Diameter-Separation of Chessboard Graphs

We define the queens (resp., rooks) diameter-separation number to be the minimum number of pawns for which some placement of those pawns on an n × n board produces a board with a queens graph (resp., rooks graph) with a desired diameter d. We determine these numbers for some small values of d.

Optimization of Piecewise Conical Nozzles: Theory and Application

An optimization study based on computational fluid dynamics (CFD) in combination with Stratford's analytical separation criterion was developed for the design of piecewise conical contraction zones and nozzles. The risk of flow separation was formally covered by a newly introduced dimensionless separation number. The use of this separation number can be interpreted as an adaption of Stratford's separation criterion to piecewise conical nozzles. In the nozzle design optimization process, the risk of flow separation was reduced by minimizing the separation number. It was found that the flow-optimized piecewise conical nozzle did not correspond to a direct geometric approximation of an ideal polynomial profile. In fact, it was beneficial to reduce the flow deflection in the outlet region for a piecewise conical nozzle to increase the nozzle performance. In order to validate the novel design method, extensive tests for different nozzle designs were conducted by means of wind tunnel tests. The measured velocity profiles and wall pressure distributions agreed well with the CFD predictions.

RCMeans: A Recursive Capacitated Means for Districting Problem

The billing process of an energy distributor in Brazil is connected to reading energy consumption logistics. An efficient, balanced and capacity enabled process has benefits with cost reducing and quality perception of the service provided. In capacitated clustering, the elements are associated with weights for construction of groups with limited capacities. This paper presents an approach to the capacitated clustering problem, applied to the consumer unit measurement groups organization in Brazil's energy distributors companies. The process of creating those measurement groups, in general, is carried out manually by expert analysts. The purpose of this problem modality is to create partitions that minimize the internal dispersion of the associated group. In this work, the RCMeans method, which is based on the K-Means technique applied to data groupings with the inclusion of the capacity constraint for the group definition, is presented. The obtained results show a comparison between the current situation and the result with the proposed method, under the cohesion analysis, separation, number of groups, silhouette index, and consumer units measurement mean time of the groups.

Optimization of Piece-Wise Conical Nozzles: Theory and Application

In this contribution, an optimization study based on computational fluid dynamics (CFD) in combination with Stratford’s analytical separation criterion was developed for the design of piece-wise conical contraction zones. The occurrence of flow separation can be formally described by a newly introduced dimensionless separation number. In the optimization process, the risk of flow separation is reduced by minimizing this separation number. It was found that the optimized piece-wise conical nozzle shape did not correspond to a simple geometric approximation of the ideal polynomial shape. In fact, it was beneficial to reduce the deflection in the outlet region for a piece-wise conical nozzle stronger than for a conventional one. In order to validate the new design method, large-scale tests for different nozzle designs were conducted. The measured velocity profiles and wall pressure distributions agreed well with the CFD predictions. The new method was applied for designing the contraction zone of a new closed-loop organic vapor wind tunnel (CLOWT) working at elevated pressure levels.