The purpose of this paper is to study the asymptotic behavior of the positive solutions of the problem tu- △u=au-b（x）up in Ω×R＋,u（0）=u0,u（t ）｜ Ω=0, as p→ ＋∞, where Ω is a bounded domain, and b（x...The purpose of this paper is to study the asymptotic behavior of the positive solutions of the problem tu- △u=au-b（x）up in Ω×R＋,u（0）=u0,u（t ）｜ Ω=0, as p→ ＋∞, where Ω is a bounded domain, and b（x） is a nonnegative function. The authors deduce that the limiting configuration solves a parabolic obstacle problem, and afterwards fully describe its long time behavior.展开更多
With the increasing demand for the clean sustainable power, the turbine design urgently turns to increase the capability significantly toward higher head for generating larger power. Currently, there are many studies ...With the increasing demand for the clean sustainable power, the turbine design urgently turns to increase the capability significantly toward higher head for generating larger power. Currently, there are many studies in the field of the bulb turbine with single-stage runner, though reports about counter-rotating tandem-runner are rare. However, the further high-head application with the single-stage runner is very difficult to achieve due to the limit of the specific speed. In this paper, a new bulb turbine with the tandem-runner is designed in order to substantially increase the applicable limit toward higher head with larger power. A half of the net head is absorbed by the frontal runner which can generate output power, while the remaining half is absorbed by the rear runner. To generate the Euler energy required for the rear runner, the frontal runner has the counter-rotation against the rear runner so that the counter-rotating tandem-runner can meet the purpose of double head and power under the same size as the conventional bulb turbine. Supply and demand of Euler energy between the two runners are thoroughly optimized through the detailed flow analysis, in order to secure the stable operation. As a result, the interference of Euler energies between the outflow from the frontal runner and the inflow to the rear runner is confirmed to be very small on the counter-rotating interface between the two runners. The prediction method of on-cam performance between the two adjustable runners is also developed numerically, which provides optimal flow between the two runners. This research provides a theoretical basis for the optimal design and operation of the counter-rotating tandem-runner bulb turbines.展开更多
基金Project supported by Fundaco para a Ciência e a Tecnologia (FCT) (No. PEst OE/MAT/UI0209/2011)supported by an FCT grant (No. SFRH/BPD/69314/201)
文摘The purpose of this paper is to study the asymptotic behavior of the positive solutions of the problem tu- △u=au-b（x）up in Ω×R＋,u（0）=u0,u（t ）｜ Ω=0, as p→ ＋∞, where Ω is a bounded domain, and b（x） is a nonnegative function. The authors deduce that the limiting configuration solves a parabolic obstacle problem, and afterwards fully describe its long time behavior.
基金supported by National Natural Science Foundation of China (Grant Nos. 50879026, 50679027)
文摘With the increasing demand for the clean sustainable power, the turbine design urgently turns to increase the capability significantly toward higher head for generating larger power. Currently, there are many studies in the field of the bulb turbine with single-stage runner, though reports about counter-rotating tandem-runner are rare. However, the further high-head application with the single-stage runner is very difficult to achieve due to the limit of the specific speed. In this paper, a new bulb turbine with the tandem-runner is designed in order to substantially increase the applicable limit toward higher head with larger power. A half of the net head is absorbed by the frontal runner which can generate output power, while the remaining half is absorbed by the rear runner. To generate the Euler energy required for the rear runner, the frontal runner has the counter-rotation against the rear runner so that the counter-rotating tandem-runner can meet the purpose of double head and power under the same size as the conventional bulb turbine. Supply and demand of Euler energy between the two runners are thoroughly optimized through the detailed flow analysis, in order to secure the stable operation. As a result, the interference of Euler energies between the outflow from the frontal runner and the inflow to the rear runner is confirmed to be very small on the counter-rotating interface between the two runners. The prediction method of on-cam performance between the two adjustable runners is also developed numerically, which provides optimal flow between the two runners. This research provides a theoretical basis for the optimal design and operation of the counter-rotating tandem-runner bulb turbines.
