On the use of multilayer Laue lenses with X-ray Free Electron Lasers

Multilayer Laue lenses were used for the first time to focus x-rays from an X-ray Free Electron Laser (XFEL). In an experiment, which was performed at the European XFEL, we demonstrated focusing to a spot size of a few tens of nanometers. A series of runs in which the number of pulses per train was increased from 1 to 2, 3, 4, 5, 6, 7, 10, 20 and 30 pulses per train, all with a pulse separation of 3.55 us, was done using the same set of lenses. The increase in the number of pulses per train was accompanied with an increase of x-ray intensity (transmission) from 9% to 92% at 5 pulses per train, and then the transmission was reduced to 23.5 % when the pulses were increased further. The final working condition was 30 pulses per train and 23.5% transmission. Only at this condition we saw that the diffraction efficiency of the MLLs changed over the course of a pulse train, and this variation was reproducible from train to train. We present the procedure to align and characterize these lenses and discuss challenges working with the pulse trains from this unique x-ray source

2008c): Convection driven melting of anisotropic metals

This paper numerically explores melting of a pure substance with the thermal conductivity of the solid phase, assumed to be anisotropic. A two-phase test case for such situations is deduced from the standard one-phase Gobin-Le Qué ré melting benchmark. The solution is presented for Prandtl number 0?02, Stefan number 0?01 and Rayleigh number 2?5610 4 which are specific for metals. Three cases are compared in terms of the terminal interface boundary position and average liquid fraction as a function of time for isotropic case and two distinctly oriented principal directions of the thermal conductivity tensor. The calculations have been performed by using the one-domain enthalpy formulation with artificial melting interval and the recently developed explicit local radial basis function collocation method (LRBFCM) which belongs to the entirely new generation of meshless methods. The results are not sensitive to the increased thermal conductivity of the solid phase in the direction parallel with the heated boundary but sensitive with the increase of the thermal conductivity of the solid phase in the direction perpendicular to the heated boundary

2008b): Local RBF collocation method for Darcy flow

Abstract: This paper explores the application of the mesh-free Local Radial Basis Function Collocation Method (LRBFCM) in solution of coupled heat transfer and fluid flow problems in Darcy porous media. The involved temperature, velocity and pressure fields are represented on overlapping sub-domains through collocation by using multiquadrics Radial Basis Functions (RBF). The involved first and second derivatives of the fields are calculated from the respective derivatives of the RBF's. The energy and momentum equations are solved through explicit time stepping. The pressure-velocity coupling is calculated iteratively, with pressure correction, predicted from the local continuity equation violation. This formulation does not require solution of pressure Poisson or pressure correction Poisson equations and thus much simplifies the Kassab and Divo formulation [Divo and Kassab (2007)]. The solution procedure is represented for a steady natural convection problem in a rectangular cavity, filled with Darcy porous media. The numerical examples include studies with different uniform discretization for differentially heated boundaries at filtration Rayleigh numbers Ra F =25, 50, 10 2 , 10 3 , 10 4 , and aspect ratios A = 1/2, 1, 2. The solution is assessed by comparison with reference results of the fine mesh finite volume method (FVM) in terms of mid-plane velocities, mid-plane and insulated surface temperatures, mid-point streamfunction and Nusselt number. The advantages of the method are simplicity, accuracy and straightforward applicability in non-uniform node arrangements

Experimental model of mould filling flow

Key words: natural and forced convection, free surface flow, mould filling The aim of our analysis is to provide a simple experimental model simulating the main flow characteristics accompanying casting processes. Hence, a hot liquid is provided under high pressure into an inclined box. The liquid propagates inside the box between two cold isothermal walls, passing obstacles simulating internal complexity of a mould. The main features of the experiment like flow acceleration and deceleration on the obstacle, a free surface flow and sudden increase of the fluid viscosity as it cools down, are typical for a solidification of melt in a mould. Opposite to a real casting, this experimental configuration allows for full control of the experimental conditions and the full field measurements of the temperature and velocity fields. Collection of the quantitative transient data of the flow should permit to verify and validate numerical models used for typical casting problems. The main aim of the investigations is to create an experimental model for validating numerical simulations of mould-filling problems