A numerical investigation into the effects of Reynolds number on the flow mechanism induced by a tubercled leading edge

Leading-edge modifications based on designs inspired by the protrusions on the pectoral flippers of the humpback whale (tubercles) have been the subject of research for the past decade primarily due to their flow control potential in ameliorating stall characteristics. Previous studies have demonstrated that, in the transitional flow regime, full-span wings with tubercled leading edges outperform unmodified wings at high attack angles. The flow mechanism associated with such enhanced loading traits is, however, still being investigated. Also, the performance of full-span tubercled wings in the turbulent regime is largely unexplored. The present study aims to investigate Reynolds number effects on the flow mechanism induced by a full-span tubercled wing with the NACA-0021 cross-sectional profile in the transitional and near-turbulent regimes using computational fluid dynamics. The analysis of the flow field suggests that, with the exception of a few different flow features, the same underlying flow mechanism, involving the presence of transverse and streamwise vorticity, is at play in both cases. With regard to lift-generation characteristics, the numerical simulation results indicate that in contrast to the transitional flow regime, where the unmodified NACA-0021 undergoes a sudden loss of lift, in the turbulent regime, the baseline foil experiences gradual stall and produces more lift than the tubercled foil. This observation highlights the importance of considerations regarding the Reynolds number effects and the stall characteristics of the baseline foil, in the industrial applications of tubercled lifting bodies.     

Exploring the characteristics,performance, and modification of Matrimid for development of thin‐film composite and thin‐film nanocomposite reverse osmosis membranes

Reverse osmosis (RO) membrane technology is widely employed to address the demands for freshwater. In this study, fabrication and performance evaluation of customized RO membranes comprised of Matrimid and polyacrylonitrile (PAN) is carried out. While exploring adoption of slip coating procedure, the effects of various modification techniques including incorporation of TiO₂ nanoparticles and polyethylene glycol (PEG) into the skin layer as well as cross‐linking were investigated. The individual and combined effects of parameters on membrane morphology, surface characteristics and performance were also examined. Despite the distinctive characteristics of involved materials, delamination‐free composite membranes were successfully formed with an intimate contact at the interface of two layers. The results also indicated that increasing concentration of Matrimid in dope solution led to increase in membrane thickness and consequently decline in water flux. In the best case, membrane prepared using 1 wt.% Matrimid in dope exhibited water flux of 0.98 LMH and NaCl rejection of 95.7%. Also, incorporation of 3 wt.% TiO₂ nanoparticles offered membranes with improved water flux of 1.37 LMH and salt rejection of 95.8%. On the other hand, water flux and salt rejection in membranes containing 5 wt.% PEG were 1.18 LMH and 96.2%, respectively. The co‐presence of both nanoparticles and PEG provided more insights about the contributing factors in tuned membranes. Modification of skin layer by cross‐linking significantly improved salt rejection at the expense of water flux. The results are scientifically interpreted and compared to the values reported in literature.     

Optimal use of the translation method and relaxations of variational problems

The translation method has been used with great success in bounding the effective moduli of composite materials. We consider here the analogous method for bounding the relaxations of variational problems. We optimize the bound over the set of all available translations. Our method is to cast this in the form of a minmax problem. Using techniques of nonsmooth analysis, we are able to identify the optimal translation bound, meanwhile proving the existence of at least one optimal combination rank-one convex quadratic and null-Lagrangian translation. The optimal translation bound proves to be a better general lower bound on relaxations of variational problems than is the polyconvexification in three dimensions. In two dimensions, we discuss the negative result that the optimal translation bound is exactly the polyconvexification. Several examples of optimal applications of translation bounds to non-convex nonlinear variational problems are given.