The paper presents a robust algorithm, which allows to implicitly describe and track immersed geometries within a background mesh. The background mesh is assumed to be unstructured and discretized by tetrahedrons. The contained geometry is assumed to be given as triangulated surface. Within the background mesh, the immersed geometry is described implicitly using a discontinuous distance function based on a level-set approach. This distance function allows to consider both, "double-sided" geometries like membrane or shell structures, and "single-sided" objects for which an enclosed volume is univocally defined. For the second case, the discontinuous distance function is complemented by a continuous signed distance function, whereas ray casting is applied to identify the closed volume regions. Furthermore, adaptive mesh refinement is employed to provide the necessary resolution of the background mesh. The proposed algorithm can handle arbitrarily complicated geometries, possibly containing modeling errors (i.e., gaps, overlaps or a non-unique orientation of surface normals). Another important advantage of the algorithm is the embarrassingly parallel nature of its operations. This characteristic allows for a straightforward parallelization using MPI. All developments were implemented within the open source framework "KratosMultiphysics" and are available under the BSD license. The capabilities of the implementation are demonstrated with various application examples involving practice-oriented geometries. The results finally show, that the algorithm is able to describe most complicated geometries within a background mesh, whereas the approximation quality may be directly controlled by mesh refinement.
The higher the efficiency of a turbocharger’s radial turbine, the lower is the necessary pressure ratio to deliver a specified power to the compressor. This, in turn, reduces the fuel consumption of the internal combustion engine as a lower pressure upstream of the turbine increases the obtained charge-cycle work. In this paper, two components of a nozzled radial turbine system are redesigned: Both the volute upstream and the 90°-bend downstream of the turbine wheel will be improved. To reduce pressure drops, a gradient-based shape optimization workflow based on adjoint methods is applied. The scheme works in an iterative manner, i.e. after running a primal and an adjoint simulation to gather shape sensitivities, the geometry is deformed and the next iteration is started. A steepest descent approach is used to guide the optimization process. As parametrization strategy the Vertex Morphing Method is used to explore design potential, while maintaining smooth surfaces. Both the volute and the bend are optimized successfully leading to an efficiency increase of the turbine system of up to 3%, depending on the load condition.
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