Local stability results for the collective behaviors of infinite populations of pulse-coupled oscillators

In this paper, we investigate the behavior of pulse-coupled integrate-and-fire oscillators. Because the stability analysis of finite populations is intricate, we investigate stability results in the approximation of infinite populations. In addition to recovering known stability results of finite populations, we also obtain new stability results for infinite populations. In particular, under a weak coupling assumption, we solve for the continuum model a conjecture still prevailing in the finite dimensional case. © 2011 IEEE.

Aerodynamic design of high end wall angle turbine stages-part I: Methodology development

A design methodology is presented for turbines in an annulus with high end wall angles. Such stages occur where large radial offsets between the stage inlet and stage outlet are required, for example in the first stage of modern low pressure turbines, and are becoming more prevalent as bypass ratios increase. The turbine vanes operate within s-shaped ducts which result in meridional curvature being of a similar magnitude to the bladeto-blade curvature. Through a systematic series of idealized computational cases, the importance of two aspects of vane design are shown. First, the region of peak end wall meridional curvature is best located within the vane row. Second, the vane should be leant so as to minimize spanwise variations in surface pressure-this condition is termed "ideal lean." This design philosophy is applied to the first stage of a low pressure turbine with high end wall angles. © 2014 by ASME.

Improving intermediate pressure turbine performance by using a nonorthogonal stator

Intermediate pressure (IP) turbines in high bypass ratio civil aeroengines are characterized by a significant increase in radius and a low aspect ratio stator. Conventional aerodynamic designs for the IP turbine stator have had leading and trailing edges orthogonal to the hub and casing end walls. The IP turbine rotor, however, is stacked radially due to stress limits. These choices inevitably lead to a substantial gap between the IP stator and rotor at the outer diameter in a duct that is generally diffusing the flow due to the increasing radius. In this low Mach number study, the IP stator is redesigned, incorporating compound sweep so that the leading and trailing edges are no longer orthogonal to the end walls. Computational investigations showed that the nonorthogonal stator reduces the flow diffusion between the stator and rotor, which yields two benefits: The stator trailing edge velocity was reduced, as was the boundary layer growth on the casing end wall within the gap. Experimental measurements confirm that the turbine with the nonorthogonal stator has an increased efficiency by 0.49%, while also increasing the work output by 4.6%, at the design point. © 2014 by ASME.

Aerodynamic design of high end wall angle turbine stages- part II: Experimental verification

An experimental investigation of a turbine stage featuring very high end wall angles is presented. The initial turbine design did not achieve a satisfactory performance and the difference between the design predictions and the test results was traced to a large separated region on the rear suction-surface. To improve the agreement between computational fluid dynamics (CFD) and experiment, it was found necessary to modify the turbulence modeling employed. The modified CFD code was then used to redesign the vane, and the changes made are described. When tested, the performance of the redesigned vane was found to have much closer agreement with the predictions than the initial vane. Finally, the flowfield and performance of the redesigned stage are compared to a similar turbine, designed to perform the same duty, which lies in an annulus of moderate end wall angles. A reduction in stage efficiency of at least 2.4% was estimated for the very high end wall angle design. © 2014 by ASME.

The effect of clearance on shrouded and unshrouded turbines at two levels of reaction

In this paper, the effect of seal clearance on the efficiency of a turbine with a shrouded rotor is compared with the effect of the tip clearance when the same turbine has an unshrouded rotor. The shrouded versus unshrouded comparison was undertaken for two turbine stage designs one having 50% reaction, the other having 24% reaction. Measurements for a range of clearances, including very small clearances, showed three important phenomena. Firstly, as the clearance is reduced, there is a "break-even clearance" at which both the shrouded turbine and the unshrouded turbine have the same efficiency. If the clearance is reduced further, the unshrouded turbine performs better than the shrouded turbine, with the difference at zero clearance termed the "offset loss." This is contrary to the traditional assumption that both shrouded and unshrouded turbines have the same efficiency at zero clearance. The physics of the break-even clearance and the offset loss are discussed. Secondly, the use of a lower reaction had the effect of reducing the tip leakage efficiency penalty for both the shrouded and the unshrouded turbines. In order to understand the effect of reaction on the tip leakage, an analytical model was used and it was found that the tip leakage efficiency penalty should be understood as the dissipated kinetic energy rather than either the tip leakage mass flow rate or the tip leakage loss coefficient. Thirdly, it was also observed that, at a fixed flow coefficient, the fractional change in the output power with clearance was approximately twice the fractional change in efficiency with clearance. This was explained by using an analytical model. © 2014 by ASME.

When is a symmetric body-hinge structure isostatic?

A symmetry-extended mobility rule is formulated for body-hinge frameworks and used to derive necessary symmetry conditions for isostatic (statically and kinematically indeterminate) frameworks. Constructions for symmetric body-hinge frameworks with an isostatic scalar count are reported, and symmetry counts are used to examine these structures for hidden, symmetry-detectable mechanisms. Frameworks of this type may serve as examples for exploration of a symmetry extension of the (now proven) 'molecular conjecture'. © 2014 Elsevier Ltd. All rights reserved.