Graph algorithms play an important role in several fields of sciences and engineering. Prominent among them are the All-Pairs-Shortest-Paths (APSP) and related problems. Indeed there are several efficient implementations for such problems on a variety of modern multi-and manycore architectures.It can be noticed that for several graph problems, parallelism offers only a limited success as current parallel architectures have severe short-comings when deployed for most graph algorithms. At the same time, some of these graphs exhibit clear structural properties due to their sparsity. This calls for particular solution strategies aimed at scalable processing of large, sparse graphs on modern parallel architectures.In this paper, we study the applicability of an ear decomposition of graphs to problems such as all-pairs-shortest-paths and minimum cost cycle basis. Through experimentation, we show that the resulting solutions are scalable in terms of both memory usage and also their speedup over best known current implementations. We believe that our techniques have the potential to be relevant for designing scalable solutions for other computations on large sparse graphs.
In this paper, detailed analysis of the tip flow of an axial compressor rotor blade has been carried out using the commercial CFD package ANSYS CFX. The rotor blade was designed such that it is reminiscent of the rear stages of a multi-stage axial compressor. The effects of varying tip gaps are studied using CFD simulations for overall pressure rise and flow physics of the tip flow at the design point and near the peak pressure point. Rig tests of a low speed research compressor rotor with 3% tip clearance provided characteristics plots for validation of the CFD results. With increase in clearance from 1% to 4%, the rotor pressure rise at the design point was observed to decrease linearly. Increase in the clearance increases the cross flow across the tip; however, the magnitude of the average jet velocity crossing the tip decreases. The tip leakage vortex was observed to stay close to the suction surface with increase in clearance.
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