On the invertibility of mappings arising in 2D grid generation problems

In adapting a grid for a Computational Fluid Dynamics problem one uses a mapping from the unit square onto itself that is the solution of an elliptic partial differential equation with rapidly varying coefficients. For a regular discretization this mapping has to be invertible. We will show that such result holds for general elliptic operators (in two dimensions). The Carleman-Hartman-Wintner Theorem will be fundamental in our proof. We will also explain why such a general result cannot be expected to hold for the (three-dimensional) cube

On a Dirichlet problem related to the invertibility of mappings arising in 2D grid generation problems

this paper depends strongly on a theorem of Carleman-HartmanWintner. This theorem is only true in two dimensional domains. In fact a straightforward generalization to more than two dimensional domains cannot be true. A counterexample to the proof of [15]forthe three dimensional case can be found by using a special harmonic function due to Kellogg [12]. This function is shown in [2]. A direct counterexample can be found in [13]. 2 Main result on smooth domain

Influence of water layer thickness on crater volume for nanosecond pulsed laser ablation of stainless steel

Under water laser ablation is a surface texturization method used to form micrometer-sized surface structures. Plasma confinement and cavitation bubble evolution play a critical role during the ablation process and their influence on material removal is strongly tied to liquid layer thickness. To influence the effects of these processes, such that material removal is at its maximum, an optimal layer thickness was found for various laser parameters. Specifically, for nanosecond pulsed laser ablation of stainless steel, however, the relation between layer thickness and volume removal is still unknown. Here, we show the relation between water layer thickness and removed material volume for a nanosecond pulsed laser. Results reveal that volume removal is at its maximum for a 1 mm water layer and drops by a factor of 2 when the layer thickness is increased to 2 mm. A further increase of layer thickness to 3 up to 10 mm shows a negligible effect on volume removal and removed volume amounts are shown to be similar to those obtained in ambient air in this water layer thickness range. This trend echo’s results obtained for nanosecond pulsed silicon ablation. The obtained results identify processing conditions which allow for faster and therefore more cost efficient texturization of stainless steel surfaces in the future.</p

Identifying the influence of bubble size and position on crater formation during underwater nanosecond laser ablation of stainless steel

Underwater laser ablation can be employed both as a means to produce nanoparticles and to texturize surfaces of various materials. In this approach, a stationary or flowing water layer above the target surface confines laser induced plasma which cools to form short lived cavitation bubbles, positively influencing the amount of removed material per laser pulse. Plasma and cavitation bubble evolution additionally give rise to bubbles which may persist in the water throughout the ablation process. These bubbles are known to have a detrimental effect on material removal rates particularly in stationary water, but the quantitative influence of bubble dimensions and position on removed material volume is currently unknown. Here we show the laser intensity profile changes induced by bubbles located at 0–0.4 Rayleigh lengths above a stainless steel surface and couple these changes to removed crater volume. Our results show that water flowing at Reynolds numbers in the range of 1–100 positively contribute to crater volumes for pulse frequencies up to 1 kHz. At 1 kHz, it was found bubbles have insufficient time to flow from the vicinity of the laser spot, regardless of the Reynolds number within the range investigated. These conclusions assist in selecting an appropriate combination of laser and flow conditions to optimize laser ablation material removal rate.</p

Demonstration of an automated CFD system for three-dimensional flow simulations

In this paper the capabilities of an automated CFD system which is currently available at NLR are demonstrated. Transonic flow around the AS28G wing/body configuration and hypersonic flow through a generic three-dimensional mixed-compression airbreathing inlet are simulated. An assessment of the level of automation of the current CFD-system is made. The problem-turnaround time lies within the order of a week for both applications