| Summary: | 碩士 === 國立中正大學 === 機械工程所 === 94 === In this thesis, the reduced-order modeling of fluid with high viscosity and low viscosity was investigated. In this research, the reduced-order modeling technique was focus on in transforming the fluid dynamics described in partial different equations to ordinary differential equations suitable for control design and analysis.
Although fluid dynamics can be formulated by Navior-Stokes equation for both high viscosity and low viscosity fluid, different viscosities introduce different flow behaviors. As a consequence, different approaches to reduced-order modeling should be developed for fluids with different viscosities. The proposed reduced-order modeling approach consists of two steps. In the first step, the fluid dynamics originally described in simultaneous partial differential equations (PDEs) are properly approximated by a single PDE. This is achieved by a nonlinear wave approximation for low viscosity fluid or by a singular perturbation for high viscosity one. In the second step, the single PDE is further reduced into lower-order ordinary differential equations (ODEs). The ODE model reduction, for low viscosity fluid, is developed through a nonlinear coordinate transformation followed by the eigenfunction expansion method. There are some problems we have not solved in this part. We will try to solve the problems in the future. While for high viscosity fluid, the goal of second step is obtained by the assumed-mode method.
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