The collapse of a compressed elastic tube conveying a flow occurs in several physiological applications and hence becomes a problem of considerable interest. Laboratory experiments on a finite length of collapsible tube reveal a rich variety of self -excited oscillations, indicating that the system is a complex, non-linear dynamical system. There are several lumped-parameter, or one-dimensional theoretical models, revealing different mechanisms that may be involved in such oscillations, but all suffer from the crude approximation of key features. It is our intention, however, to move towards a complete solution to a 2-D version of the collapsible tube problem, where part of one wall is replaced by an elastic membrane and the coupled fluid-elastic equations are solved using numerical methods. We have studied steady flow in such a channel, assuming constant membrane tension T, and obtained results for Reynolds number in the range 1-500. No steady solution was found when T fell below a critical value. There is a quite good agreement between the numerical results, when a solution was found, and predictions from the corresponding 1-D model. To investigate the stability of the steady solution as well as what occurs beyond the parameter region where a steady solution can be achieved, we have also developed a time- dependent flow simulation using the Spine method to treat the moving boundary. Preliminary results indicate a sequence of bifurcations as T is reduced or Re raised, in agreement with 3-D experiments.
展开▼
