surface is described using a level set method. A Godunov-type method and a Crank-Nicholson temporal discretization scheme are used to solve the advection equation of the level set function and to update of the momentum equation. The reinitialization procedure of the distance function is based on solving a hyperbolic equation to steady state using third-order Runge-Kutta and fifth-order WENO schemes.The conservation equations are discretized on a rectangular adaptive grid with an octree data structure and the pressure stored at the grid cell vertices. In order to avoid spurious pressure oscillations, the velocity components are stored at the cell edges. This new storage scheme combines the advantages of vertex-based schemes, in which the nodes where the pressure is stored are aligned, and cell center-based schemes, which avoid pressure-velocity coupling problems.The numerical model incorporates a continuous surface tension model based on the balanced-force algorithm proposed in [6]. A special treatment of T-nodes (nodes located at vertices, edges or faces of cells belonging to two different refinement levels) is proposed that considerably improves the efficiency of the method.Several tests in two and three dimensions have been carried out to assess the accuracy and efficiency of the proposed method. In this work we present some numerical results for a 3D kinematic test, which are compared with those obtained by other authors. We also present results for the impact of a drop of water onto a liquid surface, which are compared with experimental visualization results.Copyright

Simulation of Dendritic Growth Using a VOF Method

The volume of fluid (VOF) method is one of the most widely used methods to simulate interfacial flows using fixed grids. However, its application to phase change processes in solidification problems is relatively infrequent. In this work, preliminary results of the application of a new methodology to the simulation of dendritic growth of pure metals is presented. The proposed approach is based on a recent VOF method with PLIC (piecewise linear interface calculation) reconstruction of the interface. A diffused-interface method is used to solve the energy equation, which avoids the need of applying the thermal boundary conditions directly at the solid front. The thermal gradients at both sides of the interface, which are needed to accurately obtain the front velocity, are calculated with the aid of a distance function. The advection equation of a discretized solid fraction function is solved using the unsplit VOF advection method proposed by Lopez et al. [J. Comput. Phys. 195 (2004) 718–742] (extended to three dimensions by Hernandez et al. [Int. J. Numer. Methods Fluids 58 (2008) 897-921]). The interface curvature is computed using an improved height function (HF) technique, which provides second-order accuracy. The assessment of the proposed methodology is carried out by comparing the numerical results with analytical solutions and with results obtained by different authors for the formation of complex dendritic structures in two and three dimensions.Copyright

Direct Numerical Simulation of the First Stages of a Plunging Breaker Using a Level Set Method

A numerical study of wave breaking in shallow water is presented. The jet formed at the wave crest and the subsequent splash-up phenomenon resulting from the impact of the jet on the liquid surface are analyzed. The wave is assumed to be generated by an accelerated piston in an open channel containing liquid. The two-dimensional, incompressible, unsteady Navier-Stokes equations are solved using a local level set method to treat the interface evolution [Gomez et al., Int. J. Numer. Meth. Engng, 63, pp. 1478–1512, 2005], which permits to analyze the combined air-liquid flow. Viscous and capillary effects are retained. The level set transport and reinitialization equations are solved in a narrow band around the interface using an adaptive refined grid. Two different approaches are considered to take into account the relative movement between the piston and the end wall of the channel. The first one uses a fixed grid and introduces a mass force per unit mass equal to the piston acceleration, and the second one is based on using a moving grid, which is compressed as the piston moves forward, and an arbitrary Lagrangian-Eulerian method. The numerical results obtained for the evolution of the wave shape during the breaking process, particularly the evolution of the plunging jet, the air cavity and the complex flow resulting from the impact of the plunging jet, are compared with experimental visualization results obtained for a small-scale breaking wave, for which the breaking process is strongly influenced by surface tension. A good degree of agreement was observed between both types of results during the first stages of the breaking process.Copyright

Influence of Wave Shape on the Impact of Shallow-Water Waves on Vertical Walls

A numerical study of the impact of shallow-water waves on vertical walls is presented. The air-liquid flow was simulated using a code for incompressible viscous flow, based on a local level set algorithm and a second-order approximate projection method. The level set transport and reinitialization equations were solved in a narrow band around the interface using an adaptive refined grid. The wave is assumed to be generated by a plunger which is accelerated in an open channel containing water. An arbitrary Lagrangian-Eulerian method was used to take into account the relative movement between the plunger and the end wall of the channel. The evolution of the free surface was visualized using a laser light sheet and a high-speed camera, with a sampling frequency of 1000 Hz. Several simulations were carried out to investigate the influence of the shape of the wave approaching the wall on the relevant quantities associated with the impact. The wave shape just before the impact was changed varying the total length of the channel. The results are compared with experimental results and with results obtained by other authors.Copyright