Ruben Scardovelli

Physics and engineering design for Wendelstein VII-X

AbstractThe future experiment Wendelstein VII-X (W VII-X) is being developed at the Max-Planck-Institut fur Plasmaphysik. A Helical Advanced Stellarator (Helias) configuration has been chosen because of its confinement and stability properties. The goals of W VII-X are to continue the development of the modular stellarator, to demonstrate the reactor capability of this stellarator line, and to achieve quasi-steady-state operation in a temperature regime >5 keV. This temperature regime can be reached in W VII-X if neoclassical transport plus the anomalous transport found in W VII-A prevail. A heating power of 20 MW will be applied to reach the reactor-relevant parameter regime.The magnetic field in W VII-X has five field periods. Other basic data are as follows: major radius R0 = 6.5 m, magnetic induction B0 = 3 T, stored magnetic energy W ≈ 0.88 GJ, and average plasma radius a = 0.65 m. Superconducting coils are favored because of their steady-state field, but pulsed water-cooled copper coils are also bei...

Interface reconstruction with least-squares fit and split advection in three-dimensional Cartesian geometry

In this paper we present and analyze different volume-of-fluid (VOF) reconstruction and advection algorithms that approximate the interface separating two immiscible fluids in the three-dimensional space. The paper describes the improvement of the reconstruction when a least-square fit algorithm, which minimizes a distance functional, is applied. Its performance is tested for several smooth surfaces against other simple reconstruction methods. Then Eulerian, Lagrangian and mixed split advection schemes are presented and analyzed. In particular, one advection method is discussed that conserves mass exactly for a divergence-free velocity field, thus allowing computations to machine precision.

A mixed markers and volume-of-fluid method for the reconstruction and advection of interfaces in two-phase and free-boundary flows

In this work we present a new mixed markers and volume-of-fluid (VOF) algorithm for the reconstruction and advection of interfaces in the two-dimensional space. The interface is described by using both the volume fraction function C, as in VOF methods, and surface markers, which locate the interface within the computational cells. The C field and the markers are advected by following the streamlines. New markers are determined by computing the intersections of the advected interface with the grid lines, then other markers are added inside each cut cell to conserve the volume fraction C. A smooth motion of the interface is obtained, typical of the marker approach, with a good volume conservation, as in standard VOF methods. In this article we consider a few typical two-dimensional tests and compare the results of the mixed algorithm with those obtained with VOF methods. Translations, rotations and vortex tests are performed showing that many problems of the VOF technique can be solved and a good accuracy in the geometrical motion and mass conservation can be achieved.

On the properties and limitations of the height function method in two-dimensional Cartesian geometry

In this study we define the continuous height function to investigate the approximation of an interface line and its geometrical properties with the height function method. We show that in each mixed cell the piecewise linear interface reconstruction and the approximation of the derivatives and curvature based on three consecutive height function values are second-order accurate. We also discuss the quadratic reconstruction and fourth-order accurate expressions of the normal and curvature. We present a hierarchical algorithm to compute the normal vector and curvature of an interface line with the height function method that switches automatically between second- and fourth-order approximations and that can be applied also when the local radius of curvature is of the order of the grid spacing.

A geometrical predictor-corrector advection scheme and its application to the volume fraction function

We present a multidimensional Eulerian advection method for interfacial and incompressible flows in two-dimensional Cartesian geometry. In the scheme we advect the grid nodes backwards along the streamlines to compute the pre-images of the grid lines. These pre-images are approximated by continuous, piecewise-linear lines. The enforcement of the discrete version of the incompressibility constraint is a very important issue to determine correctly the flux polygons and to reduce considerably the integration, discretization and interpolation numerical errors. The proposed method compares favorably with other previous multidimensional advection methods as long as the initial interface line is well reconstructed. Conversely, we show that when the interface is very fragmented the total numerical error is completely dominated by the reconstruction error and in these conditions it is very difficult to assess which advection scheme is the most reliable one.

Instability growth rate of two-phase mixing layers from a linear eigenvalue problem and an initial-value problem

The temporal instability of parallel two-phase mixing layers is studied with a linear stability code by considering a composite error function base flow. The eigenfunctions of the linear problem are used to initialize the velocity and volume fraction fields for direct numerical simulations of the incompressible Navier–Stokes equations with the open-source GERRIS flow solver. We compare the growth rate of the most unstable mode from the linear stability problem and from the simulation results at moderate and large density and viscosity ratios in order to validate the code for a wide range of physical parameters. The efficiency of the adaptive mesh refinement scheme is also discussed.

Simulation of axisymmetric jets with a finite element Navier-Stokes solver and a multilevel VOF approach

A multilevel VOF approach has been coupled to an accurate finite element Navier-Stokes solver in axisymmetric geometry for the simulation of incompressible liquid jets with high density ratios. The representation of the color function over a fine grid has been introduced to reduce the discontinuity of the interface at the cell boundary. In the refined grid the automatic breakup and coalescence occur at a spatial scale much smaller than the coarse grid spacing. To reduce memory requirements, we have implemented on the fine grid a compact storage scheme which memorizes the color function data only in the mixed cells. The capillary force is computed by using the Laplace-Beltrami operator and a volumetric approach for the two principal curvatures. Several simulations of axisymmetric jets have been performed to show the accuracy and robustness of the proposed scheme.

Direct Simulation of Multiphase Flows with Density Variations

Interfacial instability plays an important role in the primary atomization of high-speed liquid jets. We present simulations of the Kelvin-Helmholtz instability of a sheared liquid-gas interface. The two-dimensional simulations of the Navier-Stokes equation with surface tension show the formation of liquid sheets at sufficiently high Weber and Reynolds numbers. The three-dimensional simulations show two scenarios, depending on the degree of three dimensionality in the initial conditions. The first scenario involves the Rayleigh instability of cylinders that are formed when the rim detaches from the sheets. The second involves a faster distortion of the rim; the precise mechanism that yields this behavior is still unknown.

A Quasi-Direct 3D Simulation of the Atomization of High-Speed Liquid Jets

In this paper a quasi-direct solution of transient three-dimensional CFD calculations based on a finite volume approach has been adopted to simulate the atomization process of high velocity liquid jets issuing an injector-like nozzle. An accurate Volume-of-Fluid (VOF) method is used to reconstruct and advect the interface between the liquid and gas phases. An extended mesh which includes the injector nozzle and the upstream plenum has been considered in order to investigate accurately the effect of nozzle flow conditions on the liquid jet atomization. Cavitation modeling has not been included in the present computations. Two different mean injection velocities, 150 m/s and 270 m/s, respectively, have been considered in the calculations as representative of semi-turbulent and fully-turbulent nozzle flow conditions. The liquid-to-gas density ratio is kept fixed at 57. The calculations show that atomisation is directly linked to the temporally and spatially correlated turbulence of the liquid jet. The bulk flow perturbation and the relaxation of the boundary layer have been found to be the basic mechanisms that generate surface perturbations of the liquid jet.© 2005 ASME

A MARKER-VOF ALGORITHM FOR INCOMPRESSIBLE FLOWS WITH INTERFACES

In this paper, we present a three-dimensional (3D) reconstruction algorithm for Cartesian grids and a split advection algorithm which is based on a two-dimensional (2D) Eulerian-Lagrangian scheme that conserves mass exactly for incompressible flows. In the Volume-of-Fluid/Piecewise Linear Interface Calculation (VOF/PLIC) method a linear function in every grid cell cut by the interface approximates the free surface or the surface between two immiscible phases. The reconstruction is not continuous, and not accurate in regions with high surface curvature or when the interface develops thin filaments. Therefore, we have developed a new 2D mixed markers and VOF algorithm that follows the motion of a smooth interface with a good conservation of volume. Results are shown for flows with nonconstant vorticity.Copyright