偏心有限长大间隙环流的动特性研究

Dynamic characteristics of an eccentric finite-length large gap annular flow

基于所建立的大间隙环流中转子运动的三维力学模型,用摄动法推导了有限长大间隙环流流场非线性控制方程的零阶摄动方程组。该方程组是一个复杂的三维非线性偏微分方程组,其求解有一定的困难。为此,提出了一种简化数值方法。该简化方法是采用作者以前获得的同心有限长大间隙环流的动特性系数来计算三维偏心有限长大间隙环流的动特性系数。与已有的数值计算结果和实验结果比较,该简化方法具有较好的实用性和精度。数值计算结果表明与同心有限长大间隙环流相比,偏心有限长大间隙环流的动特性系数不再具有主项相等,耦合项大小相等、符号相反的特点,动特性系数主项随着偏心率的增加而呈不同程度的指数增加,这意味着在大偏心情况下有限长大间隙环流的动特性系数将增大。

Based on a 3D mechanical model for a large gap annular flow developed by authors,the zero-order perturbation equations of 3D non-linear partial differential equations for the motion of an eccentric rotor in a finite-length large gap annular flow were derived here.The zero-order perturbation equations were also 3D non-linear partial differential equations,and there was a little difficulty to get their solutions.Therefore,a simplified numerical method based on the results of a finite-length concentric large gap annular flow analyzed by authors before,was put forward in order to analyze the dynamic coefficients of the eccentric rotor in the finite-length large gap annular flow.Comparing with the existing numerical results and testing ones,it was shown that this method is sufficient and accurate.Numerical results showed that the dynamic coefficients of the eccentric rotor in the finite-length large gap annular flow have no features that the main terms are equal,the coupled terms are equal and opposite,comparing with those of the concentric rotor in the finite-length large gap annular flow;all main terms of the dynamic coefficients increase exponentially with increase in eccentricity rate,this means that the dynamic coefficients of an eccentric rotor in a finite-length large gap annular flow increase greatly with a large eccentricity.