Tip clearance flow between rotating blades and the stationary casing in high-pressure turbines is very complex and is one of the most important factors influencing turbine performance. The rotor with a winglet-cavity ...
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Tip clearance flow between rotating blades and the stationary casing in high-pressure turbines is very complex and is one of the most important factors influencing turbine performance. The rotor with a winglet-cavity tip is often used as an effective method to improve the loss resulting from the tip clearance flow. In this study, an aerodynamic geometric optimisation of a winglet-cavity tip was carried out in a linear unshrouded high-pressure axial turbine cascade. For the purpose of shaping the efficient winglet geometry of the rotor tip, a novel parameterisation method has been introduced in the optimisationprocedure based on the computational fluid dynamics simulation and analysis. The reliability of a commercial computational fluid dynamics code with different turbulence models was first validated by contrasting with the experimental results, and the numerical total pressure loss and flow angle using the Baseline k-omega Model (BSL - model) shows a better agreement with the test data. Geometric parameterisation of blade tips along the pressure side and suction side was adopted to optimise the tip clearance flow, and an optimal winglet-cavity tip was proven to achieve lower tip leakage mass flow rate and total pressure loss than the flat tip and cavity tip. Compared to the numerical results of flat tip and cavity tip, the optimised winglet-cavity design, with the winglet along the pressure side and suction side, had lower tip leakage mass flow rate and total pressure loss. It offered a 35.7% reduction in the change ratio CIn addition, the optimised winglet along pressure side and suction side, respectively, by using the parameterisation method was studied for investigating the individual effect of the pressure-side winglet and suction-side winglet on the tip clearance flow. It was found that the suction-side extension of the optimal winglet resulted in a greater reduction of aerodynamic loss and leakage mass flow than the pressure-side extension of the optimal wi
This paper deals with the numerical approximation for the time optimal control problem governed by the Benjamin-Bona-Mahony (BBM) equation, which is an unspecified terminal time problem. Firstly, by projecting the ori...
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This paper deals with the numerical approximation for the time optimal control problem governed by the Benjamin-Bona-Mahony (BBM) equation, which is an unspecified terminal time problem. Firstly, by projecting the original problem with the finite element method (FEM), another approximate problem governed by a system of ordinary differential equations will be obtained. Then, the parameterisation method for the optimal time and the control function will be carried out and the unspecified terminal time problem can be reduced to an optimal parameter selection problem with a fixed time horizon [0, 1]. This optimal parameter selection problem is a standard nonlinear mathematical programming problem and can be solved by sequential quadratic programming (SQP) algorithm. Finally, some numerical simulation studies will be given to illustrate the effectiveness of our numerical approximation method for the time optimal control problem governed by the BBM equation.
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