Cloud cavitation occurrence about a sphere is investigated in a variable-pressure water tunnel using low- and high-speed photography. The model sphere, 0.15 m in diameter, was sting-mounted within a 0.6 m square test section and tested at a constant Reynolds number of 1.5 × 106 with cavitation numbers varying between 0.36 and 1.0. High-speed photographic recordings were made at 6 kHz for several cavitation numbers providing insight into cavity shedding and nucleation physics. Shedding phenomena and frequency content were investigated by means of pixel intensity time series data using wavelet analysis. Instantaneous cavity leading edge location was investigated using image processing and edge detection.The boundary layer at cavity separation is shown to be laminar for all cavitation numbers, with Kelvin–Helmholtz instability and transition to turbulence in the separated shear layer the main mechanism for cavity breakup and cloud formation at high cavitation numbers. At intermediate cavitation numbers, cavity lengths allow the development of re-entrant jet phenomena, providing a mechanism for shedding of large-scale Kármán-type vortices similar to those for low-mode shedding in single-phase subcritical flow. This shedding mode, which exists at supercritical Reynolds numbers for single-phase flow, is eliminated at low cavitation numbers with the onset of supercavitation.Complex interactions between the separating laminar boundary layer and the cavity were observed. In all cases the cavity leading edge was structured in laminar cells separated by well-known ‘divots’. The initial laminar length and divot density were modulated by the unsteady cavity shedding process. At cavitation numbers where shedding was most energetic, with large portions of leading edge extinction, re-nucleation was seen to be circumferentially periodic and to consist of stretched streak-like bubbles that subsequently became fleck-like. This process appeared to be associated with laminar–turbulent transition of the attached boundary layer. Nucleation occurred periodically in time at these preferred sites and formed the characteristic cavity leading edge structure after sufficient accumulation of vapour had occurred. These observations suggest that three-dimensional instability of the decelerating boundary layer flow may have significantly influenced the developing structure of the cavity leading edge.

This paper studies a generally applicable, sensitive, and intuitive error metric for the assessment of robotic swarm density controller performance. Inspired by vortex blob numerical methods, it overcomes the shortcomings of a common strategy based on discretization, and unifies other continuous notions of coverage. We present two benchmarks against which to compare the error metric value of a given swarm configuration: nontrivial bounds on the error metric, and the probability density function of the error metric when robot positions are sampled at random from the target swarm distribution. We give rigorous results that this probability density function of the error metric obeys a central limit theorem, allowing for more efficient numerical approximation. For both of these benchmarks, we present supporting theory, computation methodology, examples, and MATLAB implementation code.

This paper studies a generally applicable, sensitive, and intuitive error metric for the assessment of robotic swarm density controller performance. Inspired by vortex blob numerical methods, it overcomes the shortcomings of a common strategy based on discretization, and unifies other continuous notions of coverage. We present two benchmarks against which to compare the error metric value of a given swarm configuration: nontrivial bounds on the error metric, and the probability density function of the error metric when robot positions are sampled at random from the target swarm distribution. We give rigorous results that this probability density function of the error metric obeys a central limit theorem, allowing for more efficient numerical approximation. For both of these benchmarks, we present supporting theory, computation methodology, examples, and MATLAB implementation code.

SUMMARYThis paper presents an evaluation of the capability of turbulence models available in the commercial CFD code FLUENT 6.0 for their application to hydrofoil turbulent boundary layer separation ow at high Reynolds numbers. Four widely applied two-equation RANS turbulence models were assessed through comparison with experimental data at Reynolds numbers of 8:284 × 10 6 and 1:657 × 10 7 . They were the standard k-model, the realizable k-model, the standard k-! model and the shear-stress-transport (SST) k-! model. It has found that the realizable k-turbulence model used with enhanced wall functions and near-wall modelling techniques, consistently provides superior performance in predicting the ow characteristics around the hydrofoil.

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