A simplified computational model is developed so that a spectral element-Fourier method with spatial exponential convergence property is introduced as a direct numerical simulation method for a complex flow between two cylinders in a micro-gyroscope with a liquid-filled rotor.In cylindrical coordinate system,the incompressible Navier-Stokes equations is solved through using a Galerkin spectral element method both in radical and axial directions,and the Gauss-Lobatto-Legendre nodal expansion is implemented in each standardized element while the Fourier series expansion is used in azimuthal direction.Based on a specified baseline numerical example,the effects of several parameters,namely the ratio of height to radius,rotating velocity and viscosity coefficient,on the drag moments of the inner cylinder lateral surface and end surface are investigated and analysed.Results show that the two drag moments increase with these parameters and both contributions to the total drag moment are comparative in magnitude order.%建立简化计算模型,将一种具有空间指数收敛特性的谱元-Fourier法引入复杂的液浮转子微陀螺筒间流动的直接数值模拟.对于柱坐标系下不可压缩Navier-Stokes方程,在子午面的径向和轴向采用Galerkin谱元法,进行标准化的Gauss-Lobatto-Legendre节点展开,在周向采用Fourier级数展开法.设定基准算例,计算分析了高径比、旋转速度和黏性系数等参数对内筒侧面和内筒端面阻力矩的影响.结果表明,两种阻力矩都随这些参数的增大而增大,且对总阻力矩的贡献量级相当.
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